Theory of superlattice-fringe imaging of alloys I. Images formed from two beams

Abstract

The superlattice-fringe imaging technique in electron microscopy has been modelled for two ordering alloys, using multiple-beam dynamical diffraction theory. The transmitted beam and one first-order diffracted beam were combined to form the fringe image, and tilted illumination was used. Superlattice-fringe image contrast was studied as a function of degree of long-range order, specimen thickness, and diffracting conditions for an Fe₃Al alloy with B2 order and for a Cu₃Au alloy with Ll₂ order. The results demonstrate that, for a given diffracting condition, there is a critical thickness below which superlattice-fringe contrast is a single-valued and monotonically increasing function of degree of long-range order. For an electron energy of 120 keV, in the Fe-Al alloy this thickness is approximately 50 nm, whereas for Cu₃Au it is only 10 nm. Multiple-beam dynamical interactions were found to play an important role in determining the critical thickness. The implications of these results for using the technique to make quantitative measurements of degree of long-range order in inhomogeneous specimens are discussed.