LA—10160-MS-Vol.1C DE85 011902

LA-10160-MS-tM- / «

UC-34Issued: November 1984

LA—10160-MS-Vol.1C

DE85 011902

T-4 Handbook ofMaterial Properties Data Bases

Vol. Ic: Equations of State

Edited byKathleen S. Holian

Los Alamos National Laboratory Is operated by the University otCalifornia tor the United States Department of Energy undercontract W-7405-ENG-36.

PREFACE

Since I t s Inception In 1971, the Equationof State and Opacity Croup (T-4) of the LoaAlamos Sational Laboratory, has developedtheor ies and models and ca l cu l a t ed , compiled,and analyzed equation of y t a t e , opae t ty, andother related da ta . The Equation of StateLibrary , I nit lated by my predecessor,John F. Rnrnes, contaLne these data Incomputer-based dnta f i l e s ava11ahie to usersfor direct application.

This booklet Is the f i r s t in a series ofplanned T-4 Handbooks to give the user anoverview and background Information on ourcomputer-based l ib ra r i es . I t containscomputer generated equation of state data In acompressed format for quick look-up. Anexpanded version will contain more detailedInformation. Although f i r s t in a series ofplanned publications, this booklet Is notvolume la, because logically a descriptIon oftheories f&r equation of s ta te models and ofmethods for calculations should precede theresul ts of the equations of s ta te that aresummar1zed here« It Is planned that volume lawill give descriptions of theories and models,while volume Ib will be an expanded version ofthe present booklet. Other volumes willsummarize opacities and conductivities.

Walter F. HuebnerGroup Leader, T-43 May, 1984

ACKNOWLEDGMENTS

I would like to thank the fallowingmembers of Group T~4, past and present, fortheir helpful suggestions and contributions tothis document:

J . Abdallah

R. C. Albers

J. F« Barnes

R. D. Cowan

F. Dowell

B. L. Holian

G. I. Kerley

J. D. Johnson

D. Liberman

S. Lyon

r. Straub

I would also Like to glVi. special thanksto Walter Huebner (T-4 Group Leader) for hisstrong support throughout the preparation ofthis handbook. Final ly, I would 1 Ike to awarda medal for long-sufferinfc patience andexcel lerice to Vickie Hontoya for theoutstanding \ah sh^ did typing the handbonk.

I . I MTRODUCTION I

I I . HISTORICAL DEVELOPMENT 1

I I I . CURRENT PHYSICAL MORELS h

I V . n r ' E R PHYSICAL MODELS 9

V . TABLES IN THE SESAME LIBRARY 19

V I . SESAME SOFTWARE 21

V I I . OBTAINING THE SESAME LIBRARY 22

V I I I . DETAILED DESCRIPTION n r EQUATIONSOF STATE 21

IX. INDEX OF MATERIALS AND SESAME NUMBERS. . 3 0

T-A HANDBOOK OF MATERIAL PROPERTIES DATA BASKS

Vol. Ic: Equations of Stac*

Edited by

Kathleen S. Ha Iton

ABSTRACT

This manual Is a compilation ofdesc r ip t ions nf the equations of s t a t e (EOS)In the T-4 carap u te r i zed l i b r a ry of mater ia lp rope r t i e s t a b l e s . The Introduct ion giv»s cbr i e f descr ip t ion of the l i b r a r y and c.'~ Chephysics theor i e s and models which were used toca lcu la t e t"ne equations of s t a t a . Then &aehEnS I s described In d e t a i l . F i r s t , var iousphysical parameters of each thec-e 'c tcal EOSare tabulated and compared with experimentswhen a v a i l a b l e . Then the methort of generat ingthe EOS I s br ie f ly descr ibed. F i n a l l y , thetab les are plot ted In terms oi p re s su re andenergy vs densi ty along l ines of constanttemperature.

*• INTRODUCTION

T^e SESAME Equat lon-ot -3 ta te (EOS)Library Is a standardized, c^puter-basedlibrary which contains tables of thermodynamlcproperties for a wide range of materials overa wide range of physical regions (from ambientto astrophyslcal conditions). The Librarycurrently conf-ilns data for about 70materials, including metals, minerals,polymers, mixtures, and simple atomic andmolecular species. The purpose ot thisdocument is to sufficiently describe eat-h of

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ttita EDS'a EO that the users of the Library mayma e educated decisions as ro whether aparticular EOS is appropriate 'or their needs.

In thfc Library, pressure and energy (andIff aOrae' cflsea free energy) ore tabulated asfunctions of density and temperature. Forsotiiti materials, separate preSHurf r»nd energytab lea axe available for the thermalelri trunic and thermal Ionic contributions.These arc en I led twn-temperature tnblt?B.

The 1,1 brary has buen deve loped and 1 smnIntalncd by the Equation of Stnte andOpacity Group (T-4) of the TheoreticalDl v| Hlon of LOB Al amor, Nat Innnl Lnborntory,tt Is a«aliable Co al 1 Interested partles bothInside and outside the Laboratory.

This document will describe the Libraryas It Is in June 1984. However, the LibraryIs actually In a constant state of flux.EOS's for exlstlnf? materials are upgraded whenappropriate, and new ones are being constantlyadded. Moat of the EOS* s are Kenernted by themembers of uroup T-4; however, ue areconstantly on the lookout fnr quality EOS'sgenerated hy others ( e . g . , the National Bureaunf Standards anj Lawrence Livermore NationalLaboratory) to add to the Library.

The aim of the custodians of the SESAMELibrary i s to Include thermodynainical lyself-consistent EOS's that are computed withthe befit avaliable physics models and thatagree wi th avaliable experimental data—givenreal is t ic time const ra in ts .

I I . HISTORICAL DEVELOPMENT

The SESAME Equntion~of-State Library ea«eInto existence tn 1971 under the direction ofJ. Barnes. I n i t i a l l y , a l l the EOS's uurecalculated using a procedure developed byJ. Barnes and J» Rood. They generated aboutJO EOS'3 from 1972 to 1975, and since many ofthese remain In the Library, their method willbe dest ribed In some d e t a i l . Even though themethod la setni~emplrical and Is bar -d onfairly simple physical models, the EOS' sproduc t*d arc general ly adequate , cspec1 a I lyfur hlah-t^mperiiture applications. In fact ,we have no more sophisticated models today for(•ener.it tnf> tlie EOS' t of com pi lea ted compounds.

Above 1 eV (I eV =• Ubttt.5 K), Barnes andHood used old MAPLE fc.OS tables . The MAPLEtables were for thj most part calculated byH. TJ. Cowan using a Thomas-Fermt-Pl rac model^for the electronic part of the EOS. Twocorrect Ions were added to this basis: anuclear contribution and an empiricalcorrection, the purpose of which was to forcethe experimental zero-pressure density andbulk modulus to be reproduced. The MAPLEEOS' s were adequate at high temperatures, butunreliable at lnu temperatures. Most notably,they did not always accurately reproduceexperimental Hu«nntot data . When Barnes andRood began tho SESAME llbrar.. , they developeda method which would improve theIow-temperature region.

Information provided by J. Barnes at LosAl anos Na t tona1 Laboratory.

They generated the pressures on ttie coldcurve wtrh a "modifled-Morse" model at lowdensity:

n s P /P O ,

h.( = 1 + hf - 3llQ , and

B = cxfu-rlmuntnl ndlnbatlr hulk mndulun" at T-n.

The constants b and a were determined bymatching the mod-Morse cold curve onto aThomas—Fertni-Dirac cold rurve used at higherdensi t ies . (Sometimes, a s t ra ightThomas-Fermi model was used in order to obtainn better match.)

For the finite temperature isotherms(below 1 eV), Barnes and Rood ifinored thermalexaltation of the electrons and assumed thatthe total pressure Is given by the cold curvernntr I hut Ion plus n In t t l re cnntr1butInn:

P(p.T) = Pc<p) + Pn(p.T)

The thermal nuclear contribution wascalculated with a Debye model. This requiresknowledge of the GrUnelaen parameter as afunction of density which can be obtainedeither from the cold curve or, in some cas t s ,from experimental data. No melting wasIncluded.

Af ter the pressure tahle was calculated,cht? energies Were computed by inte^rat Ion tThe F.05 was then compared with experimentalHugonlat da ta • If necessary , the coef f ic I t-nt sfn the Debye model were adjusted In order toproduce a good match between the theoreticalEOS and Hugnnlot experiments.

After the SESAME low-temperature tnblewas completed, the MAPLE table was shifted sothat the 1-eV isotherms of the two tableswould match. There was always a s l ightdiscontinuity since the mod-Morse EOS did notinclude electron thermal contributions.

In expansion below 1 eV, Barnes and Roodused a v i r ia l scries EOS. The coefficients ofthe v i r ta l expansion were determined bymatching the thermal pressure and the slope ofthe thermal pressure with respect to density;it p (reference density). The van der Waalsloops were generally replaced by vaporpressures calculated from a MKXW^IIconstruct ton, unless a tension region wasspecifleally requested. This technique seemedto reproduce other theoryt i<~a 1 escima tes ofc r i t i ca l points well.

This procedure for calculating EDS's hasbeen called the Ba rnes-Cowan-Rood technique.It Is referred to often in the detailed

desertpt ions of the Library equations of statewhich follow.

I l l - CURRENT PHYSICAL MODELS

Barnes and Rood did an excellent job at|irnvtd tnR a la rge number of EOS' s for a widevariety of materials. However, In Che yearssince that t lme, other researchers have beenImproving on the F.OS's added tn the RF.SAMF.Llhrary hy using more sophist Lefited physicaltheories and models.

If computing time permitfl, theresearchers In T-U use the following methodfor Reneratlng ,-in equation of s t a t e . TheyfIrs t assume that the pressures and energiesare a iiini of three separate contr ibut ions:cold curve ( i . e . , zero-kelvin)» nucleartherma 1, and electron t h e r n i a l ( P t c i - P . +

The cold curve contributions arecalculated with electron band theory using aformulation such as APW (augmented planewave), LMTn (linearized muffin-tin o rb i t a l ) ,nr KKjl (Knrrtnfia, Kohn, and Rostoker).

Th^ e lectron the rma 1 cont riby t ians firecalculated from the INFERNO model (due to1). A. Libertnan), which Is described next insiimc rietai I.

In the INFERNO model, an atomic nucleusIs placed at the center of n spherical cavity.F.xterinr to the cavity is an clectr ic . i i lyneutral je l lium s ta . Inter ior to thr* cavl ty,stiff Lei en t electrnns are Inc 1 tided toneutral ize the nur lear eh.irgd. To Implement asolution to this system, the approximations

made are similar to those in typical band^ crueture calculatIons:

1) The electrons are treated as Independentpar t ic les In a sel f-cons latent f ie l : ' ,

2) Exchange and correlation re treated wi tha I tic a I density approximation.

1) S ta t i s t i ca l averages are treated In the"lean- field approximat Ion.

-'•) The charge density Ifi equivalent to the"muf fln-tIn" approx Imatlon used inso l id-s ta te calculations.

The model has several features whichcombine to yield superior results to previousmodels for electronic thermal exci tat Ion:

1) All electrons are treated with aninternal ly t inqia t tn t formulation so that"ennt Inuum lowering" is n itomatieal lyIncluded. The transition from hound stateto narrow resonance and then to broadresonance status is smooth as the densityor temperature Is changed.

2) The model accommodates wide ranges indensity and temperature. For example,calculations have covered compressionranp,e;s of 10 to 10 and temperatureranges of 10 to 10 eV.

1) Since the Oirac equation is used, shellstruetuTe e rfects ate 'utomatleal lvIncluded, making INTERN"! superior toThumas—rerri-firac theory in this regard.

M The htgh-denalty limit 1B essentially theThomas-Ferrai-Dirac model.

5) The low density is an ionizatlon model forions in equilibrium with free electrons.

TW zero-temperature iaothermB ohtainedfrom the INFERNO model agree better with thosefrom band structure calculations than do the•*old curves obtained from Thomas-Ferml-Diractheory. On the other hand, band theory hasnot been adequately developed to handle finitetemperatures. Therefore, the atom-in-jelliurnmodel is presently the method of choice forcomputing the contribution to the EOS from thethermal excitation of electrons.

Both the Thomas-Fermi-Dirac and theatom-in-jtillium models are most appropriatefor metallic elements. However, they can beused for nanmetallic elements and adapted tocompounds and mixtures with some loss inaccuracy in the low-pressure region.

For mixtures and certain elementsinappropriate for INFERNO, an adequate modelfor the electronic EOS Is s t i l lThoraas-Fermi-Dirac theory•

After the zero-degree and electronthermal contributions are calculated, thePANDA3* code is used to calculate the !.uclearthermal components and t-a assemble the finalEOS. The nuclear thermal EOS takes account ofsolid lat t ice vibrations, t ranslat ion!nuclear motion (for the fluid). intramolecularvibration, and rotation.

The sol id l a t t i c e vibrational terms canbe calculated using e i ther a Debye or Einsteinmod..l. A number of different options tocalculate the Eins te in or Debye temperatureand the GrUneisen parameter are provided inPANI1A. The Einstein or Debye temperature andthe GrUneisen parameter at ambient density canbe calculated in PANDA or can be determinedfor experimental data and input to PANDA.PANDA also offers interpolat ion models(including a v i r i a l expansion) which go to anideal gas at high temperatures and lowdens i t i e s . These wi l l crudely describemelting and vaporizat ion in place of a morerigorous l iquid model.

For f l u id s , PANDA has the option tocalculate contr ibut ions to the center-of—massmotion of the molecules using the CRIS model.This model i s based on a thermodynamicperturbation expansion about a hard-spherefluid in which the zero-temperature isothermof the solid i s used to obtain the effect ivepair p o t e n t i a l .

Vibrational and rotat ional contr ibutionsfor molecules are calculated using theharmonic osc i l l a to r -T ig id rota torapproximation. Vibrational frequencies androtat ional constants obtained fromspectroscopic data iiust be supplied to PAKDA.

IV. OTHER PHYSICAL MODELS

Many other phynical theo._es and modelsbesides the ones described in the previoussection have been used to calculate theequat ion-of-s ta t^ tables In the SESAMElibrary . Most notably, many good ones havecome from the equat . -m-of-state group at

Lawrence Livarmore National Laboratory. Sincethese were used for some of.the EOS's InSESAME, they wil l be described in more detai lbelow. Also described are theories developedat places other than Los Alamos NationalLaboratory ind Lawrence Livermore NationalLaboratory but which are used frequently Inthe calculation of EOS'a included in theSESAME library.

ACTEX Model (developed by Forrest Rogers atLawrence Livermore National Laboratory)

The ACTEX (Activity Expansion) model^"'treats ioni7a tion equilibrium in the presenceof plasma coupling and allows for the factthat the heavy iona may be strongly coupled( l iquid- l ike) , whereas the electrons are onlymoderately coupled (gas- l ike) . The theorybegins with a many-body perturbation expansionof the grand canonical ensemb'e pertitionfunction. Three d i s t inc t renormaiizations ..cerequired to handle the general problem,accounting for (L) formation ofelectron-nucleus composites, (2) coupling ofthe composite par t ic les to the plasma, and (3)strong coupling of heavy ions having chargeZ > 1.

To carry out numerical calculations, I tIs necessary to obtain multielectron bound andscattering s t a t e s . This Is accomplishedthrough the Introduction of effective pairpotentials. These potentials are composed ofa long-range term plus exponentially screenedCoulomb terras for each shell of coreelectrons. The paratrttera in the potentialare determined from experimental spectroscopicdata, and pi as ma-screening effects are thenadded to the long-range t a i l . The

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perturbation expansion breaks down at lowtemperature and at high densi t ies ,

SABA Model (OCCIPITAL) (as implemented byC. Rouse at Lawrence Live more NationalLaboratory)

The OCCIPITAL code calculates thecomplete solution to Sana's equation forpar t ia l ly Ionized dense plasmas and liquidmetals, which is then modified with theDebye-HUckel corrections for ionizationpotentials and Planck's theoretical part i t ionfunct ion. 8 ' 9 The EOS generated by OCCIPITAL isexact in the Ideal gas lirait4 accurate in theweakly coupled Coulomb region, but becomesincreasingly inaccurate with the onset ofstrong Coulomb interactions and electrondegeneracy.

APW

The most s o p h i s t i c a t e d method t ocalculate the zero-kelvin pressure-volumeisotherm i s with rigorous electron band theorybased on the self-consisttTi: augmented planewave (APW) method.10 Contributions fvomla t t i ce vibrations of the nuclei are notcalculated by this model; but when they areaddad (as determined from Gruneisen-Debyemodels) t the resultant zero-pleasure volume Isnormally within 331 of experiment.'

/*LMTO '

An alternative way to calculate azero-kelvin isotherm with electron band theoryis to use the linear-muffin-tin-orbital (LMTO)method. '1"1 2 The augmented plane wave methodis time consuming for computer calculat ions.

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By niaking certain approximations which lead tothe LMTO method, the calculation time for anEOS point can be reduced by one or two ordersof magnitude with very l i t t l e loss ofaccuracy.

Band-theory calculations yield a T a 0isotherm for a la t t i ce of immobile atoms, tlves ta t ic l a t t i c e . These results must becorrected for zero-point la t t ice vibrations toobtain the actual T - 0 isotherm. Theappropriate pressure correction within theGrUneisen model Is -yAE/V, where AE may betaken as the zero-point phonon anergy:

KKR

Another method for solving theSchrOdinger equation in a c r y s t a l l a t t i c e wasdevised by Korringa, Kohn, and R o s t i k e r . I tinvolves the s^rae assumptions made in the APUmethod and i s equally accura te . Two programsdevised by Williams at IBM are in use in T-4.The LMTO programs us»d a t Lawrence LiveraoreNational Laboratory are a very goodapproximation to KKR in most circumstances andare computationally faster.

Pseudopatential Perturbation Theory for SimpleMetals

Thu ph>slcal basis far the interatomicpotential for simple metals is th« adiabatlcapproximation in which the eleetron energy iacalculated as n function of the Ionicpositions. The pseudopotentlal model forsimple metals provides the means of applyingthe adiabatlc approximation to determine aneffective interatomic potential betweenions. From the pseudopotential expansion fortUe electron energies, one can write the coralsystem energy (ion cores plus conductionelectrons) as the sum of a two-body centralforce interact ion between ions pluscontributions that depend only on the totalvolume of the system. The total volume of thesystem does appear as an explicit parameter Isthe two-body interact ion, and hence, a changein volume a l te r s the pair-wise interactionbetween Ions, (Three-body and higherinteractions result from third and higherorder terms in the perturbation expansion ofthe electron-ion p•seudopotentiaiinteraction. ) The u t i l i t y of pseudopotentialtheory for s t a t i s t i c a l mechanics arises fromthe property that at fixed volume the ions naytake any arrangement without changing theeffective ion-ion Interaction.

GRAY Model (developed by R. Groverf D. Young,and E. Roycc at Lawrence Livemore NationalLaboratory)

GRAY15*16 uses a combination of physicsmodels, experimental data, and analytic f i tsto experimental data to calculate the EOS ofmonatomic materials in the solid, melt, andliquid regions.

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The EOS of the solid Is based on theDugdale-MacDonald form of the Gfunelsen-Debyemodel* The total pressure (or energy) at agiven temperature and density Is the sum ofthe zevo-degree pressure (or energy) and thethermal pressure (or energy) which Is In turna sum of independent contributions fromelectron excitations and atomic motions. Thenuclear part of the thermal EOS la baaed onthe nuclear Grllnelaen gamma coefficient YC .An analytic fit for Y^ as a function of volumeIs put inLo CRAY. Th* electronic thermal EOSIs based on the fr^e electron model: g «V ,where g Is the electronic specific heatcoefficient. GRAY uses the analytic f i ts forYr and experimental Hugoniot data to determinethe zero-degree pressure and energy, PQ(V) andE0(V), by the following formulas:

YG(V)PH(V) - PO(V)

where P CV) and EH(V) are the Hugoniotpressure and energy, and

' ~w

No Internal rotat ional or vlbrattonalcontributions to the EOS are take.n Intnaccount•

The melting transi t ion Is calculatedaccording to the Undenuinn law. The equationof state of the liquid Is given by a scalinglaw; that i s , the solid Grtmelsen EOS at agiven temperature and density is correctedwith var'.ous terms which depend on the ra t ioof the cemperature to the melting temperatureat that density. The basla of the scaling Jawis contained in Che equation for the specificheat nf the liquid:

IT/T

where Cvs is the l a t t i ce heat capacity of thesolid, T i s the me I t trig temperature, and a i sa constant determined by f i t t ing soft-spheredata on heat capacity as a function oftemperature.

The experimental data used directly inthe GRAY model ar« normal state data at I atmand room temperature (reference density % soundvelocity, GrUneisen gamma, and the electronicsp«cieic heat coefficient); the meltingtemperature at 1 atm; and the cohesive energy.

TFNUC (Implementad by F. Ree at LawrenceLivermore National Laboratory)

TPNUC calculates an electronic equationof s ta te using the Thomas-Fermi s t a t i s t i c a latom model with the Ktrzhnits form of quantumand exchange cor rec t ions . ' ' Ionic motioncontributions /ire then added to theelectronic EOS. These are baaed onOrUnelsen-llke theory at low temperature andone component plasma theory at hightemperaturd with an interpolation scheme inbetween. In the low-temperature region, theOrUnetsen gamma, yfi. Is expressed In threedifferent analytic forms. Below n density p^,,TFNUC uses the same yr as used In GRAY. Thisforces the TFNUC EOS Co join Bmoothly with theGRAY ROB. Above a density p K , yQ ia apolynomial function of volume determined by aleast squares fi t to Kopyshev's numericaldata. In between pQ and p^, the analytic farmof YQ I S designed to smoothly join the GRAYand the Kopyshev GrUnelaen gamma coefficients.The best values for pQ and p^ are determinedempirically by the user In such a wry as tominimize the difference between p^, and p^, yetalso preserve a smooth transit ion between theupper and lower analytic forms of y-. TFNUCalso includes a Lindemann law melt consistentwith the GRAY melting l ine .

Soft-sphere Model (developed by David Yout.g atLawrence Livermore National Laboratory)

The soft-sphere model is based on MonteCarlo computer ca lcu la t ions" of fluids withIn terpar t ic le potentials of the form $(r) a

e ( a / r ) n , where A < n < 12, e and o areconstants, aid r is the Interpar t ic ledistance. The computer calculations of

pressure and energy were fi t with simplefunctions that consisted of ideal gQB, s t a t i cla t t i ce , and configurational heat-capacityterms. TWo further modif icatlDns2^'2 * areneeded to make the model usable for liquidmedia. F i r s t , a negative cohesive term mustbe added to the pressure and energy. Sincethe at t ract ive part of the Lntcrparticleinteraction is poorly understood, a mean-fieldterm is ufled. Second, some liquid metals havesubstantial electron heat-capacityjnntributInns that cannot be accounted forwlth the sof t-sphere heat-capacity t^rra alone.Hence, this soft-sphere term Is multiplied bya factor wh Ich can be greater than unity.

.Si nee thr parameters in the sof t- spheremodel i-annoL east 1 v he pr«d icted from Hquidme^al data, the model Is used to fitexperimental data . SpecIflcally, the modelparameters are determined by a hest fit to(.-nthalpy, volume, and sound speed Isobars.

TIGER

TIGER22'2" calculates the EOS oF nheterogeneous mixture containing gaseour.,liquid, anJ solid components• Sincelonlzatlon is ignored, the range of validi tyis low temperature (kT < 1 eV) and lowdensity. Generally, TIGER is used in theregion In which the equation of state Issensitive to the chemical equilibrium betweenmolecules and the dissociated species "f themolecules-

The chemical potential of gaseous Bpecjtesi Is calculated with the following formula:"

RT ln(n

where n^ Is the number of -...Ic r, i-pities I,Vg Is tht gaseous molir v^'-rit:, nt.d n°(T) 1Rcne <-h-nj{ ,•-•;" •... .uncial at I atmosphere . The,•• -,,.',11.;., f, for the ftaseous mixtures IsL-alculated with ttie eraplrK-alBecUer-K! st takousky-Wilson eqiiiitttm: ^ ^

The constants a, p, 0, and < are usually giv^.nthe values df a - 0.5, p » 0.1, 0 • '*00 K, and< = 11.85, The quantity n Is the tota lnumber of moles of the gaseous species, and k,Is the "covolume" of species t- The numericalvalues of k^ are computed as follows. Foreach atom, the distance from the molecularcenter of mass Is computed. Th«n thevan der Waals radius Is addi-d to thisdistance. The volume is assumed to be 42.8r \ where r Is the largest of a l l distancescomputed in chis manner.

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The chemical potent ia ls oF the condensedspecies are evaluated by

H * =• H?*(T) •: f V,* dP , where1 l ' 1 atra l

The values cf the constants A, aredetermi r.ed from experimental data on sound=ipeed, t her ma 1 expansion , nnd HuRnnint

Tlic cmiceiU rr t Inn of each of the K^^011**and fin lid spec ies In equi I ibi ium i s determinedaccording to the (Hbbs and stnU-hlometrycond1ti tna: the f i r s t s t a tes Lhat the chemicalpo ten t ia l s of the reac«.ants and products areequal , and the second condition Is tha t theto t a l number of atoms In one mole ui r. ce r ta inmolecule i s constant ( e . g . , the t o t a l numberof s i l i con and oxygen atom in one mole ofSiO2 * s c o n s C a n C ) - These two conditionsresul t in a number of re la t ions with the samenumber of unknown concentrations (n. and n. )of the specii!°. TIGER solves theseU e r a t i v e l y . The EOS can then be calcula tedfrom knowing what the values nf n, and n,a r e .

V. TABLES IN THE SESAME LIBRARY

The SESAME Library contains tahles ofpressure; interna 1 energy; and, in some cases ,free energy as funct Ions oF temperature anddensi ty . In addi t ion, for some mate r i a l s , chc

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to ta l prasBure and energy are separated intoelectronic and nuclear components. Piefollowing types of tables can be found In theLibrary:

301; total pressure and energy tables

303: Ionic EOS (Including cold cul-'e andZero-point contributions)

104: thermal electronic tables

305: thermal nuclear tables (Includingzero-point contrlbutIon)

lO.'i: cold curve

The 301 table1" are the sum of the 306,305, and 306 table*.

The data for a l l these tables areautomatically produced ev«ry t ime an EOS isgenerated using either of the two methodsdescribed In Sections I t and I I I . However,unt i l very recently there was l i t t l e interestin the two-temperature tables, and these datawere not saved. The only way, then, togenerate accurate two-temperature tables is corecalculate the ROS's for most existingmaterials. As an a l ternat ive , R. Albers hasdeveloped an approximate scheme to separatethe total pressure and energy surfaces intothe twn components. A Cowan ion model ts usedto calculate the therma I nuclear EOS (the 305table) which may then be subtracted from thetotal thermal EOS to find the thermalelectronic component (the 304 table) . Thereare a number of fixes in the procedure whichsmooth the data and prevent crossing1 soth^rmg.

This procedure was used to generate!two-teinparature cables for many of the oldermaterials In the SESAME Library. Start ing In1982, a.Vi rew material EOS's f om T-4 havedirect ly calrulated tua-temperature rabies .The Individual EOS descriptions indicatewhether tVi* approximate scheme (via the codeTWOTKMF1) was used.

Equations of state developed in plac?sotht_-r ti :r> Lns Alamos National Laboratory onlyhave t'.ic JO 1 cables ( total pressure and

VI. SESAME SOFTWARE

SESAMF Subroutine Library

The SESAME Subroutine Library wasdeveloped to simplify use of tabular EOS d a t a .SESAME tab le s are transmitted to users onmagnetic tapes in a card image format t h a t canbe read and in te rpre ted by the u s e r ' scom put in;> system. Tha user Is a lso suppliedwith FORTRAN subroutines that preprccess thedata Intn a compact binary f i l e and updatet h i s f i l e a=) needed. The user i s suppl iedwith sunrout ines tha t search t h i s f i l e for JIRt Veil .iK! t e r t a l , load data into a local a r r a y ,and compute thermndynamU- functions by searchand interpo l a t I o n . Linear and rat tana Ifunction in t e rpo la t ion schemes are a v a i l a b l efor one and two dimensions.

