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ATOMIC STRUCTURETHE OBSERVATION OF CHEMICAL SHORT RANGE ORDER IN LIQUID
AND AMORPHOUS METALLIC SYSTEMS BY DIFFRACTION METHODS
P. Chieux, H. Ruppersberg
To cite this version:
P. Chieux, H. Ruppersberg. ATOMIC STRUCTURETHE OBSERVATION OF CHEMI- CAL SHORT RANGE ORDER IN LIQUID AND AMORPHOUS METALLIC SYSTEMS BY DIFFRACTION METHODS. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-145-C8-152.
�10.1051/jphyscol:1980838�. �jpa-00220344�
JOURNAL DE PHYSIQUE CoZZoque C8, suppldment au n O8, Toms 41, aoiit 1980, page C8-145
ATOMIC STRUCTURE.
THE OBSERVATION OF CHEMICAL SHORT RANGE ORDER IN LIQUID AND AMORPHOUS METALLIC SYSTEMS BY DIFFRACTION METHODS
P. Chieux and H. Ruppersberg
*
,Institut Laue-Langevin, GrenobZe, France Universitat des SaarZandes, Saarbriicken
The model of random dense packed hardspheres (RDPHS) has been shown to be of fundamental importance for the description of simple monatomic liquids [ I ] and it has also been successfully applied to binary sys- tems [2,31
.
Hafner demanstrated [31 that physico- chemical properties of binary melts may correctly be calculated by the intermediate of a RDPHS system, provided the chemical interactions between the 1 and 2 types of atoms were influencing only the hard sphere diameters o i which became therefore composi- tion dependent. However, the method fails if any or- dering takes place between the 1 and 2 particles. As deduced from thermodynamics, such an ordering is far from exceptional in liquid alloys [4,5], and is likely to occur in the glass phases prepared from them. Moreover in the diffraction patterns of some liquid alloys similar effects have been observed as for disordered polycrystalline substitutional alloys, with tendency for heterocoordination (short-range order) or self-coordination (cluster formation) res- pectively, both effects being described with the same formalism and under the same head-line "short- range order" by Warren, in his book on X-Ray Dif- fraction [61. We will adopt here the same nomencla- ture with a slight modification since we use the word chemical short-range order (CSRO) in order to distinguish these ordering effects from the topolo- gical short-range order of the global atomic arrange- ment which is responsible for the non-crystalline structure.Formalism
As a simple starting point, the I and 2 particles of a binary alloy are more or less randomly distributed over the iiggclicgl sites of a structure, which we call the "global structure", yielding what is called a substitutional alloy and for which the mean global
surroundings ofthe 1 and 2 particles are identical.
Of course, this approach fails in the case of parti- cles of different sizes. It has been shown however, for crystalline solid solutions that a substitution- al alloy model is a very powerful starting point, as long as the size difference is not too large. For binary melts and metallic glasses,one should there- fore try to start with the same model, the global structure being here not a crystalline structure any- more (like fcc in the case of solid Cu Au) but a RDPHS by example. Such an approach was already pro- posed by Keating in 1963 [ 7 ] . The question for CSRO would then be to gather information on the distribu- tion of the 1 and 2 particles over the sites of the global structure. From the different partial struc- ture factors which have been proposed to describe binary phases, the most directly affected by CSRO is the SCC partial structure factor which has been introduced by Fihatia and Thornton (BT)[8]. If we call b the coherent scattering amplitude and ~'(q) the coherent scattering intensity per atom, we de- fine the total structure factor S(q) or ST(q) of a binary alloy as S(q) = I~(~)/< b 2 > where < b2> =
2 2
x l b l + x2b2, xiare the atomic fractions, and q is the absolute value of the scattering vector. Accord- ing to BT, S(q) may be subdivided into
( 1 ) S(q)= a SNN(q) + c SNC(q) +
( 1 - 4
SCC(q)/xlx2, where2 2 2
(2) a =<b> /<b > ; c = ZAb<b>/<b >;
2 2
(I-a) = x1x2 Ab /<b > ; Ab = bl
-
b2 and <b> = x b1 1 + X2b2
SNN(q) oscillates around 1. It is equal to S(q) for b l = b2. Its Fourier Transform (FT) is related to the global structure of the alloy
191.
