J. Phys. Chem. W80, 84, 1 199-1203
between low atomic character (weakly bound) and high atomic character (strongly bound) solvated atoms illustrates clearly that in cationic solvation the donaticity of the solvent is crucidy important in determining the energy levels Of the ‘Jolvated species and does indeed effects very similar to those observed during the excitation of gas phase atoms. In conclusion, we once again draw attention to the limiting situation of “ionization” in the matrix bound case (Figure 1). In particular, we note that (1)the continuous nature of the transition from solvated atom to solvated electron strongly suggests that no drastic solvent reorganization is required to divorce electrons completely from low atomic chruader solvated atoms, and (2) the electronic transition energy for a state of zero atomic character (in polar solvents:)lies very close to that observed for solvated electrons in all media included in Figure 1.
References aind Notes (1) J. Jortner, ,J. Chem. Phys., 30,839 (1959). (2) J. J. Lagowski and M. J. Sienko, Ed., “Metal-Ammonia Solutions”, Colloque Weyl 11, Butterworths, London, 1970. (3) D. Copelancl, N. R. Kestner, and J. Jortner, J. Chem. phys., 53, 1189 (1970). (4) C. E. Moorce, Natl. Bur. Stand. Circ. No. 467,Vol. 1 (1949). (5) J. L. Dye in “Electrons in Fluids”, J. Jortner and N. R. Kestner, Ed., Sprlnger-Verlag, West Berlin, 1973. (6) J. L. Dye, /%re Appl. Chem. Suppl., 49, 3 (1970). (7) (a) R. Catterall arid P. P. Edwards, Chem. phys. Lett., 42,540 (1976); (b) ibld., 431, 122 (1976).
‘I 199
( 8 ) 0. H. Wannier, Phys. Rev., 52, 191 (1937). (9) R. Catterall and P. P. Edwards, J. Chem. Soc., Chem. Comniun.,
96 (1975). (10) J. w. Fletcher arid w. A. w o n , J . P~,,s. Chem., 79,3055(11875). ( 1 1) R. Catterall, M. C. R. Symons, and J. W. Tlpping, J . Chem. Soc. A , 1529 (1966). (12) W.A. Sddon, J. W. Fletcher, and R. Catterall, Can. J. Chem., 55, 2017 (1977). (13) M. Smlth and M. C. R. Symons, Trans. Fwaday Soc.,54,338,346 (1958). (14) E. Fermi and E. G. SegrB, 2.Phys., 82,729 (1933). (15) B. Bockrath and L. M. Dorfman, J. Phys. Chem., 77,1002 (1973); G. A. Salmon arid W. A. Seddon,Chem. phys. Lett.,24,366 (1974). (16) R. Catterall, J. Slater, W. A. Seddon, and J. W. Fletcher, Can. J . Chem., 54, 3110 (1976). (17) C. K. Jen, V. A. Bowers, E. L. Cochran, and S. N. Foner, phys. Rev., 126, 1749 (1962). (18) W. Weyhmann and F. M. Pipkin, Phys. Rev. A , 137,490 (lSt65). See also W. W. Duley, ibkl., 27,206 (1968),for the interpretation of optical spectra.
(19) R. Gupta, W. Happer, L. K. Lam, and 5 . A. Svanberg, Phys. Rev. A , 8,2792 (1973). (20) H. Kopfermann, “Nuclear Moments”, Academic Press, New York, 1968. (21) K. Bar-Eli and T. R. Tuttle, Jr., J . Chem. Phys., 40, 2508 (1964). (22)J. H. Sharp and M. C. R. Symons in “Ions and Ion-Pairs in Organic Reactions”, Vol. I, M. Swarc, Ed., Why-Interscience, New York, 1972. (23) M. C. R. Symons, J . Chem. SOC.,1482 (1964). (24) V. Gutmann and U. Mayer, Struct. Bonding, (Berlin), 12 (1972). (25) V. Gutmann, “The Donor-Acceptor Approach to Molecular Interactions”, Plenum Press, New York, 1978. (26) R. Catterall and M. C. R. Symons, J . Chem. Soc., 4342 (1964). (27) D. E, O’Reilly, J . Chem. Phys., 50,4320 (1969). (28) G. A. Salmon, W. A. Seddon, and J. W.Fletcher, Can. J . Chem., 52,3259 (1974).
