Lattice dynamics of BiFeO<Subscript>3</Subscript> under hydrostatic pressure

The vibrational frequencies of the BiFeO₃ crystal lattice in the cubic phase (Pm3m) and the rhombohedral paraelectric phase (R3c) are calculated in terms of the ab initio model of an ionic crystal with the inclusion of the dipole and quadrupole polarizabilities. In the ferroelectric phase with the symmetry R3c, the calculated spontaneous polarization of 136 μC cm^?2 agrees well with the experimental data. The dependences of the unit cell volume, the elastic modulus, and the vibrational frequencies on the pressure are calculated. It is found that the frequency of an unstable ferroelectric mode in both the cubic (Pm3m) and rhombohedral (R3c) phases are almost independent of the applied pressure, in contrast to classical ferroelectrics with a perovskite structure, where the ferroelectric instability is very sensitive to a variation in the pressure.     

The mystery of abnormally large volume of PbCrO<Subscript>3</Subscript> with a structurally consistent Hubbard U from first-principles

PbCrO₃ is found experimentally to be a cubic perovskite with an abnormally large lattice constant of about 4.00 Å. To date, no successful first principle calculations have been carried out for cubic PbCrO₃ perovskite. Combining the generalized-gradient approximations and a structurally consistent Hubbard U approach, the crystal, electronic and magnetic structures of PbCrO₃ are calculated to explore the mystery of abnormally large volume of PbCrO₃ in cubic structure. The crystal structure, magnetic order and half-metallic properties of PbCrO₃ are determined. For the first time, a structurally consistent Hubbard U _eff of about 8.28 eV for PbCrO₃ is calculated based on linear-response approach. With the structurally consistent U obtained by first principles, a \(Pm\bar 3m\) cubic structure with a lattice constant of about 3.98 Å for PbCrO₃ is obtained successfully. Moreover PbCrO₃ is found to be half-metallic ferromagnet with an integral magnet moment of 2.00μ _B per unit cell. The anomalously large volume of PbCrO₃ in cubic structure results from the strongly correlated electron interaction. The results obtained agree well with experimental data.     

High-pressure effect on the ferroelectric-paraelectric transition in PbTiO<Subscript>3</Subscript>

The crystal structure of lead titanate PbTiO₃ was investigated by energy dispersive X-ray diffraction at high pressures up to 4 GPa in a temperature range of 300–950 K. At the ambient conditions, the PbTiO₃ structure is tetragonal with the space group P4mm (ferroelectric phase). A structural phase transition into the cubic phase with a space group Pm[`3]mPm\bar 3m is observed at T = 747 K. It was found that the phase transition temperature decreases upon applying the high pressure with the coefficient dT _C /dP = -65 K/GPa. Dependences of parameters and volume of the unit cell on the pressure and temperature was found, and the bulk modulus and thermal expansion coefficients for the tetragonal and cubic phases of lead titanate have been calculated.     

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.     

Magnetotransport characteristics of strained La<Subscript>0.7</Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> epitaxial manganite films

The electrical and magnetic characteristics of La_0.7Sr_0.3MnO₃ (LSMO) epitaxial manganite films are investigated by different methods under conditions when the crystal structure is strongly strained as a result of mismatch between the lattice parameters of the LSMO crystal and the substrate. Substrates with lattice parameters larger and smaller than the nominal lattice parameter of the LSMO crystal are used in experiments. It is shown that the behavior of the temperature dependence of the electrical resistance for the films in the low-temperature range does not depend on the strain of the film and agrees well with the results obtained from the calculations with allowance made for the interaction of electrons with magnetic excitations in the framework of the double-exchange model for systems with strongly correlated electronic states. Investigations of the magneto- optical Kerr effect have revealed that an insignificant (0.3%) orthorhombic distortion of the cubic lattice in the plane of the NdGaO₃(110) substrate leads to uniaxial anisotropy of the magnetization of the film, with the easy-magnetization axis lying in the substrate plane. However, LSMO films on substrates (((LaAlO₃)_0.3+(Sr₂AlTaO₆)_0.7)(001)) ensuring minimum strain of the films exhibit a biaxial anisotropy typical of cubic crystals. The study of the ferromagnetic resonance lines at a frequency of 9.76 GHz confirms the results of magnetooptical investigations and indicates that the ferromagnetic phase in the LSMO films is weakly inhomogeneous.     

Dipole ordering and ionic conductivity in NASICON-Type Na<Subscript>3</Subscript>Cr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> structures

The aspects of structure, dipole ordering, and ionic conductivity of the Na₃Cr₂(PO₄)₃ crystal with the four polymorphic phases (α, α', β, and γ) have been investigated. The features of the α-Na₃Cr₂(PO₄)₃ crystal structure and its dipole ordering and relaxation polarization in the low-temperature α and α' phases have been refined. The occurrence of Na₃Cr₂(PO₄)₃ dipole ordering in the α and α' phases and high ionic conductivity in the β and γ phases is attributed to the structural changes in the rhombohedral [Me₂(PO₄)₃]^–3_3∞ crystal frame upon phase transformations α → α', α' → β, and β → γ. A model for explaining the dipole ordering and ionic conductivity phenomena in Na₃Cr₂(PO₄)₃ is proposed.     