S (q) oscil-NC
lates around 0. It is identical to zero for identi- cal global surroundings of the 1 and 2 particles.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980838
(3-146 JOURNAL DE PHYSIQUE S ( q ) oscillates around xIx2. It is identical to
CC
x1x2 if there are no distance correlated concentra- ti011 fluctuations, i.e. in the case of random substi- tutional alloys without size effect and identical thermal vibrations of the two particles. The FT of sCC/xIx2 yields pCC(r) :
(3) (2~2)-1~(~CC/xIx2
-
1) sin(qr)dq = r.pCC(r) which is given in terms of the Faber Ziman partial pair correlation functions pkR(r), (k,R = 1,2), by :(4) pCc (r) = x2 (p1 I (r) + p1 (r) + x1 (pZ2 (r)
+ P~~ (r)) - P~~ (r) /xl
4vr pCC(r) was called by Ruppersberg and Egger [9], 2 the "radial concentration-correlation function"
(RCF). The RCF is zero for distances where no atomic pairs exist (all pkR(r) terms vanish). The RCF is also identical to zero if for each k,R pair,
pkR(r) = xR.N/V, i.e. for a statistical distribution at the distance r. Finally, the RCF is positive for distances with preferred self-coordination and vice versa.
In the case of polycrystalline disordered substitu- tional alloys where the BT formalism applies also, one generally does not discuss the full RCF curve, but simply introduce [91 the Warren-Cowley short- range order parameters a :
, .. P
4vr2pCC(r) dr, for S NC = O r is the mean distance from an atom to its p th
P
coordination shell of thickness 26. Z is the total P
number of atoms in the p-th shell. If Z12 is the P
mean number of atoms 2 in the p-th shell of an atom 1 , we have
12 2 1
(6) a p = 1-
z
/(z x ) = I- z
/(zpx2)P P 2 P
and as a consequencel2 a 2 - xk/xR where
R
refers to Pthe more concentrated species. Zero, positive or negative valuesof the a parameter indicate a sta-
P .
tistical distribution or a preferred self or hetero- coordination in the p-th shell. One has observed that the RCF curves of some liquid alloys are very similar to those obtained for the polycrystalline disordered substitutional alloys. Reiter et al.[10]
showed that melting left the,CSRO of the solid Ag-Li a-solution practically unchanged. Thus it seems logi- cal to keep the same formalism for the liquid
phase
.
However, there are then no well defined coor- dination shells and eq. (5) and (6) apply only if used with an appropriate model of the global struc- ture. The a 1 parameter obtained in that way is there-fore a useful criterion of CSRO in non crystalline phases as long as the systems are close to the sub- stitutional type. A different approach must however be used if the alloys are far from substitutional or if rather complex ions are formed as we shall see later on in this paper. Finally, without measuring the whole SCC(q), one may already obtain some impor- tant information about the composition fluctuations in liquid alloys from the value of SCC(o). It has been shown by BT [81, that this value is proportio- nal to themean-squaredcomposition fluctuation <Ax > 2 which is, on the other hand, related to the curva-
ture of the free energy G in the G-x diagram :
E~~ =
-
RT aRnyl/ax2 2 is the "excess stability func- tion" introduced by Darken 1121 ; y is the activity coefficient ; R is the molar gas constant and T the temperature. According to Thompson [13], whenever E~~ is different from zero, CSRO occurs.Determination of S (q) CC-
The complete set of three partial structure factors may, in principle, be obtained from three indepen- dent scattering experiments with different scatter- ing coefficients [141. Important information may also be obtained from two or one scattering experi- ments, by comparison with models [11,15] or by dis- cussion of CSRO effects like a prepeak. If the alloy is of the substitutional type it may be assumed that SNC = 0 or is hard sphere like. There is however a severe restriction to the application of these meth- ods since the contrast for the SCC partial is often poor due to a small value of (I-a) in eqn.(l). One notices that the contrast (I-a) is composition depen- dent and is optimal at xC;) where it depends only on the ratio of the scattering lengths. xy is given by
We display on Figure 1 the optimum composition x0 1 and the corresponding contrast as a function of b2/b 1.
