Acoustic and optical phonons and their dispersion in model ferroelastics Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript>

Thefrequency dispersion curve of acoustic and optical phonons are calculated and constructed, and the density of states of the phonon spectrum is obtained for Hg₂Cl₂ crystals. The influence of the hydrostatic pressure on the frequencies of acoustic and optical phonons and their dispersion is analyzed theoretically. It is revealed that an increase in the pressure leads to a considerable softening of the slowest acoustic TA branch (soft mode) at the X point of the Brillouin zone boundary. This behavior is consistent with the phenomenological Landau theory and correlate with experiments.     

Low-temperature Raman spectra of Hg<Subscript>2</Subscript>(Br,I)<Subscript>2</Subscript> mixed crystals

Raman spectra of Hg₂(Br,I)₂ mixed crystals were studied. The spectra revealed multimode behavior of optical vibrations, which were assigned to the existence in these crystals of molecules of three types, namely, Hg₂Br₂, Hg₂I₂, and Hg₂BrI. The spectra exhibit a manifestation of phase transition effects associated with soft modes, the density of states of IR-active vibrational branches, and of nanoclusters, whose nucleation is induced by the Br-Hg-Hg-I dipole molecules.     

X-ray study of microcrystalline Hg<Subscript>2</Subscript><Emphasis Type="Italic">Hal</Emphasis><Subscript>2</Subscript> ferroelastics

The rhombic splitting of basal plane reflections and the thermal behavior of fundamental and diffuse reflections from X-points of the Brillouin zone characterizing the behavior of an order parameter and its fluctuations, respectively, were studied in polycrystalline Hg₂Cl₂ and Hg₂Br₂ samples. In the case of polycrystalline samples, a strong broadening of phase transition effects was observed, due to damaged surface layers and elastic and plastic stress fields inducing order parameter fluctuations over a wide temperature range.     

Vibrational and electronic characteristics of Zr<Subscript>70</Subscript>Pd<Subscript>30</Subscript>, Zr<Subscript>80</Subscript>Pt<Subscript>20</Subscript> icosahedral quasicrystals and their amorphous Counterparts

The heat capacity of Zr₇₀Pd₃₀ and Zr₈₀Pt₂₀ icosahedral quasicrystals and their amorphous counterparts is studied in the temperature range 1.5–500 K in order to establish a correlation between the short-range atomic order and the physical properties of these compounds. A comparison of the data made it possible to reveal changes in the vibrational spectra within the low-and high-energy ranges, as well as in the density of states, superconducting characteristics, electron-phonon interaction, and anharmonicity of the lattice thermal vibrations and to calculate the main average frequencies (moments) characterizing the vibrational spectra. The lower superconducting transition temperature T _c of the quasicrystals as compared to that of the amorphous counterparts can be associated with the decrease in the density of states on the Fermi surface, the hardening of the phonon spectrum, and the weakening of the electron-phonon coupling.     

Spectroscopic study of the behavior of the order parameter in model ferroelastic crystals of Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript>

Information is obtained about the temperature behavior of the order parameter of a phase transition by theoretical and experimental investigation of odd (acoustic and IR-active) phonons that appear in the Raman scattering spectra from the X points of the Brillouin zone (BZ) boundary in the paraphase of Hg₂Cl₂ crystals and are induced by the phase transition, unit-cell doubling, and the X → Γ folding in the BZ. The relevant critical exponents are determined, whose values are in agreement with the results of X-ray diffraction measurements and, within the Landau phenomenological theory of phase transitions, indicate that the phase transition in these crystals is close to the tricritical point.     

Correlation between the dynamics of oxygen atoms and oxidation kinetics of solid solutions based on Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>8</Subscript>

The oxidation kinetics of Bi_1.3Pb_0.8Sr₂Ca_0.8Y_0.2Cu₂O_8+δ solid solutions at different temperatures and \(p_{O_2 } = 0.21\) atm is investigated by thermogravimetry. The results obtained are compared with the previously studied oxidation kinetics of Bi_1.3Pb_0.8Sr₂Ca_0.8Y_0.2Cu₂O_8+δ solid solutions. It is found that the substitution of yttrium for calcium leads to an appreciable retardation of the initial oxidation stage associated with the oxygen diffusion. The phonon spectra of the solid solutions are examined using inelastic neutron scattering on a DIN-2PI direct-geometry spectrometer. The high-frequency (>50 meV) phonon densities of states for yttrium-containing and yttrium-free solid solutions are analyzed. The possible model is proposed for a correlation between the differences observed in the high-frequency phonon densities of states attributed to the vibrations of oxygen atoms and the differences in the oxidation kinetics of the solid solutions under consideration.     

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.     

