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Beam Statistics and Diffraction from Materials in the Critical State

Published online by Cambridge University Press:  22 January 2004

J.R. Sellar
J.R. Sellar
Affiliation:
School of Physics and Materials Engineering, Monash University, 3800 Victoria, Australia and Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
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Abstract

It is shown that room-temperature diffraction pattern spots and diffuse scatter can appear to change their size and appearance relative to reciprocal-space sublattice reflections when the scattering material corresponds in structure to a critical phase. Under such a condition, the material is considered to be continually on the verge of a phase transition and the diffraction spot will have no definite width, its apparent size in reciprocal space dependent on the strength of the scattering into the diffracted beam. It is thought that the materials described in the experiments—niobia-zirconia ceramic alloys—are capable of entering such a critical phase because of their recently suggested planar XY spin character. After first describing how the seemingly crystalline ceramic alloy can display XY-like behavior, we analyze the intensity dependence of the critical scattering from the alloy's oxygen superlattice using information-theoretic methods.

Keywords

X-Y modelcritical scatteringniobia-zirconia
Type
Research Article
Information
Microscopy and Microanalysis , Volume 10 , Issue 1 , February 2004 , pp. 112 - 115
Copyright
© 2004 Microscopy Society of America

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References

REFERENCES

Futterer, K., Schmid, S., Thompson, J.G., Withers, R.L., Ishizawa, N., & Kishimoto, S. (1995). The structure refinement of compositely modulated Nb2Zr(x−2)O(2x+1) (x = 2). Acta Cryst B 51, 688–697.CrossRefGoogle Scholar
Galy, J. & Roth, R.S. (1973). The crystal structure of Nb2Zr6O17. J Solid State Chem 7, 277–285.Google Scholar
Hyde, B.G., Bagshaw, A.N., Andersson, S., & O'Keeffe, M. (1974). Some defect structures in crystalline solids. Annu Rev Mater Sci 4, 43–92.Google Scholar
Kosterlitz, J.M. & Thouless, D.J. (1973). Phase transition in the XY model. J Phys C 6, 1181–1196.Google Scholar
Mermin, N.D. & Wagner, H. (1966). Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys Rev Lett 17, 1133–1136.Google Scholar
Schmid, S., Thompson, J.G., Withers, R.L., Petricek, V., Ishizawa, N., & Kishimoto, S. (1997). Rerefinement of composite modulated Nb2Zrx−2O2x+1 x = 7.1 to 10.3. J Solid State Chem 88, 465–475.Google Scholar
Sellar, J.R. (1999). Disorder, superlattice canting and chiral domains in zirconia-niobia ceramic alloys. Acta Cryst A 55, 220–227.CrossRefGoogle Scholar
Sellar, J.R. (2001). A frustrated planar XY model for niobia-zirconia ceramic alloys. Micron 32, 871–877.Google Scholar
Shannon, C.E. (1949). A mathematical theory of communication. Bell Syst Tech J 27, 379–423, 623–656.Google Scholar
Thompson, J.G., Withers, R.L., Sellar, J.R., Barlow, P.J., & Hyde, B.G. (1990). Incommensurate modulated Nb2Zrx−2O2x+1. J Solid State Chem 88, 465–475.Google Scholar