Showing papers on "Debye published in 1968"

Atomic Migration in Monatomic Crystals

Abstract: A theory of the diffusion-jump process in monatomic crystals is presented. The theory treats large atomic displacements causing diffusion jumps as a summation of phonon amplitudes. By using the Debye approximation to the phonon spectrum, a theoretical basis for the empirical Zener relation is established. The elastic theory gives a satisfactory quantitative account of (a) the motion energy; (b) the motion entropy; (c) the motion volume; (d) the isotope effect. Low-temperature diffusion phenomena may be examined because the theory employs a sufficiently general description of the phonon system. Attention is drawn to some enhanced diffusion effects caused by zero-point phonons. A quantum-mechanical calculation of diffusion rates for very light impurities is made with a model potential. Anomalous isotope effects are found at temperatures below the characteristic temperature of the localized mode. The relevance of these results to low-temperature annealing of radiation damage is discussed.

An experimental determination of the dipole moments of the X(1Σ) and A(1Π) states of the BH molecule

Abstract: The optical emission spectrum of the BH radical produced in a discharge tube designed to give high electric fields shows Stark effects. From these, the dipole moments of the X(1Σ+) and A(1Π) states...

PbTe Debye-Waller Factors and Band-Gap Temperature Dependence

Abstract: Experimentally verified, calculated Debye-Waller factors have been combined with a modified Lin-Kleinman pseudopotential and formalism to compute the temperature dependence of the PbTe direct band gap. The band-gap increase of 0.008 Ry between 100 and 300\ifmmode^\circ\else\textdegree\fi{}K is in fair agreement with an experimental estimate of the explicit increase.

O−−-Lücken-Dipole in Alkalihalogenidkristallen

Abstract: Dielectric loss measurements are reported for KBr, KCl, and NaCl crystals containing O−− ions. The frequency and temperature dependences can be well represented by a Debye curve.

Electrostatic probe theory for free molecular cylinders.

Abstract: An analytical expression is derived for the current attracted to a cylindrical probe surrounded by a sheath. The attracted particles are assumed to exhibit a Maxwellian distribution in the ambient plasma, which is assumed to be at rest with respect to the probe. Parameters for the potential at the outer sheath boundary and the sheath thickness are introduced and must be determined to obtain a complete solution. From a derived expression for the sheath potential and existing numerical solutions of the electrostatic field, an analytical description of the sheath thickness is obtained. In dense plasmas such that the sheath thickness is negligible, the present analysis still accounts for the acceleration of particles into the sheath region. The accuracy of the derived probe current is examined by comparing it with values obtained numerically. In general, the analytical results differ from the numerical results by less than 1%. The results given here provide simple relationships for the interpretation of current-volta ge characteristi cs. These results for Debye lengths smaller than the probe radius and the existing "orbital limited" theory for larger Debye lengths cover all possible number density and temperature regimes.

Microwave Spectrum, Ring-Puckering Potential Function, and Dipole Moment of Methylenecyclobutane

Abstract: The microwave spectra of methylenecyclobutane in the ground state and in the first six excited states of the ring‐puckering vibration have been assigned. The υ = 0 state and υ = 1 state are very close in energy and are strongly coupled giving rise to nonrigid‐rotor spectra. Analysis shows the energy difference to be 33 592 MHz. This energy difference together with the vibrational dependence of the rotational constants gives the ring‐puckering potential function to be 7.65(X4 − 9.15X2) cm−1 where X is a reduced ring‐puckering coordinate. This potential function contains a barrier to ring inversion of 160 ± 40 cm−1. The a component of the dipole moment is found to be 0.514 D in the ground state and to have the ring‐puckering vibrational dependence μa = 0.496 + 0.0051 〈X2〉υυ (debye).

