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Optimization of fluoride ion conduction in new fluorite-type anion excess solid solutions involving two substitutional cations
Solid State Ionics 59 ( 1993) 83-92 North-Holland
Optimization of fluoride ion conduction in new fluorite-type anion excess solid solutions involving two substitutional cations M. Wahbi, J.M. Reau ‘, J. Senegas and P. Hagenmuller Luboratoirede Chimie du Solide du CNRS, Universitkde Bordeaux I, 351 cows de la Liberation, 33405 Talence Cedex, France Received 3 1 July 1992; accepted for publication 25 August 1992
New fluorite-type anion excess phases have been prepared within the PbF&I’Fs-ZrF, (M’=In, Bi) systems involving simultaneously trivalent and tetravalent cations. The materials showing the highest ionic conductivity are characterized by presence of column clusters of (n = 2) size and by values of the Zr/In and Bi/Zr ratios close to l/2. The obtained results are discussed on the base of a previously set up clustering model.
1. Introduction Yint =
The fluorite-type M:+xM:2+aF2+ax solid solutions, disordered at long range, are characterized by a short range ordering under the form of defect clusters. The F- conduction mechanisms in these materials depend largely on the nature of the clusters which form progressively at rising substitution rate. Their determination based on various and complementary techniques such as neutron diffraction and 19F NMR is supported by a clustering model [ 11. Correlations between structural data and ionic conductivity properties have allowed us to show that the substitution rate x,, for which a maximum of conductivity associated with a minimum of activation energy can be observed is close to both x, rate for which the number of fluoride ions (Fi)m responsible for long range motions is the highest and to the value for which the diffusion of the mobile ions is the fastest [ 11. According to this model the sum of fluoride ions representing each type of interstitial anions and the amount of vacancies in the normal sites of the fluorite-type lattice can be respectively represented by the general functions yin, and y. which depend on three parameters, A, m and x,: Author to whom all correspondence should be addressed. 0167-2738/93/$06.00
Yo =
mx’+Axfx
x*+x;
’
(m-c-x)x3+ (A-a)x:x x*+x,2
The x, parameter
has been defined; the il [A=
(dYintl~)x=ol and m[m= (dYintl~)x+oolparaeters define respectively the clustering conditions for the lowest and highest values of x [ 11. This model applied to various solid solutions has allowed us to determine the nature of the formed clusters. Thus the existence of the n + 1: 2n : 1: 0 single-tile column clusters and of the 2n + 2 : 3n : 2 : 0 and 2n + 2 :4n : 2 : 0 two-files ones has been established respectively for Pbl_,BiXF2+X, Pbl_,InXF2+X and [2]. The four integer numbers Phi-,Zr,F,+ti nl : n2 :n3 :n4 characterizing such clusters indicate that they are constituted by the association of n, vacancies in the normal positions ( l/4, l/4, l/4) of the fluorite-type network with n2 F’ (l/2, U, u:O.365u;sO.41), n3 F” (vi, vl, v,:u1z0.40) and n4 F”’ ( u2, u2, u2: u2z 0.30) interstitial fluoride ions [ 1,3]. The materials of best conductivity in each of the three Pbl_-xM$‘+aF2+ax solid solutions (M’=In, Zr, Bi) correspond respectively to (0.10 ;sx_ ;s 0.12) for M’=In, (~~~~0.10) for M’=Zr and (x,_ -0.25) for M’=Bi: the three are characterized
0 1993 Elsevier Science Publishers B.V. All rights reserved.
84
M. Wahbi et al. / Optimizatidn offluoride ion conduction
by clusters of similar size involving n= 2 substitutional cations [ 41. In a previous paper [ 5 ] we have shown that the partial replacement in Pb,_,M:F2+x (M’=In, Bi) of one M’ ion by the other trivalent cation results in an increase of the disorder, favoring thus the enhancement of the transport properties: the materials having the highest conductivity are characterized by the formation of In’+ and Bi3+ clusters of similar size and involving n = 2 substitutional cations and by a number of In3+ clusters equal to twice that of Bi3+ clusters [ 5 1. We report in this paper the results of our investigations on the PbF2-M’F3-ZrF4 (M’=In, Bi) systems involving simultaneously one trivalent and one tetravalent cation. The existence of a large domain of solid solutions was expected between the border limit phases, PbI_,In,F2+,(0
2. Synthesis and radiocrystallographic analysis The ternary PbF2 -InF3 -ZrF4 and PbF2 -ZrF, BiF3 systems can be represented in equilateral ABG and AGC triangles, the A, B, C and G being respectively PbF2, InF,, BiF3 and ZrF, (fig. 1). The lines parallel to the AB, AC, AG, BG and CG sides of the triangles correspond to the formal substitutions: (AC)Pb2+=Bi3++F-; (AB)Pb’+ =In3++F-* (BG)In3+=Zr“++F(AG)Pb2+ =Zfl+ +2;-; and (CG)Bi’+ =ZIA+ + F-. The materials have been prepared from mixtures of PbF2, ZrF4 and M’F3 (M’=In, Bi) fluorides, in sealed gold tubes, at 550°C during 15 h. An XRD analysis of the samples obtained after quenching has revealed the existence of large domains of disordered solid solutions with the fluorite-type structure, Pbl_,In,(,_,,Zr,,F,+,(,+,, and Pbl-,Zr,,l-,) BixrF2+x(2_-rj(O
Fig. 1. Domains of solid solutions with fluorite type structure in the ternary PbF2-InF3-ZrF4 (a) and PbF2-ZrF,-BiF, (b) systems.
aries are respectively the AB, AG, DD” and AG, AC, D”D’ lines within the PbF2-InF,-ZrF, and PbF2-ZrF4-BiF3 systems, where D, D’ and D” repcompositions respectively the resent and Pbo.soBio.soFz.so Pbo.,&.,,F2.2,, Pbo.szZro.isF2.36 (fig. 1 ). The composition dependence of the unit cell parameter a, for the upper limit Pb1_,In,F2+, and Pbl_-xZrxF2+2x solid solutions is quite similar [ 6,7]. It results in an insignificant variation of a, as a function of z for the Pbl_,In,,l_,,Zr,,F2+xc,+,, compositions at given values of x. The influence of the replacement of the In’+ ion by the Z1.4+ion of smaller size is compensated by the introduction of one extra fluoride ion into an interstitial site. On the contrary
85
M. Wahbi et al. /Optimization offluoride ion conduction
ment with composition.
a$
5.94
I
an
Arrhenius-type
law
for
each
3.1. Variation of the electrical properties as a function of x for the Pb,-xInx~,-z~Zr,,F2+x(l+rJ and Pb,_,Zr,(,_,lBi,,Fz+x~*_rl compositions for fixed values of z
-
5.92’
5.90-
5.8%
1 , , , ,, me
z=o
0.10
0.20
X
0.30
0.40
Fig. 2. Variation
of a, as a function of x for various Pbl-,Zr,(,-,,Bi~=Fz+,(2-,) compositions relative to fixed z values (OGzd 1).
the replacement of the Zr4+ ion by the Bi3+ ion of larger size involves an increase of a, with rising z for the Phi _XZrX,I--s~BixrFZ+x~2--r~compositions at constant values of x (fig. 2). This result is analogous to that observed for the Pb,_,In,,,_,,Bi,,F,+, solid solutions [ 5 1.
