Thermodynamics and thermophysical properties of liquid Fe-Cr alloys Thermodynamics and...

Thermodynamics Thermodynamics and thermophysical and thermophysical properties of liquid Fe-Cr alloysproperties of liquid Fe-Cr alloys

Rada NovakovicRada Novakovic

National Research

Council (CNR–IENI)

Genoa, Italy

Mixing behaviour of liquid binary alloys: energetic & structural factors

Observable indicators: Phase diagrams. Empirical factors – physical, chemical & structural

properties of alloy constituents (liquid metals), melting points, volume, first shell coordination, radius size, valence difference, electronegativity difference...

Thermodynamic functions – heat capacity, enthalpy, activity, excess Gibbs energy.

Microscopic functions – concentration fluctuations in the long wavelength limit & CSRO (Warren-Cowley short range order) parameter.

MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,ongoing research and open questions”, September 19-23, 2011, Lerici (SP), ItalySeptember 19-23, 2011, Lerici (SP), Italy

What kind of input data are necessary for modelling?

1. Thermodynamic dataon mixing: heat capacity; enthalpy; entropy; Gibbs

energies (integral & excess).partial quantities: activities (or chem. potentials). 2. Phase diagram informationtype of alloy system: segregating or compound

forming3. Thermophysical data: molar volume, surface

tension, viscosity of pure components.4. Structural data: coordination number; neutron

diffraction data to be transformed into the microscopic functions

5. Experimental data on Thermo-Physical properties of alloys: for a comparison with theoretical results


The Fe-Cr system


Thermodynamic data of the Fe-Cr liquid phase [11Xiong] An improved thermodynamic modeling of the Fe–Cr system

down to zero kelvin coupled with key experiments[86Mas] The Fe-Cr phase diagram[76Hul;81AB;82HS;87AS] previous assessments of the p.d.[93BLee] The reassessment of the Fe-Cr phase diagram[93BLee] T=1873K: The optimised term of the excess Gibbs free energy;the enthalpy of mixing [84Bat]; the activities [80Mar;69Fru;69Gil;98Zai]. [06Vre] The presence of interm. - phase [06Ter] The melting, the enthalpy of mixing, thermal diffusivity - by atomic

simulations

Comment: The Cr-Fe phase diagram can be considered as COMPLETE (although some measurements in the liquid phase are necessary).


Results of calculations

- phase energ. favoured ( AB )

Weak influence on the energetics of the Fe-Cr liquid phase.


SURFACE TENSIONSURFACE TENSION

SURFACE TENSION MODELS

Binary systems

Ternary systems

Geometric models

EXAMPLES: Fe-Cr, Al-Nb-Ti

Surface properties of liquid binary alloys:

surface segregation & surface tension

Butler(1932) published the paper proposing his well known equation:

( i = A, B), that gives the relation between the surface tension and thermodynamics of liquids in which the bulk and surface phases are in equilibrium.

bi

si

i

Bi

a

aTkln


and combining with

and taking into account the bulk (surface) phase activity coefficients obtained by Fowler_Guggenheim method asand

the and xs can be calculated. The surface tension can be calculated inserting xs into the Butler’s equation.

MATGEN-IV.3 summer school on “Materials for Generation IV reactors: MATGEN-IV.3 summer school on “Materials for Generation IV reactors: Fundamentals, ongoing research and open questions”,Fundamentals, ongoing research and open questions”, September 19-23, 2011, September 19-23, 2011,

Lerici (SP), ItalyLerici (SP), Italy

)]}1ln([ln)]1ln(){[ln/( xxSRT Bss

BBB

)lnln( BBAAxsM xxRTG

)}1ln()1ln()21{ln(2

ln sssss

sB xx

z

}ln)1ln()21{ln(2

ln sssss

sA xx

z

Subtracting Butler’s equ. for both components,)}ln(lnln){ln/( xxSRT A

ssAAA

Surface tension calculations of binary systems

* Models based on Butler’s equation

- Regular solution

- Subregular solution

- “Central” atom

- Compound Formation Model (CFM)

- Self Aggregating Model (SAM)

An interface Liquid / Gas :

& * Probabilistic Models

Singh et al.

