Diffusional and vibrational dynamics of ZnCl2 aqueous solutions by inelastic neutron scattering

Solid State Communications, Vol. 36, pp. 541—543 Pergamon Press Ltd. 1980. Printed in Great Britain. DIFFUSIONAL AND VIBRATIONAL DYNAMICS OF ZnCI2 AQUEOUS SOLUTIONS BY INELASTIC NEUTRON SCATrERING M.P. Fontana and P. Migliardo Istituto di Fisica dell ‘Universita’ and Gruppo Nazionale Struttura della Materia del CNR, Messina, Italy and M.C. Bellissent-Funel and R. Kahn Laboratoire L Brilouin, Spectrometrie Neutronique, Orme des Merisiers, B.P.2, 91190 Gif sur Yvette, France (Received 7 February 1980 by R. Fieschi) We have studied saturated solutions of ZnC12 (and NiCI2) in D20 by timeof-flight quasi-elastic and inelastic neutron scatteringspectroscopy. Spectra were taken at room temperature as a function of transferred momentum. We find that ionic diffusion in these soluti~nsis best described by a crystal vacancy diffusion model. We also fmd evidence of collective excitations in the region of 20 meV. WE HAVE STUDIED the microscopic motion of ions in the quasi-elastic scattering could therefore be estabhighly concentrated solutions of ZnC12, NiCl2 and lished. We did not attempt a quantitative fitting of the Cu Br2 in D20 and 1-120 by quasi-elastic and inelastic inelastic part of the spectra. neutron scattering spectroscopy. Our measurements In Fig. 1 we show the to.f. spectra obtained for were carried out by using the time-of-flight spectroD20 and for the ZnCI2 and NiCI2 saturated solutions meter [I] of the EL3 reactor at the C.E.A. laboratories at 0 = 37.60°exchange momentum. From Fig. 1 it in Saclay. is apparent that substantial differences exist between Spectra were taken both in the quasi-elastic (1~Ema,, the D20 and solutions spectra. These differences are ~ 1 meV) and inelastic spectral regions as a function of fairly defined in the region of 20 meV which correexchanged momentum Q and solute molar concentrasponds to the range of vibrational energies associated tion c. In this work we shall report in a more specific with Zn—Cl and Ni—Cl complexes in solution, as deter. way the results obtained for ZnCl2 solutions in D20. mined by Raman spectroscopy [2, 3] and Exafs [5]. For saturated solutions, the spectra were taken, at room The Zn—Cl complexes have been observed by t.o.f. temperature, for 0 = 15.23, 37.60, 67.13, 87.32°, neutron spectroscopy in the molten salt as well [4]. furthermore, for 0 = 37.60°,spectra were taken at In this high energy region, the vibrational modes c = 0, 2.5, 5, 12.6 molar concentration as well as for a are certainly severely damped (transformation of the saturated solution (12.6 M) of ZnCl2 in 1120. The funda- t.o.f. scale to energy scale should probably wash out all mental parameters of our experiments were: Incoming structures). However, our spectra show that they do neutron energy E0 = 4.35 ±0.05 meV; Mean spectral exist. We feel that this is a qualitative but significant resolution in q..e. region: 0.13 meV; Mean total peak evidence for collective “optical modes” in these solucounts at zero energy transfer: l0~counts; average tions. Such evidence was expected on the basis of duration of one spectral run: 36—40 hr. Raman spectroscopic data which indicated that, at sufThe solutions were placed in a 0.5 mm thick cylin. ficiently high concentrations, the aqueous solutions of drical quartz cell with a total diameter of 10 mm. The transition metal halides showed a vibrational density of H20 solutions were contained in a rectangular section states associated with the existence of an intermediate stainless steel cell 1 mm thick, with 0.025 mm thick range of local order [1, 3]. In turn, our results confirm walls. All solutions were preparedand characterized by the conjecture based on Raman [2, 31 Exafs [5] and standard procedure already described elsewhere [21. elastic neutron scattering [6] measurements. The quasi.elastic part of the spectra was deconvolu ted We now wish to discuss the results obtained in the from the apparatus resolution function. This was deterquasi-elastic energy region. The spectral distribution of mined by using a well established procedure to yield a the scattered neutrons could be well fitted with a Lorentzian fitting of the data, on a Vanadium standard Lorentzian function for all the spectra analyzed. In sample. The true Full Width Half Maximum (FWHM) of spite of the careful analysis, a good spectral resolution ,

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DIFFUSIONAL AND VIBRATIONAL DYNAMICS OF ZnCl2

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1.0 1.5 2.0 1) Momentum transfeçQ(4 Fig. 2. Q dependence of full width at half maximum of quasi-elastic line for ZnCl 2 saturated solution in D20. In the same figure we reported White’s data on pure D20 (dashed line) and our result for D2O for reference purposes.

