Soft phonon mode at the martensitic phase transformation of AuCuZn2

The lattice dynamical property of AuCuZn₂ has been investigated by means of inelastic neutron scattering technique in connection with its martensitic phase transformation. The temperature dependent soft phonon was observed transformation. The temperature dependent soft phonon was observed around $\text{q =}\text{2}\text{3}\text{[110]}$ of TA₂ phonon branch. We have also found a premartensitic metastable phase, in which new satellite reflections at (H± $\text{2}\text{3}$, K ? $\text{2}\text{3}$, 0) have been observed around fundamental reflections with H + K = 4n. The atomic displacements of the soft phonon mode correspond to the atomic arrangement of the premartensitic phase.     

Magnetic field effects on the phonon thermal electromotive force in n-Bi-Sb semiconducting alloys

The phonon thermal electromotive force component α₂₂ (?T ‖ C ₁) prevails in n-Bi_{1 ? x} Sb_x (0.07≤x≤0.16) semiconducting alloys at low temperatures. This component increases by almost an order of magnitude in a classically strong transverse magnetic field H with H ‖ C ₃, which results in an increase in thermoelectric efficiency. The transverse Nernst-Ettingshausen coefficient Q _{12, 3} (?T ‖ C ₁, H ‖ C ₃) changes sign from negative at T > 10 K to positive at T < 10 K. The observed characteristics of the phonon thermal electromotive force and the phonon transverse Nernst-Ettingshausen coefficient are explained in terms of the theory of electron-phonon drag for electrons with a strongly anisotropic spectrum.     

A model Hamiltonian for phonon energy transfer in gas—solid collisions

Using the formalism of second quantization in the occupation number representation, a model Hamiltonian of the form H = H_loc + H_nonloc + H_loc?nonloc is developed. H_loc describes the gas atom-phonon system when the gas atom is near the surface, and the phonon operators are only in this term. H_nonmloc describes the gas atom moving in a static potential with no bound states, and H_loc-nonloc couples these two parts of H. The method of solution is to diagonalize H_loc and then to embed it in the continuum of scattering states of H_nonloc. The model is designed so that this diagonalization can be performed essentially exactly for a large class of gas-metal systems. The procedure is illustrated with a simple example which nevertheless shows how multi-phonon processes can dominate in desorption.     

Intervalley magnetophonon resonance peak of thermoelectric power in the phonon drag region of p-Te

A large peak is found at 3.2 Tesla (T) in the second derivative curve of longitudinal magneto-Seebeck coefficient (-?²α₆/?H² of p-type tellurium below 20 K under the magnetic field H6c. The peak height is rapidly increasing with decreasing temperature, in contrast to disappearance of the usual oscillation due to LO phonon which is observed between 20 and 100 K. A small peak is also appreciable in the second derivative of longitudinal magnetoresistance (-?²?₆/?H² at the same field of 3.2 T. The peaks both in -?²α₆/?H² and -?²?₆/?H² are interpreted as a resonance peak due to the intervalley scattering by longitudinal acoustic (LA) phonon between the two valleys split off by inversion asymmetry splitting (μ_BGH). This interpretation gives a value of G as 5.5 in good agreement with the value of G = 5 ± 1 determined by the Shubnikov-de Haas experiment. It is explained by t he phonon drag effect based on this interpretation that the peak of -?²α₆/?H² is much more prominent than that of -?²?₆/?H² and increases with decreasing temperature.     

Phonon conductivity of insulators and semiconductors

Phonon conductivity calculations for materials from groups IV, III–V, II–VI and I–VII are presented. The method uses an effective relaxation time for a phonon taking into account departure from equilibrium of all other phonons which participate in both three-phonon N- and U-processes. It is shown that an important role is played by the off-diagonal part of the three-phonon collision operator above the boundary regime. In particular it is found that the off-diagonal U-processes operator gives a negative contribution to the conductivity at high temperatures. The role of optical phonons in heat transport and in acoustic-optical phonon scattering is also studied. For materials with the mass ratio m₁/m₂ ? 1 we have used the Debye dispersion law in the ‘reduced zone’ scheme, while for materials with m₁/m₂ > 1 but <4 we have used the Debye dispersion law for the acoustic phonons and the Einstein dispersion law or the optical phonons. Inclusion of the optical phonons does not modify the temperature dependence of the conductivity but does change the magnitude significantly.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

On the boundedness of the eigenvalue spectrum of phonon collision operator

Anharmonicity in lattice potential leads to boundedness of the eigenvalue Spectrum of the phonon collision operator. Considering the deviation, ψ_q, in the distribution function of the phonons $\text{N}{}_{\mathrm{q}}\text{, N}{}_{\mathrm{q}}\text{=}\text{N}\text{?}{}_{\mathrm{q}}\text{+}\text{N}\text{?}{}_{\mathrm{q\psi q}}\text{(}\text{N}\text{?}\text{+ 1)}$. bar denoting equilibrium value, as an odd function of the phonon wave vector q it has been possible to obtain a lower bound, μ, on the eigenvalue spectrum of the phonon collision operator P. This satisfies the inequelity relation 0?μ?p_i?λ, where p_i are the eigenvalue of P, and λ is an upper bound on it (as given by Benin). The occurence of μ ensures for the possibility of obtaining a sequence of upper bounds on the lattice thermal transport coefficient.     

