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Diffusion and short-range order in Pb1−xInxF2+x (0⩽×⩽0.25) superionic conductor
Solid State lonics 31 (1988) 147-~ 57 North-Holland, Amsterdam
DIFFUSION AND SHORT-RANGE ORDER IN Pb,_~ln~F2+~ (0~
and J.P. LAVAL, B. FRIT Laboratoire de Chimie Min#rale Structurale, 61.4 CNRS no. 320. Universit¢; &, Limoges, 123 A venue A. Thomas, 8 706 0 Limoges Cedex, France
Received 17 June 1988; accep!e4 for publication I 1 October 1988
An investigation is made by 19F NMR of the disordered fluorite-related Pbl_xInxF2+x (0 ~ x ~ 0.25) and the ordered phase Pb2InF 7 (x = 0.33).
solid
solution
Two types of motions have been shown in Pb. In F_ and Pb InF - local mo"ions weakly i x 2+ activation energy activated (E = 0.3 eV ) and long-range motions char~d~erize~ by a clearly 2 7 higher " + (EB = 0.4 - ~.5 eV ) , close to ~Eg T deduced from ionic conductivity measurements. Composition dependence of the diffusio,, factor (Du) has beer! determined Pbl_xZrxF2+2x whose transport properties are very close.
for
Pbl_xInxF2+x
and
Correlations have been established between the composition dependence of electrical properties of Pbl_xInxF2+ x and the formation of clusters "2n+2:3n:2" which are more and ~ore extended when x increases.
1
-
whose
hand, b o t h solid s o l u t i o n s present for a very s m a l l v a l u e of x (x = 0.01) a m a x i m u m of the a c t i v a t i o n e n e r g y ° A E a , associated m x to a minimum of conductlvz[y (5). The e x i s t e n c e a n d the v a l u e of AE have been correlated w i t h the n a t u r e ~ ' t h e point d e f e c t p a i r s (nn or nnn) s u p p o s e d to o c c u r in this c o m p o s i t i o n d o m a i n . 8 PbF 2 , n o m . n a l l y pure or doped, has
fluorite
been
INTRODUCTION
Three phases have been isolated and c h a r a c t e r i z e d w i t h i n the P b F 2 - 1 n F 3 s y s t e m (1,2)
: a disordered
related
solid
anion-excess
solution
Pbl_xInxF2+ x
(0 ~: x ~ 0.27 at 820 K) phases,
P b 2 I n F 7 and
structures
and
two o r d e r e d
Pb7In5F29
are r e l a t e d
fluorite
to the
the
studies Pbl-xInx ?2+x
is a very
good
•
(0 $
x ~
0.50)
igF-NNR
of (6-8).
several The
extensive
value
of
the
in B PbF.
has
anionic
conductor (3) whose c o n d u c t i v i t y is m a x i m u m and a c t i v a t i o n e n e r g y is m i n i m u m for x =0.12 (Fig.l). It has b e e n shown for the PbI_xBZx~2+ x
by
subject
solid
solution,
w h o s e e l e c t r i c a l b e h a v i o r is a n a l o g o u s , that a m a x i m u m of d i s o r d e r a p p e a r s for the composition which involves the best electrical performance (4). On the o t h e r
F- s e l f - d i f f u s i o n
coefficient
been d e t e r m i n e d as a f u n c t i o n of t e m p e rature and the p r o m i n e n t p a r t p ] a y e d by the residual paramacnetic impuritigs has been specified. The different compositions of Pb, In F_ that we have s e l e c t e d for the 9±-x x 2+x 1F-NMR s t u d y c o r r e s p o n d to s u b s t i t u t i o n ranges as x ~ 0.025. Consequently, they
14 8
J.M. Reau et al. / Diffusion and ~ r-,ort-range order in Pb, _ ,In,F2 + . ,
are h e a t e d under a s t r e a m of HF at t = 4 0 0 ° C to e l i m i n a t e t r a c e s of o x y g e n . The s o l i d solutions Pb I InxF2+ x and Pb InF are o b t a i n e d by s y n t h e s i s of starting 2 f l u7o r i d e s in g o l d tubes sealed. The m e a s u r e m e n t s of c o n d u c t i v i t y and N . M . R . are made in i n e r t atmosphere (N2). The stuaied samples correspond to d i f f e r e n t values of x ( 0 . 0 2 5 ; 0.05 ; 0 . i 0 : 0.12 ; 0.15 ; 0.20 ; 0.25) of the Pb In F solid s o l u t i o n and to P b 2 I n F 7 l-x x 2+x (x = 0.33). 19F c o n t i n u o u s wave and p u l s e d N M R s p e c t r a have b e e n m e a s u r e d at 30 MHz (H = 7507 G) with a SWL Bruker o spectrometer, over the temperature range 1 7 0 - 4 8 0 K (i0). F r o m the c o n t i n u o u s r e s o n a n c e s p e c t r a two types of information have been c o l l e c t e d and a n a l y z e d : - the e x p e r i m e n t a l s e c o n d moment (M^ ) • . z exp. M 2 e x p. is g l v e n by the e x p r e s s l o n : +
(o) 2 ,
/
~
~
4
2
3
=
K
/ X |
0.'~0 8E
0.30
'-0.~
(eV.)
(b)
EB
\.
0.40
1/3 M 2 exp.
0.30
X ,
I
0~0 ~ig.i
0.20
- Composition Ph In i-x xr2+x
of
03C
dppendence .
for
a) the ionic c o n d u c t i v i t y at T=423K b) the a c t i v a t i o n e n e r q y (E_ and E B determined by NMP" and ;{ AE OT d e d u c e d from c o n d u c t i v i t y measurements ) .
2 - F~IPERI~tENTAL The
start~inq
fluorides,
PbF~ z
and
InF 3
j
h3g ' (h) dh +
hg'(h)
dh
where h is the algebraic deviation (in Gauss) from the H resonance field and g' (h) the d e r i v e d s ~ g n a l recorded. - the surface of the i n t e g r a u e d line, w h i c h is p r o p o r t i o n a l to the number of r e s o n a n t nuclei. When there is a partial o v e r l a p p i n g of the two curves c o r r e s p o n d i n g to m o b i l e and immobile nuclei, d e c o n v o l u t i o n g i v e s an e v a l u a t i o n of each c o n t r i b u t i o n . C l a s s i c a l p u l s e s e q u e n c e s ~/2 - T - 7 / 2 and 7/2 - T - n h a v e been used for the determination of the spAn-lattice r e l a x a t i o n times T I.
3
belong to the composition range where defect palrs form more and m o r e e x t e n d e d defects (clusters) when x i n c r e a s e s (9). This investigation, by providing substantial information about the conduction mechanlsms, could explain the composition dependence of the transport properties. M o r e o v e r , it a p p e a r e d jud~c!ous to undertake a comparative study of the o r d e r e d phase P b 2 I n F 7.
!
=
-
RESULTS
A - The solid a)
Pulsed
solution
Pbl_xInxF2+ x
resonance
Fig.2 gives the t e m p e r a t u r e d e p e n d e n c e of the ~ v e r s e cf s p i n - l a t t i c e relaxation time (T i ) for d i f f e r e n t compositions of P b l _ x l n x F 2 + x. -i Between 300 and 480 Ks T 1 has an exponential b e h a v i o r and the v a r i a t i o n law determines the activation energy of the m o b i l e fluorine nuclei. The e x i s t e n c e , for e a c h composition, of a r e s i d u a l _ ~ a l u e of T 1 at low t e m p e r a t u r e (i to i0 s ) can be
J.M. Reau et al. / Diffitsion and short-range order in Pb, _.,.In.,.F2+.,.
1000
--
373 323 ' '
273 ,
223 I
19F
198 T(K) ,__
00 = 30 MHz
149
I
321K
• x = 0.025
100
•
x = 0.05
•
x= 0.10; 0.12
•
x= 0.15
o
x= 0.20
•
x = 0.25
303 K
0 253K
..-
I
I
1
3
4
5
~
4~
1000 T(K)
Fig.2
- Temperature relaxation tions
dependence for d i f f e r e n t
-1 of T1 composi-
of P b l _ x I n x F 2 + x.