Flight time, msec Fig. 1. Time of flight spectra for: (a) D2O; (b) saturated solution of NiCl2 (c) saturated solution of ZnCI2 in D2O. Scattering angle 0 = 37.600; T = 300 K.300 K.

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and a high signal-to-noise ratio, we found no evidcnce for the “acoustic” structures reported in literature (7].

following equation i~I~’: 2 + [I for exp (— XQ2)J/r DQ 0 2r = 2 1 + DQ 0

From our fit of the q.e. spectra, we obtained the behaviour of the FWHM as a function of the exchanged momentum for shown saturated solution ZnCI2 inrefer D20.to The results are in Fig. 2; theoferror bars the calculated fitting uncertainty. Furthermore, in Fig. 2 we show the behaviour of ~Evs Q reported by White [8] for D 1, White’s results At leastwith up tothe ~E 1.5 A are in fair 20. agreement = 2DQ2 law characteristic of the line broadening in the incoherent scattering due to free single.particle diffusion [9] The behaviour of z~Evs Q for the saturated solu. tion of ZnCl 2 in D2O (a similar behaviour has also been observed for NiCl2 in D2O) is clearly anomalous and certainly quite different from that observed in many liquid systems. On a qualitative level, the basic result is that i~Eis relatively independent of Q and has a significantly lower value than in pure D2O over the Q range explored. Such a behaviour is characteristic of solid-like diffusional motion. For a single jump diffusion model characterized by a single residence time r0, the FWI-IM ~Eis:

(1)

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For the more general case of mixed jump and free diffusion, Singwi and Sjölandcr [101 have proposed the —

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2) is the where D is the diffusion exp (—toXQthe mean Debye—Waller factor andcoefficient. X is proportional sphere amplitude of vibration of a molecule about its equilibrium site. A fit of experimental data to equation (2) yields the value of hr 2 : the mean square amplitude of 0. (U) vibrations and the diffusion coefficient, D. In our case the data cannot be fitted in any way by equation (2). Thus the single particle diffusional motion which broadens the energy distribution of the incoming ncutrons must be closer to that of particles in a solid. If we use this approach we may attempt to fit the apparent oscillatory behaviour of ~E vs Q using a vacancy-like diffusional model, used to interpret the q.-e. incoherent neutron scatteringspectra observed in sodium polycrystalline sample by Ait-Salem eta!. [Ii]. According to this model, in the case of space isotropy, the behaviour of ~Evs Q should be described by:

Vol. 36, No.6 =

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DIFFUSIONAL AND VIBRATIONAL DYNAMICS OF ZnCI2 sin Qll

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where I is a jump length and r0 is the rest time. We have attempted to fit our data using equation (3). The result is shown by the solid line in Fig. 2. The best values of the parameters are! = 6.6 A and ro = 1.1 x 10-il sec. It is clear Fig. 2too thatliterally. the fit isIt only qualitative and should notfrom be taken is indicative, however, that the diffusional behaviour of the ions over the short time and distance scale investigated by our measurements is perhaps best described as the motion of atoms in an ordered local environment. The obtained values of! and r0 are certainly reasonable. For instance, the! value is close to the interionic mean separation in the saturated solution, and r0 is long enough to allow sufficient vibrational oscillation of the ions around their quasi-equilibrium position (see the inelastic contribution to the scattering). It is clear that the model analogy proposed here is no more than qualitative and more cornplete measurements with an improved model should be performed. For instance, only for saturated solutions the implicit assumption of a single diffusing entity, and therefore a single Lorentzian fit of the quasi-elastic data is justifiable. In fact in this case essentially all the water molecules are expected to be bound. But even at saturation the precise nature of the diffusing entities is not clear. In accordance with recent results obtained on similar solutions by EXAFS [51and Raman spectroscopy [21,we may assume that the diffusing entities are locally ordered complexes which include both Zn, Cl and several 1120 molecules. However at lower concentrations certainly more than one species will contribute to the q.e. FWHM and therefore the analysis must be revised accordingly. We have taken measurements as a function of concentration in ZnCl2 in D20 and in 1-120 solutions and the results of this more complex analysis will be reported in a further work. The possible role of”de Gennes narrowing” [121 due to coherent contribution to the scattering must either be ruled out or accounted for. In our case, even though the total coherent scattering amplitude in saturated ZnCl2 in D2O solutions is approximately three times the incoherent scattering amplitude we believe that the de Gennes narrowing effects on i~Eare negligible. In fact, if the observed ~E vs Q behaviour were dominated by coherence effects, the minimum in ~E (instead of being found, as here, in the 1—1.5 A’ range), were observed at about Q = 2 A-~,locationof the first maximum in the structure factor, in X-ray diffraction experiments [13]. In conclusion, even though the case of the crystalline vacancy jump model may be too unrefined for a liquid system, our data for saturated ZnCl2 solution are qualitatively well interpreted in this scheme. This fact is

