Proton Dynamics in Lithium-Ammonia Solutions and Expanded Metals

Transcription

1 Proton Dynamics in Lithium-Ammonia Solutions and Expanded Metals Helen Thompson*, Neal T. Skipper and Jonathan C. Wasse, Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom * for correspondence: tel: , fax: W. Spencer Howells, Myles Hamilton and Felix Fernandez-Alonso ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom ABSTRACT Quasi-elastic neutron scattering has been used to study proton dynamics in the system lithium-ammonia at concentrations of 0, 4, 12 and 20 mole percent metal (MPM) in both the liquid and solid (expanded metal) phases. At 230 K, in the homogenous liquid state, we find that the proton self-diffusion coefficient first increases with metal concentration, from cm 2 s -1 in pure ammonia to cm 2 s -1 at 12 MPM. At higher concentrations we note a small decrease, to a value of cm 2 s -1 at 20 MPM (saturation). These results are consistent with NMR data, and can be explained in terms of the competing influences of the electron and ion solvation. At saturation, the solution freezes to form a series of expanded metal compounds of composition Li(NH 3 ) 4. Above the melting point, at 100K, we are able to fit our data to a jump-diffusion model, with a mean jump length (l) of 2.1 Å and residence time (τ ) of 3.1 ps. This model gives a diffusion coefficient cm 2 s -1. In solid phase I (cubic, stable from 88.8 to 82.2K) we find that the protons are still undergoing this jumpdiffusion, with l = 2.0 Å and τ = 3.9 ps giving a diffusion coefficient of cm 2 s -1. 1

2 Such motion gives way to purely localised rotation in solid phases IIa (from 82.2 to 69K) and IIb (stable from 69K to 25K). We find rotational correlation times (τ rot ) of the order 2.0 ps and 7.3 ps in phases IIa and IIb respectively. These values can be compared with a rotational mode in solid ammonia with τ rot ~ 2.4 ps at 150 K. PACS: x Diffusion and ionic conduction in liquids PACS: Ex Neutron scattering PACS: Dq Amorphous semiconductors, metals, and alloys 2

3 I. INTRODUCTION The system lithium-ammonia exhibits a rich phase diagram, shown in Fig. 1, in both the liquid and solid states. In brief, dissolution of lithium metal into liquid ammonia produces highly coloured conducting solutions, in which solvation of the metal ions releases the valence electrons into the liquid. 1 At low concentrations the solutions are electrolytic, but, as the electron density is increased, the system undergoes a nonmetal-metal transition. 1-5 This transition is associated with strong liquid-liquid phase separation, with a critical point at a concentration of 4 mole percent metal (4 MPM) and a temperature of 210 K. The saturation limit of this system is 20 MPM (where the ratio Li:NH 3 is 1:4), at which point the electrical conductivity reaches around 15,000 Ω -1 cm -1 but with a conduction-band electron density of only ~ cm -3. This low electron density and high electrical conductivity means the liquid can be viewed as a highly expanded metal. 1-3 On cooling, saturated lithium-ammonia solutions follow a deep pseudoeutectic to 88.8K, giving us one of the lowest known freezing points for a metal. Once frozen into the solid state, the system then yields a series of Li(NH 3 ) 4 expanded metal compounds, to which we will return shortly. Recent structural studies of lithium-ammonia solutions have confirmed that the dominant structural motif is the strongly solvated cationic complex Li(NH 3 ) The remaining free ammonia molecules are weakly hydrogen-bonded, 7 and are able to solvate the excess electrons via formation of polaronic Bjerrum-type cavities, of approximate radius 3 Å. 1-4, 8 In broad terms, the experimental electrical conductivity data can then be explained if the cationic complexes are viewed as weak scatterers of electrons, while the free ammonia molecules act as strong scatterers. The rapid depletion of the latter population therefore accounts for the strong concentration dependence of the electrical conductivity as the system passes through the nonmetal-metal transition, in the range 1 to 8 MPM. Likewise, the average 3

