J. Phys. Chem. 1984,88, 3755-3760
3755
the probability of any given density fluctuation increases, resulting in an increased amplitude of this tail. Secondly, an increase in density places the system further inside the excitonic phase with flatter single-particle and exciton bands. The flatter bands liberate more phase space for these low-frequency transitions. Both the increased density fluctuations and the flatter single-particle bands yield an increase in the optical absorption foot at higher density, again in agreement with the Marburg experiments. The formation of these enhanced density fluctuations, with their correlated increased excitonic amplitude, may be regarded as excimer condensation.
transition ("the Marburg line") in dense mercury vapor. The previous explanations for the metal-nonmetal transition were examined and found to be deficient. The speculation as to the origin of the Marburg line was fraught with difficulties, and the Marburg line itself was not understood. We have proposed in this paper that insulating liquid mercury and dense mercury vapor comprise a (disordered, possibly inhomogenerous) excitonic insulator phase. The proposed phase diagram eliminates the mysteries of the metal-nonmetal transition and naturally explains the dielectric anomaly and optical absorption foot that characterize the Marburg line.
Conclusions In this paper we have briefly reviewed the metal-nonmetal transition in expanded liquid mercury and the dielectric/optical
Acknowledgment. We thank J. Klafter, T. Upton, F. Hensel, and W. W. Warren for helpful discussions. Registry No. Mercury, 7439-97-6.
Nuclear Magnetic Resonance Study of Lithium in Liquid Ammonia and Methylamine Yoshio Nakamura,* Masahito Niibe, and Mitsuo Shimoji Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Japan (Received: August 15. 1983; In Final Form: October 12, 1983)
The Knight shifts and the spin-lattice relaxation times of 'Li in liquid ammonia and methylamine have been investigated with a particular interest in the transition from localized to itinerant electron states in the respective systems. A considerable enhancement to the Korringa relaxation rate has been observed in lithium-methylamine solutions, while it was less pronounced in lithium-ammonia solutions. This difference appears to be related to the structural homogeneity of these solutions.
Introduction Metal-ammonia solutions show drastic changes in various properties with changes in metal concentration; form very dilute solutions which contain paramagnetic solvated electrons and solvated metal ions to concentrated solutions which show characteristics of liquid metals containing nearly free electrons.' Nuclear magnetic resonance (NMR) studies provide useful information about the state of the dissolved metals through the Knight shifts and the relaxation rates of various nuclei in these solutions. The N M R of lithium-methylamine (CH3NH2)solut i o n is ~ also ~ ~ useful ~ for the investigation of the role of the host solvent, by comparison with results in metal-ammonia (NH3) solutions. We have already reported the results of measurements of the Knight shift and spin-lattice relaxation time of 7Li in Li-CH3NH2 and Li-NH3.4y5 We have also made some detailed investigations of the N M R of 23Na and 14N in Na-NH3.6*7 The purpose of the present paper is to examine the nature of Li-NH3 and Li-CH3NH2 from the Knight shifts and relaxation times of 7Li, by adding some complementary experimental data to the earlier data for these solution^^^^^^ with an improved experimental technique. The results are also compared with those for 23Nain Na-NH3 and some interpretations of the data in the ( 1 ) Thompson, J. C. "Electrons in Liquid Ammonia"; Clarendon Press: Oxford, 1976. (2) Nakamura, Y . ;Toma, T.; Shimoji, M.; Shimokawa, S . Phys. Lett. A 1977,60, 373. Nakamura, Y.; Toma, T.; Shimokawa, S., unpublished work. (3) Holton, D. M.; Edwards, P. P.; McFarlane, W.; Wood,B . J . A m . Chem. SOC.1983, 105, 2104. (4) Nakamura, Y.;Hirasawa, M.; Niibe, M.; Kitazawa, Y . ;Shimoji, M. Phys. Lett. A 1980, 79, 131. (5) Nakamura, Y . ;Niibe, M.; Shimoji, M. J. Phys. Colloq. (Orsuy, Fr) 1980, 41, C8-32. ( 6 ) Niibe, M.; Nakamura, Y . ;Shimoji, M. J . Phys. Chem., in press. (7) Niibe, M.; Nakamura, Y . ,to be submitted for publication.
0022-3654/84/2088-3755$01.50/0
previous report for Li-NH35 are reexamined.
