N. N. Eremin

Crystal structure of larnite β-Ca2SiO4 and specific features of polymorphic transitions in dicalcium orthosilicate

The crystal structure of larnite, a natural analog of synthetic β-Ca2SiO4, has been determined: a = 5.5051(3) Å, b = 6.7551(3) Å, c = 9.3108(5) Å, β = 94.513(4)o, sp. gr. P21/n, Z = 4, and R1 = 0.0532 for 1071 reflections with I > 2σ (I). Larnite was found in skarn xenoliths (Lakargi, Kabardino-Balkaria, Russia). The mineral structure is based on a heteropolyhedral glaserite-like framework of interconnected Ca polyhedra and isolated [SiO4] tetrahedra. Based on an analysis of the layer-by-layer packing of atoms in the structures of larnite and other Ca2SiO4 polymorphs, the structural features and mechanisms of transitions from high-temperature (α, α′L, and α′H) to low-temperature (β and γ) Ca2SiO4 modifications, as well as their relationship with natural glaserite-like orthosilicates (merwinite Ca3Mg[SiO4]2 and bredigite Ca7Mg[SiO4]4), have been considered. The most likely atomic arrangement in hypothetical Ca2SiO4 models has been calculated by the method of atomistic potentials.

Computer modeling of the local structure, mixing properties, and stability of binary oxide solid solutions with corundum structure

An original technique of computer modeling of substitutional solid solutions has been applied to Al2O3-Cr2O3, Al2O3-Fe2O3, and Fe2O3-Cr2O3 binary systems. The parameters of semiempirical interatomic potentials were optimized using the experimentally studied structural, elastic, and thermodynamic properties of pure components. Among point defects, the most energetically favorable ones for all three oxides are Schottky vacancy quintets. To model (Mx1M1 − x2)2O3 solid solutions, 4 × 4 × 1 disordered supercells with M1: M2 cation ratios of 1: 5, 1: 2, 1: 1, 2: 1, and 5: 1 have been constructed in the cation sublattice containing 192 atoms. The mixing enthalpy and volume, interaction parameters, bulk moduli, and vibrational entropy were found by minimizing the interatomic interaction energy in supercells with the symmetry P1. Calculations of the Gibbs energy made it possible to estimate the fields of stability of the Al2O3-Cr2O3 and Al2O3-Fe2O3 solid solutions; these estimates were compared with the experimental data. Histograms of M-M, M-O, and O-O interatomic distances were constructed and the local structure was analyzed for the Al1.0Cr1.0O3, Al1.0Fe1.0O3, and Fe1.0Cr1.0O3 compositions.

Atomistic simulations of mixing properties and the local structure of the (Ca, Sr)10[PO4]6F2 solid solution

The thermodynamics of mixing is computed for eight different distributions of Sr and Ca over the M1 and M2 cation sites in the fluorapatite solid solution. Calculations are carried out for a 4×4×4 supercell via the semi-empirical approach using the GULP package. In the solid solution with the most energetically favorable distribution, Sr tends to occupy the M2 site rather than the M1 site and the x (Sr1): x (Sr2) ratio varies as a function of the Sr content. These structures are used for further investigation of the effect of mixing on the lattice parameters, local structure and elasticity of the Ca-Sr fluorapatite solid solution. Changes in the Sr2-F bond lengths as the Sr content increases turn out not to comply with Vegard’s rule. However, this deviation occurs in order to keep the linear dependence of the polyhedral volumes with the solid-solution composition. The obtained data allow us to estimate the structural relaxation parameters for both independent cation positions. Analysis of the bond sums also backs up the preference of Sr cations for the M2 site.

Computer modeling of the local structure, mixing properties, and stability of solid solutions of alkaline-earth metal oxides

A technique for the computer modeling of disordered binary oxide solid solutions MO-M′O in a wide composition range has been developed. The method of atomistic pair potentials was used for 4 × 4 × 4 supercells. The parameters of the potentials are optimized using the structural and elastic properties of pure components MgO, CaO, SrO, and BaO. The temperature dependences of the heat capacity and entropy are calculated for pure components. The excess mixing properties (enthalpy, volume, bulk modulus, vibrational entropy) are found for different compositions of MgxCa(1 − x)O, CaxSr(1 − x)O, and SrxBa(1 − x)O solid solutions. Temperature and composition dependences of the excess Gibbs energy were constructed, which made it possible to approximately estimate the critical decomposition temperatures and limits of component miscibility. Statistical analysis of lattice distortions in the first and second coordination spheres reveals a detailed picture of the solid-solution local structure.

Structure and thermodynamic properties of zircon-coffinite solid solutions according to the semiempirical atomistic simulation data

Structure and thermodynamic properties of zircon, coffinite, and zircon-coffinite solid solutions were subject to semiempirical atomistic simulation on the assumption of compositional disordering of mixed crystals: (Zr1 − x, Ux)SiO4, where x = 0.02, 0.05, 0.08, 0.11, 0.14, 0.28, 0.50, 0.72, and 0.86. The solid solutions significantly depart from the Vegard and Retgers laws. The (Zr1 − x, Ux)SiO4 mixed crystal structure is characterized by anisotropic expansion (largely in the a and b directions) under growth in x related to anisotropy of structural relaxation degree of the cation-oxygen interatomic spacing in the (Zr, U)O8 polyhedron. Increase in x parameters is accompanied by increase in average size of cation-oxygen polyhedrons and silica-oxygen tetrahedrons and by growth of interatomic spacing dispersion; maximum dispersion values are observed at x = 0.5–0.6. The distortions in local structures of ZrO8 and UO8 dodecahedrons and silica-oxygen tetrahedrons in the solid solution were analyzed on the basis of calculated functions of interatomic distance distribution. The obtained results demonstrate the possibility to assess numerically the structural (geometrical) disordering degree of the compositionally disordered solid solution depending on its composition. The calculated thermodynamic characteristics of solid solutions forecast the following solubility range limits: 2 mol % USiO4 in zircon and 5 mol % ZrSiO4 in coffinite under ∼1750 K.

