Debye Frequency Research Articles

Thermo‐Chemical Expansion in Strontium‐Doped Lanthanum Cobalt Iron Oxide

La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF) displays mixed ionic electronic conductivity at high temperature that makes it suitable for solid oxide fuel cell cathodes, ceramic oxygen generators, and oxygen permeation membranes. However, upon changes in temperature and oxygen partial pressure LSCF exhibits changes in volume, termed chemical expansion, which can result in mechanical failure of the aforementioned devices. The chemical expansion change with temperature also complicates thermal expansion modeling. The present work measures and models chemical expansion as a function of oxygen partial pressure (10−4−1 atm O2) and temperature (700°–900°C) using our previously modeled defect equilibria to determine the chemical expansion coefficient per oxygen nonstoichiometry (δ) of 0.031. The thermal expansion is also measured and modeled using the Morse potential and Debye frequency distribution. The results are combined to yield a model describing the thermo‐chemical expansion of LSCF.

Pressure dependence of hopping conduction in amorphous Ge alloys

The ac-conductivity of amorphous Ge-Au alloy has been measured at frequencies of 20 Hz to 1 MHz, at pressures up to 5 GPa and temperatures down to 77 K using a Drickamer-type high pressure cell. The ac-conductivity increases with increasing frequency. With increasing temperature, the rising frequency increases. From these results, temperature dependence of conductivity was obtained without shape parameters of the sample. The temperature dependence of hopping conductivity is found to be well described by a power law expected from the Multiphonon Process model. The exponent n in the power law increases with increasing pressure below 2 GPa, and decreases above 2 GPa. This pressure dependence of n agrees with the previous reported results from dc electrical resistivity measurements. The anomalous pressure dependence of n is discussed in relation to the Debye frequency, atomic distance, void size, and the density of states at the Fermi level.

CausalRLGC($f$) Models for Transmission Lines From Measured $S$ -Parameters

Frequency-dependent causal RLGC(f) models are proposed for single-ended and coupled transmission lines. Dielectric loss, dielectric dispersion, and skin-effect loss are taken into account. The dielectric substrate is described by the two-term Debye frequency dependence, and the transmission line conductors are of finite conductivity. In this paper, three frequency-dependent RLGC models are studied. One is the known frequency-dependent analytical RLGC model (RLGC-I), the second is the RLGC( f) model (RLGC-II) proposed in this paper, and the third (RLGC-III) is same as the RLGC -II, but with causality enforced by the Hilbert transform in frequency domain. The causalities of the three RLGC models are corroborated in the time domain by examining the propagation of a well-defined pulse through three different transmission lines: a single-ended stripline, a single-ended microstrip line, and an edge-coupled differential stripline pair. A clear time-domain start point is shown on each received pulse for the RLGC-II model and the RLGC-III model, where their corresponding start points overlap. This indicates that the proposed RLGC(f) model (RLGC-II) is causal. Good agreement of simulated and measured S-parameters has also been achieved in the frequency domain for the three transmission lines by using the proposed frequency-dependent RLGC(f) model.

Large Scale Simulations

In this chapter we will focus on molecular dynamics (MD) simulations with large numbers of atoms ( N > 1000). Typically, ab initio or F irst P rinciples M olecular D ynamics (FPMD) calculations are performed with smaller clusters of say 100 or fewer atoms. This choice is largely due to limitations in computing resources. The simulation procedure we will explore in this chapter is known as E mpirical P air- P otential M olecular D ynamics (EPPMD). EPPMD does not rely upon estimating the forces between atoms with D ensity F unctional T heory (DFT) as an approximation to the solution of the quantum mechanical problem, which is the computationally costly aspect of FPMD. Rather, EPPMD estimates forces between atoms from an empirical parameterization of a classical description of the potential energy, whose spatial derivative captures the pairwise-additive attractive and repulsive forces between all atoms. Because the interatomic force calculation is classical, its computational cost is minimal, and this encourages the application of EPPMD to simulations involving large numbers of atoms. Additionally, whereas FPMD simulations are typically run for durations on the order of a few picoseconds, EPPMD simulations may be extended to much longer durations (2–10 nanoseconds), which permits investigation of transport properties such as shear viscosity and phonon thermal conductivity (Fig. 1⇓) using Green-Kubo theory (Kubo 1966). The longer durations of EPPMD runs (with up to order 107 time steps) are again a consequence of the computational efficiency derived from the classical force field approximation. In this chapter we are going to refer to long duration molecular dynamics simulations involving large numbers of atoms as L arge S cale S imulations (LSS). Figure 1. Typical time scales for various molecular dynamics calculations. The value labeled as “Debye frequency” refers to the reciprocal of (3 N /4π V ) …