'i
'
|
-I0 Fig.3
k[0-3/4
Tq 1 =
]rt this
= k ~ -3/4 O
expression~
-3E A exp
[ 1 ] 4kT
k is ~ c o n s t d n t
and
EA T := T exp ~ is the d i f f u s i o n time of m ~ b i l e oions. Consequently the a c t i v a t i o n energy, measured after taking away the c o n t r i b u t i o n of p a r a m a g n e t i c impurities, is equal to 3/4 times the a c t i v a t i o n e n e r g y E A of the a n i o n i c d i f f u s i o n . The values of EA~ so c a l c u l a t e d for each s t u d i e d c o m p o s i t i o n , are g i v e n in Table i. At T ~ 4~,0 K, the a t o m i c d i f f u s i o n is
i
-5
"'
0
- Thermal line
attributed to the p r e s e n c e of very small a m o u n t s of p a r a m a g n e t i c i m p u r i t i e s (ii). In this t e m p e r a t u r e range (T ~ 230 K), the anionic motions are too slow and the relaxation is due to spin diffusion (12,13). Above 300 K, when the motions b e c o m e q u i c k e r with i n c r e a s i n g t e m p e r a t u r e , they c o n t r i b u t e to r e l a x a t i o n which is then thermally activated. In this temperature range w h e r e r e l a x a t i o n is due at the s a m e time to atomic diffusion and spin di{fusion, it has been s h o w n (14,15) that T1 can be e x p r e s s e d as :
210 K
evolution
shape
I
u
5
10
of
the
h(O)
fluorine
for P b 0 . 9 5 1 n 0 . 0 5 F 2 . 0 5 .
very quick. ~D becomes c o m p a r a b l e to the relaxation tlm n T of paramagnetic [ impurities. The ~-x p r e slsii o n . I] is no longer valid and a m a x i m u m of T -I is o b s e r v e d (Fig.2), in agreement w½th theoretical calculations (15). b) C o n t i n u o u s The shape
resonance
thermal
is g i v e n
evolution
of
fluorine
for P b 0 . 9 5 I n 0 . 0 5 F 2 . 0 5
line
in
Fig.3. The o t h e r studied s a m p l e s have an analogous behavior. At low temperature, only a broad line can be observed. At inu~easiny temperature , a b o v e a temperature T , a n a r r o w line c h a r a c t e r i z i n q the A mobile f l u o r i d e ions a p p e a r s and grows at the expense of the broad one. Above a t e m p e r a t u r e T_, the b r o a d line disappears. The v a l u e s o ~ T A and T B r e l a t i v e to each c o m p o s i t i o n are reported in Table i. The fraction f of m o b i l e fluoride ions is g i v e n by them ratio of the area of the n a r r o w line t¢, the area of the whole line. Its t h e r m a l variation is shown in
150
J.M. Reau et al. / Diffusion and short-range order in Pb, _ xln,F~. +,
TABLE
-i (TB-T A) , T 1 max
Values of T A, T B,
, Tma x,
EA
,
EB,
of Pbl_xInxF2+ x - T : temperature T AB : t e m p e r a t u r e
-
-
-i T1
: maximal
1
(EB-E A) and AE(/T for different
compositions
(0 ~< x ~< 0.25).
of appearing of the narrew line. of disappearing of the broad line. -i value of T 1 .
max -1
.
T : t e m p e r a t u r e at which T 1 Is maximum. max - E A : activation energy of anion diffusion. - E and E B : limits of the d i s t r i b u t l o n domain. (~B-EA) : w i d t h of the d i s t r i b u t i o n domain. AE : a c t i v a t i o n energy deduced from conductivity OT -
I x
I
mA
I I
I TB
I
I_ TB-T A
IT11 max
0.025 0.050 0.i00 0.120 0.150 0.200 0.250
87 82 82 82 88 98 103
313 295 285 285 301 313 326
226 213 203 203 213 215 223
175 465 490 490 870 1350 800
Fig.4 for the studied compositions. Whatever sample consldeled, f increases m w~tn temperature, but more or less r e g u l a r l y . O n e c a n s u p p o s e , for t h e s t u d l e d thermal domain, the e x i s t e n c e ¢f d i f f e r e n t e n e r g y b a r r i e r s o p p o s e d to d l s p l a c e m e n t s of m o b i l e ions, i.e. s e v e r a l t y p e s of a n i o n s , each provided w i t h an a c t i v a t i o n energy E (and c o n s e q u e n t l y a correlation time Y = Y exp ~) s u c h as E A < E < E B. U s i n g t h ~ model proposed by Bray et a]. (16) the a l l o w e d v a l u e s o f y .~ lie b e t w e e n t h e c u r v e s = ~ o ~xp =A an~Y = Y e x p EB w i t h kT B o k'~ EA
< EB
(Fig.5).
As
Y A
and
Y B
depend
on
temperature, t h e w i d t h of t h e d i s t r i b u t i o n r a n g e w l l l be a f u n c t i o n of t e m p e r a t u r e . At low t e m p e r a t u r e correlation t i m e s a r e long. When temperature increasus, Y becomes s h o r t e r a n d w h e n it is of th% o r d e r of )-1/2 ....2 e x p , ,motional narrow±ng occurs.if one
measurements.
time, > Y
contribute t9 t h e b r o a d line, w~iie those with 7 < Y contribute to t h e m o t i o n a l ! y O narrowed line. The temperature dependence
I
EA
0.343 0.320 0.265 0.265 0.265 0.291 0.308
430 446 456 456 a53 460 455
I
EB
I
P'B-EA I nso m 0.479 0.430 0.378 0.378 O . 383 0. 391 0. 430
0.132 0.123 0.107 0.107 0.109 0.132 0.143
0.475 0.443 0.372 0.372 0.375 0.423 0.451
fT0[ " 273
T(K)
73
0
%80
0,60
i-
. x = 0.025 I x=005
I
//
[
m x= 0.10;0.12
#"
0,40I
+
×:015
•
x:020
• x: 025
O,20~
~,~
calls y this critical correlation the nuclei characterized by Y
I
I
I I I Tm a x I
Fig.4
L._z'[_/"
,,
,
-50
0
50
I°C) ~
- Thermal variation of the fraction f of mobile fluoride ions for d~fferent compositlon~ of Pb In F. l-x :, z+x"
J.M. Reau et al. / D~f.htsion and short-ran,ee order in Pb, _ ,In,I:,_+,
!5 !
1,001 {'fTf7
0,75
1~~ ......
I .....
I
TA
%
q50
Fig.5
T = 303K
TIK)
- Thermal variation of the correlation times T D a c c o r d i n g to ref. (16).
T = 265K
0,25
T = 273 K T = 258K
of the fraction of mobile ions f is m determined by the variation of the d i s t r i b u t i o n ~ f the c o r r e l a t i o n times w i t h r e s p e c t to T , w h o s e v a l u e is i n d e p e n d e n t of t e m p e r a t u r e (Fig.5~. For T < T all v a l u e s of T D e x c e e d ~ and, t h e r e f o r e , f = 0. For T > T B all values of T D are s~aller than T* and f = i. In the m t e m p e r a t u r e domain TA< T < T B , 0 < fm < 1 is g i v e n by the e x p r e s s l o n : f
= I T ~ ( T ) d T /1 TBG(T)dT m TA TA
[ 2 ]
w h e r e G(T) is the a s s u m e d d i s t r i b u t i o n of c o r r e ] a t i o n times. Selecting a distribution function G(~) v a l i d for all the s t u d i e d s a m p l e s is very difficult as f does not increase m regularly with increasing temperature. Nevertheless the k n o w l e d g e of T A a n d TB allows to c a l c u l a t e the limit a c t i v a t i o n energy EB if EA has been previously determined : EA
.
y
= T ° e x p ~-~ = A T
EB
T o e X p kT B
B
E B : EA 7
[3]
" T = 243K L. . . . . . . .
Fig.6
-
j
J
o.10
0.20
.
I
×
_~
0.30
Composition dependence of f r a c t i o n f of m o b i l e fluoride_ m at diff~rent temperat,'.res Pb I In F . -x x 2+x
the ions for
0.15 w h i c h involve the lowest values of (EB-EA). C o n s e q u e n t l y the anions mobile in these materials are difficult to d i f f e r e n t i a t e on the e n e r g y level, even Jf they b e l o n g to d i f f e r e n t sublattices. On the c o n t r a r y , thermal v a r i a t i o n of f for the o t h e r c o m p o s i t i o n s (x = 0.025, ~ . 0 5 , 0.20 and 0.25) can be s p l i t t e d in three pazts a p p r o x i m a t e l y linear, indicating a c l e a r l y m o r e q u a n t i f i e d d i s t r i b u t i o n of act i v a t i o n energies. The v a r i a t i o n of f as a function of m the substitution rate 2, at different temperatures, is given in Fig.6. As one can see by comparing Fig.l and Fig.6, f changes w i t h x in the same way as th~ transport properties do.
A T a k i n g as l o w e r l l i m i t the value <,f E A ]ete':mined from T1 relaxation mea:~urements, E and the w i d t h of the d i s t r i b u t i o n B
range, (E B - EA) have been c a l c u l a t e d ~ach c o m p c s ] t i o ~ (idble I). The t h e r m a l variation of f in q u a s i - l i n e a r for m compositJonsrelatlv~ to x = 0.10, 0.12
for the and
B - The o r d e r e d Pb2InF7,
phase
Pb2InF 7
isostructural
with
K2NbF 7
(17), c r y s t a l l i z e s i n the m o n o c l i n i c s y s t e m (P21/c) s p a c e group). A p r o j e c t i o n of its s t r u c t u r e on the yOz plan is given in Fig. Ta (2,18). It is an ordered
15 2
J.M. Reau et al. / D(f'li~.don and short-range order in Pb,_ ,h;,l"2 +,
19F 00_-30MHz H0= 7507 G,
a~%.t .~
-,,,! J
"..-,' ,'"
.-'"
%.. ;,%-~
.Q
b%<,'"
.%,-o: ,
,-"
..
_7, '
'"
0:,
"m",~. .-'m;
't
.,.,. ,',,
(':')
"-._>...,,,_V_',j, O --
0 Pb(14)~ pb(34)
~,w,~,.~.~,
~
(b) __
i
i
I
-8 Fig.8
5~ Fig.7
v
7
Projection on the yOz plan of the s t r u c t u r e of P b 2 I n F 7. b) S t r u c t u r a l relations b e t w e e n the monocapped trigonal prism InF 7 and the original cube InF 8.
