Materials Transactions, Vol. 46, No. 3 (2005) pp. 643 to 650 #2005 The Mining and Materials Processing Institute of Japan
Calculation of Thermodynamic Properties and Phase Diagrams for the CaO-CaF2, BaO-CaO and BaO-CaF2 Systems by Molecular Dynamics Simulation
Won-Gap Seo*1, Donghong Zhou*2 and Fumitaka Tsukihashi
Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan
The thermodynamic properties for the CaO-CaF2, BaO-CaO and BaO-CaF2 systems were calculated by molecular dynamics (MD) simulation using the simple Born-Mayer-Huggins type potential model. The interatomic potential parameters were determined by fitting the thermodynamic properties of pure CaO, BaO and CaF2. The calculated thermodynamic properties for CaO, BaO and CaF2 were in good agreement with measured results, and the superionic conductivity on the solid-solid phase transition of CaF2 has also been successfully assessed by MD simulation. The HM , SM and GM for each binary system were calculated based on the thermodynamic parameters obtained by MD simulation and thermodynamic solution model. The calculated enthalpy interaction parameters for the BaO-CaF2 system represented the possibility of formation of the compounds such as BaO CaF2 in the BaO-CaF2 system. The calculated phase diagrams for the CaO-CaF2 and BaO-CaO systems were in good agreement with experimentally measured and CALPHAD method results. The calculated eutectic points for the CaO-CaF2 and BaO-CaO systems were about 20 mol% CaO at 1650 K and about 20 mol% CaO at 2050 K, respectively. The BaO-CaF2 system has also been estimated the liquidus lines in the CaF2-rich and BaO-rich region by MD simulation.
(Received May 31, 2004; Accepted December 1, 2004) Keywords: molecular dynamics simulation, thermodynamics, phase diagram, calcium oxide, barium oxide, calcium fluoride
1. Introduction many obscure respects. Kemp et al.4) recently reported the phase diagram for the BaO-CaO system calculated by Molecular dynamics (MD) simulation is widely used as the CALPHAD (CALculation of PHAse Diagram) method, powerful tool for the calculation of structural, dynamical and which shows the eutectic point of 14 mol% CaO at 2180 K. thermodynamic properties of the molten slags and fluxes at The phase diagram for the BaO-CaF2 system measured by high temperature. Recently, the thermodynamic properties Kojima et al.5) partially represents the phase equilibrium up and phase diagrams for the multiphase molten slags and to about 15 mol% BaO in CaF2-rich region. The availability fluxes are generally calculated using computer-based soft- of phase diagrams for barium oxide ternary systems such as 1,2) 3) ware packages such as FactSage and Thermo-Calc. BaO-CaO-CaF2 system are also limited. These programs calculate the themochemical equilibria and Therefore, the purpose of present research is to determine phase diagrams in various systems by thermodynamic the optimum potential model for the calculation of thermo- modeling based on the thermodynamic databases. However, dynamic properties of the CaO-CaF2, BaO-CaO and BaO- the application of these calculation methods is limited CaF2 systems and calculate the thermodynamic properties for because the experimentally measured thermodynamic data- each binary system by MD simulation. Finally, the phase bases are required for the calculation of thermodynamic diagrams for the CaO-CaF2, BaO-CaO and BaO-CaF2 properties of multiphase molten slags and fluxes. On the systems are estimated from the thermodynamic parameters other hand, MD simulation is to calculate the thermodynamic obtained by MD calculation. properties based on the dynamic quantities of individual particles in the solid and fluid simulation cells without any 2. Molecular Dynamics Calculation basic database. Therefore, the thermodynamics properties of various systems which are difficult to be measured by 2.1 Interatomic potential experimental methods can be effectively estimated. The interatomic potential models of MD simulation for the The CaO-based slag systems such as the CaO-CaF2,CaO- oxide and halide systems have been proposed by Hirao et 6) 7–9) CaF2-SiO2 and BaO-CaO-CaF2 systems are generally used in al., Belashchenko et al. and many other researchers. steelmaking process. Especially, the CaO-based slag systems These interatomic potential models show good agreement