Structure and dynamics of the pure and mixed fluorites <Emphasis Type="Italic">Me</Emphasis>F<Subscript>2</Subscript> (<Emphasis Type="Italic">Me</Emphasis> = Ca,Sr, Ba,and Pb)

The structure and dynamics of the crystal lattice of MeF₂ fluorites (Me = Ca, Sr, Ba, and Pb) under external hydrostatic compression (0–3.5 GPa) are calculated within the shell model in the pair potential approximation. The first-order structural phase transition from the cubic to the orthorhombic phase in these crystals under pressure is investigated. The effect of chemical pressure on the BaF₂ crystal is analyzed by the simulation of mixed crystals, namely, Ba_1?xCa_xF₂ and Ba_1?xSr_xF₂. It is demonstrated that the supercell method, as applied to the simulation of mixed crystals, results in a lower lattice energy per formula unit as compared to the lattice energy obtained by the virtual-crystal method.     

NMR parameters in column 13 metal fluoride compounds (AlF3, GaF3, InF3 and TlF) from first principle calculations

The relationship between the experimental ¹⁹F isotropic chemical shift and the ¹⁹F isotropic shielding calculated using the gauge including projector augmented-wave (GIPAW) method with PBE functional is investigated in the case of GaF₃, InF₃, TlF and several AlF₃ polymorphs. It is shown that the linear correlation between experimental and DFT-PBE calculated values previously established on alkali, alkaline earth and rare earth of column 3 basic fluorides (Sadoc et al., Phys. Chem. Chem. Phys. 13 (2011) 18539–18550) remains valid in the case of column 13 metal fluorides, indicating that it allows predicting ¹⁹F solid state NMR spectra of a broad range of crystalline fluorides with a relatively good accuracy. For the isostructural α-AlF₃, GaF₃ and InF₃ phases, PBE-DFT geometry optimization leads to noticeably overbended M–F–M bond angles and underestimated ²⁷Al, ⁷¹Ga and ¹¹⁵In calculated quadrupolar coupling constants. For the studied compounds, whose structures are built of corner shared MF₆ octahedra, it is shown that the electric field gradient (EFG) tensor at the cationic sites is not related to distortions of the octahedral units, in contrast to what previously observed for isolated AlF₆ octahedra in fluoroaluminates.     

Peculiarities of cascade photon emission and energy storage in M1−xPrxF2+x (M=Ca,Sr, Ba,x≈0.35) crystals

Peculiarities of cascade photon emission (CPE) and energy storage in M_1?xPr_xF_2+x (M=Ca, Sr, Ba, x≈0.35) crystals were studied. The investigation of lattice parameters revealed that these solid solutions belong to the fluorite structure type with the lattice constant noticeably different from that of MF₂ crystals. Absorption, emission and excitation spectra of M_0.65Pr_0.35F_2.35 were measured at LHeT and RT. As it turned out the typical for 4f²→4f² transition in Pr³⁺ emission lines are broadened as compared with the PrF₃ crystal. The analysis of the excitation spectra broadening does not allow bringing out the type of the superlattice, which is inherent to the material, but it indicates clearly the simultaneous presence of different types of the Pr centers in mixed crystals. Yet another specific feature is the higher radiation sensitivity of these fluorides relatively PrF₃, MF₂ and Pr-doped MF₂ crystals. Coloration efficiency enhances in direction Ca→Sr→Ba, and the positions of induced absorption band depend on composition of the solid solution. Colorization, thermo-stimulated luminescence and afterglow of the M_1?xPr_xF_2+x crystals denote high radiation sensitivity as compared with M_1?xCe_xF_2+x.     

Effect of hydrostatic and chemical pressure on BaF2 and BaF2: Eu2+ crystals

The effect of hydrostatic pressure on a BaF₂ crystal was studied within the shell model in the pair-wise potential approximation. The structural phase transition from the cubic to orthorhombic phase was simulated. The behavior of the unit-cell parameters of the α-and β-BaF₂ phases under hydrostatic pressure (from 0 to 12 GPa) was investigated. The fundamental vibration frequencies of BaF₂ under hydrostatic pressure (0–3.5 GPa) were calculated for both phases. The effect of chemical pressure on the BaF₂ crystal was studied by simulating Ba_1?x Me_xF₂ mixed crystals (Me=Ca, Sr). It was shown that at impurity concentrations up to 15–20 at. % the lattice constant varies in the same way as it does when hydrostatic pressure increases to P _c , which corresponds to a phase transition to the orthorhombic phase. The effect of chemical and hydrostatic pressure on BaF₂: Eu²⁺ doped crystals was also studied. The dependence of the absorption and luminescence zero-phonon line shift on the Eu²⁺-ligand distance was calculated.     

