High-energy grinding of FeMo powders M. D’Incau, M. Leoni, and P. Scardi a) Department of Materials Engineering and Industrial Technologies, University of Trento, 38100 Trento, Italy (Received 27 November 2006; accepted 21 March 2007) Iron-molybdenum powders ground in a planetary ball mill under different operating conditions were studied by x-ray diffraction line profile analysis using a recently developed whole powder pattern modeling approach. The evolution of the microstructure, expressed in terms of size distribution of coherent scattering domains, average dislocation density, and edge/screw character, shows the importance of the main process parameters: the ratio between jar and main disk rotation speeds, and ball milling time. A characteristic three-stage process is observed, with work hardening followed by particle flattening/bending before nanocrystalline grains form by a fragmentation process triggered by localized deformation. The relationship between lattice defect density and domain size suggests a progressive transition between statistically stored to geometrically necessary dislocations, with the latter mostly present as excess dislocations at the nanodomain boundary. I. INTRODUCTION Two basic parameters are usually used to describe the microstructure of a nanocrystalline material: grain size and content of lattice defects, such as vacancies, dislo- cations, faulting, etc. Transmission electron microscopy (TEM) is certainly a fundamental tool in these studies, even though a quantitative and statistically reliable mi- crostructure evaluation can be rather difficult for highly deformed materials. In these materials, the density of defects can be so high that defects and regions of coher- ent scattering (crystallites) can be difficult to single out and quantify. In any case, a reliable analysis requires a lengthy (and possibly interfering 1 ) sample preparation, and the collection and evaluation of a large number of micrographs. 1,2 Moreover, exposure to a high-energy electron beam can be responsible for annealing and microstructure evolution during the TEM observation. 3 As an alternative or complementary technique, x-ray diffraction (XRD) line profile analysis (LPA) is fre- quently used to study the average microstructural evolu- tion of nanostructured materials. 4,5 Even though it can- not give visual evidence as TEM, LPA is much faster and statistically very robust, as it analyzes a huge number of domains simultaneously. Despite the high interest in LPA, considerable ad- vances in this field during the past decade were not ap- parently considered beyond a restricted community of experts. 6,7 The majority of (even recent) studies on nanocrystalline materials is in fact based on the applica- tion of highly simplified so-called integral breadth meth- ods like the Scherrer formula (SF) or the Williamson- Hall (WH) plot, 8,9 dating back to the beginning/middle of last century. This is probably the reason for the common thought that information available through LPA is rather poor and arbitrary, as pointed out in a recent review: “ . . . The width of the Bragg reflection in an x-ray (large- angle) diffraction pattern can provide grain (or crystal, i.e., the size of the coherently diffracting domain) size information after the appropriate corrections (for instru- mental and strain effects) are incorporated. (. . .) On the other hand, the XRD technique gives only the average crystal size and this value depends strongly on which function is used when averaging over the size distribu- tion.... ” 10 The use of SF or WH is, of course, legitimate, but few workers seem aware of the limitations of these methods and of the true meaning of the information obtained. 9 The mean (effective) size provided by SF and WH is not equivalent to the grain size, as one might observe in a microscope, even in the favorable case that grains are made of single crystalline domains. In real materials, crystallites can have a distribution of shapes and sizes. Even when the shape can be considered as approximately constant (e.g., equiaxial, possibly modeled as a sphere), the size can be dispersed according to mono- or multi- modal distributions. In this case, the effective size from integral breadth methods is proportional to the ratio be- tween fourth and third moments of the size distribution (for a distribution p(D), the j-th moment is defined as: a) Address all correspondence to this author. e-mail: Paolo.Scardi@unitn.it DOI: 10.1557/JMR.2007.0224 J. Mater. Res., Vol. 22, No. 6, Jun 2007 © 2007 Materials Research Society 1744