Showing papers on "Debye published in 1971"
TL;DR: In this article, the dielectric constant of saline water was represented by an equation of the Debye form and the parameters for the parameters were given as functions of the water temperature and salinity.
Abstract: The dielectric constant of saline water may be represented by an equation of the Debye form. Equations for the parameters in the Debye expression are given as functions of the water temperature and salinity.
715 citations
TL;DR: The theory of lattice dynamics has some claim to being the oldest branch of solid state physics as discussed by the authors, and it has been used to account for the thermal and other properties of crystals.
Abstract: Lattice dynamics has some claim to being the oldest branch of solid state physics. Planck's Theory of Radiation and the Theory of Specific Heat was published by Einstein in 1907, On Vibrations in Space Lattices by Born and von Karman in 1912, and On the Theory of Specific Heat by Debye in the same year. Other early papers on lattice dynamics included those by Debye and by Waller on the effect of temperature op the scattering of x-rays by a crystal. In the 1920's Peierls made fundamental contributions to the theory of thermal conductivity and of electrical conductivity involving lattice dynamics, and in the 1930's Blackman brought to an end the acceptance of the complete validity of the Debye theory of specific heat and also contributed the first papers on anharmonic effects in the absorption of infrared radiation by ionic crystals. The work we have mentioned used the formal theory of lattice dynamics to account for the thermal and other properties of crystals. It was not until 1940 that Kellerman...
287 citations
TL;DR: In this article, the authors employed computer simulation of semiconductors with one-sided doping profiles that consist of high and low doped sections joined by steps and linear ramps and showed that a ramp cannot be distinguished accurately from a step unless its width is appreciably greater than a Debye length.
Abstract: The doping profile of a semiconductor is given only approximately by the conventional analysis of C-V measurements. The present study employs computer simulation of semiconductors with one-sided doping profiles that consist of high and low doped sections joined by steps and linear ramps. The computation yields the apparent doping profile that would be obtained by the conventional use of C-V data, and this result is compared with the actual profile, with the majority-carrier distribution, and with the outcome of a correction previously proposed in the literature. The results show that a step in the profile cannot be resolved satisfactorily to less than several Debye lengths corresponding to the doping on the high side of the profile. A ramp cannot be distinguished accurately from a step unless its width is appreciably greater than a Debye length. Furthermore, the apparent doping profile is not identical with the majority-carrier distribution with contacts far away, as has been suggested, and the discrepancy is shown to depend on the side from which depletion is done.
235 citations
TL;DR: In this article, the microwave spectrum of the reactive species thioformaldehyde (H2CS) has been studied in the ground vibrational state, and a detailed centrifugal distortion analysis has been carried out on the species H212C32S with a total of 27 transitions up to J = 27 fit to a standard deviation of 26 kHz.
186 citations
TL;DR: In this paper, the influence of a molecule's dipole moment on its ability to capture an electron into a stable bound state is examined, and it is proved that, in the fixed-nuclei approximation, a value greater than 1·625 Debye for the Dipole moment suffices to guarantee the existence of a discrete spectrum of negative ion states.
Abstract: The influence of a molecule's dipole moment on its ability to capture an electron into a stable bound state is examined. It is proved that, in the fixednuclei approximation, a value greater than 1·625 Debye for the dipole moment suffices to guarantee the existence of a discrete spectrum of negative ion states. Implications for Hartree-Fock calculations of negative ions are discussed. The interaction of electronic, vibrational and rotational motions in negative dipolar ions is studied, and conclusions are drawn for real molecules.
145 citations
TL;DR: In this paper, the electric resonance spectrum of PH3 was measured at zero electric field for three rotational states, J=4, 5, and 7 with K=3, and the dipole moment (debye) is 0.57395±0.0003.
Abstract: The electric resonance spectrum of phosphine (PH3) was measured at zero electric field for three rotational states, J=4, 5, and 7 with K=3. In addition, the J=K=2 and J=K=1 spectra were observed at several values for the electric field. The dipole moment (debye) is 0.57395±0.0003. The magnetic hyperfine constants (kilohertz) are cα=−114.90±0.13, cβ=−116.38±0.32 for the spin—rotation interaction of the 31P nucleus, and ζ α=8.01±0.08,ζβ=7.67±0.19 for the spin—rotation interaction of the 1H nuclei. The α constant is the mean interaction in the x and y directions, and the β constant is the interaction about the molecular z axis. No inversion doubling was observed (Δ〈1 kHz). The K=3 levels have K‐doubling fine structure as predicted by Nielson and Dennison, but the magnitude does not agree with their formula.
115 citations
TL;DR: In this paper, a critical examination of four Debye equations for dilute solutions is presented, which can be used to determine the relaxation time of a polar solute molecule, especially two representative formulas which are mutually independent.