containing barium oxide are attractive with the possibility of with structural properties of solid, glass and liquid phases application in hot metal pretreatment on their high basicity measured by experiments. However, these models have a and low melting temperature. However, in spite of the limitation for the calculation of thermodynamic properties importance of these slag systems, the thermodynamic such as fusion data of the CaO, BaO and CaF2 system. properties and phase diagrams of barium oxide systems have In this study, the potential energy for MD simulation was calculated by the summation of pairwise interactions be- tween ions i and j that was the Busing approximation of Born- *1Graduate Student, The University of Tokyo. *2Formerly Graduate Student, Department of Advanced Materials Science, Mayer-Huggins form of eq. (1). Graduate School of Frontier Sciences, The University of Tokyo. Now at Mitsubishi Electric Corporation, Wakayama 640-8686, Japan 644 W.-G. Seo, D. Zhou and F. Tsukihashi 2 The atomic configurations of initial cells for solid phases Zi Zje i þ j rij ðrÞ¼ þ f ðb þ b Þ exp ð1Þ were taken from the respective unit cell structures. The CaO ij r 0 i j b þ b ij i j and BaO crystal structures were composed of 1000 (Ca 500 where rij is the interatomic distance between ions i and j, Zi is and O 500) and 1000 (Ba 500 and O 500) atoms according to the valence of the ion i, e is the electron charge, f0 is the an array of 5 5 5 unit cells of rocksalt structure. The 11 standard force of 6:9478 10 N (units constant), i and bi CaF2 crystal structure was composed of 1500 (Ca 500 and F are the repulsive radius and softness parameter of the ion i, 1000) atoms according to an array of 5 5 5 unit cells of respectively. The interatomic pairwise potential terms of CaF2 structure. The atomic configurations of initial cells for eq. (1) represent the Coulomb and short-range repulsion liquid phases were set to be random in the cubic cell. The interactions without the dispersion terms. In this study, for total number of atoms was taken from 1000 to 1500. The the calculation of thermodynamic properties in the molten densities of initial cells for CaO, BaO and CaF2 liquid phases 3 3 binary CaO-CaF2, BaO-CaO and BaO-CaF2 systems, the were adopted to be 3340 kg/m , 5720 kg/m and 3180 kg/ interatomic potential parameters were calculated based on m3, respectively based on the densities of solid CaO, BaO the thermodynamic properties, especially fusion properties and CaF2 at room temperature and the densities of CaO- such as melting temperature and enthalpy of fusion of CaO, CaF2, BaO-CaO and BaO-CaF2 systems were determined to 3 3 BaO and CaF2. The interatomic potential parameters for CaO be 3180–3340 kg/m , 3340–5720 kg/m and 3180–5720 kg/ were taken from Matsumiya et al.10) that was successfully m3, respectively. All simulations have been verified using reproduced the thermodynamic properties of CaO as shown systems of 3000 atoms and there have not noticed relevant in Fig. 1. The optimum interatomic potential parameters for differences. BaO and CaF2 were calculated by fitting the thermodynamic The periodic boundary conditions were employed for each properties of BaO and CaF2 with measured results by fixing simulation system. The long-range Coulomb interactions the interatomic potential parameters of Ca-Ca, Ca-O and O-O have been summated by Ewald method. The equations of pairs for CaO. The interatomic potential parameters used in motion were integrated by fifth-order Gear’s predictor- this study are listed in Table 1. corrector algorithms using a time step t ¼ 1 10 15 s. The run durations of all simulations were carried out for 2.2 Methods for calculation 30000 time steps. At the region around the critical points The MD simulations were carried out using the isobaric such as phase transition temperatures, the simulations were and isothermal (N-p-T) ensemble. Temperature is controlled carried out using long runs up to 100000 time steps. The by velocity scaling method. Pressure is controlled by simulations for solid phases were started from the room Parrinello and Rahmann method at atmospheric pressure. temperature structures of each solid crystal and then heated up to the required temperatures. The simulations for liquid phases were heated to the initial temperature of 4000 K and 300 thermally equilibrated during the 30000 time steps in order to stabilize the highly energetic atomic configurations of initial Present work cells, and then were cooled stepwise from 4000 to 1400 K. In 250 (Heating from solid phase) Present work this study, the effect of cooling rate on the MD calculation results of all simulation systems has been verified using 200 (Cooling from liquid phase) 11) cooling rate of 0.1 K per step and relevant differences were , kJ/mol Observed not observed. Therefore, in this study, the effect of cooling
