Curvature dependence of renormalized coupling constants

The renormalization group is used to analyze the behavior of certain gravitationally significant renormalized coupling constants under a scaling of the spacetime curvature. After discussing a simple example, the results are summarized for a class of grand unified theories.     

Temperature dependence of coupling constants and the phase transition in the Coleman-Weinberg theory

It is shown that the temperature dependence of the effective Higgs boson coupling constants leads to a considerable modification of the theory of the SU(5) Coleman-Weinberg phase transition.     

Temperature dependence of the elastic constants of aluminum

The single crystal elastic constants of aluminum have been measured using a piezoelectric composite oscillator from room temperature to just 20 K below the melting point. The elastic moduli differ markedly from previous high temperature results, but match in well with previous cryogenic results. Over the temperature range investigated the isothermal bulk modulus and the two shear moduli have a simple exponential dependence on isobaric volume, and the cryogenic data indicate this dependence may be preserved down to absolute zero. As has been found previously for a wide range of materials, the isothermal bulk modulus and the shear modulus $\text{(c}{}_{11}\text{– c}{}_{12}\text{)}\text{2}$ appear to be continuous functions of volume through the melting expansion, and melting seems to find its origin in the mechanical instability associated with this shear modulus vanishing at the volume of the melt at the freezing point. Grüneisen's parameter divided by the molar volume is very nearly independent of isobaric volume.     

Temperature dependence of the elastic constants of aluminium

Published results for the temperature variation of the elastic constants of single crystal aluminium are discussed with special reference to the possibility that error propagation in the conversion of compliances to stiffness may contribute to the discrepancies between the different sets of data for the stiffnesses.     

Temperature dependence of elastic constants for ionic solids

In this paper the thermal variation of volume for NaCl, KCl, MgO and CaO has been investigated on the basis of Anderson model. We have evaluated the values of elastic constants C₁₁, C₄₄ and K_T at different temperature on the basis of Murnaghan and Tallon models. Tallon's model with second approximation presents slightly better agreement with experimental results which shows that the Anderson–Grüneisen parameter is directly proportional to the volume ratio. Tallon's model can be used to evaluate the values of elastic constants for solids at different temperatures.     

Hyperfine coupling constants and their dependence on charge densities

In paramagnetic aromatic systems the relation between the hyperfine coupling constants a _H for the protons and the spin density ρ on the adjacent carbon atom is usually given by the relation a _H = -Qρ (McConnell) in which Q is a constant characteristic for the C-H bond. In the paramagnetic ions of aromatic molecules the carbon atoms have in general besides a non-zero spin density also a non-zero excess charge density.

If one takes into account both the effect of the spin density ρ and the excess charge density ε on the C-H bond, the following formula is obtained for the proton hyperfine coupling constant:

in which Q and K are predicted to be positive constants of the same order of magnitude.

Comparison with experimental data gives Q = 31·2 gauss; K = 17 gauss.     

The conformational dependence of vicinal 15N-C-C-H coupling constants in peptides

The conformational dependence of vicinal ¹⁵N-C-C-H coupling in N-methylacetamide as a model compound for coupling in the peptide backbone is investigated by means of the self-consistent perturbation formulation for coupling constants in the INDO approximation of self-consistent-field molecular orbital theory. Because the calculated coupling constants cover a range of at least 7 Hz, they should be useful in determining the ψ angles in peptides. The prediction of opposite signs for gauche and trans coupling indicates the need for sign determination. Non-negligible coupling constants of positive sign for the gauche arrangements are undoubtedly due to a substituent effect involving the lone pair electrons on the nitrogen and the π-electrons of the carbonyl group. Calculated results are compared with the available experimental data.     

Temperature dependence of third order elastic constants of ammonium halides

The third order elastic constants of ammonium halides have been evaluated for the first time using Lundqvist three body potential incorporating the effect of thermal contributions. Theoretical investigations have been carried out above λ-temperature where both NH₄Cl and NH₄Br have cubic CsCl structure. Analysis has been extended to mixed NH₄Cl_1−x Br _x . The repulsive potential which is assumed significant up to first neighbours is taken of the Born-Mayer type. Results have been compared with the recently measured values wherever available.     

Temperature dependence of the second-order elastic constants of cubic crystals

A simplified phenomenological theory of the temperature dependence of the second-order elastic constants of crystals is considered. The temperature dependences of the second-order elastic constants are calculated for a series of cubic crystals with various types of predominant chemical bonding. Satisfactory agreement between the calculation results and experimental data is obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 235–240 (February 1999)     

Temperature and volume dependence of the elastic constants of palladium

A separation between lattice and electronic contributions to the elastic constants of Pd is obtained. The temperature dependence at constant volume is measured by applying hydrostatic pressure. The apparatus and results for Pd are presented.     

Temperature dependence of the elastic constants of a KCl-NaCl solid solution

Measurements are made of the temperature variations of the elastic constants, the factor of elastic anisotropy, the degree of deviation from the Cauchy relation and the coefficients of thermal linear expansion of a KCl-NaCl solid solution of different concentrations in the 300–640°K temperature range. An analysis is given for the dependences obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 122–125, October, 1973.In conclusion the authors thank V. N. Suslovaya for carrying out the x-ray monitoring of the concentrations of the solid solutions being investigated.     

Temperature dependence of the elastic constants of single-crystal KI-KBr solid solutions

Elastic constants C₁₁, C₁₂, and C₄₄ were measured for solid KI-KBr solutions over the temperature range 20–280 °C. When plotted as functions of the composition, elastic constants C₁₁ and C₄₄ display a significant deviation toward a negative nonadditivity. The Debye temperature calculated from the elastic constants at 0 °K is 8 ° lower than the additive value at compositions containing 66 M% KI.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 58–62, April, 1971.In conclusion the authors thank A. A. Botaki for the opportunity to measure the elastic constants.     

Temperature dependence of the elastic constants of copper,gold and silver

From an inverse power type interatomic potential energy function and the Boltzmann distribution function for interatomic distances, the second-order elastic constants of copper, gold and silver are calculated as a function of temperature without involving any undetermined parameters. The results are found to be in fair to good agreement with the experimental observations in the temperature range of-196 to 25°C.