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X-Ray Topographic Methods for Stress-Strain Tensor Analyses of Crystals

Published online by Cambridge University Press:  26 February 2011

S. Weissmann ,
W.E. Mayo  and
Z.H. Kalman
S. Weissmann
Affiliation:
Department of Mechanics and Materials Science, College of Engineering, Rutgers University, Piscataway, NJ 08854
W.E. Mayo
Affiliation:
Department of Mechanics and Materials Science, College of Engineering, Rutgers University, Piscataway, NJ 08854
Z.H. Kalman
Affiliation:
Racah Institute of Physics, Hebrew University, Jerusalem, Israel
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Abstract

Two methods for the strain tensor analysis of crystals will be presented. One of them is based on a modified x-ray back-reflection divergent (BDB) method. By the interposition of a wire grid between crystal and film, a computer-aided ray tracing technique was developed resulting in simultaneous precision measurements of d-spacings of several (hkl) planes. The strain input data for the tensor analysis are = (dn-dn°)/dn°, where dn° is the d value of the corresponding unstrained (hkl) planes, the precision of the strain measurements being ± 0.02%. The strain tensor εij obtained from the strain components, referred to the cubic coordinate system, is calculated by a least square method and the principal strains and their directions are determined. From the principal strains and known elastic constants the complete stress-strain configuration as well as the stored elastic energy are determined. An example of application to the elucidation of strains in premartensitic Al Ni crystals will be given. The other x-ray method presented is based on a computer-aided rocking curve analysis (CARCA) method, which is particularly well suited for the tensor analysis of non-uniform strain distribution in epitaxially grown microelectronic materials. This method determines not only the full elastic strain tensor, but also its distribution about a strain center with a resolution of approximately 60 Pm. As an example the strain distribution in an InGaAsP epitaxial film on an InP substrate is presented.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 82: Symposium I – Characterization of Defects in Materials , 1986 , 221
Copyright
Copyright © Materials Research Society 1987

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References

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