J. MATER. CHEM., 1991,1(3), 429-435 Reorientation of Mo-co-ordinated Water Molecules in High- hydrogen-content oxide bronzes H,,M003 and H,,Mo03 A Neutron Scattering Studyt Robert C. T. Slade,* Paul R. Hirst and Helen A. Pressman Department of Chemistry, University of Exeter, Exeter EX4 4QD, UK Variable-temperature incoherent quasielastic neutron scattering (QENS) measurements have been used to investigate motions of hydrogenic species in the oxide bronzes H1.7M003 and H,,,Mo03. In both phases there are distinct (slowly exchanging) populations of H undergoing reorientational (those present in Mo-co-ordinated H,O) and self-diffusive (those present in Mo-co-ordinated hydroxyl) motions. In H,,,MoO, the H,O molecules undergo four-fold reorientation [€,= 26+3 kJ mol-', log (z:&) = -14.4k0.71about the Mo-0 bond.In H,.,MoO,, reorientation of H,O is restricted to a 180" flip about the bisector of the H-0-H bond angle. Keywords: Quasielastic neutron scattering spectroscopy; Hydrogen molybdenum bronze; Reorientation; Self- diffusion Hydrogen molybdenum bronzes H,Mo03 are a series of single phases derived from parent layered Moo3 by topotactic insertion of hydrogen.' Interest in these materials stems from possible applications e.g. in catalysis and in electrochemical devices. Nuclear magnetic resonance ~tudies~-~ revealed high H-atom mobilities in the highest hydrogen-content phases [x = 1.7 (red monoclinic) and x =2.0 (green monoclinic)]. Incoherent inelastic neutron scattering (IINS) vibrational spectroscopy identified the presence of both co-ordinated water molecules and hydroxyl groups in the red monoclinic phase (x =1 .7).5 A neutron diffraction study determined the H-atom positions to be associated with terminal oxygens [0(3), Fig.l(a)] at the top and bottom of the Moo3 layers.6 Mo-co-ordination of water molecules is similar in the related molybdic acids Moo3 nH,O (n= 1, 2).798 In the bronze, projection of the interlayer region onto the interlayer plane (x/a =0.5) results in an approximately square grid [Fig. I@)], the O(3)atoms lying at the intersections and the H-atom sites lying on the lines. A simplistic square-grid model had been proposed previously in interpreting 2H NMR ~pectra.~ IINS spectroscopy also identifies the presence of Mo-co- ordinated water molecules in the green monoclinic phase (x = 2.0)' No diffraction study of this phase has been published, but bond strength and structural considerations" indicate that the water molecule H atoms are located in the interlayer region as in the red monoclinic phase.We have previously reported use of incoherent quasielastic neutron scattering (QENS) techniques in characterisation of two (slowly exchanging) dynamic hydrogen populations in H1.7M003.1 One population (hydrogen in hydroxyl groups) undergoes rapid self-diffusion [Dt (295 K)=4 x cm2 s-'1. The second (hydrogen in water molecules) has a higher activation barrier to self-diffusion and undergoes reorien- tational motion. We now report detailed QENS investigations of reorientation of water molecules in H1.7M003 and H2,,Mo03 and that the mechanisms for this differ in these closely related phases.Materials All sample handling was carried out under nitrogen, the materials being susceptible to oxidation by air. t Neutron scattering experiments carried out at the Institut Laue- Langevin, Grenoble, France. 0 xx a xx 0 xx X X X X "t X a xx X o XI X a xx I o X X X X o xx xx o xx a X X X X X X X "1 b Fig. 1 (a)The layer structure of molybdenum trioxide represented in terms of linked MOO, octahedra. In high-hydrogen-content hydrogen molybdenum bronzes H,MoO,, inserted H atoms are located in the interlayer region, bonded to terminal O(3) atoms.