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

Author(s)
Tetsuo Nakajima

ABSTRACT

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.

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.

Cite this paper

nullT. 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.

nullT. 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,"

References

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[1] R. M. Stern, J. J. Perry and D. S. Boudreaux, Reviews of Morden Physics, Vol. 41, 1969, pp. 275-295. doi:10.1103/RevModPhys.41.275

[2] N. Kato, Kaisetsu and Sanran (in Japanese), “Diffraction and Scattering,” Chapter 9, Toyko, 1978.

[3] A. Authier, “Dynamical Theory of X-Ray Diffraction,” Chapter 4, Oxford university press, New York, 2001.

[4] Z. G. Pinsker, “Dynamical Scattering of X-Rays in Crystals,” Springer-Verlag, Berlin, 1978.

[5] B. K. Tanner, “X-Ray Diffraction Topography,” Pergamon Press, Oxford, 1976.

[6] S. Miyake, X sen no Kaisetsu (in Japanese), “X-Ray Diffraction,” 3rd Edition, Chapter 5, Tokyo, 1988.

[7] C. Kittel, “Introduction to Solid State Physics,” 6th Edition, Chapter 7, John Wiley & Sons, Inc., New York, 1986.

[8] T. Nakajima, ECM26, Darmstadt, 2010.

[9] T. Nakajima, XTOP, Warwick, 2010.

[10] R. Kubo and T. Nagamiya, “Solid State Physics,” Chapter 4, McGraw-Hill Book Co., Inc., Hong Kong.