23Na and 14N knight shifts in concentrated solutions of sodium in ammonia

Volume

2, number

23Na

4

CHEMICAL

AND

14N

KNIGHT OF

PHYSICS

SHIFTS

IN

SODIUM

IN

LETTERS

CQNCENTRATED

ler

Pizysiques

1968

SOLUTIQNS

AMMONIA

E. DUVAL FacuEtE des Sciences

August

cycle,

69 ViZZeuvSanae, f%-ante

P. RIGNY D&urtement

de Physico-Chimie, Centre d’Etudes Nucleaires BP No. 2. 91 Cif-sur-Yvette, France

de SacZay D

and G. LEPOUTRE Laboratoire

de Chimie

Physique,

FacuZtk

Received Revised

manuscript

CathoZiques.

5; LiZZe, France

1 July 1968 received

15 July 1968

Accurate measurements of S3Na and 14N Knight shifts have been performed in solutions of sodium in ammonia in the concentrated region. Their variation with the concentration is consisteni with a model of quasi-free electrons, and their variation with temperature indicates thermal excitation of the electrons from a diamagnetic state into the conduction band, even near saturation.

1. INTRODUCTION The electrical and magnetic properties of metal solutions in liquid ammonia undergo a sharp change in the concentration range from 0.4 M to 1 M (gram atoms of sodium per liter of solution). The conductivity increases sharply with a maximum in the temperature coefficient at around 0.8 M [l]. The magnetic susceptibility per gram atom of dissolved sodium [2] or potassium [3] has a minimum at a concentration of about 0.4 M at temperatures below 238OK, whereas at 300°K it becomes very nearly independent of the concentration at above 0.4 M [4]. The knight shift [5-71 of sodium or potassium increases suddenly at this same concentration. The interpretation of this change in the electrical and magnetic properties of metal solutions in ammonia is that there occurs a change from the semi-conducting to the metallic state of the electrons in the outer shell of the dissolved metal. Below a concentration of 0.04 M the conductivity would then be of the ionic type; between 0.04 M and 1 M, the conductivity would be ascribed to hopping of electrons from one site to another [8]; above a concentration of about 1 M the conductivity tends to be of the metallic type. Susceptibili-

ty [4] and Hall constant [9] measurements show that all electrons should be free at a concentration of around 2 M. The aim of the work presented here is to study the changes which occur in the magnetic properties during ihe transition from the semi-conducting to the metallic state, and to deduce, if possible, the structure of the conduction band formed. With this in view, we have made an accurate determination of changes in the Knight shift for 23Na and I4N as a function of the temperature and of the concentration from 0.8 M to saturation. 2. EXPERIMENTAL

METHOD AND RESULTS

The solutions of sodium in ammonia were prepared by vacuum distillation of the metal and condensation of the ammonia. The measurements were carried out on a Varian D.P. 60 spectrometer. For the Knight shifts measurements the lines were observed with the wide-Line technique, the use of a low frequency mo&rlIation foilowed by phase detection. Since superstabiIization of the magnetic field was employed together with a very 237

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CHEMICAL PHYSICS LETTERS

I*

August 1968

the relaxation of the sodium nuclei is not due to the presence of unpaired electrons in the solution. In effect, the relaxation time due to the electronnucleus interaction can be estimated to be about 1 set with Korringa’s relationship; on the other hand, the relaxation tit!e of the sodium nucleus in a 2 N sodium nitrate solution, which is due to quadrupolar interaction, is about 60 msec.

