By R P Reed; A F Clark; American Society for Metals
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Example text
I. Poisson's ratio, II = -Sid SII for [lOO]-type directions should be 1/3, and this is very close to the average observed values for metals and alloys. 4 Semiempirical models Although relatively simple and related to basic principles, Leibfried's linear-chain model described in the previous section describes only the highertemperature, linear region of the C(T) curve. Even the most elegant and complicated basicprinciple models fail to describe C(T) accurately. Sacrificing fundamentals for fit leads to various so-called semiempirical models, which describe C(T) quite accurately.
In particular, Leibfried develops the solid-state physics of the linear-chain model and applies it to many physical properties, including elastic constants and their temperature derivatives. 3 follows largely from Leibfried's results. Stern (1958) developed an approach similar to Born's, but with a significant difference: Stern considered energy changes under stress variations rather than strain variations. The advantage is that stress enters the energy expression directly, where its effect can be evaluated.
109) where A and B are adjustable parameters, ~ denotes volume thermal expansivity, and R denotes V(1)/ V(O), where V is the volume. The other cubic-symmetry elastic constants, CII and C12, defied such a representation. 110) where a denotes linear thermal expansivity. But, the authors emphasized the pure empiricism and lack of a theoretical basis for this relationship. 2), the first suggestion of a function that describes accurately the temperature dependence over a wide range was by Wachtman, Tefft, Lam, and Apstein (l96l).
