Electronic Structure and Ordering in Transition Alloys and Compounds
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ELECTRONIC STRUCTURE AND ORDERING IN TRANSITION ALLOYS AND COMPOUNDS F. DUCASTELLE Office National d'Etudes et de Recherches AMrospatiales (ONERA) BP 72 92322 CHATILLON CEDEX (France) ABSTRACT Starting from a simple but realistic description of the electronic structure of transition alloys, we show that it is possible to understand why some type of ordering is preferred to another. Similar arguments are shown to apply to interstitial compounds.
INTRODUCTION The observed ordered structures of transition alloys can be classified using so-called structural maps [1,2]. The simplest one uses the coordinates (N, &-N) whereN is the mean number of d electrons and &N is the difference between the number of d electrons of the alloy constituents. A rather good separation of the structures is obtained in general [2,3]. Our aim is to account for the success of this classification. Thus we have to calculate the energy of the alloys as a function of the atomic arrangements, at zero temperature, (we do not discuss here the phase diagrams at finite temperature In general the total energy U cannot be written in terms of pair interactions, but in several recent works it has been shown that the configurational part of this energy can be written in this way [3,4,5]. We may then write, up to a constant :
U
II1V
th.
WhereV is the nth - neighbour pair interaction and q the corresponding numer of (for example) A - A pairs in an alloy A B .* Je are then reduced to finding the ground state of the Ising model. Tfis is discussed elsewhere [6,7]. As an example we show in Figure 1 the predicted ordered structures when first and second neighbour interactions only are taken into account on a FCC lattice. Some comments are in order here. In the case of transition alloys, this diagram is not very successful : some structures like A B, A2 B, A2B have never been observed. The CuPt structure itself only occurs for CuPt ! Furthermore many observed structures (Ni 4 Mo for example) are not stabilized with V1 and V only, (for a discussion, see [6]). On the other hand, the CuPt, A5 B and A,,B., structures are encountered in ordered substoichiometric NaCl carbides and nitrides [8]. Thus the previous (VI,V 2 ) diagram seems meaningful for these interstitial compounds whereas V2.does not appear to be a relevant parameter for transition alloys ; more precisely the observed structures suggest that IV 11»>> tV22 . We shall see that these trends can be unders tood.
V2 Cu Pt
""A
Cu Pt, A2 B, A5 B
, 2 B2 ,
I
-
Pt2 Mo
Fig. - Stable structures on the FCC lattice with 1first and second neighbour interactions. The structures A 2 B, A 5 B and A 2 B 2 are des-
-m
cribed in [ 12].
DOI2 , ABB
V,
Segregation Cu Au Cu 3 Au Mat.
Res.
Soc. symp. Proc. Vol.
21 (1984) @)Elsevier Science Publishing Co.,
Inc.
376
ELECTRONIC STRUCTURE We shall use a simple tight-binding model to describe the electronic structure of transition metals. The main parameters that enter this model in . its simplest form are the d atomic level C and the hopping integrals ýX
ý'Y>
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