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Small-Angle Neutron Scattering on Li-NDB Systems S. GOLDEN.The only question I would raise here concerns the capability of the Mossbauer effect to distinguish between various stoichiometrically equivalent species which have been proposed in the various chemical models of these solutions. That is, can the Mossbauer effect provide a definitive discrimination between Mand e--M+.e-, for example?
S. A. RICE. M solutions of alkali metals in ethers or amines containing “crown” cyclic ethers would provide a sufficient signal in a recoilless medium. To check the interpretation of metal-ammonia solutions, cesium salts in ammonia should also be studied. Cesium halides have been studied and the isomer shift found to vary with the halide (A. J. F. Boyle and C. J. Perlow, Phys. Rev., 149,165 (1966)). Thus the nature or existence of Cs (e.g., 6s2 or 6s1, 6p1) could in principle be probed. R. CATTERALL.If the M- model is still in the running, where is the M- band in ammonia? The M- band has been well characterized in many solvents including, e.g., MeNH2, very close to “3. To put the M- band within 5-600 cm-I of the esol- band is a very big coincidence. S. GOLDEN.Whether the M- band in NH3 and the e”3- band are within 500-600 cni-’ remains yet to be accepted and confirmed by additional work. Whether such proximity of the bands is to be expected depends upon one’s notions as to the species and transitions involved. I do not think currently available theory is either capable of excluding such proximity or of predicting it.
J. L. DYE. The question of the diamagnetic species in metalammonia solutions is connected with the presence or absence of diamagnetic species in amines which have a large infrared absorption in addition to the M- absorption band. Generally one observes a spin concentration by ESR which is far less than that
which would be required to give the ir band for any reasonable extinction coefficient. [See, for example, L. R. Dalton, J. D. Rynbrandt, E. M. Hansen, and J. L. Dye, J . Chem. Phys., 44, 3969 (1966).]
S. GOLDEN.The possibility that diamagnetic species other than alkali anions (and ion multiples of them) may be present in the alkali metal-ammonia solutions surely cannot be ruled out on the basis of the evidence now available. However, any such species can be expected to have diamagnetic susceptibilities which differ from those of the alkali metal anions and so the suggested magnetic analysis could be exploited to possibly rule out their presence.
J. W. FLETCHER. With reference to earlier results of Dye in alkali metal ethylamine-ammonia solutions and our pulse radiolysis data, the visible absorption attributed to Na- in pure EtNHz does not appear to shift with added “3. Instead the intensity of the visible band decreases whereas the ir band increases with increased NH3 composition. This and other data lead us to suggest Na- is not formed in NH3 solutions. S. GOLDEN.In the original experiments of Matalon, Golden, and Ottolenghi the position of the M- band in the amine-ammonia solution was found to shift with changing composition of the solvent, contrary to the observation made by Dr. Fletcher. On the basis of using the position of the I- band in the same solution as an extrapolating vehicle it was possible to conclude that the visible M- band in amine solutions did extrapolate essentially to the spectral region of the infrared absorption in metal-ammonia solutions. This led then to the suggestion that the M- bands are indeed to be found in metal-ammonia solutions, which has been elaborated in more detail by the work of Rubinstein, Tuttle, and Golden [J. Phys. Chem., 77, 2872 (1973)l.
Concentration Fluctuations in the Nonmetal-to-MetalTransition Range of the 7Li-ND3 System. A Neutron Small-Angle Scattering Experiment P. Chieux lnstitut Laue-Langevin, 38042 Grenoble CBdex, France (Received August 11, 1975) Publication costs assisted by lnstitut Laue-Langevin
Correlation lengths for concentration fluctuations in the 7Li-ND3 system have been studied by small-angle neutron scattering as a function of the solution concentration in the nonmetal to metal range which is also the region of the liquid-liquid immiscibility. The data fit the Ornstein-Zernike law with maximum fluctuation rather narrowly peaked a t the liquid-liquid critical concentration in good qualitative agreement with the thermodynamic predictions. Some results have already been reported1 on small-angle neutron scattering experiments performed on the Li-ND3 system in the nonmetal-to-metal transition region. These results supported the idea of large concentration fluctuations extending several degrees above the liquid-liquid critical temperature near the critical concentration. I t was of interest to extend these studies over the concentration scale in the transition region in order t o investigate the concentration dependency of the characteristic length for correlated fluctuations. This was considered worthwhile in view of the heterogeneous model developed by Jortner and Cohen2 to interpret the electronic transport properties over the whole nonmetal-to-metal transition range (-2 to 9 mol % metal (MPM)).