" ontinuous
resonance
As f]r the d i s o r d e r e d s o l i d solution ~ P b l _ x I r •xF2÷x , three thermal d o m a i n s can be
broad rig:ld
I
I
o
i
i
4
!
i
I
t-
h(G.)
a
- Thermal e v o l u t i o n of the l i n e s h a p e f o r P b 2 I n F 7.
fluorine
P b l _ x I n x F + . On the c o n t r a r y T B is much higher (Table i) and involves a larger difference (T-T ). This result is in a g r e e m e n t w i t ~ t~e t r a n s p o r t p r o p e r t i e s of P b 2 I n F 7 (3). b)
distinc
I
-4
T=210K
- a)
,stlpevst~uctt~-e of fluorite (a ~_ a ; b : 3:1 ~ "~ ; c- . ~ a /'21 n which oa<~h original " E-T. . . . ~: . . . . c u b e InF_ h a s been changed into a mono8 capped t r i g o n a l p r i s m InF 7 by s u b s t i t u t i o n of a t r i a n g u l a r face to a s q u a r e one (Fig 7b) . a)
T= 2 9 4 K
oIn(14) ,In(34)
uished
for
Pb2InF 7
(Fig.8)
:
- when T < T A (T A = 225 K), only a ] ]no characterl, sti c of an anionic [att ce is observed.
- when T < T < T 3 (T B : 476 K) two coexist A: a broa~ line and a narrow one c h a r a c t e r i s t i c of mobile f l u o r i d e ions and growing w i t h increasing t e m p e r a t u r e at the expense of the bro.:~d line.
Pulsed
resonance
In the t h e r m a l domain where two lines are observed, it has: been p o s s i b l e to show two r e l a x a t i o n t i m e s T 1 and T' 1 for P b 2 I n F 7 corresponding
to
free
induction
decays
with,
r e s p e c t i v e l y , a s l o w d e c r e a s e (narrow line) and a quick d e c r e a s e (bro~d line). T h e r m a l v a r i a t i o n of T ] ± and T]' for P b 2 I n F 7 is g i v e n in Fig. 9. An a c t i v a t i o n e n e r g y E = 0.26 eV can A be d e d u c e d from the linear part of the thermal variation of T 1 (curve a) after t a k i n g into a c c o u n t the factor 4/3 linked to paramagnetic impurities. E is low, c l o s e to values o b t a i n e d for th A d i f f e r e n t c o m p o s i t i o n s of P b l _ x I n x F 2 + x and
lines
- Above
']'B' only
The v a l u e l'.< < 1()!~) to) thdt
of
T
the n a r r o w
obtained forA d e t e r m i n e d for
line
is
Pb I n F 2 7
c o r r e s p o n d s l i k e l y to l ~ a l m o t i o n s of f l u o r i d e ions a r o u n d In cations. The interpretation of the thermal v a r i a t i o n of T' 1 (curve b) is a n a l o g o u s to that proposed for Pb In F . After - x . x 2+x coffee.ring for the c o n t r i]butlon oT p a r a m a gnetic impurities (curve c ) a n a c t i v a t i o n e n e r g y E E : 0.56 ~V results from tile linear
.I.M. Rt'atl ('I al. / D@.'fitsiotl and sht,rt-rtm~ ,, order in Pt,, _,/n,l.'2 +,
,;:(4
473 ..J
I
373 I
223
273
I
I
193 T(K)
I
15 3
Fm
|,
%o0 1000
o,5o .
\ \
.
I
__~
t
5
4
t0oo T(K)
- Temperature
depende_~ce
of
and T' 1 (curve for P b 2 I n F 7.
-i T 1
b)
variation to EA,
obtained (curve d). By c o n t r a s t EZ is relatively high and corresponas to long range diffusive motions. The relations p r o p o s e d for tb~ solid solution
I
300
I
......
400
¢,.
T (K )
variations of the fraction mobile fluoride ions for
P~2InF7.
I
(curve a) relaxations
<3/7)
.
Fig.10-Thermal f of
3
Fig.9
.
200
\
t
.
L.I
',
10
b..
.
_J
100
lu)
.
Phl_xInxF2+ x
(T
exp EB. ) are l i k e w i s e o kTB case of Pb2InF 7 (EA/E B =
= T
exp .- .a . . . o kT A verified in the 4
0.464
; TA/T B
- DIFFUSION
PLND C L U S T E R I N G
=
0.473). Of course the d i s t r i b u t i o n range (EB-E A = 0.30 eV.) c a l c u l a t e d for ~ 2 1 n F 7 is very wide, in agreement wi the o b s e r v e d transport properties. The thermal variation of f for m Pb2InF_• is shown in Fig.10. One can nc,ti
[ F ( 1 ) - F ( 2 ) - F ( 3 ) - F ( 4 ) ] forming the square face w h i c h can be considered as located in the normal anionic sites of the fluorite lattice. - the 3 F anions [ F(5)-F(6)-F(7)] constituting tie triangular face, located in the interstitial sites of fluorite lattice. Furthermore, f is nearly constant between 260 and 440 K m If ~ 0.45 (Fig.10)] and very close to f =m3/7. it is ± therefore reasonable to assign the two types of motions observed to these two kinds of anions. An a n a l o g o u s behavlor has been observed for the fluori~e-related ordered s H p o ~ s t r u c t j ~ F'b3Zr!:I0 (19).
The N M R study has a l l o w e d to determine the thermal variation of the fraction of mobile fluoride anions for different c o m p o s i t i o n s of Pbl_xInxF2+ x and for Pb InF 7. Assuming that jumps take place be[ween interstitial sites and empty ncrm/~ ~ites, the average ju,np d i s t a n c e is I =: 9 ~ <° where a is the unit-cell marameter. It ~s then p o s s i b l e to calculate the
J.M. Reau et ai. / D(l.~sion and short-range order in Pb, _ Jn,l~'2 + ,
154
Io9 ,J (sI) x=
0.10;0.12
x=0.15
,x=Q20 x~
n~O
x=0.05 x= 0D,5
<< 33
IZ
\
="
x:Q33
!I !000 T(K)
1000 L/.
2
. . . . . . . .
I
I
2.5
3.5
'
T(K)-
j,
~..
,L.--
2
I
I
I
~5
3
~5
Fig. If- Temperature dependence for different compositions of Pb~_xInxF2+ x and for Pb2InF 7 of : a) the jump frequency v b) the diffusion factor D O .
low temperature (Do=I0-10 cm2/s at 280 K) but inc ea e quickly with temperature : D O ~ 1 0 - ~ c m ~ / s at 480 K. The composition d e p e n d e n c e of log DO at 293 and 500 K is given in Fig. 12 for Pb In F . A maximum, more clearly de}[~edXa{+Xlow than high temperature, is obser~red for 0.i0 ~ x ~ 0.12 , composition for which the activation energies, determined as well by NMP experiments (EA and E H) as by ionic conductivity measurements ~a~: ~ are minima (Fig.l and Table i). So, t~e phase with the hast performance has the largest proportion of mobile fluoride ions, which are characterized by the highest mobility. Moreover, for each composition studied, the valu~ of E , activation energy determined by NMR a n # characteristic of long range motions, is very close to that of £LO~ ,. Therefore, by a n a l o g y with the orderedIphase Pb2InF7, one can suppose, .
. ,
~
,
for
the Pbl_xInxF2+ x solid solutions,the
existence of two types of motions : - local motions, weakly a c t i v a t e d and affecting only the interstitial fluoride anions (F.). - l~ng range motions, more activated, concerning anions belonging to both sublattices F and F and involving then an N i exchange between these sublattices. It appears clearly that optimal conditions of exchange ale obtained for 0.19 ~ x ~ 0.12. Fig.12 gives also the composition depend~nce of log D O at 293 and 500 K for the Pbl_xZrxF2+2x (0 ~ x ~ 0 . 1 8 ) solid solution, whose electrical properties are very close to those of Pbl_xInxF2+ x. Log D O has
been
computed
conductivity
for
Pbl_xZrxF2+2x
and NMR data p r e v i o u s l y
from
J.M. Reau et al. / D~lhtsion and short-range order in Pih _ ,In,F, + ,
155
,o
log D¢(crn2/s)
.0 /
\
Q
(°) x
(b)
O
Pbl.xlnxF2+x
• P%. Z xF-2 '
Fig.13-
a) The
4:4:2
cluster
proposed
for
proposed
for
Pbl_xZrxF2+2x b) The
4:3:2
cluster
Pbl_xInxF2+ x"
when x is smal] (x = 0.02), the defects, ~-'atively little ~xtended, get organized, constituting the 4:4~ basic cluster associating around the Zr ion, 4 vacancies in normal anionic sites, 4 ?'-type and 2 F"-type interstitial anions (Fig. 13a). - when x increases, these clusters~ more and more numerous, agglomerate p r o g r e s s i v e l y into groups of two, three... to produce the beginning of the monodimensional infinlte cluster present in -
10
11 '
.... Fig.12-
X
o,'1o
o:20
Composition dependence of log D O at 293 and 500 K for Pbl_xInxF2+ x and Pbl_xZrxF2+2x"
d e t e r m i n e d (20,21,22). A maximum of log D O a p p e a r s for x = 0.i0, compositio~ which exhibits the best electrical performance. For each gzven composition, the values of log D determined for Pbl_xlnxF2+ x and G Pbl-x ZrxF2+2x are very close and the d i f f u s i o n mechanisms in both solid solutions are p r o b a b l y of the same nature. Examination of the fluorite-related Pb3ZrF 1 and Pb2InF 7 structures has re~eale~ that anion-excess is localized within infinite columns of independent p o l y h e d r a r e s p e c t i v e l y square a n t i p r i s m s [ZrFe ] and m o n o c a p p e d trigonal prisms [InF7] (18)~ The influence of the c o m p o s i t i o n on the transport properties of the Pb Zr F solid solution has been l-x. ~ 2+2x corre±aze~ to the existence of monodimensional clusters whose length increases with the excess of anions (22) :
Pb3ZrF~e
best
e]e
performance
correspond to the composition for which th~ packing, relatively limited, involves the easiest exchange between the two anionic sublattices F. and F.. 1 Taking as elementary cluster in P b l _ x I n x F 2 + x the 4:3:2 cluster associating 3+ around the In ion, 4 vacancies in normal anionic sites, 3F' and 2F" interstitial anions (Fig. 13b), correlations between transport and structural properties analogous to those established for P b l _ x Z r x F 2 } 2 x can be extended to Pb]
In F2+ x . -x T~e thermal variation of the fractzon f of mobile fluorine ions has been m established for the Pbl_xInxF2+x solid solutions (Fig.4)
and
It has been proposed
for
Pb2InF 7
(Fig.10).