(b)The interlayer region in high-hydrogen-content hydrogen molybdenum bronzes: 0,terminal O(3) (upper layer); 0, terminal O(3) (lower layer); x, H-atom sites (no more than one occupied per 0(3)...0(3) line, no more than two occupied per 0(3), average occupancy 0.425 in H1.,Mo03 and 0.5 in H2.0M~03). The projection onto a plane midway between the layers approximates to a square grid, with H-atom sites on the lines and O(3) atoms at intersections Green monoclinic H2 .oMo03 was prepared by Zn/HCl(aq) reduction of Moo3 under flowing nitrogen.I2 Red monoclinic H1.7M003 was prepared from H2.0MoO3 by heating at 120 "C under dynamic vacuum.' X-Ray powder diffractometry (Philips diffractometer, CU-Ka radiation) confirmed both materials to be single monoclinic phases, with diffraction patterns and unit cells in good agreement with literature data.' The formulae for the materials were determined by chemical reducing-power analysis.Samples were dissolved in an excess of 0.05 mol dm-3 cerium(1v) ammonium sulphate (in 2 mol dm-3 aqueous sulphuric acid). Excess cerium(1v) ion was determined by potentiometric titration against standardised 0.05 mol dm-3 iron@) ammonium sulphate (in 2 mol dm-3 aqueous sulphuric acid). The amount of cerium(rv) ion con- sumed is related to the number of reducing electrons in HxMo03 by MoVI -X + xCerV+xCe"' + MoV' (1) Analysis of the materials studied gave x = 1.97f 0.03 (green monoclinic) and x = 1.68f0.02 (red monoclinic). Samples for neutron-scattering studies were sealed (indium gaskets) in slab-shaped rectangular cross-section aluminium cans (window thickness 0.1 mm).Chemical and X-ray analyses were reconfirmed after neutron investigations. Experimental Quasielastic neutron scattering spectra were recorded at the Institut Laue-Langevin (ILL). Measurements on the back- scattering spectrometer IN13 were made with an elastic energy resolution AEo = 8 peV (FWHM) and over an elastic scat- tering-vector magnitude range 1.19 < Qel/A-' < 5.02. Sample cans were inclined at 135" to the incident beam. Sample temperatures were controlled to fl K using standard ILL cryostats (thermostatted centre stick). Temperatures at which quasielastic scattering data were to be collected were deter- mined using constant-energy window experiments.For H~.,MoO~, measurements of scattering spectra were made at T=60, 304 and 317 K. Prior studies of samples heated in neutron scattering cans revealed partial conversion to H1.7M003 at higher temperatures. For H1.7M003, measurements of scattering spectra were made at T= 90, 255, 306,328 and 349 K. In studies of each sample the instrumental resolution function was determined using a similarly mounted vanadium sheet and empty-can scattering was also recorded. After subtraction of the empty-can scattering and the background, and correction for absorption and slab-sample geometry, sample spectra were normalised by comparison with vanadium spectra and converted to the symmetrised scattering law S(Q, o)form (each step using standard local ILL procedures).Results Self-diffusing Populations We have previously described the use of observed neutron- scattering intensities (after background subtraction) in deter- mination of the relative magnitudes of two H-atom populations separately undergoing self-diffusion and reorien- tation." At low temperature, all the H present (P'") contrib-utes only to elastic scattering [observed intensity Z(Q, Tow)]. At higher temperature, 17: quasielastic broadening occurs and, if we denote the H population observed in the instrumental energy window as PObs, =In C~bs/p'O'lln [Z(Q, Wl(Q,Tow)] + SQZi (1) where 6 is the difference in the mean-square H-atom displace- ments at the two temperatures.Plots of In [Z(Q, T)/Z(Q, Tow)] uersus QZl are shown in Fig. 2 for H1.7MO03 (ToW=9O K) and H2.,Mo03 ( qOw=60 K). Non-zero intercepts on the