I. Experimental Details We briefly recall the experimental conditions of the small-angle neutron scattering experiments. They were performed on the D11 machine of the Institut Laue-Langevin in Grenoble. The machine is installed a t the end of a neutron guide tube looking a t a cold source. A wavelength selector provided us with neutrons of a wavelength A 7 A with a resolution AA/A = 9%. The sample chamber in which the cryostat is mounted is located at the center of an 80m-long evacuated system. Forty meters on the reactor side is used for the collimation device ensured by removable sections of guide tube. The detector can be plugged a t defined distances up to 40 m on the other side. It is a BF3The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
p. Chleux
2892
11. Data Analysis
The neutron scattering signal is the sum of a coherent, incoherent, inelastic, and multiple term. For a binary system the coherent term can be expressed at k = 0, i.e., at zero angle, as in ref 1.
i
I
\-
Bdhamrtr "
01
02
03
(p;
I
or
(2)
OL
Figure 1. Intensity vs. k plot of a 4.17 MPM Li-NDS solution. Four
scales representing three different detector posltions and a wavelength change are shown. These are raw data. The statistical dlstrlbution of the experimental polnts cannot be represented on this scale. type planar multidetector composed of 4096 square cells (64 X 64 cm total area) centered perpendicular to the beam direction. A cadmium beam catcher placed in front of the detector protects it from the direct beam and masks about 110 cells. Since in our case the scattering signal obtained was always centrosymmetric, the neutrons counted in cells equidistant from the detector center could be summed. We usually obtained a series of 30 significant intensity values vs. scattering angle for one detector position. The exposure time was always taken so as to ensure a statistical accuracy of 0.2 to 0.3% for the summed intensity values. Only one detector position at 3.7 m from the sample and covering the to 8.5 X k range 1.4 X (Aw1) (at X 7 A) was used to study the concentration effect (Note: k = (47r/X) sin 8, with 28 being the scattering angle.). The temperature was stabilized to 0.2OC but read only to 2OC which is worse than our previous experimental conditions but was of no importance since we deliberately stayed away from the critical temperature. The background noise (see the BdF quartz line on Figure 1) comes essentially from the cryostat aluminum tail. It was always corrected for taking into account the transmission of the sample. The transmission was measured in situ, the neutron beam being attenuated by going through a pinhole in a cadmium plate and sent through the sample (in and out position) on the central cell of the multidetector. The beam catcher was removed for this experiment. In the 3 1 ~ 7 0detector position (see Figure l), the background corrections might slightly affect the data over a few cells, say over about three summed intensity values. The sample volume irradiated by the neutron beam was about 7 mm thick over an area 3.5 X 12 mm determined by a cadmium slit mounted on the cell. A first series of samples consisted of concentrations 1.32, 4.17, 10.9 MPM, plus a pure ND3 sample and several samples around 20 MPM concentration. More recently a series of concentrations 1.50, 2.50, 3.40, 4.45, 5.30, and 6.60 MPM was also prepared. The solutions were prepared3 at concentrations known as a priori by weighing the %i, introducing it into the quartz cells, and condensing on it known quantities of ND3 (99.8% isotopic purity). Several runs were made over a year's time, giving reproducible results. We report essentially on the last most extensive series of concentrations.
