Diffraction-contrast analysis of misfit strains around inclusions in a matrix: VN particles in α-Fe

Abstract

A new method has been developed to determine the misfit of disc-shaped precipitates in a matrix using transmission electron microscopy (TEM). The method is applicable to specimens containing a high precipitate density, where the classical TEM method, based on the extent of the precipitate diffraction contrast cannot be applied. The new method is based on evaluation of the positions of extrema in the intensity distribution due to misfitting precipitates in both bright field (BF) and dark field (DF). A model system, consisting of a single disc-shaped misfitting precipitate placed centrally in a thin specimen, has been studied first. The dynamic theory of electron diffraction has been adopted for a four-beam case. The contrast lobes in BF and DF images have been calculated as a function of, in particular, the particle radius, the foil thickness and the particle thickness. Simultaneous fitting of calculated BF and DF diffraction contrast images to the experimental images leads to determination of the precipitate misfit, and the local thickness of the specimen foil. The method has been illustrated for a nitrided Fe-2 at. ∼ V alloy with small disc-shaped VN precipitates and has led to a consistent interpretation in terms of particle size and misfit upon precipitation. The extent of elastic accommodation of misfit has been verified using high-resolution electron microscopy. The foil thickness values determined by diffraction contrast analysis agree well with independently obtained corresponding data. In addition X-ray diffraction (XRD) line profiles of the specimens have been recorded. The observed shifts and broadenings of the XRD profiles support the results obtained using TEM.