Metal-Insulator Transitrons in Metal-Ammonia Solutions N. F. Mott Cavendish Laboratory, Cambrklge, England (Received August 27, 1979)
The theory of metal-insulator transitions in doped semiconductors is outlined. New points not given in the author’s previous articles are a realistic description of the upper Hubbard band and of the sign of the thermopower near the transition. Pauli paramagnetism and a linear electronic specific heat set in at concentrations slightly below that at which nonactivated (metallic) conduction starts. A contrast is made between the “Mott-Hubbnrd” transition (Si:P, expanded fluid cesium, M-NHJ and band-crossingtransitions (expanded fluid mercury). Only in the former is a phase separation expected in fluid systems. It is concluded that the dimers in metal-ammonia are “bipolarons”, that is two cavities associated with a cation, and not two electrons in the same cavity.
The purpose of this paper is to examine the metal-insulator transition in doped silicon (e.g., Si:P) and other systems, such1 as expanded fluid cesium, in which the electrons are in a random array of one-electron centers, and to examine the implications for metal-ammonia solutions. In particular, we shall present arguments which relate to the nature of the diamagnetic dimers in these solutions. The paper develops views which I have put forward in earlier w ~ r k , l modified -~ by recent theoretical and experimental investigations. Doped semiiconductors were discussed in detail at the Scottish Sumimer School at St. Andrews in August 1978, and the published proceedings contain papers by many scientists working on the subject. As I show in my paper published theire: the transition to metallic behavior with increasing concentration appears to be of Anderson type, in which a mobility edge Ec crosses the Fermi energy EF. The behavior of the conductivity will then be as described in a number of papers (e.g., ref 1and 5) and is illustrated 0022-3654/80/2084-1199$01 .OO/O
in Figure 1. The characteristics are (a) if states are localized at EF, the conductivity u at low T obeys the law of variable-range hopping u = A exp(-B/T1i4)
(1) (b) at higher temperature charge transport is by electrons excited to the mobility edge, and Q gmin expWc - E,)J/kT (2) (c) as shown in the diagram a “minimum metallic conductivity’’ exists given by
-
urnin 0.025e2/ha (3) where a is the distance between donors or, more generally, the distance between the fluctuations in potential. If EF lies below Ec, so that states are localized at the Fermi energy, the electronic specific heat and Pauli paramagnetism are still proportional to N(EF);there is no discontinuity in these quantities at the metal-insulator 0 1980 American Chemical Society
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The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
1/T Figure 1. The electrical resistivity of a system undergoing an Anderson transition plotted as a function of 1/ f . The plots, starting at the top, are for decreasing values of E = E, - E,.
transition. That this is so for the specific heat k2TN(EF) in Si:P is shown by the experiments of Koboyashi et al.'j and Marko et al.7 Both in SkP and many other systems, behavior as shown in Figure 1is observed. The most controversial part of the theory is perhaps the existence of a "minimum metallic conductivity". Experimentally a can be varied by two orders of magnitude, giving a very satisfactory test of eq 3 (Pepper8igand Bikutski'O). On the theoretical side, while Licciardello and Thouless" and Edward@ come to the conclusion that aminexists, other workers (e.g., WegnerI3 and Gotze14)find a contrary result and numerical work by Weaire15 finds the matter unproven in two dimensions. It is agreed that, when E lies near Ec, large fluctuations in the wave function # must exist, and these may make a classical percolation theory appropriate; if so, there is then no u-, u vanishing at Ec. I have arguedlsJ6that whether they do or not depends on how the radius of the localized wave function goes to infinity as E tends to Ec. If we assume # exp(-ar), then if
-
CY a
( E , - E)s
s must be greater or equal to 2 / 3 for a minimum metallic
conductivity to exist. Since all the experimental evidence shows that u- does exist, I conclude that 2/3 is the most probable value, in agreement with Edwards.12 Of course if for some reason the distribution of centers is not random, but these is strong clustering, with clusters too large for much tunneling, a classical percolation theory may be appropriate. I believe that for any distribution a minimum metallic conductivity must in principle exist, but with strong clustering it will be small, and except at very low temperature the classical percolation theory should be valid. A treatment of this kind is used by Cohen and J o r t n e P in their description of the transition in metalammonia, and in particular for their explanation of the Hall effect. 1 think that their explanation depends essentially on their assumption about clustering; Nakamura et al.lBgive evidence in one material that clustering is not important. Moreover Damay and Chieuxlgin this volume give further evidence against their hypothesis. It must be said, however, that some distinguished schools, notably that of Sasaki,20do find evidence for the validity of a clustering model in investigating the magnetic properties of Si:P. I think that in view of all the other evidence this approach cannot be correct here. I now describe what I think to be the correct way to obtain the concentration at which the transition occurs in Si:P and other doped semiconductors, which differs slightly
Mott
D-
Do
E
(b) Figure 2. Density of states in a doped semiconductor. (a) is for low Concentrations, when the Doand D- levels have not widened into bands. c.b. denotes the conduction band. (b) The dotted lines show N(€) when the Do and D- levels have widened into the upper (2) and lower (1) Hubbard bands. (c) shows the situation when they begin to overlap.
