Christoffel matrix

T is the Christoffel matrix. The elements of for arbitrary (i.e. triclinic) symmetry are given in Table 11.1(a). The direction cosines /, are defined by... 

If the z direction is taken as the normal to the surface, and the x direction is taken as also lying in the plane of incidence, then in calculating the Christoffel matrix T for arbitrary crystallographic orientation the stiffness matrix must be transformed to these new coordinates. In the notation of (11.2), and for an incident wavevector (k x, k y, k z) in the fluid, the requirements of Snell s law become... 

Once again, our problem of determining the wave solutions associated with our medium has been reduced to a problem of matrix diagonalization. The eigenvalues of the acoustic tensor or Christoffel tensor, Aij = (A + p)qiqj + p-q Sij, are found to be... 

When the matrix multiplication represented by the Christoffel equation is performed, a set of simultaneous equations is obtained. These equations are expressions for all allowed modes of plane wave propagation in an unbounded... 

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