Gruneisen relation

Establishment of scaling over a broad temperature range in properties such as Cp, X, p 01P is very important. While scaling appears valid for x in CeSns, UPt3 and YbCuAl and for resistivity in a number of systems, it has not been established for other materials or for other physical properties such as Cp or p. This requires very careful determination of background contributions, such as phonon contributions to Cp, p and P or non-f contributions to X- Furthermore, data for Cp need to be converted to Cv, which is the quantity involved in Gruneisen relations. 

The behavior of a/T at low temperatures resembles large enhancement of C/T in HP materials. Taking into account the Gruneisen relation, which shows that a is roughly proportional to specific heat C, a is expected to have the same temperature dependence as C, that is, the present results seem to be consistent with this notion. 

Fig. 149. CuCr2S4. Lattice constant vs. temperature. The dashed line is a normal thermal expansion curve deduced by the Gruneisen relation based on the measuie-...

The relation (5.90) is known as the GrUneisen relation it predicts that the volume expansion coefficient has the same temperature dependence as the specific heat. From (5.89,90) we see that the GrLineisen parameter characterizes the thermal expansion just as the Debye temperature characterizes the specific heat. The GrLineisen relation is approximately satisfied for many compounds with values of y between 1 and 2. 

According to Gruneisen (see also Tobolsky, 1962) the following relation applies to simple molecular crystals ... 

Here Cgii, has the meaning of an elastic energy scale. One can relate this to die more phenomenological Gruneisen parameter il. Since one obtains... 

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 ... 

Fig. 4.4 Phonon dispersion relations and the vibrational density of states (VDOS) calculated for guest-free clathrate Sii36 using DFT methods at T = 0 K. At right are shown the corresponding mode Gruneisen parameters calculated using a quasi-harmonic model as a function of temperature (from [66])...

DFT calculations of the static lattice were performed within the local density approximation (LDA) using planewave basis sets and ultrasoft pseudopotentials, and the results were used to construct a force constant matrix within a large superceU model. The phonon spectrum was then evaluated as a function of temperature using quasi-harmonic models that allowed us to constmct mode Gruneisen relationships [66] (Fig. 4.4). The results indicated a dip in the V(T) relation at 80 K, that was slightly smaller than that observed for diamond-structured Si (Fig. 4.5). 

According to the generally accepted relations that connect detonation velocity at one side and the explosive density and the heat of detonation at another, the Gruneisen coefficient depends only on the volume. By integrating Eq. (5.60), the Gruneisen equation of state is obtained ... 

The Gruneisen parameter also plays a role in nonlinear acoustics, and it has been shown that there is a relation between the Gruneisen parameter and ultrasonic absorption the larger y is, the higher the absorption (19). 

Gruneisen s Law. relates thermal conductivity y, linear thermal expansion coefficient a, compressibility K and specific heat C, for a solid of volume V, by 3aV = yKC. ... 

Different strains can have different Gruneisen parameters. The general belief is that only those deformations Sy with i j that are connected to volume change will have large Gruneisen parameters. Under these circumstances, as pointed out by Yoshizawa et al. (1986), the directional thermal expansion is related to the specific heat via a generalization of eq. (1) ... 

Relation [1.177] shows that the Gruneisen parameter for the phonon i is dimensionless, and therefore the parameter y(T, V), defined by relation [1.181], is also dimensionless. 

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