Electronically induced lattice distortion in WO3 and stability of ReO3 lattice

Structural phase transitions in WO₃ and the stability of cubic ReO₃ and M_xWO₃ lattices are attributed to the screening effect involving W or Re 5d and O 2p states on the lattice vibrations. The presence of the conduction electrons in ReO₃ or M_xWO₃ is shown to suppress this effect and to stabilize the cubic lattice.     

Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in Rb2KInF6

The static and dynamic properties of cubic Rb₂KInF₆ crystals with elpasolite structure are calculated using a nonempirical method. Calculations are performed within a microscopic ionic-crystal model taking into account the deformation and polarization of ions. The deformation parameters of ions are determined by minimizing the total energy of the crystal. The calculated equilibrium lattice parameters agree satisfactorily with the experimental data. It is found that in the cubic phase there are vibrational modes that are unstable everywhere in the Brillouin zone. The eigenvectors of the unstablest mode at the center of the Brillouin zone of the cubic phase are associated with the displacements of F ions and correspond to rotations of InF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In order to describe the Fm3m → I4/m phase transition, an effective Hamiltonian is constructed under the assumption that the soft mode whose eigenvector corresponds to octahedron rotation is local and coupled with homogeneous elastic strains. The parameters of the effective Hamiltonian are determined using the calculated crystal energy for the distorted structures due to soft-mode condensation. The thermodynamic properties of the system with this model Hamiltonian are investigated using the Monte Carlo method. The phase transition temperature is calculated to be 550 K, which is twice its experimental value (283 K). The tetragonal phase remains stable down to T=0 K; the effective Hamiltonian used in this paper thus fails to describe the second phase transition (to the monoclinic phase). Thus, the transition to the tetragonal phase occurs for the most part through octahedron rotations; however, additional degrees of freedom, first of all, the displacements of Rb ions, should be included into the effective Hamiltonian in order to describe the transition to the monoclinic phase.     

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)     

Crystal fields of hexameric rare-earth clusters in fluorites

In solid solutions of alkaline-and rare-earth fluorides with a fluorite structure, ions of most elements of the rare-earth (RE) row form hexameric clusters that assimilate the minor component of the solid solutions (fluorine) and build it into the cubic fluorite lattice without changing its shape. An analysis of the EPR spectra of paramagnetic RE ions (Er³⁺, Tm³⁺, Yb³⁺) in clusters of diamagnetic ions (Lu³⁺, Y³⁺) confirms their hexagonal structure, which was established when studying the superstructures of the compounds under study. In such a cluster, a RE ion is in a nearly tetragonal crystal field, with the parameters of this field differing radically from those of single cubic and tetragonal RE centers in crystals with a fluorite structure. In particular, this field causes high (close to limiting) values of the g_∥ factors of the ground states of the paramagnetic RE ions. Computer simulation is used to determine the atomic structure of a hexameric cluster in MF₂ crystals (M = Ca, Sr, Ba). The crystal field and energy spectrum of Er³⁺, Tm³⁺, and Yb³⁺ ions in such clusters are calculated, and the spectroscopic parameters of the ground states of these ions are determined. The calculations confirm the earlier assumption that the unusual EPR spectra of nonstoichiometric fluorite phases are related to RE ions in hexameric clusters.     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

A correlation between the structural and magnetic phase transitions for the mixed systems: KMn1-xNixF3 and KMn1-xCoxF3 I. Structural phenomena

X-ray diffraction measurements of the lattice parameters as a function of temperature are reported for the mixed compounds KMn_1-xNi_xF₃ and KMn_1-xCo_xF₃ where x 0.10. From the splitting of the cubic 400 Bragg reflections the transition temperatures of the structural phase transitions were determined. In the KMn_0.99Co_0.01F₃ and KMn_0.97Ni_0.03F₃ crystals three structural phase transitions were established. It was concluded that higher admixture quantities lead to a change in phase transition character which appeared to be smeared over a temperature range.     