1000K 150
H rate was assumed to be negligible. The various properties for - T
H the each system were calculated by statistical analyses of 100 velocities and positions data after reaching the thermal equilibrium of each stimulation system. All MD calculations 50 were carried out using WinMASPHYC program (Fujitsu). Enthalpy, Enthalpy, CaO 0 3. Results and Discussion
1000 1500 2000 2500 3000 3500 4000 3.1 Pure CaO, BaO and CaF2 Temperature, K The enthalpies for solid and liquid phases of CaO, BaO and Fig. 1 Calculated and observed enthalpies of solid and liquid CaO as a CaF2 were calculated as a function of temperature. The function of temperature. enthalpies of simulated system can be directly calculated from the internal energy, pressure and volume values obtained by MD calculation. The calculated enthalpies are Table 1 Parameters of interatomic potential used for simulation. compared with observed values at the sufficiently high reference temperatures above the Debye temperature to Zi i (nm) bi (nm) neglect the quantum correction terms in this study. The Ca 2 0.19995 0.02101 enthalpy of simulated system (HT) can be calculated by Ba 2 0.25500 0.02685 eq. (2). The internal energy (UT), which is given by eq. (3) is O 2 0.18400 0.01300 obtained as the sum of potential and kinetic energy calculated F 1 0.14848 0.01160 by MD simulation. The heat capacity at constant pressure Calculation of Thermodynamic Properties and Phase Diagrams for the CaO-CaF2, BaO-CaO and BaO-CaF2 Systems 645
240 250 Present work Present work (Heating from solid phase) 200 (Heating from solid phase) Present work 200 Present work (Cooling from liquid phase) (Cooling from liquid phase) 11) 160 Observed 11) , kJ/mol Observed 150 , kJ/mol 1000K 1000K 120 H H - - T T H 100 H 80
50 40 Enthalpy, Enthalpy, Enthalpy, Enthalpy, CaF 0 BaO 0 2
1000 1500 2000 2500 3000 3500 800 1200 1600 2000 2400 2800 Temperature, K Temperature, K
Fig. 2 Calculated and observed enthalpies of solid and liquid BaO as a Fig. 3 Calculated and observed enthalpies of solid and liquid CaF2 as a function of temperature. function of temperature.
Table 2 Calculated and observed thermodynamic properties for CaO, BaO and CaF2.
CaO BaO CaF2 Observed Calculated Observed Calculated Observed Calculated Melting 3200 50 3210 10 2285 5 2290 10 1691 5 1700 10 temperature (K) fusH (kJ/mol) 79.5 55.2 58.6 27.5 29.7 20.0 4.8 2.1 H (kJ/mol) trs (1424 K 20) (1265 K 10)
(Cp), eq. (4), can be calculated from the temperature the perfect crystal cells without defects such as vacancy and dependence of enthalpy calculated by eq. (2). dislocation, are in good agreement with observed results.11) Therefore, the potential model used in this study is HT ¼ UT þ PVT ð2Þ X X reasonable to the calculation of thermodynamic properties 3 of CaO, BaO and CaF systems. The calculated thermody- UT ¼ ijðrÞþ NkT ð3Þ 2 i 6 Temperature, K Liquid-CaF (2000K) 2 2000 1800 1600 1400 1200 4 Ca-Ca -7 ) r Ca-F -1 ( s ij 2 g 2 F-F CaF 2 0 -8 β -CaF2 (1500K) 4 2 -9 0 α-CaF (800K) 4 2 -10 D Present work F Pair distribution functions, distribution Pair D Present work 2 Ca 12) Self diffusion coefficients, log D, m coefficients, Self diffusion D Derrington et al. 0 F 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 -11 0.5 0.6 0.7 0.8 0.9 Distance, nm 3 -1 10 / T, K Fig. 4 Calculated pair distribution functions for -CaF2, -CaF2 and liquid Fig. 6 Calculated self-diffusion coefficients of Ca and F ions for -CaF2 CaF2. and liquid CaF2 at various temperatures with measured results. ions can be estimated by the slopes of mean square increase with increasing time. These results show that the Ca displacements calculated as a function of time. The mean ions do not diffuse in solid CaF2, on the other hand the F ions square displacements (MSD) and the