Effects of level broadening and electron overheating in tunneling structures based on metal clusters

The effect of level broadening and electronic subsystem overheating of disk-shaped and spherical gold clusters/islands on the current-voltage characteristic of the three-electrode structure has been studied. A scheme for calculating the electronic level broadening in the one-dimensional case of rectangular barriers has been proposed. In the two-temperature electron-ion model of a metal cluster, taking into account the size dependence of the Debye frequency, the kinetic electron temperature has been estimated as a function of the bias voltage. At low ion temperatures, the broadening and electron overheating effects result in disappearance of steps of quantum and Coulomb staircases, i.e., a strong smoothness of the current-voltage characteristic even in structures on clusters consisting of a denumerable number of atoms, which is actually observed experimentally.

Effects of electron levels broadening and electron temperature in tunnel structures based on metal nanoclusters

We study the influence of energy levels broadening and electron subsystem overheating in island electrode (cluster) on current–voltage characteristics of three-electrode structure. A calculation scheme for broadening effect in one-dimensional case is suggested. Estimation of broadening is performed for electron levels in disc-like and spherical gold clusters. Within the two-temperature model of metallic cluster and by using a size dependence of the Debye frequency the effective electron temperature as a function of bias voltage is found approximately. For helium temperature of ion subsystem, the heating temperature of electrons in a quantum disc is almost one order of magnitude higher than that in a sphere; it achieves thousands of Kelvin. We suggest that the effects of broadening and electron overheating are responsible for the smoothing of current–voltage curves, which is observed experimentally at low temperatures in structures based on clusters consisting of accountable number of atoms. However, a role of the broadening is much more significant.

Multiband superfluidity and superfluid–to–band-insulator transition of strongly interacting fermionic atoms in an optical lattice

We study the multiband superfluid and the superfluid (SF) to band insulator (BI) transition of strongly interacting fermionic atoms in an optical lattice at a filling of two fermions per well. We present physical arguments to show that a consistent mean field description of this problem is obtained by retaining only intraband pairing between the fermions. Using this approach we obtain a reasonable account of the experimentally observed critical lattice depth for the SF-BI transition and the modulated components of the condensate density, and make predictions for the lattice depth dependence of the quasiparticle gap which can be tested in future experiments. We also highlight some interesting features unique to cold atom superfluids within this intraband pairing approximation; for instance, the pair field is forced to be uniform in space and the Hartree field vanishes identically. These arise as a result of the fact that while the pairing interaction is cut off at the scale of the Debye frequency in conventional superconductors, or at the lattice scale in tight binding model Hamiltonians, such a cutoff is absent for cold Fermi gases.

Studies on multiphased mixed crystals of NaCl, KCl and KI

AbstractMultiphased mixed crystals of NaCl, KCl and KI were grown by the melt method, for the first time. Densities and refractive indices of all the grown crystals were determined and used for the estimation of the composition in the crystal. Atomic absorption spectroscopic measurements were done to estimate the metal atom contents in the crystal. Lattice parameters and thermal parameters (Debye‐Waller factor, mean square amplitude of vibration, Debye temperature and Debye frequency) were determined from the X‐ray powder diffraction data. DC and AC electrical measurements were done at various temperatures ranging from 40 to 150°C. Activation energies were also estimated. The observed lattice parameters showed that the system exhibits three phases each nearly corresponds to NaCl, KCl and KI. The thermal and electrical parameters show a highly nonlinear bulk composition dependence. Results are reported. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Model calculation of the electron-phonon coupling in Cs/Cu(111)

