Internal dynamics of (H<Subscript>2</Subscript>O)<Subscript>2</Subscript> and (D<Subscript>2</Subscript>O)<Subscript>2</Subscript> dimers: III. Description taking into account inversion,exchange and bifurcation motions

Using the symmetry group chain methods, the stationary states of (H₂O)₂ and (D₂O)₂ dimers that correspond to the lowest energy barriers of the inversion, exchange via an intermediate trans configuration, and bifurcation motions are classified taking into account the real geometries of the dimers. A model that rigorously describes the interactions of the motions and leads to a simple algebraic scheme for calculating of both the positions of the levels in the energy spectrum and the intensities of transitions between them is constructed. It is important that the correctness of the model is limited only by the trueness of the choice of symmetry of the internal dynamics.     

Description of the torsional motion in the isotopically asymmetric ionic complexes ArH<Subscript>2</Subscript>D<Superscript>+</Superscript> and ArD<Subscript>2</Subscript>H<Superscript>+</Superscript>

The internal dynamics of the isotopically asymmetric ionic complexes ArH₂D⁺ and ArD₂H⁺ is considered to be a distorted dynamics of the isotopically symmetric ArH₃⁺ complex. By using the group chain methods, a rigorous algebraic model is constructed to describe the spectrum of the asymmetric complexes with an allowance for the torsional motion of the structure of hydrogen nuclei. The model is based on the geometrical group of symmetry of internal dynamics of the isotopically symmetric ionic complex, which is used here as a noninvariant group.     

A computer study of the Raman spectra of the (GaN)<Subscript>129</Subscript>, (SiO<Subscript>2</Subscript>)<Subscript>86</Subscript>, and (GaN)<Subscript>54</Subscript>(SiO<Subscript>2</Subscript>)<Subscript>50</Subscript> nanoparticles

The Raman spectra of the (GaN)₁₂₉, (SiO₂)₈₆, and (GaN)₅₄(SiO₂)₅₀ nanoparticles were calculated using the molecular dynamics method. The spectrum of (SiO₂)₈₆ had three broad bands only, whereas the Raman spectrum of (GaN)₁₂₉ contained a large number of overlapping bands. The form of the Raman spectrum of (GaN)₅₄(SiO₂)₅₀ was determined by the arrangement of the GaN and SiO₂ components in it. The nanoparticle with a GaN nucleus had a continuous fairly smooth spectrum over the frequency range 0 ≤ ω ≤ 600 cm⁻¹, whereas the spectrum of the nanoparticle with a SiO₂ nucleus contained well-defined bands caused by vibrations of groups of atoms of different kinds and atoms of the same kind.     

Description of torsional motion in ionic complexes ArH<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> and ArD<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack>

An algebraic model that describes the internal dynamics of the ionic complexes ArH₃⁺ and ArD₃⁺ in the ground electronic-vibrational state taking into account the torsional motion of the structure of identical hydrogen nuclei is constructed by symmetry-group chain methods. It is important that the correctness of this model is only limited by the correctness of the choice of geometric symmetry of the internal dynamics of the ionic complex.     

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.     

Optical phonons in Rb<Subscript>2</Subscript>TeBr<Subscript>6</Subscript> and Cs<Subscript>2</Subscript>TeBr<Subscript>6</Subscript> crystals

Raman scattering in Rb₂TeBr₆ and Cs₂TeBr₆ crystals is studied. The phonon spectra of the crystals are calculated using the factor group method. The number of Raman-active modes, their symmetries, and selection rules are found. Observed Raman spectrum lines are identified with atomic vibration modes of the crystal.     

