J. MATER. CHEM., 1994, 4(4), 501-508 Neutron Scatteringt Investigation of Hydrogenic Species in the Ammonium Molybdenum Bronze (NH,)o,,,Homo,MoO, Robert C. T. Slade* and Helen A. Pressman Department of Chemistry, University of Exeter, Exeter, UK EX4 4QD Incoherent inelastic neutron scattering (IINS) and quasielastic neutron scattering (QENS) have been used in investigation of the ammonium bronze (NH~)o.~~Ho.&~O~.The IlNS vibrational spectrum reveals the presence of NH: (in the interlayer region of the a-MOO, host) and hydroxy groups (in intralayer bridging positions as in the parent hydrogen bronze, H0.27M~03).Variable-temperature QENS measurements on instruments of differing elastic energy resolutions and differing ranges of elastic scattering vector magnitude have been used in investigation of motions of the NH; ion.Broadenings are observed in QENS spectra over a remarkably large temperature range. In analysis of all spectra it was necessary to invoke a variable ‘static fraction’ of hydrogen, this arising from the temperature-dependent defect structures associated with incomplete filling of NH: sites and consequent variations in local environment of NH: ions. Variations in the scattering law [S(Q,m)]at low temperature were consistent with reorientation of order >3 of a fraction of the NH: present and were fitted assuming a four-fold barrier. At higher temperatures, spectra were treated using the isotropic rotational diffusion model for those reorienting ions giving discernible quasielastic broadenings, this diffusion being consequent on interaction of rotations of low-energy barrier with lattice modes.The layered a-MOO, structure (Fig. 1) allows intercalation of reducing-power analysis to be H1.70+0.02M003; the method a wide range of species without drastic alteration of the oxide used involved dissolution in an excess of cerium(1v) host.’,’ Schollhorn found that ‘H,~,MoO,’ exhibits Brarnsted ammonium sulfate and back-titration against iron@) acidity and that it reacts with Lewis bases (L) to form novel ammonium sulfate, as described previo~sly.~ This compound types of intercalation cornpo~nd,~ L,H,., -,Moo,. He sug- and the other products in this study are air-sensitive. All gested that transfer of protons from the oxide lattice to the handling and storage of these materials was therefore carried Lewis base, to give LH+, takes place (the species LH’ being out in an 0,-free glove box and all water was deoxygenated equivalent to an alkali-metal cation).Blue orthorhombic prior to use. H,Mo03 (0.23<x<0.4) has H atoms located in intralayer Hl.,MoO3 was mixed with MOO, and water was added to positions, the structure (space group Cmcm) determined by form an aqueous slurry with a view to carrying out the neutron diffraction4,’ being illustrated in Fig. 1.Dickens et aL6 coproportionation reaction ( I).’’ reacted this phase with NH,(g) to obtain (NH4)o~,,H,~o,Mo03 aH,Mo03 +bMoO, =(a +b)H,Mo03; z =ay/i3a+b) ( 1)(from H0.31Mo03). Powder X-ray diffraction and reflectance FTIR spectra (in particular a weak line at 1400 cm-’ charac- The mixture (in mole ratio Hl.7Mo03:Mo03 to give product teristic of NHZ) suggest that NH; occurs in the interlayer with zzO.3, within the composition range of the blue ortho- region with little perturbation of the host layers, but no further structural studies have been undertaken.The motions of the ammonium ion have been studied using the techniques of quasielastic neutron scattering (QENS) in a wide variety of materials containing NHT, these including ammonium salts, insertion compounds, intercalates and pro- tonic conductors. We have previously reported the application of these techniques in investigation of the reorientations of NH; in the ammonium tungsten bronze (NH4)o.22W03,7 which is chemically related to the mixed ammonium/hydrogen molybdenum bronze of this paper.btL We now report (i) characterisation of the hydrogenic species C in (NH4)o~,,H,~,3Mo0, by incoherent inelastic neutron scat- tering (IINS) vibrational spectroscopy and (ii) investigation of the dynamical