Griineisen relation

These compounds are metallic conductors, and similar to YNiPb, the Bloch-Griineisen relation is also valid for Y2Ni2Pb. The magnetic ordering manifests in the temperature dependence of the resistivities through abrupt changes in the slopes (decrease of spin-disorder scattering). 

A detailed study of the electrical resistivity behavior of the La272ln and Ce272ln (T = Ni, Cu, Rh, Pd, Pt, Au) indides was performed by Kaczorowski et al. (1996a, 1996b). They evaluated the electrical resistivity data according to the modified Bloch-Griineisen relation and derived the Debye temperatures (table 17). 

Pressure influences the spectroscopic properties of the material in several ways. First, it compresses the lattices and changes their volume. This bulk effect, described by the equation of state (see Eq. 4.2.5), also alters the energetic structure of the system, especially the energies of the conduction and valence bands. Such an effect can change the energy of the band-to-band transition. Compression also alters phonon frequencies, which is described by the Griineisen relation [69] ... 

Scaling behavior and Griineisen relations 3.1. Thermodynamics of scaling... 

The magnitude of coph was calculated on the basis of the Debye model and the Griineisen relation (Oomi and Mori, 1981b). Figure 65 illustrates the values of co at ambient pressure, in which the broken line shows the result of fitting. The cOg at ambient pressure was estimated to be about — 1.5 X 10 at 0 K, which is negative and is smaller than that of Invar alloy by an order of magnitude. 

Within the Debye approximation the spectral functions oc F are proportional to (o in the energy range co kgGo (0 denotes the Debye temperature). This leads to a temperature dependence of the matrix elements Qoo from which the well known Bloch-Griineisen relation for pp follows (see Blatt 1968). For the low- and high-temperature regions the Bloch-Griineisen law reveals ... 

The Griineisen relation may also be expressed in terms of the more commonly measured mechanical properties as... 

Use the values of p given in Problem 3.13 for copper and the Griineisen relation to estimate a and the coefficient of linear thermal expansion at 300 and 50 K. Compare the results with the a values also given in Problem 3.13. Tabulate the results and give percent differences between estimated and experimental results. The specific volume of copper has been determined as 7.25 cm mol. 

Some conclusions can be drawn finm the Griineisen relation. At temperatures between 2 and 20 K, the proportionality at T for crystalline and a T for amorphous polymers holds. This can be explained fitnm equation 2 by a(T) = constant C(T), since y and K are nearly constant at these temperatures and C(T) (or y3.5) (gq temperatures above 100 K, y is not very dependent... 

Because the Griineisen ratio relates the isentropic pressure, P, and bulk modulus, K, to the Hugoniot pressure, P , and Hugoniot bulk modulus, K , it is a key equation of state parameter. 

Graphical representation, 423 Gravity, 21, 201 Griineisen s relation, 486 Guldberg s rule, 234... 

Griineisen (1926) derived a semi-empirical relation between thermal expansion, specific heat, specific volume and compressibility for solid crystalline substances. 

Assuming that the compressibility, the thermal expansion and the heat capacity reflect the same intrinsic properties of proteins, one may expect a close relation between them. For solids and synthetic polymers, the relation between the volume, V, the thermal expansion, a, the compressibility, Pt, and the heat capacity at constant volume, Cv, is given by the Griineisen parameter y ... 

Longitudinal Mode Griineisen Parameter of PVAC. In an isotropic solid the longitudinal mode Griineisen parameter (LMGP) Yl relates the frequency fL of a longitudinal sound mode of a given wave vector q to the mass density p of the sample... 

Creep rate, Young s modulus, and tensile strength are also shown to be connected with the mode parameters (the Griineisen parameter and the maximum frequency) of the fundamental vibrations. We suggest, that this relation reflects the participation of different vibrational modes in the generation of excited bonds. Therefore, powerful energy fluctuations seem to play a decisive role in the deformation, relaxation, and fracture in oriented polymers, their formation controls the kinetics of the macroscopic processes considered. 

There are some physical generalities concerning thermal expansion coefficients. One empirical correlation is that is constant for a wide range of cubic and close-packed compounds, where T is the melting point and is the volume coefficient of thermal expansion. The Griineisen equation relates ol to the compressibility Kq, the heat capacity c , and the molar volume V here y is the Gruneisen constant, a proportionality constant of first order ... 

The Griineisen analysis can be extended (Thalmeier 1988) to include the presence of a magnetic field. Starting from a Gibbs energy dG = dC/-5d7 + KdP —MAH and the concomitant relation... 

We have focused on two issues (1) the degree to which the pressure response of the electrical resistivity, magnetic susceptibility and specific heat is similar in a given material or class of materials and how this pressure dependence is related to the Griineisen parameter obtained from ambient pressure measurements and (2) the extent to which this comparison holds in both anomalous lanthanide and actinide compounds. 

To maybe considered as Kondo temperature Tk, spin fluctuation temperature Tsf, and so forth. F(T, V) relates the two strongly temperature-dependent quantities Xy and Cy but is relatively weakly dependent on temperature. Taking into account this fact and that for real solids F is often roughly constant over a wide range of temperatures, F has often been referred to as "the Griineisen constant." But in some solids such as HF... 

Both the specific heat and the coefficient of thermal expansion originate from the concept of the intermolecular potential, and accordingly these two properties are related. The present understanding of this relation is largely due to Griineisen, who developed an equation of state for solids, based upon the lattice dynamics of Debye. The latter showed that the dimensionless ratio, y, should be a universal constant defined either as... 

The macroscopic Griineisen parameter relates the coefficient of thermal expansion a to the specific heat C and the compressibility. S ... 

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