3730
J. Phys. Chem. 1984, 88, 3730-3734
TABLE 11: Concentration Dependence of the Superstructure and of the Main Peak Position of the Structure Factor for Li.nND3 n
4 495 5 595 6 7
.peak .uosition. A-' superstructure peak main peak 1 0.99 0.975 0.945 0.945 0.72-0.78
1.9 1.9 1.91 1.92 1.94 1.97
fact its position is a linear function of the inverse of the cubic root of the volume of one Li.nND3 unit, as long as n < 6. For n = 7 there is a marked change since we would have expected the peak at 0.82 A-'. Does it imply some sudden modification of the solvated ion packing as would be created by the buildup of a second solvation shell? We do not know. At Q = 0, we also detect at this concentration a strong variation of the thermodynamic limit. In the meantime as we see in Table 11, the ammonia peak has come to closer to its pure ammonia value of 2.05 A-' at -65 OC.
On more dilute simples the superstructure peak will not be detectable, and small angle scattering due to concentration fluctuations will set in." This is up to now a general observation that superstructure peaks related to a tendency to compound formation and small angle scattering related to concentration fluctuations are mutually exclusive. We have given a brief qualitative description of the local order in liquid ammonia and concentrated lithium-ammonia solutions, with an emphasis on H bonding. The field is certainly open for a more detailed quantitative description with the isotopic substitution technique applied to neutron scattering measurements, without forgetting complementary approaches such as X-ray scattering and EXAFS, which have not yet been fully exploited. Registry No. ND3, 13550-49-7;Li,7439-93-2. (12) P. Damay, F. Leclercq, and P. Chieux, this colloquium. data analysis difficulties at high Q values should be attributed to the combination of multiple scattering and inelasticity corrections. See ref Id for a recent data treatment which overcomes the problem. The present study with two wavelengths allows us, however, to obtain the high Q structure with confidence. (13) Most of the
Extended X-ray Absorption Fine Structure Studles of Ytterbium-Ammonia Solutions J. P. Lelieur,* J. GoulonJf R. Cortes,+l and P. Friantt L.A.253, Laboratoire des Surfaces et Interfaces, HEI, 59046 Lille CPdex, France, LURE, Laboratoire Propre du CNRS, associd d I'UniversitP de Paris-Sud, BBtiment 209 C, 91405 Orsay, France, E.R.A.22 au CNRS, Interactions molPculaires, Universitd de Nancy I, B.P. 239, 54506 Vandoeuvre-les- Nancy, CPdex, France, and G.R.4 au CNRS, Physique des Liquides et Electrochimie, UniversitP Pierre et Marie Curie, Paris VI, 75230 Paris CPdex 05, France (Received: August 24, 1983; In Final Form: January 26, 1984)
Extended X-ray absorption fine structure (EXAFS) measurements are reported at the LIrIedge of ytterbium in ytterbium-ammonia solutions, for solutionsof mole ratio (NH,/Yb) 294,151,and 15.6. For the first solvation shell, the determined Yb-N distance is 2.62 & 0.02 8, while the number of ammonia molecules found is slightly larger than 6. For the first solvation shell, the Yb-N distance and the number of ammonia molecules are temperature and concentration independent. Others signals, temperature and concentration dependent, are also clearly observed at distances ranging between 3.3 and 4.5 A. Various explanations for these signals are considered.