+
The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
coh
= AKT
+ BS,,(O)
with
(q)
Scc(0) = N ~ B T /
ac
T,P,N
are the mole fractions of the two constituents (c1+ cz = 1); b l , b2 are the neutron scattering lengths; VI, VZare the partial molar volumes (clV1 c2V2 = V / N ) ;N is the number of atoms in the system and V the volume of the system; k g is the Boltzmann constant: KT is the isothermal compressibility; u is the scattering cross section; il is the solid angle; G is the Gibbs free energy; and S,,(k) is the structure factor for concentration fluctuation. Relation 1 can easily be obtained from the Faber and Ziman expression for the coherent scattering of a binary mixture which is a linear combination of partial structure factors, S,j(k) CI, c2
+
(2)
coh
+
= N[clb12 c2bz2 C22bZ2(SZ2
+
- 1) +
- 1) + 2ClC2blb2(S12 - 111
(3)
and from the Bhatia and Thornton4 expression for the Sij at k = 0 relating them to the thermodynamics of the system. We see, therefore, that from p u r e e thermodynamic values we can predict the possibility of a strong coherent scattering signal in the vicinity of a critical point where the activity vs. concentration curve flattens and therefore the S,,(O) term in eq 2 diverges. The activity vs. concentration has been studied for a long time in metal ammonia. More recent work by Thompson and Ichikawa6 confirmed the divergency of Sc,(0) in the liquid-liquid phase separation region. Of course, the thermodynamics approach does not give any information on the angular dependency of the scattering signal or the S,,(k) values a t k # 0. In order to obtain experimentally the coherent scattering term all the other terms, incoherent, inelastic, multiple must be subtracted, In the previous study1 we assumed that all these terms as well as the AKT term of eq 2 had no angular dependency (gave a flat 1(k) signal) and that all the structural information belonged to the Scc(k)term, the concentration fluctuation term. This assumption was carefully checked by several runs away from the critical concentration either on pure ND3 or on solutions near saturation which gave a perfectly flat I ( k ) signal. The change of wavelength from 7 to 10 A did not affect the data at 4 MPM either. The inelasticity effects might therefore be considered as giving also negligible angular dependency. We are therefore left with a constant term to subtract from the experimental total scattering signal I ( k ) . That
Small-Angle Neutron Scattering on 7Li-ND3 Systems
2893
TABLE I
_ _ - _ ~ - ~ _ _ _ _ Parameters of eq 5
Concentration, __
A
B
C
Correlation length (8,
0.0061 ?: 0.0003 0.0028 i 0.0001 0.0032 i 0.0001 0.014 I0.003
4.14 f 0.30 2.57 f 0.10 2.74 i 0.12 1.86 i 0.85
74.6 1.8 75.6 i 1.7 82 i 1.8 65 i 1.4
26.1 I3 30.3 i 2 29.3 I2 11.5 i 7
MPM 3.42 i 4.44 t 5.32 i 6.52 i
0.03 0.04 0.05 0.06
a
term can be determined experimentally from the value of I ( k ) a t large k where the small-angle signal falls off to negligible values. This was done for the 4.17 MPM concentration and is shown on Figure 1. At the top of the drawing we have represented the four 12 scales 5 X to 30 X low3 A-l, 2 X to 13 X A-1, 0.08 to 0.3 A-l, and 0.085 to 0.48 8-1(partially represented for lack of space) corresponding to the detector positions 10, 2.50, and 0.66 m (with also the X 10 8 run for that last position). The statistical distribution of the experimental points is too narrow to be represented on the drawing. We see how well under these experimental conditions the constant can be determined. The S c c ( k )signal was shown1 to follow the classical Ornstein-Zernike law (see Figure 2)
+
SCc(k)-l= A ( T ) [ K 2 k 2 ]
(4)
where 6 = 1/K is the correlation length of the fluctuations. A ( T ) is a constant which might slightly depend on temperature. The Ornstein-Zernike relation was verified over all the investigated k range a t the 4.17 MPM concentration. We recall that we are always choosing the wavelength large enough to not see (even a t the 180" scattering angle) any feature belonging to the scattering pattern of the intramolecular distances or first neighbor distributions of the ND3 molecule or of the saturated solutions. These patterns were studied independently on a conventional diffractometer and show up at about 0 . 7 ~ 0 . A-1. 8 We are here truly in the small-angle scattering regime looking at concentration fluctuations extending over several atomic or molecular sites. to In the present study we covered only the 1.4 X 8.5 X A-1 range where most of the scattering occurs (see Figure 1).The value of the conitant term C to be subtracted from the total scattering intensity I(k) was obtained from a nonlinear least-squares fitting of the data with an Ornstein-Zernike type equation.
[ I ( k ) - C]-l = A
+ Bk2
Flgure 2.
Ornstein-Zernike plots at large k values of a 4.17 MPM Libars represent the statistical accuracy.