Experimental Section Li-NH, and Li-CH3NH2were prepared from 99.9% Li (Merck Co.), 99.99% NH, (Seitetsu Kagaku Co.), and 99% CH,NH2 (Tokyo Kasei Co.). The liquefied ammonia and methylamine were treated with lithium metal to remove traces of water and oxygen. The lithium metal was cut and introduced into an N M R cell in an argon-atmosphere glovebox. The cell of Pyrex glass was 8-mm i.d. and equipped with a Teflon valve, through which the solvent was introduced and condensed in the cell. The sample solutions were placed in an alcohol bath (ca. -40 "C) to complete the dissolution of the metal and homogenize the solutions. This procedure was followed each time when samples stored in a liquid nitrogen bath were remelted. After each measurement, the sample solutions were analyzed by evaporating the solvent and titrating the residual metal content with standard hydrochloric acid. N M R measurements were made with a Bruker SXP 4-100 pulsed FT spectrometer operating at 34.98 MHz for 7Li. The reference for N M R shifts was 7Li in a L i N 0 3 solution in the respective solvents. The spin-lattice relaxation times were measured by the standard 18Oo-r9O0 pulse sequence technique. Measurements of the relaxation times were also made for solutions of lithium salts in the respective solvents in order to evaluate empirically the contribution of the quadrupolar relaxation for 7Li. Results The Knight shift is defined as K(M) = (vs
- vr)/vr
(1)
for experiments at a fixed magnetic field, where v, and v, are the resonance frequencies of a particular nucleus M in a sample solution and the reference, respectively. As observed shifts for 0 1984 American Chemical Society
Nakamura et al.
3756 The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 I h
E
' I
15
P P v
h 10 -I
Y
Y
5
L
0
5
10
C Li Figure 1. Knight shifts of 7Liin Li-NH,: 0 , 253 K; A, 233 K 0, 218 K; 0,203 K, V, ref 5 (216 K).
20 -
15 (MPM)
I
20
Figure 3. The spin-lattice relaxation rates of 7Liin Li-NH,: 0 , 253 K A, 233 K 0, 218 K 0,203 K V, ref 5 (208 K).
5
A
h
E
-
h
0
n P
15-
h
3
x 10-
5d
0
10
C Li
20
I
(MPM)
Figure 2. Knight shifts of 7Liin Li-CHpNH2: 0,213 K 0, ref 2 (208 K); A, 3 (203 K).
'Li, Kobsd(Li),were relatively small, a correction for the difference in the magnetic susceptibilty of the sample and the reference was necessary and was made by using the relation 2a K(Li) = Kobsd(Li) + T ( x v r - x v s ) (2) where xvrand xvsare the volume susceptibilities of the reference and the sample. When magnetic susceptibility data for Li-NH3* and Li-CH3NH2 were used, values of the corrected shift, K(Li), were obtained and are shown in Figures 1 and 2. The present results are in reasonable agreement with the previous data.2*4*5 The values of K(Li) show a small concentration dependence at lower metal concentrations and then increase sharply around the composition corresponding to the metal-nonmetal (M-NM) transitions in the respective systems: around 5 MPM in Li-NH," and around 15 MPM in Li-CH3NH2,11'12 where MPM denotes the concentration expressed in mole percent of metal. The results of K(Li) for Li-CH3NH2reported recently by Holten et ale3are somewhat larger than the present ones, as indicated in Figure 2. The spin-lattice relaxation rates, l/T,, for Li-NH3 and LiCH3NH2are respectively shown in Figures 3 and 4, together with previous data.2s4-5The values of l / T I decrease with increasing metal concentration in the nonmetallic region. In Li-NH3, the values of l/Tl increase in the metallic region above 9 MPM. Such an increase in the relaxation rate, however, has not been observed (8) Depriester, A.; Fackeure, J.; Lelieur, J. P. J . Phys. Chem. 1981, 85, 272. (9) Nakamura, Y.; Yamamoto, M.; Shimoji, M. "The Properties of Liquid Metals"; Takeuchi, S., Ed.; Taylor & Francis: London, 1972; p 385. Nakamura, y.; Toma, T., unpublished work. (10) Hirasawa. M.; Nakamura, Y.; Shimoji, M. Eer. Eunsenges. Phys. Chem.'1978, 82, 815. (11) Toma, T.; Nakamura, Y.; Shimoji, M. Phi!. Mag. 1976, 33, 181. (12) Edwards, P. P. J . Phys. Chem. 1980,84, 1215.