4 proton diffusion rates measured by the NMR spin-echo pulsed-magnetic-field-gradient technique show a maximum at around 12 MPM, where the monotonic increase in the diffusion coefficient of free ammonias as a function of concentration is balanced by their 9, 10 decreasing population. Structurally, the metallic liquid regime is characterised by strong ion-ion correlations, which give rise to a pronounced pre-peak in the static structure factor at around 1 Å -1. 6, 7 The existence of this feature supports the assertion that in these systems the nonmetal-metal transition is driven by electron correlation (Mott type) rather than disorder (Anderson type). 3, 10 Recent inelastic X-ray and neutron scattering studies of the low-frequency collective dynamics of saturated lithium-ammonia solutions have shown that there is an anomalous softening of the collective excitations at around 2 times the Fermi momentum, 2 k F ~ 1 Å , 12 This softening is reminiscent of the Kohn anomaly observed in the phonon dispersion of metallic crystals, and may be indicative of an instability caused by the close interplay between electronic and ionic ordering. Saturated lithium-ammonia solutions freeze at 88.8 K: the lowest known melting point of any metal. The system then forms an intriguing series of expanded metal crystals, of composition Li(NH 3 ) 4. The first of these is cubic phase I, which is stable between 88.8K and 82.2K. 13 This compound can be viewed as a nearly free electron metal, with an electrical resistivity approximately seven times greater than that of the saturated liquid. At 82.2K the magnetic susceptibility, heat capacity and resistivity of Li(NH 3 ) 4 show discontinuities, indicative of a solid-solid phase transition to a highly correlated metal, previously called phase II and which we will hereafter refer to as IIa. This disorder-order transition is absent in Li(ND 3 ) 4, highlighting the importance of proton motion. 14 The most recent structural refinements show that both phases I and IIa can be indexed by a single bcc structure of 4

5 density of 0.57 g cm An anomaly in the electrical resistivity at around 69 K suggests a further phase transition, 16,17 to an unknown structure IIb of density 0.61 g cm -3. At 25 K the system falls into the antiferromagnetically ordered phase III. In this paper we use quasi-elastic neutron scattering to study proton dynamics in the system lithium-ammonia at concentrations of 0, 4, 12 and 20 MPM, in both the liquid and solid phases. Our data show that the diffusion of protons in the liquids reaches a maximum at around 12 MPM, reflecting the balance between free ammonia molecules and those involved in ionic solvation. Proton diffusion extends into solid phase I, suggesting possible dissociation of ammonia molecules from the tetraammonia Li(NH 3 ) + 4 unit. This is replaced by pure rotation in phase IIa and IIb. The solid-solid transition at 82.2 K can therefore be assigned to localization of the ammonia molecules (ie a disorder-order transition). II. THEORY AND EXPERIMENTAL DETAILS Quasi-elastic neutron scattering (QENS) is used to probe the dynamics of a system, expressed in terms of the positional correlations between the nuclei at different times. In this series of experiments we will exploit the fact that hydrogen (H) has a disproportionately large incoherent neutron scattering cross-section (for example σ inc (H) = barn while σ inc (D) = 2.05 barn). Information on the dynamics of the hydrogen atoms in our systems can therefore be obtained from the incoherent scattering function S ( Q, ω) using the formalism developed by van Hove. 18 Specifically, the self correlation function G S ( r, t) is the Fourier transform in space and time of S ( Q, ω) : inc inc 5

6 S inc ( Q, ω ) = exp( i t) exp( iq r) Gs ( r, t) drdt 2 ω (1) π where N 1 Gs ( r, t) = δ[ r + R i (0) R i ( t) ] (2) N i= 1 and R i (0) and R i (t) are the position vectors for atom i at times 0 and t respectively. A. Long range translation diffusion The form of G S (r,t) for times which are long compared to the mean time between atomic collisions is governed by the diffusion process. The solution of Fick s Law in this limit results 19, 20 in an incoherent scattering function of the form: 2 1 DQ S inc ( Q, ω) =, (3) π ( DQ ) + ω where D is the diffusion coefficient. The incoherent scattering function is therefore a single Lorentzian function with a half width at half maximum (HWHM) denoted by 2 Λ ( Q) = DQ. The full width at half maximum (FWHM), 2 Λ( Q), is then given by: 2 Q 2 Λ( Q) = 2 D. (4) At sufficiently small-q, this relationship is valid irrespective of the details of the diffusion mechanism. 6

