Self-consistent Phonon Approximation Research Articles

On the lattice dynamics of solid solutions with a quantum paraelectric and a ferroelectric component

Abstract The lattice dynamics of displacive type phase transitions in solid solutions with a quantum paraelectric and a ferroelectric component is considered. Using the self-consistent phonon approximation and the coherent potential approximation the phonon spectrum of the disordered lattice is obtained and the concentration dependence of the phase transition temperature is calculated. Good agreement with experimental results for (Ba, Sr) TiO3 is obtained.

Soft Mode Calculations of KTa1-xNbxO3 Solid Solutions in the Cubic Phase

The temperature dependence of the ferroelectric soft mode has been calculated in mixed KTa1-xNbxO3 crystals for various niobium concentrations within the framework of a non-linear shell model, in which the fourth-order anharmonic electron-phonon interaction is taken into account in the self-consistent phonon approximation. The variation of the soft mode frequency with temperature for different niobium concentrations(0<x<100%) is reproduced by our model, in which only two parameters related to the linear and non-linear polarizability of the oxygen ion along the oxygen-metal (Ta or Nb) chains depend on x.

The self-consistent average phonon equation of state for ionic crystals

The self-consistent average phonon (SCAP) approximation was successful in describing the thermodynamic properties of monatomic solids. This formalism was extended to ionic crystals (specifically sodium chloride) at two levels of approximation: (1) the phonon frequencies replaced by a single average frequency, and (2) the phonon frequencies replaced by two average frequencies corresponding to the usual acoustic and optic phonons. In order to compare with earlier calculations and with experiments various forms of the interatomic potential (with polarization neglected) were used. The SCAP calculation is in good agreement with experiment at low and medium temperatures but underestimates the high temperature thermal expansion. It is concluded that the SCAP formalism with polarization included should give a good approximation to the thermodynamic properties of simple ionic crystals over the entire temperature range.

A self-consistent microscopic theory of hydrogen bond melting with application to poly(d G)⋅poly(d C)

In this paper we develop a modified self-consistent phonon approximation model which displays effects which indicate melting. The model is applied to hydrogen bond melting of poly (dG)⋅poly(dC) and predicts melting at 340 K. The calculation has no parameters adjusted to fit the melting, the hydrogen bond potentials are adjusted to fit data at room temperature.

Composition, structure and properties of ferroelectrics

Abstract Ferroelectric materials of the displacive type show a strong interrelation between chemical composition and properties. Most of them are ternary or more complex chalcogenides except for a few IV-VI compounds. They usually exhibit structures of high (cubic or hexagonal) symmetry in their paraelectric phases. It is shown that in a polarizability model (refer to the included preprint) the transition temperature Tc depends on three local microscopic parameters which correlate strongly with the chemical constituents but are rather independent of the structure of ferroelectrics. The model describes thermodynamic and dynamic properties of ferroelectric materials quite well in a self-consistent phonon approximation. A non-linear extension of the model is used to discuss non-linear phenomena of ferroelectrics, such as the photo-induced properties.

Ferroelectricity in ternary compounds

Ferroelectricity has been observed almost exclusively in chalcogenides, in particular in oxides. Except for a few IV–VI compounds (SnTe, etc.) all ferroelectrics are ternary or more complex compounds. The best-investigated ternary ferroelectrics are perovskites, whose electronic and dynamical properties have been studied in detail. Generally, the ferroelectric phase transition is based on a critical cancellation of repulsive and attractive forces (Slater). The residual force governing the phase transition and related properties is the fourth-order polarizability of the chalcogen ions or a corresponding cluster polarizability of anionic groups. The thermodynamic and dynamic properties can be described quite well in a self-consistent phonon approximation, while nonequilibrium metastable excitations, such as photoferroelectric phenomena, require a more exact nonlinear treatment of the crystal polarizability.

Commensurate-Incommensurate Transition in a Two Dimensional Classical Sine-Gordon System

The critical line for the commensurate· incommensurate transition in the two dimensional classical sine-Gordon system is determined with the use of the Bethe ansatz equations for the massive Thirring model with finite hole density. Except slight differences the behavior of the critical line is the same as that obtained on the basis of the self-consistent harmonic phonon approximation.

Liquid State Thermodynamics: Application to Highly Compressed Solids

Thermodynamic properties of materials above a few hundred KBars can normally be obtained only by dynamic techniques which have the associated difficulty (from the theoretical point of view) that the high pressure states are usually also at quite high temperatures. Thus, it is important to obtain accurate estimates of the thermal contribution to the thermodynamic functions. Within the pair potential model of solids, these thermal contributions may be determined by a self-consistent phonon approximation, but this is generally a very complicated calculation. Numerous approximate methods have thus been developed to estimate the thermal contribution to the thermodynamic functions [1].