Routines are ava i lab le tc compute P and F.(and their f i r s t derivatives) as functIons ofp and T and also to compute P and T (and theirf i rs t derivatives) as functions of p and E.Physical prncdss paths can be computed fmmthe EOS's such as lsochores, i sentropes , and

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Hugoniots. Vapor-liquid coexistence curves,thermodynamic behavior of foams, and phasetransitions can also be determined.

Display Codes

Group T-4 has a number of in-housedisplay codes that combine various subroutinesmentioned in the preceding section to providetabular and graphical representation of theBOS data.

Both two— and three-dimensional graphicscodes ex i s t . Black-and-white capabilityexists for use with Tektronix, microfilm, andmicrofiche output; color graphics capabil i tyalso ex i s t s . The codes use DISSP'JV graphicssoftware hat can he made available toexternal users to adapt to their own systems•

VII. OBTAINING THE SESAME LIBRARY

To obtain SESAME EOS data and thesubroutine l ib ra ry , a user should send a l i s tof the materials required to the followingaddress:

SESAME Library, T-4, MS-B925Los Alamos National LaboratoryLoa Alamos, NM 87545.

The subroutine l ibrary will be copiedonto one tape, and tabular data will bewritten on another. Instructions, includedwith the tapes, explain how to preprocess thedata tapes and how to use the libraryroutines. Users wi l l be charged a nominal feeto cover costs to T-4.

The tapes wi l l be written in anSO-character card image format that i scompatible with the use r ' s computingf a c i l i t i e s . Standard options include the BCDcharacter set for 7-track tapes and the EBCDICcharacter set for 9-track tapes. The tapesmay be e i ther blocked or unblocked, witiieither 800, 1600, or 6250 BPI. The usershould specify e i ther 7-track or 9-tracktapes, the character se t , density, and anyother appropriate parameters.

The number of data tapes needed dependsupon the tape format, the number of materialsrequested, and the size of the tables . As arough guide, allow

one 7-track tape, 800 &P1, for each 20-25mater ials ,

one 9-track tape , 800 BPI, foi each 25-30mater ials ,

one 7-track Cape, 1600 BPI, for each 40-50mater ials ,

one 9-track tape , 1600 BPI, for each 50-60mater ia ls .

The general Group T-4 telephone number is(505) 667-7024 or (505) 667-5751.

Vl i l . DETAILED DESCRIPTION OF EQUATIONS OF STATE

Following are detailed descriptions andplots of each equation of s ta te In the SESAMELibrary. Each description is divided intothree pa r t s . The f i r s t section contains somegeneral information which Is self-explanatory.The second section is a compilation of

physical data. For convenience, experimentalvalues of the physical parametera are listedalong with Che values which are actuallyreflected by the theoretical EOS. (Thetheoretical values have an asterisk in frontof them.) In some cases, these physicalparameters were input for the models that wereused to calculate the EOS, and in other cases,these quantities were calculated from theoutput. It is usually noted in thedescriptions whether the theoretical valuesare input or output.

The physical parameters which areinch-Jeu arc

A -- atomic weightZ — atomic number

po — normal density (density of material atroom tuanperature and 1 atmosphere)

P(T = 298.15 K, po) — pressure (in the SESAMEcable) at roomtemperature and normaldensity

E(T = 29R.l^ K, pQ) — energy (in the SESAMEtable) at roomtemperature and normaldensity

T(P - 10"*" Opa, po) — temperature (in theSESAME table) at a verylow pressure (nearzero) and normaldensity

Tm — melting temperature of material at 1atmosphere

T — temperature at c r i t i ca l point (point atmaximum of the gas-liquid coexistencecurve in a P vs p diagram; at a l l

temperatures below T t the gaB andliquid wil l physically separate).

P,, - - pressure at c r i t i c a l pointP, - - density at c r i t i c a l point

YQ — Grllneiaen gsnima [y =* V l v ] at normaldensity and room temperature

Ro -— hulk modulus at normal density and room

temperature£'u — Debye temperature at normal densityEeoh — cohesive energyUj. — shock velocity (as measured in a

Hugoniot experiment)U — particle velocity (as measured in a

Hugoniot experiment)

(Note: The Hugoniot of a material can beexpressed as a functional relationship between

Users of the SESAME Library should bewarethat , although the values of the aboveparameters are for the most part given at roomtemperature and normal density, often themodels which were used to generate theequations of state expect the values to ba atzero-kelvin. Many of the tables arenormalized incorrectly because of the factthat room-temperature values of bulk modulusand Grlineisen gamma, for example, were used inmodels which expected zero-kelvin values. Thedifferences in the equations of s ta te ,however, would be very s l ight if they wererenormalized correct ly .

The third section of the detaileddescription gives a brief outline of thephysics models and theories which were used tocalculate the EOS tables . Usually only a

sentence or two 1B included to describe themodelEi here; more detai l i s given about thephysic if in Sections I I , I I I , and TV. Thethird section also has information aboutwhether the EOS has a melting transi t ion,whether .it has van der Waals loops or aMaxwell construction in the vapor-liquidcoexistence region, and how the EOS compareswith experimental data (most often Hugoniotda ta ) . Comments on the thermodynamicconsistency of the table are also included.

Also associated with each equation ofs tate in the to1lowing 3ect ion are piot s. Thef i r s t Is a plot of pressure vs density alongIsotherms. Actually the 1 ug_s nf these valuesare plot ted s Ince the ranges covered by theEOS's are very large. The values of theisotherms tn kelvtn are printed to the rightof the plot. The second plot i s of the log ofenergy vs the log of density along isotherms.

The units used in tMs manual are

temperature

density

pressure

energy

kelvin or eV(1 eV = 11604.5 K)

Mg/m3 or g/cm3

(\ Mg/m-1 5 1 g/cm3)

C,?i> (1 GPa = 0.01 MBar)

(1 MJ/kg = 0.013

shock velocity li- km/s

REFERENCES

1. J . Barnes, Phys. Rev, 153, 269 (1967).

2. D. A. Liberman, Phys. Rev. B 2j>, 4981(1979).

3. G. I . Kerley, "Users Manual for PANDA: AComputer Code for Calculating Equations ofS ta te" , Los Alamos National Laboratoryreport LA-8H33-M (November 1981). PANDAwas developed by G. 1. Kerley from the T-4code EOSLTS, which was o r ig ina l ly developedby B. 1. Bennett and modified byt . I . Bennett , J . D. Johnson, G. 1. Kerley,and R. C. Albers . Some of the ideas andmodels used in EOSLTS came from the T-4code SESAME developed by J . Barnes andJ . Rood and from the Sandia CHART-Dradia t ion hydrodynamic code IS. L. Thompsonand H. S. Lauson, "Improvements in theCHART D Radiacinn-Hydrodynamic Code I I I :Revised Analytic Equations of S t a t e , "Sandia Laborator ies report "C-RR-71 0714(March 1972)] . The PANDA code as describedIn the PANDA manual outputs 301, 303. and304 t a b l e s ; R. C. Albers and F . Doweil havemade a modified version of PANDA to output305 and 306 t ab les as well .

4. G. I . Kerley, J . Chan. Phys. 7_3, 469(1980).

5. F. J . Rogers and H. E. DeWltt, Phys. Rev.A j8, 10H (1973J.

6. F. J . Rogers, Phys. Rev. A 10, 2441(1974).

7. F. J . Rogers, In Strongly Coupled Plasmas.G. Kalrcan and P. Carlnl, Eds. (PlenumPress, New York, 1978), p. 643.

8. C. A. Rouse, Astrophys. J . U4. 435(1961).

9. C. A. Rouse, Astrophys. J . 136, 636(1962).

10. T. Loucks, Augmented Plane Wave Method(W. Benjamin, Inc . , New York, 1967). Whenthe effect of correlation becomes largerthan a feu per cent in pressure, theHedln-Lundqvlst exchange-correlationpotential is used, which i s described inA. K. McMahan, Bull. Am. Phys. Soc. 2^,1303 (1979).

11. 0. K. Andersen, Phys. Rev. B .12, 3060(1975).

12. 0. K. Andersen and 0. Jepsen, Physica(Utrecht) B 9J_, 317 (1977).

13. W. A- Harrison, Pseudopotentlals Inthe Theory of Meta'.s (W. A. Benjamin, Inc. ,New York, 1966).

14. W. A. Harrison, Phys. Rev. B£, 2408(1973).

15. R. Orover, J . Chem. Phys. ib_, 3435(1971).

16. P. firover, "High Temperature Equation ofi t a te for Simple Metals," in Proceedingsof the Seventh Symposium on ThermophyslcalProperties, edited by A. Cezalrliyan(1977), p. 67.

28

17. S. L. McCarthy, "The Kirzhnits Correctionto the Thomas-Fermi Equation of State,"Lawrence Livermore National Laboratoryreport UCRL-14362 U W i ) .

18. F. Ree, D. Daniel, and G. Haggin, "NUC - ACode to Calculate Ionic Contributions to Pand E," Lawrence Livenuore LaboratoryInternal document HTN-391 (1978).

19. W. 0. Hoover, M. Ross, K. W. Johnson,D. Henderson, J . A. Karki :", andB. C. Brown, J. Chan. Ph/s. 52, 4931(1970).

20. «. n. Hoover, G. S t e l l , E. Coldmark, andG. D. Deganl, J . Chan. Phys. j63, 5434(1975).

21. D. A. Young, "A Soft Sphere Model forLiquid Metals," Lawrence LivermoreLaboratory report UCRL-52352 (1977).

22. M. Cowperthwaite and M. H. Zwisler, "TIGERProgram Documentation", Stanford ResearchInst i tute Publication No. Z106, Vol. I(1973), Vols. I I - IV (1974).

23. F. H. Ree, "TIGER", Lawrence LiverraoreLaboratory internal document HTN~258(1976).

24. S. R. Brlnkley, J . Chan. Phys. 15, 107(1954). ~

25. R. D. Cowan and W. Fickett , J . Chem.Phys. 24., 932 (1956).

IX. INDEX Or MATERIALS AND SESAME NUMBERS

MaterU.

Air (dry)AluminaAluminumAmmoniaArgonBerylliumBrassCalcium CarbonateCarbon UquidCarbon PhenolicCnpperDeuteriumDeuterlum~TrltlumGoldHe HumHyd rogenIronKryptonLeadLlthla-BorlaLithiumLithium DeuterldeLithium HydrideMethaneMicaMolybdenumNeonNevada AlluviumNickelNitrogenOxygenPBX-9502PBX-9502

(high explosWe)Platinum

SESAME Numher

503074103712, 371355205171, 51722020410073307S3175413310, 3331, 33325263527127005760, 5761, 57625250, 52512140, 21455L80320072522290, 22917242, 724373715500, 5501, 55027 52029S0, 2981, 2982, 29835410, 541i7111310(15000, 50015010, 501181808200

3730

Polyethylene 7160(branched, completely deuterated)

Polyethylene 7171(branched, low dens i ty )

Polyethylene 71f>0(Marlex)

Polystyt-jne 7590Polyurethane 7 560Quartz 73GO, 7381,Sodium 2448Solar Mix (Ross-Aller) 5280Sta in less Steel (304) 4270Teftnn 7190

(Po'vtetrHfluoroethylcne)Tungsten 3 541Tungsten Carbide 3560Uranium 1540Water 7150, 7152Westerly Granite 7390

SESAME II15M)

Mater ia l : UraniumOrlfltnator: J . Barnes and J . RoodDate of Origin: March 1973Type of Tables Included: 301, 303, 304, 305Limits : 0 i p < 3.B * 105

E/cm0 i T t 3.7 « 10s K

BASIC PHYSICAL 1UTA

A - 218.03Z - 92

p o - 18.983

P(T fl.I1) K, p ) 1.0207MJ/kRF.(T = 298,15 K, p ) • 2.394f> x in '• v

T(P = 11" CPa, pQ) = 2.939 » 10"" K

Tm = 1405.5 K |Ref. 11

T. =• * 9837 K (ca lcula ted)

y - * 2.257 (calculated)2.07 |Ref. 21

»n =• * 112.2 HPa (used In calculntlf in of Ens)inn.7 OPa (Ref. 21

Gn = * 207.n K (used In ca l cu l a t i on of F.OS)

F. » * 2.20 MJ/k? (use.1 In ca lcu la t ion ofC ' F.OS)

HuRonlot f i t : 2.51 + 1.51 u km/siRef. 31 P

"ESCRIPTinN OF PHYSICS

This equation of state was generatedusinp, the standard Barnes-Cowan-Rood method .The electronic part of the EOS is fromTh omas-Fermi-Dirac theory; the cold curve 1Hbased on a mudi fied-Morse model; and the;therma1 nuclear contributIons are hased nn aDebye model helow 1 eV, (See Part It for amore detailed description of this method.)

The zero-pressure experimental hulkmodulus and density are reproduced by thisF.OF, and the fi t to experimental Hugoniot datais cnod. However, the equation of state Isnnt accurate at low temperatures in expansion.

The neltinj> transition is not included inthis EOS.

The thermodvnamic consistency of this RDSi R good.

The two- tempera tu re t ab les for t h i s F.OSwere der ived from the TWOTF.SP code and arcvcrv no i sy .

REFF.RF.HCES

1. Hanclhook of Chemistry and P h y s i c s .R. C. U e a s c , F.d. (CRC P r e s s , C leve l and ,Ohio, 1^7^) .

2. K. A. Hschneidner , J r . , Solid S t a t e Phys ics\h_t 275 ( 1 9 6 4 ) .

3 . S. P. Marsh, LAST, Shock Hugonlot Data( Univers i t v of Ca 11 f orni.i P r e s s , Berkeley ,1980).

1540-2

SESAME 02(120

Mate r i a l : Beryl l ium-XifiiS'l t^r: J- Barnes and J . Roodjjaie_nf_nr_l£in: Ju ly 19/3

Ty_2S_9XT5iJia_l!l£iu4si: 3 n l . 303> 3(Vl . 3H5>?0fi

Limits ; 0 T < 3.7 xlO" K

BASIC PHVS.ICAI. 11ATA

A - 1.0122'/. - A

P(T = 298 . f i K, p ) • 0.3F.(T - 29B.15 K, p") - 0.198(1 MJ/kgT(P - 10"6 CPa, p o ) • 8.1 4

pn »

P(T = 298 . f i K, p ) • 0.37(14 (;poF(T - 29B15 K ") - 0.198(1 MJ/kg

.1065 x 10 4 K

Tm = 1551 K [Ref . 1 I

T. = 10665 K iR^f. 2]9109 K iRef. ll

* 9823 K ( c a l c u l a t e d )

Yo " * 1.014 (caU-uln ted)1.16 [Ref. 4]

Ho = * 12(1.8 HPa (used In caK-ula t ion of EOS)102.3 CPa |Ref. 4 I

"•oh " * 1^" f l M J ' k S ("Sod In c a l c u l a t i o n ofEOS) [Ref. 5]

8 n = * inon K1iftO K IRef. 41

2020-1

Hugonlot F i t : U » 7.99 + 1.13 U kra/s3 I Ret. 6] P

DESCRIPTION OF PHYSICS

This equation of s tate was generatedusing the standard Rarnes-Couan-Rood meihod.The electronic part of tne EOS was calculatedwith Thomaa-Fermi-Dlrac theory; the cold curveis based on a modified-Morse model; the ioniccontributions are calculated with a model byR. D. Cowan above I eV and a Dcbye model below1 r.V. (See Part II For a detailed discussionof this procedure of EOS generation.)

The zero-pressure experimental densityand bulk modulus are reproduced by th is EOS,and the fie to experimental Hugoniot data isgood. Also, the c r i t i c a l point ia fa i r lyclose to estimated made by Merts and Magee,as well as Thompson. However, this EOS wasnot generally designed for the hot, expandedliquid metal region and i t i s not to betrusted there.

The thermodynamic consistency i s goodeverywhere.

No melting t ransi t ion is Included in th isEOS.

The tuo-temperature tables were derivedfrom the code TMOTEMP and are noisy.

A tension region for spall has beenadded.

REFERENCES

1. Handbook of Chemistry and Physics,R. C. Ueast, Ed. (CRC Press , Cleveland,Ohio, 1976).

2. A. L. Her ts , N. H. Magee, J r . , "LowTemperature Equation of State for Metals,"Los Alamos Sc i en t i f i c Laboratory reportLA-5068 (Jan. 1973).

3. S. L. Thompson, "Improvements in CHART DRadiation Hydrodynamics Code: AnalyticEquations of S t a t e , " Sandia Laboratories,Albuquerque, repor t SC-RR-7^28 (1970).

4. K. A. Gschnetdner, J r . , Solid State PhyBlcsU>, 275 (1964).

5. L. Brewer, "Cohesive Energies of theElements," Lawrence Berkeley Laboratoryreport LBL-37Z0 (1975).

fi. S. P. Marsh, LASL Shock HuRoniot Data(universi ty of California Press, Berkeley,1980).

MATERIAL SKO

P (g/cm3)

MATERIAL 2020

P (g/

SESAME J2140

Material: IronOriginator: J. Barnes and J. RoadDate of Origin: August 1973Type of Tables Included: 301, 303, 304, 305,

306Llmlta: 0 < p < 1.57 x 103 g/cm

J

0 < T < 3.7 x 108K

BASIC PHYSICAL HATAA = 55.850Z = 26

Po - 7.85 g/cm3

P(T - 298.15 K, p ) - 1.1233 GPaE(T - 298,15 K, p ) - 7.0505 x 10"2 MJT(P =• 10~6 GPa, p°) - 4.4979 x 10"4 K

Tm - 1535 K [Ref. 1]

T - 9340 K [Ref. 2]6750 K [Ref.3]

* 8830 K (calculated)

y - 1.81 [Ref. 4]* 2.035 (calculated)

B = 171.6 [Ref. 4]* 165.7 GPa (calculated)

calculation of

9D - 464 K (Ref. 1]* 470 K (used in calculation of EOS)

Hugoniot F< t : U 4.955 + 0.454 U kn/s for0.1 < U < 0.33

U =• 2.049 + 3.79 U km/a for0.34 < U < 0,79

U_ •» 3,635 + 1.802 U_ - 0.0333 Un2

for I . < 0 < 7?7 (Ref. 5] P


The iron equation of s ta te was calculatedwith the flarnes-Cowan-Rood method4 Theelec t ronic part of the F.OS was t reated withThomas™P«rml-Dirae theory, and the thermalnucLear part waa determined by a Cowan modela t temperatures ahove 1 eV and a Debyd modelfor lower temperatures. The cold curve wasbased on the modified-Morse model with oneexception. Since iron has a so l id-sol id phaset r ans i t i on (bee + hep), a composite cold curvewas constructed. The lower portion Ibee) wasbased on p = 7,85 g/cm and BQ = 165.7 GPa,and the hep part of the cold curve wascomputed with values of p = 8.08 g/cnr and BQ

= 149.5 GPa. The t rans i t ion from the bee tothe hep phase occurs at 8.4 g/ctn on thezero-kelvin isotherm. Since th i s cold curvewas used in calculating a l l thefinite™temperature isotherms, the phaset rans i t ion persis ts at high temperatures.(See Part I I for a detailed descript ion oft h i s procedure of EOS generation.)

The theoretical Hugoniot compares wellwith experiments un t i l I t reaches pressures ofapproximately 300 GPa, at which point It ?3s l i gh t l y sof t . The EOS also reproduces porousHugoniot experiments wel1. The theoreticalcold curve agrees well with three APWcalculat ions by E. Kmetko; the largestdiscrepancy Is 11% at four-fold compression.The mod-Morse cold curve does not approach theThomas-Fermi-Dirac l imit fast enough.

2UO-2

The thermodynamic cons i s t ency i s gnod.

The t w o - t e m p e r a t u r e cables were de r ivedl a t e r by the co ld TWOTEMP and are n o i s y .

REFERENCES

1. Handbook op Chemistry and P h y s i c s .P.. C. Weaat , Ed. (CRC t r o s s , C leve l and ,Ohio, 1976 ) .

2. D. A. Young and B, J . Alder , " C r i t i c a lPoints, of Meta l s from van der Waals Model ,"Phys . Rev. A 2 U> C1971).

3 . A. V. Groase and A. D. Kirshenbai I,J . I n o r g . Nuc l . Chem. 2JL> 3 3 1 U ' 6 3 ) .

4 . K. A. Gschne idne r , J r . , Sol id S t a t e P h y s i c s1_6, 275 ( 1 9 6 4 ) .

5. M. van T h i e l , "Corapendiuni of Shock WaveD a t a , " Lawrence Livermore Labora tory r e p o r tUCRL-50108, Rev. 1 (1977) .

2140-3

CdO) d

MATERIAL 2140

SESAME #2145

Material; IronOriginator: G, Kerley, J . Barnes, and J . RoodDate of Origin: June 1977Type of Tables Included: 301Limits: 0 K, p ) - 1.42235 GPaE(T = 298,15 K, p ) - 9.93465 * If2 MJ/kgT(P = 1Q"6 GPa, p°) - 1.875 * 10"4 K

Tm - 1535 K

Hugoniot Fit: See SESAME 02140


This equation of state was generated Eorthe reactor safety program and coverB only alimited range of temperatures and densities.Information about the models used to generatethis EOS is unknown.

MATERIAL 21-15

MATERIAL 2145

SESAME #2290

Material: Lithium [Ref. 1]Originator: D. Steinberg (Lawrence Livermore

National Laboratory, R- Divt ston)Date of Orifiin: unknownType of Tables Included: 301Limits: 0 n.71988 GPaE(T - 298.15 K> po) - 0.77464 MJ/kgNo zero presHure point ex i s t s In th is t a b l e .

T = 4V1.7 K [Ref. 2]m

y = * 0.92 (used in generating EOS)a = * n . 6 GPn (used in generating EOS)

Hugontot F i t : * 0.477 + 1.066 Up kra/s(used In ^u . - . a t lng EOS)


This lithium F.OS was generated from ananalytic nrllnet5,en Ens determined byD. S t e inhe rg a t Lawrence Livermo re Na t tona1Laboratory. The o r ig ina l analytic functionRives pressure as a funetlnn of energy anddensi ty. However, the SESAME Library expectsa table in whirh pressure and energy are givenat each point of a rectangular grid of densi tyand temperature. The method which was used Coturn the --vialytic function intn a

SESAME-formatted t ab l e i s documented tnRef. 3.

Even thoufih t h i s EOS has been tabulatedover a f a i r ly wide range of t empera ture andd e n s i t i e s . I t s range of va l id i ty covers onlythe area between the pr incipal adlabat and thetlugnniot. And i t should only be used up to adensity corresponding to a pressure of 5 B onthe Hugoniot.

This equation of s t a t e Is notthermodynamlL-al ly cons i s t en t because of themethod used to incorporate temperature.

REFERENCES

1. D. Steinberg, "A High Pressure Equation ofState for Li thium," Lawrence LlvermoreLaboratory, B-Diyision Progress Report( Ju ly , 1973).

2. Sargent-Welch Period!. Table of theElements (1968).

3. B. T. Bennett , "EOSSCAN: A Program tnOispi ay Equat inn-of-Sta te nata,1 ' Los AlamosNational Laboratory report LA-8737-MS(March 1981).

MATERIAL 2290

0.000E-KM2901E+035.802E*038703E+03I160E+CM1839E+042915E*04

620E4620E(M7.322E+04!.160E*D5IB39E+052.915E4-054.620E<D57.322E+051.16OE+O6l.B39E<06Z915E+064«20ED67.322E+06l.I60E*(T71B39E+072.9I5E+074.620E+OT7322E*O71160E*08

MATERIAL 2290

O.OOOE+002S01E+035B02E035B02Ea.703E*031.160E-KHIB39E+O42.91SE-KJ4

0 E 0 4<£20E7322E-HM1J60E+05B3BEH»1B3BE»

2S15E+054S20E+05732aE+D51160E+061639E+062915E+U64 620E+O67322E+06HSOEff1B39E+072.915E+0T7

7.322E+071.160E+06

P (g/cm3)

SESAME 02291

Material : Lithium [Ref. 1]Originator: D. A. Young (Lawrence Livermore

Nat ional Laboratory, H-DlviHlon)Date of OrlRlnat ton: 1978Type of Tables Inc luded: 301Limits: 10 * < p < 2 g/cm3

453 < T < 3.67 x 108 K

BASIC PHYSICAL DATA

A = 6.939

Z " 3 3p o = 0.518 g/cm

P(T = 298.15 K, pQ) =» -0.33247 GPa (outs iderange of table)

E(T =» 298.15 K, pQ) = 0.401455 MJ/kg (cohesiveenergy)

(No zero pressure point exists in this t ab le . )

Tm = 453.7 K iRef. 21

* 453.7 K (used in calculation of EOS)

Tc =* * 3741 K (calculated)

Hugoniot F i t : Us - 4.51 + 1.09 U km/s [Ref. 3]

DESCRIPTION OF PHYSICSThis lithium EOS was generated for use in

design studies of laser-fusion reactorsemploying a l i thium "waterfall". That i s whythe upper l imit of density is only four-foldcomprersed.

Three physics models were used: ACTEX forthe ionized f lu id , sof c sphere for the liquidand vapor, and a liquid mi'*' nerturbation

2291-1

theory based on pseudopetentlals for the hot,dense Liquid. Three separate EOS*a weracomputed tn overlapping regions of thetemperature-density plane, and then these werejoined along optimal boundaries* A smallamount of bll inear numerical Interpolation wasrequired for smooth joining. Fig. I shaws thereginnR over which each theory was used.

Agreement £,f the EOS with experimentalIsnbaric data iRef. A] (measuring volume,sound speed, and enthalpy) and experimentalHuRonlot data [Refs. 3 and 5| is good.

The therroodynamic consistency of th is EOSis good due to the fact: that the energy wasforced into cons Latency with the pressure inthy interpolation regions. (Joining KOSsubsurfaces invariably leads to inconsistencyalonf; boundaries.) However, this caused a ktnkIn the ultrahtfih pressure shock. Mugoniot (inan area not accessed by a fusion reac tor ) .

The quality of this EOS i s high; i t is acomposite nf three of Che more advanced EOSmodels available.

The Li Chi tin FOS has a Maxwellconstruct ion In the two-phase, liquid-vaporregion.

REFERENCES

1. D. A. Young, M. Ross, and F. J . Rogers, "ATabular Equation of State of Lithium forLaser-Fusion Reactor Studies ," LawrenceLlvermore National Laboratory reportUCRL-82182 (January , 1979).

2. Sargent-Welch Periodic Table of theElements (1968) .

3 . A. A. Bakanova^ 1. P. Dudoladov, andR. F. Trunln, F i z . Tverd. Tela 2 . 1616(1965) (English t r a n s l . r Soviet Phys.Solid Sta te Engl. TranBl. 7, 2307(1965)].

4. R. Hultgren, P. 0 . Desai, D. T. Hawkins,l l . G le l se r , K. K. Keliey, and D. D. Wagman,Selected Values of the ThelittodynamlcPropeixles of the Elements (AmericanSociety for Metals , Metals Park, Ohio,1973).

5. M. H. Rice, J . Phys. Chem. Solids 26, 483(1965).

Density (Mg/m3

Fig. 1. Temperature-density plot showing thesubregions covered by each of the theory codesused to calculate the EOS for lithium. Theshaded area is where numerical interpolationwas required to smoothly join two EOSsubsurfaces.