for Pb2InF 7 that at
T ~ 260 K,i.e. a temperature of the first slope change,the mobile anions were those located in interstitial sites. The same proposition can be extended to the
.I.M. Reau et al. / D4{fk~'ion and short-range order in Pb, _,In,F,_ + ,
156
compositions of the Pb In F ÷ solid l-x. x 2 x solutionsfor which the thermal varfation of fm is splitted in three approximately linear parts as for P b _ I n F 7. Thus, the 2 fraction f. o f i n t e r s t i t x a l anions can be identifiedlwith the fraction f of mobile anions at the temperature of m the first
o, so
.°'~
slope change for the compositions corresponding t o x = 0 . 0 2 5 , 0 . 0 5 a n d 0.20. The variation o f f. w i t h x, d e t e r m i n e d by t h i s way, is s h o w n l i n Fig.14. The regular increase of f.i w h e n x i n c r e a s e s allows an easy estimation o f f. for t h e w h o l e range of compositions and o# the extent of column clusters built up by the association of the 4:3:2 basic clusters s h o w n in F i g . 1 3 b . The column clusters can be f o r m u l a t e d 2n~: 3n:2 w h e r e n is t h e n u m b e r o f c a t i o n s In , i.e. the n u m b e r o f m o n o c a p p e d trigonal p r i s m s InF_, a n d w h e r e 2n+2, 3n a n d 2 s t a n d 7 for respectively the numbers of anionic vacancies, interstitial fluorine ions of t y p e F' and F". T h e s m a l l e s t clusters are
0,25
X !
0,10
Fig.14-
Composition t i o n f. o f sites and
#or
I
I
0.20
O.3O
dependence anions in
of the fracinterstitial
Pbl_xInxF2+ x
Pb2InF 7
(0~ x~
0.25)
(x = 0 . 3 3 ) .
TABLE
2
Comparison o£ theoretical (calculated on the basis of the 2n+2:3n:2 cluster model) (deduced from NMR experiments) number~i; :~f
"~ ~ " ' ~
I
x
=
O. 025
Theoretical
{ nF,
nF
{
= 0. 125
= 0.050
n
x : 0.I0
1
n x = 0.20
nFi
: estlmated
n
_.9o:30:')~
values
0.64
(cf.
F
= O. 205 1
(n : 3) r n
: O. 300
t { nF, , = 0.067
n* : 1.74 FN n* = 0.36 F&
(n = i0) : 1.58
n
{ nF, :
i. 8 4 5
= 0.15
: 1.56 FN
= FN
{ hE, , = 0.05
cluster
= O. 202 Fi
n
cluster R:Q:2 n : i. 733 F N n = O. 3(> / F
= i. 823
(n = 2)
{
1
values
FN
= 0.075 n
{ nF, : 0.20
F
Experimental
(n = i)
cluster 6:6:2 n F = i. 85 N n
l
{ nF, , = 0.050
1
x
t'bl-xInxl>~2+x"
values
cluster 4:3:2 n = 1.90 FN
FN
= 0.60
{ { nF, , :
text).
and experimental (nF.) sites per
: 0.6?
n
0.04
Fi
.I.M. Reau el al. / Dfftit.sion a n d short-ranee m'th'r in Pt,,
successively formulated : 4:3:2 (n=l), 6:6:2 (n=2), 8:9:2 (n=3)... The numbers of a n i o n s in the n o r m a l (nFN) a n d i n t e r s t i t i a l (nFi) sites per unit f o r m u l a P b l _ x I n x F 2 + x , e x p e r i m e n t a l and c a l c u l a t e d on the basis of the 2 n + 2 : 3 n : 2 c l u s t e r m o d e l can be c o m p a r e d in Table 2. The o b t a i n e d results i n d i c a t e c l e a r l y that the size of these 2n+2:3n:2 clusters i n c r e a s e s w i t h the c o n c e n t r a t i o n x of In 3+ cations. For low values of x, small c l u s t e r s f a v o u r a b l e to a h i g h c o n d u c t i v i t y are p r e s e n t (4:3:2 for x = 0.025, 6:6:2 for x = 0.0~). On the c o n t r a r y the c l u s t e r s present for high v a l u e s of x are large (22:30:2 for x = 0.20). S u c h clusters, v e r y extended, hinder the l o n g range d i f f u s i o n of fluorine ions and a decrease of transport prope£ties is observed when x i n c r e a s e s in the c o m p o s i t i o n d o m a i n (0.12~ x ~ 0.25). The v a l u e s of n F and nFl can be e s t i m a t e d r e s p e c t i v e l y to ~.74 a n d 0.36 (Fig.14) for the composition Pb0.90In0.10F2.10
which
offers
the best
electrical performance. It would so correspond to x = 0.i0 the 8:9:2 c l u s t e r set up by the a s s o c i a t i o n of 3 m o n o c a p p e d trigonal prisms InF_ (Table 2). C o n s e q u e n t l y the best p e r f o r m a n c e , o b t a i n e d for (0.i0 ~ x ~ 0.12), correspond to the compositions for which the 2n+2:3n:2 c l u s t e r s are e n o u g h d e v e l o p e d but not too much structured, l e a d i n g then to a m a x i m u m of d i s o r d e r . (i)
(2)
(3)
(4)
(5)
16)
J. Ravez, J. Darriet, and P. H a g e n m u l l e r , J. S o l i d State Chem.,
R. Von Der M ~ h l l 3,
234
, In, t"r'. ,
15 7
(7)
R.D. Hogg, Phys. Rev.
(8)
R.E. G o r d o n and J.H. J. Phys. C., Solid 3213 (1978).
(9)
i0
S.P. Vernon and V..]accarino Letters, 39, 48! ~ 9 7 7 )
and
P.J. Bendall, C.R.A. Catlow, J. C o r i s h and P.W.M. Jacobs, J. S o l i d State Chem., 51, 159 (1984). -
J. S6n6gas, B. Frit, J. F l u o r i n e
A.
Mikou,
Chem.,
37,
67
Laval
and
(1987).
ii - P. Laborde, G. V i l i e n e u v e and J.M. R6au, Cryst. Lett. Def. and Amorph. 15, 309 (1987).
Mater.,
12 - P.G. De Gennes, J. Phys. Chem. Solids,
7,
345
13 - M.E. R o r s c h a c h Jr., P h y s i c a (Utrecht), 30,
38
(1964).
14 - Y. Roinel and J.P. Winter, J o u r n a l de Physique, 3], 351
(1958).
(]970).
15 - T.T. Phua, B.J. Beaudry, D.T. Peterson, J.R. Torgeson, R.G. Barnes, M. Belhoul, G.A. and E.F.W. Seymour, Phys. Rev., B28, i] (]983) .
Styles
16 - P.J. Bray, D.E. Hintenlang, R.V. Mulkern, S.G. G r e e n b a u m , D.C. Tran and M. Drexhage, J. N o n - C r y s t . Solids, 56, 27 (1983). 17 - G.M. Acta
Brown and L.A. Walke., Cryst., 20, 220 (1960).
19-
Lucat, J. Pottier, J.~1. R6au, H a m e n m u i i e r and J.L. Soubeyroux, Solid State Chem., 32, 279 (1980).
20
~. P. J.
Rhandour, J.M. R6au, S. Matar and Hagenmuller, Phys. Chem. Solids, 47, 587 (1986).
21 - Ph. Darbon, J.M. C. D e p i e r r e f i x e , B. Frit, Mat. Res. Bull.,
Mikkelsen
and
(1977).
}4
(1981).
J. Seneqas, J.P. L~val and B. Frtt. .~. S o l i d State Chem. , 53, 344 (1984) .
C. P. J.
n55
J.P.
18 - P. Frit apd J.P. Laval, J. S o l i d State Chem., 39,
J.M. Reau, S. Matar, S. Kacim, J.C. C h a m p a r n a u d - M e s j a r d and B. Frit, S o l i d State Ionics, 7, 165 (1982).
21,
ii,
(1971)
S. Kacim, J.C. C h a m p a r n a u d - M e s j a r d B. Frit Rev. Chim. Miner., 19, 199 (1982).
J.B. Boyce, J.C. O'Keeffe, S o l i d State Comm.,
Strange, State Phys.,
-- P h . P.
Darbon,
J.M.
ROau
and
Hagenmuller,
Solid
State
Ionics,
2,
13]
(1981).
R6au, P. H a g e n m u l l ~ , J.P. Laval and 16,
389
(1981) .