3. Electrical properties Conductivity measurements have been carried out on powder samples pressed to form pellets, sintered at 550°C in sealed gold tubes and then quenched. The compactness of the pellets was about 90%. Vacuum evaporated gold was used as electrodes. The bulk resistance was measured by the complex impedance method using a Solartron frequency analyser. The frequency range was lo-‘-lo4 Hz and the measurements were carried out for several temperature cycles between 20 and 150°C. In the investigated temperature range, the temperature dependence of the conductivity is in agree-
Fig. 3a, b and fig. 4a, b give the variation of log ~~~~~and the activation energy AE, as a function of x for various series of Pb, _Jn,, , _=) Zr,,F,+,, 1+=) and Pb,_,Zr,,,_,,Bi,F,+,,,_,, materials corresponding to z equal to l/3, l/2 and 213. Results previously obtained for the limit solid solutions relative to z=O and z= 1 [ 5,8,9] are also reported in these figures: Whatever the values of z, a conductivity maximum associated with a minimum of activation energy appears for a particular value of the substitution rate (x,, ) . variation of with z for The xmax Pbl _,Zr,,, _=)BixrF2+x+rj shows a quasi-linear increase of x,, with increasing x (fig. 5a), behavior with analogous that observed for Pb, -,In,, I -=) BLzF2+x [ 5 1. On the contrary, x,, independent of z seems to be for Pb,_,In,(,_.,Zr,,F,+,(,+., (fig. 5b). As a matter of fact the quasi-constant value of x,,,, observed when z increases results simply from the very close values of xnl,x shown for z=O and z= 1. The conductivity maxima observed for x,, in each boundary solid solution correspond to particular compositions involving clusters of similar size [ 41. As a consequence, whatever the value of z(O
Fig. 6 represents the 2n+2:3n:2:0, 2n+2:4n:2:0 and n + 1: 2n : 1: 0 clusters proposed respectively for Pbl _XInXF2+X,Pbl _xZrxF2+2, and Pb, _XBi,F2+X. The formation of mixed clusters containing simultaneously Zr“+ and Bi3+ substitutional cations has a low probability due to the nature difference of two-file 2n + 2 : 4n : 2 : 0 clusters and one-file n+ 1: 2n: 1: 0 ones. The formation of a disordered distribution of ZF+ and Bi3+ ion clusters of the same size is much more likely and in agreement with the
M. Wahbi et al. /Optimization offluoride ion conduction
86
AE,
(eV.)
0.
0.
log
asooc (fLcm)-l
0.
0.
0.
0.
Fig. 3(a) Variation of log~&,~c as a function of x for some series of Pb,_,In,(l_,,Zr,,F~+,c,+., materials relative to fixed z values (O
linear relation previously observed between x,, and z. Such a hypothesis has been already proposed for the Pb, _JnXCI _=) BiX,F2+, compositions [ 5 1. On the contrary the structures of two-file 2n+2:3n:2:0and2n+2:4n:2:0columnclustersare very similar, with elementary polyhedra constituted by monocapped trigonal prisms (InF,) and square antiprisms (ZrFs) (fig. 6). This means that, for the Pb,_,In,,l_,,Zr,,F,+,(l+,, solid solutions involving clusters of the same size, formation of mixed clusters containing both substitutional cations and the occurrence of a disordered distribution of In3+ and Zr’+ ion clusters can be proposed. WC shall con-
sider the latter hypothesis below, by analogy with the and Pb,-,In,(,-,)Bi,,F2+x Phi-,Zr,,i-,,Bi,, F2+xC2_-rjcompositions. 3.2. Variation of electrical properties for some series of materials involving clusters of the same size Equations representing JJinl,~0, J+ , and & for the Pbl-,InXF2+X, Pb, -,ZrXF2+zr and Pb, -xBi,F2+, solid solutions are given in table 1. The identification of the formal &/yF” and the experimental nF,/nF,, ratios has allowed us to define the particular x,, values of x corresponding to the presence of clus-
M. Wahbi et al. /Optimization offluoride
ion conduction
87
AE, (eV.) 0:48
I
I
I \
I
’\
/
:
/
/
/
0.46
0.44
0.42
I
Fig. 4(a) Variationof logumaCas a functionof x for some series of Pb,_,Zr,(,_,)BixrF2+x(2_-r) (06~~ 1); (b) Variation of AE, as a function of x for some series of Pb,_xZr*(,_r~BixrF2+*o (O
1).
ters of n extension [ 11. x,, is related to x, by the equation: xi = ( n - 1)x: ( n > 1). According to model [ 1 ] x, must be close to x,,, the value for which a conductivity maximum is observed. (xS)1,=(xS)z,=fi/12-0.118, (X~)Bi=2Jz/12~0.236, 0.10;5
materials relative to fixed z values materials relative to fixed z values
(Xmax)In 50.12,
(Xm,x)Si N 0.25 .
As a consequence: (X,)1,= (XnL=&=U/l2
9
(X~)Bi=2J20/12. We shall call these values in the following x,,, x,, and 2x,, instead of (x,)1”, (x,,)z, and (Xn)Bi by reasons of simplicity.