MATERIAL 2291

-2P (g/cm3)

MATERIAL 2291

-2

P (g/cm3)

4S37E--O273UE+02145OE+03a901E+035.B02E+03I160EHH2321E+044e2E044 E 09233S+O41.BS7E+O53.667E+O57.311E+051.450E+062901E062901E065S02E+06U60E+072321E+O74.642E+0795S3E+O7BS?EOe

SESAME »2448

Material! SodiumOriginator: B. BennettDate of Origin: June 1977Types of Tables Included: 301Limits: 0 < p < 1.3143 g/om3

0 < T < 1.015 * 104 K

BASIC PHYSICAL DATA

A - 23.0Z - It

p 0 - 1.011 g/cmJ

p { * * 0.96587 g/cm3 (computed rrom tableat 298 K)

0.971 g/cm3 (experiment)E(T - 298.15 K, p f ) . 0.26914 W/kgTCP - 0, p r e f ) . 298.12 K

Tm - 370.96 K (experiment)

T - • 2538.58 K (computed)2503.25 K [Ref. 1]

lfo - 1.2 [Ref. 2)

Bo = 7.7 GPa [Ref. 2)

E c o h - 4.668 MJ/kg [Ref. 3]

6D - 158 K [Ref. 4]

Pnlsson's ratio: 1/3 (arbitrarily chosen)

DESCRIPTION Of PHYSICS

Cold Curve (T - 0 K Isotherm)

An empirical model generated from amotiified-Morse form iRcf. M above a densi tyof O.9453pQ and a Lennard-Jones (m,n) formwith m - i -85 and n => 8.08953 below t h l adensi ty was used. The l a t t e r guaranteesagreement with the assumed cohesive energy.

Nuclear Vibrat ion Contrthut.toil

A model which causes a t r a n s i t i o n from aDebye co l id to an ideal gas was used (Ref. 6 ] .This raodsl requires knowledge of the dens i tydependence of the Dehye temperature and thefirUndisen parameter. This was obtained fromthe so-ca l led Chart-D model tRef. 7 1 .

Elect ronic Excitat ion Contribution

A modified Saha—typt* theory was used.This model requires s s ingle ion iza t ionp o t e n t i a l . A value of 5.12 eV was chosen. I ti s expected t h a t , because of the magnitude ofthe c r i t i c a l temperature - 2500 K, thecon t r ibu t ion to the equation of s t a t e due toe l e c t r o n i c exc i ta t ions should be smal l .

REFERENCES

1. V, S. Bhise and C. F. BoniUa, "TheExperimental Vapor Pressure and C r i t i c a lPoint of Sodium," '.n I n t e rna t i ona lConference on Liquid M^tal Technologyin Energy Production (May 1976).

2, J . F. Barnes, "An Equation of State forSodium over an Extended Temperature andDensity Range," Thermodynamics of NuclearMate;rials 1974, Vol. I , (InternationalAtomic Energy Agency, Vienna, 1975), p.327.

1, L. Rrewer, "The Cohesive Energies of theElements," Lawrence Refkeley Laboratoryreport LRL-3720 (1975).

4. Handbook of Chemistry and Physics. 57th ed.(CRC Press, Cleveland, Ohln, 1967) p.

5. R. I. Bennett, "A Computationally EfficientExpression For the Zero" TenperatureIsotherm In Equations of State," Lofi AlamosScientific Laboratory report LA-8616-MS(1980).

6. Konner, Funtikov, Urlin, and Kolesnikova,JETP _15_, 1*1*1 (1962); Kormer, Slnitsyn,Funtikov, Urlln, and Blinov, JETP 20, 811(1965).

7. Thompson and Lauson, "Improvements In theChart-Radiation-Hydr'-flynamii: Code I I I , "Sandla L-iboratories report SORR-71 0714(March, 1972).

sag

====—--—f

MATERIAL 2448

P (fi.c.-n3)

SESAME 1)2700

Material : GoldOrlRlnator: A. Llndstrom and J . RoodDate of Origin: January 1976Type of Tablea Included: 301, 303, 104, 305

306 ' ' 'i i s i " : ° 2 8 5 :

Tm = 1337.61 K [Ref. 1]

Tc - • 8460 K (calcula ted)

Yo - * 2.225 (used In ca lcu la t ion of EOS)

Bo - * 167.6 GPa (used In ca lcula t ion of EOS)176.6 CPa [Ref. 21

Ecoh " * 1-'4B MJ/kg (used In calculat ion)1.R68 MJ/kR (Kef. 3]

9D " * 165 K (used In ca lcu la t ion) [Ref. 1)

CPa

10"

Hugonlot F i t : U 3.120 + 1.521 n k n , / s[Ref. 4] p

2700-1


The gold equation of state was generatedwith the Barnes-Cowan-Rood method. Theelectronic contribution was calculated withThomae-Fermi-Dirac theory. The cold curve Isbased on a modified-Morse model. The thermalnuclear EOS was calculated with a model fromR. D» Cowan above 1 eV and a Debye model below1 eV. (See Part I I for a detailed discussionof this method of EOS generation.)

The theoret ical EOS reproduces Hugonlotexperiments well , although i t i s soft near thehighest pressure experimental Hugoniot point.This EOS was not designed for the hot,expanded liquid metal region, BO It should notbe trusted there .

No melting t ransi t ion has been includedin this EOS.

The therroodynamic consistency i s goodeverywhere.

The two-temperature tables were derivedby the code TWOTEMP and are noisy.


REFERENCES

1. Handbook of Chemistry and Physics ,R. C. Weast, Ed. (CRC Press , Cleveland,Ohio, 1976).

2. K. A. Gschneidner, J r . , Solid S ta te Physics16, 275 C 9 6 4 ) .

3. L. Brewer, "Cohesive Energies of theElements," Lawrence Berkeley laboratoryreport LBL-3720 (1975).

4. M. van Thlel , "Compendium of Shock WaveData," Lawrence Hverraore Laboratory reportHCRL-50108, Rev. 1 (1977),

2700-3

MATERIAL 2700

MATERIAL :?

SESAME J2980

Material! MolybdenumOriginator: J. Barnes and J. RoodDate of Origin: March 1973Type of Tables Included: 301, 303, 304, 305,

306Limits: 0 < p < 2.04 « 105 g/cm3

0 < T < 3.7 x 108 K

BASIC PHYSICAL DATA

A - 95.94Z - 4 2

Po - 10.2 g/cnr

P(T - 298.15 K, p ) - 0.63866 GPaE(T - 298.15 K, p ) . 4.2209 » 10~2 MJ/kgT(P " IO~6 GPa, po) . 4.729 x 10"4 K

T - 2888 K [Ref. I]2890 K [Ref. 2)

(There are a large number of measurements ofthe melting temperature In the l i t e ra tu re ; thetwo values cited here are averages of severalmeasurements •)

T - 14300 K [Ref. 3)14590 K [Ref. 4]9470 K [Ref. 51

T. - 1.60 [Ref. 1]B - 277.9 GPa [Ref. 1]

267 Gpa (Ref. 6]261.0 GPa [Ref. 7)

Ecoh * 6-85

eD - 459 t 11 K [Ref. 1]

Hugoniot F i t : U - 5.14 + 1.22 Uo [Ref, 8jIT - 5.1 + 1.266 u£ [Ref. 9]

(Note: The values for the above parameterswhich were used In generating the EOSare unknown) •


Thia molybdenum equation of s ta te war,generated with the Barnes-Cowan-Rood method.The electronic part of the EOS Is fromThoraas-Ferral-Dlrac theory; the cold curve lahased on a modified-Morse model; and thethermal nuclear EOS Is calculated with a mode]from R. D. Cowan above 1 eV and a Debye modelbelow 1 eV. (See Part II for a detaileddiscussion of th is method of EOS generation.)

The melting transition is not included inthis EOS-

The two~teraperature tables for th isniacerial were derived from the code TWOTEMPand are noisy.


1. K. A. Gschneidner, J r . , Solid State Physicsi £ , 275 (1964).

2. R. Hultgren, P. D. Desal, D. T. Hawkins,M. Glelser, K. K. Kellny, and D. D. WagmatiSelected Values of the ThermodynamlcProperties of the Elements (AmericanSociety for Metals, Metals Park, Ohio,1973).

2980-2

3. U. Seydel, H. Bauhof, W. Fucke, andH. Wadle, High Tamp.-High Presaurea l±, 635(1979).

4. D. A. Young and B. J . Aider, Phys. Rev. A2 . 364 (1971).

5. M. M. Martynyuk, Russian J . of Phys. Chem.JU (5) , 705 (1976).

6. Ll-chung Ming and M. H. Manghnanl,J . Appl. Phys. 49 (1) , 208 (1978).

7. R. G. Hcqueen, S. P. Marsh, J. W. Taylor,J. N. Fri tz and W. J. Carter, InHigh Velocity Impact Phenomena. R. Kinalou,Ed. (Academic Press, Neu York, 1970).

a. S. P. Marsh, LASL Shock HuRoniot Data(University of California Press, Berkeley,1980).

9. L. V. Al ' t shuler , A. A. Bakanova,I . P. Dudoladov, E. A. Dynin, R. F. Trunin,and B. S. Chekln, Zhurnal PrlkladnoiMekhanlki 1 Tekhnicheskoi Fizikl .2, 3(1981) [Sov. Phys. JAMTPZ2 (2) , 145(198101.

MATERIAL 2980

1 2 3P (g/cm3)

2980-6

SESAME J2981

Material: MolybdenumOriginators: G. Kerley and J . AbclallahDate of Origin: October 1980Type of Tables Included: 301l imi ts : 8.5 °>°)

• 5.3083 »» 2.8944 «- 21b.75 K

inin HJ/kp,

Tm - 2888 K [Ref. 112890 K (Ref. 2]

* 2890 K (result of melting transi t ioncalculation)

(There are a large number of measurements ofmelting temperature In the l i t e ra tu re ; t1 ^ twnvalues cited here are averages of severalmeasurements.)

No value for T Is listed since this F.MS nnlycovers compression.

To - 1.60 [Ref. 11* 1.70 (used In calculation of F.ns)

B - 277.9 GPa [Ref. 1)267 GPa [Ref. 31261.0 GPa [Ref. 41

* 270.3 GPa (used In calculation of F.OS)

2981-1

* 6.85R MJ/k.g (used in calculation of EOS.1

9D - 459 ± 11 K [Ref. l\* 450 K (used in calculation of EOS)

Hugonlot Fit: 0, - 5.14 + 1.22 U [Ref. 5]U° - b.l + 1.266 IT [Ref. 6)

* Us - f.l + 1.24 D (used incalculation bf EOS)

DESCRIPTION OF PtftSICS

This molybdenum equation of s tate onl /covers the compression half-plane Cdt n i c i e sgreater than reference density). I t ashasically intended to be as accurate aspossible for the purpose of analyzing Hugoniotimpedance-matching experiments.

The cold curve is a composite of INFERNOand PANDA calculat ions. The PANDA part of thecold curve i s constructed from experimentalHugoniot data and so covers densities accessedby experiment. The INFERNO calculations areused at higher densities and are smoothlyjoined onto the PANDA cold curve.

The electronic contribution to the EOSwas calculated with ths INFERNO model whichsolves the Dirac equation for an atom embeddedin an electron gas. Shell structure effectsare predicted by INFERNO, unlikeThomas-Fermi—Dirac theory which is based on acontinuous electron distr ibution,

PANDA was also used to calculate thenuclear contribution to the EOS. In th i sportion of the EOS, solid la t t ice vibrations

2981-2

and fluid nuclear motion are taken intoaccount.

The molybdenum EOS includes a meltingtransition. Separate equations of state weregenerated tor the solid and liquid states, andthen a composite surface was constructed bylocating the phase boundary on each isothermat the point where the Gibha free energies areequal.

REFERENCES

1. K. A. fiachneldner, Jr., Solid State Phvaic9H;, 275 (1964).

2. R. Hultgren, P. D. De-sal, D. T. Hawki:.s,M. Glelser, K. Y, Kelley, and D. D. Wagman,Selected Values of the ThennodynamicProperties of the Elements (AmericanSociety for Metals, Metals Park, Ohio,1973).

3. Ll-chung Ming and M. H. Manghnani,J. Appl. Phys. 9_ (1) , 208 (1978).

4. R. G. McQueen, S. P. Marsh, J . W. Taylor,J. N. Fr i tz , and W. J . Carter, InHigh Velocity Impact Phenomena. R. Kinslow,Ed. (Academic Press, New York, 1970).

5. S. P. Marsh, LAS1, Shock Hugonlot Data(University of Cali"'-jrnia Press, Berkeley,1980).

6. L. V. Al'tshuler, A. A. Bakanova, I . P.Dudoladov, E. A. Dynin, R. F. Trunln, andB. S. Chektn, Zhurnal Prlkladnoi Mekhanikl1 Tekhnicheskoi Flzlkl 2, 3 (1981) ISov.Phys. JAKTP 27 (2) , 145 (1981)].

2981-3

MATERIAL 2981

P (g/crn3)

MATERIAL 2981

P (g/cm3)

SESAME (2982

Material: MolybdenumOriginator; R. c. AlbersDate of Origin: September 1982Typ»: of Tables Included: 306Limits: 9.506 < p < 256.66 g/cm3

T - 0 K

BASIC PHYSICAL DATA

A - 95.94Z - «

Po - 10.256 g/cm3

B - • 261 GPa (calculated)o


The zero-temperature cold curve wascalculated uith a se l f -cons i s ten t ,semlre la t iv l s t i c , LMTO elect ronic bandstructure code for fee molybdenum. Muffin-tinand ASA corrections are included. Angularmomentum values up to g (Jt - A) were kept.

2982-1

SESAME 1(2983

Mateilals MolybdenumOriginator: K. TratnorP a t e n t Origin: March 1983Type nf Tables: 101, 103, 30/., 305, 106Limits: 10.2 < p I 250 g/cm3

0 < T t 2.12 » 106 K

BASIC. PHYSICAL DATA

A - 95.942 - 42

P,, - i n . : 8 / c . z

P(T - 29R. I "i K, pQ) - 0.16024 CPaF.(T =• 298,15 K, pQ) - 1.15H7 x H)~2 HMV.f,T(P - 10~4 CPn, pD) • 1.1509 « 10 K

Tm - 28H8 K iRef. I)289(1 K (Rsf. 2]

* 2883 K. (used in taK-,ilatIon)(There are a large number of measurements ofmelting temperature In the l i t e r a t u r e ; the twovalues cited here are averages of severalmeasurements.)

No value for Tc Is l i s ted since th is Ens onlycovers compression.

Yo - 1.60 (Ref. 1!* 1.16 (resul t of ca lcu la t ion)

B > 277.9 CPa lRef. 11267 GPa U e f . 3]261.0 GPa [Ref. <.)

* 259 GPa ( resu l t of ca lcula t ion)

e n - 459 t 11 K (Ref. 11

2983-1

H u s o n l o t F i t : Ug » 5 .14 + 1.22 U kra/si R i f . 5]

U c » ' i . l + 1.266 U km/s

S OF PHYSICS

Th i s equat ion of s t a t e fur no lybdwuum u;is<i-fk-ra[f(l along with ctjuat Ions of sr a tc foru)(i|K.-r < 1 "* 12 > and aluminum (1713) for thepurpose of ^v,i 1 uat ln>; MiiRi'mir.tln\pedaiw«~nii( tchtnK eKperi"ii*nts . Hie >;oa 1 W.IHtu t-aU-ul ate! a si-t of EllS t-ihies based <ni t))^s.imc physlirs tnodtls.

The Ze ro-ke? 1 vin Isothfrm -/«s c;iK ul "itedwi th a s emi re l a t i v t s t t c band s t r u c t u r e mode I(LMTO) bastid on the linear-muff t n - c tn -o rh l t a lme-chod. (This if the same ..old curve anSESAME -V2982.)

The thermal elevtronU- part of the FOSw.is H^n^ratrJ with D. Uiherman's

t-1 f-consisteni; f ield model far condensedmatter (INFKHNO), INFERNO solves Che t)i raL-equat ion for an atun embedded in an e l e c t r o n^ s . Unlike F.ns*s based on Thnmas-Fe rmi-ni r;i^theory, INFKRNO t htfrmodvnami v stirfrtt'es exh ib i tKhell s t r w t w r e e f f e c t s . The nuclear thermalF.OS was based nn the nuRd.iltr-MacDonn Id form ofCrUnt;* <?en-Debye theory. rrrVineiFien s»a:nna wasc a l c i l a t e d from the cold curve according tothe following fornuh' .

7 ( V J1

where B Is bulk modulus, V i s volume, and P Ispressure . Note chat gamma i s a function ofdensi ty only, not temperature .

A melting t r ans i t i on i s included In thisEOS based on the LI ndeifiann law. The equationof s t a t e of the l iquid Is given by a scalinglaw; that i s , the sol id GrUneisen EOS at agiven temperature and dens i ty la correctedwith various terras which depend an the r a t ioof the temperature to the me I t ing temperatureat that densi ty.

At pressures between 50 and 200 C.?n, theHugonloc that th i s EOS p red ic t s Is a l i t t l esoft compared with exis t ing Hugontntexperiments; but above and below thosepressures , It matches the data weTl

Nate that only compression Is covered byt h i s EOS since l l was Intended for analysis ofllugonlnt experiments.

The F.OS Is thermodynamlcul ly consistent«verywhere.

REFERENCES

1. K. A. r.schtieldner, J r . , Solid State Physics\b_, 27S (1964).

2. R. Multgr«n, P. D. Desai, D. T. Hawkins,M. Clelser , K. K. Kelley, and D. D. Wagman,Selected Values of the TheonodynamtcPrnperttes of the Elements (AmericanSocletv for Metals, Metals Park, Ohio,1973).'

3. Li-chung Ming and M. H. Manghnanl, J .Appl . "hys. ^9 ( I ) , 208 (1978).

4. !U G. McQueen, S. P. Marsh, J . W. Tay lo r ,J . N. F r t t z , and U. J . C i r t e r , InHigh Ve loc i t y Impact Phenomena, P. KinslowEd. (Academic Press, New York, 197 Kin

1970;.

6. L. V. A l ' t : . hu l e r , A. A. llakanovii,[. P. Oiidolad'.'V, K. A. Dynin, R. P. T run in ,and B. S. Chektn, Zhurnal Pr lUadno iMekhiniki 1 TckhnUheskoi F l z i k i 2_- '( I1HI) ISov. Phys. .1AMTP _2^ ( 2 ) , 145(19HD1.

MATERIAL 29B3

P fe*m3

SESAME J3100

Material ; NickelOr ig ina tors : J> Barnes and J . RoodDate of Pcljj in: March 1973Type of Tables Included: 301, 303, KM, 305,

Limits: 0 <• p < 1.7764 * 105 g/cm1

EAS1C PHYSICAL DATA

A - 58.710Z - 28

p - a.882 g/cmJ

P ( T - 298.15 K, P I - 2 8 0 6 G P o-, , , .

T - 1726 •/. iRef. Um 1728 K (Ref. 2]

T = 9576 K [Ref. 3]c 6520 K [Ref. M

6000 K (Ref. 51 .* 9133 K. ( r e s u l t of EOS ca l cu l a t i on )

, =. 1.88 Can average of values found In the^° l i t e r a t u r e ) iRef- U

2.00 (ca lcula ted from shock wave da ta )(Bef. H .

* 2.098 ( r e s u l t of EOS ca lcu la t ion )F, = 190 GPa I Ref. ll , • 1

' * 190 GPa (used In EOS ca lcu la t ion )

BD » 427 t 14 K tRef. IJ<"M3 K (used In £OS calculation)

Hugonlo: Fi t : U » 4.646 + 1.445 U km/a" [Ref. 6J P

Ue = 4.501 + 1,627 u_ -0.0264 U 2 WsMRef. 7]

DESCRIPTION OF PHVSICS

At higher temperatures (probably above 1eV), this EOS was generated by mixing MAPLEequations of s ta te for Iron (using a numberfraction of 0.902937) and molybdenum (using anumber fraction of 0.197063). The averageatomic weight of the resulting material was6U.8625. The mixed EOS was scaled so that theatomic weight would be 58.71 and the referencedensity, pQ , '^ould be 8.882 g/cra .

At temperatures below I eV, the codeMAXWELL computed the EOS. MAXWELL assumesthat the pressures and energies are the sun oftwo contributions: a zero—degree contributionand a thermal uuclesx contribution. The coldcurve (zero-kelvin isotherm) i s based on amodified-Morse model, and the r.hermal nuclearpart la calculated by a Debye model. (SeePart II for a detailed discussion of thisprocedure of EOS generation.)

The experimental zero^pr^ssure densityand bulk modulus are reproduced by this EOS,ind £h*i f i t to experimental Hugoniot data Isgood. Also, the c r i t i c a l point i s . a i r lyclose to an estimate made by V •ng and Alder.However, this EOS was not generally designedfor the hot, expanded, liquid metal region andI t is not to be trusted there.

3100-2

No malting t r a n s i t i o n Is Included In th isEOS.

The thermodynamlc consis tency Is goodeveiywhere.

The tuo-temptjrature t ah les for th ismater ia l were derived by the code TWOTF.MP andare noisy.

REFERENCES

1. K. A. fischneidner, J r . , Solid Sta te PhysicsJjft, 275 ( 1 9 M ) .

2. S. A. Kats, V. Ya. Cbekhovskot, HighTemp.-High Pressure 1_J_, 629 (1979).

3 . 0. A. Young and B. J . Alder, Phys. Rev. A1 , 364 (1971).

4 . 1 . M. Martynyuk, Russ. J . of Phys. Cham.j l ( 5 ) , 7n5 ' 1977) .

5. A. V, Gros;,, and A. D. Kirshenbaum,J . Inorg. Nucl. Cham. 2j., 331 (1963).

6. M. van Thtel , "Compendium of Shock U.ivenata ," Lawrence Ltvermore Laboratory i"^portUCRL-50in8, Rev. I C 9 7 7 ) .

7. L. V. A l ' t s h u l e r , A. A, Rakanova,1. P. Cudoladov, E. A. [lynin, R. F. Trunin,and B. S. Chekin, Zhurnal PrikladnolMekhanlki 1 Tekhnlchaskol Flztkl _2, 3(198!) ISov. Phys. JAftTP 22 ( 2 ) , 195(H81)] ~

SESAME S32(10

Material : LertdfirlHlnacora: I. Barnes and J . RoodDate of Origin: April 1975 and August 1978Type of Tables Included: 301, 303, 304, 305,

306Limits: 0 293.1". K, p ) » 3.1576 « :0~2 MJ/kg

T . » 5158 K [Ref. 21^ 5300 K [experiment reported In Ref. 2]

3530 K |Ref. 31* 5223 K (trom calcula t ion of EOS)

Yo - 2.R4 lRef. 112.f>2 t 0.27 ( verage of values given In

l i t e r a t u r e ) [Ref. 1i2.38 * 0.35 ( i ra lo i la ted from shack wave

da ta) [Re f. II2.629 [Ref. 4)

" 1.945 (used In ca! - j t l o n of EOS)Bn = 43.82 GPa 1 Ref. 11

45.4 npa iRef. 5]* 45.63 (IPn (ufed In calculat ion of EOS)

3200-1

E c o h - 0.949 MJ/kg iR^f. 1)* 0.939 MJ/kg (used in calcula t ion

of EOS)

SD - 102 i 5 K Uef . I]* 105 K. (used in ca lcu la t ion of EOS)

Hugoniot F i t : U- = 2.0O6 + 1.538 Un km/s(P < 1.2 Mb) tltHf. 5]

Uq » 2.616 + 1.249 U km/s(P > 1.2 Mb) Itef. 5]

U<. - 1.981 + 1.603 Un -0.0378 Up

2 km/sPlRcf. ft]


At higher temperatures (probably above 1eV), th is EOS was produced bv scal ing a MAPLEtable for lead to an atomic weight of 207.19.Thomas-Fermi- Dlrac physics describes theelectronic contributions to pressure andenergy In the MAPLE t ab l e , and the nuclearcontributions ar t calculated with a modeldeveloped by R. D. Cowan.

Below 1 eV, the EOS was computed with thecode MAXWELL, which assumes that the pressuresand energies are the sum of a zero-degreecontribution and a nuclear thermalcontr ibut ion. The cold curve i s calculatedwith a modlfied-Mnrse model, and the thermalnuclear <SOS with a Oebye model. (See P*rt IIfor a detailed discussion of t h i s procedure ofEOS generation.)

The experimental zero-pressure densityand bulk modulus are reproduced by th i s EOS,and the f i t to experimental Hugoniot data IsRood. Alsn the c r i t i c a l point Is t-lose to theestimate made by Young and Aidt r . However,

this EOS was not generally designed Eor thehot, expanded» liquid metal region, and Is notto be trusted there.

No melting t ransi t ion Is Included in thisEOS.

The thermodynainie consistency is goodeverywhere•

The two-temperature tables Eor this EOSwere derived by che code THOTEMP and arenoisy.

A tension reglcn fnr spall was added tothis EOS.

1. K. A. fischneldn^r, J r . , Solid State Physics^6, 275 (196A).

2. D. A. Young, "A Soft-Sphere Model forLiquid Metals/1 Lawrence lAvermore NationalLaboratory report UCRL-52352 (1977).

3. M. M. Marcynynk, Russ. J. of Phys. Chem.Sj_ (5) , 70S (1977).

A. J. RamakrIshnan, R. flo^hler, C. H. HiRgins,>Tnd G. C. Kennedy, J . Ceophys. Res. fiji(B7), I S ^ (197B).

^. M. van Thiel, "Corapundlum uf Shock. UaveHa ta, " Lawrence Li vertnore NationalLaboratory report UCRL-'iOina, Rev. 1(1977).

C1( 1 9 B 1 1 1

32OO-"

MATKKIAI. :iXK>

f) \g tm'l

SESAME #3350

Material: CopperOr Initiators; J . Barnes and J. RoodDate of Origin; May 1974Type of Tables Included: 301, 303, 304, 305,

306Limits: 0 l p < 1.786 » 105 p/cm3

0 < T < 3.7 * 108 K

BASIC PHYSICAL DATAA - 63.54Z - 29

P() - 8.93 g / t . '

P(T - 2<3R. IS K, p n ) - 1.3225 CPaF.(T • 718,15 K, p^) - 7.4241 « \D~2 MJ/ltg

T - 1356 K [Ref. 111355.95 K |Ref. 21

T. = b544 K (Information provided by D. A.Young a t Lawrence I.lvdrmoreNational Lab-ratory)

* 75811 K (from c a l c u l a t i o n of EOS)

T • 2.DOB [Ref. 3]1.97 iRef. 1|2.00 t 0.08 (avcraRe of values In

l i t e r a t u r e ) IRef. 11" 2.00 (used in c a l c u l a t i o n of EOS)

3n - 133.5 n?a |Ref. 11137 CPa ( c a l c u l a t e u fruui measurement of

bulk sound veloci ty) IRef. 4 |* 133.9 nPa (used in ca lcula t ion of EOS)

E h - 5.32 XJ/kg IRef. 11* 5.38 W/kg (useu in calculat ion of EOS)

OJJ - Va t 2 K [FUtf. 1)* 343 (used In calculation of EOS)

lluftonlot Pi t : il_ - 4.007 + KA66 Un W sS (Ref. 4] P

U» - 3.889 + 1.520 Un -0.00071 U 2 km/6 ftef. 5j

U_ - 3.993 -*- U500 n km/sS P


An EOS for uopper from Lawrence Llv..inoreNational Laboratory was Joined onto an EOSyenerated by ttie code MAXV/ELL (which wasprobably run at temperatures lower thflr •.••V),Mj\XWEl.L uaea a modified-Morse model tocalculate the zero-kelvln contributions topressure and energy and a Dehye model for thethermal nur.lear pare. (See Part I I for adetai led description of th i s method of EOSgeneration.)

The experimental zero-pressure densityand bulk modulus are reproduced by th is EOS,and the comparison with experimental HugQntotdata is good. However, th i s EOS was notgenerally designed for the hot , expanded,liquid metal region and ts not to be trustedthere .

No melting t rans i t ion was Included inthis FOS.

i'he therraodynafic consistency is goodeverywhere.

The two-temperature tables for this EOSwere derived by the code TU0TEMP and arenoisy.

3330-2

1. K. A. Gschneidner, J r . , Solid Stat«_ PhysicsU., 2?1) (1964).

2. J . Akella and G. C. Kennedy,J . Geophys. Res. 76, C20), 4961 (1971).

1. .1. RamakrIshnan, R. BoeV i r , R. H. Hisgi"S,and G. C. Kennedy, J . Ceophys. Res. IH(B7), 3535 (\978).