vertical axis arise from a quasielastic component with neutron energy transfers at high Qel far outside the instrumental energy- transfer window (broadening to become effectively additional background at high Qel).That component is the Qcl-dependent quasielastic component of the self-diffusing population." The percentages of H present undergoing self-diffusion can be evaluated from the y-axis intercept of the high-& linear dependences and are given in Table 1. The value cited for H1,7M0O3 at 255 K is the percentage present as hydroxyl at low temperature as evaluated from broad-line NMR.2 At that J.MATER. CHEM., 1991, VOL. 1 -1 4 04-*.. 306 K P -1 4 04 Q:,/A-2 3 -0.51 -0.54 Fig. 2 Intensity ratios as a function of Qcrfor measured (IN13) QENS spectra (less apparent backgrounds) for (a) H1.7Mo03 at high tem- peratures and 90K and (b) H2.,Mo03 at high temperatures and 60K. Straight lines shown are those giving the percentages of the total 'Hpresent that are undergoing self-diffusion (see Table 1) Table 1 Self-diffusing H atom population as a percentage of total H atoms present in high-hydrogen-content hydrogen molybdenum bronzes 1.7 H2.0M003 T/K population (YO) TIK population (%) 255 10" 304 4f2 306 22f4 317 7f2 328 33f3 349 45f5 ~ " Estimated from broad-line 'H NMR spectra at low temperature' (see text).temperature diffusion has slowed to become a purely elastic component at all Qcl values." H2.oMoO3 is very nearly stoichiometric [with two H atoms per terminal O(3) in that limit] with a consequential very low proportion of H present in hydroxyl. For H1.7M003 the J. MATER. CHEM., 1991, VOL. 1 temperature dependence of the relative population diffusing (present in hydroxyl) reveals an energy preference for H-atom sites corresponding to co-ordinated water molecules, with the H-atom distribution in the interlayer region [the grid of Fig. l(b)] becoming more random at higher temperature. Scattering Spectra Spectra at the lowest temperatures (Tow)were indistinguish-able from the instrumental resolution function.Spectra at higher temperatures all showed quasielastic broadenings for both materials. These spectra were initially fitted individually to a simple analytical form, consisting of a simple scattering law s(Q, o)=Bo(QV(o)+F(Q, 0) (2) convoluted with the instrumental resolution function. The quasielastic component F(Q, o)was taken to be adequately represented by a single Lorentzian (15).The empirical elastic incoherent structure factor [EISF(Q)] is the ratio of the elastic to the total (elastic+quasielastic) intensity in the incoherent scattering spectrum EISF(Q)=Bo(Q)/CBO(Q)+ 7 F(Q, 4dol --co =Bo(Q) for normalised S(Q, o) (3) and is a measure of the time-averaged spatial distribution of the proton (incoherent scattering being dominated by the 'H present), while the time-dependent proton position is in the quasielastic term F(Q, o).EISF values at Qe, contaminated by coherent scattering (known from X-ray diffraction and confirmed using the ILL neutron diffractometer DlB) were corrected following Richardson et all3.For H1.7M003 at T>300 K a decreasing EISF at Qel<2.0 A-was a consequence of the diffusive motion, two Lorentzian quasielastic components (corresponding to diffusion and reorientation) being appropriate when broaden-ing due to diffusion is not background. EISFs Appropriate to Reorientational Motion When separate self-diffusing and reorientating populations are being observed, the observed scattered intensity is the sum of three components Iobs =12'+ +Id (4) where Z2' and ]:'are the elastic and quasielastic contributions from the rotational scattering law and Id is the (quasielastic) contribution from the scattering law for translational diffusion.The EISF appropriate to the reorientating population alone (EISF'"') is EISF'"' =Zzt/(ZS'+Z;')= zZ'/(I,,bs -Id) (5) Fig. 3 shows the reorientational EISF'"' appropriate to H2,0Mo03(317 K) and H1,7M003(328 K) and compares them to the predictions of various reorientational models for H20 molecules (see below). In the case of H2.0M~03the very small diffusing population renders Idnegligible (i.e.no correc-tions to the empirical EISF were necessary). In the case of H1.7M003,Id=O at Q2>6A-2 (see the discussion in the preceding section) and Id values at lower Qel values were evaluated from Fig.2 using deviations from the back extrapo-lated dependence at high Qel. At the lowest Qel values, corrections applied (for Bragg scattering and diffusion) are not completely adequate to remove the effects of self-diffusion. 43 1 0.51 A\\ 0 u. 0.5-0-0 2 4 6 Q,, /A -' Fig. 3 Comparison of empirical (IN13) Q,,-dependent elastic incoher-ent structure factors for reorientation (EISF"') with the predictions of various models for reorientation of terminal water molecules (see text and Fig. 4):(a)H,.,Mo03 at 328 K; (b) H,.,Mo03 at 317 K Data Analysis Reorientational Models In considering possible rotations it is pertinent to consider rotational scattering laws arising from motion of H atoms between N equivalent sites on a circle (following Barnes14)or on the surface of a sphere (isotropic rotational diffusion, following Sears'').For a population reorientating about a single axis (Barnes model) the scattering law Srot(Q,o)is then in the form of eqn.(2) (convoluted with the instrumental resolution function) with where n B,,(Qa)=N-' j0[2Qasin(np/N)] cos(2nnplN) (7) p= 1 and jo(x)=(sin x)/x for a powder sample, a is the radius (of gyration) of the circle, N is the number of sites and zn= z1 sin2(n/N)/sin2(nn/N).z1 is the half width at half maximum (HWHM) in angular frequency for the first Lorentzian and is related to the mean residence time on a site z,,, by z,,, =z1[ 1-cos (2n/N)] (8) For reorientations in which only one of the water H atoms changes position, the theoretical EISF'"' is simply related to that for both moving (EISFboth)on the same circle in the same way by EISF'"' =0.5 (1.O +EISFhth) (9) Various models for the reorientation of terminal water molecules in the interlayer region are conceptually possible.432 These can be idealised as rotations on a circle and 'theoretical' values of EISF'O' calculated. Taking the 0-H bond length as 1.0 A and the bond angle as 11 5.7" (values derived from the structure of HI MOO^^), the following models (illustrated in Fig. 4) involving O(3) atoms in adjacent layers were con- sidered: Model A, interchange of H atoms by two-fold reorien- tation about the axis bisecting the bond angle H-O(3)-H (N=2, all H moving), a 180" flip of H20; Model B, a two- fold reorientation of the water molecule about the 0(3)-H...0(3) axis, one H atom not being moved (N=2, one H atom static); Model C, four-fold reorientation about the Mo-0(3) axis (N=4, all H moving); Model D, uniaxial rotational diffusion about the Mo-0(3) axis (model C with N increased to infinity); Model E, isotropic rotational diffusion on a sphere centred on 0(3), random reorientation of H20.Models involving rotational diffusion have been included for completeness but are unlikely because (i) there is directional H-bonding (inhibiting D and E) and (ii) the impossibility of random reorientation in the presence of co-ordination to Mo (eliminating E).The variation of EISF'"' with Qelis only slight for small variations in bond length or bond angle. Examination of Fig.3 shows that, for each phase, the empirical Q,,-dependence of EISF'"' adequately matches (par- ticularly in view of the number of corrections made) the predictions of a reorientational model, but that the appropri- ate model differs for the two phases. In the case of the higher H-content phase, H2.