Simulation of ZnWO4‒MgWO4 Solid Solutions by the Method of Interatomic Potentials

Simulation of CaMoO4-NaGd(MoO4)2 solid solutions by the method of interatomic potentials is carried out. It is shown that solid solutions exist in the entire range of compositions and are close to ideal. Dependences on the composition of the lattice parameters and volume of the unit cell, density, bulk modulus, enthalpy, vibrational entropy and heat capacity are obtained. Temperature dependences of heat capacity and vibrational entropy are constructed. Analysis of the local structure and its changes depending on the composition of the Ca1-xNax/2Gdx/2MoO4 solid solution showed that in solid solution the interatomic distances of Gd-O are on average 2.62% less, and Na-O is 3.15% greater than the distances of Ca-O. In general, this leads to an increase in the lattice parameters and volume of the unit cell during the formation of Ca1-xNax/2Gdx/2MoO4 solid solutions compared to CaMoO4. Keywords: simulation, molybdates, the solid solutions, local structure.

Simulation of the solid solutions in the system of double sodium–gadolinium and sodium–europium molybdates, which are promising matrices for solid state lasers and phosphors has been carried out by the method of interatomic potentials. Two types of solid solutions have been studied, one of which contains finite components corresponding to the stoichiometric NaGd(MoO_4)_2–NaEu(MoO_4)_2 compositions with statistical distribution of cations in the crystal lattice. Another object is a cation-deficient Na_2Gd_4(MoO_4)_7–Na_2Eu_4(MoO_4)_7 system, in which we have examined the variants of statistical distribution and partial ordering of cations over structural positions. Atomistic simulation has been performed using the GULP 4.0.1 software package (General Utility Lattice Program). It is shown that when we pass from sodium-gadolinium molybdate to sodium-europium molybdate, both of stoichiometric and cation-deficient compositions, an increase in the unit cell volume is observed, while the density of the crystal, the energy of interatomic interactions in the structure, the vibrational entropy and the heat capacity decrease along with increasing europium content. The energy of interatomic interactions in the structure for cation-deficient solid solutions is less than for stoichiometric ones. Other aforementioned characteristics for cation-deficient solid solutions have greater values than for stoichiometric ones. The role of cluster europium centers in concentration quenching in NaGd(MoO_4)_2–NaEu(MoO_4)_2 solid solutions has been examined.

Simulation of the solid solutions in the system of double sodium–gadolinium and sodium–europium molybdates, which are promising matrices for solid state lasers and phosphors has been carried out by the method of interatomic potentials. Two types of solid solutions have been studied, one of which contains finite components corresponding to the stoichiometric NaGd(MoO4)2–NaEu(MoO4)2 compositions with statistical distribution of cations in the crystal lattice. Another object is a cation-deficient Na2Gd4(MoO4)7–Na2Eu4(MoO4)7 system, in which we have examined the variants of statistical distribution and partial ordering of cations over structural positions. Atomistic simulation has been performed using the GULP 4.0.1 software package (General Utility Lattice Program). It is shown that when we pass from sodium-gadolinium molybdate to sodium-europium molybdate, both of stoichiometric and cation-deficient compositions, an increase in the unit cell volume is observed, while the density of the crystal, the energy of interatomic interactions in the structure, the vibrational entropy and the heat capacity decrease along with increasing europium content. The energy of interatomic interactions in the structure for cation-deficient solid solutions is less than for stoichiometric ones. Other aforementioned characteristics for cation-deficient solid solutions have greater values than for stoichiometric ones. The role of cluster europium centers in concentration quenching in NaGd(MoO4)2–NaEu(MoO4)2 solid solutions has been examined.

