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 JMP  Vol.2 No.3 , March 2011
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
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.
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.
References

[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.

 
 
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