Author(s)

Tetsuo Nakajima

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In almost all previous works, the hyperbolic dispersion surfaces of the central proper quadrics have been crudely derived from the degree of reduction from the bi-quadratic equation by use of some roughly indefinable approximate relations. Moreover, neglecting the high symmetry of the hyperbola, both the branches have been approximated on the asymmetric surfaces composed of a pair of a branch of the hyperbola and a vertex of the ellipse without the presentation of reasonable evidence. Based upon the same dispersion surfaces equation, a new original gapless dispersion surfaces could be rigorously introduced without crude omission of even a term in the bi-quadratic equation based upon usual analogy with the extended band theory of solid as the close approximation to the truth.

Dynamical Theory X-Ray Diffraction, Gapless Dispersion Surface, Gappy Dispersion Surface.

T. Nakajima, "Remarks on the Erroneous Dispersion Surfaces From a Pair of a Hyperbolic Branch and An Elliptical Arc of the Intersected Two Laue Spheres Based on the Usual Crude Approximation," Journal of Modern Physics, Vol. 2 No. 3, 2011, pp. 146-153. doi: 10.4236/jmp.2011.23022.