alcock1984.pdf
-
Upload
seshoumaru -
Category
Documents
-
view
213 -
download
0
Transcript of alcock1984.pdf
-
8/10/2019 alcock1984.pdf
1/5
Canadian Metallurgical Quarterly, Vol. 23, No.3, pp. 309-313, 1984
Printed in Canada0008-4433/85 $3.00 + .00
Canadian Institute of Mining and Metallurgy
Pergamon Press Ltd.
/VAPOUR PRESSURE EQUATIONS
FOR THE METALLIC ELEMENTS: 298-2500K
C. B. ALCOCK, V. P. ITKIN and M. K. HORRIGAN
Dept of Metallurgy and Materials Science, University of Toronto, Toronto, M5S lA4, Canada
(Received 2 November 1983; in revised form 2 April 1984)
Abstract-Vapour pressure equations are presented for the metallic elements up to curium. For each elementa precise four-term equation and a more practically-based equation have been derived from a new evaluationofthermochemical data for the condensed and gaseous elements. It is intended that the equations should beused for ideal gases in the pressure range 10-15-10-3 atm, which covers the experimentally accessible range.The "precise" equations reproduce the data to better than 1% and the "practical" equations provide betterthan 5 % accuracy.
The vapour pressures of the metallic elements were previously
reviewed in the compilation of Hultgren et ai. [1] A critical
assessment of thermodynamic data has recently been completed
for the elements from literature data up to 1982 [2 J . These data
are for the condensed and gaseous states and hence the data for
any particular element can be combined to yield the vapour
pressure of the element as a function of temperature. These
equations are presented below for the 65 metallic elements up to
and including curium. The general equation which is employed
is a polynomial in temperature
contributions which influence the temperature dependence of
the thermal functions significantly.
In the examples which are given below for the metal
vanadium, the two-term equation is unacceptable, the three-
term equation is "practical", and the four-term equation is
"precise".
The vapour pressures listed in Table 1as input were calculated
using data from the recent evaluation for the chemical elements
logp(atm) = A + B T-1 + Clog T+ D T10-3
The fit of data to this polynomial form was made by least squares
analysis, and for each element, a two-, three- and four-term
equation was calculated in as wide a temperature interval as
seemed reasonable. Usually two temperature intervals only are
chosen, one for the solid and one for the liq uid. Based upon the
goodness-of-fit of the equations to the calculated vapour
pressures a "practical" equation with the minimum number of
terms has been selected which will reproduce the vapour
pressures to 5% or better. This criterion was se1ected as
representing a reasonable experimental error which would be
encountered in vapour pressure measurement, and which would
therefore serve most practical cases as well as reducing the
number of terms in the polynomial. The complete four-term
equation is also presented when the accuracy is improved, but it
is probably true that these equations are often over-precise when
the experimental uncertainties in the original thermochemical
data are taken into account.
The equations can, in principle, be used above the upper limit
of temperature, 2500 K, which is recommended here. It is felt
however that the thermal data for the condensed phases may
become significantly less accurate above 2300 K, and for gases,
new levels above the ground level may begin to make significant
309
Tempera-ture(K)
325424523622721820919
1018111712161315141415131612171118101909200821072206
Table 1. Vapour pressure of vanadium
log P (atm)
Calculated
Input Equation (1) Equation (2) Equation (3)
-75.109 -75.045 -75.121 -75.108-55.698 -55.684 - 55.692 -55.699-43.639 -43.653 -43.629 -43.641- 35.423 - 35.453 - 35.413 -35.424-29.466 -29.503 - 29.459 -29.466-24.950 -24.990 - 24.947 -24.949-21.409 -21.450 - 21.409 -21.408
-18.560 -18.598 - 18.563 -18.559-16.217 -16.252 - 16.223 -16.216-14.258 -14.287 -14.265 -14.257-12.596 -12.619 - 12.604 -12.596-11.168 -11.184 - 11.177 -11.168
-9.929 -9.937 -9.937 -9.930-8.844 -8.843 -8.851 -8.845-7.886 ......7.876 -7.892 -7.887-7.035 -7.014 -7.038 -7.036-6.274 -6.242 -6.273 -6.275-5.589 -5.546 -5.584 -5.590-4.971 -4.916 -4.961 -4.971-4.411 -4.342 -4.394 -4.408
-
8/10/2019 alcock1984.pdf
2/5
310 C. B. ALCOCK et al.: VAPOUR PRESSURES OF METALLIC ELEMENTS
[2]. The temperatures were chosen to illustrate the fact that the
polynomial form may be used to calculate the vapour pressure at
any selected temperature with any temperature interval. In this
case, the lowest temperature is arbitrarily set at 325 K and
calculations were made over 99 K intervals up to the melting
point of vanadium (Table 1).