Temperature evolution of the dielectric response function of Pb(Fe<Subscript>0.95</Subscript>Sc<Subscript>0.05</Subscript>)<Subscript>2/3</Subscript>W<Subscript>1/3</Subscript>O<Subscript>3</Subscript> relaxor ceramics in a wide frequency range

Electrodynamic properties of Pb(Fe_0.95Sc_0.05)_2/3W_1/3O₃ solid solution belonging to A(B'B'')O₃ perovskite structural family have been investigated by broadband dielectric spectroscopy in a wave-number range of (4 × 10^–9–4 × 10³) cm^–1 and a temperature range of 100–600 K. The influence of low-frequency relaxations on the vibrational spectrum is determined within the four-parameter factorized dispersion model. Anomalies in the behavior of the dielectric response function are found near the temperature-diffuse maximum of permittivity.     

Electrical properties,equivalent circuit,and dielectric relaxation studies on [(C<Subscript>3</Subscript>H<Subscript>7</Subscript>)<Subscript>4</Subscript>N]<Subscript>2</Subscript>Cd<Subscript>2</Subscript>Cl<Subscript>6</Subscript> polycrystalline

The Ac electrical conductivity and the dielectric relaxation properties of the [(C₃H₇)₄N]₂Cd₂Cl₆ polycrystalline sample have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 209 Hz–5 MHz and 361–418 K, respectively. The purpose is to make a difference between the electrical and dielectric properties of the polycrystalline sample and single crystal. Besides, a detailed analysis of the impedance spectrum suggests that the electrical properties of the material are strongly temperature-dependent. Plots of (Z" versus Z') are well fitted to an equivalent circuit model consisting of a series combination of grains and grains boundary elements. Moreover, the temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law and the frequency dependence of σ (ω) follows the Jonscher’s universal dynamic law. Furthermore, the modulus plots can be characterized by full width at half height or in terms of a nonexperiential decay function φ(t) = exp(t/t)^β. Finally, the imaginary part of the permittivity constant is analyzed with the Cole–Cole formalism.     

A Phenomenological Model of Structural Phase Transitions in RbDy(Wo<Subscript>4</Subscript>)<Subscript>2</Subscript>

A phenomenological model of structural phase transitions in double rubidium–dysprosium tungstate is proposed. The model is constructed by equivariant catastrophe theory methods. The temperature dependence of the heat capacity near the phase transitions at temperatures T₁ = 9 K and T₂ = 4.9 K was calculated. Comparison with the experimental data shows a satisfactory qualitative agreement. In terms of the proposed model, the low-temperature phase transition can be interpreted as isomorphic.     

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.     

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.     

Vibrational and electronic properties of the amorphous systems Ni<Subscript>44</Subscript>Nb<Subscript>56</Subscript>, Ni<Subscript>62</Subscript>Nb<Subscript>38</Subscript>, and Cu<Subscript>33</Subscript>Zr<Subscript>67</Subscript> as derived from specific heat measurements

The specific heats of the amorphous systems Ni₄₄Nb₅₆, Ni₆₂Nb₃₈, and Cu₃₃Zr₆₇ were studied in the temperature range 3–273 K. The data obtained allow one to isolate the contribution due to atomic vibrations from the experimentally measured specific heat, to determine the density of electronic states at the Fermi level and the temperature dependence of the characteristic Debye parameter Θ over a broad temperature range, and to calculate a few frequency moments that characterize the vibrational spectrum. The information derived on the average characteristics of vibrational spectra is in good agreement with earlier data on inelastic neutron scattering. In transferring from Ni₄₄Nb₅₆ to Ni₆₂Nb₃₈, the density of electronic states at the Fermi level decreases and the characteristic vibrational frequencies increase. The density of electronic states at the Fermi level for Cu₃₃Zr₆₇ is close to that for Ni₆₂Nb₃₈. The characteristic frequencies of the vibrational spectrum of the Cu₃₃Zr₆₇ system are substantially lower (by 30%) than those of the Ni₄₄Nb₅₆ and Ni₆₂Nb₃₈ systems.     

