The Vibrational Spectrum and Specific Heat of a Face-Centered Cubic Crystal

The frequency spectrum of a face-centered cubic crystal lattice is found by actually modeling the constant-frequency surfaces of the secular determinant in plaster of Paris and measuring the volume enclosed between successive surfaces. The frequency spectrum so obtained is used in the evaluation of the specific heat of a general crystal of the type treated, and numerical values are presented for the element silver. The present theory (that of Born and v. Karman) is in much better agreement with experimental values for temperatures below 100°K than is the Debye theory. Certain anomalies in the specific heat curves of silver and potassium chloride at temperatures below 10°K are not explicable in terms of the atomic model that is used.