NDs solution. The error
Li-ND3 T = 462 2'C
-
400
c
(5)
111. Results and Discussion The results are presented in Figure 3 on an intensity vs. k scale for a series of concentrations a t a temperature T = -46 f 2°C. The 20-MPM sample was actually measured at T = +5"C and the 10.9-MPM sample was taken from a preliminary series of runs. It is obvious that most of the scattering occurs for concentrations near 4 MPM. We present in Table I the values of the A, B, C parameters of eq 5 as well as the correlation length 6 for concentrations near 4 MPM. No fit of the Ornstein-Zernike equation could actually be made at the other concentrations where the signal is much too flat. It is noticeable that a t concentrations near the critical one the correlation length for fluctuations is rather concentration independent. In Figure 4 we have plotted the extrapolated I ( 0 ) - C values (see eq 5 ) for all the investigated concentrations. (Of course, at the concentrations where the Ornstein-Zernike fit was not feasible the extrapolation is rather conjectural.) We see that these values compare qualitatively well with
,250 MPM -109 MPM 150 MPM 20 MPM
.
.
5
Intensity vs. k plots showing the concentration effect. The 10.9-MPM sample was reported from another series of experiments. Flgure 3.
PO-MPM sample was measured at +5"C:The
the published S,(O) obtained from thermodynamic^.^ They are peaked at roughly the critical concentration X, = 4.5 MPM obtained independently by Katsumoto and Lepoutre (this symposium). If we now consider the Na-NH3 solutions where S,(O) has a much broader peak,5 we might expect to have significant concentration fluctuations extending over a broader concentration scale. This is of real importance since parameters of the lithium solutions are The Journal of Physical Chemistry, Vol. 79,No. 26, 1975
2894
P. Chieux
below 12 MPM. We believe that it corresponds essentially to the concentration dependent distribution function of the solvated lithium atoms in the system. In the case of the small angle neutron experiments, the choice of a large wavelength avoided any perturbation from these interference terms at high concentration, and at the lowest concentration the effect was not detectable owing to the small scattering length of the lithium atom.
Li-ND3 T=-46?2"C
Acknowledgment. Thanks are due to Professor Lepoutre and associates and especially to F. DeBaecker for a very helpful collaboration.
References and Notes
M PM
Figure 4. Comparison between the coherent signal at zero angle and S,,(O)
(1) (2) (3) (4) (5) (6)
P. Chieux, Phys. Lett. A,, 48 (6), 493-4 (1974). M. H. Cohen and J. Jortner, Phys. Rev. Lett., 30,699 (1973). P. Chieux, M. J. Sienko, and F. DeBaecker, J. Phys. Chem., this issue. A. B. Bhatia and D. E. Thornton, Phys. Rev. 6.. 2, 3004 (1970). K. lchikawa and J. C. Thompson, J. Chem. Phys., 50, 1680 (1973). P. W. Schmidt. J. Chem. Phys., 27, 23 (1957).
(ref 5).
Discussion J. JORTNER. An interesting system to study will be Li-CH3NH2
often used by necessity in computations referring to the Na system. It would be interesting to check in greater detail if the concentration dependency of the slope of the OrnsteinZernike plots is consistent with the thermodynamic parameters of eq 1. The concentration dependency of the value of C (eq 5) should also be shown to depend entirely on incoherent inelastic and multiple terms. All this would require absolute measurements and careful normalization procedures. Finally a few words must be added on the interference effects which were detected by Schmidt6 and more recently by Knapp and Bale (this symposium) using small-angle x-ray techniques. We also detected a strong scattering peak a t about 1.0 A-1 with saturated solutions of 7Li-ND3 on a conventional neutron diffractometer. This peak shifted to smaller k values with dilution and was no longer detectable
The Journal of Physical Chemistry, Val. 79, No. 26, 1975
solutions where large concentration fluctuations are exhibited in the concentration range above 10 MPM.
P. CHIEUX.These fluctuations are encountered in most of the solutions near saturation and are related to the piling of the solvated ions like large balls. Of course the effect is clearly visible when no anion is present. M. H. COHEN.I noticed a nonmonotonic variation of the background intensity on top of which the Ornstein-Zernike contribution sits. It reached a maximum near the critical concentration. Do you have any ideas for explaining it?
P. CHIEUX. I think that it should be explained simply by the concentration dependency of the coefficient of the KT term in the binary scattering law. We should however take as the two species the pure ND3 and the soluated cation. We must also be careful to take the background intensity value a t the extrapolated large k value. Finally there is some experimental uncertainty in the relative intensities of these different samples. We will try to prove more quantitatively these points in the near future.
