Showing papers on "Debye published in 1983"
TL;DR: It is found that a complex formation between the reactants can drastically change the ionic strength dependence of the rate constant of a reaction between two macromolecules, especially at low ionicstrength.
59 citations
TL;DR: In this article, the influence of solvent dipole translational relaxation via the mechanism of polarization diffusion is examined for simple models of dipole isomerization and charge transfer reactions in polar solvents.
57 citations
TL;DR: Debye screening is proven for a large class of classical Coulomb gases at low densities as discussed by the authors, including jellium systems, where particles interact with a fixed background charge, systems with arbitrarily dilute fractional charges, and systems where the charges are not integrally related.
Abstract: Debye screening is proven for a large class of classical Coulomb gases at low densities. Among the models treated are jellium systems (where particles interact with a fixed background charge), systems with arbitrarily dilute fractional charges, and systems where the charges are not integrally related. The interaction potentials of the corresponding sine-Gordon models may have no symmetry and can have infinitely many stationary points which are degenerate or nearly degenerate in energy.
45 citations
TL;DR: In this article, a modification of the Rayleigh-Debye approximation is given in two ways so that it includes the information of the refractive index of scatterers in the calculation of scattering patterns.
Abstract: A modification of the Rayleigh–Debye approximation is given in two ways so that it includes the information of the refractive index of scatterers in the calculation of scattering patterns. The improvement that is due to the modification is demonstrated by comparing the approximation with the exact Mie calculation.
27 citations
TL;DR: In this paper, the complex dielectric constant e (ω) of Ca 2 Sr(C 2 H 5 CO 2 ) 6 along the tetragonal c -axis was measured at 54 different frequencies between 10 3 Hz and 10 9 Hz.
Abstract: The complex dielectric constant e (ω) of Ca 2 Sr(C 2 H 5 CO 2 ) 6 along the tetragonal c -axis was measured at 54 different frequencies between 10 3 Hz and 10 9 Hz. In the paraelectric phase, e (ω) is well described by the Debye dispersion formula with a single relaxation time except in the vicinity of the Curie temperature T c . In the temperature region of \(0{<}T-T_{\text{c}}{\lesssim}3\) K, the second dispersion of a resonant type is observed in addition to the Debye type dispersion. The temperature dependence of the relaxation time τ of the Debye dispersion is well expressed in the temperature rarnge \(\text{1 K}{\lesssim}T-T_{\text{c}}\) by a power law, τ∝( T - T c ) - Δ with Δ =1.31, which is larger than the critical exponent γ=1.28 for the static dielectric constant obtained by extrapolation of the Debye dispersion.
23 citations
TL;DR: In this article, the effect of substitution of one isotope for another in the lithium hydride crystal has been investigated by means of the localized-continuum model introduced in earlier publications in connection with calculations of elastic properties, thermal expansion, and melting phenomena.
Abstract: The effect of substitution of one isotope for another in the lithium hydride crystal has been investigated by means of the localized-continuum model introduced in earlier publications in connection with calculations of elastic properties, thermal expansion, and melting phenomena. Theoretical analysis demonstrates that the observed lattice parameters can be accounted for within the experimental error and the accuracy of the Debye approximation by a combination of the effects of the zero-point displacement and thermal expansion. The contributions of both quantities vary for the different isotopic forms according to different values of the Debye temperature, which in turn varies approximately as the inverse square root of the cation-ion reduced mass. In addition, the analysis elucidates the nature of the quantized thermal oscillators in crystals.
23 citations
TL;DR: The Debye-Waller parameters were determined at room temperature and around 90 K for palladium metal powders with different particle sizes in this paper, where the effective values obtained were divided into the dynamic component Bd, which is due to the thermal vibration of the constituent atoms and are temperature dependent, and the static component Bs, which probably due to static displacement of the atoms and is temperature independent.