Self-consistent phonon treatment of second-order displacive ferroelectric

The high-temperature Curie-Weiss law of electric susceptibilityχ can be explained by quartic interactions between ak～ 0 optic mode, whose normal mode co-ordinateq ₀ is proportional to the polarization, and acoustic vibrations of the lattice. These interactions will either stabilize q₀ at low temperature, preventing a ferroelectric transition, or else such a transition will occur. To obtain coexisting paraelectric and ferroelectric phases at 0 °K, with distinctχ vs.T curves for each phase as observed bySaifi andCross in SrTiO₃, one must invoke anharmonic interactions between q₀ and low-lying, temperature-dependent optic modes. These interactions are treated by the self consistent phonon method, which introduces an effective harmonic HamiltonianH _h and calculates the Helmholtz functionF to first order inH-H_h. The approximation is optimized by minimizingF with respect to the renormalized optical mode frequencies appearing inH _h, for which a system of integral equations is obtained by the minimization procedure. The condition that there are enough low-lying optic modes to produce coexisting phases leads to a prediction of weak optic dispersion at 0 °K. Under these circumstances, the self-consistent phonon equations can be approximated by a pair of coupled cubic equations. From the solution of these, we conclude thatF has three minima at 0 °K in SrTiO₃, corresponding to paraelectric and two oppositely polarized ferroelectric states. 180° domain walls must be few in number and immobile under a field, except in the presence of a high dislocation concentration.     

First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions

The problem of d-dimensional Schrödinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H, H₁) of intertwined Hamiltonians one can associate another pair of second-order partial differential operators (R, R₁), related to the same intertwining operator and such that H (resp. H₁) commutes with R (resp. R₁). This property is interpreted in superalgebraic terms in the context of supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a solution to the resulting system of partial differential equations is obtained and used to build a physically relevant model depicting a particle moving in a semi-infinite layer. Such a model is solved by employing either the commutativity of H with some second-order partial differential operator L and the resulting separability of the Schrödinger equation or that of H and R together with SUSYQM and shape-invariance techniques. The relation between both approaches is also studied.     

Surface and interface optical phonon modes and electron-phonon interaction in a multi-shell spherical system

Within the framework of the dielectric continuum model, interface optical(IO) and surface optical(SO) phonon modes and the Fr?hlich electron-IO (SO) phonon interaction Hamiltonian in a multi-shell spherical system were derived and studied. Numerical calculation on CdS/HgS/H₂O and CdS/HgS/CdS/H₂O spherical systems have been performed. Results reveal that there are two IO modes and one SO mode for the CdS/HgS/H₂O system, one SO mode and four IO modes whose frequencies approach the IO phonon frequencies of the single CdS/HgS heterostructure with the increasing of the quantum number l for CdS/HgS/CdS/H₂O. It also showed that smaller l and SO phonon compared with IO phonon, have more significant contribution to the electron-IO (SO) phonon interaction. Received 16 October 2001 and Received in final form 23 January 2002 Published online 25 June 2002     

Nonohmic behavior of semiconductors in a quantizing magnetic field

We have investigated the nonohmic resistivity of a nondegenerate semiconductor in quantizing magnetic fields for the case where acoustic phonons are the dominant scattering mechanism. The type of I-V characteristics found depends upon which of three mechanism are dominant. The three mechanisms are due to collisional broadening, inelasticities due to the finite phonon energy and phonon drag. When collistion broadening is important, the nonlinearities in the current voltage characteristic arise only from electron heating, while when the inelasticities are dominant, there is also an intrinsic nonlinearity in the characteristic. Finally, when phonon drag is dominant, high frequency acoustoelectric amplification will occur when the Hall velocity exceeds the sound velocity, i.e. V_H > S.For the case where inelasticities dominate, a region of negative differential resistance is obtained that should persist even when there is considerable optical phonon scattering.     

Phonon densities of states of the thorium hydrides

The optical phonon density of states in both Th₄H₁₅ and ThH₂ is presented as measured by inelastic neutron scattering. For Th₄H₁₅ the results indicate a strong electron—optical phonon coupling.     

Phase shifts and the modified and møller wave operators

The Schrödinger operator H=?Δ+V is considered when the potential V is central, oscillating and possibly unbounded. An eigenfunction expansion for H is derived. Also, the phase shift of the generalized eigenfunctions of H is computed. The expansion and shift are, together, applied to the study of the wave operators of scattering theory. The modified wave operators, for H and H ₀=?Δ are shown to exist and be complete and a condition on V is derived which is necessary and sufficient for the Møller wave operators to exist and be complete. Spectral properties of H are also discussed.     