-,Mo03, the appropriate model is a two- fold reorientation (model A) corresponding to a 180" flip of co-ordinated H20. In the case of H1.7M003, however, a A Mo 0 V m I C MO Fig. 4 Three possible reorientational motions of terminal water mol- ecules (co-ordinated to Mo) in high-hydrogen-content hydrogen mol- ybdenum bronzes.These and further models are discussed in the text. Neighbouring 0 atoms are on an adjacent layer (see Fig. 1) J. MATER. CHEM., 1991,VOL. 1 switch of observed reorientational mechanism to four-fold reorientation (model C) is evident. Modelling the Scattering Law for H,,Mo03 The empirical S(Q,o)data were fitted to a convolution of the instrumental resolution function with a scattering law of the form S(Q,a)=U~(O)+VSrot(Q,a)+WPans(Q,o) (10) as previously." U corresponds to an elastic contribution from coherent (Bragg) scattering (at known Qel values). The rotational scattering law was in the form of eqn. (2) and (6) as appropriate to model C (four-fold reorientation). The percentage of the total population undergoing self-diffusion at a given temperature was given in Table 1.For a model of self-diffusion by discrete jumps Strans(Q,o)is a Lorentzian with Q,,-dependent halfwidth r(Q).I6 As Qel-+O, Strans(Qw) becomes identical to the scattering law for continuous diffusion and where D is the H self-diffusion coefficient. In spectra at T> 300 K, r(Q)increases rapidly with Qel so that 9""(Q,o)becomes effectively an additional background in spectra at high Qel. Spectra were initially fitted individually to the form of eqn. (7) as follows. At Qe,>2.5 A-': The diffusive contribution was taken to be background (W=0). Reorientational parameters evaluated for this high Qe, range are given in Table 2. Poor counting statistics in spectra at 349 K are reflected in the large relative uncertainty in derived values.At Qel< 2.5 A-': Ps(Q,o)was taken to be a single Lorentzian with r(Q)varying according to eqn. (1 1) and reorientational parameters fixed to the mean values in Table 2. Derived self-diffusion coefficients were 4.8 & 0.9 and 6.8k1.3 cm2 s-' at 306 and 328 K, in reasonable agreement with previous reported values."*'7 The use of eqn. (1 1) to describe the variation of r(Q)in this study will be less accurate than in previous work on IN5" at lower Qel values (Qel<1.1 A-I). A more accurate form for variation of r(Q)at the higher Qel values in this work would require a detailed model (not known) for the diffusion pathwayI6 and is not warranted by the data. In spectra at 255 K, the predicted r(Q)values are very much less than the instrumental resolution (D being very much lower) and, when convoluted with the instrumental resolution function, S(Q,a)is then indistinguishable from S(Q,W)=X~(O)+ VSrot(Q,O) (12) Spectra were initially fitted individually to this form.The evaluated reorientational parameters are given in Table 2. Fig. 5 presents final fits to S(Q, o)as a function of Tand Table 2 Reorientational parameters for water-molecule reorientation in high-hydrogen-content hydrogen molybdenum bronzes TJK HWH M/peVa 7res/lo-11s H,.,MoO,: four-fold reorientation 349 26f5 2.5 f0.6 328 15+l 4.4 f0.3 306 7.5 &0.5 8.8 k0.6 255 0.99f0.25 66k2 317 H2.,Mo0,: two-fold reorientation 8.3 k2.0 1.6k0.6 304 3.2 &1.O 4.1 & 1.4 a For the first Lorentzian in the appropriate Barnes model14 (see text).J. MATER. CHEM., 1991, VOL. 1 0.17 0 ElmeV 0.17 n i, 0.21 i i, L 0.21 I 0 ElmeV 0.21 0 ElmeV 0.21 0.26 0.26 0.26 I 10 ElrneV 0.26 0 ElmeV 0.26 Fig. 5 Fits to the empirical (IN13) scattering laws S(Q, o)obtained for H1.,Mo03as a function of Tand Qel, Top solid lines are fits to the experimental data. Fitting methods are discussed fully in the text. Other lines have the following