Thermodynamic data A tutorial course Session 5: More complicated solution phases Alan Dinsdale “Thermochemistry of Materials” SRC

This session Thermodynamic models for more complicated sorts of solution phases – Chemical ordering – Gas phases – Reciprocal systems (eg. Molten salts) – Oxide phases (eg. Spinels, Halite) – Liquids with short range ordering Oxides, slags, mattes

Chemical Ordering

Chemical ordering Phase diagrams with ordered phases are quite common Generally concerned with BCC_B2 (ordered BCC_A2), FCC_L12 and FCC_L10 (ordered FCC_A1) Ideally we would like to be able to model the disordered phases and ordered phases within the same dataset These can give rise to first order transformations (two phase regions) or second order transformations (dashed line)

Fe-Ni L1 2

Au-Cu L1 2 L1 0

Al-Ni FCC_A1 FCC_L12

Cu-Zn BCC_A2 BCC_B2 Order – disorder reaction

Fe-Ti BCC_B2 BCC_A2

Example (A, B) 0.5 (A, B) 0.5 Assume – G(A:A) and G(B:B) = 0 – G(A:B) = G(B:A) = At low temperature A and B atoms will occupy different sublattices (ordered) As the temperature increases more mixing will occur until eventually the solution becomes disordered

A:B

Gibbs energy of ordering

Model for chemical ordering We would like to model thermodynamic properties of the disordered phase from experimental data (eg phase diagram, enthalpies) using standard Redlich Kister expression Add on Gibbs energy of ordering to this disordered data set Compound Energy Formalism has the correct behaviour but gives residual Gibbs energy which needs to be subtracted off

The model works well for a wide range of chemical ordering reactions However it does not take into account short range effects For more sophisticated treatments it may be necessary to use 4 or even 8 sublattices – difficult to use

Gas phase

Model for the gas phase

Gas phase speciation

Gibbs energy of mixing

Data for gas phase species Data for gas phase species usually derived through mixture of experiment and statistical mechanics Structure of species, bond distances, vibrational and electronic frequencies deduced from spectroscopy Statistical mechanics then used to calculate heat capacity and entropy Enthalpy of formation derived from enthalpies of combustion, vapour pressure measurements Ab-initio calculations of enthalpy of formation generally not accurate enough

Isomers Ab-initio can be very useful in determining the relative stability of isomers eg NaCeI 4 Both isomers will be present in the equilibrium mixture

Reciprocal systems

This is where mixing occurs on more than one sublattice eg. Fcc (Fe, V) 1 (C, Va) 1 The reciprocal reaction V:Va + Fe:C = V:C + Fe:Va strongly favours Fe and VC. This strong reaction reduces solubility and creates a miscibility gap across the diagonal

Crystalline oxide phases

Halite phase – “FeO” (wüstite), CaO (lime), MgO (periclase), NiO (bunsenite) Spinel phase – Fe 3 O 4 (magnetite), FeAl 2 O 4 (hercynite), FeCr 2 O 4 (iron chromite), MgAl 2 O 4 (spinel) Corundum – Al 2 O 3 (sapphire), Cr 2 O 3, Fe 2 O 3 (haematite) Olivine – Mg 2 SiO 4 (forsterite), Fe 2 SiO 4 (fayalite) Clinopyroxene – MgSiO 3 (clinoenstatite), pigeonite, CaMgSi 2 O 6 (diopside) Orthopyroxene – MgSiO 3 (enstatite), FeSiO 3 (ferrosilite)

Halite phase (Ca +2, Fe +2, Fe +3, Mg +2, ….., Va) 1 (O -2 ) 1 Wüstite (Fe +2, Fe +3, Va) 1 (O -2 ) 1 – Allows the range of homogeneity to extend to compositions richer in oxygen than FeO

Spinel phase: Fe 3 O 4 Can be modelled as (Fe +2, Fe +3 ) 1 (Fe +2, Fe +3 ) 2 (O -2 ) 4 The first sublattice is tetrahedrally coordinated and the second octahedrally coordinated This is a reciprocal system with the corners of the square – (Fe +2 ) 1 (Fe +2 ) 2 (O -2 ) 4 (net charge -2) – (Fe +2 ) 1 (Fe +3 ) 2 (O -2 ) 4 (net charge 0) – (Fe +3 ) 1 (Fe +2 ) 2 (O -2 ) 4 (net charge -1) – (Fe +3 ) 1 (Fe +3 ) 2 (O -2 ) 4 (net charge +1) The charge neutral material is represented the a line on the reciprocal diagram. The position on the line is determined by minimum in Gibbs energy