from that given in ref 4. For a low concentration of centers, two sets of levels exist as shown in Figure 2a; these are the donors (DO) and the D- levels in which an extra electron is placed on a Docenter. The orbitals of the Do center have the hydrogen radius uH; for D- they decay much more slowly as exp(-ar) where 1 / a 4aH. As the distance between the centers decreases, therefore, both levels broaden, but D- broadens faster and gives the so-called upper Hubbard band, overlapping the conduction band strongly (Figure 2b, dotted lines). At concentrations, however, for which 4R/aH 1,the rapid increase of the width of the upper Hubbard band ceases, and cannot be calculated by the tight binding approximation. This approximation gives, however, for the lower band a breadth3 B = 221 where z is a coordination number, and
-
I = exp(-aR)(l
+ (&)]e2a/K
Here R is the mean distance between atoms, a = l / a H and K a background dielectric constant. When the two bands overlap, N(EF)becomes finite and a metal-insulator transition may occur. The condition for overlap should then be ZK
where x is the displacement of the upper Hubbard band below the conduction band in units of e 2 a / 2 ~the , ionization energy of a donor. Numerical work at present in progress suggests that x 'Iz at the concentration for overlap, and this leads to an expression for B of the type aR = In [ ] (4) where the term in the square brackets is large. Because of the rapid variation of the exponential with R, the value taken for x makes very little difference to R. We thus find
-
n113aHN 0.2
(5)
This is rather less than the empirical factor (0.26) found for a wide range of materials by Edwards and Sienko,2Ithe error possibly lying in the use of the tight binding approximation for the lower band. However, the consistancy
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980 1PQl
Transitions in Metal-Ammonia Solutions
X
Figure 3. Free energy of metal system showing MI transition as a function of conicentration (x) for increasiing temperatures T = 0, T , , T2.
of the constant for so many materials does indeed suggest a formula of type (4) where a variation of the factor within the logarithm by, say 2, will make little difference. We now rn k what actually happens when the two bands overlap. For a crystalline array, when any two bands cross, it is predicted that there should be a discontinuous change in the number of carriers, an electron-hole gas being formed. The argumentz2 is that the energy of an electron-hole plasma is of the form constant h2n2i3/m- cortstant e2n1j3/~ (6)
-
-
the first term representing the kinetic energy and the second the mutual potential energy of electrons and holes. This shows ai minimum for a certain value of n, giving an energy -Eo,where Eo = constant. me4/h2K2 The constant is of order 0.1, When this is equal to the band-gap AIS, there should be a discontinuous formation of an electrom-hole gas. As a consequence, the free energy of any system showing a metal-insulator transition will be as in Figure 3, and the region of the transit,ion will be unstable at low T against separation into two phases. I now arguez3that, if the system is sufficiently disordered, the extremities of the coiiduction band will not behave as E1j2but show a tail, so that the kinetic energy is not given by h2n21s/m.The energy of a plasma may thus not show a minimum. The transition is thus of pure Anderson type, though occurring still approximately where eq 5 is satisfied. This appears to be the case for Si:P where the activation energy for conduction (e2) goes continuously to zero. For Si:P one has to ask, then, when Anderson localization will give way to nonlocalized behavior as the bands increasingly overlap. DebneyZ4has calculated the condition for localization in randomly distributed centers and finds n1j3aHN 0.34 (7) Since 0.34 is greater than 0.26, we conclude that, near the transition, all states in the lower Hubbard band will be localized and those in the upper band localized only near the band edge. Thus in a slightly compensated n-type sample just before the transition the density of states should be as in Figure 4a; ez is Ec - E*, and if conduction is by hopping the thermopower is positive, as observed by Geballe and Hall2s and by Mole26(see Figure 5). There will be a very small range of concentrations where N(Ep) is finite, but still giving activated conduction (a = Ae-B/T1/‘at low T),but a finite electronic specific heat and Pauli magnetism. Metallic conduction should start when the “pseudog:ap” has a depth of about 113 of the value for free electrons. The low temperature thermopower in the metallic regime near the transition is observedze to be
Figure 4. Density of states in a doped semiconductor (a) in ohe t2 iregion (b) at the MI transition, according to the considerations of this paper.