4. S. p. Marsh, LASl Shock HuRoniot Data(University nf California Press, Berkeley,19R0).

5. L. V. Al'tahnier, A. A. Bakanova,1. P. Dudoladov, E. A. Dynin, R. F. Trunln,and B. S, Chekln, Zhurnal PtlkladnolMekhanlkt 1 Tekhnicheskot Fl j lk i 2,, 3(1981) Uov. Phys. JAOTP 22.(2), 195(1981)!.

6. A, C. Mitchell and W. .1. Nel l l s ,J . Appl. Phys. 12 ( 5 ) , 3363 (1981).

SESAME J3331

Mater ta l : Copper [Ref. llOr ig ina tor : K. TralnorDate of Origin: 19R0Type of Tables Included: 301Llmltaj IP"-1 i p < in-1 a/cnv*

300 « T < D.fl * 108 K

BASIC PHYSICAL DATA

A - 63.54Z - 29

Pu ' R.93 R/cm1

P(T - 298.15 K, po) • 2.1018 * K)"4 UPaF.(T - 298.15 K, pn) - 0.11825 MJ/kRT(P - 10 ' GPa, po) - 300 K

Tm - 1356 K iRef. 211355.95 K [Ref. 3]

* 1356 K (used in calculation of EOS)

T. =• C544 K (Information provided by D. A.Young at Lawrence LlvermoreNational Laboratory)

* 6544 K (result of calculation of EOS)

Y. - 2.008 [Ref. 4]1.97 [Ref. 212.00 > 0.08 (average nf values In

l i t e ra ture ) [Ref. 21* 1.97 (used In calculation of EOS)

Bo - 133.5 GPa |Ref. 21137 GPa (calculated from measurement of

bulk sound velocity )[Ref. 5]

c o h f' 2 i

5.'14 MJ/kg (used tn c a l c u l a t i o n of ROS>

9 n * 142 t 2K iRef. 2]

Hugnniot F i t : !!c = 4.00V + 1.^66 U km/sI t e f . 5} P

U - 3.889 + 1.520 U -0.00071 u 2 km/I iRef. M

Uc » 3.935 4 :"«)00 U km/siSef. 71 P

* Us = 4.007 + t .AH V km/s(used In eaU-ulat ion nf EOS)

The purpose (if R«a^rating t h i s F.(>5 was tacons t ruc t a global equat Ion of stiitt; uslr>R tl>ebes t nva tl.ibK- physical thanr ls;Sm

Six ilifferertt tVic-ortt ti-nl models wereused i i the gen«r.itlon:

1) rigt.r^'ts jt«t.-tron hand theory billed in thesel E-conslsCent nufttnr'ntoH plan>? wave (APW)methnci fr>r the zero-Kelvin isochern tncompression

2) St-ntl-rtPip LrU-ni ^t'Urielien-DebJe -nodeI forthe- i)'il r iphflStt rt-^lon nt tler.s it ie •' f i . norn-Tl densi ty C twu-fald veimpressed

( r.RAV )

)) Th fimn s-Ff rm t-K i rzhni t s tli«ory with nui le.trcorr-jft inns for the r e s t nf the^•nnpresston EOS (TFNUD

4) semi -tfUiplrii-ril sof t - sphere Kinde 1 forl iquid mct^ts a: low t e"\p«;ratures belnuliquid densi tv

S) rigorous quantum-stae t s t lca l - .dchanicaltheory based mi a many-body perturbationexpansion (ACTEX) for the hi}>h-temperatureion! z-HClon uqut L Lhrtum region

b) Sana model hawed nn the PJ.ant.-k-i ark inpartition function (OCCIPITAL) for themoderate-temperature innixnlinnequl 1 ihrium rej'.tnn.

Tlit- cnmpns itn pr^Hstire ;»m] t«nerj>ymirf^i r s We re i nns t rue ted by jninlnp, thesep.'iriiu- K'm sithsurffiffs ;i 1 onj; tVw Vioundnri es-,1 •-! w:i in F ( K . 2. At hi >;h I empc ra t u r - , t VicTTicuii-! s 'Tii- rt;er! sc.'t'"»r li! v i nt n din.- anotluT , -\tlow idtnpyrfiriire, however, the physics i s mori-t iim|»l rix , and thc-rtr we jv in soimi LMSL'Ss u b s t a n t i a l m J sm«i tfhf«i bt--tween ad j . u v u tthenru 'H . In t h i s c a s e , por t Inns of each F.ns••inh'iitrf fit-n i>n «• i thcT s Idc of H boundary had tohe r e p l i e d wi th num^ rK nl in te rpo Lat i on tnL-nsurt* -I smooth Find trnn t In „ m s in t n .

Th^ iopper F.ns has .H meltlnR t r a n s i t i o nbtirftff! on thi* Lindemann Law. Thy theo re t u-a I"it-11 in>: 1 Inc matches t;xpt-rimental measurementsof the melt In}1, t empe ra tu r e as n funct ion ofp re s su re up t«- fi Cpa. The two-phase r eg Inn In^xjMiisIf.n i s Mfixwtsll ^nns t r tu - t iun (nntvan der '.-.'.-lals Uinpf.).

".•tpcrinu.-nt.Hl dn ta , . .e reproduced '--e H .Kxperi i"-nt ••" which have he on compared tn t h i sRnS inc luoe Hui;nnint expe r imen t s , porn UP'iii/'nni'' _ c J:peri-nent s , i snhar f c data ,u rnp r r i s s ib i I i tv dara , and r^ l ea se t s e n t rope

The chermodynaniic consis tency i s goodeverywhere except on the boundaries betweenthe various physical models.

REFERENCES

1. A complete descript ion of t h i s EOS ia givenin K. Trainor, J . Appl. Phys. 54 . (5 ) ,2372 (1983).

2. K. A. Gschneidner, J r . , Solid S ta te Ph"9lcs1 6 , 275 (1964).

3 . J . Akella and G. C. Kennedy, J . Geophys.Res. 7J6 C20), 4969 (1971).

4 . J . RamakrIshnan, R. Boehler, ".. H. Higgins,and G. C. Kennedy, J . Geophys. Res. £3_(B7), 3535 (197B).

5. H. van Thie l , "Compendium of Shock WaveData," Laurence Llvemore Laboratory reportUCKL-50108, Rev. 1 (1977).

6. L. V. A l ' t shu le r , A. A. Bakanova, I . p.Dudoladov, E. A. Dynln, R. F. Trunin, p.rniB. S. Chekin, Zhurnal Pr ikladnoi Hekhanikli Tekhnicheskoi F iz ik i 2, 3 (1981) (Sov.Phys. JAOTP 2 M 2 ) , 195 (1981)1.

7. A. C. Mitchell and W. J . N e l l l s ,J . Appl. Phys. 5 M 5 ) , 3363 (1980).

K> I0 2

Denslly (Mg/m3)

Fig. 2. Temperature-density plot showing thesubregions covered by each of the theory codesused to calculate the EOS for copper. Theshaded areas are regions in which numericalinterpolation was required to smoothly jointwo EOS subsurfaces.

MATERIAL 3331

MATERIAL 3331

/O(g/bn3)

SESAME #3332

Material: CopperOriginator: K. TrainorDate of Origin: March 1983Type of Tables Included: 301, 303, 304, 305,

306Limits: 8.93 < p < 1000 g/cto3

0 < T < 1,16 x 106 K

BAStC PHYSICAL DATA

A - 63.54Z =• 29

Po - £ • « S'^n3

P(T = 298.15 K, p ) - 1.3603 GPaEIT - 298,15 K, | ) - 0,158^1 MJ/kgT(P - 1CT4 GPa, p°) - 9.2797 x 10"3 K

T • 1356 K (Ref. 1]1355.95 K U e t . 21

* 1356.55 K (used In calculat ion of EOS)

No value for Tc Is Included since th i s EOSonly covers compression.

y - 2.008 [Ref. 3]1.97 [Ref. 1]2.00 ± 0.08 (average of values in

l i t e r a tu re ) [Ref. 11* 0.90 ( resul t of calculat ion)

Bo - 133.5 JPa [Ref. 1]137 GPa (calculated from measurement of

bulk sound veloci ty) [Ref. 4]* 157 GPa ( resul t of calculat ion)

E c o n - 5.32 MJ/kg [Ref. 1)

3332-1

QD - 342 t 2 K |Ref. l j

Hugoniot Fit : UQ - 4.007 + 1.466 U km/a[Ref. 4] P

U - 3.889 + 1.520 U -0,00071 U * km/I [Ref. 5]3.933 + 1[ttef. 61

(No Hugoniot fit wns explicitly used in thecalculation of thia EOS.)


This equation of s ta te 'or copper wasgenerated clong with aquations of state foraluminum (#3713) and molybdenum (#2983) forthe purpose of evaluating high-pressure,impedance-raatchinc Hugoniot experiments

The zero-kelvin isotherm was calculatedby A. McMahan (Lawrence Livermore NationalLaboratory) with rigorous band theory based onthe self-consistent, augmented plane wave(APW) method.

The thermal electronic part of the EOSwas generated with D. Liberman'sself-consistent field model for condensedmatter (INFERNO). This model solves the Diracequation for an atom embedded in an electrongas. Unlike equations of state based onThojnas-Ferrui-Dirac theory, INFERNOtherraodynamic surfaces exhibit shell structureeffects.

The thermal nuclear contribution to theEOS was calculated with the Dugdale-MacOonaldform of GrUneisen-Debye theory. Gruneisen

3332-2

gamtua i t derived from Che cold curve accordingCo the following formula:

1 \ & in V 3"5 ~ ? ; 2P~~

1 " 3 S

where B i s bulk modulus, V la volume, and P ispressure. Note that gamma is a function ofdensity only, not temperature.

A melting transition is Included in thisEOS based on the Lindemann law. The equationof s ta te of the liquid Is given by a scalinglaw; that I s , the solid GrUneisen EOS at agiven temperature and density i s correctedwith terras which depend on the ra t io of thetempemture to the melting temperature at thatdensity.

At pressures above 100 GPa, the Hugoniotthat this EOS predicts is s l igh t ly atifFcompared with existing Hugoniot experiments.Below, i t matches the data well .

Note that only compression is covered bythis EOS since i t was intended for analysis ofHugoniot experiments.

The F.OS Is therraodynaraically consistenteverywhere.

3332-3

1* K. A. Gschneidner, J r . , Solid State Physics16 , 275 (1964).

2. J . Akella and G. C. Kennedy, J . Geophya.Rea. 76 (20), 4969 (1971).

3. J . Ramakrishnan, R. Boehler, G. H. Higgine,and G. C. Kennedy, J . Geophys. Res. 83(B7), 3535 (1978). ~

4. M. van Thiel, "Compendium of Shock WaveData," Lawrence Livennore Laboratory reportUCRL-50108, Rev. 1 (1977).

5. A. C. Mitchell and W. J . Nell la, J. Appl.Phys. 5_2 (5) , 3363 (1981).

3332-4

MATERIAL 3'J32

P(g/cm3)

MATERIAL 3332

I --.

P (g/cm3)

73UE-*-D'JU60E-M

j64ZE73UE»O4

2.901E*C64S12E*t»7 311E-051160E-06

SESAME 93541

Material: TungstenOriginator: B. BennettDate of Orlffln: September 1979Type of Tablaa Included: 301, 303, 304, 305,

306Limits: 0 < p < 1.9312 « 10* g/cra

0 < T < 1.16 « 10B K

BASIC PHVSICfJ. DATA

A » 183.B5Z - 74

Po - 19.237 g/i:mJ

P(T - 300 K, p ) - 4.3891 » 10"] GpaE(T - 300 K, p ) - 1.9451 « 10"4 HJ/l;gTCP - 10"6 GPa, p 0) - 298.5 K

T - 3653 K Uef . 11m 3690 K (Information provided by

0. R. Gathers i t LawrenceLivermore National Laboratory)

3695 K iRef. 21

Tp - 13400 ± 1400 K IRef. 3111950 K IRef. M18538 K [Ref. 51

* 17401 K ( r a l ru l a t ed )

1O ' 1.7B IRef. 1|1.68 (average of values found In

11terature)IRef. 11

* 1.47 (calculated)

'•541-1

n - im r.Pn l»uf. M119.k CPa iReF. 1|~l\k fiPa (calculated from shock wave dntfi)

|R«f. 71* "ill r.Ps (used in calculat ion of K(1R)

K _h - 4.54 MJ/kR lR«jf» 1)* A.fi7 >U/kR (us..-d in ca lcu la t lnn of F.OS)

Hugunint F i t : IJ_ =• A .04 + 1.21 U km/sfRef. H) P

|]fl » A.HIS + 1.2^2 U km/s[Ref. 91 P

* IL « 4.025 + 1.219 U km/s(ust-tl In cnlcull l t lon of F.nS)

TlRSCRtPTIOM OF PHYSICS

The tunp.sten ROS was calculated with thei.-odes CANDIDE (Thomas-Fermi-Oirac theory forthe e l ec t rons ) and EQS^TS. The aero - ke lv inIsotherm was obtained from Hugoniot dataas tuning the Dugdale^Macnonald form ForOrUnetsen p.amna. A Lennard-Jones t a l l wasused for dens i t i es less than p . The nuclearv ibra t ion contributions were also based on theHup,dale-MacDonaId form of GrUneisen-Debyetheory, but with a t ransi t ion to Ideal gashiRh temperatures.

No melting t ransi t ion per se Is Includedin th i s t a b l e , and i t has van der Waals loopsin expansion instead of a Maxwellconjtruction.

This tungsten EOS reproduces experimentalprincipal Hugoniot data. Also, vapor

3541-2

pressures computed from the t ab le should Rivereasonable agreement with experiment.

The two-temperature tables for thlBmater ia l were derived trom the code TWOTEMPand are noisy,

REFERENCES

1. K. A. Gschnetdner, J r . , Solid S t a t s PhysicsJ_6. 275 (1964).

2. S. A. Kats and V. fa. Chekhovskoi,High. Temp.-High Pressures U_, 629 (1979).

1. W. Fucke ,md U. Se Mel , HlRh Temp.-HighPressures U_, 419 (1980).

4. M. M. Martynyuk, RUSH. J . Phys. Chem. 5\.( 5 ) , 705 (1977).

5. D. A. Young and B. J . Alder, Pbys. Rev. A2 , 364 (1971) .

6. Li-chung Ming and H. H. Hanghnani,J . Appl. Phys. ^9 ( 1 ) , 208 (1978) .

7. M. van Th l e l , "Compendium of Shock WaveData," Laurence Livermore Laboratory reportuCRL-50108, Rev. 1 (1977).

B. S. P. Marsh, LASL Shock Hugonlot Data(Univers i ty of California Press , Berkeley,1980).

3541-3

(19HO1.

3541-4

MATERIAL 3541

Pi/m) a

SESAME «35nO

Ma terlal: Tungsten CarbideComposition: Tungsten Carbide (94 wt X)

Cobalt (6 wt !!)Originator: R. C. AlbersDate of Origin: November 1981Type of Tables Included: 301, 303, 304, 105,

306Mmit i ; 0 « n c 1.5048 x 104 g/cm3

I) < T < 3.48 x 10° K

BASIC PHYSICAL DATA

X = 94.1909Z - 3B.75335

Po - 14.97 g/cm3

P(T - 298.15 K, p ) - 2.9187 x 10~3 GPaE(T - 298.15 K, p ) - 3.1184 x 10"6 MJ/kgT(P = 10"6 GPa, p o ) = 297.4 K

Tm = 3143 K [Ref. 1]

Boilino. Temperature =• 6273 K [Ref. 1]

Y , - 1.5 [Ref. 2]

HQ = 362.4 GPa (frcra shock wave data ontungsten carbide)

* 360 GPa (a t P =• 0 , T • 298.15 K intable)


The cold curve was generated by f i t t i n gshock wave data [Ref. 3 ] . An average atomThomas^Fermi-nirac model was used for the

3560-1

thermal electronic excitations. A Chart-DGrUneisen Ion model was used for the Ion(nuclear) contributions to the EOS. There isa nonequlllbrium region in the vapor dame area(van der Waals loops) because no Maxwellconstruction was performed.

The theoretical Hugoniot reproducesexperimental shock wave data [Ref. 4].

REFERENCES

1. Handbook of Chemistry and Physica, R. C,Weast, Ed. (CRC Press.Cleveland, Ohio,1977).

2. GrUneisen constant of 1,50 is taken fromMeyers and Murr, "Shock Wave andHigh-Strain-Rate phenomena In Metals," inProceedings of the International Conferenceon Metallurgical Effects of High-StrainRate Deformation and Fabrication,Albuquerque, NM, 1980 M. A. Meyers and

L. E. Murr, Eds. (Plenum Press, New York,1981), P. 1077.

3. R. G. McQueen in High Velocity ImpactPhenomena, R. Kinslow, Ed. (AcademicPress, 1970), p. 371.

4. S. P. Marsh, LASL Shock Hugonlot Data(University of California Press, Berkeley,1980).

3560-2

09SE 1VIH3J.VH

3560-4

SESAME 03712

Mater ia l : Aluminumor ig ina to r : K. TrainorDate of Origin: 1982Type of Tables Included: 301Limits: 1Q"3 g/cm3

300 < T < 2.3 « 108 K

BASIC PHYSICAL DATA

A - 26.9815Z - 13

P o - 2.7 g/cm3

P(T - 3(10 K, po) « 1.8525 x 1Q"4 GPaE(T = 300 K, po) - 2.4950 * 10~5 MJ/kgTCP - in"'' r.Pa, po) - 300 K

T . 933.25 K IRef. 11* 933.2 K (used In L-alculatljn of F.OS)

T. - 5726 K (Ref. 2]"" 5220 K iRef. Jl

* 5726 K CcaluLated)

y - 2.136 [Ref. 4)2.19 [Ref. 51

* 2.136 (used In c a l c u l a t i o n nf EOS)Bo - 73.58 GPa (Ref. 5)

77 GPa (ca lcula ted from shock wave data)IRef. 61

E . • 11.9 MJ/kg IRef. 51* 11.9 MJ/kj, (used in calculation nf EOS)

B D - 423 t 5 K IRef. 5)

HugoiHot F i t : l)o - 5.386 + 1.339 U km/sS (Ref. 7] P

3712-1

* Us = 5.35 + 1.375 U + 0.0118 UQ2

+ 1.8 x UT* U 3 cktn/s (Ref. 8! P H

(ust*l in calculation of EOS)


The purpose of constructing this equationof s ta te was to create a wide-range tableincorporating the best possible physicaltheories that would march availableexperimental da ta . Seven different EOS modelswe re used:

1) rigorous electron band theory based on theself-eonaIstent , augmented plin^ wave(APW) method for the z^ro-kelvin isothermIn compression,

2) semi-empirical nrUneisen^-Deby« modeL forthe mult tphase tsolid-meIt-l iquid) regionat densi t ies from normal density totwo-fold compressed,

3) Thomas-Fermi-Ki rzhnits theory with nuclearcorrections for the rest of the^umpression EOS (TFNUC),

4) semi-empirical soft-sphere model for liquidmetals a t low temperatures below liquiddensity,

^) rigornu.s quantum-s tat 1st leal-mechanicaltheory based nn a many-body perturbationexpansion (ACTEX) for the high-temperaturt:ionlzatton equilihrium region,

6) Saha model based nn the Planck-Larkinpar t i t ion function (OCCIPITAL) for the

moderate-temperature ionizationequilibrium region, and

7) liquid metal perturbation theorygeneralized to account for electronicexcitation oE conduction and coreelectrons.

The composite pressure and energysurfaces were constructed by joining theseparate EOS subsurfaces along the boundariesshown in Fig. 3. In some cases, there w«?remismatches between adjacent theories, andnumerical Interpolation was necessary tosmooth ly join two suhsur faces.

This aluminum F.OS has a theoreticalme It Ing transition baaed on the hindemann law,which matches experiments measuring meltingtemperature as a function of pressure (up to 6GPa). The two-phase region Ln expansion has aMaxwell construction (not van der Waalsloops).

Experimental data are reproduced well.F.xperiments which have been compared with thisEOS include principal and porous Hugoniottixptf riments , isobaric data , andcompressibility data. Also R, G. McQueen(Croup M-fi, Los Alamos Nat Ional Laboratory)Via? measured the point on the Hugoniot atwhich melt occurs Is between 110 and 120 GPa.This RHS predicts that melting occurs at 11(1GPa on the Hugonlnt.

The thermodynamlc consistency of this EOSIs good everywhere except in the interpolation

REFERENCES

1. R. Hultgren, P. D. Desai, D. T. Hawkins,H. Gle l se r , K. K. Kelley, and D. D. Magnum,Selected Values of the ThertnodynarolcProper t ies of the Elements (AmericanSociety for Metals, Metals Park, Ohio,1973).

2. D. A. Young, "A Soft-Sphere Model forLiquid Metals," Lawrence Livermore NationalLaboratory report UCRL-52352 (1977).

3. M. M. Martynyuk, RUBS, J . of Phys. Chem.5J_ ( 5 ) , 705 (1977).

4. J . Ramakrishnan, R. Roehler, G. H. Higgins,and G. C. Kennedy, J , Geophys. Res. 83(H7), 3535 (1978).

">. K, A. Gschnetdner, J r . , Solid Sta te Physics1 6 , 275 (1964).

6. M. van Thie l , "Compendium of Shock WaveData." Lawrence Livermore Laboratory reportUCRL-50108, Rev. 1 (1977).

7. A. C. Mitchell and W. J . N e l l l s ,J . Appl. Phys. 5 2 . ( 5 ) , 3363 (1981).

8. S. P. Harsh, LASL Shock Hujjonlot Data(University of California Press , Berkeley,198(1).

9. A complete descr ip t ion of t h i s EOS i s givenIn K. Tralnor, "A New Full-Range Equationof State for Aluminum," in H-OlvislonQuarterly Report (Apri l through June 1982),Lawrence Liverraore National Laboratoryreport UCID-18574-B2-2 (1982), p. 20.

3712-4

I02

I0- 2

ACTEX

Interpolation-

- S A H A .

Soft

THOMAS-FERMIplu«

nucltareorrtctiant

perturbationthwry

APW-v

Density (Mg/m3)I0 3

Fig. 3. Temperature-density plot showing theBubregions covered by each of the theory codesused to calculate the EOS for aluminum. Theshaded area is the region in which numericalintepolation was required to smoothly juin twoEOS subsurfaces.

3712-5

MATERIAL 3712

P (g/cm3)

MATERIAL 3712

SESAME M713

Materla]: AluminumOriginator: K. TrainerDate of Origin: March 1983Type of Tables Included: 301, 303, 304, 305,

306Limits: 2.7 < p < 100 g/cm3

0 < T < 1.16 » 106 K

BASIC PHYSICAL DATA

A - 26.9815Z - 13 3

P(T - 298.15 K, p ) » - 1.9 GPaE(T » 298,15 K, p ) = 0.3567 MJ/keT(P - 10"6 GPa, p o ) - 1145.8 K

T » 933.25 K [Ref. 1!* 933.5 K (used in calculat ion of EOS)

No value for T£ t s included since th i s EOSonly covers compression.

Y •> 2.136 [Ref. 2]° 2.19 (Re£. 3]

* 0.76 ( r e s u l t of EOS calculat ion)

Bo - 73.58 GPa [Ref. 3]77 GPa (ca lcu la ted from sh-ck wave data)

[Ref. 4]* 82.02 GPa ( r e s u l t of EOS ca lcu la t ion)

E c o h - 1 1 . 9 W/kg [Ref. 3]

9 n - 423 ± 5 K [Ref. 31

Hugoniot F i t : Uc - 5.386 4- 1.339 M km/aS iRef. 51 P

UQ « 5.35 + 1.34 » km/sS (Ref. 6) P

(Mo Hugontot f t t was explici t ly us*d in thecalculation of this COS.)


This equation of s ta te for aluminum wasgenerated along with equations of otate torcopper (11*3332) and molybdenum (#2983) for thepurpose of evaluating hlg^-pressure,impedance-matching Hugonlot experiments. Thegoal was to calculate a set of EOS tablesbased on a consistent set of physical models.

The zero-kelvin Isotherm was calculatedby A. HcMahan (Lawrence LIvermore NationalLaboratory) with rigorous band theory based onthe self-consistent, augmented plane wave(APW) method.

The thermal electronic part of the EOSwas generated with D« Llberman'sself-consistent field model for condensedmatter (INFERNO). This model solves the Oiracequation for an atom embedded in an electrongas. Unlike equations of s t a te based onThonBs-Fermi-Dlrac theory, INFERNOthermodytiamlc surfaces exhibit shel l structureeffects.

The thermal nuclear contribution to theEOS was calculated with the Dug dale-Ma cDona Idform uE GrUnelsen-Debye theory. GrUneisenRamma is derived from the cold curve accordingto the following formula:

Y(V> - - ' - i I

where B i s bulk modulus, V i s volume, and P IHpressure. Note that gamma Is a Function ofdensity only, not temperature.

At pressures below 200 GPa, the Hufioniotthat th is EOS predicts ts a l i t t l e softf-omparcd wlth Hugoniot experiments• Abovt*that pressure. It matches the data well.

Note that only compression is covered bythis EOS since i t was intended for analysis ofHugoiiiot experiments.

The EOS is thermodynamically consistenteve rywhere•

REFERENCES

1. R. Hu l tg ren , P. D. Desa i , 0 . T. Hawkins,H. G l e i s e r , K. K. K e l l e y , and D. D. Wagraan,Se lec t ed Values of t he ThermodynamicP r o p e r t i e s of the Elements (AmericanSoc ie ty for Meta l s , Meta ls P a r k , Ohio,1973) .

2 . J . Raraakrishnan, R. Boeh le r , G. H. Higgins ,and G. C. Kennedy, J . Geophys. Res . ^( B 7 ) , 3535 (1978) .

3 . K. A. Gsithneidner, J r . , So l id S t a t e Physics_1_6, 275 (1964) .

3715-3

4. M. van Thiel, "Compendium of Shock WaveData»" Lawrence Llverraore Laboratory reportUCRL-50i0a, Rev. 1 (1977).

5. K. C, Mitchell and W. J . Nell ia , J . Appl.Phys. 32 (5) , 3363 (1981).

6. S, P. Marsh, LASL Shgclr. Hu^onlot Data(University of California Press, Berkeley,1980).

jy^

f

3713-5

MATERIAL 2T71J

P (g/cm3)

SESAME 03730

Material: PlatinumOrlRlnatnr: J . Barnes and J . RoodDate of orlRln: October 1972Type of Tables Included: 301, 303, 304, 305,

306

Limits: 0 < p < 2.1419 » 10" g/cm0 <; T < 3.7 x 108 K

BASIC PHYSICAL llATA

A = 195.09Z - 78

pn - 21.419 s/em3

T(P - lO"6 GPa, po) - 2 - 4 8

T = 2042 K iRef. llm

T = 14650 K iRef. 21c * 13704 K Ccnlculated)

" " l\ll (a^asi of value. In literature,IRef. U

* 2.035 (calculiteil)

r « : Z o S i » i c J Tdata) [Ref. 3]

* 282.2 GPa (used in calculation of EOS)

2.891• ' c o h . V.Mb W/kB (used in calculat ion

of EOS)

3710-1

9Q - 234 K {Ref. lj* 240 K (used In calculation of EOS)

3.68 + 1.46 U km/a [Ref- 4]3.GQ5 + 1 . 5 6 0 - 2 .63 x

™3 u 2 km/ ?

Hugoniot ? i t : Uc a

10™3 up2 km/s ?Ref, 5]


Above 1 eV, a MAPLE table far platinumwas scaled to match the reference density andatomic weight used. Below 1 eV, the codeMAXWELL computed the EOS using amodified-Morse model for the zero-kelvincontributions to pressure and energy and aDebye model for the nuclear thermalcontributions. (See Part II for a detaiLeddescription of this method of EOS generation.)