Freeze-In Transition of Anharmonic Oscillator System with Quenched Random Interactions

A simple model of strongly disordered systems composed of anharmonic oscillators with quenched random interactions is introduced and its structural phase transition is studied by making use of the replica method. A freeze-in transition characterized by Edwards and Anderson type's order parameter (q *0), the phase diagram (para-ferrodistortive-frozen), and a constant susceptibility below the transition temperature are derived in the mean field (Einstein oscillator) approximation. The self-consistent phonon approximation is also used to study the effect of spatial fluctuations, and it is shown that the phase diagram undergoes a qualitative change at the spatial dimension d=4. The relationship between our model and the Ginzburg-Landau theory of spin.glasses are discussed.

Molecular-Dynamics Calculations of Two-Dimensional Sine-Gordon Lattice

We have performed the molecular-dynamics calculations for the two-dimensional sine-Gordon lattice and obtained the internal energies and the time correlation functions of displacements. The experimental results at low temperatures are in good agreement with the analysis in terms of the self-consistent phonon approximation.

The phonon absorption line shape of solid molecular H2 and D2 as a function of density

A theoretical study is presented of the lattice dynamics of the cubic phases of solid hydrogen and deuterium as a function of density. The calculations are performed in the self-consistent phonon approximation and include cubic three-phonon processes and higher anharmonic corrections. The anisotropic part of the intermolecular potential is neglected and libronic effects are not included. The line shape of the one-phonon far-infrared absorption process is studied in detail and is found to display a complex and interesting behavior as a function of pressure. The experimental absorption line is well accounted for by the one-phonon line shapes calculated here and phonon-libron and multi-phonon absorption, which has been treated elsewhere. Phonon dispersion curves and elastic constants are also presented.

Mode damping by electrostrictive interaction in a uniaxial ferroelectric

AbstractAn electrostrictive‐type coupling model is used to study mode damping in the paraelectric phase of a uniaxial ferroelectric with an anisotropic soft‐mode dispersion. Mode linewidths are obtained by solving the phonon Green's function equation of motion in the self‐consistent phonon approximation (SPA). The dominant contribution to the damping comes from the scattering of a soft optic phonon with the absorption or emission of an acoustic phonon. The soft‐mode damping γs shows a (T – T0)1/2 behaviour while, in the isotropic limit, it becomes linearly dependent on temperature. For large anisotropy, the longitudinal acoustic attenuation α1 ∝ ω2(T – T0)−1/2X XIn (T – T0)−1/2 or ω2(T – T0)−1/2 according as the soft‐mode is under or over‐damped in the opposite limit, the corresponding dependences are ω2(T – T0)−1/2 and ω2(T – T0)−3/2, respectively. If soft‐mode interaction with other modes (e.g. phonon density fluctuations) are considered, γs becomes nearly temperature‐independent in this case α1 behaves like ω2 (T – T0)−1 which compares favourably with experimental observations on lead germanate where the soft‐mode is overdamped.

Theory of orientational epitaxy in the self-consistent phonon approximation

The theory of the orientational epitaxy phase is developed for an anharmonic solid monolayer within the framework of a self-consistent phonon approximation. This theory shows how the adatom-adatom coupling constants and adatom-substrate coupling constants in the theory of Novaco and McTague are modified by renormalization due to the zero-point motion and the thermal vibration of the adatoms. Some general conclusions about the nature of orientational epitaxy are presented and numerical results are given for argon adsorbed on basal plane graphite. These results show that while many calculated properties of the argon solid have important corrections due to the anharmonic nature of the system, the orientation angle versus lattice constant curve is not affected to any significant degree.