Monolayer or Multilayers

Surface tension calculations of ternary systems

* Models based on Butler’s equation

- Regular solution- Subregular solution- “Central” Atom- Compound Formation Model (CFM)- Self Aggregating Model (SAM)

An interface Liquid / Gas

:

& * Geometric Models (from thermodynamic

calculations of mixing properties in the bulk)

SYMMETRIC- Kohler; Colinet; Muggianu

ASYMMETRIC- Toop; Bonnier; Hillert;

GENERALIZED - Chou

Monolayer

Geometric modelsKohlerKohler

ToopToop

ChouChou

31)31(1)31(3

1323

)23(3)23(2

3212

)12(2)12(1

21 xsxsxsxs

XX

XX

XX

XX

XX

XX

);()()1;(1

)1;(1 32

3

32

223

2321113

1

31112

1

2

XX

X

XX

XXXXX

X

XXX

X

X xsxsxsxs

3/2232

323/1132

312/1122

21 )()()()()()( XXxs

XXxs

XXxsxs XXXXXX

Iso-surface tension lines of liquid Al-Ti-Nb alloys calculated by the Butler equation for the regular solution model at 2073 K. The square symbol represents the composition location of the Ti46Al46Nb8 (at.%) in the Gibbs triangle and the corresponding surface tension calculated value


Surface tension reference data of Cr


Surface tension reference data of Fe


Microscopic functions (B-T) & Thermodynamics

For ideal solution the SCC(0) becomes

The CSRO parameter and SCC(0) are related to each other by

where Z is the coordination number.

BAidCC ccS )0(

1

1

)1(1

1)0(

Zcc

S

BA

cc

1

,,

1

,,

1

,,

2

2

)0(

NPTB

BBA

NPTA

AAB

NPTA

Mcc C

aaC

C

aaC

C

GRTS


Microscopic functions & local arrangements of atoms in the melt

SCC(0) and CSRO parameter indicate chemical order & segregation (phase separation):

SCC(0) – the nature of mixing

CSRO parameter – the degree of order

Criteria for mixing behaviour

1. SCC(0) < SCC(0, id) presence of chemical order

SCC(0) > SCC(0, id) segregation

2. -1 < CSRO < 0 ordering in the melt

CSRO = -1 complete ordering

0 < CSRO < 1 segregation

CSRO = 1 phase separation


The interdiffusion coefficient (Dm) can be given in terms of the SCC(0) by

For “ideal” alloys, SCC(0)= SCC(0,id)= cAcB, then

and finally combining the last two eqs. it is obtained,

The criteria for mixing behaviour:SCC(0) > SCC (0, id) segregation Dm < Did

SCC(0) < SCC (0, id) presence of chem. order Dm > Did

)0(

)0()( **

CC

idCC

ABBAm S

SDcDcD

idABBAABBAm DDcDcDcDcD )( **

)0(

)0(

CC

idCC

id

m

S

S

D

D


Viscosity Viscosity () of liquid alloys - the atomic level structure and interactions.

The composition dependence of of liquid alloys in respect to the linear low (ideal mixture):

- a linear variation (simple liquids, e.g. Ag-Au, Sn-Pb, Bi-Pb) - positive deviations (compound forming alloys, H <<0)- negative deviations (segregating alloys, H >>0).

Sometimes the viscosity of binary liquid alloys exhibits “strange” behaviour (Bi-Ga, Bi-Cu, Ga-Hg..), i.e. the same behaviour as their thermodynamic functions (according to the theory should be opposite!)

00BBAAid cc

In the framework of the QLT the viscosity, , is related to the SCC(0) and diffusion by:

For a thermodynamically ideal mixture,SCC(0)=SCC(0,id)=c(1-c) previous equ. becomes:

with

and for the viscosity of pure components (Stokes-Einstein)

Assuming 1 = 2 = =1, it is obtained the Stokes-Einstein type relation for diffusion and viscosity:

)0()(

CC

BA

A

B

B

A

id

B

S

CCCC

D

Tk

)(A

B

B

Amid

Bid

CC

D

Tk

idBB

BidB

BBid

AA

BidA

BA D

Tk

rD

Tkand

D

Tk

rD

Tk

33

idAB

idBA

idm DcDcD

Tk

DD BidB

idA

Recently, we proposed the following viscosity

equation:

where mi and i (i=A,B) are parameters that can be calculated from the experimental data.

)0())exp()exp(

(CC

BA

ABB

B

BAA

A

id

B

S

CC

Cm

C

Cm

C

D

Tk

Results of calculationsviscosityviscosity of some binary systems

Modelling of the interfacial properties of molten Pb / FeCr substrate system: Application of the

Phase Field Method

Study of thermodynamics and thermophysical properties of the Fe-Cr, Fe-O, Pb-O, Fe-Cr-Pb, Fe-Cr-Pb-O systems

Model formulation and implementation Collection of input parameters for the Pb-Fe and Pb-Cr systems Simulations, analysis of model parameters and validation with

experimental micrographs for the Pb-Fe and Pb-Cr systems Extension of the model and implementation towards ternary

system Pb-Fe-Cr Collection of input parameters for the Pb-Fe-Cr system Simulations for the interface between molten Pb / FeCr -

substrate system Comparison with experimental micrographs for Pb / Fe-Cr

diffusion couples


Thank you for your attention!


Thermodynamics and thermophysical properties of liquid Fe-Cr alloys Thermodynamics and...

Documents

Transcript of Thermodynamics and thermophysical properties of liquid Fe-Cr alloys Thermodynamics and...