X-Ray Study of Lattice Vibrations in Aluminum

The diffuse scattering of monochromatic x-rays by a single crystal of aluminum at 300^ has been measured along seven lines in reciprocal space. Analysis of these data in terms of the Laval-James theory has yielded dispersion curves for elastic waves propagating along the three primary symmetry axes. By interpreting these dispersion curves in terms of the Born theory of lattice vibrations, values have been obtained for the nine force constants necessary to describe the general first-, second-, and third-neighbor interactions. These force constants have served as criteria in rejecting the simpler models of atomic interactions generally employed. The secular equation containing these nine force constants has been solved for the eigenfrequencies of 2791 wave vectors by machine computation. These solutions served to establish an approximate frequency spectrum of the normal modes, in which the singularities caused by the critical points are explicitly included. From this spectrum the specific heat is calculated. A comparison with measured specific heats shows the need for the inclusion of anharmonic terms in the theoretical approach.