M. 22 - J. j.
S6n6gas, Fluorine
J.P. LavaL and B. Frit, Chem., 32, 197 (1986) .
DIFFUSION AND SHORT-RANGE ORDER IN Pb,_~ln~F2+~ (0~
and J.P. LAVAL, B. FRIT Laboratoire de Chimie Min#rale Structurale, 61.4 CNRS no. 320. Universit¢; &, Limoges, 123 A venue A. Thomas, 8 706 0 Limoges Cedex, France
Received 17 June 1988; accep!e4 for publication I 1 October 1988
An investigation is made by 19F NMR of the disordered fluorite-related Pbl_xInxF2+x (0 ~ x ~ 0.25) and the ordered phase Pb2InF 7 (x = 0.33).
solid
solution
Two types of motions have been shown in Pb. In F_ and Pb InF - local mo"ions weakly i x 2+ activation energy activated (E = 0.3 eV ) and long-range motions char~d~erize~ by a clearly 2 7 higher " + (EB = 0.4 - ~.5 eV ) , close to ~Eg T deduced from ionic conductivity measurements. Composition dependence of the diffusio,, factor (Du) has beer! determined Pbl_xZrxF2+2x whose transport properties are very close.
for
Pbl_xInxF2+x
and
Correlations have been established between the composition dependence of electrical properties of Pbl_xInxF2+ x and the formation of clusters "2n+2:3n:2" which are more and ~ore extended when x increases.
1
-
whose
hand, b o t h solid s o l u t i o n s present for a very s m a l l v a l u e of x (x = 0.01) a m a x i m u m of the a c t i v a t i o n e n e r g y ° A E a , associated m x to a minimum of conductlvz[y (5). The e x i s t e n c e a n d the v a l u e of AE have been correlated w i t h the n a t u r e ~ ' t h e point d e f e c t p a i r s (nn or nnn) s u p p o s e d to o c c u r in this c o m p o s i t i o n d o m a i n . 8 PbF 2 , n o m . n a l l y pure or doped, has
fluorite
been
INTRODUCTION
Three phases have been isolated and c h a r a c t e r i z e d w i t h i n the P b F 2 - 1 n F 3 s y s t e m (1,2)
: a disordered
related
solid
anion-excess
solution
Pbl_xInxF2+ x
(0 ~: x ~ 0.27 at 820 K) phases,
P b 2 I n F 7 and
structures
and
two o r d e r e d
Pb7In5F29
are r e l a t e d
fluorite
to the
the
studies Pbl-xInx ?2+x
is a very
good
•
(0 $
x ~
0.50)
igF-NNR
of (6-8).
several The
extensive
value
of
the
in B PbF.
has
anionic
conductor (3) whose c o n d u c t i v i t y is m a x i m u m and a c t i v a t i o n e n e r g y is m i n i m u m for x =0.12 (Fig.l). It has b e e n shown for the PbI_xBZx~2+ x
by
subject
solid
solution,
w h o s e e l e c t r i c a l b e h a v i o r is a n a l o g o u s , that a m a x i m u m of d i s o r d e r a p p e a r s for the composition which involves the best electrical performance (4). On the o t h e r
F- s e l f - d i f f u s i o n
coefficient
been d e t e r m i n e d as a f u n c t i o n of t e m p e rature and the p r o m i n e n t p a r t p ] a y e d by the residual paramacnetic impuritigs has been specified. The different compositions of Pb, In F_ that we have s e l e c t e d for the 9±-x x 2+x 1F-NMR s t u d y c o r r e s p o n d to s u b s t i t u t i o n ranges as x ~ 0.025. Consequently, they
14 8
J.M. Reau et al. / Diffusion and ~ r-,ort-range order in Pb, _ ,In,F2 + . ,
are h e a t e d under a s t r e a m of HF at t = 4 0 0 ° C to e l i m i n a t e t r a c e s of o x y g e n . The s o l i d solutions Pb I InxF2+ x and Pb InF are o b t a i n e d by s y n t h e s i s of starting 2 f l u7o r i d e s in g o l d tubes sealed. The m e a s u r e m e n t s of c o n d u c t i v i t y and N . M . R . are made in i n e r t atmosphere (N2). The stuaied samples correspond to d i f f e r e n t values of x ( 0 . 0 2 5 ; 0.05 ; 0 . i 0 : 0.12 ; 0.15 ; 0.20 ; 0.25) of the Pb In F solid s o l u t i o n and to P b 2 I n F 7 l-x x 2+x (x = 0.33). 19F c o n t i n u o u s wave and p u l s e d N M R s p e c t r a have b e e n m e a s u r e d at 30 MHz (H = 7507 G) with a SWL Bruker o spectrometer, over the temperature range 1 7 0 - 4 8 0 K (i0). F r o m the c o n t i n u o u s r e s o n a n c e s p e c t r a two types of information have been c o l l e c t e d and a n a l y z e d : - the e x p e r i m e n t a l s e c o n d moment (M^ ) • . z exp. M 2 e x p. is g l v e n by the e x p r e s s l o n : +
(o) 2 ,
/
~
~
4
2
3
=
K
/ X |
0.'~0 8E
0.30
'-0.~
(eV.)
(b)
EB
\.
0.40
1/3 M 2 exp.
0.30
X ,
I
0~0 ~ig.i
0.20
- Composition Ph In i-x xr2+x
of
03C
dppendence .
for
a) the ionic c o n d u c t i v i t y at T=423K b) the a c t i v a t i o n e n e r q y (E_ and E B determined by NMP" and ;{ AE OT d e d u c e d from c o n d u c t i v i t y measurements ) .
2 - F~IPERI~tENTAL The
start~inq
fluorides,
PbF~ z
and
InF 3
j
h3g ' (h) dh +
hg'(h)
dh
where h is the algebraic deviation (in Gauss) from the H resonance field and g' (h) the d e r i v e d s ~ g n a l recorded. - the surface of the i n t e g r a u e d line, w h i c h is p r o p o r t i o n a l to the number of r e s o n a n t nuclei. When there is a partial o v e r l a p p i n g of the two curves c o r r e s p o n d i n g to m o b i l e and immobile nuclei, d e c o n v o l u t i o n g i v e s an e v a l u a t i o n of each c o n t r i b u t i o n . C l a s s i c a l p u l s e s e q u e n c e s ~/2 - T - 7 / 2 and 7/2 - T - n h a v e been used for the determination of the spAn-lattice r e l a x a t i o n times T I.
3
belong to the composition range where defect palrs form more and m o r e e x t e n d e d defects (clusters) when x i n c r e a s e s (9). This investigation, by providing substantial information about the conduction mechanlsms, could explain the composition dependence of the transport properties. M o r e o v e r , it a p p e a r e d jud~c!ous to undertake a comparative study of the o r d e r e d phase P b 2 I n F 7.
!
=
-
RESULTS
A - The solid a)
Pulsed
solution
Pbl_xInxF2+ x
resonance
Fig.2 gives the t e m p e r a t u r e d e p e n d e n c e of the ~ v e r s e cf s p i n - l a t t i c e relaxation time (T i ) for d i f f e r e n t compositions of P b l _ x l n x F 2 + x. -i Between 300 and 480 Ks T 1 has an exponential b e h a v i o r and the v a r i a t i o n law determines the activation energy of the m o b i l e fluorine nuclei. The e x i s t e n c e , for e a c h composition, of a r e s i d u a l _ ~ a l u e of T 1 at low t e m p e r a t u r e (i to i0 s ) can be
J.M. Reau et al. / Diffitsion and short-range order in Pb, _.,.In.,.F2+.,.
1000
--
373 323 ' '
273 ,
223 I
19F
198 T(K) ,__
00 = 30 MHz
149
I
321K
• x = 0.025
100
•
x = 0.05
•
x= 0.10; 0.12
•
x= 0.15
o
x= 0.20
•
x = 0.25
303 K
0 253K
..-
I
I
1
3
4
5
~
4~
1000 T(K)
Fig.2
- Temperature relaxation tions
dependence for d i f f e r e n t
-1 of T1 composi-
of P b l _ x I n x F 2 + x.
'i
'
|
-I0 Fig.3
k[0-3/4
Tq 1 =
]rt this
= k ~ -3/4 O
expression~
-3E A exp
[ 1 ] 4kT
k is ~ c o n s t d n t
and
EA T := T exp ~ is the d i f f u s i o n time of m ~ b i l e oions. Consequently the a c t i v a t i o n energy, measured after taking away the c o n t r i b u t i o n of p a r a m a g n e t i c impurities, is equal to 3/4 times the a c t i v a t i o n e n e r g y E A of the a n i o n i c d i f f u s i o n . The values of EA~ so c a l c u l a t e d for each s t u d i e d c o m p o s i t i o n , are g i v e n in Table i. At T ~ 4~,0 K, the a t o m i c d i f f u s i o n is
i
-5
"'
0
- Thermal line
attributed to the p r e s e n c e of very small a m o u n t s of p a r a m a g n e t i c i m p u r i t i e s (ii). In this t e m p e r a t u r e range (T ~ 230 K), the anionic motions are too slow and the relaxation is due to spin diffusion (12,13). Above 300 K, when the motions b e c o m e q u i c k e r with i n c r e a s i n g t e m p e r a t u r e , they c o n t r i b u t e to r e l a x a t i o n which is then thermally activated. In this temperature range w h e r e r e l a x a t i o n is due at the s a m e time to atomic diffusion and spin di{fusion, it has been s h o w n (14,15) that T1 can be e x p r e s s e d as :
210 K
evolution
shape
I
u
5
10
of
the
h(O)
fluorine
for P b 0 . 9 5 1 n 0 . 0 5 F 2 . 0 5 .