Features of the pressure-induced phase transitions in Eu<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

The structural changes induced by a 9-GPa pressure in Eu₂(MoO₄)₃ single crystals at room temperature have been studied using x-ray diffraction. It is established that a structural phase transition from the initial tetragonal phase to the new high-pressure tetragonal phase occurs rather than solid-phase amorphization that was observed previously in polycrystalline samples. The samples in the observed transition remain single-crystalline despite a significant difference (ΔV ～ 18%) between the specific volumes of the initial and final phases. It is shown that the transition from the initial state to the high-pressure phase occurs via the formation of broad transition zones featuring a continuous and smooth change of the crystal lattice parameters.     

Magneto-optical investigations of the domain structure and magnetization of the ferrite-garnet Tb<Subscript>0.2</Subscript>Y<Subscript>2.8</Subscript>Fe<Subscript>5</Subscript>O<Subscript>12</Subscript> in the temperature range of the spontaneous spin-reorientation phase transition

The transformation of a domain structure and technical magnetization of the Tb_0.2Y_2.8Fe₅O₁₂ single crystal in the temperature range of the spontaneous orientational phase transition have been investigated by the magneto-optical method. It has been shown that the phase transition is extended in a certain temperature range in which domains of the low-temperature and high-temperature magnetic phases coexist. It has been found that the evolution of the domain configuration in the temperature range of spin reorientation substantially depends on the presence of mechanical stresses in the crystal. Anomalies in the temperature dependences of the coercivity and magneto-optical susceptibility of the crystal due to the transformation of its domain structure during the phase transition have been revealed. The experimental results have been interpreted within the existing theory of orientational phase transitions in cubic crystals.     

A new allotropic form of carbon [C<Subscript>28</Subscript>]<Subscript>n</Subscript> based on fullerene C<Subscript>20</Subscript> and cubic cluster C<Subscript>8</Subscript> and Si and Ge analogs of this form: Computer simulation

The structure of a new allotropic form of carbon [C₂₈]_n having a simple cubic lattice and space group \(Pm \bar 3\) is proposed. The geometrical parameters of the building block of such a hypothetic crystal are preliminarily determined from DFT-PBE calculations of the cluster C₈@(C₂₀)₈ and the polyhedral hydrocarbon molecule C₈@(C₂₀H₁₃)₈, in which the centers of the cubic clusters C₈ coincide with the centers of the cluster C₈@(C₂₀)₈ and of the molecule C₈@(C₂₀H₁₃)₈, respectively, and dodecahedral C₂₀ carbon cages are located at the vertices of a cube. The energy of dissociation of the cluster C₈@(C₂₀)₈ into a cubic cluster C₈ and eight dodecahedral clusters C₂₀ is calculated to be 1482 kcal/mol, and the energy of each C₈-C₂₀ bond is equal to 74.2 kcal/mol. The structure of the [C₂₈]_n crystal is refined using the DFT-PBE96/FLAPW method and optimized geometry. Calculations show that the crystal is a dielectric with an energy gap of 3.3 eV. The lattice parameter a of the crystal is equal to 5.6 Å, and its density is 3.0 g/cm³. The possible existence of analogous allotropic forms of elements Si and Ge is discussed. A method is proposed for designing a hypothetic allotropic form [C₂₈]_n from C₂₀(CH₃)₈ molecules with T _h symmetry.     

Structural aspects of the antiferroelectric-paraelectric phase transition in double perovskite Pb2MgWO6 at high pressures and temperatures

The crystal structure of antiferroelectric Pb₂MgWO₆ has been studied using neutron diffraction at high pressures to 5.4 GPa at room temperature and energy-dispersive X-ray diffraction at high pressures to 4 GPa in the temperature range 300–400 K. At normal conditions, in Pb₂MgWO₆, there is an antiferroelectric phase with the crystal structure described by the orthorhombic symmetry with space group Pnma. At temperature T = 313 K and normal pressure or at room temperature and pressure P ～ 0.9 GPa, the crystal under-goes a structural phase transition to the cubic phase with space group $Fm\bar 3m$ (paraelectric phase). The temperature and pressure dependences of the lattice parameters, unit cell volume, and interatomic bond lengths have been obtained, and the thermal expansion coefficients and the bulk moduli have been calculated for the antiferroelectric and paraelectric phases of Pb₂MgWO₆.     

A theoretical investigation of structural,mechanical, electronic and thermoelectric properties of orthorhombic CH<Subscript>3</Subscript>NH<Subscript>3</Subscript>PbI<Subscript>3</Subscript>

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH₃NH₃PbI₃ have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm^?1K^?1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.     

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.     