meanings. Spectra at 255 K (a):the upper dashed line separates the elastic and quasielastic (broadened) contributions; the lower dashed line shows the background; spectra shown correspond to (left to right) eel=1.19, 1.59, 2.37, 3.44, and 4.82 A-’.Low Qel spectra at higher temperatures [(b)306 K, (d) 328 K]: the upper dashed line separates the elastic and quasielastic (broadened) contributions; the central solid line shows the contribution arising from self- diffusion; the lowest dashed line shows the background; spectra shown correspond to (left to right) Qel= 1.59, 1.99 and 2.37 kl.High Qel spectra at higher temperatures [(c) 306 K, (e) 328 K]: the upper dashed line separates the elastic and quasielastic (broadened) contributions.the lowest line shows the ‘background’ (the true background plus a contribution from self-diffusion that is ‘flat’ in the instrumental energy transfer window); spectra shown correspond to (left to right) Qe1=2.37, 3.44 and 4.71 A-’ Qel(HWHM and D fixed to the mean values of each tempera- Modelling the Scattering Law for H2@MoO3 ture), which appear satisfactory at all temperatures and Qe, values.Assumption of Arrhenius temperature dependence Attempts to fit the empirical S(Q,o)data following the for reorientational zreS gives E, =26 & 3 kJ mol-and approach used above for HI.,Moo3 were unsuccessful owing log (zrOes/s)= -14.4& 0.7. to the small size of the self-diffusing population and the relatively poor counting statistics. S(Q,o) was taken as a convolution of the instrumental resolution function with a scattering law in the form of eqn. (10) with Sro'(Q,o)appropri-ate to model A (180" flip of co-ordinated H20). D values evaluated at low Qel varied considerably at different Qel.Fixing D at a given temperature to a value appropriate to H1.7M003 did not give discernible improvements in the fits at low Qel. The empirical S(Q,o)data were fitted to a convolution of the instrumental resolution function with a scattering law of the form S(Q, 0)= U6(o)+ VSr0'(Q,o) (13) (ie.a nil self-diffusing population). Spectra at high Qel were initially fitted individually and derived reorientational param- eters are given in Table 2. Fig. 6 presents final fits to S(Q, w) as a function of Tand Qel (HWHM fixed to the mean value . I 10 EIpeV 70 (b) J. MATER. CHEM., 1991, VOL. 1 at each temperature), which are satisfactory at al) but the lowest Qel values (where a discernible, as opposed to back- ground, self-diffusive contribution would be anticipated).A wider temperature range would be required for accurate evaluation of a reorientational activation energy and prefactor for this phase. Change in Mechanism The change in mechanism from four-fold reorientation [about the Mo-0(3) axis] in H1.7M003 to two-fold reorientation [about the line bisecting the H-O(3)-H angle] in H2.0Mo03 merits discussion. Two-fold reorientation (1 80" flips) of Mo-co-ordinated water in molybdic acids Moo3 nH20 (n= 1,2) has been characterised by variable- temperature 'H NMR relaxation-time mesurements'* and is slower than the two-fold reorientation in H2.0M003. An 1 70 170 Fig. 6 Fits to the empirical (IN13) scattering laws S(Q, w) obtained for H,.oMoO, as a function of Tand Qel: (a) 304 K; (b) 317 K.Top solid lines are fits to the experimental data. The fitting method is discussed fully in the text. Other lines have the following meanings; the upper dashed line separates the elastic and quasielastic (broadened) contributions; the dotted line shows the background; spectra shown correspond to (left to right) Qel= 1.29, 2.09, 3.99 and 4.98 A-' J. MATER. CHEM., 1991, VOL. 1 butions from self-diffusing H (present in hydroxyl groups). Fitting of empirical scattering laws indicates different reorien- fHg" 6" PHH H tational motions to