Abstract: The Debye—Waller parameters were determined at room temperature and around 90 K for palladium metal powders with different particle sizes The effective values obtained were divided into the dynamic component Bd, which is due to the thermal vibration of the constituent atoms and are temperature dependent, and the static component Bs, which is probably due to the static displacement of the atoms and is temperature independent The Debye temperature θD calculated from the component Bd decreased with the increase in the component Bs, of which the relation was able to extrapolate to the θd-value determined on single crystals at Bs = 0 The decrease in θD was qualitatively explained by using a simple core-shell model, the shell part having as low a θD-value as 140 K
21 citations
TL;DR: In this paper, the effect of spatial correlation in the solvent polarization fluctuations (solvent structure) on the character of screening in an electrolyte solution is discussed, when the typical wavenumbers of the solvent-permittivity spatial dispersion are comparable with the inverse Debye-screening length.
Abstract: The effect of spatial correlation in the solvent polarization fluctuations (‘solvent structure’) on the character of screening in an electrolyte solution is discussed. It is considerable when the typical wavenumbers of the solvent-permittivity spatial dispersion are comparable with the inverse Debye-screening length. The screening then is not described by a simple Debye exponent, in contrast to the results of Radic and Marcelja. Their conclusions concerning the effective enhancement of the Debye screening length is shown to be generally incorrect, being appropriate only in the limit of small ionic concentration, when the effect leads to a small correction to the normal Debye value.
20 citations
TL;DR: The behavior of zone-centre acoustic phonons has been investigated in LaF3′ CeF3'' PrF3 and NdF3 over a wide temperature range as discussed by the authors.
Abstract: The behaviour of the zone-centre acoustic phonons has been investigated in LaF3′ CeF3′ PrF3 and NdF3 over a wide temperature range. It is shown that in spite of the trigonal structure of these crystals, their elastic properties can be well described with an approximation to hexagonal symmetry. The values of the elastic coefficients increase with increasing atomic number of the cations. The Debye temperatures were determined at temperatures from 80 to 560K with a typical value of θ D = 385 K at 300 K.
18 citations
TL;DR: Isomer shifts and Debye temperatures for substitutional 119Sn impurity atoms in the FCC metals Al, Ag, Au, Cu, Pb, Pd, Pt and Rb were determined by Mossbauer emission spectroscopy on the 24 keV gamma radiation of 119Sn.
Abstract: Isomer shifts and Debye temperatures for substitutional 119Sn impurity atoms in the FCC metals Al, Ag, Au, Cu, Pb, Pd, Pt and Rb were determined by Mossbauer emission spectroscopy on the 24 keV gamma radiation of 119Sn. The radiation sources were prepared by ion implantations of radioactive 119In and 119Sb isotopes into single crystals and high-purity foils of the respective metals. Correlations are discussed between measured isomer shifts and electronic properties of the host materials (the Fermi-level free-electron density nF1/3 and the cell-boundary electron-density parameter nWS1/3 from the Miedema theory of alloy formation). The Debye temperatures for 119Sn are interpreted in terms of the Einstein-Debye and the Mannheim models for impurity lattice vibrations.
17 citations
TL;DR: In this paper, the lattice vibrations of the two constituent atoms in the III-V semiconductors GaP, GaAs, GaSb, InP, InAs, and InSb have been studied experimentally by neutron diffraction and theoretically by calculations within the framework of various phonon models proposed in the literature for these compounds.
Abstract: The lattice vibrations of the two constituent atoms in the III–V semiconductors GaP, GaAs, GaSb, InP, InAs, and InSb have been studied experimentally by neutron diffraction and theoretically by calculations within the framework of various phonon models proposed in the literature for these compounds. The mean-square amplitudes (measured at 295 K) show a general increase with increasing lattice constant and seem furthermore to reflect the partial ionicity of the compounds. The different phonon models for the lattice dynamics are compared with each other and tested critically against the experimental data. Several models are found to be insufficient. The most satisfactory ones are some shell models.
119Sn Mossbauer impurity atoms have been implanted site-selectively on the two different substitutional lattice sites and their Debye temperatures have been determined. A rigorous result relating Debye temperatures of host and impurity atoms permits a simplified interpretation of the experimental results in terms of “Einstein-Debye force constants”. Both lower and higher force constants are deduced for the impurities as compared with the host atoms. Larger force constants are found on V sites than on the III sites for Sn in the Ga compounds, whereas the opposite holds in the In compounds. Further details can be obtained in an extended version of this paper available from the authors.
