The diffraction of X rays by distorted crystal aggregates - I

Broadening of the Debye-Scherrer lines in x-ray photographs of cold-worked metals has been attributed (i) to breaking up of the crystals into " crystallites " whose linear dimensions are less, similar10-5 cm., (ii) to the presence of crystal grains of different lattice parameters, and (iii) to distortion of comparatively large crystal grains. The broadening to be expected on the last hypothesis is worked out approximately. It is found that the " apparent strain " is given by ηidentical withβ cot Θ=2/Φhkl(0), where β is the (corrected) integral breadth of the hkl reflection, Θ is the Bragg angle, and Φhhl(e)de is the fraction of the crystal for which the tensile strain in the hkl direction is between e and e+de.