The two-term vapour pressure equation was now calculated
using these data and the result is:
log p(atm) =7.87456 - 26948.9/7: (1 )
The three-term equation is
logp =9.74444 - 27132.3/T- 0.55006910g 7: (2)
The Equation (2) is satisfactory, according to our criteria to be
used as a "practical" equation, but a more precise fit is obtained
with the four-term equation
logp =
7.55339 - 27007.7/T+ 0.19699logT - 0.171188T/1000. (3)
It can be seen in Table 1that at most temperatures this equation
gives values which depart from the input values by more than
0.02. This is an acceptable difference between the input and the
calculated values, i.e. within the limits 5% of the vapourpressure.
The Equation (3) is sufficiently precise that no further terms
need be explored.
The origins of the data which have been used for this
calculation are indicated in the Tables 2 and 3.
Table 2. Recommended equations of the vapour pressures for the elements
logp(atm) =A + B 'T-1 + ClogT+ D T'1O-3
Elemert,
state A B
2 3
Li sol 5.667 -8310
Li liq 5.055 -8023
Na sol 5.298 -5603
Na liq 4.704 -5377
K sol 4.961 -4646
Kliq 4.402 -4453
Rb sol 4.857 -4215
Rb liq 4.312 -4040
Cs sol 4.711 -3999
Cs liq 4.165 -3830
Be sol 8.042 -17020
Be liq 5.786 -15731
Mg sol 8.489 -7813
Ca sol 10.127 -9517
Sr sol 9.226 -8572
Ba sol 12.405 -9690
Ba liq 4.007 -8163
Al sol 9.459 -17342
Alliq 5.911 -16211
Ga sol 6.657 -14208
Ga liq 6.754 -13984
In sol 5.991 -12548
In liq 5.374 -12276
Tl sol 5.971 -9447
Tlliq 5.259 -9037
Sn sol 6.036 -15710
Sn liq 5.262 -15332
Pb sol 5.643 -10143
Pb liq 4.911 -9701
Sc sol 6.650 -19721
Sc liq 5.795 -17681Y sol 9.735 -22306
Yliq 5.795 -20341
La sol 7.463 -22551
La liq 5.911 -21855
Ti sol 11.925 -24991
Ti liq 6.358 -22747
Zr sol 10.008 -31512
Zr liq 6.806 -30295
Hfsol 9.445 -32482
V sol 9.744 -27132
V liq 6.929 -25011
Nb sol 8.822 - 37 818
Ta sol 16.807 -41346
C
4
-0.4440
-0.8253
-1.4030
-1.1926
-2.2890
-0.7927
-0.3413
0.2885
-0.8705
-0.3142
-1.3376
-0.7890
-0.6735
-0.5501
-0.2575
-3.2152
D
5
-0.3663
0.7437
Temperature
range
6
298-m.p.
m.p.-l000
298-m.p.
m.p.-700
298-m.p.
m.p.-600
298-m.p.
m.p.-550
298-m.p.
m.p.-550
298-m.p.
m.p.-1800
298-m.p.
298-m.p.
298-m.p.
298-m.p.
m.p.-1200
298-m.p.
m.p.-1800
298-m.p.
m.p.-1600
298-m.p.
m.p.-1500
298-m.p.
m.p.-llOO
298-m.p.
m.p.-l 850
298-m.p.
m.p.-l 200
298-m.p.
m.p.-2000298-m.p.
m.p.-2300
298-m.p.
m.p.-2450
298-m.p.
m.p.-2400
298-m.p.
m.p.-2500
298-m.p.
