Soft Potential Model Research Articles

Nonequilibrium phonon transport in amorphous layers.

Transport of nonequilibrium phonons in amorphous layers is studied. Inelastic scattering rates are calculated within the framework of the soft-potential model. It is shown that these rates can be comparable to the ones of elastic resonant scattering and are many orders of magnitude larger than those of inelastic phonon-phonon processes in crystals. The strength of the inelastic scattering is demonstrated to influence strongly the phonon signal. In particular, down-conversion effects an increase of the occupation numbers of low-frequency phonons, while up-conversion may prevent an observation of localization of high-frequency ones. Stationary phonon transport from the heat generator through the amorphous layer is shown to exhibit a strongly non-Planckian phonon signal. For the case of a strong pulse excitation of an amorphous sample the parameters of phonon transport allow the possibility of a ``hot-spot'' regime. The ``hot-spot'' evolution is shown to differ from the one in crystalline structures by the presence of slow relaxation phenomena. Some details concerning mode-conversion processes are considered. Effective inelastic surface scattering of phonons in crystalline samples, observed in experiments, is shown to be compatible with the model of a disordered near-surface layer. The theoretical results are shown to be consistent with existing experimental data.

Ultrasonic relaxations in lanthanide phosphate glasses.

The attenuation and velocity of ultrasonic waves of frequencies in the range of 10 to 90 MHz have been measured in ${\mathrm{La}}_{2}$${\mathrm{O}}_{3\mathrm{\ensuremath{-}}}$${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$ and ${\mathrm{Sm}}_{2}$${\mathrm{O}}_{3\mathrm{\ensuremath{-}}}$${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$ glasses with high lanthanide concentrations as a function of temperature between 1.5 and 400 K. Two distinct features characterize the attenuation behavior: (i) a plateau at temperatures below 15 K and (ii) a broad high-temperature peak. The former feature is interpreted in terms of the phonon-assisted relaxation of two-level systems and the latter by assuming the existence of a distribution of thermally activated relaxing centers. For both these mechanisms the product of the deformation potential squared and the density of relaxing particles decreases with increasing lanthanide-ion concentration. This result, taken together with previous observations of the properties of oxide glasses, provides physical insight into the microscopic origin of the relaxation effects and suggests that the source of the low- and high-temperature attenuation mechanisms is the same. At temperatures below 100 K, the sound velocity, after the subtraction of the relaxation and anharmonic contributions, follows a linear law as predicted by the soft-potential model for the relaxation of soft harmonic oscillators. An encouraging agreement is obtained between the parameters regulating this mechanism and those determined from the acoustic attenuation plateau.

Elastic intensity and Debye-Waller factor in the soft-potential model for glasses.

The elastic intensity (EI) and the Debye-Waller factor (DWF) is calculated in the classical approximation for the anharmonic potentials of the soft-potential model. The two quantities are different for Hamiltonian motion. If frictional forces are included, the difference between EI and DWF may be found in a quasielastic line. The EI and the DWF are calculated in a small-momentum approximation, for realistic parameters of the soft-potential model. A configurational average is performed over distributions of the coefficients of the soft potentials that are typical for glassy systems. An observable difference between the EI and DWF is found for these systems.

Low-temperature specific heat of Zr-Rh-Pd metallic glasses.

The specific heat of glassy Zr-Rh-Pd alloys at low temperatures is investigated. The results are interpreted within the framework of the model of soft atomic potentials (Karpov et al., Solid State Comun. 44, 333 (1982); Zh. Eksp. Teor. Fiz. 84, 760 (1983) [Sov. Phys. JETP 57, 439 (1983)]). Using the experimental data for the normal and superconducting states, low-energy vibrational excitation parameters are obtained.

Soft phonons in glasses

The dynamics of glasses differs strongly from the one of crystals. Coexisting with the long wavelength phonons one finds additional low energy excitations: tunneling, soft localized variations and relaxations. The soft potential model postulates a common origin of these additional excitations. In its low temperature limit (typically T < 1 K) it is equivalent to the well-known tunneling model. From general properties of the distribution functions describing the soft potentials one derives the temperature dependencies of quantities such as the specific heat or the thermal conductivity. These universal relations hold to about T = 10 K. Fitting the parameters of the model to the experimental data one finds 20–100 atoms to participate in the excitation modes. Extensions to higher temperatures are possible by introducing material dependent distribution functions. Computer simulations are used to test the assumptions of the model and to provide some insight into the microscopic origin of the modes. One finds soft vibrational modes concentrated on 10 or more atoms. These modes are centered at structural irregularities.

Low-frequency vibrational states in Spectrosil-WF.