Figure 4. The spin-lattice relaxation rates of 7Liin Li-CH,NH2 at 208 K 0,present work; 0,ref 2.
for 23Nain Na-NH3,6 the observed values of 1/ T1 being nearly constant above 5 MPM. In highly conducting samples, the applied radiofrequency field in N M R measurements is much attenuated over a distance characterized by the skin depth. We note that the diffusion of the resonating nuclei should affect observed values of T I ,if the diffusion time of the nuclei through the skin depth becomes comparable to the relaxation time of the nucleus under study. It has been shown6 that this effect is not important for 23Na in Na-NH3 because of the relatively short relaxation times of 23Na. The observed values of T I for 'Li are of the order of 10 s or 100 times longer than those for 23Nain the maximum Tl region around 8 MPM. At this composition, the skin depth is estimated to be 270 fim at 34.98 MHz with conductivity values'O of u = lo3ohm-' cm-'. On the other hand, the diffusion length at times on the order of 10 s is estimated to be 170 pm from data on the diffusion coefficient of lithium in Li-NH3.13 The skin depth becomes smaller than the diffusion length above 10 MPM, which indicates that a considerable part of the magnetization inverted by a 180' pulse in the skin depth region should diffuse away from this region in a time comparable to T I . This certainly causes a large apparent relaxation rate or a smaller T I value. We conclude thus that the increase of 1/ Tl observed in the metallic region of Li-NH,4,5 is an apparent one due to the skin depth effect and that the data of 1/ T , above 8 MPM cannot be used for further discussion. In Li-CH3NH2,on the other hand, smaller values of the conductivity and TI make this skin effect relatively small and no apparent increase of l/Tl was observed over the entire range of concentration studied. (13) Garroway, A. N.; Cotts, R. M. "Electrons in Fluids"; Jortner, J.; Kestner, N. R., Ed.; Springer: Berlin, 1973; p 213.
.
Li in Liquid Ammonia and Methylamine
The Journal of Physical Chemistry, Vol. 88, No. 17, I984 3757
I
-k-
I
0.2
1
Li-CH,NH,
ul
A
0 h
F Li
c 0
- NH3
0 .1 2
4
?IT
6
8
(lO-'poise K-'1
t
Figure 5. The spin-lattice relaxation rates of 'Li in salt solutions as a function of v/T: 0, LiN03-NH3; A, LiC1-CH3NH2.
The spin-lattice relaxation rate of 7Li in the present systems is considered to consist of three main contributions: the magnetic dipolar interaction between 7Li and hydrogen or nitrogen, the quadrupolar interaction, and the electron-nuclear contact interaction, as given by 1/Tl(Li) = (l/TI)d + ( I / T l ) q + ( l / T I ) e (3) As we are interested particularly in the electron-nuclear interaction term, (1/TJe, we must estimate the first two terms in eq 3. For this purpose we measured TI for lithium salt solutions, in which only these two terms are predominant. Observed values of T Ifor LiN03-NH3 and LiCl-CH3NH2 are shown in Figure 5 as functions of q / T . The values of the viscosity coefficient, q, were taken from the available experimental data for these solution^.'^ From the empirical relation between l / T l and q / T for the salt (1 / T I ) , ,for Li-NH3 and Li-Csolutions, the terms, ( 1 / H3NH2were estimated by using viscosity data for these metal s o l ~ t i o n s . The ' ~ ~ values ~ ~ ~ of (l/Tl)e thus obtained are shown in Figure 6 as a function of composition. They decreased with increasing metal concentration up to the transition region in the respective solvent systems. In Li-CH,NH,, the correction for nonelectronic contributions becomes comparable to the observed rates above 18 MPM and relatively large errors should be included in the estimated values of (l/Tl)e.