The experimental zero-pressure (tensityand bulk modulus are reproduced by this EOS»and the comparison with experimental Hugoniotdata i s good. However, this EOS was notgenerally intended for Che hot, expandedliquid ra<*tal region and is not to be trustedthere .

No melting transition is included in thistable .

Thermodynamic consistency i s goodeverywherem

The two-temperature tables for this EOSwere derived by the code TWOTEMP and arenoisy.

3730-2

1. K. A. Gschneidner, J r . , Solid State Physics^6, 275 (1964).

2. D. A. Young and B. J . Alder, Phys. Rev. A 3(1), 364 (1971).

3. M. van Thtel, "Compendium of Shock WaveData," Lawrence Llvermore Laboratory reportUCRL-50108, Rev. 1 (1977).

4. S. P. Marsh, LASL Shock HuRonlot Data(University of California Press, Berkeley,1980).

5. L. V. Al ' tshuler , A. A. Bakanova,I . P. Dudcladov, E. A. Dynin, R. F. Trunin,and B. S. Chekln, Zhurnal PrlkladnolMekhaniki 1 Teknicheskol Flzlkl :2, 3 (1981)[Sov. Phys. JAMTP 22 (2) , 195 (1981)1.

3730-3

MATERIAL 3730

\ ^ ^ ^

/ ii

i

0 1 Z

P (g/tm3)

O.00OE+002601E-025.6O2E*CBllflOE+032.3^1E+035B02E+O38.123E+031160E+0423aiEO423aiEO45S02E-KMU6Of*O5a3aiE-KS5B0SE+051160E-062321E+063.481E+065B02E-OT1.160E-tW3SEO>

MATERIAL 3730

SESAME J4100

Material : BraasComposition: Cu 61.5 wtl or 63.237 a t*

Zn 36.0 vt* or 35.975 at*Ph 2.5 u t* or 0.788 a t*

Originators : J . Barnes and A. LtndstroroDate ot OrlRin: Hay 1976Type of Tables Included: 301, 303, 304, 305,

306L i m i t s 6.6016 * 1CT2 < Q < 1.69 * 105 g/cm3

0 < T < 3.7 « 10B K

BASIC PHYSICAL DATA.

S » 65.3342 - 29.777

Po - 8.45 g/cm3

P(T - 298.15 K, p ) - 1.4327 GPaE(T - 298,15 K, po) =. 7.3038 x 10"2 MJ/kgT(P = 10"6 GPa, pQ) - 2.1 « 10"4 K

Tm - 1205 K [Ref. 1]

Tc - * 4642 K (calculated)

Bo - 138.9 GPa [Ref. 11* 100 GPa (used in calcula t ion)

Ecoh " * 4 ' 0 4 HJ/kB (used In ca l cu la t ion )

9 B - * 335 K (used in ca lcula t ion)

Hugontot F i t : U, . 3.74 + 1.43 U_ km/aS [Ref. 2] P

4100-1


Above 1 eV, the braBB EOS was calculatedby mixing copper (SESAME #3330), zinc (ascaled SESAME 03330), and lead equations ofstate according to the number fractions givenunder composition. Below 1 eV, the codeMAXWELL computed the EOS using amodified-Morse model for the zero-kelvincontributions to pressure and energy and aDebye model for Che nuclear thermalcontributions. (See Part H for a detaileddescription of this method of EOS generation.)

This EOS matches the experimentalHugoniot data well, but a low value of thebulk modulus was necessary to force a goodmatch between theory and experiment.

This EOS was not generally intended forthe hot, expanded liquid metal region and lanot to be trusted there.

No melting transit ion was Included Inthis EOS.

Thermodynamic consistency i s goodeverywhere.

Two temperature tables for this EOS werederived from the code TWOTEMP and are noisy.

REFE.-JNCES

]. Handbook of Chemistry and Physics.R. C. Weast, Ed. (CPC Press, Cleveland,Ohio, 1976).

1980).

MATERIAL 4100

MATERIAL 4100

41160E*0a2331E+063713E-HM

SF.SAME »4270

Mater ia l : Stainless SteelComposition: Fe 70 wtX

Cr 19 ut%Nl 11 wtS

flrIftlnator: A. LlndstromJ a t e of OrlRln: 1976Type of Tables Included: 301, 303, 304, 305,

306Limit*: fc.lf.aR « 1CT2 < n < 1.5792 » Id5 fi/cm5

0 < T < 3.7 * 10" K

BASIC PHYSICAL DATA

X - 55.3652 - 25.B02

P u » 7.R96 R/em3

P(T •> 298.15 r., po) = 1.1500 CPaF.(T - 29R.15 K, po) =• 7.1136 » H)~J MJ/kRT(P >• lO~ft pp a , po) = 2.62 * 10"4 K.

Tc - * 8713 K (calculated)

Bp « * 164.B Cl'a (used In ca lcula t ion of EOS)

F . = * 7.3 MJ/kR (used In calcula t ion of' F.OS)

HuRonlnt F i t : U., » 4.5H + 1.49 U km/sS Uef . 1) P

DESCRIPTION RF PHYSICS

Above 1 eV, three MAPU. tables Were mixedtn ^reati the F.oS fur s t a i n l e s s s t e e l : an irontab le , a lead table tha t was scaled to

4270-1

s i n u a t e nickel, and an iron table that wasseal d to simulate chromium.

Below 1 eV, the code MAXWELL computed theKHS u^ing a madtfied-Morse model for the*ero~kclvin contributions to pressure! andenergy and a flehye model for the nuclearthermal contributions. (See Part 11 for adetailed discussion of this method of EOSgeneration.)

This RDS matches experimental Huftoniotda t.i for 3*i't stainless stee 1 very wel L.However in thu hot, expanded 1iquid metalregion, It Is not to be trusted.

No melting transition was included Inthis FOS.

Thermndynamii" consistency is gondeverywhere.

Two-temperature tables for this EOS werederived from the code TWOTEMP and are noisy.

REFERENCE

1. S. P. Marsh, LASL Shock Hu^oniot Data(University nf Cal i fornia Press , Berkeley,19R0).

MATERIAL 4270

TEMPIM

SESAME 05000

M a t e r i a l : Ni t rogenCompos I t t o n : N~Of i f i lna to ra : C Kerley and J . AbdalIanData of O r i g i n : April 1981Type of Tables Included: 'JO IL i m i t s : l i r " < p l "in" B / CH 1

0 •; T < lfll! K

HAS1C PHYSICAL DATA

A » 14.00677. = 7

Po - 0.85719 g/cm3

P(T - 298. ' .5 K, pQ) = 0.34730 GPaE(T = 298,15 K, po1 = 0.24689 MJ/kcT(P - 10" 6 GPa, pQ) - 63.149 K

Tm = 63 K IRef, 11

Tt. > 126 K iRef. 2|' * 132 K ( c a l c u l a t e d )

Binding Energy: 0.2472 MJ/ki; [Ref. 3]* 0.246 MJ/kR Ccalr-uldte

Hugnnlnt F i t : llj. » 1 .49 + 1.49 Up km/s( f o r 2 .3 <• Us < 7 .4 km/s)

Uq - -1 .0 + 2.0 Uo km/s( fn r 7.4 < \t < a . 4 km/s)IRef. 41

11, = 4.06 + 0.92 U km/sv km/s)


The nitrogen EOS w a s generated inresponse to a need for thennadynamleproperties to be used tn numerical modeling ofdetonatIons.

The fluid part of the nitrogen equationof state was calculated with the CRIR model, athermodynami c perturbation theory in which theInterraa lecular forces are determined from thecold curve of the sol id. The cold curve Isdescribed by a s«mi -empirical f uiwt lona 1 formtn which certain parameters may be adjusted tofi t experimental data for the liquid. Thecold curv« formulation includes effects ofcoupli ng among v Ibrational^ rotat ional , andtranslational motions.

A crude model for the solid uses the samecold curve as that used in the CRIS model.However, i t does not account for phasetransitions associated with rotationalordering in the crystal l ine s ta te . Themelt ing t ransi t ion was Included in this EOS bycalculating separate surfaces using the solidand liquid models and then Finding the pointat which the solid and liquid pressures andGihbs free energies matched along eachisotherm. Agreement of the melting curve withexperimental data is fair ly good.

This EOS does not include effects ofmolecular dissociation or electronicexcitation, so i t -should not be completelybelieved at temperatures above where theseeffects s tar t to become important (> 1 eV).Higher temperature Isotherms were includedmainly to prevent extrapolation problems. Thetheoretical EOS was compared with many

different kinds of experiments: vaporizationand c r i t i c a l point da ta , P-V-T da ta , andHugoniot experiments. In genera l , agreementwas very good. However, for part ic leve loc i t i e s greater than 6.0 km/s, thetheore t ica l Hugoniot was s t i f f e r thanexperiments. Thts discrepancy i s probably dueto the increasing importance of dissociationat higher pressures .

REFERENCES

1. Sargent-Welch Periodic Table of theElements (1968).

2. E. W. Washburn, In te rna t iona l Cr i t i ca lTables (KcCraw-Hill, New York, 1926).

3 . T. A. Scott, Phys. l ^ t t . C 22,, 90 (1976).

4. M. van Thiel , "Compendium of Shock WaveData," Lawrence Livermore Laboratory reportUCRL-5010B, Rev. 1 (1977).

5. A complete descr ipt ion of the nitrogen EOSIs contained In G. I . Kerley andJ. Abdallah, J r . , J . Chem. Phys. 73(10) , 5337 (1980).

MATERIAL 5000

P (fi/cm3)

MATERIAL 5 0 0 0

SESAME 05001

Material : NitrogenComposition: NOriginator: National Bureau of StandardsDate of Origin: March 1982Type of Tables Included: 301Limits: 6.7125 « lO"3 < p < 0.94015 g/cm3

63.15 < T < 1.9 x 103 K

BASIC PHYSICAL DATA

S = 14.0077 = 7

Po = O.af.778 g/cm3

P(T = 298.15 K, p 1 . 0.38599 GPaE(T - 298.15 K, p 0 ; . 9.9268 x 10"2 MI/kgT(P - 10"4 GPa, pQ) » 63.18 K

Tm » 63 K iRef. 11

T - 126 K [Ref. 2]* 126.26 K (Input)

P - 3.39 * 10"3 GPa IRef. 2]* 3.410034 x 10~3 GPa (calculated)

P. - 0.31096 g/cm3 IRef. 21* 0.314 g/cm3 (input)

Triple Point Temperature: 63.148 K (Ref. 3]* 63.15 K (input)

Triple Point Pressure: * 1.246399 « 10"5 GPa(calculated)

Triple Point Denslt>-Vapor: * 6.71247 " 10~3

g/cm3 (calculat(d)Triple Point Density-Liquid: * 8.67776 * 10"1

g/cm3 (calculated)

5001-1


This nltroR^n equation of s t a t e wascalcula ted from a scr ies of computer routinesdevcloped by the National Bureau of Standardswh Ich deHc ribe thermodynamic and transportproper t ies of selected cryogens [Ref. A]. Thecomputer codes desc ribe pr .ipert ies for gaseousand liquid s ta tes s t a r t i ng at the t r i p l epo[nt . All of the propertles are caIculatcdfrom empirical equations which are derivedfrom exist ing experimental data by a weiRhtudI.-ant squares f i t of ma the ma t '.ca 1 mode Is Inthose data . The uncertainty In the calculatedpressure Is "iX or less fnr the Liquid attemperatures below t lie ..r (11 cal temperatureand fl. ~\% everywhere e l s e .

Beware that , although th is FOS i s very-a te , tlie temperature and densi ty limits-es t r ic ted .

REFKRENCRS

1. Sargent-Welch Periodic Table of the

Elements

2. F.. u. Washhurn, International Cr i t i ca lTables (McHraw-HiM, New York, 1926).

'). T. A. Scott, Pliys. Lett . C 2J7, On (1976).

4. P. P. McCarty, "Interact ive FORTRAN' IVPrograms fnr the Thermodynamir andTransport Properties of Se leered fryoguns{Fluids Pack)," National Rureau ufSt.ipidards Technical Note 1 r>2 'i (October

MATERIAL 5001

PVm) a

SESAME #5010

Mater ia l : Oxygen iRef. 11Composition; O£Originator : G. Kerley and J . AbdallahDate of Origin: April 1981Type of Tables Included: 30;Limits: 10"° < p < ID4 g/cmJ

0 < T < 108 K

BASIC PHYSICAL DATA

S = 16.0Z = 8

P(T = 298.15 K, p ) = 0.54339 GPnE(T - 298,15 K, p ) - 0.2390 MJ/knT(P = in"6 oPa, p°) - 54.39 K

Tm = 54.35 K |R=f. 2]

T = 154 K (Ref. 3)* lf.2.2 K (calculated)

Binding Energy: 0.2709 MJ/kg [Ref. 4]* (1.266 MJ/kg (used In

ca lcu la t ion of EOS)

Hugonlot F i t : U_ - 1.171 + 1.788 U - 0.6709U 2 km/s (Ref. §1

(for l iquid oxygen at 7fi.9 K)


The oxygen EOS was generated in responseto a need for thermodynamic proper t ies to beused In numerical modeling of detonat ions .

5010-1

The fluid part of the oxygen equation ofstate was calculated with the CRIS model, athern:odynamic perturbation theory in which theintermolecular forces are determined from thecold curve of the sol id . The cold curve i sbaaed on a s*.-roi-eropirical functional form inwhich certain parameters may be adjusted inorder Co fit experimental data for the 11 quid,The cold curve formulation includes effects ofcoupling among vibrat lonal , rotational, andt ranslational mot ions.

A crude model for the solid uses the samecold curve as that for the CMS model.However, i t does not account for phasetransit Ions associated wl th rotationalorclerinp, In the crystall ine s ta te . Themelting curve for oxygen wan determined byfinding where the pressures and Gibbs freeenergies of the solid and liquid phases matchat each temperature. Agreement of thismelting curve with experimental data is fa i r lygood.

This EOS does not include effects ofmolecular dissociation or electronicexcitat ion, so i t should not he entirelybelieved at temperatures above the point atwhich these effects s ta r t to become important(> I eV). Higher temperature isotherms wereIncluded tu prevent extrapolation problems •

The theoret ical EOf. was compared withmany different kinds of experimentalmeasurements; vapor-liquid coexistence curve,c r i t ica l point, s t a t i c compression data,internal energies, and Hugoniots.

5010-2

The t^neral agreement with the data wasvery good. However, at particle velocitiesgreater than 4,0 kra/a, the theoreticalHugonlot Is stiffer than che experiments. Thsdiscrepancy Is probably due to the increasingImportance < f dissociation at higherpressures. Also, the experimentally measuredIsotherm at 51 K (solid phase) disagrees withcalculations.

REFERENCES

1. A complete d e s c r i p t i o n of the oxygen F.OS I sconta ined in G. I . KerUy and J. Ahrfallah,J r . , .1 . Chem. Phys. 1 2 ( 1 0 ) , 5 3 3 7

C19B0).

2. Sargent-Welch Per iod ic Table of t heElements (1968) .

3 . E. U. Washburn» I n t e r n a t i o n a l C r i t i c a lTables (McGraw-Hill, New York, 1926) .

4 . G. E. J e l l n e k , L. -I. Slutsky andA. M. Karo, J . Phys. Chem. S o l i d s 3 3 ,1279 ( 1 9 7 2 ) .

5 . M. van T h i e l , "Compendium of Shock WaveD a t a , " Lawrence Ltvermore Labora to ry repor tUCRL-50108, Rev. 1 O 9 7 7 ) .

5010-3

MATERIAL 5010

\

•i

" V T 4* 3 * • 0 1/-J (K cmJ)

0OUOE-D05138E-011620E-02j 033E-027 338E-02177BE- 035623E-032154E-041000E-05J541E-052IWE-06IDOOE-07

MATERIAL 5010

Pig.'

SESAME

M a t e r i a l : OxyB*"proposi t ion: O«irlfilnator: National Bureau of Standardslate of Orlj-ln: March 1982" - • -F Tables Included: 301

1.0481 x 10"7 

T . 5 4 . 3 5 K iRef . Um

T , 154 K IRef- 2 l ,= . 154 .481 K ( . l " P u t

p a 0.4299 R/cm" inc . . - ." * 0.436144 g/cn' (input)

Triple Point Temperature: 54.38 K iReE. 31* 54.359 K (input)

Triple Point Pressure: * 1.490085 » 10~7 GPa(calculated)

Triple Point nensity-Vapor: * V.04812 * 10"5

g/cnr (calculated)

Triple Point Density-Liquid: * '..30619 g/cnv5(calculated)

5011-1

DESCRIPTION OP PHYSICS

This oxygen equation of s t a t e wascalculated from a se r i e s of computer routinesdeveloped by the National Bureau of Standardswhich describe thermodynamie and transportproperties of selected cryogens [Ref - 4 ] . Thecomputer programs describe the propert itrs ofthy gaseous and liquid s t a t e s s t a r t ing at thet r ip le point. AIL nf th«s propert i«s arccalculated from empirical equations which atedertvea from experimental data by a ucIghtedleast squares fit of mathematical models COthose data. The uncertainty in the calculatedpressures Is 5% for the liquid at temperaturesbelow the c r i t i c a l temperature, O.25X for thegas at r < T, , .ind 0.15% for the Fluid at T >T... *"

Beware tha t , although the KOS is veryaccurate, the temperature and density limitsare res t r ic ted .

REFERENCES

1, Sargent-Welch Periodic Table of the

2. E. W. Washburn, In terna t ional Cr i t i ca lTables (McGraw-Hill, New York, 1926).

3. R. L. Mills and E. R. Hr iUy , Phys. Rev.99, 480 (1955).

4. R. D. McCarty, " I n t e r a c t i v e FORTRAN IVComputer Programs For the Theraodynamie andTransport Proper t ies of Selected Cryogens(Fluids Pack) ," National Bureau ofStandards Technical Note 1025 (October11B0).

MATERIAL 501]

P (s, cm3)

MATERIAL 5011 _ ^TEUP 00

3T95E*024000E*02

SESAME #5030

Dry Air iPef. \\

20.95 atXAr 0.96 at*

Or j ^ i n a t o r : H. Grabnske JLawrence LI ve moreNational Laboratory)

Type of Tables Included; 301U m i t s : 10"7 1.0757 x Jo"*1 GPaE(T = 298.15 K, p ) =• 0.31313 MJ/kgTCP = KTA GPa, po) « 277.8 K


Thtf low-density region of the EOS for airwas calculated with a Lawr«snire Li verraoreNational Laboratory code cal led FM1N which isbased on a free energy Coulomb perturbat ionexpansion. Ful I molecular physics i s includedin the form of v ib r a t i ona l - ro t a t i ona l couplingcorrec t ions. The equation of s t a t e in th i sregi on agrees excel lently with the Na t lonalBureau of Standards theore t ica l molecular EOS.The hi^h-densl ty region is t rea ted with acomputer code which uses Thomas^Fermi physicsto desc rihe the e lectrons and includestemperature-dependent exchange and cor re la t ion>?F Pects . fhe nuc lear contr ibut ion is a MonteCarlo-based ion fluid which goes to a Pebyeso lid Ln the high-density ltmi t . Numerical

i n t e rpo l a t i on was used to smoothly Jo in thetwo d i f f e ren t physical models.

Thermo dynamic consistency Is gno«everywhere in t h i s F.OS.

Three HitRontot experiments have beanperformed on a i r by W. J . N e l H s , c t a l . a tLawrence Ltvcrmore National Laboratory. Thethcorct t ea l EOS i s in very poor agreement withthe highest p ressur - experiment (70 GPa) .

RFfF.RENCF.

I. A complete descr ip t ion of t h i s EOS i s givenin H. C Oraboske, "A New EOS for A i r , "Lawrence Ltvermore Laboratory inr ^rnaldocument UCID-16901 (1976).

MATERIAL 5030

1752E'(K17-IIEf 0334B1E*O35302E»03B123E-03il6C<>041741EO4

B123E-O4

34BlEfO55B02E-058I23E-05

1 116OE'O74B1E'D8

P Is/cm3)

MATERIAL 5030

I :

SESAME #5171

Material: Argon [Ref. 1]Composition: ArOriginator: N'atlonal Bureau of StandardsDate of Orlfiin; 1969Type of Tables Included: 301Limits: 4.0563 » 10"5 < p < 1.5587 s/cm3

S3.B K < T < 400 K

BASIC PHYSICAL DATA

A - 39.948Z - 18

p . - 1.4142 g/cmJ

P(T - 298.15 K, pu) - 0.26796 CPaE(T » 298.15 K, p'^) ' 0.17902 GPaT(P - 10""4 GPa, p , ) - 83.81 K

83.75 K [f^f. 2|

151 K |Ref. 31150.86 K (Input)5.0 » 10"1 GPa |Ref. 310.89805 « ^0"3 CPa (calculated)0.536 R/CIO' |Ref. 31

0.5357 R/rni1 (Input)

Triple Point Temperature: * 83.80 K (Input)Triple Point Pressure: * 6.890708 * 10"' GPa

(calculated)Triple Point Density-Vapor: * 4.0563 * 10"3

R/I-III3 (calculated)

T. Inle Pnint Density-Liquid: • 1.4142 g/cm3

(calculated)


This argon equation of s t a t e wascalculated from a se r i e s of computer routinesdcvc loped by the Nat tonal Bureau of Standardswhich describe thermodynaraic and transportproper t ies of selected cryugens iRef, \] , Thecomputer programs contain ana ly t ic equationswhich descrihe the F.OS for both the liquid andvapor phases. The analyt ic equations arcempirical ; th^y are f i t s to experimental data .In general , the equation of s t a t e representsthe different Bourcea of experimental data towithin the accuracy of the data except In theregion of tiie c r i t i c a l po in t . The types ofdata which were taken into considerat ion forthe analyt ic F.OS were P-V-T da t a , vaporpressure data, and coexistence density data .The uncertainty In the calcula ted pressures i s10/1 for the liquid a t temperatures below thec r i t i c a l temperature and 0.32 everywhere e l s e .

Beware tha t , although the EOS i s veryaccura te , the temperature and densi ty l imitsare restricted.

REFERENCES

1. A complete d e s c r i p t i o n of t he aro.on EOS i sgiven in A. L. Cosraan, R. D. McCarty, andJ . G. Hust , "Thermodyramlc P r o p e r t i e s r.fArgon from the T r i p l . P o i n t t o 300K a tPressures to 100C Atmospheres , " NationalStandard Reference ' a t a S e r i e s - Nat ionalRureau of Standards 27 (March, 1969).


•>. N. B. Vargaftlk, Tables on theThetmophyslcal Propertlea of Liquids andGaaea 2nd Ed. (John Wiley and Sons, Newfork, 1975).

5171-3

MATERIAL 5171

P (e,'on3l

MATERIAL 5171

aaeoE--oi9338E*0lI030E-OZ1125002lJ22IE-tO21317E+02M13E+02S09E02

-I 2754E+C2

J 3169E-02

35B5E*02

P (e/c-m3)

SESAME «5172

Mater ia l : Argori (Ref. 11Originator: J . WolfDrd (Lawrence Llv=rmore

National Laboratory)Date of OrlBln: October 1980Type of Tables Included: 301Limits: 10"^ < p < 10^ g/cm3

1.16 » 102 ( T < 1.16 « 108 K

BASIC PHYSICAL DATA

A - 19.948Z - 18

P o - 1.4 g/cm3

P(T - 298.15 K, p ) . 0.33043 GPaE(T = 296.15 K, p°) - 0.10131 HJ/kg(No zero pressure point In. table)

Tm - 83.75 K [Ref. 21

T. - 151 K iRef. 31P1". - 5 « 10"3 RPa [Ref. 31p^ = 0.536 g/cra3 (Ref. 31


This argon equation of s t a t e Is awide-ranging global EOS which covers Idealgas , tonic equilibrium, ideal plasma, neutralf lu id , multiphase, so l id , and meta l l ic solidcondi t ions . Fig. 4 shows the regions intenperature-densi ty space in which eachcondition occurs.

Below 1.0 eV in temperature and 0.1 g/cm3

In densi ty , argon Is a neutral f lu id , and theEOS can be described by a Lennard-Jones 6-12fluid model. At dens i t i es between 0.1 g/cra

5172-1

and 1,4 g/cm , and up to temperatures of 10eV, the argon EOS was calculated with ahigh-density fluid perturbation theory (calledr ) . This theory uaeo a pair potential withan exponential repulsive term and an inversesixth-power at t ract ive term which la added asa perturbation to the free energy of thehard-sphere reference s ta te .

In the ioniaatlon equilibrium region, twodifferent theories were used. Over most ofthe region, the EOS was calculated with arigorous quantum- statistical-mechanicaltheory based on a many-body perturbationexpansion (ACTEX). At very low densi t ies orvery high temperatures (where argon Is anIdeal gas) , n Sana model based on thePlanck-Larkin parti t ion function wasL-onBIdered sui table .

The zero-degree isotherm in compressionwas generated with electron hand theory basedon the self-consistent Linear-muffin-tin-orbital(LMTO) method.

For the rest of the compressionhalf-plane (p > p ) , the electronic part ufthe EOS was calculated with Thomas-Fermitheory modified with the Kirzhnits correctionwhich accounts for the quantum-mechanicalnature oi the electron through exchange andcorrelation terms added to the electrondis t r ibut ion function. The contributions du<;to nuclear motion were described bysemi-empirical Mie-GrUne Istjn theory at Lowtemperatures and one-component-plasma theoryat high temperatures.

Along boundaries where t heo r i e s did notmatch, bicubic sp l ine i n t e r p o l a t i o n was usedtu smoothly merge adjoining models. See theshaded regions In Fig . 4.

Favorable comparisons ex i s t with thyfollowing experimental da ta : c r i t i c a l pointd a t a , Soviet low-pressure P-V-T d a t a , s ta t ic -h igh -p re s su re da t a , Soviet shocV tube d a t a ,and Hufioniot d a t a .

The argon EOS has a Maxwell cons t ruc t i onInstead of van der Waals loops in thetvo-phase reg ion ,

REFERENCES

1. A complete desc r ip t ion of the argon EOS i sgiven in J . K. Wolford and K. S. Long,"Extended Argon Equation of S t a t e , "Lawrence Live more Laboratory i n t e r n a ldocument UCID-1B574-8O-4 (1980) .

2. Sargent-We'ch Periodic Table of theElements (1968) .

3. N. B. Vzrgaf t ik , Tables on theThertnophysical P roper t i e s of Liquids andGases 2nd Ed. (John Wiley and Sons, NewYork, 1975).

KT'

SAHA

,THCMAS-FERMI(Xut

nuclMrcoractkxtt

. SAHA

IO-1

Interpolation

Density (Mg/mJ)

f ' ig. i . Ti?mpt;rature;-density plot showing thesubreglons tOVtsrcd ky each af the theory codesused to calculate Che R0£ for argon. 7heshaded areas arc regions in which numericalinterpolation was required to smoothly jo intwo EOS subsurfaces.

5172-4

MATERIAL 5172

P (g/ctn3)

1.I60E+02Z22ECCZ221ECC3J6B7E+O27311E+021.450E+O3iBOlE+036B0ZE+O3iKjeciiKjecw

Z431E+O44642E+04B364E+041980E+053884E+O57617E+051586E+062963O065535E4'-»:1273E+D74 612E+07

(*t-m) a

5172-6

SESAME 05180

Material: Krypton iRef. 1]Originator: G. I . KerleyDate of OrlRlni December 1980Type of Tables Included: 301Limits: IQ~° U/kB

T(P - 10"6 GPa, p o ! - 116.8 K

Tm " 115.85 K iRef. 21

1 - 20Q "i l.Baf. 31c * 225 K (ca lcu la ted)

P » 5.49 » 10"3 G p a ( S e £ _ 3 ]

* 6.90 x 10 J G P a (calculated)pc = 0.911 g/cn^

* 0.795 g/cmJ (calculated)

y0 - * 2.J5 (used In calculation)

9D - * 64.5 K (used In calculation) (Ref. 4]

Hugoniot F i t : No Hugoniot experiments have beenperformed on krypton.

