The Dependence of the Debye Temperature on the Elastic Constants

Sophisticated methods have been put forward in the literature to calculate Debye temperatures from the elastic constants c ik . As a simple alternative method for cubic crystals, a relation is often used that correlates Debye temperature and bulk modulus (c 11 + 2c 12 )/3 by a square‐root law. It is shown that, with exception of the alkali metals, such a law is only poorly fulfilled for other cubic elements and compounds. If one takes, however, elastic moduli such as [ c 44 ( c 11 − c 12 ) ( c 11 + c 12 + 2 c 44 )] 1/3 or { c 44 [( c 11 − c 12 ) c 44 /2] 1/2 ( c 11 − c 12 + c 44 )/3} 1/3 instead of the bulk modulus the square‐root law is established for various cubic material classes. This procedure eventually allows to easily evaluate hitherto unknown Debye temperatures from the elastic constants with high precision.