self-diffusion coeffi- in -CaF2 diffused from the regular site of CaF2 lattice. cients of ions can be calculated by eqs. (6) and (7), Figure 6 shows the self-diffusion coefficients of Ca and F respectively. ions in -CaF2 and liquid CaF2. The self-diffusion coef- MSD ¼hjrðtÞ rð0Þj2ið6Þ ficients of F ions in -CaF2 calculated by MD simulation are in good agreement with measured results by Derrington et 1 D ¼ ðhjrðtÞ rð0Þj2iÞ ð7Þ al.12) The pair distribution functions, mean square displace- t 6 ments and self-diffusion coefficients of CaF2 assessed in this where rðtÞ and rð0Þ are the position of the ions at time t and work are also in good agreement with previous researchers’ initial position of the ions at zero time, respectively. himeans investigations calculated by Monte Carlo calculation13,14) and the ensemble average, D is the self-diffusion coefficient. MD simulation by using soft-core potential model15) and Figure 5 shows the mean square displacements of Ca and F shell model.16) ions calculated as a function of time for -CaF2 (800 K), - CaF2 (1500 K) and liquid CaF2 (2000 K). The mean square 3.2 CaO-CaF2, BaO-CaO and BaO-CaF2 systems displacements of Ca and F ions in -CaF2 show constant 3.2.1 Calculation of enthalpy of mixing, entropy of values with time. However, the F ions in -CaF2 show drastic mixing and Gibbs energy of mixing The enthalpies of mixing for the CaO-CaF2, BaO-CaO and BaO-CaF2 systems can be calculated by MD simulation at 0.15 various compositions and temperatures. The enthalpy of mixing was calculated as a difference between the enthalpy 2 Ca ions of solution at certain composition and the sum of the F ions enthalpies of pure components according to eq. (8). M ¼ ð þ ÞðÞ 0.10 H HA B XAHA XBHB 8 where HA B is the molar enthalpy of A and B binary solution, HA and HB are the standard molar enthalpies of component A 2000K and B, XA and XB are the mole fractions of component A and 0.05 B, respectively. Figures 7(a), (b) and (c) show the enthalpies of mixing for the CaO-CaF2, BaO-CaO and BaO-CaF2 systems calculated Mean square displacements, nm 800K as a function of composition at various temperatures. The 1500K enthalpies of mixing of each binary system show the negative 0.00 values in a whole composition, and they do not show the 0 1 2 3 4 5 large temperature dependence. Especially, the enthalpy of Time, ps mixing of the BaO-CaF2 system shows the exothermic Fig. 5 Mean square displacements of Ca and F ions as a function of time behavior larger than those of the CaO-CaF2 and BaO-CaO for -CaF2 (800 K), -CaF2 (1500 K) and liquid CaF2 (2000 K). systems, due to the effect of interactions between Ba and F Calculation of Thermodynamic Properties and Phase Diagrams for the CaO-CaF2, BaO-CaO and BaO-CaF2 Systems 647 2 -100 (a) CaO-CaF BaO-CaF 2 2 0 -120 kJ/mol , M H ∆ ), kJ/mol -2 2 CaF -140 X · BaO X -4 /( 1400K M H -160 1600K 1600K 1800K ∆ 1800K 2000K 2200K 2000K Enthalpy of mixing, Enthalpy 2400K 2600K -6 2200K 2800K 3000K -180 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction BaO Mole fraction CaO 2 M Fig. 8 Calculated enthalpy interaction parameters ( H =ðXBaO XCaF2 Þ) (b) BaO-CaO as a function of composition for the BaO-CaF2 system at various temperatures. (standard state: liquid). 0 kJ/mol , M H ∆ parameters, and the mixture become stable state at 50 mol% -2 BaO. This result suggests the possibility of formation of the compounds such as BaO CaF2 in the BaO-CaF2 system. The thermal properties such as internal energy, volume and pressure of the systems can be calculated by MD simulation. -4 2200K 2400K However, the entropy of mixing cannot be directly calculated 2600K 2800K by MD simulation. Therefore, in this study, the entropy of Enthalpy of mixing, Enthalpy 3000K mixing was calculated by the fractions of ions in the binary -6 melts, assuming that the CaO-CaF2, BaO-CaO and BaO- 0.0 0.2 0.4 0.6 0.8 1.0 CaF melts are completely ionic solution and all ions in the Mole fraction CaO 2 melts have random configurations. These assumptions are (c) BaO-CaF supported by calculated pair distribution functions, gijðrÞ and 2 0 running coordination numbers, NijðRÞ of each binary system. The running coordination numbers for the simulated system kJ/mol , can be calculated by eq. (9). M Z H R ∆ -20 2 NijðRÞ¼4 i r gijðrÞdr ð9Þ 0 where i is the partial number