Molecular dynamics calculations of anharmonic properties of the vibrational spectrum of BCC zirconium under pressure

The structural stability and lattice dynamics of the high-pressure bcc phase of Zr at a constant temperature T = 500 K are studied for various volumes using molecular dynamics simulation with the Animalu pair pseudopotential. Dispersion curves of the vibrational spectrum calculated by the molecular dynamics method for various volumes are compared to the phonon spectrum obtained in the harmonic approximation. It is demonstrated that, as the volume decreases, all frequencies of the vibrational spectrum increase gradually and bcc zirconium remains strongly anharmonic along all high-symmetry directions of the Brillouin zone over the entire range of volumes studied. The strongly anharmonic N _T1 phonon is significantly softened near the point of structural instability of bcc-Zr at T = 500 K and V = 0.87V ₀. As the volume decreases to V = 0.73V ₀ under pressure, the anharmonic corrections for this phonon decrease by almost an order of magnitude and the phonons near the H point of the Brillouin zone become anharmonic. The damping of the T ₁ phonon mode along the [110] direction is calculated as a function of pressure.     

On the Lie-Trotter theorems inL p -spaces

In this paper we consider operatorsH ₀ andV possessing the following properties:

1. H ₀ is a positive self-adjoint operator acting inL ²(M, γ) with γ a probability measure, so that exp(?tH ₀) is a contraction onL ¹(M, γ) for eacht>0.
2. V is a semibounded multiplicative operator acting inL ²(M, γ) {fx379-1}

Under these assumptions theorems of Lie-Trotter type are derived for the operatorsH, H ₀, V, whereH is a self-adjoint extension of the algebraic sumH ₀+V, and is built by the form method. Under the additional assumption thatV(·)∈L ²(M, γ) we prove an essential self-adjointness ofH ₀+V. The results obtained are applicable to non-relativistic quantum mechanics.     

‘Soft’ optical phonons and the morphotropic phase transition of the Pb(Ti1−x, Zrx)O3 system

Room temperature Raman scattering results for the Pb(Ti_1?x, Zr_x)O₃ system in its tetragonal ferroelectric phase are analyzed. For x ≤ 0.25, the square of the frequency of the ‘soft’ E(TO) phonon is linear in the Zr concentration. In addition, we find that the morphotropic phase transition at x = 0.535 may be associated with an instability of this ‘soft’ phonon. It is shown that changes in the short-range harmonic forces play an important role in the x-dependence of the ‘soft’ E(TO) phonon frequency.     

On the theory of complex potential scattering

We study the effect of the addition of a complex potential λV_sep to an arbitrary Schrödinger operator H = H₀ + V on the singularities of the S matrix, as a function of λ. Here V_sep is a separable interaction, and λ is a complex coupling parameter. The paths of these singularities are determined to a great extent by certain saddle points in the momentum (or energy) plane. We explain certain critical phenomena recently reported in the literature. Associated with these saddles are branch-type singularities in the complex λ plane, which are dynamical in origin. Some examples are discussed in detail.     

Optical investigation of coherent and thermal phonons in high-T c superconductors

Low-energy phonons in NdBa₂Cu₃O_7?x and Bi₂Sr₂CaCu₂O_8+x superconducting single crystals have been studied by Raman scattering and reflectivity measurements with femtosecond-scale resolution. Raman scattering provides information on equilibrium thermal phonons, whereas information about a coherent state of the phonon system is obtained by measuring in the time domain when the phonon system is pumped by an ultrashort pulse and subsequently probed by a properly gated second pulse. It is shown that both methods yield similar results for the phonon mode energies, while the energy relaxation and dephasing rates exhibit a tendency to disagreement.     

Phase transitions at high pressure in the fullerene C60 molecular donor-acceptor complex {Hg(dedtc)2}2 · C60

Raman spectra of crystals of the molecular fullerene C₆₀ donor-acceptor complex {Hg(dedtc)₂}₂ · C₆₀ (fullerene with mercury diethyldithiocarbamate) have been measured at a pressure up to 8.4 GPa and at room temperature. A phase transition has been revealed in the pressure range of 1.2–2.0 GPa, which is accompanied by a splitting of the degenerate intramolecular phonon modes H _g (1)-H _g (4) and H _g (7)-H _g (8), as well as by a softening of the H _g (2) mode of the fullerene C₆₀. As the pressure further increases to the maximum value, the intensity of the bands varies smoothly. A decrease in the pressure leads to the reverse transition to the initial state at 1.2 GPa. The splitting of the degenerate modes H _g (1)-H _g (8) and the softening of the H _g (2) modes resemble their behavior in the formation of dimers in fullerite crystals and indicate the possible formation of dimers in two-dimensional fullerene layers under hydrostatic compression of the {Hg(dedtc)₂}₂ · C₆₀ complex.     

Soft modes and high Tc in Nb3Sn

We investigate the direct effects of phonon softening on T_c in Nb₃Sn. It is inadequate to explain the high T_c, which arises instead from an unusually large electron- phonon coupling to the two Γ'₁₂ optical phonon modes.