Fig. 1 Optimum com-
contrast a function
We s e e on f i g u r e 1 t h a t u n l e s s b 2 / b l i s s m a l l e r small-angle s c a t t e r i n g (SAS) produced by c o n c e n t r a - t h a n Q.5, t h e c o n t r a s t i s l e s s t h a n 10%. T h i s i s t i o n f l u c t u a t i o n s . C r i t i c a l a m p l i t u d e s and e x p o n e n t s f o r example t h e c a s e f o r CuSn, CuZr, AuCs and tfgAl. f o r SCC(0) and f o r t h e c o r r e l a t i o n l e n g t h
5
of t h e X Ray s c a t t e r i n g g i v e s a n e x c e l l e n t c o n t r a s t f o r f l u c t u a t i o n s could be c a l c u l a t e d from O r n s t e i n - d i l u t e s o l u t i o n s of an heavy s o l u t e i n a Zernike p l o t s of SAS p a t t e r n s y i e l d i n g S(0) = 8 0 l i g h t s o l v e n t . A c o n t r a s t v a l u e o f I a t t h e o p t i m a l a t T = T + 13 K i n f i g . 2. RCF c u r v e s a r e shown composition, i s o b t a i n e d i f b l a n d b 2 h a v e d i f f e r e n t i n F i g . 3 f o r T c + 13 a n d T c + 1 5 0 K , r e s p e c t i v e l y . s i g n s a s i t i s p o s s i b l e i n n e u t r o n s c a t t e r i n g f o rwhich t h e f o l l o w i n g s e r i e s of i s o t o p e s o r e l e n e n t s have n e g a t i v e s c a t t e r i n g l e n g t h s ( r e l a t i v e phase s h i f t of T of t h e s c a t t e r e d wave): 'H, 7 ~ i , n a t ~ n , 62Ni, n a t
T i ,
Is2sm,
1 6 2 ~ y and 18%. I n t h i s c a s e , a t t h e o p t i m a l composition x;, which i s c a l l e d t h e" z e r o a l l o y " c o m p o s i t i o n , t h e sum o f t h r e e p a r t i a l s , eqn. ( I ) , r e d u c e s t o a s i n g l e p a r t i a l , SCC(q) which i s unambiguously o b t a i n e d i n a s i n g l e experiment.(x) Of c o u r s e , t h i s i s a v e r y powerful method f o r s t u d y i n g CSRO e f f e c t s .
R e s u l t s
We w i l l now p r e s e n t some examples of CSRO a s ob- t a i n e d f o r m e t a l l i c A) s e g r e g a t i n g s y s t e m s , B) a l - most i d e a l a l l o y s , C) compound forming s y s t e m s , and D) systems w i t h m e t a l t o non-metal t r a n s i t i o n o r w i t h complex i o n f o r m a t i o n .
A) The NaLi phase diagram i s dominated by a r e g i o n o f two u n m i s c i b l e l i q u i d s . The c o n s o l u t e p o i n t a t Tc = 577 ? 2 K and x . = 0.64 2 0.02 i s c l o s e t o
L1
t h e z e r o - a l l o y composition
qi
= 0 . 6 1 . S(q) = S C C ( q ) / x 1 x 2 , which was measured by Ruppersberg and Knoll [ I 7 1 a t Tc + 13 K i s shown i n F i g . 2. T h i sF i g . 2:
S(q)=Scc(q) / x I x 2 f o r l i q u i d L i O . 6 1 .Na
0.39
c u r v e i s v e r y d i f f e r e n t from a RDPHS c u r v e b u t s i m i l a r t o z e r o a l l o y c u r v e s o b t a i n e d w i t h s o l i d Ni-Cu a l l o y s [161. It i s dominated by a s t r o n g
( x ) Zero a l l o y d a t a e x i s t f o r s e v e r a l li- q u i d a l l o y s , ( s e e p a r a g r a p h on r e s u 1 t s ) i n c l u d i n g systems w i t h s t r o n g s i z e e f f e c t s , LiCa [18], L i S r
Fig. 3: RCF f o r l i q u i d L i 0 . 6 1 Na 0.39
The d o t t e d c u r v e s come from t h e c r i t i c a l SAS and have maximum amplitude a t r =
5 .