The heat capacity of Spectrosil-WF (vitreous silica containing <20 ppm of OH) in the temperature range from 2 to 16 K as well as the Raman measurements are presented. The heat capacity is similar to that of Spectrosil-B (vitreous silica containing 1200 ppm of OH) but is about 20% higher than the Heralux (vitreous silica containing 130-180 ppm of OH). The density of low-frequency vibrational states, g (ν), has been determined. It has been found that the form of g (ν) is nonquadratic, which can be explained on the basis of a soft-potential model. About 110 atoms participate in a soft mode. The Raman and infrared coupling constants have similar dependence on frequency. These are explained on the basis of a single-coupling-constant bond model

Soft modes in undercooled liquids

Abstract Recent studies of soft vibrational, tunneling and relaxational modes in glasses support the validity of the soft potential model, an extension of the tunneling model. The implications of this validity are investigated for the undercooled liquid. Using Condat and Jackle's treatment of the scattering from one-dimensional potentials, it is argued that the fast picosecond relaxation in the undercooled liquid is due to these modes and their damping. The significance of this result for current theories of the undercooled liquids is discussed.

Microscopic description of tunneling systems in a structural model glass.

We present a quantitative method which systematically finds tunneling systems in glasses and hence allows a microscopic check of the standard tunneling model. We apply this method to a two-component model amorphous alloy. The major assumptions of the standard tunneling model are qualitatively verified. Small quantitative differences in the distribution of the tunneling matrix elements explain why the experimental temperature dependence of the specific heat is superlinear and the thermal conductivity is subquadratic. Connections to the soft-potential model and recent strong-coupling models are discussed.

Thermal conductivity of Pb (Mg1/3Nb2/3) O3under the influence of high electric field

Abstract Thermal conductivity data of Pb (Mg1/3 Nb2/3) O3 (PMN) ceramics in the unpoled and poled state are presented. The measurements were performed in the temperature range from 2 K up to 100 K. The thermal conductivity exhibits glass like behaviour. The data from 2 K to 15 K can be explained in terms of the soft potential model. The thermal conductivity of the poled sample is enhanced in comparision to the unpoled one.

Analysis of the low-temperature specific heat of amorphous As x Se1−x within the soft-potential model

The soft-potential model provides a description of the specific-heat anomaly of glasses, i.e. the linear specific heatC below 1 K and the maximum ofC/T3 vs.T at temperaturesT of a few K, by three material parameters, namely the mass densityp, the sound velocityv, and the average atomic massM. The experimental results of As x Se1−x are compared with theoretical predictions of this model. The overall good agreement suggests that the soft-potential model, which is an extension of the original tunneling model for glasses, describes the glassy behavior in the whole low-temperature region up to a few K.

Heat release in glasses at low temperatures.

The long-time heat release in glasses after cooling a sample from some initial temperature ${\mathit{T}}_{1}$ to ${\mathit{T}}_{0}$ has been calculated in the framework of the soft-potential model. It is shown that there are three temperature regions where time and temperature dependences of the heat release are different. In the thermal activation region ${\mathit{T}}_{0}$g${\mathit{T}}_{\mathit{c}}$ (where ${\mathit{T}}_{\mathit{c}}$ is a characteristic crossover temperature from tunneling to activation of the order of a few kelvin) the heat release appears to be independent of ${\mathit{T}}_{1}$ and proportional to ${\mathit{T}}_{0}^{9/4}$ln(t/${\mathit{t}}_{0}$)/t\ensuremath{\approxeq}${\mathit{T}}_{0}^{9/4}$/${\mathit{t}}^{0.76}$ for tg${\mathit{t}}_{0}$, where ${\mathit{t}}_{0}$ is of the order of 100 s. In the tunneling region ${\mathit{T}}_{1}$${\mathit{T}}_{\mathit{c}}$ the heat release is proportional to (${\mathit{T}}_{1}^{2}$-${\mathit{T}}_{0}^{2}$)/t in accordance with a prediction of the standard tunneling model. And in the intermediate region ${\mathit{T}}_{0}$${\mathit{T}}_{\mathit{c}}$${\mathit{T}}_{1}$ the heat release is proportional to (${\mathit{T}}_{\mathit{c}}^{2}$-${\mathit{T}}_{0}^{2}$)/t and does not depend on ${\mathit{T}}_{1}$. It is shown that there is a distribution of the characteristic crossover temperature in the glass. This distribution can be calculated from the heat-release data in the intermediate temperature region. The distribution function has several peaks corresponding to several types of two-level systems in the glass. Choosing these distributions it is possible to explain the numerous heat-release experiments in different materials.