Introduction In recent years, the advent of synchrotron radiation in storage rings has considerably renewed the interest of the physical chemist for X-ray absorption spectroscopy,' especially for solution chemistryS2 A major advantage of this method indeed lies in the fact that it can be used for either electrolytic or nonelectrolytic solutions. Let us remember that there are two different sources of informations available from this spectroscopy: (i) the detail of the X-ray near edge structure (XANES), e.g., the energy position of absorption threshold resonance, can be used for ascertaining the oxidation state of the metal in solution; (ii) the modulation of the absorption spectrum above the absorption edge (EXAFS) has a structural content related to the radial distribution of the closest neighbors around the X-ray absorbing center. As far as metal-ammonia solutions (MAS) are concerned, X-ray absorption spectroscopy has already been used by Acrivos et alp3in a pioneering work concerning rubidium and strontium/", solutions. The results heretofore published are more detailed for the EXAFS spectra of the rubidium solution recorded at the K edge of the metal: the Rb-N distance was 3.1 A while the coordination number was close to 6. Also quite noteworthy
* Laboratoire des Surfaces et Interfaces, Lille, France. TLaboratoire Propre du CNRS, Orsay, France. Interactions Mol6culaires, Vandoeuvre-les-Nancy, France. Physique des Liquides et Electrochimie, Paris, France. 0022-3654/84/2088-3730$01.50/0
is a substantial shift of the absorption threshold of every MAS solution, as compared to the spectra of other model compounds (e.g., RbN,). These results prompted us to start a similar research program at LURE, the French National Synchrotron facility, but ytterbium/", solutions were retained as a reasonable choice because we had previously determined the phase diagram and various physical properties of this ~ y s t e m . ~Furthermore the LIIl edge of ytterbium was expected at ca. 8950 eV, Le., in the most favorable energy range of emission from the DCI machine, while the energy resolution of the monochromator is still excellent. In this short paper, we thus intend to give a preliminary account of our results on this system.
Materials and Methods X-ray Absorption Measurements. The EXAFS spectra have been recorded at LURE, on the EXAFS-I1 station, by using the X-ray emission from the DCI storage ring running under standard (1) (a) 'EXAFS spectroscopy: Techniques and Applications"; Teo, B. K.; Joy, D. C., Eds.; Plenum Press: New York, 1981. (b) Lee, P. A.; Citrin, P. H.; Eisenberger, P.; Kincaid, B. M. Reu. Mod. Phys. 1981, 53, 769. (c) Teo, B. K. Acc. Chem. Res. 19808 13, 412. (2) Goulon, J.; Goulon-Ginet, C. Pure Appl. Chem. 1982, 54, 2307. (3) Acrivos, J. V.; Hathaway, K.; Robertson, A,; Thompson, A,; Klein, M. P. J . Phys. Chem. 1980,84, 1206. (4) Hagedorn, R.; Lelieur, J. P. J. Phys. Chem. 1981, 85, 275.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3731
EXAFS Studies of Yb-NH3 Solutions conditions (1.8 GeV, 250 mA). The EXAFS I1 spectrometer has recently been described elsewhere? its major feature is a twoseparated-crystal monochromator, equipped with Si(3 11) monocrystals. The second-order harmonics are then structurally forbidden while a small mistuning of the two crystals makes it easily possible to reject the higher orders. The detectors were two gas-filled ion chambers, incorporating homemade low noise preamplifiers. The samples were contained in polyethylene cells, directly machined in the bulk material with very thin (100 pm), flat windows. The thickness of each cell was optimized in order to achieve the standard condition pe 1. These cells equipped with 0 rings were perfectly air tight and could be pumped down to 5 X lo4 torr for more than 12 h before condensation of ammonia. Materials. Solubilization of ytterbium metal in ammonia was not achieved in the cells but in a special glass vessel. This solubilization is more difficult and much slower than for alkali metals. The surface of ytterbium (Alfa Inorganics, 99.5%) was first cleaned