Incommensurate-Commensurate Transition in the Long Period Superlattice in Ag-Mg Alloys

Abstract

Long period superlattice (LPS) in alloys is a periodically modulated structure of normal ordered structure found in noble metal alloys of close-packed structure, and its modulation mode is basically that of antiphase formation. Its period is specified by 2M, where M is the number of the unit cells of the normal superlattice included in one antiphase domain of the structure, and experimentally M is usually not an integral number1–3. The period 2M which exists in one of the directions of the cubic fee lattice (one dimensional (LPS) is determined by the superposition of either two (AB type alloys) or four (A3B type alloys) Q vectors with the length of 2kF in the directions, in which flat parts of the Fermi surface exist. At these parts, split Brillouin zone boundaries contact1–3 By superposing charge density waves (CDW) with these Q vectors and by comparing the resultant wave with the atomic arrangement, it is found that the larger atoms of alloys (such as Au atoms in the Cu-Au alloys) always occupy the maximum parts of the charge density while the smaller atoms occupy the minimum parts. Then antiphase boundaries exist where the deviation of the location of atoms from this condition becomes maximum. Further, if atoms are assumed to shift towards the charge density maximum, 4 the result agrees well with experimental data on atomic shifts by Iwasaki, et al. 5–8(Fig. 1). In other words, the LPS is considered to be a modulated structure created by the formation of CDW in the three dimensional crystal 1–3 and the antiphase formation is a more efficient way to compensate the charge distributions of CDW in ordered alloys than static phonons commonly observed in one- and two-dimensional systems.