very quick. ~D becomes c o m p a r a b l e to the relaxation tlm n T of paramagnetic [ impurities. The ~-x p r e slsii o n . I] is no longer valid and a m a x i m u m of T -I is o b s e r v e d (Fig.2), in agreement w½th theoretical calculations (15). b) C o n t i n u o u s The shape
resonance
thermal
is g i v e n
evolution
of
fluorine
for P b 0 . 9 5 I n 0 . 0 5 F 2 . 0 5
line
in
Fig.3. The o t h e r studied s a m p l e s have an analogous behavior. At low temperature, only a broad line can be observed. At inu~easiny temperature , a b o v e a temperature T , a n a r r o w line c h a r a c t e r i z i n q the A mobile f l u o r i d e ions a p p e a r s and grows at the expense of the broad one. Above a t e m p e r a t u r e T_, the b r o a d line disappears. The v a l u e s o ~ T A and T B r e l a t i v e to each c o m p o s i t i o n are reported in Table i. The fraction f of m o b i l e fluoride ions is g i v e n by them ratio of the area of the n a r r o w line t¢, the area of the whole line. Its t h e r m a l variation is shown in
150
J.M. Reau et al. / Diffusion and short-range order in Pb, _ xln,F~. +,
TABLE
-i (TB-T A) , T 1 max
Values of T A, T B,
, Tma x,
EA
,
EB,
of Pbl_xInxF2+ x - T : temperature T AB : t e m p e r a t u r e
-
-
-i T1
: maximal
1
(EB-E A) and AE(/T for different
compositions
(0 ~< x ~< 0.25).
of appearing of the narrew line. of disappearing of the broad line. -i value of T 1 .
max -1
.
T : t e m p e r a t u r e at which T 1 Is maximum. max - E A : activation energy of anion diffusion. - E and E B : limits of the d i s t r i b u t l o n domain. (~B-EA) : w i d t h of the d i s t r i b u t i o n domain. AE : a c t i v a t i o n energy deduced from conductivity OT -
I x
I
mA
I I
I TB
I
I_ TB-T A
IT11 max
0.025 0.050 0.i00 0.120 0.150 0.200 0.250
87 82 82 82 88 98 103
313 295 285 285 301 313 326
226 213 203 203 213 215 223
175 465 490 490 870 1350 800
Fig.4 for the studied compositions. Whatever sample consldeled, f increases m w~tn temperature, but more or less r e g u l a r l y . O n e c a n s u p p o s e , for t h e s t u d l e d thermal domain, the e x i s t e n c e ¢f d i f f e r e n t e n e r g y b a r r i e r s o p p o s e d to d l s p l a c e m e n t s of m o b i l e ions, i.e. s e v e r a l t y p e s of a n i o n s , each provided w i t h an a c t i v a t i o n energy E (and c o n s e q u e n t l y a correlation time Y = Y exp ~) s u c h as E A < E < E B. U s i n g t h ~ model proposed by Bray et a]. (16) the a l l o w e d v a l u e s o f y .~ lie b e t w e e n t h e c u r v e s = ~ o ~xp =A an~Y = Y e x p EB w i t h kT B o k'~ EA
< EB
(Fig.5).
As
Y A
and
Y B
depend
on
temperature, t h e w i d t h of t h e d i s t r i b u t i o n r a n g e w l l l be a f u n c t i o n of t e m p e r a t u r e . At low t e m p e r a t u r e correlation t i m e s a r e long. When temperature increasus, Y becomes s h o r t e r a n d w h e n it is of th% o r d e r of )-1/2 ....2 e x p , ,motional narrow±ng occurs.if one
measurements.
time, > Y
contribute t9 t h e b r o a d line, w~iie those with 7 < Y contribute to t h e m o t i o n a l ! y O narrowed line. The temperature dependence
I
EA
0.343 0.320 0.265 0.265 0.265 0.291 0.308
430 446 456 456 a53 460 455
I
EB
I
P'B-EA I nso m 0.479 0.430 0.378 0.378 O . 383 0. 391 0. 430
0.132 0.123 0.107 0.107 0.109 0.132 0.143
0.475 0.443 0.372 0.372 0.375 0.423 0.451
fT0[ " 273
T(K)
73
0
%80
0,60
i-
. x = 0.025 I x=005
I
//
[
m x= 0.10;0.12
#"
0,40I
+
×:015
•
x:020
• x: 025
O,20~
~,~
calls y this critical correlation the nuclei characterized by Y
I
I
I I I Tm a x I
Fig.4
L._z'[_/"
,,
,
-50
0
50
I°C) ~
- Thermal variation of the fraction f of mobile fluoride ions for d~fferent compositlon~ of Pb In F. l-x :, z+x"
J.M. Reau et al. / D~f.htsion and short-ran,ee order in Pb, _ ,In,I:,_+,
!5 !
1,001 {'fTf7
0,75
1~~ ......
I .....
I
TA
%
q50
Fig.5
T = 303K
TIK)
- Thermal variation of the correlation times T D a c c o r d i n g to ref. (16).
T = 265K
0,25
T = 273 K T = 258K
of the fraction of mobile ions f is m determined by the variation of the d i s t r i b u t i o n ~ f the c o r r e l a t i o n times w i t h r e s p e c t to T , w h o s e v a l u e is i n d e p e n d e n t of t e m p e r a t u r e (Fig.5~. For T < T all v a l u e s of T D e x c e e d ~ and, t h e r e f o r e , f = 0. For T > T B all values of T D are s~aller than T* and f = i. In the m t e m p e r a t u r e domain TA< T < T B , 0 < fm < 1 is g i v e n by the e x p r e s s l o n : f
= I T ~ ( T ) d T /1 TBG(T)dT m TA TA
[ 2 ]
w h e r e G(T) is the a s s u m e d d i s t r i b u t i o n of c o r r e ] a t i o n times. Selecting a distribution function G(~) v a l i d for all the s t u d i e d s a m p l e s is very difficult as f does not increase m regularly with increasing temperature. Nevertheless the k n o w l e d g e of T A a n d TB allows to c a l c u l a t e the limit a c t i v a t i o n energy EB if EA has been previously determined : EA
.
y
= T ° e x p ~-~ = A T
EB
T o e X p kT B
B
E B : EA 7
[3]
" T = 243K L. . . . . . . .
Fig.6
-
j
J
o.10
0.20
.
I
×
_~
0.30
Composition dependence of f r a c t i o n f of m o b i l e fluoride_ m at diff~rent temperat,'.res Pb I In F . -x x 2+x
the ions for
0.15 w h i c h involve the lowest values of (EB-EA). C o n s e q u e n t l y the anions mobile in these materials are difficult to d i f f e r e n t i a t e on the e n e r g y level, even Jf they b e l o n g to d i f f e r e n t sublattices. On the c o n t r a r y , thermal v a r i a t i o n of f for the o t h e r c o m p o s i t i o n s (x = 0.025, ~ . 0 5 , 0.20 and 0.25) can be s p l i t t e d in three pazts a p p r o x i m a t e l y linear, indicating a c l e a r l y m o r e q u a n t i f i e d d i s t r i b u t i o n of act i v a t i o n energies. The v a r i a t i o n of f as a function of m the substitution rate 2, at different temperatures, is given in Fig.6. As one can see by comparing Fig.l and Fig.6, f changes w i t h x in the same way as th~ transport properties do.
A T a k i n g as l o w e r l l i m i t the value <,f E A ]ete':mined from T1 relaxation mea:~urements, E and the w i d t h of the d i s t r i b u t i o n B
range, (E B - EA) have been c a l c u l a t e d ~ach c o m p c s ] t i o ~ (idble I). The t h e r m a l variation of f in q u a s i - l i n e a r for m compositJonsrelatlv~ to x = 0.10, 0.12
for the and
B - The o r d e r e d Pb2InF7,
phase
Pb2InF 7
isostructural
with
K2NbF 7
(17), c r y s t a l l i z e s i n the m o n o c l i n i c s y s t e m (P21/c) s p a c e group). A p r o j e c t i o n of its s t r u c t u r e on the yOz plan is given in Fig. Ta (2,18). It is an ordered
15 2
J.M. Reau et al. / D(f'li~.don and short-range order in Pb,_ ,h;,l"2 +,
19F 00_-30MHz H0= 7507 G,
a~%.t .~
-,,,! J
"..-,' ,'"
.-'"
%.. ;,%-~
.Q
b%<,'"
.%,-o: ,
,-"
..
_7, '
'"
0:,
"m",~. .-'m;
't
.,.,. ,',,
(':')
"-._>...,,,_V_',j, O --
0 Pb(14)~ pb(34)
~,w,~,.~.~,
~
(b) __
i
i
I
-8 Fig.8
5~ Fig.7
v
7
Projection on the yOz plan of the s t r u c t u r e of P b 2 I n F 7. b) S t r u c t u r a l relations b e t w e e n the monocapped trigonal prism InF 7 and the original cube InF 8.