TL;DR: In this paper, generalized expressions for the free energy difference between normal and superconducting states are derived for the case of an energy dependent (ED) electronic density of states (EDOS) with normal and paramagnetic impurity scattering included.
Abstract: Generalized expressions for the free energy difference between normal and superconducting states are derived for the case of an energy dependent (ED) electronic density of states (EDOS) with normal and paramagnetic impurity scattering included. The derivation starts from the Eliashberg expression for the grand thermodynamic potential and ends in explicit formulas for the case of a symmetric Lorentzian model EDOS. Some numerical results are given for the critical magnetic field deviation function and the ratio 2Δ0/kBTc of the Δ0 to the critical temperature Tc. For a peak at the Fermi energy of half width less than the Debye energy (ωD), the modified Eliashberg theory is needed to describe its effect on the thermodynamic properties, whereas for a half width greater than ωD, the corrections to a flat approximation are small.
TL;DR: By X-ray diffraction measurements made in the temperature range 293 to 1173 K following properties of TiC0.967 are investigated: amplitudes of thermal vibrations of Ti and C atoms, Debye characteristic temperature, and static displacement of Ti atoms around a vacancy in the carbon sublattice as mentioned in this paper.
Abstract: By X-ray diffraction measurements made in the temperature range 293 to 1173 K following properties of TiC0.967 are investigated: amplitudes of thermal vibrations of Ti and C atoms, Debye characteristic temperature, and static displacement of Ti atoms around a vacancy in the carbon sublattice.
Durch rontgenographische Messungen der Braggschen Maxima werden im Temperaturbereich 293 bis 1173 K folgende Eigenschaften von TiC0,967 untersucht: Amplituden der Warmeschwingungen der Titanatome bzw. Kohlenstoffatome, charakteristische Debye-Temperatur und statische Verruckungen der Titanatome in unmittelbarer Nahe einer Kohlenstoffleerstelle.
TL;DR: In this article, the thermodynamics of the massive Thirring model with the help of the Bethe Ansatz approach are discussed with a finite Debye cut-off to investigate effects of the lattice discreteness.
Abstract: The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.
TL;DR: In this paper, a high-frequency plane-wave incident upon an infinite aluminum circular cylindrical shell immersed in and filled with water is determined by applying the Sommerfeld-Watson transformation to the classical Rayleigh normal-mode series solution.
Abstract: Acoustical scattering resulting from a high‐frequency plane‐wave incident upon an infinite aluminum circular cylindrical shell immersed in and filled with water is determined by applying the Sommerfeld–Watson transformation to the classical Rayleigh normal‐mode series solution. The resulting contour integrals are computed by both the saddle point method and by summing residues over poles which correspond to the zeros of a 6 ×6 determinant resulting from satisfying the necessary boundary conditions. The Bessel functions and their derivatives which appear in the 6 × 6 determinant are evaluated using asymptotic representations of both the Airy and Debye type depending upon the region of the complex plane. Emphasis is placed on the transitions in the scattering characteristics as the shell goes from a solid cylinder to a thin‐walled shell. This dual behavior will be discussed in terms of the number and trajectories of allowed modes of the scatterer, the dispersion curves of various modes, and the contributions of the various modes to the scattered pressure field.
TL;DR: In this article, the critical voltage phenomena observed in high-voltage electron diffraction provide a sensitive method for determining submicroscopic alloy parameters such as Debye temperatures, the extent of long-range order and atomic scattering factors.
Abstract: The systematic critical voltage phenomena observed in high-voltage electron diffraction provide a sensitive method for determining submicroscopic alloy parameters such as Debye temperatures, the extent of long-range order and atomic scattering factors. Only a very limited number of critical voltages can be observed in the voltage range usually available, 100-1200 kV, so that quantitative interpretation of the data must be based on a few-parameter model which incorporates all the pertinent factors. A satisfactory model has been developed which can be used to interpret or compute the critical voltage of ordered b.c.c. binary alloys as functions of composition, temperature and long-range order. This model can also be used to analyse the Debye-Waller factors of these alloys measured by X-ray or neutron diffraction techniques, and thus provide supplementary information about the vibrational behaviour of these systems.