7 B. The Chudley-Elliott jump diffusion model At larger Q values, incoherent QENS can be used to extract further information on the diffusion mechanism. Chudley and Elliott developed a model for such a Markovian process. 21 The self-correlation function thus obeys the master equation and yields the incoherent 19, 20 scattering function: 1 Λ( Q) S inc ( Q, ω) =, (5) 2 2 π Λ ( Q) + ω where 2 Λ( Q) is the full width at half maximum as before. The Chudley-Elliott model for liquids assumes that an atom or molecule is enclosed in a cage formed from other atoms or molecules, 21 and every so often performs a jump into a neighbouring cage. The assumptions are that the jump length, l, is identical for all sites, and the jump direction is random. Diffusion in liquids is isotropic, and so we find that: Λ ( Q) 1 sin( Ql) = 1. (6) τ Ql This form of the function can be fitted to the full width at half maximum vs. Q in order to extract the mean residence time, τ, and the jump length, l, of a diffusing particle. The diffusion coefficient is then given by the relation: 2 l D =. (7) 6τ 7

8 C. Isotropic Rotational diffusion The incoherent scattering function for rotational diffusion on the surface of a sphere of radius R gives: 22 S inc h l( l + 1) τ (, ω) = 0 ( ) δ ( ω) + rot Q j Q R (2l + 1) jl ( Q R) (8) 2 l= 1 π h 2 l( l + 1) + ( hω) 6τ rot where j ( Q R) is the l th spherical Bessel function, and τ rot is the characteristic correlation l time. In the context of our experiments, we retain only the first two terms in Eq. 8 (l = 0, 1). Such an approximation is justified because higher-order terms only have a significant contribution at larger momentum transfers than those probed in the experiments. In the context of these experiments, rotating entities have characteristic radii of 1 2 Å, thus the truncation to the first two terms is valid here. In addition, no systematic broadening of the QENS line shape with Q is observed for the data to which rotational diffusion has been assigned: giving further evidence that the truncation used here is justified. Within the scope of this series truncation, the (Q-independent) full width at half maximum is then given by: h 2h 2 Λ( Q ) = l( l + 1) =. (9) 3τ 3τ 8

9 D. Experiment and Data Analysis Measurements of S inc (Q,ω) over a range of Q values can therefore be used to extract the diffusion rate, and details of the diffusion process, for protons which are undergoing translational motion. On the other hand, QENS broadening which is independent of Q 19, 20 indicates a localized motion. Quasi-elastic neutron scattering experiments have been performed on ammonia at 40 K, 80 K, 150 K and 230 K, 4 MPM and 12 MPM lithium-ammonia solutions at 230 K and saturated (21 MPM) solutions at 40 K, 75 K, 85 K, 100 K and 230 K. The experiments were performed on the high-resolution inverted spectrometer IRIS at the pulsed neutron spallation source ISIS of the Rutherford Appleton Laboratory. 23 The samples were prepared in-situ: ammonia was condensed onto a piece of lithium metal held at 230 K. A specially designed stainless steel annular cell, with wall thicknesses of 0.1mm and an annular sample thickness of 1 mm, was used to contain the sample. In the Q-range of interest (0.4 to 1.2 Å -1 in the liquid samples at 230 K, and up to ~1.8 Å -1 for the lower temperatures), the total scattering is ca %, hence multiple scattering can be safely neglected. This is corroborated by the Lorentzian fits of the QENS data which show no signs of deviation from Fickian diffusion in the low-q limit. Each sample spectrum was measured using the pyrolitic graphite (002) and (002) offset settings ( PG002 and PG002_offset respectively), in order to observe both the very narrow and very broad components present in the data. The energy windows were from -400 µev to 400 µev for the PG002 setting, and -200 µev to 1200 µev for the PG002_offset setting. In our analysis, we report on data from whichever setting was most appropriate. For example, the wider energy window of the latter makes it more suitable for the study of 9