Abstract: There are four Debye equations for dilute solutions which can be used to determine the relaxation time of a polar solute molecule. This paper offers a critical examination of these equations, especially two representative formulas which are mutually independent. If the solute molecule has a non-rigid configuration and has two relaxation times, τ1 and τ2, for overall and internal rotations, respectively, average relaxation times will be obtained from these equations based on measurements at a single frequency. However, the analysis of this paper shows that under a certain condition (if a proper frequency for the measurement and a suitable equation for the calculation are employed) one may make a crude estimate regarding one of the two relaxation times. Further, the ratio of two relaxation times seems to afford a clue for investigating the mechanism of internal rotation. In addition, Cole-Cole dispersion and atomic polarization problems are also discussed.
109 citations
TL;DR: In this article, a phenomenological model is proposed to explain and estimate the temperature dependence of elastic constants, which leads to a simple expression for the elastic constant and also for the coefficient of the thermal expansion.
Abstract: This analysis presents a new approach to the problem of temperature dependence of elastic constants, which leads to a simple expression. A phenomenological model is assumed to explain and estimate the temperature dependence of elastic constants. The model consists of the usual harmonic oscillator with the applied force term plus a third‐order term representing the anharmonicity of the oscillator. The state function ψ is evaluated in terms of the Hermitian polynomials using perturbation methods. The average mean displacement of the mass points (atoms or molecules) is obtained by using the state function and Maxwell‐Boltzmann distribution. Consequently, the expression for the elastic constant and also for the coefficient of the thermal expansion is obtained. The result is again averaged over the range of frequencies, using Debye spectrum. The final expression shows good agreement with experimental results and other theories.
86 citations
TL;DR: In this article, a scheme was developed for selecting a manageable number of configurations (less than 200) to be used in a configuration interaction calculation to obtain the electric dipole moments of closed-shell diatomic molecules.
Abstract: A scheme has been developed for selecting a manageable number of configurations (less than 200) to be used in a configuration interaction calculation to obtain the electric dipole moments of closed‐shell diatomic molecules. Calculations have been performed on LiH (Re = 3.015 a.u.), CO (Re = 2.132 a.u. and R = 2.2853 a.u.), CS (Re = 2.89964 a.u.), and NaLi (R = 5.5 a.u.). A dramatic improvement over the restricted Hartree–Fock value is obtained. At Re the RHF, CI, and experimental dipole moments (in debye) are LiH: 6.00, 5.86, 5.83; CO: − 0.27, 0.12, 0.11; and CS: 1.56, 2.03, 1.97.
85 citations
TL;DR: In this paper, the microwave transitions of O3 have been observed to the frequency of 320 GHz, and the spectrum recalculated to obtain new rotational constants for the molecule, including the Stark effect.
64 citations
TL;DR: Using low-energy electron diffraction (LEED) as discussed by the authors, the Debye-Waller factors for Cr(100 and Mo(100) surfaces at near normal incidence were measured and it was found that the derived effective Debye temperature as a function of electron energy fluctuates about a curve which increases smoothly with energy.
TL;DR: In this article, a toroidal and poloidal representation of symmetric, traceless, divergenceless, 3-dimensional tensor fields is developed and the properties of the field in the near and far field zones are discussed.
TL;DR: In this paper, the variation of elastic constants of MgO with temperature has been measured from 4.2 to 300 K, in units of 1010 N/m2, with a limiting value of θ 0 = 948 K for the Debye characteristic temperature.
Abstract: The variation of elastic constants of MgO with temperature has been measured from 4.2 to 300 K. The values of the elastic constants at 4.2 K, in units of 1010 N/m2, are C11 = 30.67, C12 = 9.371 and C44 = 15.76. This gives a limiting value of θ0 = 948 K for the Debye characteristic temperature
TL;DR: In this paper, a new interpretation of the intrinsic polarization of pure ice single crystals is presented, which visualizes L, D pair formation as a one-step process: a proton shifted by near-infrared phonon excitation to an empty corner of its H2O tetrahedron.
Abstract: Neither the polarization of pure ice single crystals can be understood on the basis of rotating H2O molecules nor the conduction through such crystals by assuming migrating H3O+ and OH− ions. Bjerrum's concepts of L‐, D‐defect and ionic‐defect formation are a useful starting point, but the subsequent development of double‐well models leads into serious difficulties. A new interpretation of the intrinsic polarization of ice Ih visualizes L, D pair formation as a one‐step process: a proton shifted by near‐infrared phonon excitation to an empty corner of its H2O tetrahedron. Subsequent intramolecular proton transfers, slightly field directed, inscribe a dipole moment into the disordered proton system of the ice crystal; the defects die off by recombination. Thus the polarization builds up from a statistically triggered pulse spectrum; its correlation period is the waiting time, until the same H2O molecule forms again a defect pair. This waiting period, the relaxation time of the Debye spectrum, connects the ...