density of ion i and R is the distance of the first minimum of gijðrÞ. The calculated pair -40 distribution functions and running coordination numbers of 1400K 1600K Ca-Ca, Ca-O, Ca-F, O-O, O-F and F-F in 50 mol% CaO- Enthalpy of mixing, Enthalpy 1800K 2000K 50 mol% CaF2 melt at 2400 K shown in Fig. 9 represent that 2200K all ions in the simulation cell are randomly distributed, which -60 0.0 0.2 0.4 0.6 0.8 1.0 do not have specific ionic bonding such as network structure. Mole fraction BaO Typically, the molten slags and fluxes containing BaO and CaO show the high basicity, and BaO and CaO in these melts Fig. 7 Calculated enthalpies of mixing as a function of composition for the have the role of network modifier.17,18) Therefore, these (a) CaO-CaF2, (b) BaO-CaO and (c) BaO-CaF2 systems at various oxides in melts are characterized by the ionic nature, and do temperatures. (standard state: liquid). not have covalent bonding structure. The molten slags and fluxes containing CaF2 show the decrease of viscosity and 18) melting temperature with the addition of CaF2 in melts. It ions in the BaO-CaF2 melts. Figure 8 shows the enthalpy also represents that the Ca and F ions in melts do not have any M interaction parameters ( H =ðXBaO XCaF2 Þ) calculated as a structure, and all ions are randomly distributed. These function of composition at various temperatures of the BaO- previously measured results are in good agreement with the CaF2 system. The calculated enthalpy interaction parameters results of structural properties in the melts calculated by MD show the minimum values at each temperature when the XBaO simulation. Therefore, these assumptions of random config- equals 0.5. It represents that the BaO-CaF2 system shows the uration applied for the calculation of entropy of mixing of strong composition dependence of the enthalpy interaction each binary system in this study are reasonable. 648 W.-G. Seo, D. Zhou and F. Tsukihashi 6 ) Ca-Ca r ( ij Ca-O N 4 Ca-F O-O 2 O-F numbers, F-F Running coordination 0 50mol%CaO-50mol%CaF ) 2 r ( ij 2400K g 4 2 functions, Pair distribution distribution Pair 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Distance, nm Fig. 9 Calculated pair distribution functions and running coordination Fig. 10 Calculated entropies of mixing for the CaO-CaF2, BaO-CaO and numbers of Ca, O and F ions in the 50 mol% CaO-50 mol% CaF2 melt at BaO-CaF2 systems as a function of composition. 2400 K. results are lower than observed values with decreasing The configuration entropy makes a great contribution to temperature. As stated above, these differences are consid- the entropy of mixing in the ionic melts, and the thermal ered due to the underestimation of enthalpies of fusion for entropy is numerically much less than the configuration pure BaO, CaO and CaF2 based on the overestimation of entropy. In this study, the thermal entropy is assumed to be Coulomb energy by assuming that the BaO, CaO and CaF2 in negligible. The entropy of mixing is expressed by eq. (10). this study are perfect ionic crystal. M A+B A B Figure 13 shows the calculated phase diagram for the S ¼ SConf ðXASConf þ XBSConf Þð10Þ CaO-CaF system compared with measured results by Ries et 0 !1 2 Xn al.19) and Chatterjee et al.20) The calculated eutectic compo- B N !C sition and temperature for the CaO-CaF system are about B i C 2 B i¼1 C 20 mol% CaO and 1650 K, respectively. The calculated phase SConf ¼ k lnB Qn C @ A diagram is in good agreement with measured results of the ðNi!Þ i¼1 eutectic point of 20 mol% CaO at 1630 K. Figure 14 shows the calculated phase diagram for the A+B A B where SConf , SConf and SConf are the configuration entropies of BaO-CaO system. The phase diagram for the BaO-CaO the A and B binary, pure A and pure B solutions, k is the system has not been measured experimentally. Recently, 4) Boltzmann’s constant and Ni is the number of ion i per mole Kemp et al. reported the phase diagram with the eutectic of system. Figure 10 shows the calculated entropies of point about 14 mol% CaO at 2180 K obtained by CALPHAD mixing for the CaO-CaF2, BaO-CaO and BaO-CaF2 systems. method. They calculated the phase diagram of BaO-CaO The Gibbs energies of mixing for the CaO-CaF2,BaO- system from estimated excess thermodynamic properties. CaO and BaO-CaF2 systems were calculated as a function