O<Subscript>2</Subscript> photodesorption from a Ag<Subscript>8</Subscript>O<Stack><Subscript>2</Subscript><Superscript>-</Superscript></Stack> cluster

The decay path of an Ag₈(O₂)^- cluster photoexcited by a 3.1 eV photon is elucidated using time-resolved photoelectron spectroscopy. Photoabsorption results in the formation of an excited state giving rise to a peak in the photoelectron spectra with well-resolved vibrational finestructure. With a lifetime of about 100 fs this bound state decays into an anti-bonding state which dissociates into O₂ and Ag₈^- on a timescale of 10 ps. In the photoelectron spectra, this corresponds to a broad maximum shifting gradually towards higher binding energy while the O₂ and Ag₈^- separate. Finally, the spectrum of bare Ag₈^- appears. This process is unique to small clusters, because on metal surfaces excited state lifetimes are too short to allow for direct dissociation.     

Ionic displacements and structure of disordered PbFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript>

A sequence of structural models of unit cells of complex oxides with perovskite-type structure has been constructed to refine the average structure of PbFe_1/2Nb_1/2O₃ (PFN) at temperatures above the ferroelectric Curie point (T _C ～ 110°C). Owing to the analysis of the probability theory considerations, each model is characterized by only two positional fitting parameters. With the use of the intensities of 95 symmetrically independent X-ray reflections from a PFN single crystal at 160°C, a model with the R factor below 3% (K = 2.44%) was chosen. The ravine method has been used to verify the existence of a single minimum for the R factor with respect to the fitting parameter.     

Quasi-two-dimensional ferroelectricity in KNbO<Subscript>3</Subscript>/KTaO<Subscript>3</Subscript> superlattices

First-principles density functional theory is used to calculate the phonon spectrum in the paraelectric phase, the ground-state structure and polarization distribution in the polar phase, and energies of ferro- and antiferroelectrically ordered phases of free-standing (KNbO₃)₁(KTaO₃) _n ferroelectric superlattices with n = 1–7. It is established that quasi-two-dimensional ferroelectricity with polarization oriented in the layer plane, which weakly interacts with polarization in neighboring layers, appears in potassium niobate layers with a thickness of one unit cell in the superlattices. The possibility of using of such ferroelectric superlattices as a medium for three-dimensional information recording is shown.     

Magnetic structure of the Sr<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>4</Subscript>Cl<Subscript>2</Subscript> two-subsystem antiferromagnet according to nuclear quadrupole resonance data

The magnetic structure of the Sr₂Cu₃O₄Cl₂ two-subsystem antiferromagnet is studied by the nuclear quadrupole resonance (NQR) method on the ^{63, 65}Cu and ³⁵Cl nuclei. The resonance spectrum above T _N2 = 40 K is determined by the Zeeman splitting of the levels of the ^{63, 65}Cu nuclei of the copper atoms at the Cu1 site with the first-order quadrupole perturbation. The magnetic field on the copper nuclei is equal to 93 kOe. The spectrum below n is significantly different: it includes a low-frequency part, which is associated with the ordering of the second magnetic subsystem Cu2. The splitting of the NQR lines of ³⁵Cl is observed above and below T _N2. This fact indicates the ferromagnetic ordering of the moments of the Cu1 subsystem, which are located along the c axis of the crystal, and makes it possible to determine the direction of the magnetic field on Cu1 copper as (110).     

Electric field-induced formation of a new commensurate phase of the [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CuCl<Subscript>4</Subscript> crystal

The formation of a new commensurate phase with a dimensionless wave number q = 1/3 in an [N(CH₃)₄]₂CuCl₄ crystal under the action of an external electric field is analyzed theoretically. The phase diagram is constructed on a plane specified by two coefficients of the thermodynamic potential in the presence and in the absence of an external electric field.     

A new commensurate phase on the theoretical phase diagram of the [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CuCl<Subscript>4</Subscript> crystal

A theoretical phase diagram of the [N(CH₃)₄]₂CuCl₄ crystal with a new commensurate phase characterized by a dimensionless wavenumber q = 2/5 is constructed on a plane specified by two coefficients of the thermodynamic potential. This diagram is used as the basis for the construction of a theoretical pressure-temperature (P-T) phase diagram. The theoretical P-T phase diagram thus obtained is compared with the experimental P-T phase diagram.