V. S. Urusov

A geometric model of deviations from Vegard's rule

There is much evidence that X-ray measurements of sufficient accuracy reveal deviations from the linear dependence of unit-cell parameters on composition, i.e., departures from Vegards rule. The dependence of such deviations on composition for a random solid solution with one substitutional position (Ax1 Bx2C is usually of a parabolic form: δa=x1x2σ where σ is positive. Many attempts to explain these observations are based on elastic models. It is known that less than 50% of the predictions of these models are correct. An alternative model under consideration is a simple geometric one. It is concerned with secondary atomic displacements around substitutional defects, i.e., shifts of the second nearest neighbors. The result is structurally dependent and the analysis deals with binary solid solutions of B1 (CN=6), B3 (CN=4), and B2 (CN=8) structure types. For instance, in sodium chloride structure-type solid solutions, the following simple equation is valid, δh=(3/2)x1x2(R)2/R, where R is the difference in interatomic distances of pure components and R is the average interatomic distance. Calculations for NaCl−KCl, NaCl−NaBr, KCl−KBr, and other systems are in good agreement with experimental data.

Radiation resistance of LaPO4 (monazite structure) and YbPO4 (zircon structure) from data of computer simulation

The radiation resistance of the monazite LaPO4 and the compound YbPO4 (zircon structure type) has been investigated using the computer simulation. The number of Frenkel pairs, which are formed in the structure of these minerals after the passage of a primary knock-on thorium atom with an energy of 30 keV, has been calculated by the molecular dynamics method. The formation of Frenkel pairs and their recombination in the motion of recoil nuclei in the structure of the studied minerals have been discussed. It has been shown that the probability of the “survival” of Frenkel pairs in the LaPO4 monazite is significantly lower than in the YbPO4 compound. The tendency of these minerals toward amorphization under radiation damage has been described numerically. The obtained results have demonstrated that one of the main factors determining the radiation resistance of orthophosphates LnPO4 is the type of crystal structure, and the compounds with the monazite structure are more radiation resistant than the compounds with the zircon structure.

Electron Density distribution and bonding in silicates

This paper summarizes the recent results of the investigation of bonding in silicates obtained by precision X-ray diffraction. The experimental electron density distribution is compared with theoretical electron density maps calculated for model silicate molecules. The characteristic features of the chemical bonds in ortho-, ring-, chain- and framework silicates are discussed.

Murataite–Pyrochlore Series: A Family of Complex Oxides with Nanoscale Pyrochlore Clusters

identified murataite in a Synroc matrixwith imitators of HLRWs from PO Mayak, a radiochemicalfacility for production and reprocessing of nuclear fuel in theRussian Federation. Five volume percent of this phaseaccumulated about 40% of the total uranium present in thesample,andthisledtodetailedinvestigationsofthechemistryand properties of murataite, in particular, its chemicaldurability and radiation resistance.

Radiation resistance of the xenotime YPO4 from the computer simulation data

The radiation resistance of the mineral xenotime YPO4 has been investigated using computer simulation methods. The optimal criteria for the appropriate choice of the parameters of the interatomic potentials used for the simulation of α-decay in minerals have been proposed. The formation of a cascade of displaced atoms in the structure of xenotime after the passage of a primarily knocked thorium atom with an energy of 20 keV has been studied using the molecular dynamics method. The specific features of the formation and annealing of individual defects in the structure of xenotime have been considered using the Mott-Littleton method. The dependences of the energy of formation of Frenkel pairs and the probability of their annihilation during the annealing of a cascade of atomic displacements on the distance between the vacancy and the interstitial site have been analyzed within the framework of the supercell approximation.

A modular model of the crystal structure of the pyrochlore-murataite polysomatic series

This paper reports on the results of a structural investigation of an important group of synthetic compounds with derivative structures of the mineral murataite, a potential matrix for immobilization of radioactive wastes. A model describing the structure of the entire group of compounds is proposed on the basis of analyzing the results obtained using chemical (electron microprobe) analysis methods, high-resolution transmission electron microscopy (high-resolution electron images and microdiffraction patterns), and X-ray diffractometry of a large array of artificial murataite ceramics. In essence, the proposed structural model is as follows: in the structure, layers of two (pyrochlore and murataite) packing types alternate along the [111] direction of the cubic supercell, so that the resulting structures can undergo substitutional and displacive modulations. Experiments on irradiation of different murataite modifications with heavy ions demonstrate that these modifications have close values of the radiation resistance, which is higher than that of the pyrochlore coexisting with them.

Simulation of a defect region in KDP crystals doped with divalent iron ions. Comparison of defects induced by di-and trivalent metals

The crystal structure of FeII-doped KDP crystals was simulated with the use of specially developed partly covalent potentials. Different variants of introduction of impurity into the structure were analyzed. The M1 position was found to be more favorable for both isolated divalent and trivalent metal ions. Upon optimization, the coordinates of the FeII ion are (0.25, 0.44, 0.125). The FeII ions can aggregate to form “clusters” energetically more favorable than isolated defects. It seems that FeIII ions cannot form aggregates.

Modular nature of the polysomatic pyrochlore-murataite series

Synthetic analogues of murataite, a very rare mineral—a complex oxide of REE, actinide, Ti, Fe, and other elements,—are of great interest as confinement matrices of radioactive wastes. They are produced by sintering (1200–1300°C) and melting (1500–1600°C) with subsequent crystallization of the melt. Four structural varieties of murataite distinguished by unit-cell parameters have been established by TEM study. All these varieties are derivatives of the fluorite structure designated as murataite 3C, 5C, 7C, and 8C depending on repetition factor of a parameter of the fluorite subcell. The structural features of the synthetic murataite varieties are analyzed in this paper based on data obtained from high-resolution electron microscopy, microdiffraction, and X-ray refinement. The hypothesis of a modular structure of the members of polysomatic pyrochlore-murataite series has been confirmed. At the same time, the structural modules are zero-dimensional rather than two-dimensional as had previously been suggested. The combinations of zero-dimensional modules in 3D space create the entire structural diversity of the polysomatic series.

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.