Rearrangement of the vibration spectrum of Zn<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Cd<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se solid solutions with varying composition

Experimental lattice reflection spectra of Zn_{1 ? x} Cd _x Se bulk crystals are interpreted and analyzed for compositions x = 0.08, 0.21, and 0.30 crystallizing in the cubic zinc blende structure and x = 0.45, 0.65, and 0.80 crystallizing in the hexagonal wurtzite structure. The lattice vibration modes for all the compositions are divided, according to their frequency, into ZnSe- and CdSe-like vibrations. On a phase transition at x > 0.3, a marked jump (7–8 cm^?1) in the frequency of lattice modes is observed, but the largest changes take places in the mode oscillator strengths. However, the summed oscillator strength of the ZnSe- and CdSe-like vibration modes changes only slightly during the phase transition, which corresponds to the double-mode type of rearrangement of the vibration spectrum of Zn_{1 ? x} Cd _x Se solid solutions with varying x. An analysis of the lattice modes is accompanied by the comparison with the parameters of the lattice modes of Zn_{1 ? x} Cd _x Se (x = 0–0.55) epitaxial layers grown on a GaAs substrate by molecular-beam epitaxy.     

Lattice dynamics and Raman scattering spectrum of elpasolite Rb<Subscript>2</Subscript>KScF<Subscript>6</Subscript>: Comparative analysis

Raman scattering spectra of elpasolite Rb₂KScF₆ are studied in a wide temperature range including two phase transitions: from the cubic to the tetragonal phase and then to the monoclinic phase. The experimental Raman scattering spectrum is compared with the lattice vibration spectra of these phases calculated using an ab initio approach. A number of anomalies (caused by structural rearrangement during the phase transitions) are revealed and quantitatively analyzed in the ranges of both the intramolecular vibrations of the octahedron molecular ScF₆ ions and low-frequency intermolecular lattice vibrations. The interaction between low-frequency intramolecular vibrations and the intermolecular modes is found to be significant, and strong resonance interaction of the rotational soft modes (which are recovered below the phase transition points) with hard low-frequency vibrations of the rubidium ion sublattice is detected. These interactions are shown to substantially complicate the spectra.     

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.     

Synthesis and physical properties of negative thermal expansion materials Zr1−xMxW2O8−y (M=Sc, In, Y) substituted for Zr(IV) sites by M(III) ions

Zr_1−xM_xW₂O_8−y (M=Sc, In and Y) solid solutions substituted up to x=0.04 for Zr(IV) sites by M(III) ions were synthesized by a solid-state reaction. X-ray diffraction experiments from 90 to 560 K revealed that all solid solutions had a cubic crystal structure and showed negative thermal expansion coefficients. The lattice parameters of Zr_1−xM_xW₂O_8−y were smaller than that of ZrW₂O₈ probably due to oxygen defects, though the ionic radii of substituted M³⁺ ions were larger than that of Zr⁴⁺. Order-disorder phase transition temperatures of the substituted samples drastically decreased in the order of Y, In and Sc compared to the percolation theory, and decreased with increasing M content.     

Investigation of specific features of the lattice dynamics and the ferroelectric transition in perovskite crystals

The specific features of diffuse X-ray scattering in BaTiO₃, KNbO₃, and PbTiP₃ perovskite crystals have been investigated. The former two perovskite compounds in cubic, tetragonal, and orthorhombic phases exhibit anomalous sheets due to diffuse X-ray scattering, whereas no similar sheets are observed in the case of diffuse X-ray scattering in PbTiO₃. For these compounds, the phonon spectra are calculated in the quasi-harmonic approximation within the polarizable-shell model, and the mechanism of stabilization of the soft mode above the temperature of the phase transition to the ferroelectric state is considered. It is demonstrated that, in the cubic phase of BaTiO₃ and KNbO₃ crystals, there exist quasi-one-dimensional “soft” modes of vibrations of ions in M-O-M-O- chains, where M = Ti or Nb. In PbTiO₃, this feature of the soft mode has not been revealed. The pair correlation functions of simultaneous atomic displacements in BaTiO₃, KNbO₃, and PbTiO₃ are determined and used to calculate the intensity of diffuse X-ray scattering. The results obtained are in good agreement with experimental data. This is a strong argument in support of the hypothesis that the specific features of diffuse scattering are associated with the existence of quasi-one-dimensional correlations of atomic displacements in the soft optical mode and that the ferroelectric transition in perovskites is a displacive ferroelectric phase transition. The possible influence of the specific features revealed in the phonon spectra of the perovskite crystals on the processes of nuclear magnetic resonance and X-ray absorption (extended X-ray absorption fine structure spectra) is briefly discussed.     

