Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-13T15:42:56.398Z Has data issue: false hasContentIssue false
  • English
  • Français

Crystallite-size distributions and diffraction line profiles near the peak maximum

Published online by Cambridge University Press:  10 January 2013

Giuseppe Allegra  and
Sergio Brückner
Giuseppe Allegra
Affiliation:
Dipartimento di Chimica, Politecnico di Milano, P.zza L.da Vinci 32, I-20133 Milano, Italy and Dipartimento di Chimica, Univ. di Modena, via G. Campi 183, I-41100 Modena, Italy
Sergio Brückner
Affiliation:
Dipartimento di Chimica, Politecnico di Milano, P.zza L.da Vinci 32, I-20133 Milano, Italy and Dipartimento di Chimica, Univ. di Modena, via G. Campi 183, I-41100 Modena, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of crystallite-size distribution on the shape of X-ray diffraction peaks from powder samples is investigated focusing the attention on the region within the top half of intensity. It is shown that, unlike profile tails, this central region can markedly depart from the Lorentzian shape for crystallite-size distributions that are quite acceptable from the physical point of view. Goal of this paper is to correlate the well-known m parameter in the Pearson VII function or the η weight in the pseudo-Voigt function with a number of different distributions of crystallite dimensions ranging from the δ function of all-equal-sized crystals to a very broad distribution. The suitably normalized curvature at the peak is a possible new parameter; its correlation with m and η is shown. Also, a procedure is suggested to derive the volume-average crystal thickness 〈Tw〉 from the FWHM and the knowledge of either m or η.

Type
Research Article
Information
Powder Diffraction , Volume 8 , Issue 2 , June 1993 , pp. 102 - 106
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allegra, G. (1982). Acta Cryst. A 38, 863–867.CrossRefGoogle Scholar
Allegra, G., and Ronca, G. (1978). Acta Cryst. A 34, 1006–1013.CrossRefGoogle Scholar
Alvarez, A. G., Bonetto, R. D., Guerin, D. M., Plastino, A., and Rebollo Neira, L. (1987). Powder Diff. 2, 220–224.CrossRefGoogle Scholar
Averbach, B. L., and Warren, B. E. (1949). J. Appl. Phys. 20, 885–886.CrossRefGoogle Scholar
Bertaut, F. (1949). C. R. Acad. Sci. Paris 228, 187–189.Google Scholar
Bertaut, F. (1983). Acta Cryst. A 39, 818–819.CrossRefGoogle Scholar
Bouman, J. and De Wolff, P. M. (1942). Physica, 9, 833–852.CrossRefGoogle Scholar
De Keijser, T. H., Langford, J. I., Mittemeijer, E. J., and Vogels, A. B. P. (1982). J. Appl. Cryst. 15, 308–314.CrossRefGoogle Scholar
Hall, M. M., Veeraraghavan, V. G., Rubin, H., and Winchell, P. G. (1977). J. Appl. Cryst. 10, 66–68.CrossRefGoogle Scholar
Hecq, H. (1981). J. Appl. Cryst. 14, 60–61.CrossRefGoogle Scholar
Jones, F. W. (1938). Proc. Roy. Soc. London A 166, 16–43.Google Scholar
Patterson, A. L. (1939). Phys. Rev. 56, 978–982.CrossRefGoogle Scholar
Rao, S., and Houska, C. R. (1986). Acta Cryst. A, 42, 6–13 and 14–19.CrossRefGoogle Scholar
Smith, W. L. (1976). J. Appl. Cryst. 9, 139–141.CrossRefGoogle Scholar
Stokes, A. R., and Wilson, A. J. C. (1942), Proc. Camb. Phil. Soc. 38, 313–322.CrossRefGoogle Scholar
Wertheim, G. K., Butler, M. A., West, K. W., and Buchanan, D. N. E. (1974). Rev. Sci. Instrum. 11, 1369–1371.CrossRefGoogle Scholar
Wilson, A. J. C. (1949). X-ray Optics (Methuen, London) pp. viii and 127.Google Scholar
Wilson, A. J. C. (1963). Mathematical Theory of X-ray Powder Diffractometry (Philips Technical Library, Cambridge), Chap. IX.Google Scholar
Young, R. A., and Sakthivel, A. (1988). J. Appl. Cryst. 21, 416–425.CrossRefGoogle Scholar