mechanically, then the metal was cut into small pieces, and they were weighted with a microbalance before introduction into the pyrex vessel. A known amount of ammonia, dried on alkali metal, was condensed on ytterbium at dry ice or liquid nitrogen temperature. The solution was then introduced into the polyethylene cell via pyrex tubing which was sealed off after this transfer. Results have been obtained for solutions corresponding to various mole ratios R = NH3/Yb = 294, 151, and 15.6, or equivalently for xz = 0.0034,0.00659, and 0.0603. The first and second solutions are more dilute than the lower limit of the miscibility gap, the third being by contrast slightly more concentrated than the upper limit of the miscibility gap. The rather high dilution of the first solution required us to accumulate up to 19 scans of EXAFS spectra in order to improve the signal/noise ratio. On the other hand, we use the commercially available compounds YbF3 and Ybz03as standard references for our EXAFS experiments. Analysis of the EXAFS Data. The analysis of the spectra includes the usual “preparation” of the data, Le., (i) removal of the pre- and postedge background contribution to the whole absorption coefficient p(E) by a fast smoothing procedure, (ii) normalization of the spectra with respect to the edge jump, (iii) transformation from the photon energy scale to the photoelectron wavenumber scale k = ((2m,/h2)(E which implies the definition of the energy threshold Eo above which the photoelectron is free. For a discrete Gaussian distributed lattice, the normalized oscillatory component x(k) of the absorption coefficient is given by the approximate EXAFS formula X(k) = 1 4 -Eexp(-2u:k2)IFj(k,~)IA(Rj,k)sin (2kRj k j R:
+ rC;.(k)) (1)
where Fj(k,r) and +j(k) denote respectively the backscattering amplitude and the total phase shift for thejth shell, whereas uf is the mean-squared relative displacement of the absorber/scatterer pair from the distance R? Neither the analytical formulation of x ( k ) given in eq 1 nor the parametrization of the functions Fj(k,a) and +j(k) proposed by Teo and Lee6 on the basis of pseudo ab initio calculations are fully satisfactory from a theoretical point of view but it is now well recognized that quite reliable distances can be determined within these approximations as long as one keeps slightly adjustable the energy offset Eo involved in the definition of k: e.g., the possible effect of IC;.(k) of the cationic charge states can thus be compensated by a slight shift of Eo. The prediction of the EXAFS amplitude is not yet fully satisfactory, even if eq 1 is corrected in order to take into account the finite energy resolution of the monochromator as discussed by Lengeler and Eisenberger’ and other experimental limitations such as (5) Goulon, J.; Lemonnier, M.; Cortes, R.; Retournard, A.; Raoux, D. Nucl. Instrum. Methods, in press. (6) Teo, B. K.; Lee, P. A.; Simmons, A. L.; Eisenberger, P.; Kincaid, B. M. J . Am. Chem. SOC.1977, 99, 3854. (7) Lengeler, B.; Eisenberger, P. Phys. Reu. B 21, 1980, 4507.
thickness effects? A major difficulty is the evaluation of the factor Aj(k) accounting for the loss of coherence of the photoelectron due to inelastic p r o c e s ~ e sand ~ ~ tentatively ~ written as Aj(k) = S 2 ( k )exp(-2rjRj/k)
(2)
where
-
S 2 ( k ) = [(So2- l)/.n] arctan [ ( k k,)a]
+ (Soz+ 1)/2
(3)
So2,k,, and a being predetermined fixed parameters which can be transferred from one system to the other without major changes (0.7 < So2< 0.8, k, = 9 A-I, a E 7 A). rj has to be adjusted more carefully, e.g., by using model compounds for which the Debye-Waller term can be evaluated from vibrational spectroscopy.’O The fourier-transformed spectra jii(R) reproduced in this paper are all corrected for phase shifts and amplitude of the dominant shell j according to