The solid solution range with fluorite-type structure appearing in the PbFz-InF,-ZrF, system can be represented in the orthonormal (At, Ay) reference (fig. 7). At is the bissectrix of the (AB, AG) angle of the equilateral ABG triangle where the apexes figure PbF2, InF3 and ZrF, (fig. la). In this reference the t and x parameters are bound by the linear relation: t =x( a/2 ). Compositions characterized by the formation of clusters of n dimension are located on the D, line parallel to Ay and the border limit compositions are Phi _,In,,F,+, (L,,) and (Lz,). Crossing from L,, to Lz, Pbr-,Zr,,F2+ti~ corresponds to following substitution process: yIn3+ =yZr4+ + yF-. In other words the compositions located on the D, line may be represented by the general formulation Pbl_,Inx_,,,Zr,Fz+x,+,, (0 d y d x,,) . The total number of clusters present in a material characterized by the parameter y is thus: N= 1(&I -Y)l~lI*+
[vlnlz,
*
88
M. Wahbi et al. /Optimization offluoride ion conduction
a)
OP’ l
P”
n=2
O “P n=3
7.
0
0.2
I
x
0.4
0.6
1
0.8
b) max.
I
0.25 -(
. zr
0.20 -
0 P’ l P”
0.15 -
D “P
n=2
o_lo,~________-_~____.+--_---~-----------
n=3 1
0.05-
c)
0
0.02
0.04
0.06
0.08
1
Fig. S(a) Variation of x,,,, as a function of .z for the compositions; (b) Variation of x,, Pbl-,Zr,(,-I~Bi,,F2+,(2-,) as a function of z for the Pb,_,In,(,_,,Zr,,F,+,(,,,, compositions.
Whatever the value of y, N is constant. The variation of log a6Oacas a function of y is given in fig. 8 for some series of materials corresponding to fixed values of the cluster extension n: Whatever n, a conductivity maximum appears for a particular value y,, of y. yman increases with n. Compositions relative to various values of ymax and n are located on a curve called C which shows a maximum when n = 2. The values of ymax correspond to ymax =x,/3, i.e. to materials characterized by the value r= l/2 of the Zr/In ratio (z= l/3).
. Bj Q P' l
P”
o“P
n=2 n=3
Fig. 6. Representation ofthe 2n+2:3n:2:0 (a); 2n+2:4n:2:0 (b ); and n + 1: 2n : 1: 0;(c ) clusters proposed respectively in the Pb,_,InXF2+,, Pb,_,ZrXFz+ti and Pbl-XBiXFZ+X solid solutions.
Materials having the highest electrical conductivthe limit Pb1_,InXF2+X and between solid solutions can be written rePbl-,ZrXFz+ls spectively as: ity
89
hf. Wahbi et al. /Optimization offluoride ion conduction Table 1 Analytical expressions of y,,, ya, yr,, y, for the
Pb~_-xInxF~+x, Pb~-,ZrxFz+z,and Pb,_,Bi,F2+X solid solutions.
Pbl_,In,F~+x
Pb,--XZr&+zx
Pb,_,BiJ%+,
cluster yint YO yF’ yF” &
2n+2:3n:2:0 (3X3+5x:x)l(x~+x:) (2x3+4x:x)/(x2+x:) 3x 2x:xl(xr+xf) 0.118
y&yF” nF’f+
3(x2+x:)/2x: 3n/2
2n+2:4n:2:0 (4x3+6x:x)/(x2+x:) (2x3+4x:x)/(x2+x:) 4x 2x:x/(x*+x:) 0.118 2(X2+xf)lx: 2n
n+l:2n:l:O (2x3+3x:x)/(x2+x:) (x3+2x~x)/(xz+x:) 2x x:x/(xz+xf) 0.236 2(X2+x:)/x: 2n
(n.cnl)-1 =,t log c6O”C
I I
(OasO.27)
) ‘; ; I I
’
---_
z&/3
I
I
0.05
Fig. 7. Representation of the Pb,_,In~“_,Zr,P,+,+, tions in the orthonormal (At, Ay) reference.
comPosi-
I
0.10
I
0.15
Y,
w
0.20
Fig. 8. Variation of 10ga~~~c as a function of y for the (0~ y6 x,, ) materials relative to fixed n Pb,-,In,,-,Zr,Pz+,+, values.
Pbo.ss2 1%I I8 Fz.I I 8
i.e.Pbo.dno.118
(FN),.~~~(F)o.~~~(F”)o.I,s
and pbo.ssz i.e.
Zro.11sF2.236
Pbo.ss2Zro.ll~(FN)1.646(F’)~.472(F”)~.1~8
.
Both compositions are characterized by the same number of normal FN -and interstitial F”- fluoride ions; consequently, the substitution process along the D, lines could be written: yIn3+ =yZr4+ +yF’- , In a similar way the solid solution range with
structure shown in the fluorite-type PbF2-ZrF4-BiF3 system can be represented in the orthonormal (Ax, Ay) reference (fig. 9). The materials characterized by formation of clusters of n dimension are located on the D, line parallel to Ay and correspond to the general formulation The limit Pbl-,,-yZrx.-yB12YF2+~” (ObyGx,). compositions are pbi-,Zrx~F2+2,(Lz,) and pb1-z*.Biti~F2+2xn (Lni). Crossing from Lzr t0 Lni corresponds to substitution process: yPb2++yZr4+=2yBi 3+. This process results in replacement of a number of Zr4+ clusters by a number of Bi3+ clusters twice larger.
90
M. Wahbi et al. /Optimization offluoride ion conduction
i.e. to materials characterized by the value r= l/2 of the Bi/Zr ratio (z= l/3). - Compositions relative to different values of n and Y,, are located on a C-curve which shows a maximum when n=2 (fig. 10).
/ //z=2/
\
3
\ \
/ \
\
= /&2
\ \ \
\ \
\
\ \
; 0.18 23
-
X
4. Discussion
,/ * ‘A/3
\
\ 0.50 -gf 4
n
Fig. 9. Representation of the Pb, _xn_yZrx~_yBi2yF2+2 compositions in the orthonormal (Ax, Ay) reference.
