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Refinement of Lattice Parameters and Determination of Local Elastic Strains

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Indexing of Crystal Diffraction Patterns

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 326))

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Abstract

Having an indexed diffraction pattern, the next goal is to determine lattice parameters with high accuracy. From the computational viewpoint, the problem of refinement of lattice parameters in the process of structure determination is closely related to determination of elastic strains. This chapter describes computational aspects of two example methods for diffraction-based determination of micro-strains; one method relies on convergent beam electron diffraction patterns and the other on Kossel patterns.

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Notes

  1. 1.

    Broadening is also caused by crystalline defects, small crystallite sizes (in the case of X-rays) and by instrumental effects.

  2. 2.

    The assumption of plane strain is often made, but it is not justified in the presence of anisotropy.

  3. 3.

    Here and below, it is assumed that there are no distortions of the pattern recording medium or device.

  4. 4.

    If the pattern is registered with a large camera length and a low-index zone axis parallel to the optical axis of the microscope, the lines corresponding to reciprocal lattice nodes high on the Ewald sphere are referred to as high order Laue zone (HOLZ) lines.

  5. 5.

    Such lines are located far from low-index zone axes.

  6. 6.

    Take for instance procedures for strain determination; they could be limited to calculation of the strain tensor components with the assumption of plane stress conditions (e.g., [39]), in the plane strain approximation (e.g., [40]), or some other selected components are determined (e.g., [9]).

  7. 7.

    The older methods are reviewed in [57, 58].

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  1. Polish Academy of Sciences, Institute of Metallurgy and Materials Science, Kraków, Poland

    Adam Morawiec

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Morawiec, A. (2022). Refinement of Lattice Parameters and Determination of Local Elastic Strains. In: Indexing of Crystal Diffraction Patterns. Springer Series in Materials Science, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-031-11077-1_14

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