Journal of the Graduate Research Center


The problem of the determination of the frequency spectrum for the Born-van Karman model for an element having body-centered cubic lattice structure is described. The model is the simple one in which only central force interactions between nearest and next-nearest neighbors are considered. The extensive program for the computation by an electronic computer of the frequency distributions for eighteen values of the ratio of the two force constants is described, and the tabular histograms which resulted are given. The use of linear interpolation to obtain frequency distributions for other values of the ratio is discussed. Comparisons are made with the distributions obtained by others through less extensive calculations for the same model. A comparison is made with the spectrum for vanadium, which was deduced from neutron diffraction experiments. The use of histograms for calculating the thermal energy of a crystal is described.

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