0.05
0.10
0.15
Fig. 10. Variation of log u60-c as a function of Y for the Pb,_,_,,Zrx~_,Bi2,F2+~~(0~y~~.) materialsrelativeto fixed n values. Fig. 10 gives the variation of log 0660.oas a function of y for various series of Pb,_,,_,ZrX~_,Bi2yF2+2x(Oby~x,) materials corresponding to fixed values of n. These results are analogous to those obtained for the Pb, _xn_yInxn_.~BiZyF2+xn+y compositions [ 51: - Whatever the value of n, a conductivity maximum is observed for a particular value ymaxof y. - The values of y,,, correspond to ymax=x,,/5,
Comparison of electrical and structural properties of the particular Pb, _XM:2+‘IF2+,(M’= In, Zr, Bi) compositions characterized by the presence of clusters of n = 2 dimension shows that the highest conductivity is observed for the material which has the lowest activation energy, the largest percentage of F” -ions and the smallest cluster concentration (table 2). Recall, on the other hand, that the (Fi), ions responsible for long range motions within these solid solutions are the interstitial fluoride ions of F” -type 11341. Let us consider the Pb,_,,InX,_,Zr,Fl+X,+ycompositions located on a D, line, the extremities of which are L,, and Lzr (fig. 7 ) . Going from L,, to Lzr corresponds to a decrease of the YFNpercentage when the number of clusters of II size is constant. The replacement in the Li, phase of (y/n) In3+ clusters by (y/n) Zr4+ clusters results in an increase of cationic disorder and a cluster disorder which favor enhancement of electrical conductivity but simultaneously in a decrease of the Yr” percentage which is unfavorable. The observed conductivity increase shows that disorder is prevailing. On the contrary, replacement in the Lzr phase of (y/n) Zr4+ clusters by (y/n) In3+ clusters leads to increasing disorder and simultaneously to higher percentage of YF”which are both favorable to larger conductivity. A conductivity maximum occurs consequently for a particular value y,, of y. Along the D, lines cationic disorder is maximum for the Pb,_,InX~_,Zr,,F,+,+, compositions corresponding to y=x,/2 and the highest value of the YFN-percentage is obtained for Li, (y= 0). This results in the appearance of a conductivity maximum for 0~ y
91
h4. Wahbi et al. /Optimization offluoride ion conduction Table 2 Electrical and structural properties for the Pb,_,M:Z+“F2+, of n = 2 extension.
x
usoeC(n cm)-’ A& (ev) (YF”)(%) cluster number per unit cell
(M’=In, Zr, Bi) compositions characterized by the formation of clusters
PL,In,F2+,
Pbl-,ZrxS+ti
PbdhF2+x
b.phase
L,phase
Laiphase (n=2)
(n=2)
0.118 7x lo-’ 0.34 5.57 0.059
Crossing from Lz, to Lsi, which corresponds to a yPb’+ +yZr4+ = 2yBi 3+ substitution process, is characterized by increasing cluster concentration when the yF##-percentage iS constant. As a decrease of the cluster concentration and an increase of the yr#, percentage have a similar influence on transport properties, the behavior withy of the conductivity of the Pb,_,_,Zr,,_,Bi*,F1+, materials can be explained. For a given n-parameter the maximum of disorder corresponds to the Phi -4x.,3Zrzxn/3Bi,,3F2+~” compositions (Y= x,/3) relative to the value r= 1 of the Bi/Zr ratio (z= l/2). The Lzr phase (y= 0) is characterized by the smallest cluster concentration. y,, must consequently be within the O< ymax
(n=2)
0.118 6x 1O-4 0.37 5.27 0.059
0.236 3x10-4 0.39 5.27 0.118
Table 3 Values of amrfor
(Ml.,=),
(Mz,&,
(%+I
and
BPbSnF4.
%ooK (&I
(MInBi) [5] x”=$/12(n=2) Pbl_~“,,,/JIn4,,,5Bilf~Fz+6~/~ BPbSnF,
x.=J2/12(n=2)
cm)-’
= 1.7x 10-Z =5x1o-2
1101 three phenomena occur simultaneously for the (PbIn-Bi ) compositions, according to the yPb2++yIn3+=2yBi3+ + yF’- substitution process. Within three domains of solid solutions, the highest ionic conductivity is observed for the materials called (Min.zr), (Mzr,si) and (Mrn,Bi) which are characterized by the presence of column clusters of it= 2 dimension (x, = @/ 12) and values of y,, equal respectively to xn/3, x,/5 and x,/5. These phases are among the best fast fluoride ion conductors so far obtained (table 3 ) .
5. Conclusions New fast ionic conductors with the Pb,-,In,,,-,,Zr,,Fz+,(l+,, and Pbl-,Zr,(i-,, BiX,F2+,(2-,) (0 d z B 1) formulations have been found in the PbF2 -InF3-ZrF, and PbF2-ZrF,-BiF, systems. Whatever z, an ionic conductivity maximum appears for x,, and the compositions relative to x,, are characterized by for-
hi. Wahbi et al. /Optimization ofjluoride ion conduction
92
mation of n = 2 extension column clusters. The variation withy of the F- ion conductivity for the Pb,_,1n,_,Zr,F,+,+, and Pb,_,_,Zr,,_, (0 QG x,) series involving clusters of Bi&+2X, similar size has been determined. Materials with the best electrical properties are those for which the Zr/ In and Bi/Zr ratios are close to l/2. ThPan rnnlll+a I llkJk lclUUlLD confirm those previously obtained in investigating the Pb,_-xn_-yInxn_-yBi2yF2+xn+Y solid solutions.
References [ 1 ] J.M. R&m, M. Wahbi, J. SC&as and P. Hagenmuller, Phys. Status Solidi (b) 169 (1992) 331.
[2] J.M. Reau, M.El. Omari, J. S&i&as and P. Hagenmuller, Solid State Ionics 38 ( 1990) 123. [ 31 AK. Cheetham, B.E.F. Fender, B. Steele, R.I. Taylor and B.T.M. Willis, Solid State Commun. 8 ( 1970) 17 1. [ 41 J.M. R&au,J. Se&as and P. Hagenmuller, Proc. ICAM 9 1, EMRS 1991 Conf. A2-V8 (Strasbourg, 1991).
,617,” Wnhh;
TM
7
Phys.
Status
Solidi
(a) 125 (1991) 517. [ 61 S. Kacim, J.C. Champamaud-Mesjard and B. Frit, Rev. Chim. Miner. 19 (1982) 199. [ 71 J.P. Laval, C. Depierretixe, B. Frit and G. Roult, J. Solid State Chem. 54 (1984) 260. [ 8 ] J.M. R&au, J. S&&as, J.P. Lava1 and B. Frit, Solid State Ionics 31 (1988) 147. [ 91 Ph. Darbon, J.M. Reau, P. Hagenmuller, Ch. Depierrefixe, J.P. Laval and B. Frit, Mat. Res. Bull. 16 ( 198 1) 389. [ lo] J.M. RCau, C. Lucat, J. Portier, P. Hagenmuller, L. Cot and S. Vilminot, Mat. Res. Bull. 13 (1978) 877.