+
t 10
-0lo.o
C Li
20 (MPM)
Figure 6. The electronic contribution of the spin-lattice relaxation rates of 'Li. Li-NH,: 0 , 253 K; A, 233 K; +,V, 218 K; 0 , 203 K. LiCH3NH2: 0, 208 K.
nucleus and Ne and :x are respectively the number of the unpaired electrons and the electron paramagnetic susceptibility per unit volume of solutions. It is known' that the number of unpaired electrons is not equal to that of the dissolved metal nuclei, Nn, because of the spin-pairing phenomena in dilute solutions. In the metallic region, Ne (= N,) is the number of conduction electrons per unit volume and ( I+(Li)12)avmeans the average over all the electronic states at the Fermi 1 e ~ e l . lIf~ we introduce the density of nuclear spins at an unpaired electron,16P(Li), by the relation P(Li)Ne = (l$(Li)12)avNn
(5)
then, eq 4 becomes K(Li) = ( $ )Ax PXve (Li)
= ($);y*P(Li) T XmP
(6)
where x m P is the electron paramagnetic susceptibility per mole of the metal and NAis the Avogadro number. The analyses of Knight shift data are often obstructed by lack of accurate data Discussion on the electron paramagnetic susceptibility. Since magnetic Measurements of the N M R shifts provide precise and direct susceptibility data obtained by static measurements contain information about the effective local field at a nucleus under study. contributions from all the species present in sample solutions, a In metal-ammonia (amine) solutions, this local field is mainly direct determination of the electronic paramagnetic susceptibility due to the Fermi contact interaction between the resonating nuby the ESR method is preferable. However, no such measurecleus and the s electrons. The dynamics of the contact interaction ments have so far been reported for these two systems. Thus, for can be investigated from measurements of the relaxatiion rate of Li-CH,NH,, we estimated values of xmP from our earlier data the nucleus. The composition and temperature dependence of the on the static susceptibility9 by using the Wiedemann law. For Knight shift and the spin-lattice relaxation rates in the two Li-NH3, it was very difficult to deduce the paramagnetic consystems, Li-NH3 and Li-CH3NH2, will be discussed with a tribution from the static data of Depriester et a].,* which show particular interest in the transition from localized to itinerant a large diamagnetic contribution in the intermediate composition electron states in the respective solvents. range. Therefore, we used the values of xmP determined from both Knight Shift. The Knight shift of lithium nuclei in lithiumthe static and the resonance measurements for Na-NH3,l8J9 ammonia (amine) solutions, which arises from isotropic hyperfine assuming that these values are independent of cationic species as interactions between unpaired electrons and a lithium n u ~ l e u s , ~ ~ J ~a first approximation. The values of x m P used in the present is written as analyses are shown in Figure 7. The values for Li-CH3NH2 decrease monotonically with increasing metal concentration, while the curve for Na-NH3 shows a minimum around 2 MPM, in(4) dicating extensive spin pairing around this composition. It should be noted that the curve for metylamine solutions resembles that where (I$(Li)12)av is the average electron spin density at the of ammonia solutions above room temperature,20s21where spin pairing should certainly be less pronounced.
(14) Demortier, A.; Lobry, P.; Lepoutre, G. J. Cbim. Phys. 1971,68,498. Shimoji, M. J. Chem. SOC., (15) (a) Yamamoto, M.; Nakamura, Y.; Faraday Trans. 1 , 1972, 68, 135. (b) Uchibayashi, K.; Nakamura, Y.,
unpublished work. (16) McConnell, H. M.; Holm, C. H. J . Cbem. Pbys. 1959, 26, 1517. (17) Abragam, A. "The Principles of Nuclear Magnetism"; Clarendon: Oxford, 196 1.
~
~~~~~~
(18) Lelieur, J. P.; Rigny, P. J . Chem. Phys. 1973, 59, 1142. (19) Hutchison, Jr., C. A.; Pastor, R. C. J. Chem. Pbys. 1953, 21, 1959. (20) Suchannek, R. G.; Naiditch, S.; Klejnot, 0. J. J . Appl. Pbys. 1967, 38, 690. (21) Schindewolf, U. 2.Phys. Chem. 1978, 112, 153.
Nakamura et al.
3758 The Journal of Physical Chemistry, Vol. 88, No. 17, 1984
c
4
X 1
0
10
c LI
20 (MPM)
Figure 9. The temperature coefficient of the Knight shift of 7Li: A, Li-NH3; 0, Li-CH,NH,, ref 2; - - -,Na-NH,, ref 6.