The RCFs a r e p o s i t i v e o v e r l a r g e d i s t a n c e s , i n d i c a t i n g f l u c t u - a t i o n s w i t h p r e f e r r e d s e l f - c o o r d i n a t i o n . The s m a l l peaks a t 3 and 4 a r e r e l a t e d t o p r e f e r r e d Li-Li and Na-Na d i s t a n c e s . With t h e assumption t h a t each atom i s surrounded by 10 n e i g h b o u r s , a v a l u e s of1
0.5 and 0 . 3 were o b t a i n e d f o r t h e two t e m p e r a t u r e s from E q . ( 5 ) , which means t h a t a L i atom h a s 8 and 7 . L i n e i g h b o u r s i n s t e a d of 6 f o r a random d i s t r i - b u t i o n . On approaching T from 590 K , t h e RCF w i l l remain almost i n v a r i a n t a t s m a l l d i s t a n c e s , however, t h e r - r a n g e of p o s i t i v e p C C ( r ) w i l l d i v e r g e a t T
c' There a r e numerous systems where SAS, i . e . s e g r e - g a t i n g tendency h a s been observed. SAS was d e t e c t e d c l o s e t o t h e e u t e c t i c composition of l i q u i d Ag/Ge [24] and was r e l a t e d t o a n h y p o t h e t i c a l m i s c i b i l i t y gap i n t h e undercooled l i q u i d . A reminescence of a c r i t i c a l t r a n s f o r m a t i o n which o c c u r s f a r below t h e m e l t i n g p o i n t h a s indeed been observed by Weber e t a l . [25] f o r t h e magnetic n e u t r o n s c a t t e r i n g from s p i n f l u c t u a t i o n s i n l i q u i d Fe, Co and N i . SAS h a s been observed i n Na/Cs [261 and, w i t h a v e r y s m a l l a m p l i t u d e a l s o i n Na/K [27]. S t e e b and coworkers d e t e c t e d more o r l e s s pronounced SAS i n A l / S n , I n [281, [29], Cd/Ga [301 and Cu/Bi, Sb [311, [ 1 8 1 . T h e d ~ n a m i c a 1 s t r u c t u r e f a c t 0 r S ~ ~ ( q , w ) h a s [ 3 2 ] r n e l t ~ . F o r t h e l a s t m e n t i o n e d C u / S b s y s t e m , been measured f o r L i Pb[20]. The amorphous TiCu
[ 2 ] ] , [22] and ~ i1 2 3 1 have been i n v e s t i g a t e d a t ~ i i ~ 0 t 0 P i c s u b s t i t u t i o n e x p e r i m e n t s were performed, a composition n e a r x u . and though t h e b e s t S C C - c o n t r a s t was o n l y 10 %,
JOURNAL DE PHYSIQUE
C8-148
the authors could calcurate SCC(q). SCC(o)/x 1 2 x came out to be 2.5, and the RCF was different from the LiNa curves shown in Fig. 3 and looked more or less like the upside down RCF of compound forming system shown in Fig. 7. SAS observed in the S(q) of amorphous samples seems not related to composi- tion fluctuations but to effects such as voids, dislocations etc.. This is shown, for example, by Steeb et al. for FegoBz0 [34].
Let us add a comment on the detection of SAS in segregating systems. If the partial molar volumes
- vi
of the 1 and 2 species are different, the con- centration fluctuations become correlated with density fluctuations and are then visible also in the small angle parts of Sm(q) and SNC(q) as it is shown for CuPb alloys by Fabre-Bont6 et al. [33].The (I-a) contrast introduced to indicace the strength of the SCC(q) partial is then not adequate anymore to describe the possibility of SAS detec- tion in S(q). As a matter of fact the appropriate contra* C for SAS in S(q) is proportional to the difference between the scattering amplitudes per unit volume of the two components [42].
One notices that this contrast is composition de- pendent through the partial molar volumes and is also affected by isotopic substitution in neutron scattering experiments 143, 441. In the zero alloy case C simply equals I/x x
1 2' B) For the liquid zero alloy Li
0. 68ca0. 32' S ~ ~ ( 0 ) has been found by Ruppersberg 1181 to be almost ideal, i.e. equal to x,x2 (see Eqn. (7)). The strong oscillations of S (q) as displayed on
CC
figure 4 are due to the large size difference (a /a =0.78) between the two species and are
Li Ca
therefore very similar to the RDPHS curve calcu- lated in the PY approximation.