TL;DR: In this paper, the specific heat of the layer compound SnSe2 was measured in the temperature range from 2.7 to 280 K, and the overall temperature dependence of the heat is dominated by the lattice contribution, which yields a limiting Debye characteristic temperature at absolute zero θD (0) = 140 ± 2K.
TL;DR: In this paper, the authors measured complex dielectric constants of Ca 2 Sr(C 2 H 5 CO 2 ) 5 along the ferroelectric c -axis along with the dipolar part of the static dielectrics of the Ca 2 s − e ∞ constant.
Abstract: Complex dielectric constants of Ca 2 Sr(C 2 H 5 CO 2 ) 5 along the ferroelectric c -axis have been measured for as-grown and annealed crystals between 1 kHz and 1 GHz around their Curie temperatures, T c The magnitude of the resonant type dispersion which appears in the low frequency region decreases by annealing The ratio of the relaxation time of the Debye dispersion, τ, to the dipolar part of the static dielectric constant, e s - e ∞ , can be expressed as τ/( e s - e ∞ )= A exp ( U / k T ) except in the vicinity of T e for the as-grown crystal as well as for the annealed one The activation energy U decreases whereas the value of A increases slightly by annealing A narrow distribution of τ is found in the as-grown crystal contrary to the annealed one which shows the monodispersive Debye relaxation
TL;DR: In this article, the dielectric dispersion and circular dichroism of melittin in n-butanol saturated with water have been investigated at frequencies of 200 kHz to 50 MHz.
TL;DR: The modified Debye integral (MDI) as discussed by the authors is a diffraction formula for focused wavefields which is constructed so as to satisfy the reciprocity principle, and may be considered as a generalization of the Debye-integral and also as a refinement on the diffraction integral derived by Hopkins.
Abstract: It is shown that focused wavefields satisfy a reciprocity principle concerning the roles of the focal point and the observation point. According to this principle, the diffracted field at a point P2 of a converging spherical wave centred on the focal point P1 is the complex conjugate of the diffracted field observed at P1 if the focal point is at P2. The commonly used Debye integral representation of focused wavefields violates the reciprocity principle. Therefore we derive a new diffraction formula for focused wavefields which we call the modified Debye integral (MDI). It is constructed so as to satisfy the reciprocity principle, and may be considered as a generalization of the Debye integral and also as a refinement on a diffraction integral derived by Hopkins. For focusing of a two-dimensional perfect wave we show that the MDI gives the same f-number dependent parabolic phase factor on the geometrical focal line as is obtained numerically in the Kirchhoff approximation. For focusing of three-dimensiona...
TL;DR: In this paper, it was shown that amorphous samples are Debye ($D$) random when some average quantities are equal to the corresponding averages evaluated over the largest available sets.
Abstract: It is shown that amorphous samples are Debye ($D$) random when some average quantities are equal to the corresponding averages evaluated over the largest available sets. The physical consistency of this condition requires that the interphase specific surfaces are proportional to the product of the corresponding volume fractions. The coefficient of proportionality $\ensuremath{\mu}$ is the only parameter which appears in the correlation function, whose analytical expression is simply $\mathrm{exp}(\ensuremath{-}\ensuremath{\mu}r)$, independently of the number of the phases constituting the $D$-random sample. Furthermore, $D$ randomness amounts to requiring that the system of linear differential equations be linear and that its form remain invariant when two phases are combined into a single one.
TL;DR: In this article, the Debye-Waller factor and the one-particle density function were derived for a chain of atoms, each atom sitting in a double quadratic oneparticle potential, with adjacent atoms linked by strong harmonic coupling forces.
Abstract: Expressions for the one-particle density function and Debye-Waller factor are derived for a chain of atoms, each atom sitting in a double quadratic one-particle potential, with adjacent atoms linked by strong harmonic coupling forces. Working within the framework of classical mechanics, exact numerical results are obtained and compared with analytical expressions which are exact at zero temperature but only approximate at finite temperature. It is shown that the pseudo-Schrodinger and transfer integral equations give essentially the same results at all temperatures. The one-particle density function at low temperature consists of two equally weighted gaussians, corresponding to phonon-like modes about the local minima in the potential. As the temperature increases a centrally placed soliton peak grows and dominates the distribution at high temperatures. The mean-square displacement is linear at high temperatures and linear extrapolation back to zero temperature gives a positive intercept on the mean-square displacement axis. These results are discussed in the context of the disorder model and experimental DWF data from structurally transforming crystals.
