By Harold J. Hovel
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This equation has been derived on the assumption that y does not vary with temperature. Consequently, if y depends on the temperature and if we compute y from Eq. (4),we obtain the value of some parameter which, generally speaking, is not the usual Gruneisen parameter = - d log 8/d log K Let us use the symbol y' to represent the Griineisen parameter y computed from the Griineisen equation in its normal form when y =f(T). We shall now ascertain its physical meaning. Let us use the thermodynamic relations From (7) we obtain or Hence, 2.
A second type of analysis' accounts for the temperature dependence by allowing y, the Gruneisen parameter, to be temperature dependent. The temperature dependence is considered to be due to the occurrence of higher order processes. For example, four-phonon processes would give a T-' dependence for the conductivity. Neither this nor the above approach seems conclusive at this time. ' The appropriate parameters are listed in Table 111, and the curve of y2 vs the mass ratio for the various 111-V compounds is shown in Fig.
4), to compute y. b. The Temperature Region in Which fi Becomes Equal to Zero Since B = 0 and, consequently, the volume remains constant, Eq. (10) can be written as Replacing Cv by dE/dT, we obtain 48 S. I. NOVIKOVA The solution of this equation is y=- A (11) Evib’ where A is a constant. From Eq. (11) it follows that when u = 0 the Gruneisen parameter y, unlike y’, does not become zero. c. y = o In this case Eq. (10) simplifies to (2) V 3uv =-. XEvib Let us determine the temperature at which y becomes zero.