Microwave Spectrum of Cyclohexanone

Abstract: The microwave spectrum of cyclohexanone has been investigated in the frequency region from 7.7 to 23.4 Gc/sec. The R- and Q-branches for both the a- and the c-type have been assigned for the vibrationally ground state. The rotational constants obtained are A=4195.30 Mc/ sec, B=2502.57 Mc/sec, and C=1754.49 Mc/sec. From these values it can be concluded that the molecules have the chair form. The value of the component of the dipole moment |μa| is 2.74±0.03 D, and that of |μc| is 0.86±0.03 D. The value of the total dipole moment is 2.87±0.04 D, a value which is in agreement with that obtained by Debye’s method. For the structural parameters Romers’ data obtained by the electron diffraction seems to be nearly correct.

Dielectric relaxation in clathrates

Abstract: Dielectric parameters (permittivity and loss factors) have been measured for clathrates based on ice (gas hydrates), quinol and Dianin's compound with particular attention to the frequency and temperature ranges displaying the reorientational dipole dispersion of the guest molecules. Many such processes conformed to the simple Debye form. Enthalpies (in kcal mole–1) and entropies (in cal mole–1 deg.–1) of activation for this reorientation were evaluated from Eyring's rate equation, and effective dipole moments (in D) for the guest were derived from the Bottcher-Onsager equation.[graphic omitted] Most of these ΔH*E are less than those for the reorientation of the same or similar molecules in inert solvents. In Dianin's compound, permittivity data were obtained and the freedom of the dipole to reorient assessed for single molecules of o-C6H4Cl2, C6H5NO2,C6H5CN, C6H5CH2CN, t-C4H9CN, and for two molecules of HCOOH, CH3COOH, CH3NO2, and (CH3)2CO per cavity; for (CH3CN)2 per cavity, ΔH*E= 2.10±0.15; ΔS*E=–2.9; µ= 7.0D; (CH3CH2CN)2 and (CH3OH)n gave extended absorptions. The possible resonance form of small-molecule absorptions is considered.

Debye-Waller Factors in Rare-Gas Solids

Abstract: Mean-square amplitudes for inert-gas solids neon, argon, krypton, and xenon have been calculated as a function of temperature. The results are presented for the cases of zero pressure and constant volume. A nearest-neighbor ($m\ensuremath{-}6$) Mie-Lennard-Jones potential was used, and lowest-order anharmonic contributions were taken into account by the frequency-shift method.

Low‐Temperature Thermal Properties of Calcium Tungstate

Abstract: The heat capacity of a single crystal of CaWO4 was determined by adiabatic calorimetry from 5° to 350°K and found to be without transitions or thermal anomalies. Deviation of the curve from normal sigmate shape is shown to be due to internal vibrations of the WO4= ions. Apparent Debye θ's for the lattice‐only heat capacity and for that of the acoustical spectrum show “normal” deviation from simple Debye theory. Values of the heat capacity (Cp), entropy (S°), enthalpy function [(H°–H0°) / T], and Gibbs function [(G° / H0°) / T] at 298.15°K are 27.28, 30.21, 16.02, and −14.19, in calories per gram formula mass·degree Kelvin.

Motional States of Protons and Dielectric Dispersion of Hexammine Nickel Chloride

Abstract: Dielectric losses have been measured in hexammine nickel chloride crystals, which contain a system of protons (${\mathrm{H}}^{+}$ ions) that is responsible for a motional phase transition. The losses are well approximated by Debye curves, both above and below the transition temperature. Since this transition is not accompanied by the onset of a dipolar moment, long-range forces may be neglected, as in the similar but more complex case of hydrogen-bonded ferroelectrics, and the present results may shed light on the dynamical model of this class of substances.

Acoustic Attenuation in Solids

Abstract: With the help of the correlation-function formula given by McLennan, an expression for the viscosity tensor is obtained within the Hartree-Fock approximation using the cubic anharmonic momentum-flux operator. In the Debye approximation for phonons and with a simple expression for relaxation time, solutions are obtained for the coefficients of viscosity at low temperature. These solutions are used to calculate the attenuation of longitudinal and transverse sound waves at 300\ifmmode^\circ\else\textdegree\fi{}K. The calculations are compared with experiment for Ge and Si, and good agreement is found.

