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.