By Nagnibida N. I.
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The position of a pixel in the detector is deﬁned by the (x,y) coordinates, where the detector center is deﬁned as x ¼ y ¼ 0. 9 Relationship between a pixel P and detector position in the laboratory coordinates, XLYLZL. calibration, and spatial correction. The diffraction space coordinates (2u, g) for a pixel at P(x,y) are given by x sin a þ D cos a 2u ¼ arccos pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ D2 þ x2 þ y2 g¼ ð0 < 2u < pÞ x cos a À D sin a Ày arccos qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ jx cos a À D sin aj y2 þ ðx cos a À D sin aÞ2 ð2:8Þ ð Àp < g pÞ ð2:9Þ The unit diffraction vector components fh1 ; h2 ; h3 g in the sample coordinates S1S2S3 corresponding to each pixel can then be calculated by Eq.
Causes of peak broadening, while increasing FWHM, typically also reduce the maximum intensity at the same time. Therefore, overall variation of the integrated intensity is less signiﬁcant compared to the variations of FWHM and Imax. 2 Diffraction Patterns The above diffraction condition is based on the existence of long periodicity of crystalline materials. In general, X-ray diffraction can provide information on the atomic arrangement in materials with long-range order, short-range order, or no order at all, like gases, liquids, and amorphous solids.
New York, 1996. 2. B. D. , Addison-Wesley, Reading, MA, 1978. 3. B. E. Warren, X-Ray Diffraction, Dover Publications, New York, 1990. 4. R. Jenkins and R. L. , New York, 1996. 5. A. J. C. Wilson, International Tables for Crystallography, Kluwer Academic Publishers, Boston, MA, 1995. 6. F. D. Bloss, Crystallography and Crystal Chemistry, Holt, Rinehart and Winston, New York, 1971. 26 INTRODUCTION 7. F. C. , New York, 1972. 8. T. C. W. -D. , New York, 1997. 9. C. , Fundamentals of Crystallography, IUCR and Oxford University Press, New York, 1992.
A basis for the space of functions analytic in a disk by Nagnibida N. I.