Long period stacking order in close packed structures of metals

Abstract The origin of the stabilization of close packed structures with periodic stacking order in relation to the specific shape of the Fermi surface is investigated. For this purpose, the crystal structures of Au-Mn alloys between 20 and 28% Mn have been analyzed systematically. The structures in these alloys are quite sensitive to a change in composition and each specimen invariably includes several structures which make usage of electron microscopes indispensible for the analysis. The application of electron microscopes to a systematic analysis of crystallographic structures is thus explored and a systematic method of identifying close packed structures and their relations is then established. This allows us to identify all the structures existing in this composition range unambiguously. The structures thus identified are: Au 4 Mn at and around 20% Mn; ∝″(the two-dimensional long period superlattice Au 3 Mn, first identified in single crystal thin films) at around 21–22% Mn, and a series of structures with long period stacking order between 23 and 28% Mn which are of direct interest here. These latter structures have periodic modulations of the stacking order of the M = 1 superlattice (a one-dimensional long period superlattice with antiphase boundaries at each Cu 3 Au type unit cell, often referred to as DO2 2 ), and can be specified as 1 R (the original M = 1 structure with 6 layers in a unit structural period), 5 H (10 layers), 3 R (18 layers) and 6 H 1 and 6 H 2 (both 6 layers). Although varying amounts of these structures coexist in specimens over this composition range, the statistical order of appearance with increasing Mn content is 5 H → 3 R → 6 H (6 H 1 and 6 H 2 ), with coexisting unmodulated M > = 1(1 R ) most noticeably in the composition range of 5 H and 3 R structures. The relation between the size of the Fermi surface and the order of appearance of these modulated structures indicates that these modulations are created in order to shift the Brillouin zone boundaries of the M > = 1 structure to proper places of the Fermi surface when the size of the Fermi surface (or the electron-atom ratio) deviates from the exact value which stabilizes the M = 1 structure. In other words, the modulation in stacking order is an effort of the alloys to create Brillouin zone boundaries at proper places of the Fermi surface in order to reduce the energy of electrons. It can thus be concluded that with respect to their origin, structures with long period stacking order belong to the same category as the long period superlattice, and that “stacking fault boundaries” are, like “antiphase boundaries” a form of low energy boundary which enables the modulated close packed structures to become more stable than the unmodulated structure. In the case of the M = 1 structure, the symmetry of the basal plane allows for the modulation boundary by a unit slip of amount l 6a〈112〉 without destroying the degree of order. Thus the energy to create the boundaries is low and this makes the modulation of the M = 1 structure more favorable. Remarks are made concerning the applicability of these explanations to other metallic systems.