DETERMINATION OF ORIENTATION DISTRIBUTION-FUNCTIONS FROM INCOMPLETE POLE FIGURES BY ITERATIVE SERIES EXPANSION METHOD

Quantitative texture analysis based on the calculation of crystallite orientation distribution functions (ODF) is necessary to accurately evaluate physical and mechanical anisotropies of polycrystal materials. In the ODF calculation, an analytical method using incomplete pole figures measured by the reflection method alone is convenient, particularly for the materials difficult to prepare thin specimens for the transmission method. In the present study, the complete ODF's including the odd terms for ghost correction were determined from incomplete pole figures by the iterative series expansion method for cubic, hexagonal and tetragonal materials. To check the reliability of this method, they were compared with the ODF's calculated from complete pole figures by an ordinary method or from incomplete pole figures by other methods. The ODF's determined from the incomplete pole figures measured up to a tilt angle of 70-degrees coincided approximately with those determined from the complete pole figures. This method can therefore be utilized for the ODF analysis with sufficient reliability instead of the conventional method using the complete pole figures. As an attempt, the possibility of the ODF analysis from one incomplete pole figure was examined. However, it was found that the quantitatively exact texture analysis was considerably difficult in this case, though preferred orientations could be determined from the ODF obtained. A technique to determine the ODF from the incomplete pole figures measured at adjacent diffraction lines was also tested for the texture of titanium aluminide. The result indicated that the ODF could be exactly determined even from somewhat overlapped incomplete pole figures by reducing the range of measurement in the alpha angle and simultaneously increasing the number of pole figures.