Optimization of fluoride ion conduction in new fluorite-type anion excess solid solutions involving two substitutional cations M. Wahbi, J.M. Reau ‘, J. Senegas and P. Hagenmuller Luboratoirede Chimie du Solide du CNRS, Universitkde Bordeaux I, 351 cows de la Liberation, 33405 Talence Cedex, France Received 3 1 July 1992; accepted for publication 25 August 1992
New fluorite-type anion excess phases have been prepared within the PbF&I’Fs-ZrF, (M’=In, Bi) systems involving simultaneously trivalent and tetravalent cations. The materials showing the highest ionic conductivity are characterized by presence of column clusters of (n = 2) size and by values of the Zr/In and Bi/Zr ratios close to l/2. The obtained results are discussed on the base of a previously set up clustering model.
1. Introduction Yint =
The fluorite-type M:+xM:2+aF2+ax solid solutions, disordered at long range, are characterized by a short range ordering under the form of defect clusters. The F- conduction mechanisms in these materials depend largely on the nature of the clusters which form progressively at rising substitution rate. Their determination based on various and complementary techniques such as neutron diffraction and 19F NMR is supported by a clustering model [ 11. Correlations between structural data and ionic conductivity properties have allowed us to show that the substitution rate x,, for which a maximum of conductivity associated with a minimum of activation energy can be observed is close to both x, rate for which the number of fluoride ions (Fi)m responsible for long range motions is the highest and to the value for which the diffusion of the mobile ions is the fastest [ 11. According to this model the sum of fluoride ions representing each type of interstitial anions and the amount of vacancies in the normal sites of the fluorite-type lattice can be respectively represented by the general functions yin, and y. which depend on three parameters, A, m and x,: Author to whom all correspondence should be addressed. 0167-2738/93/$06.00
Yo =
mx’+Axfx
x*+x;
’
(m-c-x)x3+ (A-a)x:x x*+x,2
The x, parameter
has been defined; the il [A=
(dYintl~)x=ol and m[m= (dYintl~)x+oolparaeters define respectively the clustering conditions for the lowest and highest values of x [ 11. This model applied to various solid solutions has allowed us to determine the nature of the formed clusters. Thus the existence of the n + 1: 2n : 1: 0 single-tile column clusters and of the 2n + 2 : 3n : 2 : 0 and 2n + 2 :4n : 2 : 0 two-files ones has been established respectively for Pbl_,BiXF2+X, Pbl_,InXF2+X and [2]. The four integer numbers Phi-,Zr,F,+ti nl : n2 :n3 :n4 characterizing such clusters indicate that they are constituted by the association of n, vacancies in the normal positions ( l/4, l/4, l/4) of the fluorite-type network with n2 F’ (l/2, U, u:O.365u;sO.41), n3 F” (vi, vl, v,:u1z0.40) and n4 F”’ ( u2, u2, u2: u2z 0.30) interstitial fluoride ions [ 1,3]. The materials of best conductivity in each of the three Pbl_-xM$‘+aF2+ax solid solutions (M’=In, Zr, Bi) correspond respectively to (0.10 ;sx_ ;s 0.12) for M’=In, (~~~~0.10) for M’=Zr and (x,_ -0.25) for M’=Bi: the three are characterized
0 1993 Elsevier Science Publishers B.V. All rights reserved.
84
M. Wahbi et al. / Optimizatidn offluoride ion conduction
by clusters of similar size involving n= 2 substitutional cations [ 41. In a previous paper [ 5 ] we have shown that the partial replacement in Pb,_,M:F2+x (M’=In, Bi) of one M’ ion by the other trivalent cation results in an increase of the disorder, favoring thus the enhancement of the transport properties: the materials having the highest conductivity are characterized by the formation of In’+ and Bi3+ clusters of similar size and involving n = 2 substitutional cations and by a number of In3+ clusters equal to twice that of Bi3+ clusters [ 5 1. We report in this paper the results of our investigations on the PbF2-M’F3-ZrF4 (M’=In, Bi) systems involving simultaneously one trivalent and one tetravalent cation. The existence of a large domain of solid solutions was expected between the border limit phases, PbI_,In,F2+,(0
2. Synthesis and radiocrystallographic analysis The ternary PbF2 -InF3 -ZrF4 and PbF2 -ZrF, BiF3 systems can be represented in equilateral ABG and AGC triangles, the A, B, C and G being respectively PbF2, InF,, BiF3 and ZrF, (fig. 1). The lines parallel to the AB, AC, AG, BG and CG sides of the triangles correspond to the formal substitutions: (AC)Pb2+=Bi3++F-; (AB)Pb’+ =In3++F-* (BG)In3+=Zr“++F(AG)Pb2+ =Zfl+ +2;-; and (CG)Bi’+ =ZIA+ + F-. The materials have been prepared from mixtures of PbF2, ZrF4 and M’F3 (M’=In, Bi) fluorides, in sealed gold tubes, at 550°C during 15 h. An XRD analysis of the samples obtained after quenching has revealed the existence of large domains of disordered solid solutions with the fluorite-type structure, Pbl_,In,(,_,,Zr,,F,+,(,+,, and Pbl-,Zr,,l-,) BixrF2+x(2_-rj(O
Fig. 1. Domains of solid solutions with fluorite type structure in the ternary PbF2-InF3-ZrF4 (a) and PbF2-ZrF,-BiF, (b) systems.
aries are respectively the AB, AG, DD” and AG, AC, D”D’ lines within the PbF2-InF,-ZrF, and PbF2-ZrF4-BiF3 systems, where D, D’ and D” repcompositions respectively the resent and Pbo.soBio.soFz.so Pbo.,&.,,F2.2,, Pbo.szZro.isF2.36 (fig. 1 ). The composition dependence of the unit cell parameter a, for the upper limit Pb1_,In,F2+, and Pbl_-xZrxF2+2x solid solutions is quite similar [ 6,7]. It results in an insignificant variation of a, as a function of z for the Pbl_,In,,l_,,Zr,,F2+xc,+,, compositions at given values of x. The influence of the replacement of the In’+ ion by the Z1.4+ion of smaller size is compensated by the introduction of one extra fluoride ion into an interstitial site. On the contrary
85
M. Wahbi et al. /Optimization offluoride ion conduction
ment with composition.
a$
5.94
I
an
Arrhenius-type
law
for
each
3.1. Variation of the electrical properties as a function of x for the Pb,-xInx~,-z~Zr,,F2+x(l+rJ and Pb,_,Zr,(,_,lBi,,Fz+x~*_rl compositions for fixed values of z
-
5.92’
5.90-
5.8%
1 , , , ,, me
z=o
0.10
0.20
X
0.30
0.40
Fig. 2. Variation
of a, as a function of x for various Pbl-,Zr,(,-,,Bi~=Fz+,(2-,) compositions relative to fixed z values (OGzd 1).
the replacement of the Zr4+ ion by the Bi3+ ion of larger size involves an increase of a, with rising z for the Phi _XZrX,I--s~BixrFZ+x~2--r~compositions at constant values of x (fig. 2). This result is analogous to that observed for the Pb,_,In,,,_,,Bi,,F,+, solid solutions [ 5 1.