Figure 7. The composition dependence of the electron paramagnetic susceptibility: 0,Li-CH,NH, (208 K), ref 9; - - -,Na-NH, (243 K). 1O Z 2 ,
coefficients of K(Li) in the nonmetallic region may primarily be due to the temperature variation of xmP,as shown for Na-NH,$ the temperature coefficients of xmPin Li-CH3NH2 are of the order of and show a similar composition dependence to those of K(Li). Relaxation Time. The Fermi contact interaction between the nuclear spins and the unpaired electron spins also causes the dominant nuclear relaxation. In the localized electron region, the spin-lattice relaxation rate due to this interaction can be written as17,22
Calculated values of P(Li) from eq 6 are shown in Figure 8 for the present systems. The values of P(Li) for Li-CH3NH2 increase continuously up to the saturation point (22 MPM), while those for Li-NH, become less composition dependent above 2 MPM, as found for Na-NH3.6 It has been often assumed16q22 that only the cation-electron encounter species, called "monomers", are responsible for the contact interaction and so the spin density at the monomer nucleus is evaluated. However, there is still some ambiguity about the fraction of such monomers as a function of composition and temperature, so that we evaluate the spin density only in the metallic region, where P(Li) is equal to (I$(Li)12)a1. The values obtained are 7 X loz1cm-' for Li-CH3NH2(22 MPM) and 6 X lo2' cm-, for Li-NH, (8 MPM). These values are about 0.5% of the corresponding electron spin density in the free lithium atom.23 It is interesting to note that these values are nearly equal to the spin densities at the monomeric species in the nonmetallic region of the respective systems.' As the spin density at the lithium nucleus is not greatly different in the two solvent systems, the large difference in the Knight shifts is mainly due to the difference in the electron paramagnetic susceptibility or the degree of the spin pairing in the respective systems. As shown in Figure 9, values for the temperature coefficient of the Knight shift, d In K(Li)/dT, for Li-NH, and Li-CH,NH, decrease with increasing metal concentration. The values for Li-NH, are close to those for Na-NH3.6 Large temperature
under the assumption that only monomeric species are responsible for the relaxatioin as well as for the shift. Here, X, is the fraction of monomers, 7, is the correlation time of the electron-nuclear contact interaction, wL,and W , are respectivley the angular frequencies of 'Li and the electron, and A is the hyperfine coupling constant to be determined from the Knight shift data. In our earlier analysis for Li-NH3,5 the interaction was averaged for all metal ions and somewhat different expressions for (l/T,), and K(Li) were used. For Na-NH3, for which reliable magnetic susceptibilty data are available, we have evaluated values of 7, using eq 7; values of 7, obtained in his way decrease by a factor of about lo2,when we approach from a dilute solution (0.5MPM) to the transition region (4 MPM).6 We note that the reliability of such estimated 7, values depends upon the accuracy of the knowledge of Xo in eq 7, which is not always sufficient for quantitative purposes. The estimation of 7, for Li-NH3 was made without considering the monomeric entities in our previous paper,5 and its value was found to decrease by a factor of lo2 with concentration. Edwards et aLZ4have given another estimate of 7, in Li-CH3NH2 using the correlation time formalism of Warren:5 showing also an abrupt decrease of 7, in the transition region. From these results we may conclude that the decrease of (1/ TI), in the nonmetallic region is predominantly attributed to the decrease of the correlation time T, or the residence time of an unpaired electron on a particular nuclear site with increasing mobility of the localized electron. We have reported that such a decrease of 7,is well correlated to the increase of the electrical conductivity in Na-NH3,6 using the random-flight model. We note that the observed values of (l/T1), as well as other properties such as the electrical conductivity or the magnetic susceptibility are continuous between the localized electron and the nonlocalized or itinerant electron regions. These behaviors in metal-ammonia (amine) solutions appear to arise from the diminution of unpaired carrier electrons by spin-pairing phenomena on the nonmetallic side and from the
(22) O'Reilly, D. E. J . Chem. Phys. 1964, 41, 3129. (23) Knight, W. D. 'Solid State Physics"; Seitz, F.; Turnbull, D., Ed.; Academic Press: New York, 1956; Vol. 2, p 93.
(24) Edwards, P. P.; Buntaine, J. R.; Sienko, M. J. Phys. Reu. E 1979,19, 5835. (25) Warren, Jr., W. W. Phys. Rev. B 1971, 3, 3708.
