MPIB model

The MPIB model gives very accurate equations of state, binding energies and phase transformation pressures for alkali-halides and alkaline-earth oxides [36].It appears to he the only electron gas potential model to give a good account of the B1 and Bl phases of CaO. We show in seetion 4 that it also gives excellent results when applied to more eomplex minerals. However, this success is attained at a eonsiderable inerease in eomputational complexity. Furthermore, there is no simple way to implement lattiee dynamics with MPIB potentials. 

As illustrations, we present results from calculations on a few silicates and oxides selected from those discussed in the introduction. Our intent here is to illustrate some of the strenghts and weaknesses of the VIB and MPIB models. We do not attempt to present complete modeling results for any given material. Since our primary interest is the reliable simulation of high pressiue properties, we mostly limit the examples to those properties for which there are some relevant high pressure data. 

Figure 4. Equation of state for silicate perovskites. a) Both VIB and MPIB models give a good account of the compressibility and density of CaSiO 3 perovskite, which i s predicted to be cubic, in accord with data, b) Calculated MgSiO 3 equations of state compared with data. The MEG calculation [66] used rigid ions it gave poor absolute densities but excellent compressibility and thermal expansivity. The breathing ion methods (MPIB and PIB) fare much better. R H and K J stand for Ross and Hazen [67] and Knittle and Jenaloz [68], respectively. LAPW calculation from Stixrude and Cohen [23].

Practical applications require an explicit form for and and a choice of ionic electron densities n (r). Early formulations of the theory used electronic charge densities derived from Hartree-Fock atomic codes. For a review of the various implementations of electron gas potentials we refer the reader to Wolf and Bukowinski [28], Gordon and LeSar [34] and Chizmeshya et al. [29]. In the remainder of this report we concentrate on topics relevant to applications of the VIB [28, 35] and MPIB [36] models. Both models... 

The MPIB and VIB [35] models attempt to improve the aeeuraey of the earlier models and to overcome some of the difficulties associated with the use of Hartree-Fock wave functions. We have already stated some of the advantages of using the density functional approach to obtain ionic wave-functions they were amply demonstrated by the PIB model which replaced the Hartree-Fock equation with a density functional implementation of the Dirac equation [21]. The MPIB is so called because it also adopts the density functional approach to obtain ionic charge densities (specifically anon-relativistic version derived from the Herman-Skillman [48],but replaces the potential inside the Watson shell with the spherical average of the potential due to the rest of the material, IF (r)[36] ... 

Other thermodynamic parameters like thermal expansivity and eom-pressibility follow directly from standard relationships (e.g., [50]. Elastic constants are readily calculated from the acoustic phonon branches of the VIB model (e.g., Chizmeshya, et al., [29]). MPIB elastic constants have not yet been calculated. 

Figure 1. a) MgO equation of state. VIB model calculations the calculated B1 equation of state without scaling is from Chizmeshya et al. [29]. The other calculations include oxygen scaling in the kinetic energy density, b) MPIB room temperature equation of state compared to date and a band structure derived equation of state (APW). 

Figure 10. Estimated solubility between MgSiO 3 and CaSi03 perovskites. The solvus curves are estimates based on an MPIB averaged atom model [62]. At temperatures below the curves, the solution decomposes into two perovskites with compositions indicated by the intercepts of the solvus curves with the corresponding constant temperature line.

Figure 11. Effect of Ca on distortion of (Mgi j Ca c)Si03 perovskite. Results based on MPIB averaged atom model [62],...

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