Dislocation Effects on the Diffraction Line Profiles from Nanocrystalline Domains
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DIFFRACTION line profile analysis (LPA) is extensively used in materials science to gather information on plasticity, to measure the extent of deformation and work hardening, and to characterize nanocrystalline phases (e.g., see References 1, 2 and references therein). Measuring the size of coherently scattering domains is the most common application of LPA, dating back to colloidal metal studies of about one century ago,[3,4] whereas the approach to determine type and quantity of lattice defects is not only comparatively newer but also well established and popular in applied research, especially in metallurgy.[1,2,5–7] Most LPA studies and applications concern X-ray diffraction (XRD) from powder or bulk polycrystalline materials, as this is the most frequent case in metal plasticity studies. Even if traditional methods to determine the concentration of line and planar defects can be found in textbook,[4,7] the topic is still an object of active research and methodological developments. Despite the broad interest in methods and applications, surprisingly few studies have investigated the validity and general reliability of LPA results. This is probably due to the difficulty in obtaining equivalent evidence from other experimental techniques to validate LPA. For example, it is relatively easy to observe dislocations by transmission electron microscopy (TEM), but a quantification of their density in the range of interest of LPA applied to extensively cold-worked metals (q > 1014 m2) is quite difficult to obtain.[8] ALBERTO LEONARDI, Post-Doctoral Bursary, and PAOLO SCARDI, Full Professor of Materials Science and Technology, are with the Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano, 77, 38123 Trento, Italy. Contact e-mail: [email protected] Manuscript submitted January 23, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS A
A viable alternative to assess the validity of LPA is using atomistic simulations to build polycrystalline microstructures. Aggregates of crystalline domains can be produced with controlled shape and size distribution, including known type and amount of lattice defects.[9,10] Molecular dynamics (MD) can be used to equilibrate the simulated systems, thus providing atomic coordinates of realistic microstructures, which can be used to simulate the corresponding powder pattern by means of the Debye scattering equation (DSE).[11,12] LPA methods can then be used and tested against the simulated data, which can be considered, to this specific purpose, as equivalent to the experimental data typically collected on plastically deformed materials. So far relatively few papers have explored this approach, and generally using simplified integral breadth methods.[13,14] In this study, we focus on the effect of line defects, observed in a nanocrystalline Pd domain inside a cluster of grains providing a realistic environment, to assess the effect of dislocations on the diffraction pattern. While the general validity of the hypotheses underlying the Krivoglaz–Wilkens theory
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