10 translational diffusion. The elastic energy resolution was 17.5 µev. 23 The 51 detectors were grouped into 17 groups of three detectors in each case, giving a momentum transfer range of Å -1. Our experimental data were corrected for absorption and background and empty can subtraction, as implemented using the standard analysis package MODES. 24 This procedure provides us with the dynamic structure factors, S(Q,ω), which we have seen are here dominated by incoherent scattering from the protons. The dynamic structure factors were analysed using the Bayesian fitting routine QUASILINES, 24, 25 a method which determines the most likely number of Lorentzian components required to fit the data. The fitting function is given by: N f ( Q) i S( Q, ω ) = A0 ( ω) + Ai R( ω) B( ω) σ ( w) (10) i= 1 π ( ω + f ( Q) i ) where R(ω ) is the energy resolution of the instrument which is convoluted with a number of Lorentzians, N, and δ (ω) a delta function representing the elastic peak. B(ω ) represents a sloping background and σ (ω ) is a term representing statistical noise. The fitting procedure allows us to determine the on Q-dependence of the half width at half maximum of the Lorentzian components. 10

11 III. RESULTS AND DISCUSSION In all cases the scattering function was well-represented by a single Lorentzian component. A typical fit to the quasi-elastic neutron spectra is presented in Fig. 2, in which the data are shown together with the least squares curve fit of the Lorentzian component convoluted with the resolution function plus the sloping background. Fig. 3 shows an example of the broadening of the measured spectra with Q for the saturated lithium-ammonia solution at 230 K. In both cases the narrow Lorentzian represents the resolution function for the PG002 analyser. In the liquid samples, there is no elastic line: however, some samples required an elastic line and the Lorentzian component in the fit. This was due either to incomplete sample cell subtraction, or coherent scattering from the lithium and nitrogen atoms, which would give rise to greater amplitude around the elastic line, but beyond the resolution of the PG002 analyser. The elastic line amplitude is known to make no difference to the widths of the quasielastic components. The plots of the full width at half maximum vs. Q 2 are shown in Figs. 4 and 5, together with the Chudley-Elliott model or Fick s Law fits. The fitting model was chosen according to whether the FWHMs were proportional to Q 2 up to the maximum energy width of the analyser, or whether they reached an asymptote at higher Q values. It can be seen that for the liquid samples at 230 K, a simple diffusion model (Fick s law) provides a satisfactory fit to the data. The diffusion coefficients obtained from the Fick s Law fit are given in Table I. The data taken from the samples at lower temperatures (Figs. 5 and 6) have FWHMs which are well within the energy window of the PG002 analyser. There is still a difference between the data taken using the PG002 and the PG002_offset analysers, which is due to the fact that the PG002_offset energy window is not symmetric. Therefore, the fitting procedure 11

