Elastic constants of polycrystalline copper at low temperatures. Relationship to single-crystal elastic constants

Elastic constants of polycrystalline copper are determined between 4 and 295 K by measuring ultrasonic velocities, longitudinal and transverse. Five elastic constants are given: longitudinal modulus, shear modulus, Young's modulus, bulk modulus (reciprocal compressibility), and Poisson's ratio. Considering eight theories of single-crystal :polycrystal elastic constants, the Hershey-Kröner-Eshelby theory agrees best with observation, within 1% for the shear modulus, G. (Voigt and Reuss first-order bounds on (G differ by 29%.) A problem exists concerning the calculation of the Debye temperature of polycrystalline aggregates.