Lattice dynamics of MF3 crystals (M = Al, Ga, and In)

The phonon spectra, Born effective charges, and dielectric constants ε_∞ for the □AlF₃, □GaF₃, and □InF₃ crystals (where □ is a vacancy) have been calculated in terms of the generalized Gordon-Kim method. The calculated spectra of lattice vibrations contain no imaginary vibrational frequencies. This suggests the stability of the cubic phase of these compounds but contradicts the observable structural transition from cubic to rhombohedral phase. It is assumed that such a transition in the □AlF₃, □GaF₃, and □InF₃ crystals is brought about by structural defects. The calculated spectrum of lattice vibrations of the “completely defective” crystal M□F₃ (M = Al, Ga, and In) indicates a strong instability of the cubic phase. Within the mean crystal approximation, the cubic phase of M _x M _1?x F₃ crystals appears to be unstable at small x≤0.05.     

Theory of an Fm3m→I4/m structural phase transition in an Rb2KScF6 crystal

An Rb₂KScF₆ crystal having an elpasolite structure undergoes a sequence of Fm3m→I4/m→P12₁/n1 structural phase transitions where the transition to the tetragonal phase is associated with “rotation” of the ScF₆ octahedron. An effective Hamiltonian is constructed to describe the Fm3m→I4/m transition using the approximation of a local mode for which we selected a “soft mode” whose eigenvector corresponds to the rotation of the octahedron. The effective Hamiltonian also includes the relationship between the local mode and the homogeneous elastic strains. The parameters of the effective Hamiltonian were determined using the generalized Gordon-Kim model of an ionic crystal which allows for the deformability and polarizability of the ions. The thermodynamic properties of a system with this model Hamiltonian were investigated using the Monte Carlo method. The calculated phase transition temperature of 250 K is almost the same as the experimental value (252 K). The tetragonal phase remains stable as far as T=0 K and a second transition (to the monoclinic phase) cannot be obtained using this effective Hamiltonian. This suggests that if the transition to the tetragonal phase is mainly associated with “rotations” of the octahedrons, in order to describe the phase transition to the monoclinic phase the effective Hamiltonian must allow for additional degrees of freedom mainly associated with the motion of rubidium ions.     

Effect of cation substitution on the lattice dynamics and ferroelectric instability of cubic BaTiO<Subscript>3</Subscript> and BaZrO<Subscript>3</Subscript> doped with Bi and La ions

The spectra of lattice vibration frequencies of solid solutions Ba_{1 ? x} Bi_2x/3? _x/3Ti(Zr)O₃ and Ba_{1 ? x} La _x Ti(Zr)_{1 ? x/4}? _x/4O₃ are calculated in terms of a generalized Gordon-Kim model with inclusion of the dipole and quadrupole polarizabilities. Over the entire concentration range, the calculated phonon spectra contain a ferroelectric soft mode. The effect of various interactions on the ferroelectric instability of these solid solutions is studied. It is shown that the character of ferroelectric instability is largely determined by the mechanism of charge compensation.     

Lattice dynamics of K2NaAlF6, K3AlF6, and Na3AlF6 crystals with the elpasolite structure

This paper presents the results of a nonempirical calculation of the static and dynamic properties of K₂NaAlF₆, K₃AlF₆, and Na₃AlF₆ crystals with the elpasolite structure. The calculation is based on a microscopic model of an ionic crystal that allows for the deformability and polarizability of the ions. The deformability parameters of the ions are determined by minimizing the total energy of the crystal. The total energy is regarded as a functional of the electron density, using the local Thomas-Fermi approximation and taking into account exchange (correlation) effects. The results of the calculations of the equilibrium lattice parameters and of the permittivities are in good agreement with the experimental data. Unstable vibrational modes are found in the spectrum of the lattice vibrations, with these modes occupying the phase space in the entire Brillouin zone. Zh. éksp. Teor. Fiz. 114, 1742–1756 (November 1998)     

Lattice dynamics of a Rb2KScF6 crystal in unstable cubic and tetragonal phases and in a stable monoclinic phase

The results of a nonempirical calculation of the static and dynamic properties of a Rb₂KScF₆ crystal with elpasolite structure in cubic, tetragonal, and monoclinic phases are presented. The calculation is performed on the basis of a microscopic model of an ionic crystal that takes account of the deformability and polarizability of the ions. The deformability parameters of the ions are determined from the condition that the total energy of the crystal is minimum. The computational results for the equilibrium lattice parameters are in satisfactory agreement with experimental data. Unstable vibrational modes are found in the vibrational spectrum of the lattice in the cubic and tetragonal phases. These modes occupy the phase space throughout the entire Brillouin zone. The characteristic vectors of the most unstable mode at the center of the Brillouin zone of the cubic phase are related to the displacements of the fluorine ions and correspond to rotation of ScF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In the tetragonal phase the most unstable mode belongs to the boundary point of the Brillouin zone and condensation of this mode leads to monoclinic distortion with doubling of the unit-cell volume. In the monoclinic phase unstable modes are absent in the vibrational spectrum of the lattice. Fiz. Tverd. Tela (St. Petersburg) 41, 1297–1305 (July 1999)     

Luminescence induced in diamond by He+ ion implantation into SiC/C composites with an inverse opal structure

The photoluminescence induced in diamond by helium ion implantation into SiC/C nanocomposite samples and their structure revealed by high-resolution transmission electron microscopy have been investigated. It has been found that, apart from crystallites of silicon carbide, graphite, and amorphous carbon, in the structure of the composites there are spherical carbon particles containing concentric graphite-like shells (onion-like particles). It has been established that onion-like particles are formed during high-temperature treatment of SiC/C nanocomposites in the course of their preparation. It has been shown that, after the implantation with the subsequent thermal treatment, nanocomposite samples exhibit a luminescence characteristic of N-V centers in diamonds. The assumption has been made that the diamond crystallites are formed at the center of onion-like particles during high-temperature treatment of the composite.     

