Broadening of X‐ray diffraction lines of crystals containing dislocation distributions

Abstract

The first part of the paper deals with a brief review over the present stage of the (kinematical) theory of the broadening of X-ray diffraction lines of crystals containing dislocation distributions. In the second part experiments of X-ray line broadening of plastically deformed Cu and NaCl single crystals are reported by which the validity of the theoretical approaches are tested. It is shown that values of the dislocation density and the elastically stored energy derived from broadened X-ray diffraction lines agree well with corresponding data obtained by other experimental techniques.Der erste Teil der Arbcit gibt cinen knappen tfberbliek uber den gegenwiirtigen Stand der (kinematischen) Theorie der Verbreiterung von Rontgonbeugungslinien von Kristallen mit Versetzungen. Im zweiten Teil wird uber Linienverbreiterungsexperimcnte an plastisch verformten Cu-und NaC1-Einkristallen zur Prufung der theoretischen Ansiitze berichtet. Es wird gezeigt, daB die Werte fiir die Versetzungsdichte und die elastiseh gespeicherte Energie, die aus den verbreiterten Rontgenlinien gewonncn wurden, gut mit entsprechenden Ergebnissen nach anderen experimentellen Methoden ubereinstimmen.

Anisotropic diffraction peak broadening and dislocation substructure in hydrogen-cycled LaNi5and substitutional derivatives

“…The orientation factors 1 i for re¯ections in the hexagonal crystal system and for different dislocation types have been expressed analytically by Klimanek & Kuz Ïel (1988). The parameter P from the Krivoglaz theory has approximately the same meaning as the parameter M from the theory of Wilkens (1970), i.e. it characterizes the spatial distribution and correlation between dislocations.…”

“…4) which can be taken as further evidence for a shape change of the -hydride precipitates. According to Wilkens (1976), M ) 1 (i.e. P ) 3) means that the dislocations are accompanied by long-range strain ®elds (as dislocation pile-ups), and M ( 1 (i.e.…”

X-ray diffraction line broadening due to dislocations in non-cubic materials. I. General considerations and the case of elastic isotropy applied to hexagonal crystals

“…The results of the theoretical work have been verified and used successfully by several authors in investigations of the dislocation content of both plastically deformed single crystals (e.g. Dubrovskiy & Locko, 1968;Wilkens & Bargouth, 1968;Matucha, Franzbecker & Wilkens, 1969;Wilkens, 1976;Wilkens, Herz & Mughrabi, 1980;Karasevskaya & Ryaboshapka, 1980;Ungar, Mughrabi & Wilkens, 1982;Ungar, Mughrabi, R6nnpagel & Wilkens, 1984) and polycrystalline materials (e.g. Oettel, 1971Oettel, , 1973Dao Van Tan, 1972;Yamada, Tanaka & Furusawa, 1974;Klimanek, Grosse & Hensger, 1982;Klimanek, Scherke & Bergner, 1982;Wang Yuming, Lee Shanshan & Lee Yenchin, 1982;Wang Yuming & Zhang Zigung, 1984;Ungar, Toth, Illy& Kovacs, 1986;Tung, Zwui & Wang, 1986).…”

“…A suitable average value of In P can be estimated from the shape of an experimentally measured diffraction line profile according to Wilkens (1970b), if the dislocation content of different grains is similar.…”

Atomistic Model of Metal Nanocrystals with Line Defects: Contribution to Diffraction Line Profile

“…The f * is a smooth function of L/R e obtained by Wilkens in a heuristic way, to grant integrability of Eq. 1 (Wilkens, 1970b). The anisotropy of the elastic medium and of the dislocation strain field, which depends on the specific dislocation type (e.g., edge or screw) and slip system, is accounted for by the anisotropy or contrast factor C hkl .…”