An ill-posed problem of crystal physics

✍ Scribed by N.G. Volkov; T.I. Savelova

• Publisher: Elsevier Science
• Year: 1983
• Weight: 481 KB
• Volume: 23
• Category: Article
• ISSN: 0041-5553
• DOI: 10.1016/s0041-5553(83)80135-9

✦ Synopsis

A formulation of the problem of determining the distribution function of texture samples from pole figures is examined. The existence, uniqueness and stability of the solution are analyzed.

A solution of the problem of the reproducibility of the orientation distribution function in texture samples of polycrystalline materials from the pole figures is of important theoretical and practical significance. This problem belongs to the sphere of integral geometry and, like the majority of the inverse problems of mathematical physics, is ill-posed, /1/. Many papers have been devoted to this problem (see for example the reference in /2/). The ambiguity of the usual solution was pointed out in /3/, and this paper also suggested an explicit method (but without proof) for determining that part of the orientation distribution function which it is possible to find from the pole figures.