Integral Diffractometry of Nanoscale Defects in an Elastically-Bent Single Crystal

A. P. Shpak, V. B. Molodkin, A. I. Nizkova

G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

With the purpose of development of the new high-informative diagnostic techniques for the determination of the randomly distributed nanoscale defects (RDND), which are invisible by tradition non-destructive methods such as the x-ray topography, for which such small defects in one dimension or in three dimensions are appeared outside the method sensitivity limits, the basic physics are developed for the method of the strain-dependent total integrated reflecting power (TIRP), which appears unique sensitive to RDND. For the first time, the presence of uniform elastic-strain dependence is theoretically and experimentally proved for the diffuse-scattering integral intensity, the extinction coefficients caused by the scattering on microdefects, for both coherent ($\mu_{ds}$) and diffuse ($\mu^{*}$) components of TIRP and effective static Debye–Waller factor with index, which is considered to be proportional to the integrated intensity of diffuse scattering. The nature of possible mechanisms of both additive and nonadditive influence of the elastic strains (ES) and RDND on the TIRP is revealed at the various degrees of the reflection asymmetry, which gives the possibility of the essential strengthening of the ES influence on the TIRP. As shown, the non-additivity of the mutual influence of the RDND and ES on the TIRP value of the Laue reflections is evidence of the presence of large (in two dimensions) RDND. The large (in two dimensions) RDND influence on the TIRP value becomes comparable with the elastic-strain influence at the any bending strength and at the any asymmetry degree of the Laue reflections at issue due to the essential importance of extinction effects caused by the scattering at those RDND and due to the relative rise of their influence on the TIRP with the ES increase. Small (in three dimensions) defects at the any degree of the reflection asymmetry cause the additive influence of the RDND and ES on the TIRP value due to the weak manifestation of the mentioned extinction effects for such defects. The possibility is proved for separation of the influence of RDND and only ES on the TIRP. These influences are separated by division of the expressions for TIRP into the factors, which are dependent only on the RDND characteristics and only on ES. In addition, for the first time, the corrections for the strain dependences of the Bragg and diffuse TIRP contributions are phenomenologically separated into factors, which are dependent only on the RDND characteristics and only on ES. In this case, the mentioned-corrections’ dependence on the RDND characteristics is found in an explicit form. For the first time, this provides for the feasibility of the adequate quantitative determination of the RDND characteristics by the fitting of the theoretical and experimental strain dependences of TIRP.

Keywords: X-rays, Laue-diffraction, monocrystal, microdefect, elastic bending.

PACS: 61.10.Dp, 61.10.Kw, 61.46.+w, 61.72.Dd, 61.72.Ff, 81.70.Ex

DOI: https://doi.org/10.15407/ufm.05.01.051

Citation: A. P. Shpak, V. B. Molodkin, and A. I. Nizkova, Integral Diffractometry of Nanoscale Defects in an Elastically-Bent Single Crystal, Usp. Fiz. Met., 5, No. 1: 51—86 (2004) (in Russian), doi: 10.15407/ufm.05.01.051

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