occur in the two phases. For H1.7M003 the spectra were satisfactorily modelled assuming a four-fold reorientation about the Mo-0 axis [an approximate four-fold symmetry is evident in models of the interlayer region, see Fig.l(b)] with E,=26+ 3 kJ mol-I andrHiAHP" HrHH H log (zrOes/s)= -14.4& 0.7. For the higher-H-content H2.0M003, H/!IH 0-H / TH HTHH H rH Fig. 7 An ordered arrangement in the interlayer region of H,.,MoO,. Filled and open oxygens are co-ordinated to Mo atoms in different layers (see Fig. 1). H20molecules can reorient only via rotation about the 'molecular C, axis' (model A). Reorientation about the Mo-0 bond (four-fold reorientation, model C) is prevented by the restriction that no O..-O line may be occupied by more than one H approximate four-fold symmetry is, however, apparent in the interlayer region in the bronzes studied in this work [see Fig.l(b)]. The interlayer separation is smaller in H2,0M~03 (in which it is slightly smaller than in MOO, itself),' which may restrict higher-order reorientation in the higher H-con- tent phase. The near-complete co-ordination of each O(3) atom by two H atoms in H2.,Mo03 may lead to local ordering of the interlayer grid as in Fig. 7, with consequent inhibition of higher-order reorientation [no grid line may be associated with two H atoms, see Fig. I@)] and with non- stoichiometry (co-ordinated hydroxyl groups in place of HzO) arising at a boundary between differently ordered regions. Conclusions The high-hydrogen-content hydrogen molybdenum bronzes H1.7M003 and H2.0M~03 both contain Mo-co-ordinated H20 molecules. The 0 atoms of H20 are at the top and bottom of Moo3-like layers, with the H in the interlayer region.Incoherent QENS spectra (instrument IN1 3 at ILL) detect reorientation of HzO in both phases, and additional contri- HrHd-reorientation is restricted to 180" flip of H20 about the line bisecting the bond angle H-0-H. We thank the Institut Laue-Langevin for access to spec-HrHtrometer IN13. We thank the SERC for grants in support of the Exeter neutron scattering programme and for studentships for P.R.H. and H.A.P. We thank Drs. A. Magerl, C. Ritter and R. C. Ward for practical assistance and helpful discussions. References 1 J. J. Birtill and P. G. Dickens, Muter. Res. Bull. 1978, 13, 311. 2 R. C. T. Slade, T. K. Halstead and P. G. Dickens, J.Solid State Chem., 1980, 34, 183. 3 A. C. Cirillo, L. Ryan, B. C. Gerstein and J. J. Fripiat, J. Chem. Phys., 1980, 73, 3060. 4 C. Ritter, W. Miiller-Warmuth and R. Schollhorn, J.Chem. Phys., 1985,83, 6730. 5 P. G. Dickens, J. J. Birtill and C. J. Wright, J. Solid State Chem., 1979, 28, 185. 6 P. G. Dickens, A. T. Short and S. Crouch-Baker, Solid State lonics, 1988, 28-30, 1294. 7 B. Krebs, Acta Crystallogr., Sect. B, 1972, 28, 2222. 8 J. R. Gunter, J. Solid State Chem., 1972, 5, 354. 9 R. C. T. Slade, T. K. Halstead, P. G. Dickens and R. H. Jarman, Solid State Commun., 1983, 45, 459. 10 P. G. Dickens, R. H. Jarman, R. C. T. Slade and C. J. Wright, J. Chem. Phys., 1980,77, 5500. 11 R. C. T. Slade, P. R. Hirst, B. C. West, R. C. Ward and A. Magerl, Chem. Phys. Lett., 1989, 155, 305. 12 0. Glemser and G. Lutz, 2.Anorg. Allg. Chem., 1957, 264, 17. 13 R. M. Richardson, A. J. Leadbetter, D. H. Bonsor and G. J. Kruger, Mol. Phys., 1980,40, 747 14 J. 0. Barnes, J. Chem. Phys., 1973, 58, 5193. 15 V. F. Sears, Can. J. Phys., 1973, 58, 5193. 16 M. BCe, Quasielastic Neutron Scattering. Principles and Appli- cations in Solid State Chemistry, Biology and Materials Science, Adam Hilger, Bristol, 1988, ch. 5. 17 R. E. Taylor, M. M. Silva-Crawford and B. C. Gerstein, J. Catal., 1980, 62, 401. 18 R. H. Jarman, P. G. Dickens and R. C. T. Slade, J. Solid State Chem., 1981, 39, 387. Paper 0/05628F; Received 14th December, 1990