Bismuth germanium oxide is a piezoelectric crystalline material belonging to the cubic group (class.

Bismuth germanium oxide is a piezoelectric
crystalline material belonging to the cubic group (class 23). The elastic
constants, piezoelectric constant in Coulombs per square metre and relative
permittivity constants are c11 = 12.8 × 1010N/m2 , c44 = 2.55 × 1010N/m2 , c12
= 3.05 × 1010N/m2 , e14 = 0.99C/m2 and ε11 = 3 × ε0. The density of
the material is ρ = 9200kg/m3 . The piezoelectric coupling coefficient and
the permittivity matrices are identical to the case of a class 43¯ m material.
(i) Assume that the material is isotropic and that c44 = (c11 − c12) 2,
and compute the Rayleigh SAW velocity. The direction of propagation is the x
axis and the free surface is normal to the z axis. (ii) Calculate the Rayleigh
SAW velocity and the electromechanical coupling coefficient when the assumption
of isotropy is not made. What is the percentage error in the isotropic
calculation?