298-m.p.
m.p.-2500
298-2500
298-2500
Refs
7
[2,4,8J
[2,4 J
[2-4,8J
[2-4J
[2, 4, 8 J
[2,4J
[2,4,8J
[2, 4J
[3,4,8J
[2-4 J[2,4,8 J
[2, 4 J
[3,4,8J
[2-4,8J
[3,4 J
[2-4J
[3,4 J
[2, 3, 8 J
[2,3 J
[2, 4, 6, 10J
[2,4J
[2,4 J
[2,4J
[2,4,6J
[2,4J
[2,4,8J
[2, 4J
[2, 4, 8 J
[2, 4J
[2, 4J
[2J
[2, 4J
[2, 6 J
[2,4,6J
[2, 4J
[2-4,11,12J
[2,3J
[2-5, 13J
[2, 3, 14 J
[2-4,15J
[2-4J
[3,4 J
[2,4J
[2,4 J
-
8/10/2019 alcock1984.pdf
3/5
C. B. ALCOCK et al.:VAPOUR PRESSURES OF METALLIC ELEMENTS 311
Table 2-cont.
Element, Temperaturestate A B C D range Refs
2 3 4 5 6 7
Cr sol 6.800 -20733 0.4391 -0.4094 298-2000 [2,4JMo sol 11.529 -34626 -1.1331 298-2500 [2-4 J
Wsol 2.945 -44094 1.3677 298-2350 [2,4JWsol -54.527 -57687 -12.2231 -2200-2500 [4 JMn sol 12.805 -15097 -1.7896 298-m.p. [2,6JRe sol 11.543 -40726 -1.1629 298-2500 [2, 16JFe sol 7.100 -21 723 0.4536 -0.5846 298-m.p. [2,3,6JFe liq 6.347 -19574 m.p.-2IOO [2JRu sol 9.755 -34154 -0.4723 298-m.p. [2 JOs sol 9.419 -41198 -0.3896 298-2500 [2,6JCO sol 10.976 -22576 -1.0280 298-m.p. [2,6,17JCO liq 6.488 -20578 m.p.-2150 [2JRh sol 10.168 -29010 -0.7068 298-m.p. [2 JRh liq 6.802 -26792 m.p.-2500 [2 JIr sol 10.506 -35099 -0.7500 298-2500 [2J
Ni sol 10.557 -22606 -0.8717 298-m.p. [2,3JNiliq 6.666 -20765 m.p.-2150 [2, 3JPd sol 9.502 -19813 -0.9258 298-m.p. [2, 18, 19JPd liq 5.426 -17899 m.p.-2100 [2 J
Pt sol 4.882 -29387 1.1039 -0.4527 298-m.p. [2,20JPt liq 6.386 -26856 m.p.-2500 [2JCU sol 9.123 -17748 -0.7317 298-m.p. [2,3,8JCU liq 5.849 -16415 m.p.-1850 [2,3,21 JAg sol 9.127 -14999 -0.7845 298-m.p. [2, 6, 8JAg liq 5.752 -13 827 m.p.-1600 [2JAu sol 9.152 -19343 -0.7479 298-m.p. [2 JAu liq 5.832 -18024 m.p.-2050 [2 JZn sol 6.102 -6776 298-m.p. [2, 3, 8JZn liq 5.378 -6286 m.p.-750 [2JCd sol 5.939 -5799 298-m.p. [2,6,8JCd liq 5.242 -5392 m.p.-650 [2 JHg liq 5.116 -3190 298-400 [2, 6, 8JCe sol 6.139 -21 752 298-m.p. [2,5,7JCe liq 5.611 -21200 m.p.-2450 [2,7,21 JPr sol 8.859 -18720 -0.9512 298-m.p. [2JPr liq 4.772 -17315 m.p.-2200
[2 JNd sol 8.996 -17264 -0.9519 298-m.p. [2,5,6JNd liq 4.912 -15824 m.p.-2000 [2,22JSm sol 9.988 -11 034 -1.3287 298-m.p. [2,23 JEu sol 9.240 -9459 -1.1661 298-m.p. [2,5,7JGd sol 8.344 -20861 -0.5775 298-m.p. [2,6JGd liq 5.557 -19389 m.p.-2250 [2 JTbsol 9.510 -20457 -0.9247 298-m.p. [2,5-7JTb liq 5.411 -18639 m.p.-2200 [2JDy sol 9.579 -15336 -1.1114 298-m.p. [2, 7, 24 JHo sol 9.785 -15899 -1.1753 298-m.p. [2, 5, 6 JEr sol 9.916 -16642 -1.2154 298-m.p. [2,6, 25, 26 JEr liq 4.688 -14380 m.p.-1900 [2 ]Tm sol 8.882 -12270 -0.9564 298-1400 [2, 6 JYb sol 9.111 -8111 -1.0849 298-900 [2,5,6JLu sol 8.793 -22423 -0.6200 298-m.p. [2,6JLu liq 5.648 -20302 m.p.-2350 [2 J
