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ORDERING TRANSITION IN OMEGA PHASES
A. Dubertret, M. Fayard
To cite this version:
JOURNAL. DE PHYSIQUE Colloque C7, supple'ment cru no 12. Tome 38, dPcembre 1977, pcrge C7-462
ORDERING TRANSITION
IN
OMEGA PHASES
A. DUBERTRET and M. FAYARD
Laboratoire de Mktallurgie structurale des Alliages ordonnCs E.N.S.C.P., 1 1, rue Pierre-et-Marie-Curie, 75231 Paris Cedex 05, France
R6sum6. - La transformation
p
+ w d'alliages Ti-Zr-0 et Ti-Hf-0 entraine une mise en ordre des atomes mktalliques.Abstract. - p -+ w transition in Ti-Zr-0 and Ti-Hf-0 occurs with ordering of metallic atoms.
During the transformation of b.c.c. metals and rent site l(a) and 2(d). Their variation is proportional alloys, equivalent positions of the b.c.c. are transform- to the square of the long range order parameter S as ed into la : (O,O, 0) and 2d : (113, 213, z ; 2/3, 1/3,3) far as the space group is not changed into P
3
m l . non equivalent positions if W phase is described in In P 6/mmm W structure, the varying with order P5
m 1 space group. If z is taken equal to 1/2 the3
noinn to zero structure factors obey the rule :axis is changedinto- a 6 fold axis and-the space group into P 6/mmm.
By measuring X ray intensities diffracted by pure o
phases in the Ti-Zr-0 [l, 2, 31 and the Ti-Hf-0 [4] sys- tems, it has been shown that Zr (or Hf) atom is prefe- rentially located in l(a), and Ti in 2(d), with a perfect order of cations for a ratio Ti/Zr equal to 2. This ordering of metals seems to be governed by the diffe- rence in atomic radii as discussed elsewhere [3], [5]. In such a P 3 m l group there are no conditions limiting the possible reflections. No reflection can then be called a superstructure reflection.
If z = 112 (i.e. if the group is P 6lmmm) some struc- ture factors have zero intensity in the disordered phase as a result of statistical occupation of the diffe-
(see the table in the appendix). Then the only qualita- tive information got from multibeam electron diffrac- tion patterns is as follows [6] : the absence in the h,
k, 0 zone of beams such as h
-
k # 3 n indicates aP 6/mmm disordered structure. Any other informa- tion on long range order has to be found by measuring the kinematical X ray or neutron diffracted intensities. Thus, the
P
-t o transition may be understood as atwo stage transition, probably acting together :
ordering in the b.c.c. structure (resulting in a
P
3
m 1 structure with z = 1/3), followed by a displa- cive transformation [7,8] changing z = 113 to z = 112 and the group into ,P 6/mmm as shown in figure 1.Ordering transition
t
Displac~ve transition
C-
l m 3 m ~ 7 r n l P 6/mmm
2 atoms in 2 a : (0, 0, 0 ; 112, 112, 112) 1 atom in l a : (O,O, 0) l atom in l a : (0, 0,O)
General : h, k, l : h + ' k
+
I = 2 n 2 atoms in 2 d : (113, 213, s 213, 113, 5) 2 atoms in 2 d : (1/3,2/3,1/2 ; 213,113, 112) No extra conditions with z = 113 General : no conditionsp b.c.c., structure as seen from a pro- General : no conditions No extra conditions jection on the { 11 1 ] plane. No extra conditions Omega ordered structure.
Possible cc Intermediate structure.
Appendix
Let us suppose that the crystallographic structure of located in l a and 2d wyckoff positions. We have :
o phases is described in the P 6/mmm space group, 1 species A in l(a) : O,0,0.
with the two kinds of atoms (Ti and Zr for example) 1 species D in 2(d) : 113, 213, 112 ; 213, 113, 112.
ORDERING TRANSITION IN OMEGA PHASES C7-463
with : From this formulae, one can see that all reflections
A = (1/3
+
2/3 S ) Zr+
(213-
2/3 S ) TiD = (213
+
113 S ) Ti+
(113-
113 S ) Zr where S is a long range order parameter describing the relative population of Ti and Zr in 2d and l a sites as in the usual superstructure.We have : Fhkl = fA
+
fD e2niX+
f D eZniY with : h + 2 k l X = - 2 h + k l 3+
-
2 and Y =---
3+
-
2 which leads to : 1Fh.u 12=fA2+2fD2+2fAfDX (COS 2
nX+
COS' 2 n Y )+
2 f; cos 2 n(X- Y)with h
-
k = 3 n and I = 2 n' will be in phase, and do not depend on the value of S. We call theses reflec- tions not varying with order.In the complete disordered phase, formulae I can be written :
1
F,,,1'
= f 2[3+
C COS
2 nX+
COS 2 Z Y+
+
cos 2 7t(X-
Y ) ] a (11) with f A = f D = l13 f i r+
2/3 f ~ i =f
which shows that among all the reflections which vary with order, called varying with order, all the reflections with h
-
k # 3 n and l = 2 n' have zero intensity. We call these varying with order, going to zero.(1) Theses results are summarized in table I.
h + 2 k I 2 h + k I Fm hkl X =
-
+
-
Y E -3 2 3 +z
Disordered Phase Fhkl Ordered Type("1
Phase 10.0 113 213 0 W f A-
f ~ )
v.0.
11.0 1 1 2 4 ( f ~+
2f ~ )
24(fA+
2 fD) N.V. 20.0W
W
0 W f A-
f D )v.0.
11.1 312 312 - 24( f ~
+
2f ~ )
3 24(fA-
2 f D )v.
21.o
413 00.2 1 Etc.(*) Type : V. : Varying with order.
V.O. : Varying with order, going to zero, condition h - k f 3 n ; l = 2 n'.
N.V. : Not varying with order condition : h
-
k = 3 n ; l = 2 n'.References
(f*
+
2f ~ )
48 3 W f A $- f D )
v.
0 2 4 ( f ~
-
f D )v.0.
2 4 ( f ~
+
2f ~ )
24(fA+
2 f ~ ) N.V.[ l ] FYKIN, L., GLAZOVA, V. and KORNILOV, I., Dokl. Akad. Nauk [5] DUBERTRET, A. and FAYARD, M., Third Internatlonal Confe-
SSSR 182 (1968) 576. rence on Titanium. Moscou. May 18-21 (1976).
l21 FYKIN, L., KORNILOV, I. et al., Dokl. Akad. Nauk SSSR 194 [6] GJONNES, J . and MOODIE, A. F., Acta Crystallogr. 19 (1965) 65.
(1970) 1374. [7] DE FONTAINE, D., Acta Met. 18 (1970) 275.
L31 DECHAMPS, M., P., DUBERTRET, A. and FAYARD, M., [8] DE FONTAINE, D., PATTON, N. E. and WILLIAMS, J. C., Met. Mat. Res. Bull. 7 (1972) 1369. Trans. 4 (1973) 2701.
[4] CHAUFFOUR, D . and DUBERTRET, A., Internal report (E.N.S.C.P.)