----
RDPHS (PY)Fig. 4: S(q) = sCC(q)/xIx2 of the Li-Ca zero alloy
The raising part of the RCF of fig. 5, between 2 and 2.7 is similar to the radial distribution function of pure Lithium the later having however its maximum at 3 A, where the RCF already de- creases due to the negative peak of the Li-Ca pairs.
0
The 4 A peak belongs to the Ca-Ca pairs.
Fig. 5: RCF of the Li-Ca zero alloy
Other almost ideal systems have been found, but one must be cautious because in some cases the contrast problem was not perceived. A RDPHS be- havior has been observed by Wagner 1411 for amor- phous Ni0.35 (Zr,Hf)0.65 alloys for which the X Ray SCC contrast is between 2.5 and 5.8%. Chemi- cal effects are also absent from the scattering pattern of Ni60Nb40 [22] for which the contrast amounts to 3%. For other glasslike alloys which are presented at this conference, the SCC contrast is certainly too small (0.2% for Mg30Ca70 1351 and Mg70Zn30 [36] to allow the observation of CSRO.
C) A tendency towards compound formation has been detected in the diffraction pattern of numerous alloys including the important Fe-C melts [37].
However the partial S CC(q) curves are known in a few cases only. The one obtained from Lithium zero alloys are displayed on figure 6. SCC(o) is smaller than xIx2 for this group of substances and corres- ponds closely to the value calculated from activity coefficients according to Eqn. 7.
Fig. 6:
--- -
3 for compound
forming Lithium zero alloys (temperature near melting 0 1 2 3 4 q, A-' point)
9.2
For Li 0.5 a superlattice peak observed in the low temperature solid, transforms on heating into a broad peak typical of CSRO in the solid disordered solution. Practically unaltered by melting this becomes the main SCC peak of the liquid [lo], loca-
ted at qc, as displayed on the figure.
The first peak of the SNN partial, at qN, which generally dominates the total scattering pattern of binary alloys is located at higher q values. A simple sticky hard sphere model gives a peak posi- tion ratio = 0.61 [ I l l . The main peak of the S
CC partial is therefore observed, depending on the strength of the CSRO and on the contrast, as a more or less intense "prepeak". Such a prepeak has first been detected by Steeb and Hezel f381 in the X Ray diffraction pattern of AgMg alloys. In the case of LiOa8 PbOa2 the SCC peak is very strong, see fig. 6, and is even higher than the S(q) peak of pure metals near the melting point. It is much weaker for Li 0.7 MgOe3. A strong CSRO effect like in the first case would be detected in S(q) even with a contrast of only 2%; a contrast of 20%
would be required in the second case.
The RCF curves are shown on figure 7.
-
Li0.8 Pb0.2-
Fig. 7:4 r r 2 p C C ( r )
---
Lim Ag028 RCF curves Lie,, Mgo,3- for compoundforming Lithium zero alloys
0 2 4 6 8 g r , 8
In all three cases there is a negative peak at the nearest neighbor distance indicating a preferred hetero-coordination. There are good reasons to believe that the alloys are of the substitutional type with SNN(q) not too far from a RDPHS curve [ 9 ] . If we assume therefore a mean value of ten nearest neighbors, the short-range order parameter al turns out to be -0.25 for Li Pb (prelimi-
0.8 0.2
nary result only, [la]), -0.15 for the LiAg and -0.04 for the LiMg alloy. Thus, referring to Eqn.6, we have maximum ordering in Li 4 Pb near the melting point. From these results, it seems that the highest excess-stability function, i.e., the smallest SCC(o) might be correlated with the highest SCC peak and the most negative
eel
value.This is not necessarily the case however since one might imagine a segregation tendency between a pure element and an hetero-coordinated cluster, which will give at the same time a prepeak and SAS.
On the other hand the heights of the main SCC and RCF peaks are not directly connected either. The figure 8 displays ~ C F curves calculated from the complete S CC(q) curves of Li4Pb and from only the positive part of the first peak of q(S CC -x 1 x 2 ) . We see that the strength of the SCC peak is in that case characteristic of the range of CSRO effects in real space, its width yielding a correlation length which for extended CSRO will probably be strongly affected by temperature. The a parameter
1
itself depends on the whole SCC partial and one must be cautious at interpreting total S(q) curves.