Th sol 8.668 -31483 -0.5288 298-m.p. [4,8,9JTh liq -18.453 -24569 6.6473 m.p.-2500 [2,9J
Pa sol 10.552 -34869 -1.0075 298-m.p. [7,9,27.28 ]
Pa liq 6.177 -32874 m.p.-2500 [9 JU sol 0.770 -27729 2.6982 -1. 5471 298-m.p. [2,4,5,8,9 JUliq 20.735 -28776 -4.0962 m.p.-2500 [4,9]
Np sol 19.643 -24886 -3.9991 298-m.p. [2,9JNpliq 10.076 -23378 -1.3250 m.p.-2500 [9 ]
Pu sol 26.160 -19162 -6.6675 298-600 [2,4,9,29JPu sol 18.858 -18460 -4.4720 500-m.p. [2,4,9,29JPu liq 3.666 -16658 m.p.-2450 [4,9JAm sol 11.311 -15059 -1.3449 298-m.p. [7,9,27JCm sol 8.369 -20364 -0.5770 298-m.p. [9JCmliq 5.223 -18292 m.p.-2200 [9 ]
-
8/10/2019 alcock1984.pdf
4/5
312 C. B. ALCOCK et al.: VAPOUR PRESSURES OF METALLIC ELEMENTS
Table 3. "Precisely fitted" equations of the vapour pressures for the elements
logp(atm) =A + B T-1 + Clog T+ D Tl0-3
Element, Temperature
state A B C D range
2 3 4 5 6
Li sol 7.790 -8423 -0.7074 298-m.p.
Li liq 8.409 -8320 -1.0255 m.p.-l000Na 1iq 8.400 -5634 -1.1748 m.p.-700
Kliq 8.233 -4693 -1.2403 m.p.-600
Rb 1iq 8.316 -4275 -1.3102 m.p.-550
Cs liq 8.232 -4062 -1.3359 m.p.-550
Be sol 4.933 -16869 0.6521 -0.3210 298-m.p.
Ca sol 4.751 -9278 0.5348 -0.6766 298-m.p.
Sr sol 4.809 -8385 0.4150 -0.5970 298-m.p.
Ba sol 8.403 -9524 -0.8280 -0.5551 298-m.p.
Al sol 7.124 -17246 0.0639 -0.3369 298-m.p.
Alliq 10.578 -16946 -1.3133 m.p.-1800
Ga 1iq 3.624 -13829 0.7579 -0.3141 m.p.-1600
In sol 8.532 -12680 -0.8495 298-m.p.
In liq 9.919 -12568 -1.5298 0.3377 m.p.-1500
TI sol 8.994 -9624 -0.9887 298-m.p.
Tl1iq 8.628 -9383 -1.0086 m.p.-l100
Sn sol 8.274 -15834 -0.7398 298-m.p.Sn liq 2.719 -15107 0.8036 -0.1033 m.p.-1850
Pb sol 8.336 -10303 -0.8782 298-m.p.
Pb liq 8.532 -10093 -1.0750 m.p.-1200
Y sol 6.421 -22138 0.2848 -0.3099 298-m.p.
Y liq 13.745 -22215 - 2.1235 m.p.-2300
La sol 7.514 -22553 -0.3323 0.0062 298-m.p.
La liq 6.524 -21977 -0.1667 m.p.-2450
Ti sol 7.704 -24772 0.1252 -0.3752 298-m.p.
Ti liq 16.370 -25229 -2.6574 m.p.-2400
Zr sol 7.779 -31376 -0.0354 -0.1658 298-m.p.
Zr liq 1.584 -28764 1.3555 m.p.-2500
Hfsol 8.936 -32449 -0.5041 -0.0331 298-m.p.
