Atomic Size Effect in the X-Ray Scattering by Alloys

Abstract

In a random solid solution, if the two atoms have appreciably different sizes, the nearest-neighbor distances and to a lesser extent the higher neighbor distances will be of three kinds, γAA, γAB, and γBB. The effect produces modulations in the diffuse intensity similar to those produced by short-range order. The size effect is important when the difference in scattering power is large, the difference in size is large, and the short-range order is small. The size effect is illustrated by a single crystal pattern of Cu3Au and a powder pattern of Ni3Au2. An asymmetry in the wings about a fundamental reflection is a result of the size effect.

High-entropy alloys: a critical assessment of their founding principles and future prospects

“…This level of strain is no greater than those predicted and measured in both dilute and concentrated binary alloys. 189,190,[196][197][198][199][200][201] Indeed, the displacements are of similar size to those expected from thermal vibrations around room temperature 185,190,196 and, therefore, cannot be described assevere.…”

“…It is true that diffraction peak intensity should decrease with increasing lattice strain around solute atoms, and that these localised static displacements have a similar effect on intensity as thermal vibrations. [188][189][190][191][192][193] Typical lattice strains from solute atoms are not thought to generate significant levels of peak broadening, 190,191 as is observed in alloys with high dislocation densities or small crystallite sizes. However, it should be noted that a number of effects can influence the peak intensity and diffuse scattering observed in a diffraction pattern, including crystallographic texture, thermal vibrations and fluorescence.…”

“…Hence, attentive assessment of high-quality experimental data is needed before any comment can be made on the magnitude of lattice distortions. [189][190][191][192][193][194] In addition, the levels of strain considered historically have been small, allowing for particular estimations to be made, and the effects of severe lattice distortions may be different.…”

X‐ray and Neutron Diffuse Scattering Measurements

“…Equation 28 is a result given by Borie and Sparks (1964) that avoids an earlier assumption of radial displacements first given by Warren et al (1951). Shown in Figure 23 is …”

“…Our use of the double sum requires that the pairs of atoms be counted in both directions, that is, a p, q pair will become a q , p pair such that i (δ p -δ q ) = −i(δ q − δ q ) as shown in Figure From the definition of an average lattice, the weighted average of the displacements for all the kinds of pairs formed for any coordination shell is zero (Warren et al, 1951),…”