These two
para meters,^^
and correlation length, might be sufficient to characterize the CSRO ofthe system. An interesting additional information is revealed by the RCF1s: the compound formation tendency seems to be correlated with a relative contraction of the 1-2 nearest neighbor distance as compared to the mean 1-1 and 2-2 distances
[lo].
Fig. 8:
-
from the total &(q)5 from the first peak
0
-5
The SCC(q) and the other partials of Co0.83P0.17 were obtained by Bletry from ~olarized neutron measurements,[52],an a l close to -0.21 indicates maximum ordering. Maximum ordering has also been observed by Boos and Steeb for liquid Mg0.7Bi0.3 [39] and by Masumoto et al. for glassy Gdo.8 Si0.2 [40]. About 10 to 50% of maximum ordering was de- tected by Sakata [22] in CuTi glasses. Partial ordering (al = -0.1 for a max = -0.67) was obser-
1
ved by Ruppersberg et al. [23] for amorphous TiOe6Nioe4. For this system an irreversible de- crease of SCC(o) was observed on annealing.
We should point out that almost nothing is known about CSRO and its variation with temperature and during heat treatments of metallic glasses. For no binary system there exist a complete study of
c8-150 JOURNAL DE PHYSIQUE
composition and temperature variation of RCF curves.
Very little, if nothing is known from diffraction experiments about CSRO in non substitutional type of alloys.
D) Diffraction experiments might help to elucidate the nature of bonding in more complicated disor- dered metallic systems. Let us first take the solu- tions of alkali metals in their molten salts, a well known case of transition from metallic to
ionic behavior[451. The partial structure factors ofthe molten salts have been considerably investi- gated both on the theoretical and on the experi- mental side [46]. The figure 9 displays the characteristic features of the total structure factors S(q) obtained for different chlorine iso- topes and the S NN, SCC partials of a typical pure- ly ionic alkali halide salt. (One reminds that in this case, x l = x2 = 0.5 and the SCC partial be- comes effectively a charge fluctuation partial SCC or S =
7
1 (S+++S---2S+-)). In alkali halide49
systems S NC(q) is found equal to zero which yields S (q)
++ - S--(q). The system is totally described
T- 810% Fig. 9:
Total and partial structure factors
with two partials, SNN,
sCC.
One notices on the figure 9 that the first maximum of the total structure factor corresponds to the main peak of SCC whose position q is related to the perio- dicity of the charge oscillation. The second maxi- mum in S(q) corresponds to the main peak of SNN at qN and is related to the nearest neighhor dis- tance r+-. The relative position of these two peaks is very accurately defined in the alkali halide series, qc/qN = 0.67,which is different from the value 0.61 observed in compound forming alloys. This produces the typical alternance of
S and Sm peaks in the total structure factor.
49
If one mixes a molten salt with an alkali metal one observes the set of patterns displayed on the figre
10 [44]. The addition of salt produces a broad peak culminating at the qN value of the pure molten salt (q = 2.33
ib1).
This effect is even more visibleN
on the Fourier transforms of figure 1 1 where one detects the characteristic r+- distance of the salt,
%,
at a concentration of only 5% KC1 in K.It would of course be quite interesting to obtain detailed partial structurefactors for this system and this is the object of further investigation [44]. Since it turns out that the main potassium metal peak just occurs at the qc position of the salt SCC peak we have even no qualitative proof of charge oscillations.
Fig. 10: Fig. I I:
S(q) for K-KC1 and the pair correlation functions
We just may state from the appearance of a peak at qN that a local order similar to the salt is already present in the strong metallic region f441 of this systen (the electrical conductivity is still
lo3
Q-'cm-l at a concentration of 50%K- in KC1 for T
-
800°C). A simple way to under- stand this fact is the tendency for separation into a salt like and a metal like phase as is Known from thermodynamics and is consistent with the observed significant SAS. (A crude estimate of the correlation length for the flue- tuations measured by SAS is 3 A).A very similar behavior is observed for the Au-Cs system studied by Steeb et al. [47] where the 50%
Au-Cs alloy is ionic like. One notices on the figure 12 all the trends of the K-KC1 system, in- cluding the significant SAS.