processes involving interlayer NH,f by QENS. Experimental Materials Red monoclinic H1.7M003 was prepared by the method of Sermon and Bond (hydrogen spillover).8 X-Ray powder diffractometry (XRD; Philips PW 1050 diffractometer, Cu-Ka ”t radiation) confirmed the product to be a single monoclinic L a phase. The formula of this compound was determined by Fig. 1 a-MOO, structure, represented in terms of vertex- and edge- sharing of MOO, octahedra.The filled circles show the intralayer 7 Neutron scattering experiments were carried out at the Institut sites partially occupied by hydrogen in orthorhombic (Cmcmi Laue-Langevin, Grenoble, France. H,MoO,. rhombic phase'') was heated in a sealed glass tube [sealing under vacuum accomplished with the aid of cooling in N2( l)] at 1OO'C for 14 days. The product was washed in 0,-free water and then dried under dynamic vacuum for 24 h. XRD and reducing-power analyses confirmed a single orthorhombic phase of composition H0~,,~0,02Mo03. NH,(g) was passed over the blue orthorhombic phase and the temperature of the reaction vessel was maintained at < 18 "C. The gas flow and temperature were maintained for 40 h to ensure complete reaction.6 XRD confirmed the pcoduct was a siFgle orthorhombic pbase with a= 3.840(2) A, b= 32.39(1) A, and c=3.725(1) A, in good agreement with Dickens et aL6 Kjeldahl-type analysis (for NHJ content) was used to establish the formula of the product.Dissolution of the sample (ca. 1 g) in an excess of 0.1 mol dm-3 NaOH(aq) was followed by boiling for 30 min. Ammonia evolved was absorbed by an excess of standard 0.1 mol dm-3 HCl(aq), which was then back-titrated against standard 0.1 mol dm-3 NaOH(aq) using methyl red as indicator. The formula of the mixed ammonium/hydrogen molybdenum bronze in this study was (NH4)0.24+0.01H0.03M003* Neutron Scattering Experiments Incoherent Inelastic Scattering (IINS) The IINS spectrum of (NH4)0.24H0.03M003 over the range 200-2000 cm-l was collected on the instrument INlBeF (energy resolution z8%) at the Institut Laue-Langevin (ILL, Grenoble), the sample being contained in an aluminium slab- shaped can and held at a T <20 K (by use of a standard ILL cryos tat ).Incoherent Quasielastic Scattering (QENS) QENS spectra were recorded at the ILL using the back- scattering spectrometer IN13 and the focusing time-of-flight spectrometer IN6. Samples for neutron studies were sealed in slab-shaped A1 cans (window thicknesses 0.1 mm) of rectangu- lar (IN13) or circular (IN6) cross-section, using In wire gaskets and A1 nuts and bolts. Sample cans were inclined at 135" to the incident beam. Sample thicknesses were chosen to give < 10% scatter of the incident beam.Sample temperatures were controlled to+ 1 K using standard ILL cryostats. IN13 Measurements. Measurements on IN13 were made with an elastic energy resolution AEo=8 peV (fwhm) aqd over an elastic scattering vector magnitude range 1.19 <Qel/A-' <5.02. Spectra were recorded over an energy window of -75 to + 75 peV. Data acquisition times were typically >24 h. Empty can and vanadium (a similarly mounted V sheet sample) spectra were recorded (at 80 K over the same energy window) for use in data reduction and analysis. Temperatures at which quasielastic scattering data were to be collected were determined using constant-energy window experiments. In such an experiment the monochromator is held at a constant temperature equal to that of the analyser crystal and thus only neutrons of zero energy transfer are detected (i.e.only neutron intensity in the elastic channel is measured). In the absence of rotational or diffusive motions the elastic intensity I,, decreases gradually with temperature as a result of atomic vibrations (Debye-Waller attenuation). A more rapid decrease with increasing temperature takes place when discernible quasielastic broadening in the instru- mental energy window occurs. At still higher temperatures the quasielastic component broadens to become additional 'background' and a return to a less rapid decrease of elastic intensity takes place. The anticipated