V sol 7.553 -27008 0.1970 -0.1712 298-m.p.
Nb sol 7.596 -37729 0.1441 -0.0706 298-2500
Mo sol 8.186 -34387 -0.0374 -0.1914 298-2500
Wsol -0.557 -43830 2.5145 -0.2074 298-2350
Wsol -110.184 -28414 35.4537 -3.6057 2200-2500Mn sol 6.504 -14794 0.4354 -0.6608 298-m.p.
Re sol 9.368 -40550 -0.4647 -0.1053 298-2500
Ru sol 5.944 -33895 0.7895 -0.2381 298-m.p.
Os sol 10.356 -41273 -0.6908 0.0459 298-2500
Co sol 6.436 -22348 0.5578 -0.4319 298-m.p.
Rh sol 8.721 -28923 -0.2168 -0.1076 298-m.p.
Ir sol 9.679 -35042 -0.4773 -0.0497 298-2500
Ni sol 9.397 -22547 -0.4663 -0.1114 298-m.p.
Pd sol 7.824 -19728 -0.3414 -0.1560 298-m.p.
Pt liq 21.257 -30921 -3.8960 m.p.-2500
Cu sol 7.810 -17687 -0.2638 -0.1486 298-m.p.
Cu liq 11.209 -17427 -1.4742 m.p.-1850
Ag sol 7.715 -14935 -0.2779 -0.1701 298-m.p.
Au sol 8.035 -19291 -0.3496 -0.1276 298-m.p.
Au liq 10.298 -18898 -1.2222 m.p.-2050
Zn sol 8.435 -6923 -0.7523 298-m.p.
Cd sol 8.405 -5944 -0.8052 298-m.p.Ce sol 7.340 -21834 -0.3851 0.0266 298-m.p.
Ce liq 6.023 -21278 -0.1127 m.p.-2450
Pr sol 5.167 -18556 0.3775 -0.4546 298-m.p.
Pr liq 11.917 -18693 -1.9565 m.p.-2200
Nd sol 4.542 -17061 0.6421 -0.5233 298-m.p.Nd liq 12.396 -17249 -2.0554 m.p.-2000Sm sol 3.881 -10753 0.8499 -0.6986 298-m.p.Eu sol 6.479 -9340 -0.1659 -0.3600 298-m.p.
Gd sol 5.158 -20706 0.5450 -0.3265 298-m.p.
Gdliq 10.606 -20505 -1.3598 m.p.-2250Tb sol 6.460 -20307 0.1472 -0.3066 298-m.p.Tb liq 11.803 -20052 -1.7216 m.p.-2200
-
8/10/2019 alcock1984.pdf
5/5
C. B. ALCOCK et aI.: VAPOUR PRESSURES OF METALLIC ELEMENTS 313
Table 3. cont.-
Element, Temperaturestate A B C D range
2 3 4 5 6
Dy sol 7.184 -15217 -0.2717 -0.2355 298-m.p.Ho sol 6.502 -15734 -0.0278 -0.3146 298-m.p.Er sol 7.669 -16529 -0.4312 -0.2116 298-m.p.Tm sol 7.062 -12185 -0.3098 -0.2019 298-1400Lu sol 7.347 -22347 -0.1187 -0.1288 298~m.p.Lu liq 18.851 -23540 -3.5093 m.p.-2350Th sol 11.954 -31682 -1.6430 0.2519 298-m.p.Th liq 59.574 -36981 -16.3130 1.9822 m.p.-2500Pa sol 4.601 -34501 1.0093 -0.4616 298-m.p.Pa liq 10.230 -34019 -1.0555 m.p.-2500Np sol 11.585 -24562 -1.0343 -1.1906 298-m.p.Np liq 16.266 -24018 -3.2613 0.2585 m.p.-2500Pu sol 18.958 -17609 10.5178 - 8.7185 298-600Pu sol 93.527 -22254 -30.9041 8.4953 500-m.p.Pu liq 12.992 -17587 -2.9370 0.4145 m.p.-2450Am sol 6.977 -14854 0.1914 -0.4699 298-m.p.Cm sol 3.571 -20128 1.1098 -0.4830 298-m.p.Cmliq 19.537 -21434 -3.8591 m.p.-2200
REFERENCES
1. R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelleyand D. D. Wagman, Selected Values of the ThermodynamicProperties of the Elements. ASM, Metals Park, Ohio (1973).
