On the suitability of peak profile analysis models for estimating dislocation density

Abstract

Work-hardening in crystalline materials, i.e., increase in their flow stress during plastic deformation, follow a square root dependence on density of dislocations present. Dislocation density, defined as the length of dislocations per unit volume (m/m3), is thus an important parameter for simulating flow properties of a material. A number of techniques based on line profile analysis of x-ray diffraction peaks have evolved over the years for estimating dislocation density in addition to direct measurements on the basis of transmission electron microscopy. However, all these techniques suffer from certain limitations and the effectiveness of a specific technique is difficult to establish as different researchers have used different techniques to estimate dislocation density on individual samples. In the present work, suitability of x-ray line profile analysis techniques, based on moment analysis of tail portions of individual diffraction peaks (termed as variance methods), for estimating dislocation densities has been verified on the basis of their estimation in commercially pure aluminium as well as pure copper samples deformed for varying degrees of deformation. The accuracy of estimated values of dislocation density has been confirmed: (i) by comparing them with those estimated by transmission electron microscopy analysis; and, (ii) on the basis of variations in their values that are expected to follow the observed work hardening behaviour. This study has established that line profile analysis of x-ray diffraction peaks obtained using a laboratory x-ray diffractometer can make a reliable estimate of dislocation density in metallic samples provided they contained a significant amount of deformation.