Introduction to Solid State Physics · Problem 11

CRYSTAL BINDING AND ELASTIC CONSTANTS — Charles Kittel

Physics — Solid State · elastic-constants-cubic-crystals

Problem

Effective shear constant. Show that the shear constant

\frac{1}{2}(C_{11} - C_{12})

in a cubic crystal is defined by setting the shear strain component

e_{xy} = -e_{yx} = \frac{1}{2}\epsilon

and all other strain components equal to zero, the stress component

X_y = \frac{1}{2}(C_{11} - C_{12})\epsilon

. Recall the relations (32) and the energy density (43).