Na ON

3. DISCUSSION The Knight shift (for a metal) is given by:

(1)

3 (iEMPERPTURE&03

Fig. 1. Knight shifts for nitrogen and sodium for concentrations of O.&S- 1-1.42-1.75-2.45-4.95 (saturation) gram-atoms of sodium per liter of solution. The slope of these graphs decreases as the concentration increases.

slow scanning it was possible to measure the Knight shifts to within & 0.2 X 10-5. Frequencies of about 11.260 MHz for the sodium and of about 4.1 MHz for the nitrogen were used. Jn fig. 1 are given the values of the Knight shifts for concentrations of between 0.84 gram-atom per liter of sodium and saturation, and for temperatures of between 282 and 215OK, the scale being logarithmic, plotted against the reciprocal of the absolute temperature. The shape of the sodium lines have been studied on the dispersion signal obtained without modulation using the high-resolution 15.1 MHz unit. The diameter of the samples is 5 mm and the homogeneity of the field has been reduced to a minimum; it was not possible however to rotate the conducting samples. The lines are not visibly deformed by the skin effect which results simply in a decrease in the signal intensity with increasing conductivity of the solution. Increasing concentrations give more narrow lines. The width corresponds to a relaxation time T2 of about 20 msec for a concentration of 1 gram-atom of sodium per liter of solution, and to about 60 msec at saturation. A study of the absorption signal obtained by the mean passage method shows that the longitudinal relaxation time T1 = T2. It is possible to say that under these conditions 238

for any nucleus N; x, is the susceptibility of the solution per gram-atom of sodium dissolved, No is Avogadro’s number and (+ (IV) ]2>, is the electron density at the nucleus iV, averaged on all the orbits at the Fermi level. From the definition of x,, the wave functicn $ should be normalized to the volume of the sample divided by the number of Na atoms which it contains. The values of the susceptibility have been meas ured by Suchannek et al. 14-Jat about 28OC; it is thus possible to deduce the value of the electronic density on 23Na and 14N using formula (1). The at 28OC have been obtained by values of (m/H)Na extrapolating the straight lines obtained experimentally. Fig. 2 thus represents respectively the values of the electron density on sodium 23 and on nitrogen 14 as a function of the sodium atom concentration per liter of solution. The use of the static susceptibility implies that the diamagnetic

Fig. 2. Electronic density on 23Na and 14N as a function of the concentration. The wave function ia normalized in the volume per gram-atom of sodium dissolved.

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CHEMICAL PHYSICS LETTERS

contributions to the susceptibility as well as that of the localized electrons, either paired or unpaired, which may be present in the solution, are negligible. At low concentrations, the electronic density on the sodium depends little on the concentration, according to McConnell and Holm [5 and varies between 0.017 and 0.024 x lo24 cm- J . Above a concentration of 0.5 M it increases rapidly and becomes more or less proportional to the concentration. The electronic density at the nitrogen nucleus is proportional to the concentration both at low and high concentrations. The relative variations of the Knight shifts for 23Na and 14N at low concentrations, as a function of the concentration implies that the unpaired electron exists in two different states. It is reasonable to assume that at concentrations of under 0.4 M, the electron can be trapped either by the cavity potential which it creates itself by attracting polarized ammonia molecules, or by the potential of the Na+ ion screened by the polarization of the solvent. From this generally accepted hypothesis it is possible to visualize the transition from the localized to the unlocalized state and then to the metallic state in the following way. Arnold and Patterson [8] have shown that above a concentration of 0.04 M the conduction could be interpreted by a hopping process from one site to another. However, if the electrons can pass from one screened Na+ ion to another by a tunnel effect, at low concentrations, they will pass preferentiaily from a cavity to a screened Naf, since the average distance separating these latter sites is less than in the case of the two former sites. This mechanism liberates sites and thus makes it possible for transport of electrons to occur by hopping from one cavity to another when the reciprocal of the exchange integraI between them, measuring the time taken for electrons to pass from one to the other, is small compared to the lifetime of an empty cavity. At a concentration of about 0.4 M, at which point the Knight shift starts to increase rapidly, the ammonia molecules can be considered as an approximation to form either a cavity or to screen an Na+ ion. When the ratio of the mean overlap energy to the mean potential energy of the electron in a site becomes sufficiently great, the electrons become delocalized [lo, 111. The set-up is then similar to that considered by Mott for strongly doped semi-conductors [ 121; when the concentration is such that the energy of the electrons subjected to the attraction of the uniform density charges of the screened Naf and of the cavities is equal, in absolute value, to that of the free electrons, the electrons will be in the metdllic state.