, /i
T Flgure 5. Thermopower as a function of Tin the nonmetallic rmegion, from Mole.*’
n-type, changing sign with increasing concentration as the transition to the metallic state is approached. This implies that the “tail” at the top of the lower Hubbard band extends further than that at the bottom of the upper band. Following the calculations with the tight binding approximation of Cyrot-Lackmann and GaspardF7applicable we think only to the lower band, further work is necessary to confirm this. If I were to look for a discontinuity at the transition, or the resulting two-phase region, I would choose (a) a liquid in which the position of the centers was less random than in Si:P; (b) a Mott transition rather than a band-crossing transition, where the full and empty bands correspond to atomic s and p orbitals or vice-versa. The reason is that, for the former, excitation into the upper Hubbard band involves a charge transfer from one center to another, giving a small oscillator strength, and consequently a [small value of K in UH = h2K/me2and a large change in n a t the transition. I turn now to fluid cesium and metal-ammonia. These of course do show two phase regimes with a critical point. For cesium both the present author4 and Freyland28have pointed out that a a t the critical point is near amin(as it is for M-NI13), in contrast with fluid mercury where1 u Q-l cm-1. I think that Cs and M-NH3 are both,
-
1202
The Journal of Physical Chemistry, Vol. 84, No.
Mott
10, 1980
I
n
I
I Figure 7. Suggested potential energy curve for a pair of solvated electrons.
-
-
& - L L - d
0
01,
08
1.2
1.6
2.0
~[gcrn-~I
Figure 8. Susceptibility x8 of expanded fluid cesium as a function of density (below) and conductivity (above), from Freyland.”
therefore, materials where disorder does not turn the Mott transition into an Anderson transition. The reason must be that electrostatic repulsion between the ions gives strong short-range order, and the remaining disorder is not, sufficient, as it is for the band-crossing transitions in fluid mercury, to get rid of the discontinuity. A very interesting property of fluid cesiumz8 is the magnetic behavior shown in Figure 6. As the density is decreased there is a marked increase in the susceptibility, which we believe to be due to correlation enhancement (Brinkmanand Ricem). As one approaches the transition, it drops again. I believe this is because the broadening of the density of states due to disorder becomes more important than the Brinkman-Rice enhancement, I consider one of the most interesting experiments that can be carried out in the area of this conference is to quench a metal solution in some fluid which allows the liquid disorder to be quenched in from a temperature in which there is only one phase. I believe at low T a discontinuity in the plot of number of current carriers against concentration (and hence of the conductivity at low T, ought to be observed, and the activation for conduction should drop discontinuously to zero. No direct experimental proof of this phenomenon has yet been obtained. Next we consider the “dimers” in M-NH, in which pairs of electrons form some complex (possibly with M+) which is in a singlet state. We note that according to FreylandZs near the critical point in Cs some 10% of the atoms appear to form pairs (Cs,). In M-NH3 the question of whether the pairs are of similar kind, or whether they consist of two electrons in the same cavity, was discussed in several papers at Weyl IV. Thompson30(p 146) lists many papers giving a theoretical treatment of two electrons in the same cavity and comes to the conclusion that it is likely that this form of dimer is stable against separation into two isolated solvated electrons, even when correlation ( (e2/rI2))is included. One piece of evidence that this is the kind of dimer which forms as the concentration is increased is its long lifetime (Catterall and Symons31); this favors a small center, since the plot of energy against distance R should be as given in Figure 7 and e2/KR0should be a measure of the potential barrier for escape. If the lifetime is lo4 s, we should have for the barrier W 106 1012e-W/kT
-
giving W
- 15kT - 1/3 eV, and with
K
= 23, Ro = 15 X
