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Sure! Let’s carefully derive the expression for the velocity of a transverse wave propagating along the \[100] direction in a cubic crystal step by step, manually. --- ### Step 1: Basics of elastic waves in crystals For a cubic crystal, the stress-strain relationship is expressed in terms of elastic constants $C_{ij}$ in Voigt notation. For cubic crystals, the stiffness matrix has three independent constants: $$ C_{11},\quad C_{12},\quad C_{44} $$ * $C_{11}$: longitudinal stiffness along principal axes * $C_{12}$: coupling between normal stresses * $C_{44}$: shear stiffness The equation of motion ___ ___ ___ __________ _____ _________ _____ _______ ______ ____ ______ _____.
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