Line broadening driven by elastic anisotropy in high

Line broadening driven by elastic anisotropy in high-pressure x-ray
diffraction patterns
Anil K. Singh1, Chellayyan Balasingh1, and Kenichi Takemura2
Materials Science Division, National Aerospace Laboratories, Bangalore 560017, India.
National Institute of Metals and Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305
0044, Japan.
Line broadening arising from the combined effect of elastic anisotropy and
nonhydrostatic stress distribution in the sample has been examined in the past by a
number of investigators [1, and the references therein]. Large asymmetry arising from
this source in the high-pressure diffraction profiles was predicted [2]. The fact that large
asymmetry is not observed in practice prompted us to reexamine this issue in the
framework of lattice strain theory [3-5]. Our finding that the broadening from this source
is absent for the reflections of the type (hhh) and (h00) is in agreement with the
conclusion of the earlier study [2]. We have compared the magnitude of broadening with
the observed widths of diffraction lines from niobium. The conditions under which
contribution from this source can lead to asymmetric broadening are discussed. The
estimates of the magnitudes of the effect suggest that the asymmetry in practice is small.
The analyses of niobium line profiles presented show a small asymmetry in diffraction
peaks consistent with the theory.
[1]. A. K. Singh and C. Balasingh, J. Appl. Phys. 90, 2296 (2001).
[2]. N. Funamori, M. Funamori, and R. Jeanloz, J. Appl. Phys. 82, 142 (1997).
[3]. A. K. Singh, J. Appl. Phys. 73, 4278 (1993);74, 5920 (1993).
[4]. T. Uchida, N. Funamori, and T. Yagi, J. Appl. Phys. 80, 739 (1996).
[5]. A. K. Singh, C. Balasingh, H. K. Mao, R. J. Hemley, and J. Shu, J. Appl. Phys. 83,
7567 (1998).