Optical and electronic properties of heusler Cu<Subscript>2</Subscript>MnAl alloy with shape memory effect

A ferromagnetic Heusler Cu₂MnAl alloy with a shape memory effect has been studied in the wide spectral region of 0.25–2.80 μm (0.44–5.35 eV) at room temperature using spectral ellipsometry methods. Dispersion dependences for optical constants n(hν) and κ(hν), dielectric permeability ε(hν), and optical conductivity σ(hν), which is proportional to the interband density of electronic states, have been analyzed. Optical conductivity spectra have been calculated by mathematical modeling based on data for the electronic state densities in both subbands of electrons with spins oriented along and against the magnetization direction. A model of indirect transitions based on the Berglund–Spicer formula has been shown to describe the experimental spectrum only in general terms. The main contribution to the conductivity in the high-frequency spectral region is due to direct transitions of electrons in the vicinities of L, X, and Γ points of the Brillouin zone coupled with Cu atoms whereas low-energy anomalies in the absorption spectrum σ(hν) are caused by electrons coupled with Mn and Al atoms.     

Anomalous low-frequency phonons in ZrB<Subscript>12</Subscript>

The influence of pressure and temperature on low-frequency lines (100–300 cm^–1) in Raman spectra of ZrB₁₂ and LuB₁₂ single crystals has been investigated. These spectral features have been identified as one-phonon and two-phonon excitations of the acoustic branches of the phonon spectrum. It has been found that the observed spectra of ZrB₁₂ single crystals are more structured and indicate the development of phonon anomalies with a decrease in the temperature. Despite the fact that the low-frequency features in the phonon spectrum of ZrB₁₂ are characterized by a high value of the isothermal Grüneisen parameter, their isobaric Grüneisen parameter has a negative value. This indicates large contributions from the fourth-order anharmonicity, which significantly exceed the volume effects. The appearance of narrow lines in the frequency range from 155 to 175 cm^–1 at temperatures T < 100 K suggests the possibility of a structural transition with an incomplete softening of the lattice.     

Electronic structure of prototype AFe<Subscript>2</Subscript>As<Subscript>2</Subscript> and ReOFeAs high-temperature superconductors: A comparison

We have performed ab initio LDA calculations of the electronic structure of newly discovered prototype high-temperature superconductors AFe₂As₂ (A = Ba, Sr) and compared it with the previously calculated electronic spectra of ReOFeAs (Re = La, Ce, Pr, Nd, Sm). In all cases, we obtain almost identical densities of states in a rather wide energy interval (up to 1 eV) around the Fermi level. Energy dispersions are also very similar and almost two dimensional in this energy interval, leading to the same basic (minimal) model of the electronic spectra, determined mainly by Fe d orbitals of the FeAs layers. The other constituents, such as A ions or rare-earth Re (or oxygen states) are more or less irrelevant for superconductivity. LDA Fermi surfaces for AFe₂As₂ are also very similar to that of ReOFeAs. This makes the more simple AFe₂As₂ a generic system to study the high-temperature superconductivity in FeAs-layered compounds. The text was submitted by the authors in English.     

Pseudogap behavior in Bi<Subscript>2</Subscript>Ca<Subscript>2</Subscript>SrCu<Subscript>2</Subscript>O<Subscript>8</Subscript>: Results of the generalized dynamical mean-field approach

Pseudogap phenomena are observed for the normal underdoped phase of different high-T _c cuprates. Among others, the Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σ_k hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σ_k in the spirit of our recently proposed DMFT + Σ_k approach taking into account pseudogap fluctuations. In the present model, Σ_k describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x ² − y ² orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σ_k quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σ_k successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σ_k Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments. The article was submitted by the authors in English.     

Nanoclusters in mixed crystals Hg<Subscript>2</Subscript><Emphasis Type="Italic">Hal</Emphasis><Subscript>2</Subscript>

The Raman spectra of mixed Hg₂(Br,I)₂ and Hg₂(Cl,Br)₂ crystals were investigated. The multimode behavior of optical vibrations induced by presence of three types of molecules (Hg₂ Hal′₂, Hg₂ Hal″₂ and Hg₂ Hal′Hal″) in the crystals was observed experimentally and is discussed theoretically. Phase transition effects such as soft modes, density of states, IR vibration branches, and anti- and ferroelectric nanoclusters induced by polar Hal′-Hg-Hg-Hal″ molecules and their immediate environment, were observed in the Raman spectra.     

Comparative analysis of the phonon modes in AgNbO<Subscript>3</Subscript> and NaNbO<Subscript>3</Subscript>

The lattice dynamics of silver niobate AgNbO₃ and sodium niobate NaNbO₃ is calculated from first principles. The unstable modes (i.e., tilting of oxygen octahedra and ferroelectric atomic displacements) in silver and sodium niobates are analyzed. It is shown that the existence of ferroelectric modes is associated primarily with the instability of the atomic positions of silver and sodium in the crystal lattice. The dynamic charges in the structure of silver and sodium niobates are determined. According to the first-principles calculations, both silver and sodium niobates in the ground state (T = 0) are characterized by ferroelectric atomic displacements and frozen tilting of oxygen octahedra, with the only difference being that the tilting modes of the oxygen octahedra in silver niobate correspond to the M point of the Brillouin zone, whereas those in sodium niobate are attributed to the R point of the Brillouin zone. The results of these calculations are in good agreement with experimental data.     

