Diffraction line broadening of crystals containing small-angle boundaries

The paper deals with a theoretical investigation of the shapes of the X-ray diffraction lines of crystals containing periodically distributed small-angle boundaries (SAB) of pure tilt character. The Fourier transforms of the diffraction lines are computed and subsequently subjected to a Warren–Averbach (WA) analysis. The following results are obtained: (i) the apparent mean particle size is larger than the spacing D between the SAB by a factor which is about 2 for D/d≃ 1 and decreases to ≈ 1 with increasing D/d (d = spacing between the dislocations within the SAB). (ii) A pronounced 'hook effect' is produced which is 'forbidden' under the assumptions of the WA analysis but is often observed experimentally. It reaches a value of ≃ 16% for D/d = 1 and decreases with increasing D/d. (iii) The so-called mean square strains ([epsilon]²_L〉 are significantly smaller and decrease much more rapidly with increasing distance variable L than predicted by an exact calculation. (iv) It turns out that the results of the present paper fit well to corresponding results obtained from model calculations published elsewhere for crystals containing so-called restrictedly random distributions of dislocations. Items (i) to (iv) are discussed briefly with respect to the interpretation of experimental results obtained from plastically deformed crystals by means of the WA analysis.