3. Electrical properties Conductivity measurements have been carried out on powder samples pressed to form pellets, sintered at 550°C in sealed gold tubes and then quenched. The compactness of the pellets was about 90%. Vacuum evaporated gold was used as electrodes. The bulk resistance was measured by the complex impedance method using a Solartron frequency analyser. The frequency range was lo-‘-lo4 Hz and the measurements were carried out for several temperature cycles between 20 and 150°C. In the investigated temperature range, the temperature dependence of the conductivity is in agree-
Fig. 3a, b and fig. 4a, b give the variation of log ~~~~~and the activation energy AE, as a function of x for various series of Pb, _Jn,, , _=) Zr,,F,+,, 1+=) and Pb,_,Zr,,,_,,Bi,F,+,,,_,, materials corresponding to z equal to l/3, l/2 and 213. Results previously obtained for the limit solid solutions relative to z=O and z= 1 [ 5,8,9] are also reported in these figures: Whatever the values of z, a conductivity maximum associated with a minimum of activation energy appears for a particular value of the substitution rate (x,, ) . variation of with z for The xmax Pbl _,Zr,,, _=)BixrF2+x+rj shows a quasi-linear increase of x,, with increasing x (fig. 5a), behavior with analogous that observed for Pb, -,In,, I -=) BLzF2+x [ 5 1. On the contrary, x,, independent of z seems to be for Pb,_,In,(,_.,Zr,,F,+,(,+., (fig. 5b). As a matter of fact the quasi-constant value of x,,,, observed when z increases results simply from the very close values of xnl,x shown for z=O and z= 1. The conductivity maxima observed for x,, in each boundary solid solution correspond to particular compositions involving clusters of similar size [ 41. As a consequence, whatever the value of z(O
Fig. 6 represents the 2n+2:3n:2:0, 2n+2:4n:2:0 and n + 1: 2n : 1: 0 clusters proposed respectively for Pbl _XInXF2+X,Pbl _xZrxF2+2, and Pb, _XBi,F2+X. The formation of mixed clusters containing simultaneously Zr“+ and Bi3+ substitutional cations has a low probability due to the nature difference of two-file 2n + 2 : 4n : 2 : 0 clusters and one-file n+ 1: 2n: 1: 0 ones. The formation of a disordered distribution of ZF+ and Bi3+ ion clusters of the same size is much more likely and in agreement with the
M. Wahbi et al. /Optimization offluoride ion conduction
86
AE,
(eV.)
0.
0.
log
asooc (fLcm)-l
0.
0.
0.
0.
Fig. 3(a) Variation of log~&,~c as a function of x for some series of Pb,_,In,(l_,,Zr,,F~+,c,+., materials relative to fixed z values (O
linear relation previously observed between x,, and z. Such a hypothesis has been already proposed for the Pb, _JnXCI _=) BiX,F2+, compositions [ 5 1. On the contrary the structures of two-file 2n+2:3n:2:0and2n+2:4n:2:0columnclustersare very similar, with elementary polyhedra constituted by monocapped trigonal prisms (InF,) and square antiprisms (ZrFs) (fig. 6). This means that, for the Pb,_,In,,l_,,Zr,,F,+,(l+,, solid solutions involving clusters of the same size, formation of mixed clusters containing both substitutional cations and the occurrence of a disordered distribution of In3+ and Zr’+ ion clusters can be proposed. WC shall con-
sider the latter hypothesis below, by analogy with the and Pb,-,In,(,-,)Bi,,F2+x Phi-,Zr,,i-,,Bi,, F2+xC2_-rjcompositions. 3.2. Variation of electrical properties for some series of materials involving clusters of the same size Equations representing JJinl,~0, J+ , and & for the Pbl-,InXF2+X, Pb, -,ZrXF2+zr and Pb, -xBi,F2+, solid solutions are given in table 1. The identification of the formal &/yF” and the experimental nF,/nF,, ratios has allowed us to define the particular x,, values of x corresponding to the presence of clus-
M. Wahbi et al. /Optimization offluoride
ion conduction
87
AE, (eV.) 0:48
I
I
I \
I
’\
/
:
/
/
/
0.46
0.44
0.42
I
Fig. 4(a) Variationof logumaCas a functionof x for some series of Pb,_,Zr,(,_,)BixrF2+x(2_-r) (06~~ 1); (b) Variation of AE, as a function of x for some series of Pb,_xZr*(,_r~BixrF2+*o (O
1).
ters of n extension [ 11. x,, is related to x, by the equation: xi = ( n - 1)x: ( n > 1). According to model [ 1 ] x, must be close to x,,, the value for which a conductivity maximum is observed. (xS)1,=(xS)z,=fi/12-0.118, (X~)Bi=2Jz/12~0.236, 0.10;5
materials relative to fixed z values materials relative to fixed z values
(Xmax)In 50.12,
(Xm,x)Si N 0.25 .
As a consequence: (X,)1,= (XnL=&=U/l2
9
(X~)Bi=2J20/12. We shall call these values in the following x,,, x,, and 2x,, instead of (x,)1”, (x,,)z, and (Xn)Bi by reasons of simplicity.