Statistical mechanics of cation ordering and lattice dynamics of PbZr<Subscript>x</Subscript>Ti<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> solid solutions

An effective Hamiltonian for Zr-Ti cation ordering in PbZr_xTi_1?xO₃ solid solutions is written out. To determine the parameters of the effective Hamiltonian, a nonempirical calculation is performed within an ionic-crystal model taking into account the deformation and dipole and quadrupole polarizabilities of ions. The thermodynamic properties of cation ordering are studied using the Monte Carlo method. The calculated phase transition temperatures (180 and 250 K for the concentrations x=1/3 and 1/2, respectively) are much lower than the melting temperature of the compound under study. At such temperatures, the ordering kinetics is frozen and, in reality, the phase transition to the ordered phase does not occur, in agreement with experimental observations. Within the same ionic-crystal model, we calculated the high-frequency permittivity, Born dynamic charges, and the lattice vibration spectrum for a completely disordered phase and certain ordered phases. It is shown that soft vibration modes, including ferroelectric ones, exist in the lattice vibration spectrum of both the completely disordered and the ordered phases.     

Statistical mechanics of cation ordering in PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

A model Hamiltonian for B cation ordering (Sc-Nb(Ta)) in PbSc_1/2Nb_1/2O₃ and PbSc_1/2Ta_1/2O₃ solid solutions is constructed. The parameters of the model Hamiltonian are determined from the ab initio calculation within the ionic crystal model with allowance made for the deformability and the dipole and quadrupole polarizabilities of the ions. The temperatures of the phase transition due to the ordering of the B cations are calculated by the Monte Carlo method in the mean-field and cluster approximations. The phase transition temperatures calculated by the Monte Carlo method (1920 K for PbSc_1/2Ta_1/2O₃ and 1810 K for PbSc_1/2Nb_1/2O₃) are consistent with the experimental data (1770 and 1450 K, respectively). The thermodynamic properties of the cation ordering are investigated using the Monte Carlo method.     

First Principles Investigation of the Magnetic,Magnetoelectric, and Optical Properties of Double Perovskites Containing Ions of Transition Metals LaPbTSbO<Subscript>6</Subscript> (T = Fe,Co, Ni)

Within the first principles approach implemented in the VASP package, a correlation between magnetic, electronic, polarization, and optical properties, on the one hand, and the structural ordering of cations, on the other hand, is investigated in double perovskites LaPbTSbO₆ (T = Fe, Co, Ni). Two types of cation ordering are considered: simultaneous layered (LL) and checkerboard (RR) ordering of both cations. These two types of ordering are chosen due to their significance; namely, the ordering RR is one of the most implementable types of cation ordering in double perovskites, and compounds with layered ordering can be considered as a heterostructure consisting of periodically alternating metal–nonmagnetic metal layers, which is of interest for experimental synthesis and investigation. It is found that the type of cation ordering in compounds with T = Fe and Ni radically changes the magnetic and/or electronic properties of the compound. Moreover, it is found that low-symmetry stable phases are polar for both types of cation ordering, and the values of spontaneous polarization are evaluated.     

Lattice dynamics and the phase transition from the cubic phase to the tetragonal phase in the LaMnO<Subscript>3</Subscript> crystal within the polarizable-ion model

The paper reports on the results of ab initio calculations of the static and dynamic properties of the LaMnO₃ crystal with a perovskite structure in the cubic, rhombohedral, and orthorhombic phases. The calculations are performed within the ionic crystal model, which takes into account the deformability and polarizability of the ions. It is revealed that the spectrum of lattice vibrations in the cubic phase contains unstable vibrational modes, which occupy the phase space in the entire Brillouin zone. The eigenvectors of the softest mode at the boundary point R of the Brillouin zone are associated with the displacements of the oxygen ions and correspond to the “rotation” of the MnO₆ octahedron. The condensation of one, two, and three components of this mode leads to the tetragonal, orthorhombic, and rhombohedral distortions of the structure. The structural phase transition is described in terms of the local mode approximation with the use of the double perovskite unit cell, in which the MnO₆ octahedron is explicitly separated. The parameters of the model Hamiltonian are determined. The static properties are investigated by the Monte Carlo method. The calculated temperature of the phase transition from the cubic phase (9800 K) is considerably higher than the melting temperature of the crystal under investigation. The calculated frequencies of long-wavelength lattice vibrations in the experimentally observed orthorhombic and rhombohedral phases are in reasonable agreement with experimental data.