DESC->~"TIQN OF PHYSICS

The l iquid and vapor phases of kryptonwere computed with tha CRIS model, which i sbased upon per turbat ion theory. The fluid F.Ob

5180-1

requires an expression for the potentialenergy of a molecule in the force field of i t sneighbors; th is function uaa derived from thezero-kelvin isotherm of the Bolide The coldcurve was constructed by f i t t ing aGrttneiseir-Debye model to low-temper at urecompression data for solid krypton and thensmoothly joining that onto ThomaB-Fermi-Diracs t a t i s t i c a l atom thaory used at higherdensities* Thomas-Fenoi^Dirac theory was alsoused to calculate contributions from thermalelectronic excitation at f inite temperatures.

The solid EOS at finite temperatures labased on a Debye model which takes intoaccount contributions from z-3ro-"point andthermal l a t t i c e vibrations. Agreement betweentheory and experimental data for Helmholtzfree energy vs temperature is very good in thecase of krypton, which shows thnt the Debyemodel is satisfactory in this case.

The fluid EOS also compares very wellwith measured isothermal compression data,sound speeds, and vaporization data. TheHugoniot has not been experimentally exploredyet for krypton; however, a theoret icalprediction for i t has been included in thiswriteup.

Melting i s included Ln this EOS, and theexperimental melting curve agrees fa i r ly wellwith theoret ical predictions up to 240 K.

The krypton EOS has van der Waals loopsinstead of a Maxwell construction.

5180-2

REFERENCES

1. A complete descr ip t ion ai how the kryptonEOS was constructed Ls siven LnC. I . Kerley and P. M. Henry, "Theore t ica lEquations of State for tVte Rare " a s e s , " LosAlamos Sc i en t i f i c Laboratory import LA-8062(January 1980).

2. SareenL-1-Mch Periodic Table of theElements (196a) .

1. N. 8. VarRaftlk, ' 'abl^a -MI theTh^rmophvnUal Propert ies of Liquids ^ndGa£cs 2nd Ed. ( John Hllev and Soni , I n c . ,Sew York, 19751.

4. G. L. Pol lack , Rev. Hod. Phys. }b^, 748(19f4)

5180-3

MATERIAL 5180

SESAMR »M5nMa t er 1 a 1: HydroRenr i r l p t n a t n r : Na t iona l (Uireau of StandardsDate nf Or m i n i I 9KCIType of Tables Inc luded : M lLimi t s : 1.274S x in ' ( p ( o.innf-n (./on

11.S <; T < 4(11) K

BASIC PHYSICAL hATA

A = 1.00747

PIT = l i 'M.lS K, p ) • 0.229(11 fiPnKlT - 2•)K; 1 •> K, p ) - 2.BHT> M.1 IkeTIP » i n " ' i:i"a> „ " ) . n . m v.

K

^O"1 CPii ( . d l . u l . i' p./,-m (used inp . » * l.">uH

Trlpl- "nint Tttnn.T.itiire: * 11.8 K (used Ini-al .-i l latlnn)

Tr ip l e Point P r t i s o r , : * 7 . ( m i n i « 10"5 GPa( .al . - i i l . i ted)

T r l p K - P c i i n t

T r t M e P. iUt

i e n s i r v-V.- ipnr : * ft.1727

p / . m ' . • a l i ' u lv n s i t v - l . i n i i l d : * 1 .H217

1

li r s

MF PHYSICS

Tills hvilrni;en e q t n t i n n of s t a t e was• .ll ••Hi ,ited frnm .i s e r i e s nf .-omputer r o u t i n e sdeveloped liv t he Nat ional Hureau nf Standard iwhi.-h des- ' r ibe the thermodvnami r and t r a n s p o r tp r o p e r t i e s nf se lcr - ted 'TVOJ'enR 1 Re f . 1 ) . The• nr.puter p fne tans deserfhe p r o p e r t i e s fnr the.'.asenus and l i q u i d s t a t e s s t a r t i n g a t t he

t r i p l e point. The F.PS i s calculated from a-J 2—term dnplrical equation which was derivedErou. a weighted, least squares f i t ofexperimental data. The uncertainty In thepressure is ^ for the lic\ulc at temperatureshelaw the cr i t ica l temperature, 0.2SX for thegas at T < T c i and u.2X everywhere e l se .

Beware thnt, although this F.OS Is veryaccvirate, the temperature and density limitsarc restr icted.

RF.Ff.HF.NCF,

1. R. IK McCarty, " I n t e r a c t i v e FORTRAN IVComputer Programs for the Thermodvnanlc andTranspor t P r o p e r t U s nF S e l e c t e d Cryoftens( c l u i d s Psck) ," Nat iona l Hureau nfStandards Technical Note 1^25 (October

5250-2

MATERIAL 5250

SESAME #5251

Material : HyJrogenComposition; Natural Mix of Hydrogen IsotopesOriginators ; R. C. Albers and J . D. JohnsonDate of Orlfiln: September 197AType of Tables Included: 301, 303 304Limits: 0 < p < 1.7517 « 103 g/cm3

0 < T < 1.) < l(l' K

BASIC PHYSICAL DATA

A - 1.00797Z 1

Po - B.83R5 * 10"2 R/i-m3

PCT - 298.15 K, p ) . 0.31349 GPaE(T - 298.15 K, p ) . 3.4055 MJ/kcTCP - 10"" GPn, pQ) - 9.522 » 10-* K

BRSCRIF'TION OF PHYSICS

This EOS was created by I so top ica l lyscal ing tli« deuterium EOS (SESAME S52ft3) t -create a natural mix of hydrogen I -n topes .

5251-1

MATERIAL 5351

MATERIAL 5251

SESAME 0 5263

Material: Deuterium (Ref. 1}Cotappaition; 0»Originator: G, KerleyDate of Origin: January 1972Type of TabUs Included: 301, 303, 304. 305,

306Limits: 0 " 298,15 K, p ) => 0.31349 GPaE(T - 298.15 Kt o ) •» 1.7044 MJ/kgTCP - 1CT6 fipa, p^) - 8.2875 * 10"* K


This la a uide~ranglng aquation of s ta teFor dduteriura which t r e a t s the molecularso l id , metallic s o l i d , and fluid phases of thematerial . The various physical effects whichare taken Into account by t h i s EOS atedissociat ion, ion iza t ion ,vibracional-rotat ional e f fec t s , thermalelectronic exc i t a t ions , and phase t rans i t ions .The gas-liquid coexistence region Is notCreated because the c r i t i c a l temperature (33K) is well below the range of the table .

The cold curve was calculated with ananalytic expression which was derived byEitting compresslbili cy experiments at lowdensit ies and band theory calculations at highdensities.

Nuclear contrlbutlonp In the metall icsolid were calculated with Debye theory* TheLennard-Jones and Devonshire theory ce l l modelwas used to calculate the EOS of the solidmolecular deuterium.

The CRIS model was used to calculate thethermodynamlc properties of the f luid. Thismodel uses the zero-temperature isotherm ofthe solid and a hard-sphere equation of s t a t e .

Because of dissociation and lonizat lon,the fluid la a complicated mixture ofmolecules, atoms, protons, and electrons. Tosimplify the problem, separate equations ofstate were derLved for the pure molecular gaaand pure atomic gas. These resul ts werecombined by determining the fraction ofdissociation using an equilibrium calculation^

The contrtbutions of excited electronicstates and ionization to the EOS calculatedwith Saha theory at low densities andThomas-Ferrai-Dirac theory at high dens i t i e s .Normally, a smooth transit ion between the twotheories i s impossible, but in thiB case, theSaha model was modified to join di rect ly ontoThomas-Fermi-Dlrac theory.

Separate equations of state werecalculated for each of the three phases- Thecoexistence l ines between the phases weredetermined by finding the pressures andtemperatures at which two adjoining phaseshave equal Gibbs free energies.

Agreement between the calculated andexperimental single"shock Hugoniots andbetween calculated and experimental reflectedshock Hugonlots i s very good.

5263-2

5263-3

MATERIAL 5263

p (g/cm3)

MATERIAL 5263

SESAME 05271

Material! DeuCerlum-TritiuraCoropQsltlon: OT 50S

T, 50*Originators: ft! C. Albers and J. D. JohnaonDate of Orlfiin: September 1982Type of 'fables Included: 301, 303 304i.lmtts: 0 <. p < 4.3707 « 10^ n/cm3

0 (, T < 3.7 x 10B K

BASIC PHYSICAL DATA

2 - 1Pn » 0.22053

P(T - 2i..1.15 K, pn) • O.M34R GPa.3649 MJ/k..479 * 1O"-1

DESC".IPT'.ON OF F1W5ICS

E(T - 29B.15 K, p ) = 1.3649 !U/kgTCP - 10"6 GPa, p ) - 3.4

This EOS was generated by isotoplcal lyscal ing the deuterium EOS (SESAME #5263).

5271-1

MATERIAL 5271

SESAME 05280

Material: Rosa-Aller Solar MixtureComposition: H 93.3926 atX

He 6,47554 a t*7. = 8.2BS6 0.1111824 a t l

Or ig ina to r : N. H. MagedDate of Or ig in : April 1977Type of Tables Included; 301Limi t s : 10 < p < 1Q1* g/cm3

n'tL16 * t£r K 1.16 x 10' K

BASIC PHYSICAL DATA

A" - 1.22267 - 1.0744

Po - 0.


This equation of s ta te was generated by*:he code MOOP in ccr.juni.tion with *multi£requeney opacity calculation ior amixture of elements which i s known as thestandard astrophyslcal mixture for the sun.The EOS of each element was calculatedseparately then mixed according to the numberfraction above. The model used for the EOSwas an ideal gaq with plasma correct ions . Attemperatures greater than 100 eV, an averageion model was used; below 100 eV, the detailedconfiguration was calculated. Since MOOP isnor. used at low temperatures and highdens i t i es , that portion of the EOS was fil ledin with extrapolated values in order to obtaina rectangular grid of temperature and density.

5280-1

MATERIAL 5280

^^Swtri t l^ lSwStlLiHwStl — rvl > mliipJta

\\ \\ \ 1 \T1

15280-4

SESAME 1/5410

Material: NeonOrlplnator: J. Barnes and J. RoodDate of Origin: November 1975

3(14, 305,Type

Limit

A -Z -

P °

of

a:

20101.

Tt

00

ibles

< P< T

.183

44 B/cn

Included:

< 2.8R x 10< 3.7 x 10°

301, 3033065 g/cm3

K

BASIC PHYSICAL DATA

,3

P(T - 298.15 K, p ) - 0.39128 GPnF.(T » 298,15 K, p ) - 0.34022 RJ/teT(P - 10 ' 6 GPa, p 0 ) - 7.636 » 10"' K

Tm - 24.55 K (ReE. 1]

Tc = 44.4 K (Ref. 2]?^ - 2.65 x IO~3 G ? a (nef, 21o - 0.483 g/cm3 iRef. 2]The theorfitlcal c r i t i c a l point that is

actually in this EOS launknown.

9D = 67 K IRef. 3]


Tills equation of state Is undocumented.However, Ic was most likely generated with thestandard BarneM-Cowan-Rood procedure. Thati s , above 1 eV the E()S was taken from an oldMAPLE table In which the contributions due tothe electrons are based on Thomas-Ferml-DIracphysics and the nuclear thermal part of theF.OS Is based on a model developed by R. D.

Cowan. Below 1 eV, the EOS cons i s t s of a coldcurve calculated wlf-h the modi fried-Morse modeland nuclear thermal contr ibut ions from a Debyemodel. (See Part I I for a mare detaileddiscussion of the Rarnes-C.owarr-Roodprocedure*)

No Hugonlot experiments have beenperformed on neon.

The EOS i s thermodynatnically consis teateverywhere.

The two-temperature tab les were derivedhy the code TWOTEMP and are nolay.

REFERENCES


?. N. B. Vargaftlk, Tables on theThetmophysteal Proper t ies of LlquldB.andGases Znd Ed. (John Wiley and Sons, NewYork, 1975).

3. G. L. Pollack, "The Solid Statfc of RareGases," Rev. Mod. Phys. 2£» 7 4 8 (1964).

MATERIAL 5410 TOIP(K)

MATERIAL 5410

PCg/cm3)

SESAME 115411

Mater ia l : Neon (Ref. \\Orig ina to r : National Bureau of Standard aDate of Origin: 1965Type of Tables Included: 301LtmttB! 5.1028 « \CT* ( / r V

25 i T t 5»0 K

BASIC PHYSICAL nATA

A - zn.lfl'lz • in

Po - 1.2403 B/CIH3

P(T - 298.IS K, p ) - 0.71819 GPaKCT - 298,15 K, p ) - 0.26968 MJ/kgT(P • 10"* GPa, p0) - 25.017 K

Tm - 24.55 K IRef. 2)

Tr - * 44.40 K (input)P " - * 2.657086 » in"3 GPa (calculated)P^ - * 0 4 8 3 8/cm (input)* 0.483 (input)

Tr ip le Point Temperature; * 25 K (Input)Tr ip le Point Pressure: * 5.102339 * l t r ' CPa

(calculated)Triple Point Density-Vapor: * 5.103 « 10"3

g/cm3 (calculated)Triple Point Denslty-Uqutd: * 1.240 g/cm^

(calculated)

DF.SCRIPTION OF PHYSICS

This ne<"n equation of s t a t e wascalculated from a series of computer routinesdeveloped by the National Bureau of Standardswhich describe the therraodynamic and transportproperties of selected cryogens [Ref. 11. The

computer programs describe pionertlet for thegaseous and liquid s t a t e s s t a r t ing at thet r ip le point. The neon EOS ir. calculated froman 18-terni empirical equation which wasderived from a weighted, least squares f i t ofexperimental data . The uncertainty In thepressure is 10% for the liquid at temperaturesbelow the c r i t i ca l temperature and 0.5%everywhere e l s e .

Bewa re Chat, a It hough thls EOS Is verya, .iir.ite , the temperature and density limitsare res t r ic ted .

REfERENCES

1. R. n. MtCarty, " Interact Ive FORTRAN IVComputer Pi ograLis for the Theraodynrtmit; andTransport Propert ies of Selected Cryogens(Fluids Pack.)," National Bureau ofStandards Technical Note 1025 (USGovernment Printinp Office, Washington, DC,October 1980).

2. Sargent-Welch Periodic Table of theElements

MATERIAL 5411TCJIPIK)

P(g/cm3)

MATERK- 5411

SESAME 1)5500

M a t e r i a l : Methane [Ref. U

udled: 3

T r r T v - 5 s/cm

20 <• T < 10* K

pmsic/J.

I . 3.20B527. - Z.O 3

p o - 0.45302 g/cm J

P C T - 298.15 K, p 0 ) - ;E ( T - 298,15 K. P o ) - °-.",6 ,a

n9

KC T a

T ( P . 10" 6 GPa, P o ) " 7J-628 K

T . JO.688 K U t P - ° " " ' ^ J -™ • 90.688 K (theoretical value)

T - 190.53 K (Ret. 31c * 200 K (calculated;

P . 4 5957 * 1Q~3 GPa iRef. 31c * 5*58 x 10"3 GPa (calculated)

p , 0.1628 g/cm3 IRef. 3]c * 0.145 g/cm3 (calculated)

In1;iculatlon)

112 K lR=f. *1

55OH-1

DESCRIPTION QF PHYSICS

The methane EOS was constructed over awide range of temperatures and densi t ies ,primarily for the purpose of studyingliquified natural gas technology. Both solidand fluid phases are covered by this equationoF stare.

At low densi t ies , the cold curve of thesolid was derived frssi the Buckinghamexponential~6 Intermolecular potential. Athigh densit ies, Thoraaa-Ferrai-Dirac theory wasused to calculate the cold curve. The densitychosen to be the boundary between the twotheories was determined by requiring a goodmatch of theory to Hugoniot experiments.

The thermodynaraic properties of the solidphase of methane were assumed to be the sum ofseveral different contributions:

E(p,T> - EcCp) + EV(T) + ER(T) + EL(p,T)

PCp.T) - Pc(p) + PLCp,T)

Pc and Ec are the cold curve pressuresand energies. E and ER are vibrational androtational contributions to the EOS, which inthis case were calculated using therigid-rotator, harmonic oscil latorapproximation. P, and E^ are la t t icecontributions to the pressure and energy whichwere derived by using the Debye model.

The following equations were used tocalculate the thermodynamic properties ofliquid methane:

E(p,T> - EV(T) +ERCT)

P(p,T) * PTR(p,T)

P.™ and E-j-p ar« the t ranslat lonalcontributions which arise from thecanter-of-*masa motion of the molecules in theintermolecular force fluid. Phase werecalculated with the CRIS model which uses thesolid cold curve to describe the forces.

Separate aquation-of-state tables werecalculated for the solid and fluid phases;then a composite table with a meltingtransi t ion was constructed by determiningwhere the pressures and Gibbs free energies ofthe two phases match at each temperature. Inorder to match experimental melting transitiondata , the solid energies were decreased by0.016 RJ/kg relative to the fluid energies.

The zero of the energy of th is table wasset at the tr iple point for the liquid.

The theoretical methane EOS reproducesmany different kinds of experiments well,Including compressibility experiments,isothermal data, c r i t i c a l point data,measurements of saturation temperatures, heatsof vaporization, and sound ve loc i t i es . The

5500-3

theory a lso reproduces single-shock Hugonlocand ref lected Hugonlot measurements.

This EOS, however, does not Includedissocia t ion e f f e c t s , BO I t should beconsidered prel iminary for temperatures above3000 K.

There are Maxwell constructions in thetwo-phase region in expansion.

REFERENCES

1. A complete desc r ip t ion of the t h eo r e t i c a lEOS for methane 1B given in G. I . Kerley,J . Appl. Phys. H ( I O ) , 5369 (1980).

2. V. M. Cheng, W. B= Daniels, andR. K, Crawford, Phys. Rev. B U , 3972(1975).

3 . R. D- Goodwin, J . Res. N a d , Bur,Stand. Sec. A76_, 81 (1972).

A. S. M. Bre i t lung , A* D. Jones andR. H. Boyd» J . Chem. Phys, , H , 3959(1971).

5500-4

MATERIAL 5500

SESAME f/5501

Material; Methane [Ref. 1]Composition: CH,Originator: G. I . KerleyDate of Origin; January 1980Type of Tables Included: 301Limits: 10~ l u < p < 2.5 g/cm3

20 < T ( 10" K

BASIC PHYSICAL DATA

X - 3.208522 - 2 . 0

p 0 = 0.45302 g/cnr1

P(T - 298.15 K, p ) - 0.31719 GPaE(T - 298,15 K, p") - 0.45689 MJ/kgT(P = 10"b GPa, PQ) - 93.544 K'

DESCRIPTIOM OF PHYSICS

This equation of s ta te Is Iden t ica l toSESAME S5500 except that the vapor-liquidcoexistence region has nonequllibriumvan der Waals loops In order to define thesuperheated l iquid and supercooled vaporstates.

REFERENCE

1. A complete d e s c r i p t i o n of t he methane EOSI s g iven in G. I . Ker ley , J . App l . Phys..51. ( 1 0 ) , 5368 C1980).

IOQS iviaaivw

MATERIAL 5501

-aL - - - - -

SESAME 1)5502

Material : Methane (Ref. I]Composition: CHOriginator: National Bureau of StandardsDat6 of Origin: 1974Type of Tables Included; 301Limits: 2.5173 » 10"° T(P = ID"4 GPa, po) » 90.724 K

Tm » 90.688 K (at P - 0 bar) iRef. 2]

Tc - * 190.555 K (Input)Pc - * 4.598838 « 10"3 GPa (calculated)P c . - * 0.1641 s/cm3 ( Input)

Triple Point Temperature: * 90.68 K (Input)Triple Point Pressure: * 1.17435 « 10"5 GPa

(calculated)Triple Point Density-Vapor: * 2.5173 » 10"4

g/cm3 (calculated)Triple Point Density-Liquid: • O.451H s/cm'

(calculated)


This methane equation of s ta te wascalculated from a s e r i e s of computer routinesdeveloped by the National Bureau of Standardswhich describe the thermodynamic and transport

5502-1

3972

5502-2

MATERIAL 5502

MATERIAL 5502

II

»068E>0!101BE+Q2U29E+O21240E+02135IE+O2

82EO2U82E1573E+021.684E<-02

95EO21T95EI905EtD22016E+O22.126E+02

BEO2E34BE2569E+02a790E+023011E+O2

2EO23232E3453E+023ffHE+02

B95E0Z3B95E04116E+024337E+024558E+024779E*025OO0E*02

P (g/cm3)

SESAME #5520

Mater ial : Ammonia iRef. I]Composition: NH~Originator : National Bureau of StandardsDate of Origin: UnknownType of Tables Included: 301Limits: 1Q~3 0.28434 GPaE(T - 298,15 K, p_) - -0.79939 MJ/kgT(P - 10"A GPa, p0) = 19.55 K

Tc = * 405.4 K (cheoretical value)


This equation of s t a t e for ammonia wasderived by the National Bureau of Standards.I t t r e a t s gaseous and l iquid ammonia over arange of temperature that s t a r t s a t the t r i p l epoint and goes to twice the c r i t i c a l pointtemperaturea and i t extends to pressures of500 GPa. The general approach was toconstruct a free energy surface in which thefree energy for the ideal gas i s combined withthe free energy contribution for thetemperature-density surface determined by aleast-squares f i t to P-p-T experimental data.(The analytic equation used was a 44-tenu t

double power ser ies function of temperatureand dans i ty . ) All other thermodynamic

5520-1

properties were calculated from the Htlmholtzfrte energy surface hy differentiation.

The tables of thermodynamlc propertiesare thermodynamicslly consistent and agreewith existing experimental data to within theassigned error tolerance of the data. Eventhoug':. only P-p-T data were used in theleast-squarea fitting process, the derivedthermodynamic surface also agrees withhigh-quality experimental calorimetric dataand with data for the coexisting phases of thesaturated liquid and vapor.

The melting transition (pressure VBtemperature) was calculated with the Clapeyronequation. The liquid vapor saturationboundary was determined by finding the pointswhere the Gibbs free energies for the twophases are equal• The reference state for thethermadynarcic surface is defined to be theideal gas at zero kelvin.

All chemical reactions such asdissociation are ignored. Dissociation isonly important far the dilute gas attemperatures aboue 600 K.

Beware that, although this EOS is veryaccurate* the temperature-density limits arerestricted.

REFERENCE

1. A complete d e b c r i p t t o n of the ammonia EOSi s g iven in L. Haar and J . S. G a l l a g h e r ,"Thenuodynamic P r o p e r t i e s of Ammonia," J .Phys . Chem. -Ref* Data ]_ ( 3 ) , 635 ( 1 9 7 8 ) .

MATERIAL 5520

r -

MATERIAL 5520

SESAME 05760

Mater ia l : Helium [Ref. UOriginator : H. C. Grahoske (Lawrence

Llvermore National Laboratory)Date of Or ig in : August 1974Type of TabUs Included: 301Limits: 0 < p < A.6784 x 103 g/Cm

0 C T <. 1.16 x 108 R

BASIC PHYSICAL DATA

A =• 4.00260Z = 2

P(T = 298.15 K, pQ) =* 0.28858 GDaE(T =» 298,15 K, p o ) » 1.0064 MJ/kgT(P - 10"6 Gpa, p^) =• 8.995 x lO"5 K


This i s a high-quai l cy, wide-rangeequation of s t a t e for helium whichincorporates several different th oreticalmodels:

1) Perturbation theory - used in thelow-teraperature region which ischaracterised by short-range Interatomicforces in a neutral fluid system. Thefree energy Is computed by a perturbationrelative to a reference system of hardspheres. The perturbation model 1B basedon the Mansoori-Canfleld method.

2? ACTEX - used in the low-density,Intermediate-temperature region where thephysical effects to be considered arepartial lonlzation» partial degeneracy,

5760-1

and weak-to-moderate Coulomb interactions.ACTEX is a rigorousquantum-statistical-mechanical theorybased on a many-body perturbationexpansion of the grand canonical partitionfunction.

FMIN - used in the low-density,intermediate-temperature region in thoseareas jhere ACTEX does not converge. FM1Ni s based on a percurbation expansion indensity. It includes effects of electrondegeneracy and electron exchangeinteract Ions.

TFNUC - used in the high-density region.The electronic part of the EOS wasgenerated with Thomas-Fermi theory.Ef fects of electron exchange and quantumcorrection terras are also included (basedon a model by Kirzhnits). The ioniccontributions to the EOS are based onplasma theory, Monte Carlo-Coulomb fluidcalculations and solid GrUneisen theory atlow temperatures.

REFERENCE

R. J . O l n e s s , H. C. Graboske,K. W. Jchnson , M. Ross , and F . J . Rogers,"The Equat 'on of S t a t e of Helium i n theTemperature Range 0 .02585-10 eV," Lawrence-Livermore Labora tory r e p o r t UCIR-740(December 1973) .

5760-2

MATERIAL 5760

MATERIAL 5760

P (g/cm3)

SESAME 45761

Material: HeUum-4Composition: Hellum-4Originator: R. C. AlberBDate of Origin: March 1981Type of Tables Included: 301, 303, 304, 305,

3 I 3 0 6

0 < p < 103 g/cnr,0 < T < 1.16 « 10b K

BASIC PHYSICAL DATA

A - 4.00Z6Z - 2

Po - 0.4 g/cmJ

P(T - 298.15 K, p ) - 1.0713 GPaE(T - 298.15 K, pQ) - 1.6464 Kj/kg

Tc - 5.2 K iRef, 1]P - 2.26 » 10 ,GPa (Re£. 1]p c - 0.0675 g/cn3 [Ref. 11

Yo - 3.05758 (a t p™. - 0.14513 g/cm3 andTREF - 0 K)

6D - 10.15 K (a t P R E F - 0.14513 g/cm3 andTREF " ° K )

Hugonlot P i t : (No data)

DESCRIPTION OF PHISICS

The thermal electronic contributions tothis EOS were calculated with three differentmodels: Saha, Thomas-Fermi-Dirac, a\td INFERNO.INFERNO EOS's always exhibit metalHc-l ike

5761-1

behavior , even at the lowest d e n s i t i e s andtemperatures where helium I s a c t u a l l y anI n s u l a t o r . The e lec t ronic EOS was thereforemassaged over an extensive region to force i tto go smoothly from the meta l l i c INFERNO modelCo the Insula t ing Saha model.

A modified PANDA code generated the t o t a lequation of s t a t e . The CRIS model withquantum cor rec t ions was used for the thermalion component of the l iquid EOS. A cons is ten tset of Dehye temperatures and GrUnelsenparameters was generated from experimentaldata and reasonable ex t rapo la t ions of themodels. These were put in to t ab l e s whichPANDA could then in te rpo la te on to find theseq u a n t i t i e s when required. The cold curvewhich i s needed for the CRIS model waaconst ructed In several stages* An i n i t i a lcold curve was derived from experimentalHugoniot data and corrected for zero-poin tc o n t r i b u t i o n s . A Lennard-Jones t a i l was addedto the low—density end, and aThomas-Femi-Dirac cold curve was merged ontothe h igh-dens i ty end.

REFERENCES

1. J . Wilks, The Propert ies of Liquid andSolid He 1lum (Clarendon Press , Oxford,1967).

2 . P. R. Roach, J . B. Ketterson, and Chia-WeiWoo, Phys. Rev. A 2, 543 (1970) .