The solid solution range with fluorite-type structure appearing in the PbFz-InF,-ZrF, system can be represented in the orthonormal (At, Ay) reference (fig. 7). At is the bissectrix of the (AB, AG) angle of the equilateral ABG triangle where the apexes figure PbF2, InF3 and ZrF, (fig. la). In this reference the t and x parameters are bound by the linear relation: t =x( a/2 ). Compositions characterized by the formation of clusters of n dimension are located on the D, line parallel to Ay and the border limit compositions are Phi _,In,,F,+, (L,,) and (Lz,). Crossing from L,, to Lz, Pbr-,Zr,,F2+ti~ corresponds to following substitution process: yIn3+ =yZr4+ + yF-. In other words the compositions located on the D, line may be represented by the general formulation Pbl_,Inx_,,,Zr,Fz+x,+,, (0 d y d x,,) . The total number of clusters present in a material characterized by the parameter y is thus: N= 1(&I -Y)l~lI*+
[vlnlz,
*
88
M. Wahbi et al. /Optimization offluoride ion conduction
a)
OP’ l
P”
n=2
O “P n=3
7.
0
0.2
I
x
0.4
0.6
1
0.8
b) max.
I
0.25 -(
. zr
0.20 -
0 P’ l P”
0.15 -
D “P
n=2
o_lo,~________-_~____.+--_---~-----------
n=3 1
0.05-
c)
0
0.02
0.04
0.06
0.08
1
Fig. S(a) Variation of x,,,, as a function of .z for the compositions; (b) Variation of x,, Pbl-,Zr,(,-I~Bi,,F2+,(2-,) as a function of z for the Pb,_,In,(,_,,Zr,,F,+,(,,,, compositions.
Whatever the value of y, N is constant. The variation of log a6Oacas a function of y is given in fig. 8 for some series of materials corresponding to fixed values of the cluster extension n: Whatever n, a conductivity maximum appears for a particular value y,, of y. yman increases with n. Compositions relative to various values of ymax and n are located on a curve called C which shows a maximum when n = 2. The values of ymax correspond to ymax =x,/3, i.e. to materials characterized by the value r= l/2 of the Zr/In ratio (z= l/3).
. Bj Q P' l
P”
o“P
n=2 n=3
Fig. 6. Representation ofthe 2n+2:3n:2:0 (a); 2n+2:4n:2:0 (b ); and n + 1: 2n : 1: 0;(c ) clusters proposed respectively in the Pb,_,InXF2+,, Pb,_,ZrXFz+ti and Pbl-XBiXFZ+X solid solutions.
Materials having the highest electrical conductivthe limit Pb1_,InXF2+X and between solid solutions can be written rePbl-,ZrXFz+ls spectively as: ity
89
hf. Wahbi et al. /Optimization offluoride ion conduction Table 1 Analytical expressions of y,,, ya, yr,, y, for the
Pb~_-xInxF~+x, Pb~-,ZrxFz+z,and Pb,_,Bi,F2+X solid solutions.
Pbl_,In,F~+x
Pb,--XZr&+zx
Pb,_,BiJ%+,
cluster yint YO yF’ yF” &
2n+2:3n:2:0 (3X3+5x:x)l(x~+x:) (2x3+4x:x)/(x2+x:) 3x 2x:xl(xr+xf) 0.118
y&yF” nF’f+
3(x2+x:)/2x: 3n/2
2n+2:4n:2:0 (4x3+6x:x)/(x2+x:) (2x3+4x:x)/(x2+x:) 4x 2x:x/(x*+x:) 0.118 2(X2+xf)lx: 2n
n+l:2n:l:O (2x3+3x:x)/(x2+x:) (x3+2x~x)/(xz+x:) 2x x:x/(xz+xf) 0.236 2(X2+x:)/x: 2n
(n.cnl)-1 =,t log c6O”C
I I
(OasO.27)
) ‘; ; I I
’
---_
z&/3
I
I
0.05
Fig. 7. Representation of the Pb,_,In~“_,Zr,P,+,+, tions in the orthonormal (At, Ay) reference.
comPosi-
I
0.10
I
0.15
Y,
w
0.20
Fig. 8. Variation of 10ga~~~c as a function of y for the (0~ y6 x,, ) materials relative to fixed n Pb,-,In,,-,Zr,Pz+,+, values.
Pbo.ss2 1%I I8 Fz.I I 8
i.e.Pbo.dno.118
(FN),.~~~(F)o.~~~(F”)o.I,s
and pbo.ssz i.e.
Zro.11sF2.236
Pbo.ss2Zro.ll~(FN)1.646(F’)~.472(F”)~.1~8
.
Both compositions are characterized by the same number of normal FN -and interstitial F”- fluoride ions; consequently, the substitution process along the D, lines could be written: yIn3+ =yZr4+ +yF’- , In a similar way the solid solution range with
structure shown in the fluorite-type PbF2-ZrF4-BiF3 system can be represented in the orthonormal (Ax, Ay) reference (fig. 9). The materials characterized by formation of clusters of n dimension are located on the D, line parallel to Ay and correspond to the general formulation The limit Pbl-,,-yZrx.-yB12YF2+~” (ObyGx,). compositions are pbi-,Zrx~F2+2,(Lz,) and pb1-z*.Biti~F2+2xn (Lni). Crossing from Lzr t0 Lni corresponds to substitution process: yPb2++yZr4+=2yBi 3+. This process results in replacement of a number of Zr4+ clusters by a number of Bi3+ clusters twice larger.
90
M. Wahbi et al. /Optimization offluoride ion conduction
i.e. to materials characterized by the value r= l/2 of the Bi/Zr ratio (z= l/3). - Compositions relative to different values of n and Y,, are located on a C-curve which shows a maximum when n=2 (fig. 10).
/ //z=2/
\
3
\ \
/ \
\
= /&2
\ \ \
\ \
\
\ \
; 0.18 23
-
X
4. Discussion
,/ * ‘A/3
\
\ 0.50 -gf 4
n
Fig. 9. Representation of the Pb, _xn_yZrx~_yBi2yF2+2 compositions in the orthonormal (Ax, Ay) reference.
