A method for calculating the low temperature surface specific heat of a crystal lattice

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Abstract
A new method is presented for calculating the surface specific heat of a crystal lattice in the harmonic approximation. As an illustration it is applied to an isotropic elastic continuum with stress-free boundaries and the result is in agreement with previous authors. The method clearly shows the contributions to the surface specific heat from the various types of mode that can exist in the presence of a surface and, in particular, how the contribution from the bulk modes is closely related to the difference between the form of these modes in a semi-infinite and an infinite crystal.

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