MATERIAL 5761

MATERIAL 5761

-5 - 4 - 3 - 2 - 1 0 I 2 3

SESAME »5762

Material : Helium (Ref. IIOriginator : National Bureau of StandardsDate of Origin: 1973Type of TableB Included: 301LlmltB: 1 • 1626 « 10~3 < p < 0.3 g/cm3

2.18 < T < 1.3 » 103 K

1ASIC PHYSICAL DATA

A - 4.00262 - 2

P(T - 298.15 K, p ) » 0.14451 GPaE(T - 298.15 K, p ) » 1.0002 MJ/kgT(P - 10~4 CPa, p0) » 2,6081 K

Tm - 8.45 K iRet. 21

T - * 5.2014 K (Input)Fc = * 2.27464 x 10J1 CFa (calculated)pc - * 0.06964 g/cm3 (input)

Lambda Temp: * 2.172 K (Input)Lambda Pressure: * 4.963285 x 10~5 GPa

(calculated)Lambda Density-Vapor: * 1,1625 x ] ) ' * g/cm

(calculated)Lambda Density-Liquid: • 0.1462 g/cm3

(calculated)

DESCRIPTION OF PHVSICS

This helium equation of s ta te wascalculated from a series of computer routinesdeveloped by the National Bureau of Standardswnich describe the therraodynamic and transportproperties of selected cryogens. The computer

5762-3

programs deacribe properties for the gaseousand liquid states s tar t ing at the t r iplepoint. The helium EOS uaa calculated frnm a32-term empirical equation which was derivedfrom a weighted, least-squares f i t toexperiment a I data. Tlie utu*-*rralnty In thepressure la 10% for the liquid at temperaturebelow the cr i t ical temperature and 0.2Xeverywhere telse.

Htiuare that, although th i s EOS is veryaccurate, the temperature and density limitsare restr icted.

REFERENCES

1. R. n. McCarty, " I n t e r a c t i v e FORTRAN IVComputer Programs for the Themodynamlc andTransport P r o p e r t i e s of Se l ec t ed Cryogens(F lu ids Pack) , " Na t iona l Bureau ofStandards Technical Note 1025 (USGovernment P r i n t i n g O f f i c e , Washington, DC,October 1980).

2 . Sargent-Welch P e r i o d i c Table of theElements (1968) .

MATERIAL 5762

MATERIAL 3762

SESAME #7111

Material : NevadaComposition: SiO*

H,0K,0

cSo

Alluvium. 71i, 12

432

.6

.1

.0

.5

.4

wt%wt%wt%wtZwtX

plut lesser amounts of olzheroxides

Originators: J, Barnes and J. RoodDate of Origin: September 1975Type of Tables Included: 301, 303, 304, 305,

306Limits; 1.8359 » 10"2 < o < 4.7 » 10* g/cm3

0 < T < 3.7 « 10B K

BASIC PHYSICAL OATA

X • 18.7611 » 9.3659

P o - 2.35 g/cm3

P(T » 298.15 It, p ) - 1.5646 GPaE(T = 298,15 K, p") - 0.33733 HJ/kgT(P - 10"6 GPa, p°) - 1.913 » 10"4 K

DESCRIPTION OP PHVSICS

This equation of s t a t e i s undocumented.However, i t was most l i ke ly generated vich theBarnes~Cowan~Rood procedure. That i s , above1 eV, the e lec t ronic part of the EOS wascalculated with Thomaa-Fermi-Dirac theoryusing an average atomic weight oi 18.761 andan average atomic number of 9.3659. Thenuclear thermal and cold curve contr ibutionsabove 1 eV are based on a model byR. D, Cowan. Below 1 **. "he EOS consists ofa cold curve calculated •a'<\'^ a modified~Horse

7111-1

model and nuclear thermal contributions from aDebye model. (Pee Part II for a more detaileddiscussion of this procedure of EOSgeneration.)

The EOS is thermodynaraically consistenteverywhere.

Hugdniot experiments have been performedby R. G. McQueen for Nevada tuff starting atin i t ia l densities of 1.8 g/cm3 .nd 1.54 g/cm3.(These densities are porous relative to thereference density of this r 5.) Agreement withthese experiments is fair.

The two-temperature "blee were derivedby using the cou, TWOTEMP ^nd are noisy.

a i l - 2

MATERIAL 7111

P (g/cm3)

MATERIAL 7111

SESAME J715O

Material: Water [Ref. llComposition; HjOOriginator: F. H. Ree (Laurence I.iveraore

National Laboratory)Hate of Origin: June 1977Type of Tableslncluded: 301Limits: 2 * 10"* g/cm! < p I 400 g/cm3

300 « T < 1.74 « 10° K

BASIC PHYSICAL "ATA

S = 6.00531 • 3.3333

p0 - 0.9982 g/cm3

P(T - 298.15 K, p ) - 3.092 10'E(T •» 298,15 K, p ) - 1.942 « 10"z HJ/kgT(P « 10"6 GPa, po) - 295.29 K

Tc - * 647.3 K (from theoretical EOScalculation)

Pc = * 21.408 MPa (calculated)pc - * 0.305 g/cm1 (calculated)

Hugoniot F i t : * U- - 1.4829 + 2.1057 u -0.1744 u 2 + 0.010085 B 3 km/s(used inPcalculatlon of EOS)


This Is a wide-range, high-quaLltyequation of s t a t e for water. Severaldifferent theoret ica l models were used togenerate i t :

1) TIGER - calculates the EOP of aheterogeneous mixture containing gaseouscomponents (H, Hj, 0, o 2 , OH, and H20) and

7150-1

liquid components (H.,0) using theBecker-Kiatlakowaky-Hilson equation,lonization ia assumed to he negl igible .The TIGER region extends in density from 2x tO"6 g/cm3 to 2.5 x 10~2 g/cro3, and intemperature from 0.1 eV to 1.0 eV.

OCCIPITAL - used in the high-temperature,low-density region in which HjO i scompletely dissociated into electrons,ions, and neutral atomic hydrogen andoxygen. The concentrations of each ofthese species is obtained with the Sanaequation, and the thermodynamlc propertiesare calculated assuming that eachcomponent of the mixture behaves like anIdeal gas.

TFCMIX - us«sB Thomas-Fermi theory tocalculate an electronic EOS. TheKirzhnits correction ia added to accountfar the wave nature of electrons and theelectron exchange contribution. Nuclearcontributions to the EOS are based enplasma theory, Monte Carlo- Coulomb fluidcalculations, and solid Grttneisen-Debyetheory at low temperatures. The TFCMIXregion covers high densities a ttemperatures greater than 40 eV.

MAvSTER - Below temperatures of 40 eV andat pressures below 15 GPa on the coldcurve, MASTER was use4 tophenoroenologieally correct the EOS foratomic shell structure and electroniccorrelations. This is to ensure that theexperimental Hugoniot data wil l bereproduced.

Experimental Region - covets temperaturesof 0.08 eV t o 0.1 eV and d e n s i t i e s l e s sthan 1.25 g/cnr*. Analytic f i t s to threed i f f e ren t experimental sources w*?re usedto generate the ROS In t h i s a rea :Schmidt 's steam tab le [Ref. 2 ] , Burnham'ss t a t i c compression data [Ret . 31 , andBrldgraan's data [reported in Refs. 4 and5 1 .

HugoniQC data are reproduced well by t b t sEOS.

REFERENCES

1. A complete desc r ip t ion of t h i s EOS i s give.iin F . H. Ree, "Equation of State of Water ,"Lawrence Llvermore Lahortory reportUCM.-5219O (December 1976).

Z. E. Schmidt, P rope r t i e s of Water and SteamSI-Uni t3 . (ClarendonPress, Oxford, 1969).

3. C. W, Burnham, J . R. Hoilovay, andM. F. Etavis, "Thermodynaraic P r o p e r t i e s ofHjO t o 1000 C and 1 kbar ," The GeologicalSociety of Anerl a Special Paper No. 132(1969).

4. M, H. Rice and J . M. Walsh, J . Chem.Phys. ^ 6 , 824 (1957).

5. G. A. Gurtman, J . H. Kirsch, andC. R. Has t ings , J . Appl. Phys. 42,, 851(1971) .

MATERIAL 7150

7

5

3

'

-1

-3

-5

-7

1

5 ? § 5 s ^ - ^ —

^ ^ ^ i^ 1

I !

!!i

-5 -4 -3 -2 -1 0P (g/cm3)

» O 25B02E+021.16OEfO3I-741E+032IKt03

e L 31.16OE-KM29O1E»O46.963E>04U60E+052901E05

1 1 82.801L*066963E*061.160E»07aS01ET076.9B3E*O71160E*0B

MATERIAL 7150

P (g/fcm3)

SESAME 07152

Mate r i a l ; Wat*r U e f . \]Composition: H?OOrig ina tor : National Bureau of StandardsData of Origin: May 19B1Type of Tables Included: 301Ltmlta: 1Q"*B < p < 1.4 g/<:m3

250 <! T < 4000 K

BASIC PHYSICAL DATA

3 =• 6.(10111t o 3.33333

t»(T =• 2^8.15 K, p o ) « 6.1643 * 10"3 GPaF(T = 298.15 K, p ) = 0,I0A23 MJ/kgT(P =• 10~6 GPa, p o ) - 28U8 K


This EOS for wacer was ca lcula ted fromana ly t i c equations which were derived by theNational Bureau of Standards from f i t t i n gexperimental d a t a . The data selected for theder iva t ion of the thermadynaraic surface wereprimari ly P-p-T da t a , but they a l sc used datafor che enthalpy of the sa tu ra ted l iqu id andfor the isothermal compress ib i l i t y of theliquid below l00°C. The thermodynamic surfacecovers a range froci the freezing point to 4000K and from the d i l u ' e gas to well in excess ofi HPa. The l iqu id and gaseous s t a t e s forundissociated water a re desc r ibed . Thereference s t a t e i s defined TO be the l iquid a tthe t r i p l e po in t , for which s t a t e the in t e rna lenergy and entropy are ze ro .

7152-1

Beware tha t , although t h i s equation of3Cace Is very accurate , the range oftemperature and density cowered i s l imi ted.

REFERENCE

1. L. Haar and J* S, Gallagher, "ATherraodynaraic Surface for Water: TheFormulation and Computer Programs t "National Bureau of Standards In te rna lrepent 81-22S3 (May m i ) .

7152-2

MATERIAL 7[b2

MATERIAL 713=1

Pie/

SESAME 07160

Material: Deutero-polyethylene (branched,completely deuterated)

Composition; CDpOrlRlnator; F. Dowel IDate of Origin: September 1982Type of Tables Included; 301, 303, 304, 305,

306Limits; 0 < p < 2.0949 * 103 g/cm3

0 < T < 1.16 x 109 K

BASIC PHYSICAL DATA

S =• 5.3468I - 2.666667

p o - 1.047b e/cm3

P(T = 298.15 K, p ) = 2.36.i x 10"4 GPaE(T - 29S.15 K, p ) - -6.3649 x 10"5 HJ/kgT(P - 10"6 GPa, p o) = 298 K

PESCRIPTION OF PHYSICS

This EOS Is an Isotopic scaling of SESAME1)7171.

MATERIAL 7160

SESAME 97171

Material : Polyethylene (branched, low-densi ty)[Ref. 1]

Composition: CH«Originator : F . uowellDate of orlfi ln: September 1982Type of Tables Included: 301, 303, 304, 305,

306Limits: 0 < p < 1.832 * 103 g/cm3

0 < T < 1.16 * 109 K

BASIC PHYSICAL DATA

4.67572.66670.916 g/em3

?(T - 298.15 K, p ) » 9.0859 * 10"5 GPaE(T - 298,15 K, p ) - -5.1977 * 10"5 RJ/lcg

( ~ 6T(P GPap

" 298 K

Yo " * 0.561 (used In ca lcula t ion)(ca lcu la ted from experimental values for

the constant pressure heat capac i ty , thei sen t rop lc bulk modulus, and thethermal expansion coeff ic ientat p o )

E . > 1.C3 HJ/kg (estimated from Ref. 21* 3.35 HJ/kg (used In ca lcu la t ion)

binding-1.6323 HJ/kg( s e t 90 that zero of energy i s a t

P=0 and T=298.15 K)

Hugonioc F i t : U - 2.5331 + 1.7648 U - n.0469U 2 km/9 for 0.7 ° U <4?9 km/s (Ref. 3] P

(used In calculat tan of cold curve)

DRSCRIPTION OF PHYSICS

This is an equation of state for branched(low-density) polyethylene. The models usedtQ generate this F.OS do not expLiclry t reatpolyethylene as a polymer; however, sinceexperimental data are used in the models, thepolymeric nature Is Implicitly included Inparts of the EOS.

The EOS for polyethylene is treated asthe sum of three contributions: zero kelvln,thermal e lec t ronic , and aolid la t t i cevibrations. The cold curve waa calculated atlow densit ies in compression from experimentalHugonlot data assuming a Mie-Grtlneisen model.This was smoothly joined onco high-densityThomas-Ferrai-Dirac calculations. Forp <C 0,911 g/cm , the cold curve was calculatedwith an analytic Lennard-Jones formula with anr~^ a t t rac t ive terra.

The thermal electronic contributions tothe EOS were calculated withThomas-Fermi-Dirac theory assuming an averageatomic weight of 4,6757 and an average atomicnumber of 2.666667.

The solid l a t t i c e vibrations weredescribed by a Dehye model which was modifiedto extrapolate to an ideal gas at hightemperatures or low densit ies. At densi t iesbelow reference density, a v i r ia l expressionwas used.

This EOS Joea not Include effects for theglass t ransi t ions or meitlng. Also, i t hasvan der Waals loops in expansion instead of aMaxwell construction.

Hugoniot data are reproduced very well bythis EOS. Stat ic measurements ofpressure—rolume-temperature dat^ were alsocompared *rich theory, and agreement was withinr.12% to 2.91%, except for one data point inthe liquid s t a t e .

This EOS i s therraodyn; aiically consistenteverywhere.

REFERENCES

1. A complete deacl ip t ion of t h i s "SOS ta givenin F . Doweii, "A Simple EOS for Branche'(Low-Density) Polyethylene," Los Alamot.National Laboratory report LA-9559-MS(October 1982).

2. C. W. Bunn, "The Melting Points of ChainPolymers," J . Polym. Sc i . 1£, 323(1955) .

3 . S. P. Mffrsh, L>",L Shock HuRoniot Data.(Univers i ty of California P r e s s , Berkeley,1980).

7171-3

MATERIAL 7171

SESAME (mao

Material: Polyethylene (Marlex) (Ref. 1]Composition: CIKQrlRlnatori F. DowellDate of OrlRln: September l°82Type ot Tables Included: 301, 303, 304, 305,

306Limits: 0 « p < 1.908 * 10J g/craJ

0 < T < 1.16 « 109 K

BASIC PHYSICAL DATA

A - 4.67571 - 2.6667

P(T - 298.15 K, p ) • 7.8334 x 10"5

E(T •T(P •

298,15 K, p10"6 GPa, pQ

-5.200 x 10"- 298 K

GPaMJ/kg

Vo - * 0.739 (used in calculation)(calculated from experimental values

for laentropic bulk modulus,thermal expansion coeff icient , andconstant pressure heat capacity a t p )

BG » 4.48 GPa (Ref. 21

Ecoh * * < l - 0° i u ' k 8 ( u a e d l n calculation)(This Is higher than the estimatedexperimental value.)

Hugonlot F i t : * U. - 7-.8233 + 1.6810 D -0.0339 U l km/a for0.7 < U F< 5.4 km/s(Ret. 21 (used lncalculation of EOS)

7180-1

This i s an equation of s ta te for" l inear" , high-density polyethylene (Marlex).The models used to generate th is EOS do notexpl ic i t ly treat Warlrx as a polymer; houever,since experimental data are used in themodels* tha polymeric nature of Marlex isimplici t ly included in parts of the EOS*

The cold curve of th is EOS was calculatedat low densities from experimental Hugonlotdata assuming a Mie-GrUneisen model. Thislow-pressure part of the cold curve wassmoothly joined onto high-densityThotaas-Fermi-Dirac ^era-degree calculations.At p < 0.949 g/cir*. the cold curve uascalculated with an analytic Lennard-Joneaformula with «.n r~*** at t ract ive term.

The thermal electronic contributions tothe EOS were calculated withThomas-Fermi-Dirac theory assuming :a averageatomic weight of 4.6757 and an average atomicnumber of 2.666667.

The solid l a t t i c e vibrations werecalculated with a Debye model which wasmodified to extrapolate to an ideal gas athigh temperatures or low dens i t i e s . Atdensit ies below reference densi ty, a v l r ia lexpression was used.

The solid binding energy was set to-1.6836 MJ/kg in order for the zero of energyto be at P = 0 and T - 298.15 K.

This EOS does not include effects for theglass transitions or melting. I t has

7180-2

van der Waala loops In expansion instead nf aMax we1X cons t ruet ion•

1 ugonlot data are reproduced very well byt h i s EOS. Sta t ic measurementpressure-volume-temperature data were alsocompared with theory, and agreement was within0-5X in densi ty , except for one data point inthe l iquid s t a t e .

The therraodynamic consistency of th i s EOSi s good everywhere.

REFERENCES

1. A complete descr ip t ion of t h i s EOS i s givenin F. Dowell, "A Simple EOS for "Linear"(High Density) Polyethylene (Marlex)," LosAlamos National Laboratory reportLA-9564-MS (November 1982).

2. S. P. Harsh, LASL Shock Hugonlot Data(University of California Press , Berkeley,1980).

' r, ri

•j'L

MATERIAL 7160

MATERIAL 71B0

SESAME 07190

Mater ia l : Teflon (Polyte t raf luoroethylene)Uef . 11

Composition: CF^Originator: F. Dowell and J. n. JohnsonDate of QrlRln: August 1982Type of Tables Included: 301, 303, 304, 305,

306Limits: 0 < p < 4.304 x 1Q3 g/cm3

0 < T < 1.16 x 109 K

BASIC PHYSICAL DATA

S = 16.6691 ' 8.0p0 - 2.152 g/cm-

,-4"(T - 298.15 K, pQ) - 1.0574 x 10F.(T • 298,15 K, p ) - -1.5399 x 10"5 MJ/kgTCP - 10"6 GPa, pQ) - 2^8 K

Yo - * 0.455 (used In calculation)Ccalculat>id from experimental valueB forthe constant pressure heac capacity,the laentroplc bulk modulus, and thethermal expansion coefficient at p )

V. . • 0.324 MJ/kg [estimated from Ref. 2]C • 1.150 RI/kg Cused In calculation)

binding(set so that zero of energy Is atP-0 and T-298D15 K)

Hugoniot F i t ; UR « 1.571 + 1.961 U - 0.0537 U 2

kra/s for 0.6 < 0 < 4.4 km/s(used in calculat ion ofcold curve) [R*f. 3]

this


Teflon is a polymer which is a chain of2 molecules. The nodels used to generateis F.OS do not expl ic i t ly t reat teflon as a

polymer; however, slnce experimental data areused tn the models, the polymeric nature iaImplicitly included In parts of ttv* EOS.

The F.OS for teflon is treatec as the sumof three contributions: zero kelvVn, thermale lec t ron ic , «ind solid l a t t i ce v ibra t ions . Thecold curve was calculated at low dens i t i es Incompreysion from experimental Hufioniot dataassuming a Mie-Grllnelsen model. This wassmoothly joined nnto high-densityThomas-Fenui-Dirnc calculations. Forp < 2.140 g/cnr, the cold curve was ca lcul i tedwith an analytic Lennard-Jones formula with anr~^ a t t r a c t i v e term.

The thermal electronic contributions tothe F.OS were calculated withThomas-Fermi-Pirac theory assuming an averageatomic weight of 16.669 and an average atomicnumber of 8.

The sol id l a t t i c e vibrations werecalculated with a Debye model which wasmodified to extrapolate to an Ideal gas athigh temperatures or low dens i t ies . Atdens i t ies below reference density, a v l r i a lexpression was used.

7190-2

This EOS does he-', i. elude effects forstructural transit ions, the glass t ransi t ion,or melting. Also, It h«s van der Waals loopsIn expansion instead of a Maxwellconstruction^

Hugoniot data are reproduced very w«lL bythis EOS. Static measurements ofprtissur^valume-temperaturt: data uer<; alsocompared with theory, and agreement was wi thin3-8X in density.

This EOS i s thermodynamically consistenteverywhere.

REFERENCES

1. A complete descr ipt ion of t h i s EOS i s givenin F. Dowel', and J . D. Johnson, "A SimpleEOS for Polytetrafluorj*:thylene (Tef lon) ,"Loa Alamos National Laboratory repor tLA-9439-MS (August 1982).

2. C, U. Bunn, "The Melting Po in t s of ChainPolymers," Ju Poly. Sc i . _16, 323 (1955).

1* S. P. Marsh, LASL Shock HuRoniot Data(Univers i ty of California P r e s s , Berkeley,1980).

7190-3

MATERIAL 7190

" * " ' • " ' ~ ' ' T •

-1 0 !

£ (g/cm3)i

- - 1

j

1i

!

i

ii11

a

ooooe-rooaoooE+oz•1529E+0276ffiE+02173QE*Q34554E-K33L247E+043JJ38E+O47B62E-'O4

3713E+051I63E-06

r-*"T?E 077977E+ff73713E+05

MATERIAL 7190

P (g/on3)

SESAME J7242

Material: Lithium DeuterldeComposition: L1°DOriginators: J. Abdallah and J. D. JohnsonDate of Origin: September 1981Type of Tables Included: 301, 303, 304, 305,

306Limits: 0 < p < 1,564 x 104 ^^^i

0 < T < 3.7 » 10" K

BASIC PHYSICAL DATA

5 = 4.041397Z - 2.0

pQ - 0.78201 g/cm3

P(T - 298.15 K, p ) - 0.35756 GPaE(T - 298,15 K, p°) » 0.45727 HJ/kgTCP - 10~6 GPa, pQ) - 25.50 K


This EOS for lithium deuter ide wascreate-', by lsotoplcal ly scaling SESAME #7370(l i thium hydride) . The or iginal l i thiumhydride EOS was calculated with the standardBarnes-Cowan-Rood method.

MATERIAL 7242

5M2E+06l.160E*O72321E+OT5B02E+C71.160E+0BZ221E+083713E*OB

MATERIAL 7242

t :>i

O.OOOE+002.901E-KESB02E+02U60E+032321E+035B02E+03B.J23E+03I160E-CM2321E+045 2 EU60E+052321E+055.602E+05U60E+062.321E+06

E3.4aiEO65B02E+061J60E+O7_321Em

5B02E+O71.160E+082.321E+033713E+08

P (g'cm3)

SESAME *7243

Material: Lithium IVuterideComposition: Li Doriginator: K. TrainorOatc^nf Origin: February 19^3Type of Tables Included: 301, 303, 304, 30%

Limits

S - 42 - 2

p n » 0

P(T -

: 10"*0 <

.0

.0

.802 j

298.15

< P <T < 2 .3

BASIC

K. D )

. 306IQT s / cm J

x 108 K

PHYSICAL

- 1.4195

DATA

rcpnE(T =* 298.15 K, p°) a 1.5232 MJ/kgT(P - 10~6 GPa, pQ) a 2.24605 x 10"4 K

BQ - 32.2 GPa [Ref. ll* 30 GPa (used in calculation)


This equation of s tate for Li D wasgenerated with a fast-response method. F i r s t ,an electronic EOS was calculated wlchThomas-Fenni-DIrac theory. Two correct ionswere added to that basis : an ion correctionbased on a model by R. D. Cowan and anempirical correction which forces theexperimental zero-pressure density and bulkmodulus to be reproduced. In the case of th isEOS, however, a bulk modulus of 30 GPa wasused Instead of the experimental value of 32.2GPa in order for the expericfc iral Hugoniotdata to be reproduced. The theoret ical EOSwas tweaked to match a series of Hugoniot

7243-1

experiments by S. P. Harsh [Ref. 1) . (Thereare six sets of data, five of which s t a r t atIn i t i a l ly porous densit ies.) The referencedensity used for th is EOS (0.802 g/cnr*) i sbased on measurements by S. P. Marsh andassumes that the Li D sample is contaminatedwith 2 wt% of water.

This EOS I s not designed to be accurateat low temperature (<0.5 eV), part icularly inthe vapor—liquid coexistence region inexpansion. Also, zero pressure Is at thereference density on the cold curve, not atroom temperature.

The EOS la therraodynamicaily consistenteverywhere-

S. P, Marsh, "Hugoniot Equations of Statefor L16H, Li6D, LtnH, and UnD," Los AlamosScientific Laboratory report LA-4942 (July,1972).

MATERIAL 7243

MATERIAL 7343

SESAME C/7252

Material: Lithia-Roria Glass [Ref.Composition: Llon 27.7 atX

B2n2 72.1 at%Orifitnattir: G. I . KerleyPats of Origin: November 1978TvpeLltnl

A =>

oft s :

n6.

Tabin0 i

.07440 I

T

Included: 301< p < 4.jj » 103

s/c.

BASIC HireSICAL DATA

m1 ( a t T=298.15K)

P(T = 2 9 8 . 1 j :'., o ) = - 0 . 6 1 8 2 4 GPaF.CT = 2 9 8 , 1 5 K, P Q ) = 8 . 2 5 l i » 1 0 " 1 Ml ,'kK

T(? = 10"" GPa, po) =» 35.46 K

1n- * 1.2 (used In calculation)B()

a 56.04 GPa (measured In shock waveoxperiraents)

Et.oh = 40.7 MJ/kg(estimated from cohesive energies ofseparate components)

Dh.- CRIPTION OF PHYSICS

Hugonlot data for l l th ia -bor ia glass andfor Lmdema" glass show a sol id-sol id phasetransi t ion at approximately 9 GPa. Twoseparate EOS tables were computed for the twophases ;tnd then merged to create a multiphaseKcS. The pl'ise t r ans i t i on on each isotherm IsIwazr ' JJ. the point at which the pressuresand Gthbs free energies of the two phases areequal.

The cold curves for each of the equationsof state were computed from the shock wavedata assuming a Mie-*Gr\lneisen model. TheGrllneisen parameter was assumed to be of theform:

y(p> -

For the low density phase.

p0 » 2.215 g/rm3 ,

Yo - 1.2 , and

Us - 5.03 + 1.4 U km/s

The slope of the Hugoniot relation waschosen on the assumption that the phasetransition occurs at 9,2 GPa.For the high density phase,

fo ' 1-2 , and

tlc = 5.4 + 1.38 U km/s .b p

7252-2

The reference density of the hlgh-fle"ngttyphase was estimated by extrapolating theHugoiviot data Co zero pressure.

The calculation of the EOS for bothphases also Included nuclear vibration andelectronic excitation contributions. Thenuclear term was calculated with a Debye modelwhich was modified to go to an ideal gas a thigh temperatures. The electroniccontributions were calculated with theThomas—Fermi—Dlrac model.

Above temperatures of 0.22 eV> a Maxwellconstruction waB performed In the vapor-llquidcoexistence region. Below 0.22 eV,van der Waala loops (negative pressures) wereretained in order to have a tension region forspall uodelst

The agreement of this EOS withexperimental Hugoniot data la very good(including modeling of the phase t r a n s i t i o n ) .

The l l t h i a - t o r l a glass equation of s ta tela most accurate near the Hugoniot and at hightemperatures (due to inclusion ofThomas-Ferrai-Dirac electronic exci ta t ions) .The vapor dome region is reasonable.

The EOS ia thermodynamically conuistent.everywhere.

REFERENCE

1. G. I . Ker ley , "An EOS for U t h l a - B o r i aG l a s s , " Los Alamos Sc i en t i f i c Laboratorymemorandifln T-4-SL-5 to D i s t r i b u t i o n(December 11 , 1978).

7252-3

MATERIAL 7252

y^yf

; ^ ; ^ - - ^ ; ^\ -•y^yy'iy^-y-''^"^ \, yy'-y^yy',- -y^^' 1' '"- 'y'-'/yy y'y ^ *~1 'y^-^^yy^^i /yy/'/ y>'

'^yyy''"

' 1

1

11

1'

1

-5 -4 -3 -2 -IjO (g/cm3)

OOOOE'OO2960E-025459E-021000K.03Z512E'O36309E-03I585E-O4J981E-CH1000E»053539E»05I253E-064 434E*06157QE*07

r-~"

!