12 for the offset analyser would be less accurate as it is not able to see enough of the energy range on the neutron energy loss side. For these samples, the data sets taken using the PG002 analyser have been fitted with the Chudley-Elliott model for jump diffusion processes (Eq. 5); the resulting parameters and diffusion coefficients are given in Table II. A. Proton dynamics in liquid lithium-ammonia solutions In liquid ammonia at 230 K, a single Lorentzian convoluted with the resolution function fitted the data satisfactorily. The FWHM of the quasielastic component showed a clear Q 2 dependence, giving a diffusion coefficient for the ammonia molecules of ~ cm 2 s -1, to be compared with the value obtained by NMR of cm 2 s Increasing the concentration of metal present in solution gives rise to a large increase in volume of 12%, 29% and 48% with respect to pure ammonia for solutions of 4, 12 and , 26, 27 MPM respectively, caused by the accommodation of excess electrons in the solution. In addition, hydrogen-bonding is progressively disrupted as the metal content is increased. 8 This is likely to be the dominant mechanism which allows the observed concomitant increase in the rate of diffusion with concentration, from cm 2 s -1 at 4 MPM, to cm 2 s -1 at 12 MPM. Again these values follow the same trend as those obtained via NMR, 9 as shown in Fig. 7. Given the reduction in hydrogen bonding in addition to the decrease in viscosity as the concentration is increased from 0 MPM to 12 MPM, a large increase in the rate of proton diffusion is expected. The degree of hydrogen-bonding decreases further upon increasing the metal concentration, such that at 21 MPM, no trace of hydrogen-bonding remains. This leads one to expect a further increase in the rate of ammonia molecule diffusion. In fact, if anything the diffusion rate decreases, to cm 2 s -1 at saturation. When lithium is added to liquid 12

13 ammonia, the lithium atoms dissociate into ionic and electronic species, which are in turn solvated by ammonia molecules. At concentrations above 12 MPM, the majority of ammonia molecules are incorporated into the solvation shells of the lithium cations, and the rate of diffusion of these four-fold ionic species is then restricted by their increased mass and steric hindrance. 9 The diffusion processes in ammonia and lithium-ammonia solutions are therefore governed by a subtle balance between hydrogen-bonding within the solvent and ionic solvation. This has interesting implications for the lithium-methylamine system, 4, 5, 28 where the greater mass of the solvated ion species may further impede the diffusion of the solvent molecules. Furthermore, the solvation of the excess electrons, which occurs only at dilute metal concentrations in lithium-ammonia solutions but is observable up to saturation in the lithium-methylamine system, 28 may indeed give rise to a further reduction in the proton diffusion rate. We also note that it is possible to form amorphous solids by fast quenching metal-ammonia solutions of intermediate concentrations. 29 These historically important Ogg Glasses have been reported to exhibit exotic electronic properties but their molecular structure and dynamics are entirely unknown. B. Solid ammonia and lithium-ammonia compounds The solid phase of ammonia was measured primarily in order to provide a comparison with the solid 21 MPM compounds. No quasi-elastic broadening was observed in solid ammonia at temperatures of 40 K and 80 K. However, at 150K a Q-independent broadening of the QENS line shape is observed, (Fig. 6) with a FWHM of ~180 µev. We assign this to rotational motion, with a characteristic correlation time τ rot of ~2.4 ps (Eq. 9). 13

14 In contrast to this, the expanded metal compounds exhibit clear quasi-elastic broadening at 40K (ie in solid phase IIb). In this regime the QENS spectra may be fitted satisfactorily with a single Lorentzian convoluted with the resolution function. This component does not show any systematic Q 2 dependence, (see Fig. 6) and can therefore be assigned to a rotation of the ammonia molecules at ~ 60 µev, consistent with τ rot ~ 7.3 ps. For the saturated lithium-ammonia compound at 75 K (ie in solid phase IIb), the rotation occurs at a higher energy of ~ 225 µev, giving a characteristic correlation time of τ rot of ~ 2.0 ps. We assign this mode to rapid rotational diffusion of the protons on the surface of the metalammonia Li-(NH 3 ) 4 complexes. The rotational constant of an undistorted ammonia molecule is around 0.8 mev, and so uniaxial rotation about the about the Li-N axis is likely to be too fast to be resolved by our current experiment. Indeed, previous incoherent neutron scattering studies of calcium-hexammonia compounds at 1.7K have shown clearly defined excitations at 1.20, 2.35 and 3.50 mev which can be assigned to rotation of a distorted ammonia about the Ca-N axis. 30 Increasing the temperature of the Li(NH 3 ) 4 compound to 85 K takes us through the phase IIa I solid-solid transition. In solid phase I we find that the QENS broadening is now Q-dependent, and can be fitted to the Chudley-Elliott jump-diffusion model (Eq. 5). Fitting to this model produces an average jump length of l = 2.0 Å and a residence time of τ = 3.9 ps. These values in turn give a diffusion coefficient of cm 2 s -1. This diffusive motion of the protons in our expanded metal compound suggests a plastic (molecular glass) phase, and is consistent with that proposed in the system calcium-hexammonia. 30 Above the melting point, at 100K, we are still able to fit our data to a jump-diffusion model, with a mean jump length (l) of 2.1 Å and residence time (τ ) of 3.1 ps. This model gives a diffusion coefficient cm 2 s -1. For comparison, at 230K we observe Fickian diffusion with coefficient