“Normal” spinel Inverse spinel

More components

Complicated liquids

A number of system show very negative Gibbs energies of mixing in the liquid phase Not possible to use the standard Redlich- Kister model to represent the thermodynamic properties Examples – Cu-S, Fe-O, CaO-SiO2

Miscibility gaps

Three main approaches to assess data for these systems Associated solution model – Assume the liquid contains species (like the gas) but they interact in a non-ideal way Ionic Liquid model – Uses the two sublattice model with ions, charged species and charge vacancies. Essentially it in one big reciprocal system Modified quasichemical model focusing on bonds rather than chemical entities All models have their strong points and failings. We do need a universal model for the liquid. We don’t have one yet !

Associated solution model In a gas phase there will be a number of species mixing ideally – C, C 2, C 3, C 4, C 5, CO, CO 2, C 2 O, C 3 O 2, O, O 2, O 3 The amount of each species will be determined through obtaining a minimum in the Gibbs energy for a given temperature and pressure The associated solution model postulates that there are similar species in the liquid, or at least they might correspond to compositions of stable crystalline phases – CaO, Ca 2 SiO 4, CaSiO 3, SiO 2 Again the amount of these species will be obtained my minimising the Gibbs energy. Note that these species interact in a complicated way

Good points and bad points It works ! Tends to underestimate miscibility gaps Has various parameters which can be used to improve agreement with experimental data Not really very predictive No unique set of parameters eg. play off between species Gibbs energies and interactions between the species Not really physically based Does have capability to model other sorts of properties eg. viscosities

Ionic Liquid model Based on Compound Energy Model – eg. Liquid salt system could be represented by (Li +, Cs + ) 1 (F -, I - ) 1 – This is a reciprocal system and there is a very strong tendency for the small ions to bond together and for the big ions to bond together – The combination LiF+CsI is strongly favoured over LiI+CsF – This leads to big miscibility gap across the diagonal of the reciprocal system ….. which is found experimentally, although this model does tend to over predict miscibility gaps

Liquids with different valency ions (Li +, Ca +2 ) p (F -, Br - ) q – Ratio of sites p:q between the two sublattices varies from 1:1 to 1:2 – The model defines q to be the average charge on the cation sublattice and p to adopt a value to maintain electroneutrality – Can be extended to model silicates (Ca +2 ) p (O -2, SiO 4 -4, SiO 3 -2, SiO 2 ) q – Looks rather different from associate model but under certain circumstances the data are interchangeable

Ionic liquid model can be used for metal – oxygen systems. Here it is necessary to introduce charged vacancies (Fe +2, Fe +3 ) p (O -2, Va -q ) q Again q is set to be average charge on the cation sublattice. Here though the vacancies also have a charge of –q For simple systems the model works well, however it always tends to over-predict miscibility gaps. This can make it very difficult to model multicomponent systems

Good points and Bad points It works well for simple systems Tends to over-estimate miscibility gaps and doesn’t really have parameters available for controlling them Makes modelling of multicomponent systems difficult

Modified Quasi-chemical model

Often the minimum is not at 50%

Quasi-chemical approach to molten salts

LiF-KCl diagonal

The quasi-chemical model is really the only one which works for molten salts It is horrendously complicated The associate model predicts complete mixing between the pure salts – incorrect entropy of mixing The ionic liquid model overestimates the tendency towards formation of miscibility gaps The quasichemical model reflects to tendency for preferential bonding between pairs of cations and anions (first nearest neighbour interactions) Second nearest neighbour interactions require use of “quadruplets”

Good points and bad points Seems to have better predictability for high affinity metallic systems Appears to work well for oxide systems (according to the authors) but beware of small ternary interactions which have a big effect, the possible need for associates, and systems which are just not well represented The only really good model for molten salts …. but it is a nightmare mathematically

General thoughts about liquids We do not have a good model – Function of temperature (strange cp behaviour, metallic glasses) – Function of composition (metals, slags, salts, aqueous) Lots of miscibility gaps – Cu and Cu 2 S, Cu 2 S and S, CaSiO 3 and SiO 2, Cu and Cu 2 O We would like a single model to represent the thermodynamic properties across all composition and temperature space Challenge for the next generation !