The third-order elastic shear constants of face-centred cubic and body-centred cubic metals

It is found that one of the six third-order constants of cubic crystals of sufficiently high symmetry and two combinations of the remaining five constants relate to strains in which the volume is unchanged. These shear constants are 1/8( C 111 -3 C 112 +2 C 123 ), C 456 and ½( C 144 - C 155 ). The electrostatic and repulsive ion-ion contributions to these constants are obtained in general terms for face-centred cubic and body-centred cubic metals. The electrostatic contributions are positive for face-centred cubic metals and negative for body-centred cubic metals. The repulsive contribution to C 456 is relatively insignificant in face-centred cubic metals whereas it predominates in body-centred cubic metals. These two contributions are not able to account for the observed third-order shear constants of noble metals, particularly C 456 . It is shown that it is necessary to include the energy of the conduction electrons. Detailed calculations cannot be made, however, until the third-order constants have been determined at low temperatures.