Effect of a Rare-Earth Ion on the Structural Instability in RFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> Crystals

The dynamics of the crystal lattice of RFe₃(BO₃)₄ (R = Pr, Nd, Sm, Gd, Tb, Dy, and Ho) compounds in the high-symmetry R32 phase has been calculated. Significant changes in spectra of compounds with various rare-earth ions have been obtained only near the edge Λ point of the Brillouin zone (qΛ = 1/3(?2b₁ + b₂ + b₃, where b₁, b₂, and b₃ are the reciprocal lattice vectors) for acoustic oscillation branches. A decrease in the frequency of an acoustic mode at the point Λ has been revealed in all studied compounds. This frequency depends on the type of rare-earth ion and decreases from a compound with Pr to a compound with Ho down to imaginary values. Such a behavior of the frequency of the unstable acoustic mode is in good agreement with experimental data on the dependence of the temperature of the R32 → P3₁21 structural phase transition on the type of rare-earth ion in ferroborates.     

Density functional study of Pu<Subscript>2</Subscript>C<Subscript>3</Subscript>

The structural, magnetic, electronic, vibrational, thermodynamic and elastic properties of plutonium sesquicarbide (Pu₂C₃) are investigated based on density functional theory. The use of the Hubbard term to describe the 5f electrons of plutonium is discussed according the lattice parameters and magnetism. The calculated lattice constants, magnetism and density of states agree well with the experimental data or other theoretical calculations. The Pu-C bonds of Pu₂C₃ have a mixture of covalent character and ionic character, while covalent character is stronger than ionic character. The phonon frequencies and the assignment of infrared-active, Raman-active and silent modes at Γ point are obtained. Furthermore, the enthalpy difference H-H₂₉₈, entropy S, heat capacity and linear thermal expansion coefficient α of Pu₂C₃ have been calculated and compared with the available data. Lastly, the calculated elastic properties predict that Pu₂C₃ is ductile metal. In addition, the effect of spin-orbit coupling on the structural, magnetic, and electronic properties of Pu₂C₃ has been discussed. We hope that our results can provide a useful reference for further theoretical and experimental research on Pu₂C₃.     

Structure and lattice dynamics of PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>: Ab initio calculation

The crystal structure and phonon spectrum of PrFe₃(BO₃)₄ are ab initio calculated in the context of the density functional theory. The ion coordinates in the unit cell of a crystal and the lattice parameters are evaluated from the calculations. The types and frequencies of the fundamental vibrations, as well as the line intensities of the IR spectrum, are determined. The elastic constants of the crystal are calculated. A “seed” frequency of the vibration strongly interacting with the electron excitation on the praseodymium ion is obtained for low-frequency A₂ mode. The calculated results are in agreement with the known experimental data.     

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.     

The structural properties of RbMnX<Subscript>3</Subscript> (X = F,Cl, Br) halides

The results of nonempirical calculation of energies of three polytypes (cubic, two-layer hexagonal, and six-layer hexagonal) are given for RbMnX₃ (X = F, Cl, Br) crystals. The calculation is performed using an ionic crystal model with regard for the deformability and the dipole and quadrupole polarizabilities of ions. The behavior of these crystals under the action of hydrostatic pressure is studied. It is demonstrated that, at normal pressure, the RbMnCl₃ and RbMnBr₃ crystals have a six-layer hexagonal structure. At pressures above 11 kbar, RbMnCl₃ passes to a phase with a cubic structure; RbMnBr₃ at pressures above 90 kbar passes to a phase with a two-layer hexagonal structure. The RbMnF₃ crystal under normal conditions has a cubic structure and experiences no phase transformations under the effect of pressure. The obtained results are in satisfactory agreement with the known experimental data.     

Effect of lattice deformation and phase transitions on the electronic spectra of TlGaS<Subscript>2</Subscript>, TlGaSe<Subscript>2</Subscript>, and TlInS<Subscript>2</Subscript> layered semiconductors

The effect of the lattice deformation on the electronic spectra of TlGaS₂, TlGaSe₂, and TlInS₂ layered semiconductor crystals is analyzed. It is shown that changes in the band gap of these semiconductors due to thermal expansion and a change in the composition under hydrostatic or uniaxial pressure can be described within a unified model of the deformation potential. The main feature of this model is the inclusion of deformation potentials with different signs, which is characteristic of other semiconductors with a layered structure. An analysis of the lattice deformation of the studied semiconductors in terms of the proposed model of the deformation potential has revealed that, in the immediate vicinity of the phase transitions, the crystal lattice under pressure undergo an unusual deformation.     

Hydrostatic pressure-induced phase transitions in RbMnCl<Subscript>3</Subscript>: Raman spectra and lattice dynamics

Raman scattering spectra of RbMnCl₃ are measured at room temperature under high hydrostatic pressure. The results are interpreted based on first principles lattice dynamics calculations. The experimental data obtained correlate with the calculations in the low frequency domain but disagree slightly in the region of high-frequency vibrations. The transition from the hexagonal to the cubic perovskite phase observed earlier (near 0.7 GPa) was confirmed, and new transitions to lower symmetry distorted phases were discovered (at 1.1 and 5 GPa).     

Weak ferromagnetism along the triad axis of FeBO<Subscript>3</Subscript> crystals

Weak ferromagnetic moment along the triad axis of FeBO₃ crystals has been calculated on the basis of the single-ion model taking into account the cubic invariant of the crystal field in the spin Hamiltonian.