EVALUATION
OF MICROSTRUCTURE PARAMETERS FROM POWDER X-RAY DIFFRACTION DATA
Takashi
Ida and Hideo Toraya
Ceramics
Research Laboratory, Nagoya Institute of Technology, Asahigaoka, Gifu 507-0071,
Japan (ida@crl.nitech.ac.jp)
Recently,
we have developed a new method to deconvolute instrumental aberrations from
powder X-ray diffraction data [1].
The effects of spectroscopic distribution of the source X-ray, axial
divergence, flat specimen and sample transparency are all eliminated by a fast
Fourier transform calculations. As
compared with the conventional method of Stokes [2], our method is advantageous
at the following points: (i) no measurement of reference sample is needed, (ii)
integrated peak intensity is strictly conserved or properly corrected after the
deconvolution, (iii) the systematic peak shifts are automatically corrected,
(iv) the whole diffraction data are simultaneously treated no matter how
complicated the peak pattern may be, and (v) the propagation of statistical
errors is properly evaluated.
Those features are particularly useful for evaluation of microstructure
parameters, the finite crystallite size and amount of structural defects in
crystallites.
We have also
developed an advanced algorithm for numerically evaluating the theoretical
diffraction peak profile from spherical crystallites with log-normal size
distribution (SLN profile) [3].
The algorithm efficiently evaluates the precise model profiles even for
extremely broad size distribution, while the method originally proposed by
Langford et al. [4] and a modified version of Popa and Balzar [5] are
only applicable to restricted widths of distribution. Curve fitting analysis based on the SLN profile model
provides a simple way to estimate both mean and width of crystallite size
distribution from each of experimental diffraction peak profiles.
Our original methods
are applied to estimate microstructure parameters of a fine SiC powder sample
(JFCC, RP-2). The deconvolution of
the instrumental aberration from experimental powder X-ray diffraction data has
revealed the intrinsic 'super-Lorentzian' line shape [6], which is
characteristic of the SLN profile for broad size distribution. The logarithmic standard deviation of
the distribution is estimated at 0.93(3), which is in good agreement with the
value 0.97 estimated by a laser diffraction method. It is also shown that the anisotropic features in shifts of
the peak positions and also variation of the peak widths dependent upon the
Miller indices indicate the existence of deformation-type stacking fault along
111-direction, the frequency of which is estimated at about 0.005(1) based on
the PatersonŐs model for stacking faults [7].
References
1 Ida, T. and
Toraya, H. (2002). J. Appl.
Cryst. 35, 58-68.
2
Stokes, A. R.. (1948). Proc. Phys. Soc. London 61,
382-393.
3
Ida, T., Shimazaki, S., Hibino, H. and Toraya, H. J. Appl. Cryst.
(submitted).
4
Langford, J. I., Lou‘r, D. and Scardi, P. (2000). J. Appl. Cryst. 33,
964-974.
5
Popa, N. C. and Balzar, D. (2002). J. Appl. Cryst. 35,
338-346.
6
Wertheim, G. K., Butler, M. A., West, K. W. and Buchanan,
D. N. E. (1974). Rev. Sci. Instrum.. 11,
1369-1371.
7
Paterson, M. S. (1952). J. Appl. Phys. 23,
805-811.