10
20 CLI (MPM) Figure 8. The density of nuclear spins at an unpaired electron: Li-NH, (218 K); Q A , Li-CH3NH2 (208 K). 0
0, V,
Li in Liquid Ammonia and Methylamine
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3759
100 I
concentrations are, however, in good agreement with those preThe electrical conductivities dicted by the Mott criterion.l0.’ at the same electron concentration differ by a factor of about lo2 between the two solvent systems, indicating a much stronger interaction of electrons with the solvent in Li-CH3NH2 than in M-NH,. Another prominent difference is in the thermodynamic stability of the respective systems. As is well-known,’ M-NH3 shows a liquid-liquid phase separation, the critical composition being close to that for the M-NM transition. The critical temperature for the phase separation is 209.7 K for Li-NH3 and 23 1.5 K for Na-NH,.’ But for Li-CH,NH2 recent measurements28 indicate no liquid-liquid phase separation down to 180 K between 3.5 and 17.4 MPM in spite of earlier suggestions of its presence.27 We suppose that the behavior of Li-CH3NH2 in the present temperature range around 208 K corresponds to that of Li-NH, at room temperature or even higher temperatures, sufficiently far from the critical temperature of phase separation; consequently the microscopic inhomogeneity due to the instability of solutions could not be observed in such a state of Li-CH,NH2. In fact, we have already given thermodynamic evidence29that the inhomogeneity or clustering trend is not important in Li-CH,NH2 in contrast to the case of M-NH3.,0 This instability of solutions in the transition region of M-NH, may be related to the partial delocalization of the electronic wave functions in solutions. As shown in the analysis of the Knight shift, the density of nuclear spins seen by an unpaired electron, P(Li), attains a metallic value around 2 M P M in Li-NH3 (Figure 8), as well as in Na-NH3,6 at considerably lower metal concentrations than that associated with the bulk metallization (-5 MPM) monitored by the electronic transport properties. Around 2 MPM in M-NH,, a large portion of the dissolved electrons form spin-pairing species, and we suppose that the remaining unpaired electrons, mostly in the form of monomers, are clustering and that the electronic wave functions are delocalized over several sites, giving a metallic value of P(Li). There exist other evidence for the partial delocalization of the wave function in M-NH3 prior to bulk metallization. We note that an asymmetry in the ESR signa131and a corresponding decrease in the electron spin-lattice relaxation time Tle32set in a t 1-2 M P M in Na-NH,, where the dc conductivity is still nonmetallic ( 10-’-1Oo ohm-’ cm-’). Metallization at high frequencies has also been inferred around 2.5 MPM in Li-NH, and Na-NH, from measurements of the microwave dielectric con~ t a n t . , ~In Li-CH3NHz, on the other hand, a decrease of T,, and an increase of the dc conductivity occur approximately at the same composition, -15 MPM,24 reflecting the absence of a significant concentration fluctuation around the transition region.29 Thus, enhancement of the relaxation rates in M-NH, is expected to occur in solutions with lower dc conductivities compared with more homogeneous solutions, in agreement with the experimental results shown in Figure 10. An examination of the enhancement factor in M-NH, near the critical temperature for phase separation and at high temperatures will be very interesting to confirm the present argument. For further studies of N M R in metal-ammonia (amine) solutions (MAS), we certainly require precise data for the electron paramagnetic susceptibility of solutions as a function of composition and temperature. It is interesting to note that the paramagnetic susceptibility of Na-NH3 (Figure 8) resembles that of liquid and gaseous Cs measured by F r e ~ l a n d over , ~ a wide density range. H e has reported an enhancement of the paramagnetic susceptibility on the metallic side of the M-NM t r a n ~ i t i o nwhich ,~~ ’sZ6
ti
c V
4
.c . l -
o,
10 V
c
4
.c
c w
1
I
I
100
10
1000
0(si’cm-’) Figure 10. The Korringa enhancement factors as a function of electrical conductivity: 0, Li-CHSNH2(208 K); 0,Li-NH, (218 K); V,Na-NH, (253 K), ref 6 ; A, liquid Ga2Te3,ref 25.