15 10-5 cm 2 s -1. Figure 8 shows the comparison between IRIS and NMR data for the saturated lithium-ammonia solutions over the temperature range K. IV. CONCLUSIONS We conclude that the system lithium-ammonia provides a rich variety of proton dynamics in both the solid and liquid phases. Our quasi-elastic neutron scattering experiments have probed this system at concentrations of 0, 4, 12 and 20 mole percent metal (MPM) in both the liquid and solid (expanded metal) phases. At 230 K, in the homogenous liquid state, we find that the proton self-diffusion coefficient first increases with metal concentration, from cm 2 s -1 in pure ammonia to cm 2 s -1 at 12 MPM. At higher concentrations we note a small decrease, to a value of cm 2 s -1 at 20 MPM (saturation). The trend in these results is consistent with NMR data, 9 and can be explained in terms of the competing influences of solvent-solvent hydrogen bonding and ion solvation. 8 At saturation, the solution freezes to form a series of expanded metal compounds of composition Li(NH 3 ) 4. Above the melting point, at 100K, we are able to fit our data to a jump-diffusion model, with a mean jump length (l) of 2.1 Å and residence time (τ ) of 3.1 ps. This model gives a diffusion coefficient cm 2 s -1. In solid phase I (cubic, stable from 88.8 to 82.2K) we find that the protons are still undergoing this jump-diffusion, with l = 2.0 Å and τ = 3.9 ps giving a diffusion coefficient of cm 2 s -1. The diffusion of protons in this solid phase points towards a plastic crystal (molecular glass) of the type suggested in calcium-hexammonia. 30 Such motion gives way to purely localised rotation in solid phases IIa (from 82.2 to 69K) and IIb (stable from 69K to 25K). We find rotational correlation times 15

16 (τ rot ) of the order 2.0 ps and 7.3 ps in phases IIa and IIb respectively. This can be compared with a rotational mode in solid ammonia with τ rot ~ 2.4 ps at 150 K. This current research raises a number of questions that will be addressed in future investigations. There is a clear need to understand the dynamics of the compound Li(NH 3 ) 4 below 25K, ie in the antiferromagnetic phase. In this regime, QENS would allow us to study excitations analogous to those observed in Ca(NH 3 ) 6 and thereby to probe the ammonia geometry. At lower concentrations, there is also the possibility of forming amorphous solids by fast quenching of the liquids. Sixty years ago these Ogg Glasses were were reported as superconductors. 29 ACKNOWLEDGEMENTS We would like to thank Prof. Peter Edwards for many useful discussions, and EPSRC and CCLRC for financial support. REFERENCES [1] J. C. Thompson, Electrons in Liquid Ammonia (Clarendon, Oxford 1976). [2] N. F. Mott, Metal-Insulator Transitions (Taylor and Francis, London 1990). [3] N. F. Mott, J. Phys. Chem. 84, 1199 (1980). [4] P. P. Edwards, Adv. Inorganic Chem. R. 25, 135 (1982). [5] P. P. Edwards, J. Phys. Chem., 88, 3772 (1984). [6] J. C. Wasse, S. Hayama, N. T. Skipper and H. E. Fischer, Phys. Rev. B. 61, (2000). 16