" ontinuous
resonance
As f]r the d i s o r d e r e d s o l i d solution ~ P b l _ x I r •xF2÷x , three thermal d o m a i n s can be
broad rig:ld
I
I
o
i
i
4
!
i
I
t-
h(G.)
a
- Thermal e v o l u t i o n of the l i n e s h a p e f o r P b 2 I n F 7.
fluorine
P b l _ x I n x F + . On the c o n t r a r y T B is much higher (Table i) and involves a larger difference (T-T ). This result is in a g r e e m e n t w i t ~ t~e t r a n s p o r t p r o p e r t i e s of P b 2 I n F 7 (3). b)
distinc
I
-4
T=210K
- a)
,stlpevst~uctt~-e of fluorite (a ~_ a ; b : 3:1 ~ "~ ; c- . ~ a /'21 n which oa<~h original " E-T. . . . ~: . . . . c u b e InF_ h a s been changed into a mono8 capped t r i g o n a l p r i s m InF 7 by s u b s t i t u t i o n of a t r i a n g u l a r face to a s q u a r e one (Fig 7b) . a)
T= 2 9 4 K
oIn(14) ,In(34)
uished
for
Pb2InF 7
(Fig.8)
:
- when T < T A (T A = 225 K), only a ] ]no characterl, sti c of an anionic [att ce is observed.
- when T < T < T 3 (T B : 476 K) two coexist A: a broa~ line and a narrow one c h a r a c t e r i s t i c of mobile f l u o r i d e ions and growing w i t h increasing t e m p e r a t u r e at the expense of the bro.:~d line.
Pulsed
resonance
In the t h e r m a l domain where two lines are observed, it has: been p o s s i b l e to show two r e l a x a t i o n t i m e s T 1 and T' 1 for P b 2 I n F 7 corresponding
to
free
induction
decays
with,
r e s p e c t i v e l y , a s l o w d e c r e a s e (narrow line) and a quick d e c r e a s e (bro~d line). T h e r m a l v a r i a t i o n of T ] ± and T]' for P b 2 I n F 7 is g i v e n in Fig. 9. An a c t i v a t i o n e n e r g y E = 0.26 eV can A be d e d u c e d from the linear part of the thermal variation of T 1 (curve a) after t a k i n g into a c c o u n t the factor 4/3 linked to paramagnetic impurities. E is low, c l o s e to values o b t a i n e d for th A d i f f e r e n t c o m p o s i t i o n s of P b l _ x I n x F 2 + x and
lines
- Above
']'B' only
The v a l u e l'.< < 1()!~) to) thdt
of
T
the n a r r o w
obtained forA d e t e r m i n e d for
line
is
Pb I n F 2 7
c o r r e s p o n d s l i k e l y to l ~ a l m o t i o n s of f l u o r i d e ions a r o u n d In cations. The interpretation of the thermal v a r i a t i o n of T' 1 (curve b) is a n a l o g o u s to that proposed for Pb In F . After - x . x 2+x coffee.ring for the c o n t r i]butlon oT p a r a m a gnetic impurities (curve c ) a n a c t i v a t i o n e n e r g y E E : 0.56 ~V results from tile linear
.I.M. Rt'atl ('I al. / D@.'fitsiotl and sht,rt-rtm~ ,, order in Pt,, _,/n,l.'2 +,
,;:(4
473 ..J
I
373 I
223
273
I
I
193 T(K)
I
15 3
Fm
|,
%o0 1000
o,5o .
\ \
.
I
__~
t
5
4
t0oo T(K)
- Temperature
depende_~ce
of
and T' 1 (curve for P b 2 I n F 7.
-i T 1
b)
variation to EA,
obtained (curve d). By c o n t r a s t EZ is relatively high and corresponas to long range diffusive motions. The relations p r o p o s e d for tb~ solid solution
I
300
I
......
400
¢,.
T (K )
variations of the fraction mobile fluoride ions for
P~2InF7.
I
(curve a) relaxations
<3/7)
.
Fig.10-Thermal f of
3
Fig.9
.
200
\
t
.
L.I
',
10
b..
.
_J
100
lu)
.
Phl_xInxF2+ x
(T
exp EB. ) are l i k e w i s e o kTB case of Pb2InF 7 (EA/E B =
= T
exp .- .a . . . o kT A verified in the 4
0.464
; TA/T B
- DIFFUSION
PLND C L U S T E R I N G
=
0.473). Of course the d i s t r i b u t i o n range (EB-E A = 0.30 eV.) c a l c u l a t e d for ~ 2 1 n F 7 is very wide, in agreement wi the o b s e r v e d transport properties. The thermal variation of f for m Pb2InF_• is shown in Fig.10. One can nc,ti
[ F ( 1 ) - F ( 2 ) - F ( 3 ) - F ( 4 ) ] forming the square face w h i c h can be considered as located in the normal anionic sites of the fluorite lattice. - the 3 F anions [ F(5)-F(6)-F(7)] constituting tie triangular face, located in the interstitial sites of fluorite lattice. Furthermore, f is nearly constant between 260 and 440 K m If ~ 0.45 (Fig.10)] and very close to f =m3/7. it is ± therefore reasonable to assign the two types of motions observed to these two kinds of anions. An a n a l o g o u s behavlor has been observed for the fluori~e-related ordered s H p o ~ s t r u c t j ~ F'b3Zr!:I0 (19).
The N M R study has a l l o w e d to determine the thermal variation of the fraction of mobile fluoride anions for different c o m p o s i t i o n s of Pbl_xInxF2+ x and for Pb InF 7. Assuming that jumps take place be[ween interstitial sites and empty ncrm/~ ~ites, the average ju,np d i s t a n c e is I =: 9 ~ <° where a is the unit-cell marameter. It ~s then p o s s i b l e to calculate the
J.M. Reau et ai. / D(l.~sion and short-range order in Pb, _ Jn,l~'2 + ,
154
Io9 ,J (sI) x=
0.10;0.12
x=0.15
,x=Q20 x~
n~O
x=0.05 x= 0D,5
<< 33
IZ
\
="
x:Q33
!I !000 T(K)
1000 L/.
2
. . . . . . . .
I
I
2.5
3.5
'
T(K)-
j,
~..
,L.--
2
I
I
I
~5
3
~5
Fig. If- Temperature dependence for different compositions of Pb~_xInxF2+ x and for Pb2InF 7 of : a) the jump frequency v b) the diffusion factor D O .
low temperature (Do=I0-10 cm2/s at 280 K) but inc ea e quickly with temperature : D O ~ 1 0 - ~ c m ~ / s at 480 K. The composition d e p e n d e n c e of log DO at 293 and 500 K is given in Fig. 12 for Pb In F . A maximum, more clearly de}[~edXa{+Xlow than high temperature, is obser~red for 0.i0 ~ x ~ 0.12 , composition for which the activation energies, determined as well by NMP experiments (EA and E H) as by ionic conductivity measurements ~a~: ~ are minima (Fig.l and Table i). So, t~e phase with the hast performance has the largest proportion of mobile fluoride ions, which are characterized by the highest mobility. Moreover, for each composition studied, the valu~ of E , activation energy determined by NMR a n # characteristic of long range motions, is very close to that of £LO~ ,. Therefore, by a n a l o g y with the orderedIphase Pb2InF7, one can suppose, .
. ,
~
,
for
the Pbl_xInxF2+ x solid solutions,the
existence of two types of motions : - local motions, weakly a c t i v a t e d and affecting only the interstitial fluoride anions (F.). - l~ng range motions, more activated, concerning anions belonging to both sublattices F and F and involving then an N i exchange between these sublattices. It appears clearly that optimal conditions of exchange ale obtained for 0.19 ~ x ~ 0.12. Fig.12 gives also the composition depend~nce of log D O at 293 and 500 K for the Pbl_xZrxF2+2x (0 ~ x ~ 0 . 1 8 ) solid solution, whose electrical properties are very close to those of Pbl_xInxF2+ x. Log D O has
been
computed
conductivity
for
Pbl_xZrxF2+2x
and NMR data p r e v i o u s l y
from
J.M. Reau et al. / D~lhtsion and short-range order in Pih _ ,In,F, + ,
155
,o
log D¢(crn2/s)
.0 /
\
Q
(°) x
(b)
O
Pbl.xlnxF2+x
• P%. Z xF-2 '
Fig.13-
a) The
4:4:2
cluster
proposed
for
proposed
for
Pbl_xZrxF2+2x b) The
4:3:2
cluster
Pbl_xInxF2+ x"
when x is smal] (x = 0.02), the defects, ~-'atively little ~xtended, get organized, constituting the 4:4~ basic cluster associating around the Zr ion, 4 vacancies in normal anionic sites, 4 ?'-type and 2 F"-type interstitial anions (Fig. 13a). - when x increases, these clusters~ more and more numerous, agglomerate p r o g r e s s i v e l y into groups of two, three... to produce the beginning of the monodimensional infinlte cluster present in -
10
11 '
.... Fig.12-
X
o,'1o
o:20
Composition dependence of log D O at 293 and 500 K for Pbl_xInxF2+ x and Pbl_xZrxF2+2x"
d e t e r m i n e d (20,21,22). A maximum of log D O a p p e a r s for x = 0.i0, compositio~ which exhibits the best electrical performance. For each gzven composition, the values of log D determined for Pbl_xlnxF2+ x and G Pbl-x ZrxF2+2x are very close and the d i f f u s i o n mechanisms in both solid solutions are p r o b a b l y of the same nature. Examination of the fluorite-related Pb3ZrF 1 and Pb2InF 7 structures has re~eale~ that anion-excess is localized within infinite columns of independent p o l y h e d r a r e s p e c t i v e l y square a n t i p r i s m s [ZrFe ] and m o n o c a p p e d trigonal prisms [InF7] (18)~ The influence of the c o m p o s i t i o n on the transport properties of the Pb Zr F solid solution has been l-x. ~ 2+2x corre±aze~ to the existence of monodimensional clusters whose length increases with the excess of anions (22) :
Pb3ZrF~e
best
e]e
performance
correspond to the composition for which th~ packing, relatively limited, involves the easiest exchange between the two anionic sublattices F. and F.. 1 Taking as elementary cluster in P b l _ x I n x F 2 + x the 4:3:2 cluster associating 3+ around the In ion, 4 vacancies in normal anionic sites, 3F' and 2F" interstitial anions (Fig. 13b), correlations between transport and structural properties analogous to those established for P b l _ x Z r x F 2 } 2 x can be extended to Pb]
In F2+ x . -x T~e thermal variation of the fractzon f of mobile fluorine ions has been m established for the Pbl_xInxF2+x solid solutions (Fig.4)
and
It has been proposed
for
Pb2InF 7
(Fig.10).
