Configuration of Antiphase Domains in One-Dimensional Long Period Superstructural Alloys
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CONFIGURATION OF ANTIPHASE DOMAINS IN ONE-DIMENSIONAL LONG PERIOD SUPERSTRUCTURAL ALLOYS N. KUWANO*,
Y. TOMOKIYO**,
K. OKI* AND T.
EGUCHI*
Department of Materials Science and Technology, Graduate School of Engineering Sciences and **HVEM LAB, Kyushu University, Fukuoka 816, Japan
ABSTRACT The configuration of antiphase domains in a one-dimensional long period superstructure (LPS) was examined theoretically. As LPS is composed of two kinds of antiphase domains, the domain-arrangement is described by f(n) , where f(n) is the existence probability of n which is the number of the majority domains between two minority ones. The equations for f(n) were derived using statistical approaches or thermodynamical ones, and f(n) predicted from the equations were compared with those obtained experimentally.
INTRODUCTION Several ordering alloys including Cu Au-II, a'Ag-Mg and soon have a long period superstructure (LPS) which can be derived from Ll lattice by inserting periodic antiphase boundaries. It is well known that the period obtained by diffraction experiment is usually non-integral in the unit of the dimension of the Ll lattice. Fujiwara[l] proposed that a'Ag-Mg which has a period between 1.7 and 2.0 is made of a mixture of antiphase domains lengths of which are M=l and 2. He classified the mode of the configuration of the domains into four categories, and concluded that c'Ag-Mg has an "irregurar arrangement with uniform mixing". However, he did not refer to the origin of the realization of the configuration. The present authors[2-4] have examined the configurations of the antiphase domains in several alloy-systems using high resolution electron microscopy, and confirmed that the LPSs in a Cu-Al, ac"Cu-Pd as well as c'Ag-Mg are quite generally composed of domains t e lengths of which are discretely [71] and [M]+l, where R is the averaged value of the period and [R] the integral part of A7. In this work, we deduced the the mixing modes of the antiphase domains statistically and thermodynamically to find physical implication of the domain arrangements.
DIFINITION OF
f(n)
Photo. 1 shows examples of the direct observation of LPS in a'Ag-Mg. Since the sites for the minority atoms in an ordered binary alloy appear in a strong contrast under a proper observation condition[5-7], as seen in Photo. l(a), the configuration of antiphase domains can be known directly. When a small objective aperture is used to select a few split order-reflections, a fring contrast is obtained, as seen in Photo.l(b). The spacing of the fringes is not always equal to the real length of the domains. But when the observation is carried out carefully, the information of the arrangement can be obtained correctly. An example of the actual arrangement of domains in a'Ag-Mg thus obtained is shown in Table 1. However, such an enumeration of the domain
lengths, or {M},
is not convenient to describe the arrangement. As the LPS
has been found to be composed of domains with two discrete lengths; M=1 and 2 in Ct'Ag-Mg, the row of the numbers of the major
