1. Thermodynamic Models and Databases for Molten Salts and Slags Arthur Pelton Centre de Recherche en Calcul Thermochimique École Polytechnique, Montréal, Canada  Model parameters obtained by simultaneous evaluation/optimization of thermodynamic and phase equilibrium data for 2-component and, if available, 3-component systems.  Model parameters stored in databases  Models used to predict properties of N-component salts and slags  When combined with databases for other phases (gas, metal, etc.) can be used to calculate complex multi-phase, multi-component equilibria using Gibbs energy minimization software.

2. Reciprocal molten salt system Li,K/F,Cl  Liquidus projection

3. Section of the preceding phase diagram along the LiF-KCl diagonal  A tendency to de-mixing (immiscibility) is evident.  This is typical of reciprocal salt systems, many of which exhibit an actual miscibility gap oriented along one diagonal.

4. Molecular Model  Random mixture of LiF, LiCl, KF and KCl molecules.  Exchange Reaction: LiCl + KF = LiF + KCl  G EXCHANGE < O  Therefore, along the LiF-KCl «stable diagonal», the model predicts an approximately ideal solution of mainly LiF and KCl molecules.  Poor agreement with the observed liquidus.

5. Random Ionic (Sublattice) Model  Random mixture of Li + and K + on cationic sublattice and of F - and Cl - on anionic sublattice.  Along the stable LiF-KCl diagonal, energetically unfavourable Li + - Cl - and K + - F - nearest-neighbour pairs are formed. This destabilizes the solution and results in a tedency to de-mixing (immiscibility) – that is, a tedency for the solution to separate into two phases: a LiF-rich liquid and a KCl-rich liquid.  This is qualitatively correct, but the model overestimates the tedency to de-mixing.

6. Ionic Sublattice Model with Short-Range-Ordering  Because Li + - F - and K + - C l - nearest-neighbour are energetically favoured, the concentrations of these pairs in solution are greater than in a random mixture:  Number of Li + - F - pairs = (X Li X F + y) Number of K + - Cl - pairs = (X K X Cl + y) Number of Li + - Cl - pairs = (X Li X Cl - y) Number of K + - F - pairs = (X K X F - y)  Exchange Reaction: LiCl + KF = LiF + KCl  This gives a much improved prediction.

7.  For quantitative calculations we must also take account of deviations from ideality in the four binary solutions on the edges of the composition square.  For example, in the LiF-KF binary system, an excess Gibbs energy term, G E, arises because of second-nearest-neighbour interactions: (Li-F-Li) + (K-F-K) = 2(Li-F-K) (Generally, these G E terms are negative:.)  is modeled in the binary system by fitting binary data.  In predicting the effect of within the reciprocal system, we must calculate the probability of finding an (Li-F-K) second-nearest- neighbour configuration, taking account of the aformentioned clustering of Li + - F - and K + - Cl - pairs. Account should also be taken of second-nearest-neighbour short-range-ordering.

8. Liquidus projection calculated from the quasichemical model in the quadruplet approximation (P. Chartrand and A. Pelton)

9. Experimental (S.I. Berezina, A.G. Bergman and E.L. Bakumskaya) liquidus projection of the Li,K/F,Cl system

10. Phase diagram section along the LiF-KCl diagonal  The predictions are made solely from the G E expressions for the 4 binary edge systems and from  G EXCHANGE. No adjustable ternary model parameters are used.

11. SILICATE SLAGS  The basic region (outlined in red) is similar to a reciprocal salt system, with Ca 2 + and Mg 2 + cations and, to a first approximation, O 2 - and (SiO 4 ) 4 - anions.  The CaO-MgO-SiO 2 phase diagram.

12.  Exchange Reaction: Mg 2 (SiO 4 ) + 2 CaO = Ca 2 (SiO 4 ) + 2 MgO  G EXCHANGE < O  Therefore there is a tedency to immiscibility along the MgO-Ca 2 (SiO 4 ) join as is evident from the widely-spaced isotherms.

13. Associate Models  Model the MgO-SiO 2 binary liquid assuming MgO, SiO 2 and Mg 2 SiO 4 «molecules»  With the model parameter  G°< 0, one can reproduce the Gibbs energy of the binary liquid reasonably well: Gibbs energy of liquid MgO-SiO 2 solutions

14.  The CaO-SiO 2 binary is modeled similarly.  Since  G EXCHANGE < 0, the solution along the MgO- Ca 2 SiO 4 join is modeled as consisting mainly of MgO and Ca 2 SiO 4 «molecules».  Hence the tendency to immiscibility is not predicted.

15. Reciprocal Ionic Liquid Model (M. Hillert, B. Jansson, B. Sundman, J. Agren)  Ca 2 + and Mg 2 + randomly distributed on cationic sublattice  O 2 -, (SiO 4 ) 4 - and neutral SiO 2 species randomly distributed on anionic sublattice  An equilibrium is established: (Very similar to: O 0 + O 2 - = 2 O - )  In basic melts mainly Ca 2 +, Mg 2 +, O 2 -, (SiO 4 ) 4 - randomly distributed on two sublattices. Therefore the tendency to immiscibility is predicted but is overestimated because short-range-ordering is neglected.

16.  The effect of a limited degree of short-range-ordering can be approximated by adding ternary parameters such as:  Very acid solutions of MO in SiO 2 are modeled as mixtures of (SiO 2 ) 0 and (SiO 4 ) 4 -  Model has been used with success to develop a large database for multicomponent slags.

17. Modified Quasichemical Model A. Pelton and M. Blander  «Quasichemical» reaction among second-nearest-neighbour pairs: (Mg-Mg) pair + (Si-Si) pair = 2(Mg-Si) pair  G° < 0 (Very similar to: O 0 + O 2 - = 2 O - )  In basic melts: –Mainly (Mg-Mg) and (Mg-Si) pairs (because  G° < 0). –That is, most Si atoms have only Mg ions in their second coordination shell. –This configuration is equivalent to (SiO 4 ) 4 - anions. –In very basic (MgO-SiO 2 ) melts, the model is essentially equivalent to a sublattice model of Mg 2 +, Ca 2 +, O 2 -, (SiO 4 ) 4 - ions.

18.  However, for the «quasichemical exchange reaction»: (Ca-Ca) + (Mg-Si) = (Mg-Mg) + (Ca-Si)  G EXCHANGE < 0 Hence, clustering (short-range-ordering) of Ca 2 + -(SiO 4 ) 4 - and Mg 2 + -O 2 - pairs is taken into account by the model without the requirement of ternary parameters.  At higher SiO 2 contents, more (Si-Si) pairs are formed, thereby modeling polymerization.  Model has been used to develop a large database for multicomponent systems.

19. The Cell Model M.L. Kapoor, G.M. Frohberg, H. Gaye and J. Welfringer  Slag considered to consist of «cells» which mix essentially ideally, with equilibria among the cells: [Mg-O-Mg] + [Si-O-Si] = 2 [Mg-O-Si]  G° < 0  Quite similar to Modified Quasichemical Model  Accounts for ionic nature of slags and short-range- ordering.  Has been applied with success to develop databases for multicomponent systems.

20. Liquidus projection of the CaO-MgO-SiO 2 -Al 2 O 3 system at 15 wt % Al 2 O 3, calculated from the Modified Quasichemical Model

21. Liquidus projection of the CaO-MgO-SiO 2 -Al 2 O 3 system at 15 wt % Al 2 O 3, as reported by E. Osborn, R.C. DeVries, K.H. Gee and H.M. Kramer