Gallium arsenide is a piezoelectric crystalline material belonging to the cubic group (class 43¯ m). The elastic constants, piezoelectric constant in Coulombs per square metre and relative...

Gallium arsenide is a piezoelectric crystalline material belonging to the cubic group (class 43¯ m). The elastic constants, piezoelectric constant in Coulombs per square metre and relative permittivity constants are c11 = 11.88 × 1010N/m2 , c44 = 5.94 × 1010N/m2 , c12 = 5.38 × 1010N/m2 , e14 = 0.154C/m2 and ε11 = 12.5 × ε0. The density of the material is ρ = 5307kg/m3 . The piezoelectric coupling coefficient and the permittivity matrices are given by

Hence, show that the general solution is the superposition of four-plane wave solutions, each with a unique decay constant and each satisfying boundary conditions associated with a piezoelectric surface. State the four boundary conditions that the solutions must satisfy and calculate the Rayleigh SAW velocity and the electromechanical coupling coefficient. The direction of propagation is the x1 axis (100 axis) and the free surface is normal to the x3 axis (001 axis). Comment on your results.