543

in good agreement with the structural characteristics of aqueous solutions of strong Il—I electrolytes of transition metal halides at high concentrations. Recent Raman [2,3] and EXAFS [5] measurements clearly indicate the presence, at sufficiently high concentrations, of a solute-dominated local structure extending over interionic separation distance~.The data imply that2” most in the solutions are of the (Me X~) type. of At the highanions concentrations such complexes interact with the hydrated metal ions to form structures reproducing, at the local level, the ordering of the corresponding crystal. This phenomenon is particularly evident in ZnCI 2 solutions, where the ionic complexes tend to form “polymeric” chains [14]. The very low molar ratio (2.5 to 1) between water and salt molecules at saturation point makes the electrolytic solution hardly distinguishable from the molten salt itself. Therefore it is not surprising that far from the strictly hydrodynamic limit, the diffusion of ions in such solutions should resemble ajump diffusion in a crystal more than a free diffusion in a liquid. REFERENCES 1.

R. Kahn, Spectrometre a temps dc vol, in Introcluction a Ia spectrometrie neUtronique, Deuxierne partie, pp. 76—93, Lab. L. Brillouin, C.E.A. Saclay Int. Rep. (1974). 2. M.P. Fontana, G. Maisano, P. Migliardo & F. Wanderlingh,J. Ozem. P/zys. 69,676 (1978). 3. M.1’. Fontana, G.Solid Maisano, Migliardo23, & 489 F. Wanderlingh, StateP.commun. (1977). 4. i.K. Wilmshurst & J.M. Bracker, Molten Salts, (Edited by Mamantov), pp. 291—313. New York, (1969). 5. A. Fontaine, P. Lagarde, D. Raoux, M.P. Fontana, C. Maisano, P. Migliardo & F. Wanderlingh, Ph vs. Rev. Lett. 41, 504 (1978); P. Lagarde, A. Fontaine, D. Raoux, A. Sadoc & P. Migliardo, J. Chem. Plzys. 72, 3061 (1980). 6. R.A. howe, M.S. Howells & J.E. Enderby,J. Ph,vs. L4 11(1974). 7. C7, G. Cubiotti, F. Sacchetti & M.C. Spinelli, Solid State Commun. 27, 249 (1978). 8. J.W. White, Her. Bunsenges Physik C’hem. 71, 379 (1971). 9. See, e.g., T. Springer, Quasi-e!astic Neutron Scatteringfor the Investigation ofDiffusive Motions in Solids and Liquids. Springer-Verlag, Berlin (1972). 10. K.S. Singwi & A. Sjölander, Phys. Rev. 119, 863 (1960). 11. M. Ait-Salem, T. Springer, A. I-Ieidemann & Aldefeld, Phil.P!zysica Mag. A39, 797 (1979). 12. B. P.G. de Gennes, 25, 825 (1959). 13. R.F. Kruh & C.L. Standley, fnorg. Che,n. 1,941 (1960); D.L. Wertz & J.R. Bell, J. !norg. Nuc!. Chem. 35, 137 (1973). 14. D.E. Irish, B. McCarrol & T.F. Young,J. Chem. Phys. 39, 3436 (1963).