decrease of the density of states at the Fermi level, N(EF),on the metallic side of the transition region, the number of carriers being approximated by kBTN(EF). The spin-lattice relaxation rate in the itinerant electron region can be compared with values calculated from the Korringa relation by using the observed Knight shift, K(Li)17
where yLiand ye are the gyromagnetic ratios of 7Li and the . Korringa electron and h is the Planck constant devided by 2 ~ The relation is derived under the assumption that free s electrons make the dominant contribution to the shifts and the relaxation rates and no correction for the electron-electron correlation effects is considered. In the regions between 4 and 8 MPM in Li-NH, and between 15 and 22 M P M in Li-CH3NH2, it has been suggestedl*lOJ1 that the strong scattering description is reasonable for the behavior of electrons deviating significantly from the free electron state. Although no rigorous theory for N M R relaxation in this strong-scattering region has been developed, we refer to the correlation time formalism proposed by WarrenZSfor the relaxation rate in liquid semiconductors and metals, which is given by
where N ( E F )is the electronic density of states at the Fermi level and TNMR is the lifetime of an electron on a particular nuclear site. The Korringa enhancement factor H is defined asZs
H I ( ~ / T I ) J ( ~ / T I =) K T N~M~R~/ ~ ” F ) (10) which is a measure of the tendency for electron localization in the system. The experimental values of the enhancement factor H for Li-CH3NH2 and Li-NH,, as well as those for Na-NH,,6 are shown in Figure 10 as a function of the electrical conductivity u. A considerable enhancement has been found in Li-CH3NH2 in the region with u = 10-400, as already pointed out by Edwards,12while the enhancement is much smaller in Li-NH,. Even smaller values of H have been found in Na-NH3.6 It is noted that the curve of H vs. u for Li-CH,NH2 is similar to the curve for some liquid semiconductors such as Ga2Te3,25in which H i s proportional to 6’both in the weakly localized region and in the localized region. Warren has derived this proportionality from the Brownian motion model for “weakly localized” electrons.2s The observed different behavior of the magnetic relaxation as a function of u in Li-CH3NH2 and Li-NH3 certainly reflects the difference in the states of dissolved electrons in the respective solvents in the temperature range studied. A significant difference between the two solvent systems is the composition at which the M-NM transition occurs. It is - 5 MPM in M-NH3 and 15 MPM in Li-CH3NH,. These critical
-
(26) Edwards, P. P.; Sienko, M. J . Am. Chem. SOC.1981, 103, 2967. (27) Buntaine, J. R.; Sienko, M. J. J . Collque., (Orsay, Fr.) 1980, 41,
CS-36.
(28) Hagedorn, R.; Sienko, M. J. J . Phys. Chem. 1982, 86, 2094. (29) Nakamura, Y.; Horie, Y.;Shimoji, M. J. Chem. Soc., Faraday Tram. 1 1974, 70, 1376. (30) Jortner, J.; Cohen, M. H. Phys. Reo. B 1976, 13, 1548. (31) Catterall, R. J. Chem. Phys. 1965, 43, 2262. (32) Pollak, V. L. J. Chem. Phys. 1961, 34, 864. (33) Breitschwerdt, K. G.; Radscheit, H. Ber. Bunsenges. Phys. Chem. 1976, 80, 191.
(34) Freyland, W. Phys. Rev. B 1979, 20, 5104.
J. Phys. Chem. 1984, 88, 3760-3764
3760
may be described by the Brinkman-Rice theory, and he has also given direct evidence for the formation of diamagnetic molecules like Cs2 in the nonmetallic region. A detailed investigation of the paramagnetic susceptibility in MAS will thus be needed in order to test the Brinkman-Rice enhancement and also to examine the relation between the formation of spin-paired chemical species and formation of the antiferromagnetic insulator phase predicted from Mott-Hubbard theory.35
Conclusions The main features of our N M R investigation on Li-NH3 and Li-CH3NH2 can be summarized as follows: (1) The electron spin densities at the lithium nuclei deduced from the Knight shift data are nearly the same in both systems. The values of ( I+(Li)12)," in the metallic region is about 0.5%of the corresponding value for the free lithium atom. Larger Knight shifts in Li-CH3NH2 are mainly due to the larger paramagnetic susceptibility or less pronounced spin-pairing in Li-CH3NH2. (35) Mott, N. F. "Metal-Insulator Transitions"; Taylor and Francis:
London, 1974.