where g(k) is a symmetrical Kaiser window function minimizing the side lobes of the FT signals. When practicable, we thus use the Lee-Beni criterion of coincidence of the maxima of (jij(R)I and Im jij(R) in order to fix Eo.” It is also often desirable to refine the amplitude parameters (N,, uj) and we have been led to develop a package of fast but safe fitting routines. The fitting procedures always require a reduction as much as possible in the number of independent parameters because of well-known correlation effects. Fourier filtering in the R space is common practice for reducing the number of contributing shells. Reference to model compounds is also helpful for fixing amplitudes parameters. Let us conclude briefly that the aim of the data analysis is to determine the distance Rj, the number of sites in a given coordination shell, and the dispersion of distances uy
Results As illustrated by Figure la, the LIII EXAFS spectra of the various considered Yb-NH3 solutions all exhibited a strong “white line” commonly referred to as the “absorption threshold resonance”.12 As previously reported by other authors,I3 this peak is a general feature of LII1edges for all rare earth elements in 2+ and 3+ valence states and is largely due to transitions into empty 5d states. As illustrated also by Figure I b which displays the details of the edge spectra of YbzO3 and a given Yb-NH3 solution, an apparent shift of nearby 7 eV toward lower energy is observed which compares well with the similar shifts reported between Sm2+ and Sm3+or Yb2+ and Yb3+.I3 Instead of considering the maximum of the white line, one may also choose to take as reference the energy of the maximum of the first derivative of these edge spectra, more representative of the threshold itself one would then observe a smaller shift of 5.2 eV, which also compares well with the typical 5-eV Eoshift per electron charge transfer assumed for compounds of different i0ni~ity.I~One may thus infer from this observation that ytterbium in the present MAS is in the 2 oxidation state. Figure 2 displays the Fourier transformed spectrum x(R) of Yb F, obtained by inserting in eq 4 the total phase shift function (8) Goulon, J.; Goulon-Ginet, C.; Cortes, R.; Dubois, J. M. J. Phys. 1982, 43, 539. (9) Stern, E. A.; Heald, S.M.; Bunker, B. Phys. Rev. Lett. 1979,42, 1372. (10) Goulon, J.; Goulon-Ginet, C.; Chabanel, M. J. Solution Chern. 1981,
10, 649. (11) Lee, P.; Beni, G. Phys. Rev. B 15, 1977, 2862. (12) Brown, M.; Peierls, R. E.; Stern, E. A. Phys. Reu. B 15, 1977, 738. (13) Launois, H.; Rawiso, M.; Holland-Moritz, E.; Pott, R.; Wohlleben, D.Phys. Reu. Lett. 1980, 44, 1271. (14) Bunker, B. A.; Stern, E. A. Phys. Rev. B 27, 1983, 1017.
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The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 0
Lelieur et al.
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3
-110
-40
40
110
100
510
440
360
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Figure 3. EXAFS corrected pseudo-radial distribution %,(I?) at the ytterbium LIII edge for a dilute ytterbium-ammonia solution ( x 2 = 0.0034) at -60 OC.
21,
) / ,
,
,
,
,
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Figure 1. (a) Typical EXAFS spectrum at the LIIledge of ytterbium in ytterbium-ammonia solutions for mole ratio x2 = 0.0034 (Le., mole fraction R = 294) at -60 O C . The background preedge has been sub-
stracted. (b) Normalized LIIIabsorption edges of ytterbium in Yb203 and in Yb-NH3 solution (x2 = 0.061). These spectra have been recorded on the EXAFS I station at LURE.
1
1
3
4
5
b
7
8
9
IO
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Figure 2. EXAFS corrected pseudo-radial distribution zl(R) at the
ytterbium LIIIedge for powdered YbF3.
qYbF(k) of the Yb/F pair and the amplitude function F ( k ) of fluorine scatterers? The E,, value was then classically set according to the Lee-Beni criterion." This spectrum is largely dominated by the coordination shell of the fluorine at the expected distance R(Yb-F) = 2.25 f 0.02 &I5 where a second, rather broad signal, assigned to a more disordered Yb-Yb shell, is still apparent. Figure 3 reproduces the Fourier transformed spectrum x(R)of the most dilute Yb-NH3 solutions (x2 = 0.0034), obtained by now inserting in eq 4 the phase shift function qybN(k) of the Yb/N (15) Zalkin, G.; Templeton, A. J . Am. Chem. SOC.1953, 75, 2453.