3/23 2 A. So small a value favors two electrons in one cavity rather than a “diatomic molecule”. However, this estimate may be changed if the metal ion is part of the complex, The increasing conductivity above 0.1 mpm has been ascribed by various authors to hopping from doubly charged to singly charged centers ( Q n ~ a g e rCohen , ~ ~ and Thompson,33Catterall and Mott2). One may have two mechanisms in parallel, the drift of the solvated electrons and the hopping. This could correspond to the two-carrier model of Lelieur et On the other hand, I believe that the spinless complex which has lower energy than two isolated solvated electrons must be of molecular type (“bipolarons”). Such bipolarons they are known elsewhere in physics, notably in Ti407;31’35 could well exist here, bonded by covalent forces. Evidence for this model is given by Schindewolf? in this volume. My reason for prefering it is the following. As pointed out by the present author,l such bonding will have little effect on the characteristics of the metal-insulator transition, the bonding energy being small compared with the other energies involved. On the other hand, if a cavity containing two electrons is the state with lowest energy, then the transition would be of band-crossing type (like that in fluid mercury), and we do not think that a two-phase region would then be expected, for the reasons already given for mercury. To summarize, the application of the model developed for Si:P to metal-ammonia implies the following. (1)The D- states in a cavity exist, and the electron does not stay here long enough to polarize the medium round them. As we have said, they are probably not the dimers. (2) The cavities still remain at the metal-insulator transition. The metal is like that in ex metallic transition-metal oxide, the electrons moving in a narrow “tight binding” band, and with an absorption spectrum similar to that of the isolated solvated electron. The paper by A c r i v o ~and ~ ~ co-workers in this volume seems to show that, when the material is just metallic (a 200 0-’cm-’), the electron density at the cations is still small, most of the electron density being in cavities. Finally I add a few words about the Hall effect: Acrivos and Mottse have applied Friedman’s40theory to the Hall constant in the metallic pseudogap region, and I believe that all the evidence4suggests that this is correct for these systems. On the other hand, recent ~ o r kshows ~ ~ that i ~ ~ in the nonmetallic region, in particular in inversion layers and impurity conduction, the theory is not applicable, and for these systems the Hall effect is in my view simply not understood. I am therefore very reluctant to use the Wall effect to find out what is happening in metal-ammonia in the nonmetallic regions.
-
References and Notes (1) N. F. Mott, J . Phys. Chem., 79, 2915 (1975). (2) R. Catterall and N. F. Mott, Adv. Phys., 18, 665 (1969).
J. PhyS. Chem. 1980, 84, 1203-1205
(3) N. F. Mott, “Metal-Insulator Transitions”, Taylor & Francis, London, 1974. (4)N. F. Mott iii ”The Metal-corMehl TransiticKls in Disordered Systems”,
Proceedings of the 19th Scottish Universities Summer School in Physics, SUSSP publication, University of Edinburgh, 1978,p 149. (5) N. F. Mott, M. Pepper, S. Polli, R. H. Wallis, and C. W. Adkins, Proc. R . SOC. London, Ser A , 345, 196 (1975). (6) N. Koboyatshi, S.Ikehata, S. Koboyashl, and W. Sasaki, Solid State Commun., 24, 67 (1977). (7) J. R. Marko, J. P. Harrison, and J. D. Quirt, Phys. Rev. B , 10,2448
(1974). (8) M. Pepper, Commun. Phys., 1, 147 (1976). (9) M. Pepper, J . Noncryst. Solids, 32, 181 (1979). (10) G. Bikubski, Phil. Iwsg., in press. (11) D. C. Licciardello and D. J. Thouless, J Phys. C,8,4157 1975); Phys. Rev. Lett., 35, 1475 (1975). (12) S. F. Edwards, J . hloncryst. Solids, 32, 113 (1979). (13) F. J. Wegner, Z . Phys. B., 23, 327 (1976). (14) W. Gotre, J . Phys. C , 12, 1279 (1979). (151 D. Weaire and B. Kramer. J. Noncwst. Solids, 32. 131 1979). (l6j N. F. Mott, Commun. Phys., 1, 203 (1976). (17) M. H. Cohen and J. Jortner, J. Phys. Chem., 79, 2900 (1Y75). (18) Y. Nakamura, U. Horie, and M. Shimoji, J . Chem. SOC.,Faraday Trans. I, 70, 1376 (1974). (19) P. Damay and P. Chieux, paper in this issue. (20) W. Sasakl, S.Ikehata, N. Kobayashi, and S. Kobayashi, “Physics of Semiconductors”, Conference Series No. 43,Institute of Physics, London, 1!348,p 923. (21) P. P. Edwards and M. J. Sienko, Phys. Rev. B, 17, 2575 (1978).
