Theoretical Strength of a Perfect Crystal

Abstract

A mathematical procedure is presented for applying the Born stability criteria to the determination of the mechanical stability of cubic crystals in the presence of applied forces and deformations. The general procedure presented is suitable for use in conjunction with an electronic computer and is independent of the specific model of interatomic interactions which may be used in numerical calculations. In the present study, specific calculations are performed for a body-centered-cubic (bcc) crystal lattice with an uniaxial force applied perpendicular to a face of a unit cell. The atoms in the crystal are assumed to interact via the two-body Morse interatomic-potential function determined by Girifalco and Weizer [Phys. Rev. 114, 687 (1959)] for bcc iron. Two ranges of stability, a bcc phase and a body-centered-tetragonal (bct) phase, were found to exist. The bct phase has a theoretical strength of 0.9\ifmmode\times\else\texttimes\fi{}${10}^{11}$ dyn/${\mathrm{cm}}^{2}$ with a corresponding theoretical strain of about 7%. These values are fairly close to the values of 1.3\ifmmode\times\else\texttimes\fi{}${10}^{11}$ dyn/${\mathrm{cm}}^{2}$ tensile strength and about 5% strain experimentally observed for iron whiskers.