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

  • S. Weissmann (a1), W.E. Mayo (a1) and Z.H. Kalman (a2)

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.

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1. Newman, B.A., J. Appl. Phys. 3, 191 1970.
2. Imura, T., Weissmann, S. and Slade, J.J. Jr., Acta Cryst. 15, 786 1962.
3. Slade, J.J., Weissmann, S., Nakajima, K. and Hirabayashi, M., J. Appl. Phys., 35, 3373 1964.
4. Berg, H.M. and Hall, E.L., Advances in X-ray Analysis, 18, (Plenum, New York, 1974), p. 454.
5. Kalman, Z.H., Lee, L.H., He, X.C. and Weissmann, S., (paper submitted to Met. Trans.).
6. Rusovic, N. and Warlimont, H., Phys. Stat. Sol. A, 44, 609 1977.
7. Tanner, L.E., Pelton, A.R. and Gronski, R., J. Phys. (France) 43, suppl. 12, 169 1982.
8. Shapiro, S.M., Noda, Y., Fujii, Y. and Yamada, Y., Phys. Rev., 830, 4314 1984.
9. Nagasawa, A. and Ueda, Y., J. Phys. Soc., Japan, 45, 1249 1978.
10. Nagasawa, A., Makita, T. and Takagi, Y., J. Phys. Soc, Japan, 51, 3876 1982.
11. Mayo, W.E., Chaudhuri, J. and Weissmann, S., Non-destructive Evaluation and Applications of Materials Processing, (Conf. Proc. ASM, 1984), p. 129.

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

  • S. Weissmann (a1), W.E. Mayo (a1) and Z.H. Kalman (a2)

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