for Pb2InF 7 that at
T ~ 260 K,i.e. a temperature of the first slope change,the mobile anions were those located in interstitial sites. The same proposition can be extended to the
.I.M. Reau et al. / D4{fk~'ion and short-range order in Pb, _,In,F,_ + ,
156
compositions of the Pb In F ÷ solid l-x. x 2 x solutionsfor which the thermal varfation of fm is splitted in three approximately linear parts as for P b _ I n F 7. Thus, the 2 fraction f. o f i n t e r s t i t x a l anions can be identifiedlwith the fraction f of mobile anions at the temperature of m the first
o, so
.°'~
slope change for the compositions corresponding t o x = 0 . 0 2 5 , 0 . 0 5 a n d 0.20. The variation o f f. w i t h x, d e t e r m i n e d by t h i s way, is s h o w n l i n Fig.14. The regular increase of f.i w h e n x i n c r e a s e s allows an easy estimation o f f. for t h e w h o l e range of compositions and o# the extent of column clusters built up by the association of the 4:3:2 basic clusters s h o w n in F i g . 1 3 b . The column clusters can be f o r m u l a t e d 2n~: 3n:2 w h e r e n is t h e n u m b e r o f c a t i o n s In , i.e. the n u m b e r o f m o n o c a p p e d trigonal p r i s m s InF_, a n d w h e r e 2n+2, 3n a n d 2 s t a n d 7 for respectively the numbers of anionic vacancies, interstitial fluorine ions of t y p e F' and F". T h e s m a l l e s t clusters are
0,25
X !
0,10
Fig.14-
Composition t i o n f. o f sites and
#or
I
I
0.20
O.3O
dependence anions in
of the fracinterstitial
Pbl_xInxF2+ x
Pb2InF 7
(0~ x~
0.25)
(x = 0 . 3 3 ) .
TABLE
2
Comparison o£ theoretical (calculated on the basis of the 2n+2:3n:2 cluster model) (deduced from NMR experiments) number~i; :~f
"~ ~ " ' ~
I
x
=
O. 025
Theoretical
{ nF,
nF
{
= 0. 125
= 0.050
n
x : 0.I0
1
n x = 0.20
nFi
: estlmated
n
_.9o:30:')~
values
0.64
(cf.
F
= O. 205 1
(n : 3) r n
: O. 300
t { nF, , = 0.067
n* : 1.74 FN n* = 0.36 F&
(n = i0) : 1.58
n
{ nF, :
i. 8 4 5
= 0.15
: 1.56 FN
= FN
{ hE, , = 0.05
cluster
= O. 202 Fi
n
cluster R:Q:2 n : i. 733 F N n = O. 3(> / F
= i. 823
(n = 2)
{
1
values
FN
= 0.075 n
{ nF, : 0.20
F
Experimental
(n = i)
cluster 6:6:2 n F = i. 85 N n
l
{ nF, , = 0.050
1
x
t'bl-xInxl>~2+x"
values
cluster 4:3:2 n = 1.90 FN
FN
= 0.60
{ { nF, , :
text).
and experimental (nF.) sites per
: 0.6?
n
0.04
Fi
.I.M. Reau el al. / Dfftit.sion a n d short-ranee m'th'r in Pt,,
successively formulated : 4:3:2 (n=l), 6:6:2 (n=2), 8:9:2 (n=3)... The numbers of a n i o n s in the n o r m a l (nFN) a n d i n t e r s t i t i a l (nFi) sites per unit f o r m u l a P b l _ x I n x F 2 + x , e x p e r i m e n t a l and c a l c u l a t e d on the basis of the 2 n + 2 : 3 n : 2 c l u s t e r m o d e l can be c o m p a r e d in Table 2. The o b t a i n e d results i n d i c a t e c l e a r l y that the size of these 2n+2:3n:2 clusters i n c r e a s e s w i t h the c o n c e n t r a t i o n x of In 3+ cations. For low values of x, small c l u s t e r s f a v o u r a b l e to a h i g h c o n d u c t i v i t y are p r e s e n t (4:3:2 for x = 0.025, 6:6:2 for x = 0.0~). On the c o n t r a r y the c l u s t e r s present for high v a l u e s of x are large (22:30:2 for x = 0.20). S u c h clusters, v e r y extended, hinder the l o n g range d i f f u s i o n of fluorine ions and a decrease of transport prope£ties is observed when x i n c r e a s e s in the c o m p o s i t i o n d o m a i n (0.12~ x ~ 0.25). The v a l u e s of n F and nFl can be e s t i m a t e d r e s p e c t i v e l y to ~.74 a n d 0.36 (Fig.14) for the composition Pb0.90In0.10F2.10
which
offers
the best
electrical performance. It would so correspond to x = 0.i0 the 8:9:2 c l u s t e r set up by the a s s o c i a t i o n of 3 m o n o c a p p e d trigonal prisms InF_ (Table 2). C o n s e q u e n t l y the best p e r f o r m a n c e , o b t a i n e d for (0.i0 ~ x ~ 0.12), correspond to the compositions for which the 2n+2:3n:2 c l u s t e r s are e n o u g h d e v e l o p e d but not too much structured, l e a d i n g then to a m a x i m u m of d i s o r d e r . (i)
(2)
(3)
(4)
(5)
16)
J. Ravez, J. Darriet, and P. H a g e n m u l l e r , J. S o l i d State Chem.,
R. Von Der M ~ h l l 3,
234
, In, t"r'. ,
15 7
(7)
R.D. Hogg, Phys. Rev.
(8)
R.E. G o r d o n and J.H. J. Phys. C., Solid 3213 (1978).
(9)
i0
S.P. Vernon and V..]accarino Letters, 39, 48! ~ 9 7 7 )
and
P.J. Bendall, C.R.A. Catlow, J. C o r i s h and P.W.M. Jacobs, J. S o l i d State Chem., 51, 159 (1984). -
J. S6n6gas, B. Frit, J. F l u o r i n e
A.
Mikou,
Chem.,
37,
67
Laval
and
(1987).
ii - P. Laborde, G. V i l i e n e u v e and J.M. R6au, Cryst. Lett. Def. and Amorph. 15, 309 (1987).
Mater.,
12 - P.G. De Gennes, J. Phys. Chem. Solids,
7,
345
13 - M.E. R o r s c h a c h Jr., P h y s i c a (Utrecht), 30,
38
(1964).
14 - Y. Roinel and J.P. Winter, J o u r n a l de Physique, 3], 351
(1958).
(]970).
15 - T.T. Phua, B.J. Beaudry, D.T. Peterson, J.R. Torgeson, R.G. Barnes, M. Belhoul, G.A. and E.F.W. Seymour, Phys. Rev., B28, i] (]983) .
Styles
16 - P.J. Bray, D.E. Hintenlang, R.V. Mulkern, S.G. G r e e n b a u m , D.C. Tran and M. Drexhage, J. N o n - C r y s t . Solids, 56, 27 (1983). 17 - G.M. Acta
Brown and L.A. Walke., Cryst., 20, 220 (1960).
19-
Lucat, J. Pottier, J.~1. R6au, H a m e n m u i i e r and J.L. Soubeyroux, Solid State Chem., 32, 279 (1980).
20
~. P. J.
Rhandour, J.M. R6au, S. Matar and Hagenmuller, Phys. Chem. Solids, 47, 587 (1986).
21 - Ph. Darbon, J.M. C. D e p i e r r e f i x e , B. Frit, Mat. Res. Bull.,
Mikkelsen
and
(1977).
}4
(1981).
J. Seneqas, J.P. L~val and B. Frtt. .~. S o l i d State Chem. , 53, 344 (1984) .
C. P. J.
n55
J.P.
18 - P. Frit apd J.P. Laval, J. S o l i d State Chem., 39,
J.M. Reau, S. Matar, S. Kacim, J.C. C h a m p a r n a u d - M e s j a r d and B. Frit, S o l i d State Ionics, 7, 165 (1982).
21,
ii,
(1971)
S. Kacim, J.C. C h a m p a r n a u d - M e s j a r d B. Frit Rev. Chim. Miner., 19, 199 (1982).
J.B. Boyce, J.C. O'Keeffe, S o l i d State Comm.,
Strange, State Phys.,
-- P h . P.
Darbon,
J.M.
ROau
and
Hagenmuller,
Solid
State
Ionics,
2,
13]
(1981).
R6au, P. H a g e n m u l l ~ , J.P. Laval and 16,
389
(1981) .
M. 22 - J. j.
S6n6gas, Fluorine
J.P. LavaL and B. Frit, Chem., 32, 197 (1986) .