Clinical considerations in the treatment of pain

The influence of the order parameter's phase fluctuations on the Meissner effect is studied for strong anisotropic layered superconductors in the presence of a weak magnetic field, H, less than the lower critical field Hc1 (H<Hc1). The Josephson coupling between the layers can be realized in quasi-two dimensional (quasi-2d) superconductors when the interlayer tunnelling integral J⊥ satisfies the condition J⊥<κTc(2)<ϵF, where ϵF and Tc(2) are the Fermi energy and the mean-field transition temperature for a single superconducting layer, respectively. The system of equations of motion is obtained for the order parameter phases ϕj(r→) at the r-th point of the j-th layer. This system of coupled equations is investigated by applying the self consistent phonon approximation (SCPA) method. There exists the plasmon mode in the Josephson coupled layered superconductors in the frame of the SCPA approximation. The square of the transverse effective velocity, vph,⊥, of collective excitations become proportional to the interlayer phase–phase correlator 〈cos (ϕj−ϕj−1)〉. When this correlator approaches zero, correlations of the superconducting phases on the different layers disappear, i.e. the phase transition from quasi-2d superconducting state to a pure 2d state occurs at the critical temperature Tc1. The transverse rigidity of the system and the plasmon's effective velocity vph,⊥ vanish at this temperature. Tc1 is less than Tc(2) and (Tc(2)−Tc1)∼Tc(2)(κTc(2)/ϵF). In the temperature interval of (Tc1−T)∼Tc1(κTc1/ϵF) ln (κTc1/J⊥) below Tc1, the fluctuations of the order parameter's phases become essential in the quasi-2d superconductor. In this interval the ratio of the longitudinal λ‖ and transverse λ⊥ components of the London penetration depths, λ‖/λ⊥, should exhibit strong temperature dependence, unlike the prediction of the usual Ginzburg–Landau phenomenological theory. λ‖ and λ⊥ diverge at different critical temperatures, namely at Tc2≡Tc(2) and Tc1, respectively. At Tc1<T<Tc2 the phases ϕj on the different layers become non-correlative and the Kosterlitz–Thouless vortices appear in each superconducting layers.

Temperature-dependent lattice dynamics and equations of state of solid hydrogen

A numerical computation of the temperature dependence of the pressure volume relations of fcc parahydrogen was carried out within a somewhat modified self-consistent phonon approximation. The effect of the hard core in the intermolecular potential was treated with a short-range correlation function. The hydrogen Hugoniot, specific heat, and average sound velocities were also calculated and comparison with experimental data was made where possible.

Self-consistent phonon calculation of structures and thermodynamic properties of small argon crystallites

The self-consistent phonon approximation is applied to small crystallites of $N$ argon atoms, in the range $3\ensuremath{\le}N\ensuremath{\le}15$. The temperature dependence of the lattice constant, frequencies, internal energy, free energy, specific heat, and entropy, for each cluster size, is reported. The variation of these quantities with $N$ is also given. The equilibrium structures are quantum mechanically determined at each temperature and are found to agree with classical results. Comparisons with normal-mode calculations and with bulk behavior are given.

Self-Consistent Structure of Metallic Hydrogen

A calculation is presented of the total energy of metallic hydrogen for a family of face-centered tetragonal lattices carried out within the self-consistent phonon approximation. The energy of proton motion is large and proper inclusion of proton dynamics alters the structural dependence of the total energy, causing isotropic lattices to become favored. For the dynamic lattice the structural dependence of terms of third and higher order in the electron-proton interaction is greatly reduced from static lattice equivalents.

Effects of internal strains on the elastic constants of HCP hydrogen and deuterium

Expressions for effects of internal strains on elastic properties of solids are derived for the case of an anharmonic crystal and applied to hydrogen and deuterium. The calculation is carried out within the framework of the self-consistent phonon approximation. Onlyc11,c12, andc66 = 1/2(c11 − c12) are affected, and the resulting corrections are 10% ofc11 and 30% ofc12 for the present case. When due allowance is made for these effects, a previous calculation which did not include them is in better overall agreement with experiment.

Elastic constants of solid hexagonal close-packed hydrogen and deuterium

Zero-pressure elastic constants for hcpp-H2 ando-D2 atT=0 K are calculated within the framework of the self-consistent phonon approximation with cubic anharmonicities. A pairwise additive model potential of the Barker-Pompe form, which reproduces the equation of state in the solid over a wide range of pressures, is used for the calculations. Debye temperatures and Gruneisen constants are also presented and the results are compared with recent experiments on the velocity of sound, inelastic neutron scattering, and specific heat.

Self-consistent phonon calculations and equations of state of solid hydrogen and deuterium

A numerical computation of the ground-state energies and zero-temperature pressure-volume relations of fcc para-${\mathrm{H}}_{2}$ and ortho-${\mathrm{D}}_{2}$ was carried out within the framework of the self-consistent phonon approximation. The calculations employed two recently proposed pair potentials and are expected to be valid up to several hundred kilobars. The effect of the hard core in the intermolecular interaction was treated with a short-range correlation function. The pressure dependence of the phonon density of states, sound velocities, and bulk moduli were determined and comparison with experimental data was made where possible.