The Design of a Dielectric Spectrograph

Abstract: The design and principle of operation of a transistorized dielectric spectrograph operating at a frequency of 1650 ±1 MHz are presented. The apparatus has high sensitivity and can measure the dielectric constant to a relative uncertainty of 1×10-7 and the loss tangent to about 2×10-7. It can be used up to pressure ranges of 100 atm or better. The apparatus is particularly useful for the quick measurement of very small dipole moments (less than 1 Debye) to an accuracy better than 1 percent. The results for mixtures of helium with 1) carbonylsulfide, a linear molecule, 2) carbontetrafluoride, a spherical top, and for 3) pure nitric oxide, a diatomic molecule, are briefly presented.

Plane collisionless sheaths between field- modified emitting electrodes and thermally ionized plasmas exemplified by cesium.

Abstract: This paper describes a theory for plane collisionless sheaths separating plasmas ionized by thermal electrons from emitting electrodes affected by sheath fields. Examples for cesium plasmas and thermionic‐diode configurations show sheath effects over ranges of conditions: temperatures from 1400° to 2400°K for electrodes, from 1600° to 2400°K for plasma atoms and ions, and from 1700° to 2700°K for plasma electrons; plasma‐electron number densities from 1012 to 1015 cm−3; and work functions from 1.5 to 5 V. Sheath drops from 0 to 2.1.V and net currents from 0 to over 100 A cm−2 result. Over‐all sheath characteristics correlate with work function minus plasma potential, plasma‐electron concentration (Nep), electrode temperature (TE), and an emission Debye length λDE≈6.9(TE/Nep)1/2. Effective sheath widths range from 1.7 to 2.6 emission Debye lengths.

Debye-Waller Factors of Tetragonal Barium Titanate

Abstract: The anisotropic temperature parameters of tetragonal BaTiO 3 are studied theoretically on the basis of thermal diffuse X-ray scattering, and the effect of piezo-electricity is particularly noted. The calculations of the average temperature parameters along the a - and the b -axis respectively are B 11 P =0.69 and B 33 P =0.20 (in A 2 units) in the unclamped case and B 11 E =0.72 and B 33 E =0.29 in the clamped case. These results are then compared with previous experimental results from X-ray (Evans) and neutron diffraction (Frazer).

Elastic Scattering of Light by Binary Mixtures above and below the Critical Solution Temperature. I. Methanol Cyclohexane

Abstract: An investigation was made of the light‐scattering properties of the methanol–cyclohexane binary system in the one‐phase region above the critical solution temperature Tc and in the two‐phase region below Tc. Measurements were made down the critical isochore for T > Tc and along the methanol‐rich side of the coexistence curve for T < Tc. A modification of the Ornstein–Zernike–Debye theory of light scattering was found to be in reasonable agreement with the results for T < Tc. The Debye parameter “l” was 14.5 ± 0.5 A above Tc and 14.0 ± 1.3 A below Tc. The ratio of the extrapolated zero‐angle inverse intensity at any ΔT below Tc to that quantity at the same ΔT above Tc was 3.6. The persistence length for fluctuations below Tc as determined by the Debye theory was of the same order of magnitude as the thickness of the binary interface.

X-ray Debye temperatures for Al, Nb and Pb

Abstract: Data from neutron scattering experiments are used to calculate X-ray Debye temperatures for Al, Nb and Pb.

The Debye characteristic temperature at T = 0 for cubic crystals

Abstract: Two formulae for calculating the Debye characteristic temperature at T = 0 for cubic elements are compared. One formula is due to de Launay and is derived from lattice dynamics. The other formula is the simple Debye formula expressed in terms of elastic constants from relations derived by Voigt and Reuss. Provided the anisotropy of the solid elements is not excessively large the two formulae give almost the same results. Even for the largest anisotropies which appear in nature the difference between the two formulae is less than 3%.