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Thermodynamic properties of mixing in the ternary (Ba,Sr,Ra)SO 4 solid solution are determined using first principles based total energy calculations and Monte Carlo simulations. Two levels of theory, which correspond to the regular mixing and the generalized Ising model, are considered. The results show that the regular mixing parameters increase along the row of Ba-Ra, Ba-Sr and Sr-Ra binary systems proportionally to the squared difference of molar volumes of the end-members. The magnitudes of pairwise interactions similarly increase along the same row, manifesting a tendency to short-range ordering (SRO). In the (Ba,Sr)SO 4 system the SRO effect is approximately equivalent to a 40% decrease in the value of the regular mixing parameter. The ternary solid solution is well described as a regular mixture with the binary parameters W BaRa = 2.47 ± 0.22, W BaSr = 4.95 ± 0.75 and W SrRa = 17.50 ± 1.40 kJ/mol. These values imply that admixing RaSO 4 to the (Ba,Sr)SO 4 solid solution stabilizes Ba-rich and destabilizes Sr-rich compositions. Consequently, an addition of a small amount of RaSO 4 to a Sr-rich solid solution leads to a nucleation of a Ba-and Ra rich phase. This phenomenon, predicted in our thermodynamic modelling study, is directly confirmed by our experiments on recrystallizing a powder of celestite with traces of Ba in the presence of an aqueous Ra-bearing solution. At a measurably high content of Ra in the system Ra-uptake by celestite occurs via a formation of a Ra-rich phase. The aqueous concentration of Ra in such systems would be governed mainly by the common anion effect caused by the relatively high solubility of Sr-rich sulphates. At lower Ra contents the retention of Ra would be enhanced both by the common anion and the dilution effects. Our simulations with the GEM-Selektor code predict that the optimum condition for Ra uptake is achieved when the barite solid solution contains 10 ± 5 mol % of SrSO 4 .

The order-disorder phase transition in the Nd x Zr 1-x O 2-0.5x system is studied by complementary techniques which include wet chemical synthesis of a series of compositions with various Nd/Zr ratios with the final annealing at 1873 K, X-ray diffraction, oxide melt solution calorimetry and ab initio thermodynamic modeling.Our structural data indicate the transition from ordered to disordered pyrochlore at x ~ 0.31at a temperature of1873 K. Our calorimetric data show a transition enthalpy of ~30 kJ/mol, which corresponds to an entropy of disordering of ~16 J/K/mol. The latter value is significantly smaller than the configurational entropy of transition computed under the

[1] Thermodynamic properties of MgSiO 3 tetragonal majorite have been calculated at high pressures and temperatures within the quasi-harmonic approximation based on density functional theory using the local density approximation (LDA) and the generalized gradient approximation (GGA). The LDA results compare exceptionally well with measured thermodynamic properties. A classical Monte Carlo simulation based on results from a cluster expansion method demonstrates that disorder between magnesium and silicon in the octahedral sites in MgSiO 3 majorite does not occur below 3600 K at transition zone pressures. The ensuing calculations on phase boundaries of MgSiO 3 between majorite, perovskite, and ilmenite show that a much better agreement with experiment can be obtained by using GGA rather than LDA, for LDA underestimates the transition pressures by as much as 11 GPa. The Clapeyron slopes predicted by GGA and LDA are close to each other: 0.9-1.7 MPa/K for majorite-perovskite transition, 6.9-7.9 MPa/K for majorite-ilmenite transition, and −7-−3 MPa/K for ilmenite-perovskite transition. The triple point predicted by GGA is located at 21.8 ± 1 GPa and 1840 ± 200 K which is ∼400 K lower in temperature than most experimental estimates. This result suggests that ilmenite is restricted to lower temperatures and that the majorite to ilmenite transition may occur in cold subducting slabs in the transition zone. Our calculation also reveals that wadsleyite decomposes to an assemblage of majorite plus periclase above 2280 K with a large negative Clapeyron slope (−22-−12 MPa/K) and that ringwoodite decomposes to ilmenite plus periclase below 1400 K (1.2 MPa/K). These two decomposition transitions may influence hot plumes and cold slabs near 660 km depth, respectively. Further calculations show that discontinuities in density, bulk modulus, and bulk sound velocity associated with the majorite to perovskite transition in MgSiO 3 are much larger than those from the postspinel transition in Mg 2 SiO 4 at conditions close to 660 km depth. This suggests that the large density discontinuity at 660 km depth as proposed by PREM (9.3%) might be accounted by a piclogite compositional model or marginally accounted by a pyrolite compositional model with, for example, 50 vol % ringwoodite, 45 vol % majorite, and 5 vol % other phases (such as calcium perovskite) at the bottom of the transition zone, provided that the density contrast between majorite and perovskite will not be greatly altered by the presence of other elements such as Fe, Al, Ca, and H. On the other hand, the smaller density discontinuity at 660 km depth as derived from impedance studies (4-6%) disfavors sharp contributions to seismic discontinuities from the majorite to perovskite transition.

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Thermodynamic mixing properties and subsolidus phase relations of the rhombohedral carbonate system, (1-x)·CaCO 3 -x·MgCO 3 , were modelled with static structure energy calculations based on well constrained empirical interatomic potentials. Relaxed static structure energies of a large set of randomly selected structures in a 4x4x1 supercell of R3c calcite (a = 4.988 Å, c = 17.061Å) were calculated with the General Utitility Lattice Program (GULP). These energies were cluster expanded in a basis set of 12 pair-wise effective interactions. Temperature-dependent enthalpies of mixing were calculated by the Monte Carlo method. Free energies of mixing were obtained by thermodynamic integration of the Monte Carlo results. The calculated phase diagram is in good agreement with experimental phase boundaries.