The Density of Tunneling and Vibrational States of Glasses within the Soft-Potential Model

Numerical calculations of the density of tunneling and vibrational states of glasses within the soft-potential model (an extension of the tunneling model to include soft vibrations) are reported and compared to analytical approximations. Using a specific assumption on the asymmetry of the soft potentials, one is able to describe the anomalous features of the specific heat Cp and the thermal conductivity of glasses over the entire low temperature range, up to and including the peak in Cp/T3 and the second rise of the thermal conductivity above the plateau. Es wird uber numerische Rechnungen zum Modell weicher Potentiale berichtet (eine Erweiterung des bekannten Tunnelmodells fur Glaser auf eine gemeinsame Beschreibung von Tunnelzustanden, weichen Schwingungen und Relaxationen). Die Ergebnisse werden mit analytischen Naherungen verglichen. Eine spezielle Annahme uber die Asymmetrieverteilung der weichen Potentiale ermoglicht eine Beschreibung der Glasanomalien der spezifischen Warme Cp und der Warmeleitung im gesamten Tieftemperaturbe-reich, einschlieslich des Maximums in Cp/T3 und des erneuten Anstieges der Warmeleitung oberhalb des Plateaus.

Low-temperature specific heat and thermal conductivity of glasses.

The soft potential model (an extension of the tunneling model to include soft localized vibrations) is shown to describe the anomalous features of the specific heat ${\mathit{C}}_{\mathit{P}}$ and the thermal conductivity of glasses over the entire low-temperature range, up to an including the peak in ${\mathit{C}}_{\mathit{P}}$/${\mathit{T}}^{3}$ and the second rise of the thermal conductivity above the plateau.

Soft potential model and universal properties of glasses

It is shown that all the universal properties of glasses can be explained in the framework of the Soft Potential Model (SPM). At low temperatures (below a few kelvin) this model is equivalent to the well-known model of two-level systems of Anderson, Halperin, Varma and Phillips, which explains quite well the universal low-temperature properties of glasses. The SPM predicts that in addition to two-level systems there are soft harmonic oscillators in glasses which are responsible for their universal behavior, especially at higher temperatures.Both the two-level systems and harmonic oscillators are described by anharmonic soft atomic potentials by the uniform way. They interact with phonons (or electric field) by means of bilinear terms with the same coupling constant for both types of low-energy excitations. The elastic interaction between soft atomic potentials leads to a density of the low-energy excitations, which does not depend on the concentration of defects in the glass structure.

Soft Modes in Undercooled Liquids

Abstract Recent studies of soft vibrational, tunneling and relaxational modes in glasses support the validity of the soft potential model, an extension of the tunneling model. The implications of this validity are investigated for the undercooled liquid. Using Condat and Jackle's treatment of the scattering from one-dimensional potentials, it is argued that the fast picosecond relaxation in the undercooled liquid is due to these modes and their damping. The significance of this result for current theories of the undercooled liquids is discussed.

Interaction of soft modes and sound waves in glasses.

The soft potential model (an extension of the tunneling model to include soft localized vibrations) is shown to describe the anomalous features of the specific heat, the sound absorption and the thermal conductivity of glasses over the entire low temperature range.

Soft localized vibrations in glasses and undercooled liquids

Abstract Many unsolved riddles in the glassy and liquid state of matter seem to be connected with the low-frequency excitations in the millielectron volt range. In glasses, an interpretation of neutron scattering and specific heat data in terms of the soft-potential model (an extension of the tunnelling model) indicates a relatively high number of atoms partaking in a soft vibrational or tunnelling mode. The estimated number of about 100 participating atoms has been confirmed recently by numerical work in a glass of soft spheres. In the undercooled liquid, the number of soft modes seems to increase with increasing temperature. An explanation for their localization is attempted in terms of the balance between their vibrational entropy and the energy needed for their destabilization.

Anharmonic potentials and vibrational localization in glasses.

The soft-potential model (an extension of the well-known tunneling model for two-level states in glasses) has been formulated in terms of soft-mode eigenvectors in order to characterize the localization of these modes. The interaction with high-frequency modes explains the absence of very small restoring-force constants. A quantitative comparison to specific-heat and neutron-scattering data from vitreous silica, amorphous selenium, and vitreous boron trioxide shows that both the two-level systems and the low-energy vibrational states can be explained by the same distribution of localized modes.

Theory of inelastic Ne scattering from the Ni(111) surface

The recent inelastic Ne scattering data for Ni(111) by Feuerbacher and Willis are theoretically analyzed in the framework of the distorted wave Born approximation. A Ne-surface soft potential model is inferred from two-body Ne-Ni interactions and the many-body effects due to the phonon-induced surface electron charge redistribution are qualitatively described by three-body forces. The surface-projected phonon densities for the Ni(111) surface are calculated from a force constant model including three-body forces. The cut-off produced by the softness of the Ne-Ni potential accounts for the observed cross-over from Rayleigh-wave to bulk phonon scattering regimes. The one-phonon picture correlates well with experiments for outgoing angles slightly apart from the specular condition (Rayleigh-wave regime) whereas for larger deviations from the specular condition (bulk phonon regime) multiphonon contributions are important.

Analysis of the superfluid properties of helium films

The healing length and other properties of helium films are analyzed in terms of a soft-potential model. The roton gap and the sound velocity may depend on the film thickness below 2.89 atomic layers.Received 11 December 1978DOI:https://doi.org/10.1103/PhysRevB.20.4482©1979 American Physical Society