Thermodynamics and thermophysical properties of liquid Fe-Cr alloys

1
Thermodynamics and thermophysical properties
of liquid Fe-Cr alloys

• Rada Novakovic
• National Research
• Council (CNRIENI)
• Genoa, Italy

2
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.

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What kind of input data are necessary for
modelling?

• 1. Thermodynamic data
• on mixing heat capacity enthalpy entropy
  Gibbs energies (integral excess).
• partial quantities activities (or chem.
  potentials).
• 2. Phase diagram information
• type of alloy system segregating or compound
  forming
• 3. 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

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4
The Fe-Cr system
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Thermodynamic data of the Fe-Cr liquid phase

• 11Xiong An improved thermodynamic modeling of
  the FeCr system down to zero kelvin coupled
  with key experiments
• 86Mas The Fe-Cr phase diagram
• 76Hul81AB82HS87AS previous assessments of
  the p.d.
• 93BLee The reassessment of the Fe-Cr phase
  diagram
• 93BLee T1873K The optimised term of the
  excess Gibbs free energy
• the enthalpy of mixing 84Bat
• the activities 80Mar69Fru69Gil98Zai.
• 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).

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Results of calculations
?- phase energ. favoured ( AB ) ? Weak
influence on the energetics of the Fe-Cr liquid
phase.
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Results of calculations

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• SURFACE TENSION
• SURFACE TENSION MODELS
• Binary systems
• Ternary systems
• Geometric models
• EXAMPLES Fe-Cr, Al-Nb-Ti

9

• 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.

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Subtracting Butlers equ. for both components,

• and combining with
• and taking into account the bulk (surface) phase
  activity coefficients obtained by
  Fowler_Guggenheim method as
• and
• the ? and xs can be calculated. The surface
  tension can be calculated inserting xs into the
  Butlers equation.
• MATGEN-IV.3 summer school on Materials for
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11
Surface tension calculations of binary systems

• Models based on Butlers 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

12
Surface tension calculations of ternary systems

• Models based on Butlers 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

13

• Geometric models
• Kohler
• Toop
• Chou

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15
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
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Surface tension reference data of Cr
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17
Surface tension reference data of Fe
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18
Results of calculations

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Results of calculations

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Results of calculations

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• 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.

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• 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) lt SCC(0, id) presence of chemical order
• SCC(0) gt SCC(0, id) segregation
• 2. -1 lt CSRO lt 0 ordering in the melt
• CSRO -1 complete ordering
• 0 lt CSRO lt 1 segregation
• CSRO 1 phase separation

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Results of calculations
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• 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) gt SCC (0, id) segregation ? Dm lt Did
• SCC(0) lt SCC (0, id) presence of chem. order ? Dm
  gt Did

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Results of calculations

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• 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
  ltlt0)
• negative deviations (segregating alloys, ?H
  gtgt0).
• 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!)

27

• 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)

28

• Recently, we proposed the following viscosity
• equation
• where mi and ?i (iA,B) are parameters that can
  be calculated from the experimental data.

29
Results of calculationsviscosity of some binary
systems
30
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

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• Thank you for your attention!

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