A simplified calculation scheme is proposed for the analysis of the phonon-induced lifetime broadening of surface-electronic states. The aim has been to include the details of the electron and phonon structures. In contrast to the present analysis based on phonon Debye models, where all is hidden in the parameters Debye frequency ${\ensuremath{\omega}}_{D}$ and electron-phonon coupling constant $\ensuremath{\lambda}$, our procedure gives a single multiplicative fitting parameter ${V}_{d}^{2}$ for the spectral Eliashberg function, where ${V}_{d}$ represents the effective deformation potential. We apply this procedure to the image and surface states of Cu(111) and to the quantum-well state and the recently found gap state of $p(2\ifmmode\times\else\texttimes\fi{}2)\ensuremath{-}\text{Cs}/\text{Cu}(111)$. We demonstrate that the crucial contribution to the electron-phonon coupling by the overlayer localized low-frequency phonon modes is well captured by the scheme. The presented scheme should be useful for combined experimental and theoretical studies of overlayer systems for which still no full first-principles calculation of the electron-phonon coupling has been presented due to the complexity of the system.

Superconductivity in B-doped diamonds

Results of theoretical studies on the surprising discovery of superconductivity in B-doped diamonds are presented. It is stressed that the critical temperatures are very high irrespective of the small density of states at the Fermi energy and the presence of strong disorder as deduced both experimentally and theoretically. It is concluded that this strong attractive interaction comes from particular situation where carriers are doped into the covalent bonds of diamond structure, which naturally have very high Debye frequency. It is indicated that such transformation of covalent bonds into conduction bands by carrier doping can be a candidate for higher critical temperature.

Thermal parameters of MgSO 4·7H 2O and NiSO 4·7H 2O crystals added with urea and thiourea

Pure and impurity-added (with urea and thiourea) MgSO 4·7H 2O and NiSO 4·7H 2O single crystals were grown by the free-evaporation method from aqueous solutions. Density was measured by the flotation method. X-ray diffraction data were collected for powder samples and used for the estimation of thermal parameters like Debye–Waller factor, mean-square amplitude of vibration, Debye temperature and Debye frequency. The thermal parameters do not vary in a particular order with respect to impurity concentration, which could be attributed to the random disturbance created by the impurity molecules in the hydrogen-bonding system of the MgSO 4·7H 2O and NiSO 4·7H 2O lattices.

X-ray diffraction studies on (NaCl) x(NaBr) y−x(NaI) 1−y crystals

We have grown (NaCl) x (NaBr) y − x (NaI) 1− y crystals by the melt method for various values of x and y. Thermal parameters like Debye–Waller factor, Debye temperature, mean square amplitude of vibration and Debye frequency were determined using the X-ray powder diffraction intensity data. The results obtained are reported here.

Phonon-assisted transport of a reactive atom in the lattice of a solid metal catalyst

The transport of a reactive atom on the surface, or dissolved in the bulk, of a metal catalyst occurs by motion of the atom between occupied and unoccupied sites in the host lattice. The energy required to surmount the potential barrier separating two such sites is obtained by the annihilation of a phonon at the Debye frequency of the lattice. We consider the Hamiltonian perturbation that stimulates this motion to involve either (1) anharmonic coupling of the reactive atom to the lattice, or (2) strain energy associated with the reactive atom entering the lattice as a hard sphere. In either case, the atomic jump rate depends upon the temperature, the mass of the metal atom, the Debye temperature of the metal, and the mass, binding energy, and local mode temperature of the reactive atom in an occupied site. Although the temperature dependence of the jump rate is the same in both cases, there is in the case of the anharmonic model an extra dependence on the binding energy, which does not appear in the case of the strain model. The temperature dependence of the jump rate successfully accounts for the curvature of Arrhenius plots of the diffusion coefficients for hydrogen atoms in various transition metals and for oxygen atoms in silver.

Studies on multiphased mixed crystals grown from NaBr and KCl

We have grown multiphased binary and ternary mixed crystals by the melt method using the miscible alkali halides, viz. NaBr and KCl and physically characterized. Thermal parameters like Debye–Waller factor, Debye temperature, Debye frequency and mean square amplitude of vibration were determined using the X-ray powder diffraction intensity data. DC and AC electrical measurements were carried out by using the parallel plate capacitor method at various temperatures. Activation energies (DC and AC), mean jump frequency, compressibility and mean sound velocity were also determined. The results obtained are reported here.