pair and the relevant amplitude function F N ( k )of the nitrogen scatterers. The Eo value was again adjusted according to the above-mentioned Lee-Beni criterion: it is noteworthy that the shift Eo = -7 eV derived by this method is again consistent with a typical change in the ionicity of the cation 3+/2+. The spectrum shown in Figure 3 is also clearly dominated by the signal of the coordination shell at a distance R(Yb-N) = 2.62 f 0.02 8,. However, some additional signals are clearly observable at somewhat larger distances, Le., in the range 3.3 8, < R < 4.5 A, the level of these signals exceeding by far the noise level. It is the first time, at least to our knowledge, that such additional signatures can be observed in MAS. A clear assignment of these signals is not yet possible however, but we may observe immediately that the corresponding distances are too short to correspond to metal-metal distances. Figure 4a-c also reproduces the Fourier-transformed spectra x ( R ) of the most concentrated solution (x2 = 0.06), but at various temperatures: T = -38, -58, and -85 "C. The signal ascribed to the coordination sphere at R(Yb-N) = 2.62 f 0.02 8, is not appreciably altered, while, interestingly, additional signatures at larger distances appear to be much more affected (in phase and amplitude) by the temperature variation. It should be noted for instance that these additional signals shown in Figure 3 and Figure 4a exhibit exactly the same phase: this observation confirms the physical nature of this signal observed in two independent experiments. Curiously at lower temperatures, Le., -58 "C, one may observe (Figure 4b) a more intense signal at -3.3 A, while at -85 OC (Figure 4c) these additional signatures tend to vanish. On the other hand, it was attractive to try to extract from these experiments some indications about the coordination number of the metal in these solutions. Thus the signal of the coordination shell was filtered out, back-transformed into the k space, and then fitted against a single-shell model according to eq 1. The same procedure was also carried out on the signal of the coordination shell observed for the two considered model compounds Yb,O, and YbF3. The only parameters adjusted in our least-squares optimization procedure were respectively N , , u12,and R,.Figure 5, a and b, displays the quality of the fits achieved for either the model compound (YbF3)or one solution (xz= 0.06, T = -85 " C ) . No significant variation of N , , u12,or R,is detected for the various considered solutions: N I = 6.6 f 0.6; u12= 0.0095 A 0.001 A2; R, = 2.62 f 0.02 8, while for the reference compound YbF,, we obtained under similar conditions (i.e., with the same values of rl = 0.4 A-2): N , = 8.0;
u12= 0.004 f 0.0005
A2; R1= 2.25
f 0.02
8,
The limited transferability of amplitude parameters does not allow us to refine further an absolute determination of the coordination number N , . However, it is worth emphasizing here
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3133
EXAFS Studies of Yb-NH3 Solutions
t
' '
I
'
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Figure 5. (a) Fourier back-transformed data (dotted line) and nonlinear least-squares best fit (full line) of the spectrum shown in Figure 2. (b)
Fourier back-transformed data (dotted line) and nonlinear least-squares best fit (full line) of the spectrum shown in Figure 4c for a single-shell contribution of Yb-N. bands and such a correlation has been practically used for Pt, Ir, Au, and Pd.16-18 The absence of any significant temperature or concentration dependence of the Yb-N distance in the first coordination shell is fully consistent with the results reported by Acrivos et al. for rubidium-ammonia solution^.^ The distances rubidium-nitrogen and ytterbium-nitrogen have been found equal to 3. l 3 and 2.62 A, respectively. The ionic radii of Rb+ and Yb2+ are respectively 1.47 and 1 13 A.I9 Therefore the difference between the metal-nitrogen distance and the relevant ionic radius amounts to 1.63 A for the Rb+/NH3 system and to 1.49 A for the Yb2+/NH3 solutions. These values are reasonably close, and their relative difference might reflect the effects of both the larger Coulombic attraction of the divalent cation and the slightly more covalent character of the Yb-N band. Further experiments might help to clarify this point. Of paramount interest is the observation in our spectra of other signatures beyond the first coordination shell, Le., at distances ranging between 3.3 and 4.5 A. The amplitude of these signals is definitively above the noise level of the present experiments. At -38 OC, this additional signal is peaking at ca. 3.30 A, but it becomes broader at -58 'C, ranging now between 3.3 and 4.5 A, while its amplitude decreases markedly at -85 "C. Also noteworthy is the perfect reproducibility of the phase of these signals for the spectra shown in Figure 3 and Figure 4a and which I
I
2
3
4
5
6
7
8
9
10
11
R (AI
Figure 4. EXAFS corrected pseudo-radial distribution n l ( R ) at the ytterbium LIll edge for a ytterbium-ammonia solutions (x2 = 0.0603): a, -38 OC;b, -58 O C , c, -85 OC.