A raman study of hydrostatic pressure induced phase transitions in Rb2KInF6 crystals

The Raman spectra of the elpasolite (Rb₂KInF₆) crystal have been studied in the pressure range from 0 to 5.3 GPa at a temperature of 295 K. A phase transition at a pressure of approximately 0.9 GPa has been found. An analysis of the variations in the spectral parameters has led to the conclusion that the phase transition to a distorted phase is accompanied by the doubling of the volume of the primitive cell of the initial cubic phase. Numerical calculations of the lattice dynamics in the Rb₂KInF₆ crystal have been performed. The numerical simulation has established that the phase transition at a pressure of 0.9 GPa is associated with condensation of the F _lg mode. A probable high-pressure phase is the phase with space group C2/m.     

Atomistic computer simulation studies of La1−xSrxVO3

Static computer simulation techniques have been employed for structural investigation of the La_1−xSr_xVO₃ series. Potential parameters for V³⁺-O²⁻ and V⁴⁺-O²⁻ have been derived which reproduces the crystal structures of end members with sufficient accuracy. Variations of lattice parameters and bond distances with Sr concentration have been studied. The calculated lattice parameters decrease with increase in the Sr concentration. A structural phase transition from orthorhombic to cubic is observed at 50% Sr doping level.     

Investigation of gain characteristics in mixed crystals LiMeF4 (Me = Y,Lu, Yb) doped by Ce3+ ions

Differential gain spectra in the range 295–335 nm were measured in crystals of scheelite structure LiY_{1 ? x} Lu _x F₄ (x = 0–1), doped by Ce³⁺ ions. It is shown that variation of Lu³⁺ and Y³⁺ ions relative content in LiY_{1 ? x} Lu _x F₄ crystals allows to manipulate the spectral width of the amplification band. Cross-sections of excited-state absorption at the wavelengths of Ce³⁺ luminescence, probability ratios of formation and thermal destruction of color centers depending on the Y³⁺ ions content in LiY_{1 ? x} Lu _x F₄ crystals were estimated. Even better gain characteristics have been demonstrated by LiLuF₄:Ce³⁺, doped by Yb³⁺ ions. The highest optical gain coefficient with a wide amplification band among studied samples was observed in LiLuF₄:Ce³⁺ crystal, codoped by Yb³⁺ ions.     

Infrared absorption investigation of the role of octahedral groups upon the phase transition in the Rb2KMoO3F3 crystal

The infrared absorption spectra of the oxyfluoride Rb₂KMoO₃F₃ have been measured in the frequency range corresponding to stretching vibrations of the Mo-O anion octahedron with the purpose of clarifying their role in the phase transition. A semi-empirical calculation of two possible configurations of quasioctahedral MoO₃F₃ groups has been performed. The results of the investigations have demonstrated that some octahedra in the crystal structure change the local symmetry from C _3v to C _2v due to the phase transition (T = 197 K).     

Structural and magnetic properties of Ce(Cu,Ni)2 pseudobinary phases

The stability of the pseudobinary phases obtained by partial substitution of Ni with Cu, Ag or Au in the cubic Laves phase CeNi₂, or by partial substitution of Cu with Ni in the orthorhombic compound CeCu₂ has been investigated. No solid solubility of Cu, Ag and Au in the CeNi₂ cubic lattice could be detected. In contrast, pseudobinary orthorhombic phases, corresponding to the formula CeCus_2?xNi_x, exist over the range x = 0 to 1. For these phases, crystal structures and magnetic properties have been determined. In every case, the electronic configuration of cerium appears to be unaffected to the Ni content, and corresponds to the trivalent state. The Ni atoms are in a non-magnetic state. The magnetic susceptibility of CeCu₂ in the region from 530 to 900 K shows anomalous behaviour, which should be due to a metamagnetic transition.