Odd Triplet Pairing in Clean Superconductor/Ferromagnet Heterostructures

We study triplet pairing correlations in clean ferromagnet (F)/superconductor (S) nanojunctions, via fully self-consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle alpha between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and alpha. The triplet amplitudes are largest at times on the order of the inverse Debye frequency, and at that time scale they are long-ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.

Vibrational instability, two-level systems, and the boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.

Electron–phonon coupling constant of cuprate based high temperature superconductors

The electron–phonon coupling constant in two-dimensional cuprate high temperature superconductors has been determined by the ultrasonic method. The electron–phonon coupling constant in the Van Hove scenario λ VH was found to increase with transition temperature T c . λ VH is in the range of 0.025–0.060 which is 10–100 times smaller than the conventional three-dimensional Bardeen–Cooper–Schrieffer coupling constant. The characteristic Debye temperature θ D does not correlate with T c . These findings show that the interplay between the Debye frequency and electron–phonon coupling in the two-dimensional system and their variations have a combined effect in governing the transition temperature.

Studies on (NaCl) x (KBr) y-x (KI)1-y solid solutions: 1. Lattice and thermal parameters

Solid solutions of NaCl, KBr and KI were prepared by the melt method for the first time. Densities and refractive indices of all the prepared solid solutions were determined and also used for the estimation of the bulk composition in the crystal. Lattice parameters and thermal parameters like Debye–Waller factor, mean square amplitude of vibration, Debye temperature and Debye frequency were determined from the X-ray powder diffraction data. The observed lattice parameters showed the existence of three phases in solid solutions each nearly corresponds to NaCl, KBr and KI. The thermal parameters show a highly non-linear bulk composition dependence.

Analytical investigation into the mechanism of dielectric losses due to interlayer polarization

The theory of dielectric space-charge polarization losses describes well both the model of an inhomogeneous dielectric [1] and the polarization resulting from mosaic blocks of alkali-halide crystals [2]. The Debye frequency dependences e*(ω) and tan δ(ω) with non-Arrhenius relaxation time are calculated in the first approximation of perturbation theory [3, 4] with the use of a nonlinear system of the Fokker-Planck and Poisson equations for the interlayer polarization with allowance for tunnel transitions of relaxation oscillators. For the Maxwell mechanism of space-charge relaxation, tan δ(ω) also has the Debye form [5]. It should be noted that in studies cited above the electric field was considered uniform, and the nonlinearity of the initial system of equations was not investigated. This paper removes these restrictions and elaborates a theory of relaxation mechanism.

Change in the vibrational properties of bulk metal glass with time

The velocity of ultrasonic longitudinal and transverse waves in ${\mathrm{Zr}}_{46.75}{\mathrm{Ti}}_{8.25}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ bulk metal glass has been measured at $298\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ after its annealing for different times at $523\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, a temperature $97\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ below its apparent ${T}_{g}$. Elastic constants and vibrational contribution to thermodynamic properties have also been determined. At $298\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the normalized value of the instantaneous bulk and shear moduli, $K$ and $G$, increases with the annealing time, $t$, according to the relation $[1\ensuremath{-}\mathrm{exp}\text{\ensuremath{-}}{(kt)}^{n}]$ with $k=7.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, $n=0.5$. It is found that $K(t)=a+bG(t)$, where $a$ and $b$ are constants. In terms of a recent model for viscous flow, an extrapolated increase in $G$ with $t$ corresponds to an approximate three-fold increase in viscosity and 5% decrease in the mean-square atomic displacement at $298\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The increase in $K$ and $G$ corresponds to a 2.4% increase in the Debye frequency, and 0.3% and 2.4% decrease, respectively, in the Debye heat capacity and entropy, and 0.86% increase in the Debye energy. The Poisson's ratio decreases with $t$, i.e., the glass becomes laterally stiffer. The $K(t)=a+bG(t)$ relation is consistent with a relation obtained for Lennard-Jones interactions. In the potential energy landscape paradigm, annealing appears to shift the state point of a glass to a deeper and more-curved minimum.