Papers by Author: Siegfried Matthies

Abstract: The texture index F2 (1£ < F2 £ ¥ , F2 = 1 – random distribution) is up to now the only parameter used in a global way to characterize the degree of anisotropy of a given ODF – the foremost question to be answered in applied TA. However, one number is a quite poor characteristic, and a concrete F2-value can hardly be interpreted. It depends on many parameters and may belong to very different orientation distributions. Introducing so-called ODF-channels a one-dimensional ODFchannel histogram can be got for any ODF. Its form and spectral properties provide a comprehensive characterization of the character of anisotropy of a given ODF.

Abstract: One of the design goals of the neutron time-of-flight (TOF) diffractometer HIPPO (HIgh Pressure - Preferred Orientation) at LANSCE (Los Alamos Neutron Science Center) was efficient quantitative texture analysis. In this paper, the effects of the HIPPO detector geometry and layout on texture analysis, particularly the shape and dimensions of the detector panels, are investigated. An aluminum sample with a strong and asymmetric texture was used to determine the methodological limitations of various methods of quantitative texture analysis. Several algorithms for extracting the orientation distribution function (ODF) from the TOF-spectra are compared: discrete orientations at arbitrary positions, harmonic method in Rietveld codes (MAUD and GSAS) and discrete methods in MAUD. All methods provide a similar representation of the main texture component, but discrete methods have a fundamental advantage over harmonic methods in characterizing regions of the ODF with low orientation densities. For HIPPO data of the present sample, harmonic expansions beyond lmax= 12 introduce subsidiary maxima and minima, which are consistently identified as artifacts. The results of our analysis establishes HIPPO as an efficient instrument to quantitatively determine preferred orientations in relatively short measuring times, if the texture features are not exceedingly sharp (full-width at half-maximum (FWHM) in the ODF > 20-30°).

Abstract: The calculation of the Eshelby tensor occupies the dominant part of time in modern selfconsistent schemes modeling texture developments. A further time-reduction can be got representing the denominator in the explicit expression of the integrand of the Eshelby integral by finite series, leading to known library integrals. The possibility to get fast converging series depends on the degree of anisotropy of the stiffness tensor C. As universal (any symmetries) parameter, in order to classify the degree of anisotropy of a given C-data set, the variance s0 of the normalized determinant D0(C,r) of the Christoffel matrix is suggested. s0 can exactly be determined without great effort. For typical C-sets time reducing factors in the order of 2 – 8 have been got. Beyond this special result the anisotropy parameter 0 £ s0 < 1 seems to be of general importance. 3d-figures of D0(C,r) show characteristic (and sometimes unexpected ‘beautiful’) individual faces of the elastic properties of monocrystalline or textured polycrystalline substances.