2. C. B. Alcock and V. P. Itkin, to be published.3. D. R. Stull and H. Prophet, JAN AF Thermochemical Tables (2dedn),
Nat. Stand. Ref. Data Ser., Nat. Bur. Stand. (U.S.), 37 (1971); M. W.Chaseetal.,Supplements:J.phys. Chem.Ref. Data3,311-480 (1974);4, 1-175 (1975); 7,793-940 (1978); 11, 695-940 (1982).
4. L. V. Gurvich, I . V. Veits and V. A. Medvedev et aI.,Term odinam icheskie Svoist va I ndividual' nykh V eshches tv
(Thermodynamic Properties of Individual Substances), Vols 1-4.
Izdatel'stvo "Nauka", Moscow (1978-1982).5. D. D. Wagman, W. H. Evans and V. B. Parker et aI.,The NBS Tables
of chemical'thermodynamic properties, J. phys. Chem. Ref. Data 11,supplement 2 (1982).
6. I. Barin and O. Knacke, Thermochemical Properties of InorganicSubstances. Springer, Berlin (1973); I. Barin, O. Knacke and O.Kubaschewski, Thermochemical Properties of Inorganic Substances,Supplement. Springer, Berlin (1977).
7. V. A. Medvedev, G. A. Bergman and L. V. Gurvich et al.,Termicheskie Konstanty Veschchestv (Thermal Constants of
Substances), Vols 1-10. VINITI, Moscow (1965-1981).8. CODATA Recommended Key Values for Thermodynamics,
Codata Bull. 28 (1977).
9. F. L. Oetting, M. H. Rand and R. J. Ackermann, Thermodynamics ofActinide Elements and Compounds, Part 1. The Actinide Elements,IAEA, Vienna (1976).
10. Y. Takahashi, H. Kadokura and M. Yokokawa, J. chem. Therm.15,65 (1983).
11. W. Bendick and W. Pepperhoff, J. Phys. F: Metal Phys. 12, 1085(1982).
12. W. M. Cash and C. R. Brooks, J. chem. Therm. 14, 351 (1982).13. C. B. Alcock, K. T. Jacob and S. Zador, Zirconium: Physico-
Chemical Properties of its Compounds and Alloys, Spec. Issue No.6, pp. 7-65. IAEA, Vienna (1976).
14. Ya. I. Gerassimov, V. M. Glasov and V.B. Lazarev et aI., Dokl. Akad.N auk SSSR 235, 846 (1977).
15. P. J. Spencer, Hafnium: Physico-Chemical Properties of itsCompounds and Alloys, Spec. Issue No.8, pp. 9-53. IAEA, Vienna(1981).
16. L. P. Filippov and F. G. EI'darov, J. Eng. Phys. 32, 180 (1977).17. A. S. Normanton, Metal Sci. 9, 455 (1975).18. O. Vollmer and R. Kohlhaas, Z. N aturf. 24a, 1669 (1969).19. A. P. Miiller and A. Cezairliyan, Int. J. Thermophys. 1,217 (1980).20. H. Yokokawa and Y. Takahashi, J. chem. Therm. 11, 411 (1979).21. L. K. Kuntz and R. G. Bautista, Metall. Trans. 7B, 107 (1976).22. L. A. Stretz and R. G. Bautista, High Temp. Sci. 7, 197 (1975).23. V. M. Polovov, Soviet Phys. JETP 38,775 (1974).24. E. B. Amitin, W. G. Bessergenev, Yu. A. Kovalevskaya and I. E.
Paukov, J. chem. Therm. 15, 181 (1983).25. J. M. McCormack, P. R. Platt and R. H. Saxer, J. chem. Engng Data
16, 167 (1971).26. R. W. Mar and R. G. Bedford, J.less-common Metals 71,317 (1980).27. R. O. A. Hall, J. A. Lee and M. J. Mortimer et aI., J.low Temp. Phys.
41, 397 (1980).28. M. H. Bradbury, J. less-common Metals 78,207 (1981).29. F. L. Oetting and R. O. Adams, J. chem. Therm. 15,534 (1983).