Griineisen constant

The expansion coefficient of a solid can be estimated with the aid of an approximate thermodynamic equation of state for solids which equates the thermal expansion coefficient with the quantity where yis the Griineisen dimensionless ratio, C, is the specific heat of the solid, p is the density of the material, and B is the bulk modulus. For fee metals the average value of the Griineisen constant is near 2.3. However, there is a tendency for this constant to increase with atomic number. 

The temperature independence of this contribution to the Griineisen constant is the main difference between Eq. (84) and the original calculation by Phillips. The numerical value of the expression should be nearly the same for all substances and is about 8. This suggests that the direct coupling to phonons is a potential contributor to the elastic Casimir effect at temperatures around 1 K. Remember, however, the sign of the expression in Eq. (84) is unknown and its numerical value of lO only provides an estimate from the above. 

Here, Vj, Ej and v, E are the specific volume and specific internal energy for the starting state of the expl and for the state at the Chapman-Jouguet (c-J) points, respectively p is the pressure at the C-J points p, v, p, E and T are the press, specific volume, density, specific internal energy, and temp of the DP respectively Q(vi) is the heat of expl p0 and E0 are the elastic components of pressure and energy which depend only on density 7 is the Griineisen constant of the DP ... 

Table 6.5 Griineisen Constants for Some Ionic Solids at Room Temperature ...

The parameter Kp is also known as the isothermal bulk modulus, and a as the volume expansion coefficient. They are interrelated by means of the Griineisen constant, y ... 

Wada, Y., Itani, A., Nishi, T., and Nagai, S., Griineisen constant and thermal properties of crystaUme and glassy polymers, J. Polym Sci. A-2,7, 201-208 (1969). 

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... 

Table 3.7. Room Temperature Griineisen Constants for Selected Materials...

The Griineisen constant at 22.2 K is considerably lower than the room temperature value given in Table 3.7. 

Of what value is (a) the Debye temperature, (b) the Griineisen constant, and (c) the Lorenz law What purpose do they serve in design ... 

We define the Griineisen constant y(q) of the linear chain by the following relation ... 

Further careful comparison of the Raman spectra reveals a systematic change in the peak position of these two Raman bands. Figure 7.9 shows the relationship between Raman peak position and inverse crystallite size as determined by the (003) peak from powder X-ray diffraction. The top x-axis scale is the crystallite size L By using the above value k(L) (=96.3 + 36.7-L ) and the previously reported Griineisen constants (0.79 for the Aig mode and 1.15 for the Eg mode), the crystallite size dependence of the Raman frequency shifts is deduced to be w = 590.5 - 177.8 for the Aig mode and oj = 480.2 - 210.0for the Eg mode. The calculated results based on the lattice-expansion model are shown as dotted lines. Comparing calculated and experimental results, we see that the observed frequency shift in the A g mode is much less than expected from the lattice-expansion model. It is clear that the lattice expansion model is not sufficient to explain the dependence of frequency shift on crystallite size. Therefore, another contribution — the phonon confinement effect — should be considered. 

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