TL;DR: A lower bound for the value of the dipole moment of superoxide dismutase (SOD) was established in this paper, where the authors showed that the rate constant of the reaction between superoxide (O − 2 ) and SOD decreases upon increasing the ionic strength.
TL;DR: In this article, the Debye field was integrated with the Inglis-Teller Stark merging of spectral lines, and the deformation of the spectral lines was calculated using an electrostatic quantum model which allowed an immediate, and therefore an integrated, inclusion of the debye screening.
Abstract: The change of the energetic quantum levels of electrons in atoms or ions within plasma due to the electrostatic energy of the Debye sphere, is discussed on the basis of an electrostatic quantum model which permits an immediate, and therefore an integrated, inclusion of the Debye screening. The resulting Debye field leads to an alternative (temperature dependent) formulation of the Inglis-Teller Stark merging of spectral lines. In the new model the drowning of lines gives values closer to the Inglis-Teller limit than values given by the quantum approximation of the hydrogenic model. The straightforward calculation of the polarization shift based on the new model is closest to the experimental values and is between the very low values given by the semiclassical approach and the too high values given by the quantum approach of the hydrogenic effective charge model.
TL;DR: In this paper, an approximate analytic calculation of the magnetic scalar potential for a two-component plasma was presented, where an exponential approximation of the dominant terms of GB and HB was used.
Abstract: In this paper we have presented an approximate analytic calculation of the magnetic scalar potentialsgB andhB for a two-component plasma. We have shown that a “modified” Debye potential removes the well-known divergence of the friction coefficient forVab∥ → 0, the Coulomb loganithm entering into the equation for the magnetic scalar potentials in a natural way, without cutting off the k integration. In the course of the calculation, an “exponential” approximation of the dominant terms of GB andHB was used. This approximation has not modified the Coulomb logarithm (cf. for example [2, 4, 5]). But the influence of the magnetic field is involved in the.
TL;DR: In this article, the potential of the shielded Coulomb interaction with a two-dimensional Debye shielding radius was investigated theoretically, taking into account the field of charge carriers in the media surrounding the film.
TL;DR: In this paper, the Debye-Waller factors for low energy electron diffraction (LEED) for thin films are considered in harmonic and anharmonic approximation, and numerical calculation for some parameters describing thin film dynamics of the lattice particle in the case of the high temperature limit is presented.
Abstract: The Debye-Waller factors for low energy electron diffraction (LEED) for thin films are considered in harmonic and anharmonic approximation. The numerical calculation for some parameters describing thin film dynamics of the lattice particle in the case of the high temperature limit is presented. The results show an interesting distribution of the Debye-Waller factor in the direction perpendicular to the thin film surface as well as its anisotropic character.
TL;DR: In this paper, an empirical relationship connecting the Debye temperatures θM and θH of a metal and its hydride respectively with the heat ΔHf of formation of the hydrides was derived from experimental data reported by various investigators.
Abstract: Nuclear resonance scattering of γ rays has recently been used to obtain information on the Debye temperatures θD, of metal hydrides. In particular the contribution of nickel to the θD of Mg2Ni, LaNi5 and their hydrides was estimated. It was assumed that the different behaviour of θD for nickel in the two cases (i.e. an increase upon hydrogenation in Mg2Ni and no change in LaNi5) could be related to the different stabilities of the two hydrides. Consequently an empirical relationship connecting the Debye temperatures θM and θH of a metal and its hydride respectively with the heat ΔHf of formation of the hydride was derived from experimental data reported by various investigators. It appeared, however, that two ambiguous calculating procedures were used to derive the θH values. One of these procedures was used consistently in the present work for all the metal-hydrogen systems and the original phenomenological rule was changed accordingly. The qualitative theoretical considerations preceding the derivation of the empirical relation are briefly presented. Some experimental data recently reported in the literature are discussed in terms of the proposed empirical rule. In particular the obvious exceptions associated with the group IVa metal hydrides TiHx and ZrHx are attributed to the Jahn-Teller effect in these systems.