A modified Houston-Nakamura approximation is suggested for counting lattice frequencies. This method is tested on a transversely vibrating two-dimensional lattice and found to give excellent agreement with the exact Bower-Rosenstock solution. Following Houston, the method interpolates between symmetry lines or planes to obtain frequency contours within the Brillouin zone. The difference is that the interpolation does not follow the spherical harmonic approximation of Houston but suggests contours of specified form intermediate between circles and straight lines in two dimensions and between spheres and planes in three dimensions. Nakamura's procedure of using separate approximations in different regions of the Brillouin zone is also followed.
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Jenn-Lin Hwang (1955) studied this question.
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