METHOD FOR HIGHLY ACCURATE NUMERICAL SPATIAL INTEGRATION: APPLICATION TO LATTICE DYNAMICS OF CUBIC TYPE CRYSTALS

摘要

The vector-interpolation method for machine computation of the frequency distribution G(v) of lattice vibrations is greatly improved and extended./ A procedure is developed which permits one to design an exactly uniform N-vector distribution (for any M) inside one of the typical 1/48 symmetry-irreducible trihedral solid angles which characterize highest cubic symmetry. We have chosen N = 489 for reasons discussed, and give a table of direction cosines p ,q,r to ten decimals of the K = 1,2,...,N vectors. It is shown that by permutations and sign changes of these p ,q.r one can generate an exactly uniform distribution of 23,472 vectors to the full 4π steradians. Thus, our results may find application in several areas outside lattice dynamics.