of The excess enthalpies and entropies were obtained by the composition at various temperatures. The Gibbs energy of relationship of Redlich-Kister coefficients with empirically mixing was calculated from the enthalpy and entropy of fitted parameters based on previously measured thermody- mixing based on the thermodynamic parameters obtained namic properties of various oxide and halide mixtures. In from MD simulation and ionic solution model. Figures 11(a), Fig. 14, the phase diagram for the BaO-CaO system (b) and (c) show the calculated Gibbs energies of mixing for calculated by MD simulation shows the eutectic point about the CaO-CaF2, BaO-CaO and BaO-CaF2 systems. 20 mol% CaO at 2050 K. This result has a difference about 3.2.2 Calculation of phase diagrams for the CaO-CaF2, 6 mol% CaO and 130 K with the eutectic point reported by 4) BaO-CaO and BaO-CaF2 systems Kemp et al. However, the calculated phase diagram for the The phase diagrams for the CaO-CaF2, BaO-CaO and BaO-CaO system shows similar shape as phase equilibrium BaO-CaF2 systems were estimated by Gibbs energies of obtained by CALPHAD method. The calculated and ob- mixing calculated as a function of composition at various served eutectic points for the CaO-CaF2 and BaO-CaO temperatures. The Gibbs energies of fusion of pure BaO, CaO systems are summarized in Table 3. and CaF2 for the calculation of phase diagram were evaluated Figure 15 shows the calculated and measured phase from the heat capacities at constant pressure based on the diagrams for the BaO-CaF2 system. The phase diagram for 5) temperature dependence of enthalpies calculated by MD the BaO-CaF2 system has been measured by Kojima et al. simulation, eq. (4). Figure 12 shows the Gibbs energies of Only CaF2-rich region up to about 15 mol% for the BaO- fusion of pure BaO, CaO and CaF2 calculated as a function of CaF2 system was measured. In the present work, the phase 11) temperature with observed results. These calculation diagram for the BaO-CaF2 system cannot be also calculated Calculation of Thermodynamic Properties and Phase Diagrams for the CaO-CaF2, BaO-CaO and BaO-CaF2 Systems 649 4 60 (a) CaO-CaF 2 0 Present work kJ/mol 11) , kJ/mol , Observed M 40 G -4 fusion o ∆ CaO G ∆ -8 20 BaO -12 -16 1600K 1800K 2000K 2200K 0 2400K 2600K CaF2 Gibbs energy of mixing, Gibbs energy -20 2800K 3000K Gibbs energy of fusion, Gibbs energy 0.0 0.2 0.4 0.6 0.8 1.0 -20 Mole fraction CaO 1200 1600 2000 2400 2800 3200 Temperature, K 0 (b) BaO-CaO Fig. 12 Calculated and observed Gibbs energies of fusion of pure BaO, CaO and CaF as a function of temperature. kJ/mol 2 , M G -4 ∆ -8 3200 CaO-CaF 2 -12 2800 2200K 2400K 2600K 2800K Gibbs energy of mixing, Gibbs energy 3000K -16 2400 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction CaO 2000 (c) BaO-CaF K Temperature, 0 2 Present work 1600 Ries et al.19) , kJ/mol Chatterjee et al.20) M G ∆ 1200 -20 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction CaO Fig. 13 Calculated phase diagram for the CaO-CaF system. -40 2 1400K 1600K -60 1800K 2000K Gibbs energy of mixing, Gibbs energy 2200K 3500 BaO-CaO 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction BaO 3000 Fig. 11 Calculated Gibbs energies of mixing as a function of composition for the (a) CaO-CaF2, (b) BaO-CaO and (c) BaO-CaF2 systems at various temperatures. (standard state: liquid). 2500 2000 in a whole composition range because of the possibility of K Temperature, formation of the compounds such as BaO CaF2 based on the 1500 results of calculated enthalpy interaction parameters of the Present work W.J.M. van der Kemp et al. 4) BaO-CaF2 system. However, the liquidus lines in CaF2-rich 1000 and BaO-rich region of the BaO-CaF2 system have been 0.0 0.2 0.4 0.6 0.8 1.0 estimated by MD simulation. In Fig. 15, the calculated Mole fraction CaO liquidus line of the BaO-rich region in the BaO-CaF2 system 21) shows drastic decrease with the addition of CaF2. Lee et al. Fig. 14 Calculated phase diagram for the BaO-CaO system. 650 W.-G. Seo, D. Zhou and F. Tsukihashi Table 3 Calculated and observed eutectic points for the CaO-CaF2 and BaO-CaO systems. CaO-CaF2 BaO-CaO Calculated4Þ Observed19;20Þ Calculated Calculated (CALPHAD) Temperature (K) 1633 1650 2180 2050 XCaO (mol%) 20 20 14 20 2500 model. 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