Energy band structure and X-ray spectra of phenakite Be<Subscript>2</Subscript>SiO<Subscript>4</Subscript>

The electronic structure of crystalline phenakite Be₂SiO₄ is investigated using x-ray emission spectroscopy (XES) (Be K _α XES, Si L _{2, 3} XES, O K _α XES) and x-ray absorption spectroscopy (XAS) (Be 1s XAS, Si 2p XAS, O 1s XAS). The energy band structure is calculated by the ab initio full-potential linearized augmented-plane-wave (FLAPW) method. The total and partial densities of states and the dispersion curves for the Be₂SiO₄ compound are presented. It is shown that the top of the valence band and the bottom of the conduction band of the Be₂SiO₄ compound are predominantly formed by the oxygen 2p states. According to the results obtained, the electron transition with the lowest energy supposedly can occur at the center of the Brillouin zone. The effective masses of electrons (0.5m _e ) and holes (3.0m _e ) for the Be₂SiO₄) compound are estimated.     

Dynamics of the Lattice and Thermal Capacity of ZnP<Subscript>2</Subscript> and CdP<Subscript>2</Subscript> Tetragonal Crystals

Oscillation frequencies of tetragonal ZnP ₂ and CdP ₂ crystal lattices are calculated for the Keating model. Results of numerical calculations of the phonon spectra in the most symmetric directions and at points of the Brillouin zones are presented. The calculated function of phonon frequency distribution is used to calculate the thermal capacity of CdP ₂. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 15–17, July, 2005.     

Spectral properties of RuAl<Subscript>2</Subscript> and RuGa<Subscript>2</Subscript> compounds: Ellipsometric analysis

The optical properties of RuAl₂ and RuGa₂ intermetallic compounds have been investigated in the spectral range of 0.22–14 μm. The nature of interband light absorption has been interpreted based on a comparative analysis of calculated and experimental frequency dependences of optical conductivity. The data obtained confirm the existence of pseudogaps with a width of ~0.8 eV localized at the Fermi level in the electron densities of states of these materials, which was predicted in previous energy-band calculations.     

Photoacoustic spectroscopy of thin films of As<Subscript>2</Subscript>S<Subscript>3</Subscript>, As<Subscript>2</Subscript>Se<Subscript>3</Subscript> and GeSe<Subscript>2</Subscript>

Photoacoustic spectroscopy (PAS) is one of the important branches of spectroscopy, which enables one to detect light-induced heat production following the absorption of pulsed radiation by the sample. As₂S₃, As₂Se₃ and GeSe₂ exhibit a wide variety of photo-induced phenomena that enable them to be used as optical imaging or storage medium and various electronic devices, including electro-optic information storage devices and optical mass memories. Therefore, accurate measurement of thermal properties of semiconducting films is necessary to study the memory density. The thermal conductivity of thin films of As₂S₃ (thickness 100 μm and 80 μm), As₂Se₃ (thickness 100 μm and 80 μm) and GeSe₂ (thickness 120 μm and 100 μm) has been measured using PAS technique. Our result shows that the thermal conductivity of thicker films is larger than the thinner films. This can be explained by the thermal resistance effect between the film and the surface of the substrate.      

Atomic dynamics of an Al<Subscript>0.62</Subscript>Cu<Subscript>0.255</Subscript>Fe<Subscript>0.125</Subscript> icosahedral quasicrystal

The atomic dynamics of an Al_0.62Cu_0.255Fe_0.125 icosahedral quasicrystal is investigated using inelastic neutron scattering (the isotopic contrast method). The partial vibrational spectra of copper, iron, and aluminum atoms in the icosahedral quasicrystal and the total spectrum of thermal vibrations of the compound are directly reconstructed from the experimental data for the first time. It is found that the vibrational energies of copper and iron atoms fall in relatively narrow ranges near 16 and 30 meV, respectively, whereas the vibrational energies of aluminum atoms lie in a wide range (up to 60 meV).     

Inelastic neutron scattering in Zr<Subscript>2</Subscript>NiH<Subscript>1.9</Subscript> and Zr<Subscript>2</Subscript>NiH<Subscript>4.6</Subscript>

In this paper we report the results obtained from inelastic neutron scattering measurements on Zr₂NiH_1.9 and Zr₂NiH_4.6 using triple-axis spectrometer at Dhruva reactor, Trombay. The spectrum up to 35 meV represents largely the lattice modes of Zr and Ni atoms. The vibrational frequencies of hydrogen atoms are expected predominantly at higher energies. The phonon spectra from 35–180 meV were recorded using a Be filter as analyser. In order to analyse the observed neutron spectra, we assume a set of Ein-stein modes due to the hydrogen atoms which are delta functions in energy. These delta functions are broadened by the resolution of the instrument. The vibrational frequencies obtained from the fitting of the observed phonon spectra have been assigned to various tetrahedral sites in both the compounds.