Diffraction from Planar Faults in the β-Brass-Type Ordered Structures

Abstract

Diffraction effects due to a/8[110](11̄0)- and a/6[111](1̄1̄2)-type stacking faults and a/2[111](11̄0)- and a/2[111](1̄1̄2)-type antiphase boundaries in β-brass structures have been considered. The stacking faults broaden both the fundamental and the superstructure peaks, while only the latter class is affected by the antiphase boundaries. The magnitude of broadening, for the two stacking faults, varies from one reflection to another as well as among different orders of the same reflection leading to strong anisotropy in the particle sizes derived from the broadened peaks. When different orders of the same reflection are broadened differently by faulting, the measured particle size anisotropy is found to depend on the fault type as well as on the manner in which strain contributions are removed from the total broadening. Several strain correction procedures have been considered and expression for particle size due to faulting for each case is given. The effects of the two stacking faults differ in several ways. For example, while the (211) fault broadens all fundamental orders of a reflection to the same extent, the broadening due to (110) generally increases with the order of the reflection. All powder reflections along [111], however, are unaffected by the (110) faulting. These and other differences in the broadening behavior lead to quite dissimilar particle size anisotropies for the two stacking faults. Among other stacking faults that may also occur in β-brass structure, the a/6[111](11̄0)- and a/6[111](3̄21)-type faults predict particle size anisotropies identical to that for the a/6[111](1̄1̄2) fault. The a/3[1̄1̄1̄](1̄1̄2)-type fault, on the other hand, broadens the fundamental reflections to the same extent as the a/6[111](1̄1̄2) fault, but it affects the superstructure peaks differently; on this basis it is possible to distinguish between these two fault types from their diffraction effects. In addition to broadening, the stacking faults also lead to small peak shifts of varying magnitudes and directions which, in the case of powder peaks, occur only when there are spacing changes at the faults, but the relative shifts of the various powder peaks due to the (110) and (211) faults are similar; the same is also true of the antiphase boundaries