Table of Contents 
Textures and Microstructures
Volume 30, Issue 3-4, Pages 207-227
http://dx.doi.org/10.1155/TSM.30.207

Comments to a Publication of T.I. Savyolova Concerning Domains of Dependence in Pole Figures

S. Matthies1,2,3 and C. Esling1

1Université de Metz, Laboratoire LETAM URA CNRS 2090, ISGMP, Jle du Saulcy, METZ Cedex 01 F-57045, France
2Seoul National University, School of Materials Science & Engineering, Seoul 151-742, South Korea
3Mueller-Berset-Str. 3, Dresden D-1309, Germany

Received 12 July 1996; Accepted 5 December 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A questionable publication of T.I. Savyolova is analysed. The paper claims, that it is possible to determine Ph(y) pole figure values for y∈Y(h;h0,Y0) using only data from y∈Y0 of a single pole figure Ph0(y). The contradiction to the common knowledge can be resolved well understanding that there is a general difference between the term solutions (or continuation of solutions) of an ultrahyperbolic equation (satisfied by the axis distribution function A(h, y)) and the term pole figure. Pole figures considered in texture analysis are two-dimensional projections of a three-dimensional object (the ODF f(g)). For limited data sets the equation ΔhA(h,y)=ΔyA(h,y) bears only a necessary, but not sufficient character in order to get solutions of interest, i.e. it cannot be guaranteed that a h-specific continuation of a starting solution Ph0(y) will be a “h-projection” of the same ODF, which belongs to a concrete sample and possesses the “h0-projection” Ph0(y).

Consequently, to name such a h-specific continuation “pole figure” is incorrect. The consideration of formal (unambiguous only by artificial conditions) continuations of solutions may be mathematically interesting, but is of no practical importance for texture analysis. Examples (already considered by the authors about twenty years ago) are given, how to construct in a much more simple way continuations of solutions of the same useless type like in the paper under discussion.