Thermodynamics of mixing in an isostructural solid solution: Simulation methodologies and application to the rutile-cassiterite system

Abstract The accuracies of two different approaches to model thermodynamic mixing properties of solid solutions are explored using the rutile-cassiterite solid solution as an example. Both methods employ an expansion of the configurational enthalpy in terms of pairwise interactions energies. In the first method the partition function is directly computed from the excess energies of all Ti/Sn configurations within a 2 × 2 × 4 supercell. In the second method the free energy of mixing is calculated by a thermodynamic integration of the thermally averaged enthalpies computed with the Monte Carlo method using an 8 × 12 × 16 supercell. The phase relations derived from Monte Carlo simulations agree well with the available experimental data, under the condition that the free energy is corrected for the effect of the excess vibrational entropy. The direct calculation of the partition function provides reasonable phase relations only when the configurational entropy is corrected to be consistent with the ideal mixing in the high-temperature limit. Advantages and drawbacks of the both approaches are discussed. The findings are generally applicable to models of isostructural solid solutions.

Atomistic and Ab initio modeling of CaAl2O4 high-pressure polymorphs under Earth’s mantle conditions

Semi-empirical and ab initio theoretical investigation of crystal structure geometry, interatomic distances, phase densities and elastic properties for some CaAl2O4 phases under pressures up to 200 GPa was performed. Two independent simulation methods predicted the appearance of a still unknown super-dense CaAl2O4 modification. In this structure, the Al coordination polyhedron might be described as distorted one with seven vertices. Ca atoms were situated inside polyhedra with ten vertices and Ca–O distances from 1.96 to 2.49 Å. It became the densest modification under pressures of 170 GPa (density functional theory prediction) or 150 GPa (semi-empirical prediction). Both approaches indicated that this super-dense CaAl2O4 modification with a “stuffed α-PbO2” type structure could be a probable candidate for mutual accumulation of Ca and Al in the lower mantle. The existence of this phase can be verified experimentally using high pressure techniques.

Atomistic computer modeling of the local structure and mixing properties of a grossular-uvarovite solid solution

An original methodology for the atomistic computer modeling of solid solutions was applied for the study of the mixing properties and local structure of the grossular-uvarovite, i.e., Ca3Al2[SiO4]3 Ca3Cr2][SiO4]3, garnet series. The parameters of the interatomic potentials for end members of this series were optimized using experimental data on their structural, elastic, and thermodynamic characteristics. The optimized model of the potentials allowed us to describe the elastic, structural, and thermodynamic characteristics of grossular and uvarovite and estimate the energy of point defects in these crystal structures. Calculations of the mixing properties and local structure for seven different compositions of the solid solution were carried out on a “Chebyshev” supercomputer (Moscow State University) in a 2 × 2 × 4 supercell of the garnet-type structure containing 2560 atoms. Mixing properties, such as the enthalpy of mixing, parameters of interaction, excess mixing volume, deviation of bulk modulus from additivity, and the vibrational and configuration contribution to the entropy of mixing, were determined. This allowed us to estimate the stability field for the grossular-uvarovite solid solution. Histograms of the interatomic distances M-O (M = Ca, Al, Cr, Si) and O-O in supercells were plotted and the parameters of relaxation and changes of the CrO6 and AlO6 octahedron volumes were estimated. The data of the simulation are quite consistent with the experimental data on this system and supplement it significantly.

Computer modeling of the local structure and mixing properties of a solid solution of MgAl2O4-MgCr2O4

An original method of the atomistic computer modeling of substitutional solid solutions is applied to the noble spinel MgAl2O4-magnesia chromite MgCr2O4 binary system. The parameters of the interatomic potentials in the partially ionic approximation are optimized using the experimental values of the structural, elastic, and thermodynamic characteristics of these minerals. The point defect formation energy is estimated. The modeling of Mg(AlxCr1 − x)2O4 solid solutions is carried out in a supercell of the 4 × 4 × 4 structural type of spinel that contains 3584 atoms; the GULP 3.4.9 program, which is implemented in the SKIF Chebyshev supercomputer (Moscow State University), is used. The mixing properties of the solid solution such as the mixing enthalpy, the interaction parameters, the mixing volumes, the deviations of the compression moduli from additivity, and the oscillatory entropy were determined. Calculations of the Gibbs energy have yielded the assessments of the stability fields of the MgAl2O4-MgCr2O4 solid solution and the comparisons of these assessments with the experimental data. Histograms of interatomic spacings are plotted and the values of the relaxation parameters of the Cr-O and Al-O bonds are estimated; these values agree well with the experimental values obtained by measuring the optical absorption spectra on a Cr3+ ion.

Diffusion Paths for Interstitial Impurities in Different Polymorphic Modifications of Niobium Silicide Nb 5 Si 3

Structural models of the α, β, and γ modifications of Nb5Si3 silicides, which are used as a reinforcing phase in composites obtained in situ based on the Nb‒Si system, have been constructed by computer simulation methods. A geometric analysis of unit cells is performed using the H-poisk program to estimate the voids existing in the structures. The results of measuring the number of voids and their sizes are reported. A conclusion about possible diffusion paths of interstitial boron, carbon, nitrogen and oxygen atoms is drawn based on the calculation results, and the solubility of these impurities in the structure of each Nb5Si3 modification is estimated.