TL;DR: In this article, the lattice dynamics of β-ZnS, GaP and β-SiC have been investigated on the basis of a rigid ion model with seven parameters, and results are obtained for the dispersion curves and effective calorimetric and X-ray Debye temperatures.
Abstract: The lattice dynamics of β-ZnS, GaP and β-SiC has been investigated on the basis of a rigid ion model with seven parameters. Results are obtained for the dispersion curves and effective calorimetric and X-ray Debye temperatures and are shown to compare favourably with the available experimental data. Calculated values of equivalent Debye frequencies are also reported.
01 Jan 1971
TL;DR: In this paper, the theoretical expressions for the Mossbauer fraction and for the thermal shift contain Debye integrals and it is shown how these integrals can be evaluated easily by means of infinite series.
Abstract: If a Debye spectrum is assumed for the frequencies of lattice vibrations, the theoretical expressions for the Mossbauer fraction and for the thermal shift contain Debye integrals. It is shown how these integrals can be evaluated easily by means of infinite series. Only a few terms of these series provide adequate accuracy. A short numerical table is presented.
TL;DR: In this paper, the Debye characteristic temperatures and the coefficient of thermal expansion for the Pd-Ag-Au ternary-alloy system were measured in the temperatures range 80-298°K.
Abstract: X‐ray measurements of the Debye characteristic temperatures ΘM and the coefficient of thermal expansion for the Pd–Ag–Au ternary‐alloy system are presented The integrated intensities of Bragg reflections and lattice parameters were measured in the temperatures range 80–298°K For all the alloys, the predominant lattice disturbance was due to thermal vibrations No significant effect due to static displacements was found Debye temperatures were found to range from a low of 184°K for gold to a high of 290°K for palladium, with silver intermediate at 226°K The mean coefficient of thermal expansion was found to range from 98×10−6 for palladium to 179×10−6 for silver Gruneisen's relationship between the meansquare atomic‐vibration amplitude and the thermal expansion for cubic solids has been found to be valid for these alloys and the constant γZ2 was found to be 0167 The results suggest that a general weakening of the cohesive forces might be taking place as the smaller palladium atoms are replaced by
TL;DR: In this paper, the dipole interaction energies have been calculated for two-dimensional arrays of point dipoles in a medium of unit dielectric constant for point dipole moments of 1.5 Debye spaced 4.81 A apart.
TL;DR: In this article, an interatomic potential for Kr determined from high energy molecular beam results, gas viscosities, second virial coefficients of the gas and zero-temperature lattice spacing, cohesive energy and Debye theta of the solid, was used to calculate phonon dispersion curves and elastic constants for solid Kr at 0°K.
TL;DR: In this article, the electric dipole moments of polar solutes in polar solvents were calculated based on the approaches of Debye, Onsager, Weaver and Parry and Buckingham.
Abstract: Equations based upon the approaches of Debye, Onsager, Weaver and Parry and Buckingham are developed for calculating the electric dipole moments of polar solutes in polar solvents and employed for 21 solutes in benzene, chlorobenzene and ethyl acetate solutions. Consistent results are obtainable from the measurements made in the non-polar and both polar solvents.
TL;DR: The microwave spectrum of divinyl ether has been observed and a, b, and c type rotational transitions of one conformer assigned in this paper have been obtained from Stark effect measurements and is 0.782 debye.
TL;DR: In this article, an analytical expression for the saturation current regimes of a current-voltage characteristic for a spherical free-molecular electrostatic probe surrounded by a finite sheath was given.
Abstract: An analytical expression is given for the saturation current regimes of a current-voltage characteristic for a spherical free-molecular electrostatic probe surrounded by a finite sheath. The original derivation was based on the usual assumptions of a Maxwellian distribution of energies in a quiescent plasma. The current-voltage characteristic depends on parameters involving the sheath thickness and the electrostatic potential at the outer edge of the sheath. The latter parameter depends only on the ion/electron temperature ratio and is uniquely obtained from a transcendental equation. The sheath thicknesses are obtained from numerical solutions of the potential fields, and an empirical expression is derived to fit the numerical data. These results, which are for Debye lengths smaller than the probe radius, plus the "orbital limited" theory for larger Debye lengths cover most of the number density and temperature regimes obtained in laboratory and flowfield plasmas.
TL;DR: In this paper, four high precision methods are employed to calculate the Debye temperatures of alkali halides, and the results obtained by the four methods are compared among themselves and with the experimental data.
Abstract: Four high precision methods are employed to calculate the Debye temperatures of alkali halides. The results obtained by the four methods are compared among themselves and with the experimental data.
