# Heat capacity of rotating crystals

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Heat capacities C[lowered v] due to lattice vibration of rotating cubic crystals are calculated. The frequency distribution function from which C[lowered v] is obtained is determined approximately by a technique due to Betts. In the case of cubic crystals under rotation, the frequency distribution function g([omega], [theta], [Phi]) has tetragonal symmetry. Betts's approximation scheme Involves expanding g([omega], [theta], [Phi]),in terms of tetragonal harmonics, which are linear combinations of spherical harmonics. Applying the orthogonality condition of spherical harmonics, the distribution function g([omega]), which is the integral g([omega], [theta], [Phi]) of over the solid angle, can be expressed approximately as a linear combination of along four directions: A(100), B(001), 0(101), and B(110). Since ([omega], [theta], [Phi]) can be determined exactly from the secular equation determining the normal mode frequencies (omega), the frequency distribution function g([omega]), and hence the heat capacity C[lowered v] can be determined. The molar heat capacities C[lowered v] of three face-centered crystals: Ag, Au, and Ou rotating with a constant angular velocity along an axis of symmetry are calculated. The results indicate an increase of specific heat due to rotation at temperatures below 10[raised -4] [degree]K for a rotation as large as 10[raised 6] revolutions per second.