A Profile-Based Method of Determining Intragranular Strains Using Kossel Diffraction Patterns


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Kossel microdiffraction is one of a few experimental methods of investigating heterogeneities of elastic stresses within crystallites. With digitally recorded back-reflection Kossel patterns, one can determine absolute lattice parameters, and hence lattice strains and stresses, based on geometry of Kossel lines, but the strain resolution of this approach is limited by finite widths of the lines. A new method is proposed which considerably improves the resolution in cases when the patterns originate from areas with similar lattice orientations. The method is based on determination of differences between pattern geometries: lattice strains are calculated from mutual shifts of intensity profiles of Kossel lines. The strain accuracy of this profile-based approach was estimated. It is demonstrated that the limit of strain resolution reaches a few parts per hundred thousand, i.e., it is nearly one order of magnitude better than that of the conventional Kossel-based lattice parameter refinement. This improvement concerns the critical range of lattice strain, and it constitutes a qualitative leap in resolution. The paper describes main aspects of the new approach and strain resolution tests.



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Edited by:

M. François, G. Montay, B. Panicaud, D. Retraint and E. Rouhaud




A. Morawiec, "A Profile-Based Method of Determining Intragranular Strains Using Kossel Diffraction Patterns", Advanced Materials Research, Vol. 996, pp. 52-57, 2014

Online since:

August 2014



* - Corresponding Author

[1] W. Linnik, Über eine Abänderung der Drehkristallmethode zur Untersuchung der Kristall-struktur mit Röntgenstrahlen, Z. Phys. 61 (1930) 220 – 226.

DOI: https://doi.org/10.1007/bf01339662

[2] W. Kossel, V. Loeck, H. Voges, Die Richtungsverteilung der in einem Kristall entstandenen charakteristischen Röntgenstrahlung, Z. Physik 94 (1935) 139 – 144.

DOI: https://doi.org/10.1007/bf01330803

[3] R. Tixier, C. Waché, Kossel patterns, J. Appl. Cryst. 3 (1970) 466 – 485.

DOI: https://doi.org/10.1107/s0021889870006726

[4] V.V. Lider, X-ray divergent-beam (Kossel) technique: A review, Crystallogr. Rep. 56 (2011). 169 – 189.

DOI: https://doi.org/10.1134/s106377451102012x

[5] K. Lonsdale, Divergent-beam X-ray photography of crystals. Philos. Trans. R. Soc. London A240 (1947) 219 – 250.

[6] H.J. Ullrich, J. Brechbühl, J. Bauch, H. Lin, Detektion von Kossel-Linien mittels marCCD-Detektor, In: HASYLAB annual report (1998) 887 – 888.

[7] S. Däbritz, E. Langer and W. Hauffe, New observation method for divergent beam X-ray diffraction patterns, J. Anal. At. Spectrom. 14 (1999) 409 – 412.

DOI: https://doi.org/10.1039/a806922k

[8] E. Langer, S. Däbritz, C. Schurig, W. Hauffe, Lattice constant determination from Kossel patterns observed by CCD camera, Appl. Surf. Sci. 179 (2001) 45 – 48.

DOI: https://doi.org/10.1016/s0169-4332(01)00261-6

[9] D. Bouscaud, A. Morawiec, R. Pesci, S. Berveiller, E. Patoor, Strain resolution of SEM-based Kossel microdiffraction, submitted.

DOI: https://doi.org/10.1107/s1600576714019402

[10] D. Stephan and V. Geist, Theoretische Intensitätsprofile von Kossel-Linien und Vergleich mit experimentellen Linienprofilen ({111} PKα-Interferenzen von GaP-Einkristallen bei Protonenstoss-anregung), Exp. Techn. Phys. 34 (1986) 153 – 167.

[11] G. Nolze and V. Geist, On the intensity of Kossel reflections, Cryst. Res. Technol. 27 (1992) 421 – 430.

DOI: https://doi.org/10.1002/crat.2170270321

[12] A. Morawiec, R, Pesci, J.S. Lecomte, Semiautomatic determination of orientations and elastic strain from Kossel micro-diffraction, Ceram. Trans. 201 (2008) 163 – 169.

DOI: https://doi.org/10.1002/9780470444214.ch17

[13] A. Morawiec, A program for refinement of lattice parameters based on multiple convergent-beam electron diffraction patterns, J. Appl. Cryst. 40 (2007) 618 – 622.

DOI: https://doi.org/10.1107/s0021889807018262

[14] http: /personal. imim. pl/adam. morawiec/A_Morawiec_Web_Page/downloads. html.