Crystals of ferroelectric‒ferroelastic gadolinium molybdate Gd2(MoO4)3, calcium molybdate CaMoO4, and double sodium‒gadolinium molybdates of stoichiometric (Na1/2Gd1/2MoO4) and cationdeficient (Na2/7Gd4/7MoO4) compositions, which are used to design solid-state lasers, phosphors, and white LEDs, have been simulated by the interatomic potential method. Their structural, mechanical, and thermodynamic properties are calculated using a unified system of interatomic potentials and effective ion charges, which demonstrated transferability and made it possible not only to describe the existing experimental data but also to predict some important physical and thermodynamic properties of molybdate crystals. The influence of the deviation from stoichiometry and partial ordering of cations on sites in nonstoichiometric crystals on the properties and local structure of sodium‒gadolinium molybdates is discussed.

Strontianite (SrCO3)-aragonite (CaCO3) solid solutions have been simulated by the interatomic potential method. The composition dependences of the unit cell parameters, the unit cell volume, and bulk modulus have been constructed. It has been shown that the volume of the unit cell and bulk modulus show small negative deviations from additivity. The local structure of solid solutions has been analyzed. It has been established that the enthalpy of mixing is positive and, for the equimolar composition, reaches a maximum of 2.45 kJ/mol. Based on the composition dependences of the Gibbs free energy for the temperature range of 300–650 K, the solvus of the system has been constructed. According to the obtained data, the solubility of aragonite in strontianite under ambient conditions is 5.5 mol %, while that of strontianite in aragonite is 2.8 mol %. The miscibility gap of the system disappears at around 450 K. The calculated results have been compared with the experimental data.

The strontianite (SrCO3)–witherite (BaCO3) solid solutions have been simulated using the interatomic potential method. The dependences of the unit cell parameters, the unit cell volume, and the bulk modulus on the composition of the solid solution have been constructed. It has been shown that the unit cell volume and the bulk modulus exhibit negative deviations from the additivity. An analysis of the local structure of the solid solutions has been carried out. It has been found that, for the equimolar composition of the BaxSr1–xCO3 solid solution, the relaxations of the barium and strontium positions are equal to 60 and 56%, respectively. It has been established that the enthalpy of mixing is positive and, for the equimolar composition of the solid solution, reaches a maximum value of 3.4 kJ/mol. The obtained results have been compared with the experimental data. The solvus of the BaxSr1–xCO3 system has been constructed based on the dependences of the Gibbs free energy on the composition in the temperature range from 300 to 1000 K.

Gadolinium molybdate Gd2(MoO4)3 orthorhombic ferroelectric ferroelastic (β'-phase) is simulated by the method of interatomic potentials. The simulation is performed using the GULP 4.0.1 code (General Utility Lattice Program), which is based on the minimization of the energy of the crystal structure. Parameters of the gadolinium–oxygen interatomic interaction potentials are determined by fitting to the experimental structural data and elastic constants by a procedure available in the GULP code. Atomistic modeling using the effective atomic charges and the system of interatomic potentials made it possible to obtain reasonable estimates of structural parameters, atomic coordinates, and the most important physical, mechanical, and thermodynamic properties of these crystals. Temperature dependences of the heat capacity and vibrational entropy of the crystal are obtained. The calculated parameters of gadolinium–oxygen interaction potentials can be used to simulate more complex gadolinium-containing compounds.

The interatomic potential method in an ionic approximation was used to model the protonation of forsterite crystals. The formation of isolated OH− groups in iron-free and iron-bearing crystals and neutral clusters of protonated cation vacancies was considered. It was shown that the presence of trivalent impurities may significantly facilitate protonation processes owing to their reduction to a divalent state or formation of clusters with cation vacancies. In most cases, charge balancing of hydrogen-bearing defects by magnesium vacancies is energetically favorable over that involving silicon vacancies.

The structure of oxygen hole centers in forsterite crystals has been simulated using the interatomic potential method. The energies of isolated oxygen hole centers, as well as the energies of their clusters with intrinsic and extrinsic defects of the crystal, have been estimated for different arrangements of point defects in the structure. It has been shown that the most energetically favorable position for isolated oxygen hole centers is the O3 position, in which the gain in the formation energy is equal to 0.17 eV as compared to the O2 position and 1.66 eV as compared to the O1 position. The maximum energy gain due to the association energy can be achieved when the oxygen hole centers are located at the vertices of the tetrahedron with a silicon vacancy. The presence of chromium in the forsterite crystal can increase the probability of the formation of silicon vacancies. The obtained results have been discussed in terms of the experimental investigations of the color centers generated in the Mg2SiO4 and Mg2SiO4: Cr crystals under ionizing radiation.

