Models of Long-Period Superstructures
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MODELS OF LONG-PERIOD SUPERSTRUCTURES
J. KULIK AND D. de FONTAINE Lawrence Berkeley Laboratory, Materials and Molecular Research Division, University of California, Berkeley, California 94720, U.S.A.
ABSTRACT The cause of the stability of long period superstructures is still something of a mystery. Typically, two very different models have been proposed: according to model I, the period of the superstructure (or modulation) is determined by lowering of the electronic energy resulting from the formation of a new Brillouin zone. According to model II, competing short-range interactions tend to produce long-period structures, the wavelength of which is determined by configurational entropy considerations. Model I is exemplified by the Sato and Toth theory, apparently applicable to long-period superstructures in Cu-Au, for example. Model II is exemplified by the Axial Next Nearest Neighbor Ising Model, for which a low-temperature free energy expansion has recently been given by Fisher and Selke. The latter model appears to apply to long-period superstructures in Ag 3 Mg. INTRODUCTION Long period superlattices resulting from periodic antiphase boundaries are known to occur as stable structures in many binary alloy systems [1]. One of the best known of such structures is that of CuAu II, which is stable from about 380C to about 4100C. Below this temperature range, the tetragonal CuAu I phase, consisting of planes of gold and copper atoms alternating along the c-axis, is stable. The orthorhombic CuAu II phase can be viewed as a regular long period modulation imposed on the CuAu I structure. This modulation occurs along one direction perpendicular to the c-axis and is a result of antiphase boundary planes at which the gold and copper layers are interchanged. Similar periodic antiphase structures have also been found in a wide range of CuAu alloys (Cu3Au exactly at stoichiometry is a notable exception.)and in a large number of other binary systems. A curious feature of these long period superlattices is the fact that the size M of the antiphase domains as measured by diffraction experiments is often not an integer. An explanation for this phenomenon was offered by Fujiwara [2] who showed that sharp superstructure reflections corresponding to non-integral M could result from appropriate mixing of domains of different sizes. An alternative model presented by Jehanno and Pdrio [31 allows for a certain amount of disorder at each antiphase boundary with the result that the boundaries become sinuous and the spacing fluctuates about the average M value. Portier et al. (4] have recently pointed out that Fujiwara's model seems to apply to the alloy system Ag 3 Mg. Studies on this alloy suggest that M varies discontinuously with concentration, taking only values which can be specified by well defined ratios. In contrast, the average domain size M of CuAu varies continuously with concentration, often taking on incommensurate values as indicated by the overlap without superposition of satellites from adjacent fundamental reflections
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