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(22) W. F. Brinkman and T. M. Rice, Phys. Rev. 8 , 7, 1508 (1973). (23)N. F. Mott, Phil. Mag., 37, 377 (1978). (24)B. T. Debney, J. Phys. C , 10, 4719 (1977). (25)T. H. Geballe and G. W. Hail, Phys. Rev., 98, 940 (1953). (26) P. J. Mole, Ph.D. Thesis, Cambridge, 1978. (27)F. Cyrot-Lackmann and J. P. Gaspard, J . Phys. C,7, 1829 (‘1974). (28) W. Freylend, J. Noncryst. Solids, 35, 36, 1313 (1980). (29) W. F. Brinkman and T. M. Rice, Phys. Rev. D , 2, 1324 (1970). (30) J. C.Thompson, “Electrons in Liquid Ammonia”, Oxford University Press, Oxford, 1976. (31) R. Catterall and M. R. C. Symons, J. Chem. SOC.A , 13, part XXIV (1966). (32) L. Onsager, Rev. Mod. Phys., 40,709 (1968). (33) M. H. Cohen and J. C. Thompson, Adv. Phys., 17, 857 (1968). (34)J. P. Lelieur, P Damay, and G. Lepoutre in “Electrons in Fluids”, Colloque Weyl 111, J. Jortner and N. R. Kestner, Ed., Springer Verlag, West Berlin, 1973,p 203. (35) S. Lamis, C. Schleirker, 8. K. Chakraverty, R. Buder, and M. Marezio, Phys. Rev. 8 , 14, 1429 (1976). (36) M. Gourmala, C. Schlenker, and M. Mercier, “Physics of Semiconductors”, B. L. H. Wilson, Ed., Institute of Physics Iierles No. 43, 1978,p 469. (37) E. Schindewolf, paper in this issue. (38) A. Robertson, J. V. Acrivos, A. Thompson, M. P. Klein, and K. Hathaway, paper in this Issue. (39) J. Acrivos and N. F. Mott, Phil. Mag., 24 (1971). (40) L. Friedman, J . Noncryst. Solids, 6, 329 (1971). (41)Papers by various authors in Phil. Mag., 38, 463-549 (197’8). (42) C. J. Adkins, J . Phys. C , 11, 857 (1978).
Influence of Critical Fluctuations of Concentration on the Transport Properties of Metal-Ammonia Solutions Pierre Damay’ Laboratoire des Surfaces nt Interfaces LA 253, Ecole des Mutes Etudes Industrielles, 59046 Lille, France
and Pierre Chieux Instnut Laue-Langevin, 156X, 38042 Grenoble-C%ex, France (Received July 17, 1979)
The metal-to-nonmetaltransition in metal-ammonia solutions is too difficult to be completely and quantitatively understood from a microscopic point of view (Mott). Jortner and Cohen supposed that the solution was not homogeneous in order to solve the problem from a classical standpoint by use of macroscopic methods. We first analyze the nonhomogeneous model. The structure of the solution must be proposed from specific experiments able to determine a structure and not to interpret transport properties. From structural and thermodynamic considerationswe show that the Jortner-Cohen model is unlikely. From recent data obtained by neutron scattering we consider the influence of critical concentration fluctuations on the transport properties of these solutions.
The metal-to-nonmetal transition in metal-ammonia solutions (MAS) is a very difficult topic for which no quantitative description has been given yet by a microscopic the0ry.l A large amount of work has already been devoted to the problem (see Thompson2 for an exhaustive review), the most elaborated approaches being those of Mott1p3 and J~rtner--@ohen.~ We make here some comments based on recent experimental observations about this last model. Jortner and Cohen made the hypothesis that the solution was not homogeneous or bimodal for concentration between 2.3 and 9% of metal. In that concentration range the system was considered as a mixture of microscopic regions of either 9 or 2.3% concentration. A percolation problem was then posed. The size of the microticopic regions was quite large (about 30 A across); the percolation could be treated classically by a refinement of the effective medium theory (EMT).4 Numerous transport properties were accounted for by this 0022-3654/80/2084-1203$0 1.OO/O
model in the above concentration range. The question raised then was to find experimental support for such a structure where the local concentration fluctuates around two poles and the microscopic regions have rather well-defined boundaries, Le., a micelle type of model. Such information may easily be obtained by light, X-ray, or neutron scattering, the last technique being more adapted for experimental reasons. We shall now review the most recent results obtained by small angle neutron scattering (SANS) and see how they could support the Jortner-Cohen model. In the second part we will show how the structural information presently available may influence the electronic transport properties. Microstructure of MAS as Studied by Neutron Scattering SANS experiments were performed on Na and Li ijolutions in liquid ND3 at concentrations near 4% in imole 0 1980 American Chemical Society