Simulation of Huanzalaite MgWO4 by the Method of Interatomic Potentials

Paramagnetic centers formed by impurity Yb3+ ions in synthetic forsterite (Mg2SiO4) grown by the Czochralski technique are studied by X-band CW and pulsed EPR spectroscopy. These centers are single ions substituting magnesium in two different crystallographic positions denoted М1 and М2, and dimer associates formed by two Yb3+ ions in nearby positions М1. It is established that there is a pronounced mechanism favoring self-organization of ytterbium ions in dimer associates during the crystal growth, and the mechanism of the spin–spin coupling between ytterbium ions in the associate has predominantly a dipole–dipole character, which makes it possible to control the energy of the spin–spin interaction by changing the orientation of the external magnetic field. The structural computer simulation of cluster ytterbium centers in forsterite crystals is carried out by the method of interatomic potentials using the GULP 4.0.1 code (General Utility Lattice Program). It is established that the formation of dimer associates in the form of a chain parallel to the crystallographic axis consisting of two ytterbium ions with a magnesium vacancy between them is the most energetically favorable for ytterbium ions substituting magnesium in the position М1.

The impurity defects in CaMoO4 are simulated by the method of interatomic potentials. The dissolution energies of monovalent, divalent, and trivalent impurities are calculated, their comparative analysis is performed, and the main patterns of change are presented. The most probable localization of defects is determined. In the case of heterovalent impurities, the most energetically favorable mechanism for their charge compensation has been found, both due to intrinsic crystal defects and under conjugate isomorphism. It is shown that the formation of impurity clusters with intrinsic crystal defects and (to a greater extent) the formation of clusters of different-valence impurities may significantly reduce the dissolution energy of impurities. The formation of neutral clusters of univalent impurities with oxygen vacancies not only makes it possible to increase the solubility of impurities but also reduces the probability of the formation of color centers.

Crystals of sodium–gadolinium molybdates of two compositions: stoichiometric (Na1/2Gd1/2MoO4) and cation-deficient (Na2/7Gd4/7MoO4) composition in which 1/7 of the corresponding cation positions are not occupied are simulated by the method of interatomic potentials. For cation-deficient crystals, two kinds of cation position distribution are considered: the statistical distribution of sodium, gadolinium, and unoccupied cation positions in the I41/a structure and their partial ordering in the I space group. As a result of the simulation, structural characteristics of sodium–gadolinium molybdates agreeing well with the known experimental data are obtained. In addition, a number of important elastic and thermodynamic properties of these compounds are predicted. The results obtained in the partial-occupancy approximation and by constructing a 7 × 2 × 2 supercell are compared. The local structure of sodium–gadolinium molybdates are analyzed in detail. The influence of the deviation from the stoichiometry as well as cation ordering on the properties of these crystals is discussed.

Impurity defects simulation in sodium-gadolinium molybdate NaGd(MoO4)2 was carried out using a method of interatomic potentials. The dissolution energies of tri-, di- and monovalent impurities were estimated. The dependences of the dissolution energy on the ionic radius of the impurity were plotted. For heterovalent substitutions, the most energetically favorable mechanism for charge compensation has been found, both due to intrinsic crystal defects and according to the conjugate isomorphism scheme. The positions of the most probable localization of defects are determined. The effect of disordering of sodium and gadolinium ions at equivalent positions on positional differences in the energy of defects is estimated. A comparison of the solubility of impurities in NaGd(MoO4)2 and its isostructural CaMoO4 indicates that, although isovalent substitutions are energetically more favorable than heterovalent ones, the mechanism of conjugate isomorphism, which ensures electrical neutrality, can equalize these processes.

Simulation of Sanmartinite ZnWO4 by the Method of Interatomic Potentials