17 [7] H. Thompson, J. C. Wasse, N. T. Skipper, S. Hayama, D. T. Bowron and A. K. Soper, J. Am. Chem. Soc. 125, 2572 (2003). [8] H. Thompson, J. C. Wasse, N. T. Skipper, C. A. Howard, D. T. Bowron and A. K. Soper, J. Phys. Cond. Matter 16, 5639 (2004). [9] A. N. Garroway and R. M. Cotts, Phys. Rev. A. 7, 635 (1973). [10] S. Hayama, J. C. Wasse, N. T. Skipper and H. Thompson, J. Chem. Phys. 116, 2991 (2002). [11] C. A. Burns, P. Giura, A. Said, A. Shukla, G. Vankó, M. Tuel-Benckendorf, E. D. Isaacs and P. M. Platzman, Phys. Rev. Lett. 89, (2002). [12] F. Sacchetti, E. Guarini, C. Petrillo, L.E. Bove, F. Demmel and F. Barocchi, Phys. Rev. B. 67, (2003). [13] N. Mammano and M. J. Sienko, J. Am. Chem. Soc. 90, 6322 (1968). [14] P. Chieux, M. J. Sienko and F. DeBaecker, J. Phys. Chem. 79, 2996 (1975). [15] A. M. Stacy and M. J. Sienko, Inorg. Chem. 21, 2294 (1982). [16] M. D. Rosenthal and B. W. Maxfield, J. Solid State Chem. 7, 109 (1973). [17] J. A. Morgan, R. L. Schroeder and J. C. Thompson, J. Chem. Phys. 43, 4494 (1965). [18] L. van Hove, Phys. Rev. 95, 249 (1954). [19] R. Hempelmann, Quasielastic neutron scattering and solid state diffusion (Clarendon, Oxford, 2000). [20] G. L. Squires, Introduction to the Theory of Thermal Neutron Scattering (Cambridge, New York, Cambridge University Press 1978). [21] C. T. Chudley and R. J. Elliott, Proc. Phys. Soc. (London), 77, 353 (1961). [22] V.F. Sears Can. J. Phys. 44, 1999 (1966). [23] M. A. Adams, W. S. Howells and M. T. F. Telling, The IRIS User Guide, 2 nd edition, Rutherford Appleton Laboratory Technical Report (RAL-TR , 2001) 17

18 [24] M. T. F. Telling and W. S. Howells, GUIDE IRIS data analysis, ISIS Facility, Rutherford Appleton Laboratory (2000), & W. S. Howells, MODES manual, ISIS Facility, Rutherford Appleton Laboratory (2003). [25] D. S. Sivia, C. J. Carlile, W. S. Howells and S. Konig, Physica B. 182, 341 (1992). [26] Z. Deng, G. J. Martyna and M. L. Klein, Phys. Rev. Lett. 71, 267 (1993). [27] M. Diraison, G. J. Martyna and M. E. Tuckerman, J. Chem. Phys, 111, 1096 (1999). [28] R. A. Ogg, Phys. Rev. 69, 243 (1946). [29] C. J. Page, D. C. Johnson, P. P. Edwards and D. M. Holton, Zeit. Phys. Chemie 184, 157 (1994). [30] F. Leclercq, P. Damay and P. Chieux, J. Phys. Chem. 88, 3886 (1984). 18

19 TABLES Sample Diffusion Coefficient / 10-5 cm 2 s -1 PG002_offset 0 MPM 5.6 ± MPM 5.5 ± MPM 7.8 ± MPM 7.0 ± 0.7 TABLE I. Diffusion coefficients for the ammonia and lithium-ammonia solutions at 230 K, measured using the PG002_offset setting. Sample l / Å t / ps D / 10-5 cm 2 s MPM, 100 K 2.1 ± ± ± MPM, 85 K 2.0 ± ± ± 0.1 TABLE II. Diffusion coefficients and Chudley-Elliott model parameters for the saturated lithium-ammonia solutions at 100 K and 85 K. 19