SESAME 17281

Material: 5alt iRof. 1]JoapoaltIon: NaClOriginator: A. Herts and N. MaReeDate of OrtKtnt November 19P1Type of TabU.i Included: 301LUl t s : 0 < p s 2.In » \0i g/cm1

lift < T < 5.fl » 10n K

BASIC PHYSICAL DAT <

p o - 2.165 g/.-mJ

[»(T - 29R.IS K, p ) - 0.26335 GPaE(T - 29H.15 K, pQ) - B.AQ61 * 10"2

(There la no zero-pressure point Inth i s t « b l e . )


The equation of s tate for sal t wascalculated with a code developed by A. Hertswhich pruduees an EOS whtch Is similar Insp i r i t to those generated with theBarnes-Cowan—Rood procedure. The zero-degreeIsotherm was calculated from an analyticexpression which was adjusted to reproduceexperimental Hugoniot data, the cohesiveenergy, and the tensi le strength. Theanalyt U: formula ensures that the experimentalzero-pressure density and bulk modulus arereproduced. The thermal electroniccontributions to the EOS at f in i tetemperatures were calculated with Thomas-Fennitheory. The thermal nuclear contributions arebased on a randel by Thompson and are embodieJin the following formulas:

7281-1

r i s the Grllneisen ratio, and * la aninterpolation function of density andteaperatura which allows the equations tosmoothly transit from low to high temperature*

The boundary of the liquid-vaporcoexistence region Is found by determining atwhat pressure for a given temperature that theCibbs free energy i s equal at the upper andlower densities. Inside the two-phase region,the pressure is made constant (equal to thevalue on the boundary), whereas the energy i sa linear interpolation between the values acthe upper and lower densities.

This EOS i s theraodynamically consistenteverywhere. It is fairly good throughout mostof the c«alid and vapor legions t thoughInaccurate in the vicinity of the cr i t icalpoint.

R&FEKSKCE

1. The nethod of generat ing t h i s EOS i sd e s c r i b e d In A. L. Herts and H, H. Ma g e e ,J r . , "Low Temperature Equation o f S t a t e forMetals," tos Alamos Scientific Laboratoryreport LA-5068 (January 1973).

MATERIAL 7331

£ "• "' ~2__

P (g/

SESAME #7 330

10"io":

c;p<Mj/kg

Mater ia l : Calcium Carbonate (Ref. 1!Compos it ton: CaCO..OrlKlnator: F. H. Ree (Lawrence Livermore

Nat ional Laboratory, " -Div i s ion)Date of Or ig in : !")aiType of Tables Included: 301Limits: 0.25 < p < 1000 g/cm

300 < T < 2.9 » 10R K

BASIC PHYSICAL DATA

A = 20.01797. » 10.

po - 2.71 g/cm3

r(T - 29S.15 K, p ) • 1.501E!T - 298,15 K, p°) • 1.200T(P « It)"6 CPa, pQ) - 290.11

T^ = * 1612 K (used In calculation) iRef. 2|

, n • * 0.55 (ussd in calculation)

gD - * 900 K (used in calculation)

HiiKonlot F i t : * U_ » 4.2 + 1 .05 U - 0.1 U 2

km/s^used in calculat ion)


This is a high-quality, wide-range,multiphase ROS which incorporates severalHiffereot physical models:

1) GRAY - A semi-empirical model which usesthe Hrunelsen model to calculate the EOSfor the solid (assumed to be harmonic:).

The solid is also assumed to be In thearagonlte phase, except for the roomtemperature isotherm which Includes ametastable phase transit ton from aragoniteto ca lc l te . The liquid s ta te iscalculated by modifying the solid freeenergy by an entropy correction associatedwith Loss of order. The GRAY regionextends from densities of 2.71 g/cm toH.ft g/cm and from temperatures nf0.02S eV to 1.0 eV.

TIGER/CHtiq - These models were used In thelow-temperature, low- density region whichIs sensitive to the chemical equilibriumbetween f!nro-, find the dt ssoc t ated spec lesof Caen-,. TtGER calcul.ites saseous F.nSpropenies of the mixture using nffecker-Kisclakovsky-UlUon modtl. CMEQwas used in tile vapor-solid region todetermine the equllibrium concent rationsof the chemical species by theextent-of-react ion variable method.

- This model covers theh 1 gh-1«mperature, Iow-density region Inwhich ClaCO, is assumed to be completelydissociated Into electrons, ions, andneutral atoms. The concentrations of eachtif these species ire obtained from theSana equatIon, and the thermodynamicprop^rt ies are ca Lculnted assuming thateach component nf the mixture behaves like

l

TFNUC - calcuiates electroniccontributions to the EOS usingThomas-Fermi theory with Kirzhnitscorrections for the wave nature ofelectrons and the electron exchange

7330-2

cont r ibu t ion- Nuclear cont r ibut ions arecalcula ted with a GrUnelsen model a t lowtemperature and the one-component-plasmamodel at high temperature.

Agreement between the theo re t l ea lHugntiiot and experiments Is gnod abovepressures of 20 GPa.

REFERENCES

1. A complete de sc r ip t i on of t h i s EOS i s givenin F. H. Ree, "Equations of State of CaCO-,and I t s Mixtures with ^ O , " LawrenceLlverraore National Laboratory reportUCRL-53113 (March 1981).

2. R. C. Weast, CRC Handbook of Chemistryand Physics (CRC Press , I n c . , Cleveland,Ohio, 1977-1978).

7330-3

MATERIAL 7330

SESAME 07371

Material: Lithium HydrideComposition; LinHOriginator: K. TrainorDate of Origin: September 1981Type of Tables Included: 301

116 < T i 1.86 x 10° K

BASIC PHYSICAL DATA

5 = 4.02 - 2.0pu - 0.775 g/cm

J

P(T = 298.15 K, po) = 0.8315 GPaE(T = 298,15 K, p ) =• 0.84589 MJ/kgT(P - 10"6 CPa, p0) - 13.55 K

Bo =• 31.4 GPa iRef. 11* 28 GPa (Input Into calculation)

Hugoniot F i t : U. = 6.426 + 1.167 U km/aS [Ref. 11 p


The equation of state for LinH assumesthat natural lithium (92.5* Li and 7.5% LI6)is in Che compound. It was generated withThomas-Fermi theory for the electronic part oftt EOS and with a Cowan model for the tonEOS. An empirical correction was also addedto ensure that the zero-pressure experimentaldensity i s reproduced. In order to match theHugoniot experiments, a bulk modulus of 28 GPa(Instead of the experimental value of 31.4GPa) was used in the empirical correctionpackage.

The L1H zero-degree Isotherm comparesmoderately wel l with APW band theoryc a l c u l a t i o n s by F. Perroc [Ref. 2 ] , al though

_at 19 g/cm , the APW zero-degree p ressu re isapproxlma te ly 20% lowti r .

Thermodyn.'unic consistency i s Roodeverywhere eucept In the two-phase r e g i o n .

REFERENCES

I . S. P, Harsh, "Hugoniot Equations of Sta teof Li^H, Li n, U n H, LlnD," Los AlamosS c i e n t i f i c Laboratory report LA-4942 (July

7

2. F. P e r r o t , Phys. Stac. Sol. (B) 77, 5170 9 7 6 ) .

7371-2

MATERIAL 7371

-2 -I 0P (g/cm3)

MATERIAL 7371

SESAME S7380

Material: QuartzComposition: SIO^QrlRlnators: J . Barnes and J . RoodDate of Origin: August 1973Type of Tables Included: 301, 303, 304, 305,

306Umlta: D ( p < 4.408 x 10* g/cm

0 < T < 3.7 x 10a K

BASIC PHYSICAL DATA

5 - 20.0281 - 10.0

po •> 2.204 g/cm3

?(T - 298.15 K, pQ) - 0.o2538 C.VnE(T - 298,15 K, po) - 0.18958 MJ/kgT(P - 1Q~5 GPa, p o ) - 3.662 x 10"4 K

Bo • * 37.05 GPa (used In calculat ion)

E c o h - 28.6 MJ/tcg (used In calculat ion)(calculated by adding cohesive energiesof each compound)

0D - » 494 K (used In calculation)

Hugoniot F i t : Us - 1.3 + 1.56 U km/s lEef. 1](for high-prissure phase)


This equation of s t a t e 1B undocumented.However, i t was most l ikely generated with theBarne5~Cowan-Rood procedure. Above 1 eV, theelectronic part of the EOS was calculated withThonas-Ferrai-nirac theory using an averageatomic weight of 20.028 and an average atomic

number of 10. The nuclear thermal and coldcurve c o n t r i b u t i o n s are based on a model byR, D. Covmn.

The low-temperature EOS was t r e a t e d in aspec ia l manner s ince quartz has a s o l i d - s o l i dphase t r a n s i t i o n . The reference dens i t y ofquartz i s 2.20/+ g/cm with a hulk maduluB of37.05 GPa. But the high-densi ty phase has anapparent d e n s i t y of 4.285 g/cm and bulkmodulus of 560 GPa. So for the cold cu rve ,two sepa ra t e c a l c u l a t i o n s using themodified-Moree model were performed. Thesewere joined at. a point determined by the phnset r a n s i t i o n shown in the Hugoniot d a t a . Thethermal nuc lear con t r ibu t ions to the EOS belowt eV were based on a Debye model.

The EOS i s therraodynamically c o n s i s t e n teverywhere.

The two-temperature t ab les were de r ivedby the code TWOTtIMP and are no i sy .

REFERENCE

U S. P. Marsh, LASL Shock Hugoniot Data{Univers i ty of California P r e s s , Berke ley ,1980).

MATERIAL 7380

0 1 2/0(g/cm3)

MATERIAL 7380

SESAME 17381

Material: QuartsComposition; SiO2

Originator? R. C. AlberaDaee of Origin: February 1981Type of Tables Included; 301, 303, 304, 305,

3£6L i m i t s : D < p < 2 . 2 0 4 « 10* E / c m

0 < T < 1 0 5 eV

BASIC PHYSICAL DATA

X - 20.028t » 10.0

Po - 2.204 g/cm3

P(T - 298.15 K, p ) - 1.692 * 10"2 GPaE(T - 298,15 K, p°) - 0.4241 MJ/kgT(P - 10"8 GPa, PQ) - 292.66 K

yo - * 0.036 (used In calculation)Bo - * 36.6 GPa (used In calculation)

Polsson r a t i o = 0.167

Ecol> " * 3 O - 5 7 W/^8 (used In ca lcula t ion)

Hugonlot F i t : Us - 4.075 + 1.606 U km/s forU < 0.708 km/sP

!)„ - 5°212 ta/s for 0.708 < U< 2.61 tan/8 P

V. - 0.801 + 1.69 U for U >S 2.61 W i P P

DESCRIPTION OF PMSICS

The cold curve at low density wasgenerated from a special kinked Hugoniot ( tosimulate the effect of a phase t r ans i t ion) .

7381-1

This was matched onto a Thomas-Fenni-Diraccold curve at very high pressures. Thethermal electronic component o* •*.._. f,0S wascalculated by mixing Thnrscr^nnl-Dlrac EOS'afor silicon and nrjfrc ;- -1*. Cowan model wasused for the * •••> inu*I Ionic component. Hence ,this r..»^ It. very good for two-temperature

,-; •.•••stions that subtract off a Cowan modelTor the ionic degrees of freedom.

7381-2

MATERIAL 7381

10

e

6

A

2

0

-2

-4

-8

[

[

—y \

\ \1\

o.oooe>oo

vsXEmvsXEm1499E<043229E+046«

0 1 Z

|0(g/cm3)

£9E0632ESC-K166957E+08M99E-KT732Z3E*076357E-HJ7l499E-rCB3229E*066.8S7E»06

MATERIAL 7381

SESAME *?382

Material: Quartz [Ref. 1]Composition: S107

Originator: F. 11. Ree (Lawrence LiverraoreNational Laboratory, H-Dlvislon)

[late of Orlaln: 1176Type of Tables Included: 301Umlta: I .6 » 10~° i p i 150 g/cm1

1 1 6 < T < 2 . 9 « 1 O R K

BASIC PHYSICAL DATA

S - 20,02832 - 1 0

p o - 2.65 g/cm-1

P(T - 298.15 K, p i • 1.52(1 * 10"2 fiPaE(T =• 298.15 K, p ) = 0.3379 w /kgT(P •• 10"8 CPa, p°) • 185.67 K

T = * 1996 K (a -quar rz ) (used in ca l cu la t ion )

Tc > 1.0 eV (Ac tua l ly , no t rue c r i t i c a l pointex i s t s in the SIO^ system because a l a rgeamount of liqMtcI s i l icon is present aboveO.fi eV, and t h i s d i s t o r t s the charac terof the vapor- l iquid equi l ibr ium.)

1O =• * 0.6 (used in calcula t ion)

HuRonlot F i t : * Us » 3 , 6 ' + 1.85 I) - 0.6374u 1 + 0.1&695 U 3

Pl . l8M \ 0 u

9.0375 xlo"5 U 5 P

W B P

(used in calculation)

7382-1


This i s a uide-range, multiphase EOSwhich incorporates five different theore t ica lmodels;

1) TIKER - calculates the EOS Eor aheterogeneous system of mixturescontaining several gaseous, l i qu id , andsolid components using aBecker-Kistlakowsky-Wilson model.Tonlzation is assumed to be n e g l i g i b l e .

2) CRAY - calculates the thermodynamiTpropert ies of the alpha-quartz,s t i shov i t e , and Liquid phases using th-GrUneisen raod^l. The solid i s assumed tobe harmonic. No internal ro ta t ion ,v ibra t ion , or electronic contr ibut ions aretaken into account because the model i sonly used below 1 eV.

3) OCCIPITAL - used in the region where theSiO2 molecule is completely dissociatedinto electrons, ions, and neutral atoms.The concentrations of each of thesespecies i s obtained with the Sanaequation, and the thermodynamic propert iesare calculated assuming that the mixturebehaves like an Ideal gas.

4) TFCMIX - uses Thomas-Fermi theory tocalcula te an electronic EOS. TheKirzhnits correction is added to accountfor the wave nature of e lectrons and theelectron exchange contribution. A nuclearcorrect ion based on a model by Warren i salso added.

7382-2

5) MASTER - phenomenologlcally corrects theEOS at low temperature, low compressionfor atomic shell structure, and electroniccorre la t ions .

Agreement between the theoreticalHugoniots and the experimental data is goodbelow 100 GPa. At higher pressures, however,the theoret ical Hugoniots l i e below theexperiments •

REFERENCE

1. A complete d e s c r i p t i o n of the EOS i s givenin F . H. Ree, "Equat ion of S t a t e of t heS i l i c o n Dioxide Systems," LawrenceLivermore Labora tory report UCRL-521S?(November 1976) .

MATERIAL 7382

a

6

4

.-». 2

a. 0

-2

-4

-6

I 1

^ ^ ^ "

'^ ^^

]

! l-3 -2 -I 0

P(gcm3)

1 I:50E-U2

•).64ZE»02

1B57E*O3

E 3 2 1 E O 54 642EfO59283E+052!»1E,O69263E«062-901E-OV9283E»07

MATERIAL 7382

Material'. Westerly GraniteCompos itinn: S 73.9

14.94.53.3

FeO 2 .0p lus t r a c e amounts of o the r oxides

Or lR lna to r s : J . Barnes and .1. RoodHate of Or ig in : March 1975Type of Tables Inc luded : 3 0 1 , 303, 304, 305,

306U n i t s : 2.0523 » 10"2 /cm3

0 < T < 3.7 « 10° K

BASIC PtrvsicAL DATA

7, = 20.f.697 = 10.272

Po = 2.627 ? / c n 3

P(T - 298.15 K, p ) • 0.84726 GPaECT - 29B.15 K, p°) • 0.16352T(P = 10"6 Gpa, p°) - 3.578 x lO"" K

y - * 1.9756823 (calculated)Bo - * 53.2 CPa (used In calculation)

(calculated from C = 4.5 km/s)

Hugonlot F i t : U = 4 . 9 3 + 0 .372 U km/s for1 < U < 2 .1 P

U = 2 . 1 0 : p + 1.629 U km/s for2 .5 < U < 4 .1 fRef. 11


No formal documentation e x i s t s fo r theEOS for wes te r ly g r a n i t e . However, frompiecing toge ther the notes made dur ing th*c a l c u l a t i o n , i t seems Chat the EOS wasRenerated with the Rarnes-Cowan-Rood method.At high tempera tures , the EOS was c a l c u l a t e dby mixing four MAPLE t a b l e s : oxygen, s i l i c o n ,aluminum, and a c h l o r i n e - l i k e e lement . (The•silicon EOS was ac tua l ly a Z-scaled aluminum.)The MAPLE t ab l e s are based onThomas-Fermi-Dirac theory for the e l e c t r o n i cpart of che EOS, and the nuclear thermal andcold curve con t r ibu t ions in the MAPLE t a b l e sare from a model by R. D. Cowan.

The cold c-iive of the g ran i t e EOS wasca l cu la t ed with a modified-Morse model. Atlow tempera tu re , nuclear thermal c o n t r i b u t i o n sbased on i, Debye model were added t o the coldcurve component of the EOS.

The two-temperature t ab les for t h i s EOSwere der ived by the code TWOTEMP and a r enoisy.

REFERENCE

I, M. van T h i e l , "Compendium of Shock WaveData , " Lawrence Llvermore Laboratory repor tUCRL-5O108, Rev. 1 (1977).

MATERIAL 7390

P (g/cm3)

MATERIAL 7390

P (g/cm

* - m.vr:7 - 1".

a. P . '

. * 29.7 5' " h

, ,ugnnl<.t F " : US " y'

7410-1.


No Formal documentation e x i s t s for thealuminum oxide equation of s t a t e . However, i twas most l i k e l y generated with theBarnes-Cowan-Rood procedure. At hightemperature , the thermal e l ec t ron ic part ofthe EOS was generated with Thomas-Fermi-Dirn.-theory using an average atomic weight of20.3S2 and an average atomic number of 10,The nuclear thermal and cold curvecon t r ibu t ions at high temperature are bused ona model by R, D. Cowan.

At low temperature, the EOS c o n s i s t s oftwo c o n t r i b u t i o n s : a cold curve c a l c u l a t e dwith a modified-Morse model and a nuclearthermal part based on a Debye model.

The EOS i s thermodynamically cons i s t en teverywhere.

The two-temperature tab les were derivedwith the code TWOTEHP and are no i sy .

REFERENCES

1. S. P. Harsh, LASL Shock Hugonlot Data(Univers i ty of California P r e s s , Berkeley,1980).

2. H. van Th i e l , "Compendium of Shock WaveData ," Lawrence Liverraore Laboratory reportUCRL-50108, Rev. 1 (1977).

MATERIAL 7410

P (g/cm3)

MATERIAL 7410

fj Is/cm3!

SESAME 07520

Material! MicaComposition: 0 56.1 wt%

SI 16.7 wt%Mg 12.6 wt2Al 7.6 utXFe 4.5 wtJH 2.4 wtZ

Originators: J . Barne8 and J. RoodDate of OrlRln: May 1974Type of Tables Included: 301, 303, 301, 305,

30fiLlmlta: 2.1094 x 10"2 < g < 5.4 x 104 g/cm3

0 < T < 3.7 » 108 K

BASIC PHYSICAL DATA

S - 13.524Z - 6.8697

p o - 2.7 g/cra3

P(T - 298.15 K, p ) - 1.0820 GPaE(T - 298,15 K, p ) - 0.19713 HJ/kgT(P - 10"6 GPa, p o ) - 2.B180 x 10"5 K


No documentation at a l l e x i s t s for themica Ens. However, I t was probably generatedwith the standard Barnes-Cowan-Rood method.See Part I I for a more deta i led d e s c r i p t i o n oft h i s method of EOS generation.

7520-1

MATERIAL 7520

SESAME 07541

Material; Carbon Phenolic {Ref. 11Composition: C 64.18 at*

H 29.50 at*0 5.9r artN 0.34 at*

Originator: J . D. JohnsonDate of OrlRln: April 1981Type of TablaB Included: 301, 303, 304, 305,

306Limits : 0 < p < 1.516 « 10J g/cm

0 < T < 3.7 x 108 K

BASIC PHYSICAL DATA

S - 9.0105Z " 4.648

po - 1.45 g / a 3

P(T - 298.15 K, p ) - -2.2470 x 10~3 GPaE(T - 298.15 K, p 0 ; - 1.2573 x 10"4 HJ/kgT(P » 1O"6 GPa, po) - 299 K

y - * 0.5 (used In calculation)

Hugonlot F i t : Us - 3.05 + 1.0 U km/s(produred best f i t to Hugoniotdata in calculation)


The thermal electronic part of th i s EOSwas calculated ui.<.tuThomas-Ferrai-Dtrac theoryusing an average atomic weight of 9.0105 andan average atomic number of 4.648. Thethermal nuclear model used was CHART D, andthe cold curve was calculated from Hugonlot

data in the experimental range andThomaa-Ferrai-Dirac theory a t high pressures.Far the expanded part of the cold curve, aLennard-Jones potent ial was joined smoothly tothe derived cold curve used in che compressedregion.

The code EOSLTS merged the variouscomponents of the EOS: nuclear thermal,electron thermal, and cold curve.

The fie of the theore t ica l EOS toHugonloC data is good. The user shouldbeware, however, that there is greatva r i ab i l i ty between one sample of th i ssubstance and another. In the expandedregion, the vapor dome region is veryapproximat&.

This EOS has van der Waals loops insteadof a Maxwell construction, Theraodynamicconsistency is good everywhere.

REFEBgHCE

1. J« D. Johnson and B. Bennett, "An EOS forCarbon Phenolic," Los Alamos NationalLaboratory report LA.-9176-MS (March 1982).

MATERIAL 7b4\

-1 0 I

Pfofcm3)

MATERIAL 7541

SESAME #7560

Material: PolyurethaneComposition: C 62,3 wt%

0 23.3 vtlN 7.3 ut?.H 7.1 wtZ

Originators: J . Barnes and J .Bato of Origin: October 1974Tvpe of Tables

Limits: 0 i; pU < 7

A = 7.03841 - 3.7629

0n - 1.265 g/c

Included: 101,306

<. 2.53 < Iff R /s 3.7 < IU8 K

BASIC PHYSICAL

mJ

Rood

303, 30^, 101!

CXI?

DATA

P(T = 298.15 K, p ) . 0.83376 GPaE(T - 298,15 K, p ) » 0.6592 MJ/kg.T(P - 10"b RPa, p 0) - 3.6097 * 10"1* K

Bo » 5.4 GPn iRef. 11

Hugoniot F t t . U . 1.999 + Z.101 U - 1.351Up

2 km/a iRef. 21


This equation of s ta te is completelyundocumented. However, i t was probablygenerated with the standard Barnes-Cowan-Roodmethod. See Par t II for a more detai leddescript ion of the procedure.

KEFF.HF.NCF

1. S. V. Miirsli, I.AS1. Shuck HuBunlnt lint.i

( U n i v e r s i t y nf C a l l t n r n i n I T C S H , Berke ley ,

198(1).

1. M. van T h i c i , "Comp^nciium of StmLk UiivfDn ta , " Lnwren tv Ltvcrmorc- LaS.nratitry r epor tUCRI.-IDinR, Rev. 1 ( 1 9 7 7 ) .

MATERIAL 7560

SESAME #7590

Material : PolystyreneComposition: CHOrig ina tors : J . Barnes and A. LindstroroDate of Or ig in : January 1976Type of Tables Included: 301, 303, 304, 305,

Limits: 0 < p < 2.088 « in4 g / cm 3

O C T C 3.7 « 10 8K

BASIC PHYSICAL DATA

S - 6.51Z - 3.b

P(T - 298.15 K, p ) • 1.0003 GPaE(T = 298,15 K, p ) - 0.81249 MJ/kgT(P - 10"6 GPa, po) - 3.0028 x 10"' K

T . * 13860 K (calculated)Pc = * 3.2295 » 10"2 GPa (calculated)

y = * 1.18 (used in calculation)B = 3.77 GPa [Ref. 11

4.08 GPa [Ref- 2]

Hugoniot F i t : U. - 2.746 + 1.319 U km/sS iHef. 3] P

DESCRIPTION OF POTSICS

The polystyrene equation of s tate wasgenerated uith the standard Barnes-Cowan-Hoodprocedure. At higher temperatures (probablyabove 1 aV) , the EOS was generated by scalingHAPLE table »18. The MAPLE table consists of

7590-1

an e l e c t r o n i c EOS calcula ted withThomas-Fermi-Dirac theory and cold curve andnuclear thermal con t r ibu t ions based on a modelby R. D. Cowan.

Below 1 eV, the Ef>5 in the sum of twoc o n t r i b u t i o n s : a cold curve baaed on amodlfied-Morse model and nuclear thermalcon t r ibu t ions ca l cu la t ed with a Debye model.See Par t I I for a more deta i led d e s c r i p t i o n ofth i s method of EOS generat ion.

The EOS l a thermodynamlcally c o n s i s t e n teverywhere.

The two-temperature tnbles were der ivedwith the code TWOTEHP and are nolay.

REFERENCES

1. S. P. Marsh, LASL Shock HuRoniot Data(Univers i ty of California P r e s s , Berkeley*1980).

2. Handbook of Chemistry and Physics ,R. C. Weast, Ed. (CRC Press , Cleveland,Ohio, 1976).

3. H. van T h l e l , "Compendium of Shock WaveData ," Lawrence Llvermore NationalLaboratory repor t UCKL-50108, Rev, 1(1977) .

MATERIAL 7590

P(g/cm3)

MATERIAL 7590

5B02E051160Ett>5i321E-rO634S1E*O65B02E*06

, IJ60E+07J 2.3Z1E-O7I 5B£E£+O7j ]I60E~0BJ 2321E-08

J 3713E-08

SESAME #7831

M a t e r i a l : Carbon LiquidO r i g i n a t o r : 0 . I . Kerlevbat* Jf QriRln: October 1981Type of Tables I n c l u d e d : 301Limi t s : 0 .23 < p < 100 (-/cm1

n t T < i o K

BASIC PHYSICAL DATA

A - 1 2 . f i l lZ - 6

P(T = 2 9 R . 1 5 R , p ) = 4 7 . 2 S 1 GPaE{T = 2 9 8 . I S K, p Q ) - 4 . 2 9 0 9 M J / k g

DESCRIPTION OF PtIYSICS

This equation ol state describes themetallic fluid phase of carbon. I t s purposeis to aid in the design and interpretation ofhigh-pressure, shock wave experiments based onthe impedance-matching techniques. Thezero-kelvin Isotherm (cold curve) wascalculated with electron band theory based onthe self-consistent, linear-muffIn-tin-orbital(LMTO) method. The contributions from thecenter-of-mass motion of the molecules(nuclear thermal contributions) were computedwith the CRIS hard-sphere perturbation theoryfor fluids. The thermal electronic part ofthe EOS was calculated with the INFERNO code.INFERNO solves the Mrac equation for an atomembedded in an electron gas. Wave functionsand energies are obtained for both boundstates and the continuum.

MATERIAL 7831

OOOOE-00I98?E»0211O1E-O27768E.021OTE>O32787E>035279E-031000E*O42S12E-046309E-(Ml5a££»053961E-K)5I0O0E+O625I2E-066309E*06

P [g/c

MATERIAL 7831

SESAME t'8180

Material: PBX-9502 (high explosive)Composition: C 25.245 ut i

H 24.491 at*N 24.146 at*0 24.148 ar tF 1.474 ntXCl 0.494 « a

Originators: C. Mader and J . RoodDate of Origin: July 1981Type of Tables Included: 301, 303, 304, 305,

306Limits: 1.4797 x 10"2 < o < 3.788 x 10* g/cm

0 ( T ( 3.7 " ID8 K

BASIC PHYSICAL DATA

X - 10.980013Z - 5.598417

po - 1.894 g/cm3

P(T • 298.15 K, p ) - 0.5061 GPaE(T - 298,15 K, p ) = 0.2674 MJ/kgTCP - 10~6 GPa, p°) - 3.6779 x 10"3 K


No documentation exists for th i s EOS, andthe models used in the calculation areunknown.

The dens i t i e s and energies of theor iginal EOS were sealed by a factor of1.029348 in order to bring the referencedensity in l ine with the experimentallymeasured va lue .

8180-1

MATERIAL 6180

MATERIAL B1B0

P (g*m3)

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