s(q) g(r> Fig. 12:
S(q) and e(r) for Au-Cs [47]
Here again the first S(q) peak of the pure metai is located at about the qc position of the salt and prevents any estimate on charee oscillations for the metal-rich alloys. Close to the pure salt concentration the qc peak becomes however detectable at about 1.2
W-',
and it is inte- resting to note that qc/qNz 0.60 which is between the value of 0.57 observed for CuCl and the value of compound forming alloys, but distinctly different from the value of the al- kali halides.We shall now consider a class of metallic systems where large structural units, complexes or clus- ters with rather strong interatomic bonding, exist in the liquid state, such as the alkali metal suboxides of Rb or Cs which display unusual structures in the solid 1481. The figure 13 shows a typical stable atomic arrangement or cluster in which two oxygen atoms are surrounded by two face sharing octaedra of Rb atoms. This cluster is found in the metallic solid compounds Rbg02 and Rb60 displayed on the same figure. The inter- atomic distances within the cluster are characte- ristic of the ~ b + and 02- ionic radii (the Rb-0
' j 0 0 ~ C ~ O C ' , ' , 0
%%PI 1 ~ 1
0 ~ 0 0 ~ 0 O 0 0 0 0 0 0
1g1
lSHI
R p0 0 0 0 0 ~ ~ 0 0 o 0 0
Fie. 13
0
distances are 2.70 and 2.80 A). The intercluster Rb-Rb distances are longer than intra-cluster distances and comparable to interatomic distances in the pure metal. This is why these systems have been referred as "complex" metals, in the sense
that the simple ions of the metal were replaced by complex ionic clusters. The question is to know if these structures are conserved in the melt. The figure 14 displays the S(q) of the Rb60 liquid at a temperature of 4 7 O ~ as compared to the S(q) of the pure metal at the same temperature, both obtained from neutron scattering measurements. Since these systems do not offer the possibility of isoto~ic
Fig. 14: S(q) and g(r) of liquid Rb60 as compared to pure Rb(---) from 1481
substitution it will be quite difficult to obtain par- tial structure factors. Another approach should be in- vestigated. The Fourier transform (see fig. 14) of the total structure factor displays well defined short in- teratomic distances of 2.8 and 4.0
1
attributed by com- parison with the solid to intracluster bonds. An appro- priate analysis is therefore as in the molecular sys- tems, to test several solid state cluster geometries by fitting the corresponding molecular form factor on the medium and high q part of S(q). In this framework the prepeak of the structure factor should correspond to the average intercluster distance. The height of this peak is not as strong as what one would expect for a pure molecular system which indicates some looseness in the packing or weakness in the cluster stability.c8-1.52 JOURNAL DE PHYSIQUE
As seen from the strength of the Rb 0 main peak which This series of examples shows clearly to what 6
corresponds to the Rb metal peak a significant amount wide extend on the experimental as well as on theo- of excess free ~b atoms is still present in liquid retical and computer simulation side the field is Rb60 as might be expected (cf. fig. 13). Obviously open to further investigation.
these comments await for a more quantitative data 1
.
J.D.VJEEKS, D. CHAMDLEF. & H.C .M<DERSEN, J . Chem.evaluation. It is interesting to note that the pre- peak to main peak position ratio equals 0.68/1.,58 =
0.43, which as compared to the qc/qN ratio obtained previously is quite small. This confirms the idea of rather complex clusters as opposed to simple CSRO effects between the two atomic species.
The solutions of alkali metals in liquid ammonia 1491 present some analogy with the alkali metal suboxides since, roughly speaking, in the highly concentrated region the ions of the metal are replaced by "solvated" ions. This is especially the case for the Li-Amnonia system, Lithium being the only alkali which forms a compound, Li(NH3)4 with the solvent. The figure 15 displays the diffraction pattern of the pure deuterated solvent at 20'~ and of the Li-4ND3 solution at -65OC 1501. The prepeak
Fig. 15 Fig. 16
,?,'
x-4 -./..,-,.