August 1968

The average disposition of ammonia molecules existing as a cavity or as a screen around the sodium ion can be preserved, at least partially, after the transition, with a varying number of moIecules per cavity or per screen. However, it is possible to imagine that the electron density on the nitrogen is approximately inversely propcrtional to the number of ammonia molecules contained in the volume, when the wave iunctbn is wxmalized in the volume of a cavity or of a screen. Taken overall, the electronic density both at the nitrogen and aC.Go sodium nuclei, becomes inversely prc;;rrrtional to the number of ammonia molecules to which the wave function is normalized. We can thus see that the electronic density on 23Na and 14N (fig. 2) is very nearly proportional to the concentration. In fact, in this model, the conductionelectron wave function can be regarded as a plane wave, orthogonalized to the internal electronic orbitals & of the ammonia and cf the sodium ion, of the type

where the difference in modulation between the sodium and the ammonia is small. The square of the normalization factor is then inverseLy proportional to the number of centers (NH3 molecules or sodium ions), or to the volume in which the wave function is normalized. The results given in fig. 1 show that the Knight shifts increase with the temperature, the temperature coefficient decreasing as the concerltration increases. This therma? variation of the Knight shift can be related to the thermal variation of the conductivity [I] as well as to variations in the susceptibility 121. In effect, the slope Idlogu/d(I/liT) 1 of the conductivity is close to that of the Knight shift for nitrogen, 1d lOg(Ali/H)N/d(l/kT) 1 from a concentration of 1.5 gram-atoms of Na per liter up to saturation (0.333 electron-volts for one, 3.0052 electron-volts for the other, at saturation). Furthermore, it is possible to calculakz a temperature coefficient A logW/A(l/kT) between 238’K and 192OK using the susceptibility measurements expressed in gram-atoms of dissolved sodium [2]; the value found for a concentration close to saturation (4.3 gram-atom of sodium per liter of solution) is 0.0052 electron-volts, i.e. equaI to the temperature coefficient for the Knight shift of nitrogen at saturation. These results suggest a thermal excitation of the electrons from a diamagnetic state to the conduction band. The high value of the Fermi energy (about one thousand degrees) that can be estimated for very concentrated solutions, either from conductivity or from 239

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CHEMICAL PHYSICS LETTERS

susceptibility measurements, indicates that the diamagnetic level must then be inside the conduction band. Finally, it can be seen in fig. 1 that the temperature coefficient for the sodium Knight shift is higher than that for nitrogen for concentrated solutions. This difference is perhaps due to the decrease in the polarization of the ammonia molecules surrounding the sodium ion as the temperature increases.

The authors are grateful to Professor Friedel

for

guidance,

and to Dr.

discussions. This research supported ‘,y the D.R.M.E.

240

REFERENCES [l] C. A.Kraus [2] [3] f4] [5] [6] [7] [S]

ACKNOWLEDGEMRNTS J.

J. M. Winter

has been partially

for

August 1968

[9] [lo] [ll] [12]

and W. W. Lucasse, J. Am. Chem. Sot. 44 (1922) 1941. E. Huster, Ann. Physik 33 (1938) 477. C. A. Hutchison Jr. and R. C. Pastor, Rev. Mod. Phys. 25 (1953) 285. R. G. Suchannek, S. Naiditch and C. J. Klejnot, J. Appl.Phys. 38 (1967) 690. H. M.McConnell and C. H. Holm. J. Chem. Phys. 26 (1957) 1517. J. V. Acrivos and K. S. Pitzer, J. Phys. Chem. 66 (196%) 1693. D. E.O’Reilly, J. Chem.Phys. 41 (1964) 3729. E. Arnold and A. Patterson Jr., in: Solutions Meti-Ammoniac, Eds. G. Lepoutre and M. J. Sienko, p. 160. D-S. Kyser and J. C. Thompson, J. Chem. Phys. 42 (1965) 3910. P. W. Anderson, Phys. Rev. 109 (1958) 1492. N. Mott, Adv.Phys. 16 (1967) 49. N.Mott. Phil. Map. fi IlWil\ 3~