20 FIGURE CAPTIONS FIGURE 1. Phase diagram of the system lithium-ammonia adapted from Ref. 9. L I: nonmetallic (dilute) liquid. L II: metallic (concentrated) liquid. L I-II: liquid-liquid phase separation. S I, S IIa and S IIb are expanded metal solid phases of composition Li(NH 3 ) 4. Diamonds represent the state points studied in this paper. FIGURE 2. Representative fit to the quasi-elastic neutron scattering spectrum at Q = 0.46 Å -1 using the PG002 graphite analyser, for the pure ammonia liquid at 230 K. Points with uncertainty limits - experimental data; solid line - Bayesian fit (Eq. 10). The narrow Lorentzian represents the PG002 analyser resolution function. FIGURE 3. Representative broadening of the quasi-elastic neutron scattering spectrum as a function of Q. Data shown were obtained using the PG002 graphite analyzer and a 21 MPM lithium-ammonia solution at 230K. The narrow Lorentzian represents the PG002 analyser resolution function. FIGURE 4. Quasi-elastic full width half maximum (FWHM) vs. Q 2 together with the Fick s Law fit to the data, for the PG002_offset dataset. The samples comprise (a) liquid ammonia, and lithium-ammonia solutions at (b) 4 MPM, (c) 12 MPM and (d) 21 MPM, all at 230 K. Note that the resolution at the elastic line is 17.5 µev. FIGURE 5. Quasi-elastic FWHMs vs. Q 2 for the PG002 dataset, together with the Chudley- Elliott jump diffusion model fit (Eq. 6). The samples are saturated lithium-ammonia solutions at 100 K (a) and 85 K (b). Note that the resolution at the elastic line is 17.5 µev. 20

21 FIGURE 6. Q-independent quasi-elastic broadening representing localised motion in crystalline samples of ammonia at 150 K and saturated lithium-ammonia at 75 K and 40 K. Note that the resolution at the elastic line is 17.5 µev. FIGURE 7. Proton diffusion coefficients for ammonia and lithium-ammonia solutions of varying concentrations at 230 K: comparison of QENS with NMR measurements taken from Ref. 9. FIGURE 8. Diffusion coefficients for the saturated lithium-ammonia solutions at varying temperatures: comparison between QENS measurements and NMR data taken from Ref

22 Figure 1. HELEN THOMPSON

23 0.014 S(Q,ω) / arbitrary units Q = 0.46 Å Energy transfer / mev Figure 2. HELEN THOMPSON

24 Q = 0.83 Å Q = 0.72 Å Q = 0.59 Å Q = 0.46 Å -1 E / mev Figure 3. HELEN THOMPSON

25 4a MPM, 230 K Data - PG002_offset Fick's law fit - PG002_offset 800 FWHM / µev Q 2 / Å -2 4b MPM, 230 K Data - PG002_offset Fick's law fit - PG002_offset 800 FWHM / µev Q 2 / Å -2

26 4c MPM, 230 K Data - PG002_offset Fick's Law fit - PG002_offset FWHM / µev Q 2 / Å -2 4d MPM, 230 K Data - PG002_offset Fick's law fit - PG002_offset FWHM / µev Q 2 / Å -2 Figure 4. HELEN THOMPSON

27 5a MPM, 100 K Data - PG002 Chudley-Elliott fit 400 FWHM / µev Q 2 / Å -2 5b MPM, 85 K Data - PG002 Chudley-Elliott fit FWHM / µev Q 2 / Å -2 Figure 5. HELEN THOMPSON

28 Rotational Modes 21 MPM, 75 K 21 MPM, 40 K 0 MPM, 150 K FWHM / µev Q 2 / Å -2 Figure 6. HELEN THOMPSON

29 10 8 D / 10-5 cm 2 s PG002 offset data NMR data Metal Concentration / MPM Figure 7. HELEN THOMPSON

30 8 6 IRIS data NMR data D / 10-5 cm 2 s Temperature / K Figure 8. HELEN THOMPSON