International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 
International Tables for Crystallography (2018). Vol. H, ch. 3.2, pp. 259260
Section 3.2.3.4. Anisotropic strain broadening^{a}Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794–3800, USA 
Strain broadening is often observed not to be monotonically dependent on the magnitude of the dspacing, but to have a more complicated dependence on the direction of the diffraction vector G. An illustration of the effect in cubic Rb_{3}C_{60} is shown in Fig. 3.2.5 (Stephens, 1999). The lower part of the figure shows an apparently irregular trend of diffraction peak widths on diffraction angle 2θ.
Whatever the nature of random internal stresses and strains, it can be argued on general grounds that strain broadening depends on a combination of fourthrank tensors. On the assumption that the distribution of random strains is Gaussian, each diffraction peak has Gaussian shape, and the variance of the inverse dspacing squared is a quartic form in the reflection indices (hkl). This can be expressed aswhere the sum is over terms with . This leads to a contribution to the width of a diffraction peak proportional to for angledispersive measurements, and for timeofflight neutron measurements. Strain broadening in real samples frequently leads to peak shapes that are closer to Lorentzian than Gaussian, and the justification of this expression breaks down because the second moment of the distribution of d^{−2} is then not defined. Nevertheless, this method is often successful at modelling the phenomenology of anisotropic peak broadening.
The parameters arise from the nature of the strain and the values of elastic constants for any particular sample. Typically, they must therefore be regarded as phenomenological, and can be adjusted in fitting a model to observed data. They are constrained by the symmetry of the Laue group of the sample, which leads to restrictions on the terms for the various Laue classes, listed in Table 3.2.1 (Popa, 1998).

References
Popa, N. C. (1998). The (hkl) dependence of diffractionline broadening caused by strain and size for all Laue groups in Rietveld refinement. J. Appl. Cryst. 31, 176–180.Google ScholarStephens, P. W. (1999). Phenomenological model of anisotropic peak broadening in powder diffraction. J. Appl. Cryst. 32, 281–289.Google Scholar