TL;DR: In this article, the dipole moment was interpreted as being due to O−− ions associated with anion vacancies, and the activation energies for reorientation of dipole were 0.60 eV, 0.56 eV and 0.50 eV for RbJ.
Abstract: Dielectric loss measurements are reported for RbCl, RbBr, and RbJ crystals containing O−−ions. The frequency and temperature dependence can be approximated by a Debye curve. The dipole moment is interpreted as being due to O−− ions associated with anion vacancies. Activation energies for reorientation of the dipole are 0.60 eV for RbCl, 0.56 eV for RbBr, and 0.50 eV for RbJ.
TL;DR: In this paper, a tensor of the Debye effective frequencies is constructed for the surface atoms in the case of a semispace and a plane-parallel plate of arbitrary thickness.
Abstract: The acoustical asymptotics of the spectral distribution of the vibrations of separate atoms in dependence on their positions in the crystal are considered for the cases of a semispace and a plane-parallel plate of arbitrary thickness. The general solution of the problem is obtained in the case of an arbitrary orientation of the boundary surfaces with respect to the crystallographic axes. In the elastically isotropie continuum approximation this solution is analysed in detail. For the surface atoms the tensor of the Debye effective frequencies is constructed. The method is taken from the dynamics of a crystal with extended defects which in the case under consideration are the stress-free plane boundaries and is based on an accurately solving of integral equations such as the Dyson ones. The results obtained are discussed in connection with the mean square fluctuations of the positions and momenta of the crystal atoms determining the intensity and the energy position of the Mossbauer no-phonon line and the Debye-Waller factor in the cross section of the low-energy particles. They are also discussed with respect to the surface contribution to the low-temperature heat capacity. In particular, the statistical weight of the Rayleigh waves in the scale of the squared frequencies is shown to be proportional to √ω2 as well as the density of the three-dimensional phonon states. Thus the surface vibrations do not lead to deviations of order T2 from the T3-behaviour of the lattice thermal capacity. Such deviations are due to the surface not in itself as a two-dimensional manifold but to its closeness, leading to quantization of the volume vibrations and to appearance of new specific modes.
[Russian Text Ignored].
TL;DR: In this paper, the longitudinal and transverse acoustic velocities of high-purity polycrystalline thulium and ytterbium have been measured by a pulse technique at a frequency of 10 MHz between 4·2 and 300°K.
TL;DR: In this article, the 1-0 and 2-0 vibration-rotation bands of the H79Br molecule have been respectively calculated to be 10.65+or 0.22 and 0.008 cm-2 atm-1 at 294 K.
Abstract: From the data on the line strengths, the band strengths of the 1-0 and 2-0 vibration-rotation bands of H79Br molecule have been respectively calculated to be 10.65+or-0.22 and 0.174+or-0.008 cm-2 atm-1 at 294 K. From the vibrational matrix elements involving the Morse and anharmonic oscillator wave functions, two sets of values for the dipole moment coefficients M1 and M2 have been calculated. They are M1=0.316 debye AA-1, M2=0.518 debye AA-2 or M1=0.344 debye AA-1, M2=-0.096 debye AA-2. These values are compared with the values reduced from the low-resolution data.
TL;DR: In this article, a method for calculating the vibrational frequency spectrum of a model linear polymer is given for calculating a Debye lattice with a cutoff frequency ωL. The model is a chain of N masses having bending and stretching force constants.
Abstract: A method is given for calculating the vibrational frequency spectrum of a model linear polymer. The model is a chain of N masses having bending and stretching force constants. Each mass is quasiharmonically coupled to a Debye lattice which has a cutoff frequency ωL. Each of the 3N free chain eigenfrequencies ωj becomes a band with a low frequency cutoff ωj min2= ωj2, a high frequency cutoff ωj max2= ωj2+ωL2, and a pseudo‐n‐dimensional Debye distribution gj(ω)=nωn−1/(ωj maxn−ωj minn) for ωj min〈ω〈ωj max. The total frequency distribution agrees closely with the results by Genensky and Newell for the Stockmayer and Hecht lattice using their force constants and compares reasonably well with results of GF matrix calculations for polyethylene.
TL;DR: In this article, an angular force model has been applied to investigate the lattice dynamics of platinum metal and the calculated results show satisfactory agreement with the observed phonon dispersion curves and with Debye-Waller factors.
Abstract: An angular force model has been applied to investigate the lattice dynamics of platinum metal. The calculated results show satisfactory agreement with the observed phonon dispersion curves and with Debye—Waller factors. The calculated calorimetric Debye temperatures, however, show a substantial disagreement with the experimental results; possible causes of this disagreement are discussed.
TL;DR: In this paper, a recent reanalysis of perturbation theory results for the anharmonic free energy of a crystal shows elastic θe1 ≠ thermal θc despite earlier findings that θ e1=θc.