Ordered Structures on the BCC Lattice with First, Second, Third and Fifth Neighbour Interactions
- PDF / 276,245 Bytes
- 6 Pages / 418.68 x 637.2 pts Page_size
- 82 Downloads / 228 Views
ORDERED STRUCTURES ON THE BCC LATTICE WITH FIRST, SECOND, THIRD AND FIFTH NEIGHBOUR INTERACTIONS A. FINEL, F. DUCASTELLE Office National d'Etudes et de Recherches AMrospatiales (ONE RA) BP 72 92322 CHATILLON CEDEX (France) ABSTRACT Using a method of linear inequalities similar to that introduced previously by Kanamori and others, we determine the ground state of the Ising model on the BCC lattice in the presence of first, second, third and fifth neighbour interactions. Thirteen new structures are found ; the C 11 (MoSi and B 11 (T - TiCu) in particular are found to be stabilized by thirA andfor Some regions of the phase diagram however fifth neighbour interactions. are still not completely known.
INTRODUCTI ON A problem of great interest in the study of binary alloys is the determination of phase diagrams. Due to the complexity of the task, it is easier coherent phase diagrams, i.e. to consider only those structo consider first tures that may be built up on a fixed underlying crystalline structure. At zero temperature and assuming pair interactions, we are then reduced to the problem of determining the ground state of the Ising model. In the case of first and second neighbour interactions, the solution is rather easy and has been given several years ago in the case of FCC and BCC lattices [1,2]. More complicated cases have been handled by Kanamori and others, using geometrical linear inequalities involving pair probabilities [3 4,5] The method has been recently e4tended by Sanchez and de Fontaine [6]. A general formulation of this method, which is closely connected with linear programming will be given elsewhere [7]. We give here an outline of the method and present a study of the BCC lattice with first, second, third and fifth neighbour interactions. We find that some observed structures such as C 11.b. (Mo Si 2.) or B 11 (1'TiCu) are stabilized by third and fifth neighbour interactions. Several new structures are also shown to be stable for certain values of the interaction parameters.
ISING MODEL : GROUND STATE AND CONFIGURATIONAL POLYHEDRON We start from the lattice-gas formulation of the Ising model for an alloy Ac Bl1-c EK.V •th
V.
is
Mat.
Res.
the i
neighbour pair interaction and q. N. the corresponding number neighbour pairs. Let p be the is the total number of it I eh ra. L occupation number taking value 4 or 0 depending on the site n being occupied by an A atom or not, then qi is equal to the average
Data Loading...