that the existence of the compound Yb(NH3Ix is known, and it was found experimentally from vapor pressure measurements that x is larger than 6 and close to 6.5.4 Thus the EXAFS results reported here seem to be rather reliable.
Discussion These observations are, at least in part, consistent with the earlier EXAFS experiments carried out on M A S 3 Indeed, the formal oxidation state 2+ of ytterbium in ammonia, clearly established from the measured edge shifts, was not unexpected. In fact, the apparent discrepancy between the 7-eV shift of the white line and the 5-eV shift of the maximum of the first derivative of the edge spectra may result simply from a broader width of the white line in the trivalent Yb3+ compounds. It is now well recognized17 that variations of the peak area under the white line are related to variations of the density of states in the d valence
(16) Lytle, F. W.; Wei, P. S.P.; Greegor, R. B.; Via, G. H.; Sinfelt, J. H. J . Chem. Phvs. 1979. 70. 4849. (17) Horiley, J. A. J.'Chem. Phys. 1982, 76, 1451. (18) Rossi, G.; Jaeger, R.; Stohr, J., Kendelewicz, T.; Lindau, J. Phys. Rev. B 27. 1983. 5154. (I$),Si&ko,M. J.; Plane, R. A.; Hester, R. E. "Inorganic Chemistry"; W. A. Benjamin: New York, 1965.
3134
J . Phys. Chem. 1984, 88, 3134-3740
refer to different metal concentrations. Indeed, according to the phase diagram of our system: the solution was homogeneous at -58 OC, but solid ammonia should have been deposited below ca. -78 OC: therefore we expect at -85 OC a lower effective mole ratio of NHJYb, the number of ammonia molecules available for a second solvation shell of the Yb2+ cation being thus substantially reduced, while the “metallic character” of the solution increased. The temperature dependence of these unknown signatures may thus support their assignment to additional shells of light elements, Le., nitrogen atoms. In discussing this point, one should also keep in mind that the peak observed at 3.3 8, (Figure 4b) occurs at a distance much too short, to be assigned to some Yb-Yb signal, e.g., resulting from an incomplete dissolution of the CFC Yb metal ( a = 5.468 AM). On the other hand, such a short Yb-N distance (3.3 A) of the second solvation shell would still require some penetration of the nitrogen atoms of this shell into the proton sphere of the first solvation shell, since the expected N-H bond length is ca. 1.1 A. A quantitative analysis of the amplitude of this additional signal suggests further the presence of only a small number of ammonia molecules (1 or 2) in this second shell. It thus becomes attractive (20) Klemm, W.; Bommer, H. 2. Anorg. Chem. 1937, 231, 138.
to tentatively assign this signal to the nitrogen atoms of ammonia molecules of solvated electrons interacting with the solvated cation. Such an interpretation would also explain why this signal is vanishing at lower temperature. Let us emphasize here that the observation of this signal is indeed possible in EXAFS spectra, because the time scale of the X-ray absorption processes ( s) is shorter than the relaxation time of the solvated electron ( s). As the interacting solvated cation and solvated electrons may take different relative configurations, various temperature-dependent signatures might be observed, such as these of Figures 3, 4a, 4b, and 4c. Further work is clearly required before the present hypothesis can be definitely admitted, and a new set of EXAFS experiments is now in progress, in order to refine our present conclusion. This preliminary study, however, gives a valuable illustration of the potentiality of X-ray absorption spectroscopy for a better understanding of the structure and properties of metal-ammonia solutions. Acknowledgment. The authors are indebted to the team of the “Laboratoire de l’accilirateur liniaire” (Orsay), for running the DCI machine over dedicated beam time sessions, and to Prof. Lepoutre for stimulating discussions. Registry No. Yb,7440-64-4; NH,, 7664-41-7.