(2) A large enhancement in the Korringa relaxation rate is observed in the metallic and transition regions of Li-CH3NH2. The enhancement is considerably smaller in the corresponding regions of Li-NH3. The differences may be attributed to the partial delocalization of the electronic wave functions prior to bulk metallization in Li-NH3, due to a more pronounced concentration fluctuation in the transition region of this system. (3) The relaxation rate due to the electron-nuclear contact interaction decreases with increasing metal concentration in the nonmetallic region of both systems. This reflects the shortening of the correlation time of the contact interaction with increasing mobility of the localized electrons. (4) The increase in the relaxation rate of 7Li above 8 MPM in Li-NH3 reported earlier4s5is found to be an apparent one which is caused by decreasing the skin depth in the metallic region.
Acknowledgment. Valuable cooperation and discussion with various colleagues, particularly with Messrs S. Shimokawa, M. Yamamoto, T. Toma, and M. Hirasawa, are gratefully acknowledged by Y.N. Registry No. Li, 7439-93-2; NH3, 7664-41-7; CH3NH2,74-89-5.
Electron Spin Resonance of Lithium-Ammonia Solutions in the Range of the Metal to Nonmetal Transition Pierre Damay,* FranGoise Leclercq, Laboratoire de Chimie Physique L.A.253 CNRS-E.HEI, 59046 Lille CZdex, France
and Pascal Devolder UniversitZ des Sciences et Techniques de Lille, U.E.R. de Chimie-59650 Villeneuve D'Asco, France (Received: August 24, 1983; In Final Form: October 30, 1983) A detailed ESR investigation of lithium-ammonia solutions in the metal to nonmetal range is presented. The shape of the ESR line is studied with the Dysonian formalism. In order to get the precision that our data require, we derived the analytical expression for the first and second derivatrives of the Dysonian line. The line parameters (width, asymmetry, g shift) are determined as a function of temperature for 21 samples. Some differences with the Dysonian line appear in the dilute range (1.5% in metal). As for several transport properties (conductivity, thermopower, etc.) the temperature coefficient of the line width shows a maximum at 2.5%. The abrupt variation of the g shift at 2.4% seems to locate the metal to nonmetal transition in a very narrow concentration range. The temperature coefficient of the g shift indicates that the locus of the transition shifts toward lower concentration as the temperature increases.
Introduction The metal to nonmetal transition in solutions of alkali metal and alkaline earth metals has been a subject of interest and controversy during the past 10 years. In disordered systems most of the physical properties and particularly transport properties are strongly influenced by the local structure and the molecular dynamics. It is thus expected that experimental methods acting as local probes will provide the most valuable information. Conduction electron spin resonance (CESR) has been recognized' as a powerful technique to study the metal to nonmetal transition mostly since the resolution of recent apparatus allows one to measure the temperature dependence of the line parameters. We have published CESR results for lithium-ammonia solutions* but the temperature variations of the parameters seemed at first sight somewhat erratic in the 1.5-3 MPM (mole percent metal) range (although the apparatus resolution was good). So and M. J. Sienko, J. Phys. Chem., 79, 3000 (1975). (2) P. Damay, J. P. Lelieur, and P. Devolder, J . Phys., 41, C8-24 (1980). (1) P. Damay
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we decided to undertake a more detailed study in this range of concentration where several transport properties show an extremum.3 The analysis of the data is based on the Dyson equation4 for a thick plate for which a numerical resolution has been given by Feher and Kip.5 A more precise resolution was needed for analyzing our data; we report in the Appendix the result of the analytical expression we derived for the first and the second derivative of the line. This new resolution of the Dyson equation allows an accurate determination of the line parameters and permits an easy check of the thick plate model. Indeed this model should not be valid in the 1 MPM range since the skin depth reaches 1 mm (the sample thickness is 2.5 mm). We report here the ESR results obtained for 21 lithium-ammonia samples with very dense scanning in the 1.5-4 M P M concentration range. (3) J. C. Thompson in "Electrons in Liquid Ammonia", Clarendon Press, Oxford, 1976. (4) F. J. Dyson, Phys. Rev., 98, 349 (1955). (5) G . Feher and A. F. Kip, Phys. Rev., 98, 337 (1955).
0 1984 American Chemical Society