0.05
0.10
0.15
Fig. 10. Variation of log u60-c as a function of Y for the Pb,_,_,,Zrx~_,Bi2,F2+~~(0~y~~.) materialsrelativeto fixed n values. Fig. 10 gives the variation of log 0660.oas a function of y for various series of Pb,_,,_,ZrX~_,Bi2yF2+2x(Oby~x,) materials corresponding to fixed values of n. These results are analogous to those obtained for the Pb, _xn_yInxn_.~BiZyF2+xn+y compositions [ 51: - Whatever the value of n, a conductivity maximum is observed for a particular value ymaxof y. - The values of y,,, correspond to ymax=x,,/5,
Comparison of electrical and structural properties of the particular Pb, _XM:2+‘IF2+,(M’= In, Zr, Bi) compositions characterized by the presence of clusters of n = 2 dimension shows that the highest conductivity is observed for the material which has the lowest activation energy, the largest percentage of F” -ions and the smallest cluster concentration (table 2). Recall, on the other hand, that the (Fi), ions responsible for long range motions within these solid solutions are the interstitial fluoride ions of F” -type 11341. Let us consider the Pb,_,,InX,_,Zr,Fl+X,+ycompositions located on a D, line, the extremities of which are L,, and Lzr (fig. 7 ) . Going from L,, to Lzr corresponds to a decrease of the YFNpercentage when the number of clusters of II size is constant. The replacement in the Li, phase of (y/n) In3+ clusters by (y/n) Zr4+ clusters results in an increase of cationic disorder and a cluster disorder which favor enhancement of electrical conductivity but simultaneously in a decrease of the Yr” percentage which is unfavorable. The observed conductivity increase shows that disorder is prevailing. On the contrary, replacement in the Lzr phase of (y/n) Zr4+ clusters by (y/n) In3+ clusters leads to increasing disorder and simultaneously to higher percentage of YF”which are both favorable to larger conductivity. A conductivity maximum occurs consequently for a particular value y,, of y. Along the D, lines cationic disorder is maximum for the Pb,_,InX~_,Zr,,F,+,+, compositions corresponding to y=x,/2 and the highest value of the YFN-percentage is obtained for Li, (y= 0). This results in the appearance of a conductivity maximum for 0~ y
91
h4. Wahbi et al. /Optimization offluoride ion conduction Table 2 Electrical and structural properties for the Pb,_,M:Z+“F2+, of n = 2 extension.
x
usoeC(n cm)-’ A& (ev) (YF”)(%) cluster number per unit cell
(M’=In, Zr, Bi) compositions characterized by the formation of clusters
PL,In,F2+,
Pbl-,ZrxS+ti
PbdhF2+x
b.phase
L,phase
Laiphase (n=2)
(n=2)
0.118 7x lo-’ 0.34 5.57 0.059
Crossing from Lz, to Lsi, which corresponds to a yPb’+ +yZr4+ = 2yBi 3+ substitution process, is characterized by increasing cluster concentration when the yF##-percentage iS constant. As a decrease of the cluster concentration and an increase of the yr#, percentage have a similar influence on transport properties, the behavior withy of the conductivity of the Pb,_,_,Zr,,_,Bi*,F1+, materials can be explained. For a given n-parameter the maximum of disorder corresponds to the Phi -4x.,3Zrzxn/3Bi,,3F2+~” compositions (Y= x,/3) relative to the value r= 1 of the Bi/Zr ratio (z= l/2). The Lzr phase (y= 0) is characterized by the smallest cluster concentration. y,, must consequently be within the O< ymax
(n=2)
0.118 6x 1O-4 0.37 5.27 0.059
0.236 3x10-4 0.39 5.27 0.118
Table 3 Values of amrfor
(Ml.,=),
(Mz,&,
(%+I
and
BPbSnF4.
%ooK (&I
(MInBi) [5] x”=$/12(n=2) Pbl_~“,,,/JIn4,,,5Bilf~Fz+6~/~ BPbSnF,
x.=J2/12(n=2)
cm)-’
= 1.7x 10-Z =5x1o-2
1101 three phenomena occur simultaneously for the (PbIn-Bi ) compositions, according to the yPb2++yIn3+=2yBi3+ + yF’- substitution process. Within three domains of solid solutions, the highest ionic conductivity is observed for the materials called (Min.zr), (Mzr,si) and (Mrn,Bi) which are characterized by the presence of column clusters of it= 2 dimension (x, = @/ 12) and values of y,, equal respectively to xn/3, x,/5 and x,/5. These phases are among the best fast fluoride ion conductors so far obtained (table 3 ) .
5. Conclusions New fast ionic conductors with the Pb,-,In,,,-,,Zr,,Fz+,(l+,, and Pbl-,Zr,(i-,, BiX,F2+,(2-,) (0 d z B 1) formulations have been found in the PbF2 -InF3-ZrF, and PbF2-ZrF,-BiF, systems. Whatever z, an ionic conductivity maximum appears for x,, and the compositions relative to x,, are characterized by for-
hi. Wahbi et al. /Optimization ofjluoride ion conduction
92
mation of n = 2 extension column clusters. The variation withy of the F- ion conductivity for the Pb,_,1n,_,Zr,F,+,+, and Pb,_,_,Zr,,_, (0 QG x,) series involving clusters of Bi&+2X, similar size has been determined. Materials with the best electrical properties are those for which the Zr/ In and Bi/Zr ratios are close to l/2. ThPan rnnlll+a I llkJk lclUUlLD confirm those previously obtained in investigating the Pb,_-xn_-yInxn_-yBi2yF2+xn+Y solid solutions.
References [ 1 ] J.M. R&m, M. Wahbi, J. SC&as and P. Hagenmuller, Phys. Status Solidi (b) 169 (1992) 331.
[2] J.M. Reau, M.El. Omari, J. S&i&as and P. Hagenmuller, Solid State Ionics 38 ( 1990) 123. [ 31 AK. Cheetham, B.E.F. Fender, B. Steele, R.I. Taylor and B.T.M. Willis, Solid State Commun. 8 ( 1970) 17 1. [ 41 J.M. R&au,J. Se&as and P. Hagenmuller, Proc. ICAM 9 1, EMRS 1991 Conf. A2-V8 (Strasbourg, 1991).
,617,” Wnhh;
TM
7
Phys.
Status
Solidi
(a) 125 (1991) 517. [ 61 S. Kacim, J.C. Champamaud-Mesjard and B. Frit, Rev. Chim. Miner. 19 (1982) 199. [ 71 J.P. Laval, C. Depierretixe, B. Frit and G. Roult, J. Solid State Chem. 54 (1984) 260. [ 8 ] J.M. R&au, J. S&&as, J.P. Lava1 and B. Frit, Solid State Ionics 31 (1988) 147. [ 91 Ph. Darbon, J.M. Reau, P. Hagenmuller, Ch. Depierrefixe, J.P. Laval and B. Frit, Mat. Res. Bull. 16 ( 198 1) 389. [ lo] J.M. RCau, C. Lucat, J. Portier, P. Hagenmuller, L. Cot and S. Vilminot, Mat. Res. Bull. 13 (1978) 877.