Statistical ALCHEMI: General formulation and method with application to Ti-Al ternary alloys

Recent advances in the theory of characteristic X-ray emission from crystals under dynamic electron diffraction conditions are used in developing a new fully quantitative statistical method for atom location by channelling-enhanced microanalysis (ALCHEMI). Limitations imposed by delocalization, disorder and occupancy of interstitial sites are clarified. A fully computerized method for automated data collection and analysis from incoherent channelling patterns formed by the variation in characteristic X-ray emission as a function of orientation is used for the first time. The precision and accuracy of this method are investigated using both experimental and simulated data from the ordered gamma-phase in ternary Ti-Al alloys. It is shown that 1 at.% Ga, Hf and Mo additions partition onto Al sites, Ti sites and both sites respectively, and contrast in X-ray incoherent channelling patterns confirms that these ternary atoms are not located on interstitial sites. The traditional ratio ALCHEMI technique is shown to have severe limitations in comparison with statistical methods.