A Critical Crossover in Metal-Ammonia Solutions (Na-ND,) Angle Neutron Scattering
As Observed by Small
Pierre Damay, Francoise Leclercq, LA253 CNRS-Ecole des Hautes Etudes Industrielles, 59046 Lille, France
and Pierre Chieux* Institut Laue Langevin, 156 X , 38042 Grenoble Cedex, France (Received: November 2, 1983; In Final Form: January 15, 1984)
A detailed investigation of the concentration fluctuations related to liquid-liquid immiscibility in the Na-ND, system has been performed by small angle neutron scattering. The explored reduced temperature range (T = ( T - T,)/T,) extends from t = 6 X to t = lo-’. It is observed that, a few degrees away for T,, the critical index v, changes rather abruptly from near mean-field-like values to critical values.
The study of critical phenomena in metal-ammonia solutions has been a topic of interest for the past 15 years.’ This system is one of several to present a liquid-liquid phase separation linked to a metal to nonmetal transition. It is also a case where the critical properties for the phase separation show a peculiar behavior. The critical indices were supposed to obey the mean field theory until it was discovered that the index p for the phase diagram switched to the critical value 0.33 very near the critical temperature TCe2The question over the existence of a crossover near the critical point was raised. Most of the transport properties have been measured in the metal to nonmetal transition range of the metal-ammonia system, Le., the electrical conductivity, Hall effect, thermoelectric power.’ A few measurements of the correlation length 5 for concentration fluctuations have already been performed by small angle neutron scattering (SANS) on the lithium-deuterated ammonia system at different concentrations between 2 and 9% metal., They showed that the Ornstein-Zernike formalism could be used: and (1) J. C. Thompson, “Electrons in Liquid Ammonia”, Clarendon Press, Oxford, 1976. (2) P. Chieux and M. J. Sienko, J . Chem. Phys., 53, 566-70 (1970). (3) P. Chieux, Phys. Lett. A, 48,493-4 (1974); J. Phys. Chem., 79,2891-4 (1975); P. Chieux and P. Damay, Chem. Phys. Lett., 58, 619-21 (1978). (4) L. S. Ornstein and F. Zernike, Phys. Z., 19, 134 (1918).
0022-3654/84/2088-3734$01.50/0
that for reduced temperature greater than a near mean field behavior was obtained. The aim of the present work is to pursue this study along the critical isochore of the Na-ND, system (the critical concentration is near 4.1% metal) with improved temperature measurement and control (0.02 K instead of 0.2 K) in order to investigate in detail the region nearest to the critical point. As is known5 SANS is a powerful tool for the study of critical fluctuations. The main interest lies in the fact that the q, 4 range investigated is much larger than for static light-scattering experiments (q = (4a/X)sin 0, where 20 is the scattering angle). In practice correlation lengths from 5 to 3000 are detectable. This enables one to verify the correlation lengths and to check for a crossover a few degrees away from the critical point. SANS experiments are furthermore especially appropriate for opaque systems such as found near a metal to nonmetal transition. In the first part of this paper, we present the experimental setup and the preparation of the samples. Then we give the formalism which is adapted to the case where a large temperature range is investigated. Next, we develop the data analysis with an emphasis on the correction for background and weakly temperature-dependent terms. Finally, the parameters v, Eo, and T, are obtained (5) P. Damay and P. Chieux, Z . Naturforsch. A , 34, 804-9 (1979)
0 1984 American Chemical Societv