0 5 1 1.5 -A'' one observes is not due, as in aqueous solutions of NiC12, f c r example, 151
1
to the metal-metalcorrelations alone because lbLil is too small to produce such an effect. The prepeak to main peak position ratio has again a very low value, it slightly shifts from 0.52 to 0.50 while diluting from Li-4ND3 to Li-6ND3 and-it may be as low as 0.38 for Li-7ND3 (see fig. 16). One must how- ever notice that the radius ratio of ND
3
Li is large,
-
2.76, and not much is known about systems with such a large size effect. One be- lieves however, that the solvated ion picture is adequate and that the prepeak is related to it.Phys. 54 (1971) 5237-47
2. E.W.CP.UNDKE, D. HENDEWON, J.A.BARKEF. & P.J.
LEONARD, !lolec.Phys. 2 (1 973) 8811 3. J. HAFNER,TJhys.Rev.A 16 (1977) 351
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ley Publ. D.eading, Efass. 1969
7. D.T.KEATING, J. Appl.Phys. 34 (1963) 923
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10. H.WITEP.,H.RUF'PERSBEP,G,!J/SPEICHEP.,Inst .Phys.
Conf .Ser. 30 (1977) 133
1 1 . J.BLETSv,Z.Naturforsch.33a(1978)327 I.?. L.s.~AP-XEN, Trans.AIME L39 (1967)80 13. J.C.THOY?SON, J.Physique Co11.4 (1974) 367 14. P'CHIEUX, in "Neutron Diffraction'!, Ed.H.DACFS,
Springer Verl. Berlin, 1978
15. R.EVANS,?I.EI.TELO DA GMIA,Phil.Vag.B41(1980)351 16. J.~~IJEN,S.I?ADELAP.R,Phys.Rev.B17(1978)409 17. H.~UPPERSBERG,TJ.KNOLL,Z.Naturf.32A(1977)1374 18. H.F.UPPEF,SBEBG, not published
19. H.T?UPPELISBERG,J.SAAR,W.SDEICHEI?,this colloq.
fl. SOLTL?ISCH,D. r]UITM%NN ,H.RUPPERSBERG J .B. SUCK.
this colloquium
M.SAKATA,N.COI.LAV,IJ.A.DAVIES,J.Phys.F9(1979)L235 W.SAKATA,N.COWLAT4,H.A.DAVIES,this colloq.
H.RIIPPEP.SBERG,D. LEE,C.N. J.'JAGNER,J.Phys .F10(1980) M.C.BELLISSENT-FUNEL,J.Phys.F9(1$79)987
N.ClEBErl,~~J.KNOLL,S.STEEB,J.Appl.Cryst. 1 1 (i978)638 TI. J.HUIJBEN ,!?.VAN DEF LUGT,N.I(EIYERT,J.DE HOSSGft, C.VAN DIJK,Physica B97B(1979)338
B.P.ABLAS,W.VAN DEE LUCrT,J.Phys.F10(1980)531 ll.ZAISS,S.STEEB,G.S.BAUEB,Phys.Chem.Liq.6(1976) 2 1
HOEHLE4,S.STEEB,Z.Naturforsch.30A (1975) 775 G.HEIWANN,Doctor Thesis,Univ.Stuttgart, 1080
!l.ZAISS,S.STEEB,G.S.BAUER,Phys.Chem.Liq.6(1976)21 T,!.KNOLL,S. STEEB,Phys .Chem.Liq.4(1973)39
M.FAVitE-BONTE-,J.BLETRY,P.HICTFR P.DESRE,this col.
S.STEEB,E.NOLD,H.LkXPARTEP, this colloq.
3 . E. SUCK,H.F.UDIN ,H. J. GUENTHEXODT
,
D .TOEaANEK,C.M0SWL,J.J.GLAESErl,this colloq.
T.?!IZOGUCEI,T.KUDO,E.KATO,S.~MIADA,this colloq.
M.WEBEF,,S.STEEB,Z.Naturforsch.33A(I978)799 S.STEEB,R.HEZEL,Z.Phys.191(1966)398 A.BOOS,S.STEEB,Phys.Lett.63A(1977)
T.tNSWfOTO,T.FUKUNAGA,K.SUZUKI ,Bull .her .Phys
.
Soc.23(1978) 467
C.N.J.\.JAGNES,D.LEE. this colloauiiim 42. P.DAEIA~,P.CHIEUX,Z haturforsch:34a(l979)804 43. P.CHIEUX,P.DAMA~!,Chem.Phys.Lett.58(1978)619 44. J.?.JAL,J.DUPUII,P.CHIEUX, this colloq.
45. EI.A.BPEDIG, in "?lolten Salts Chemistry", Ed.
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The changes in CSRO or configuration with concen- 51. G.W.NEILSON,R.A. HOWE, J.E. ENDERBY,Chem.Phys.
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