form of data from a constant-energy window experiment is thus a gradual decrease in elastic intensity at high and low temperatures, with a J.MATER. CHEM., 1994, VOL. 4 1 0 60 120 180 i7K Fig. 2 Constant-energy window experiments for (NH,)o,24H,,o,Mo0,. Elastic intensities (Iel) are normalised to the same monitor count. steeper decrease (a 'step') when quasielastic broadening would be discernible. The experimental results for (NH4)o~,4Ho~03Mo03are shown in Fig. 2. QENS spectra as a function of Qel were recorded at 105 and 115 K and were summed in pairs in order to improve the counting statistics at each temperature. IN6 Measurements. Measurements used an incident neutron wavelength Lo =5.1 A ando scattering vector magnitudes for elastic scattering Qel<2.1 A- (at a scattering angle 8, Qel= 47r sin O/&).Data acquisition times were typically 2 h. The experimental Q,,-dependen t resolution function was deter-mined using a similarly mounted vanadium sheet sample, and cadmium and empty-can scatterings were also determined. Quasielastic scattering spectra as a function of Qel were recorded at seven temperatures: 119, 151, 175. 200, 225, 260 and 295 K. Data Reduction. After subtraction of background and empty- can scattering (and Cd scattering in the case of IN6), scattering spectra were corrected for absorption and slab geometry and converted to the symmetrised scattering law S(Q,co)form (all steps using standard ILL procedures), where Q is the scat- tering vector. Results IINS Vibrational Spectrum The spectrum for (NH4)o~,4Ho~03Mo0, is shown in Fig.3. The antisymmetric and symmetric deformations of NH; are evi- dent at 177 meV (1420 cm-l) and 207 meV (1660 cm-l), respectively. The hydrogen positions in the parent blue orthorhombic H,Mo03 (0.23<x <0.4) have been defini-tively shown (by diffraction studie~~~~) to be in intralayer Mo, -0-H groupings (Fig. 1), the in-plane deformation of which leads to an intense peak at 157 meV (1260 cm-l) in the IINS spectrum of that compound. The peak at 152 meV (1220cm-') in the IINS spectrum in this study of (NH4)o~,4Ho~o,Mo03can similarly be assigned to deformation of Mo,-0-H. The strong scattering at 35 meV (280 cm-') and 50 meV (400 cm-') is due to torsional motions of NHZ. The peak at ca.75 meV (600 cm-l) and the broad scattering at 80-120 meV (640-960 cm-') cannot be definitively assigned, but combinations and overtones are likely in IINS spectra. As we have reported for the related hexagonal ammonium tungsten bronze (NH4)o.22W03,11 the spectrum in the energy range 110-170 meV (880-1360 cm-l) lacks any features assignable to the presence of NH, molecules (which could otherwise have intercalated as neutral molecules). It might be argued that the feature at 152 meV (assigned above J. MATER. CHEM., 1994, VOL. 4 503 wavenumber/crn-’ 0 440 880 1320 1760 2200 ,j 50 100 150 200 250 energy transfedme\/ Fig. 3 Inelastic neutron scattering spectrum for (NH4),~,4H,,,3Mo03 at T<20 K by us to to deformation of Mo,-0-H) is sufficiently broad possibly to be more than one overlapping band (and hence a contribution from a small quantity of neutral ammonia mol- ecules).It is, however, no broader than the peaks at higher energy transfers that are assigned to deformations of the NH: ion, and the instrumental energy resolution is low (CU.8%). It follows from the discussion above that the the hydrogen environments in (NH4)0.24H0.03M003are (i) in NH: formed on intercalation and (ii) in intralayer hydroxy groups as in the parent hydrogen bronze (Fig. 1).The ammonium ions will be in interlayer positions, as there are no sufficiently large intralayer sites. QENS Spectra The approach adopted in initial examination of all experimen- tal spectra was the same.Spectra were fitted individually to a simple analytical form, consisting of a simple scattering law S(Q,a)= Bo(Q)d(o)+F(QP) (2) convoluted with the instrumental resolution function. The quasielastic component F (Q,co)was taken to be adequately represented by a single Lorentzian (L).The empirical elastic incoherent structure factor [EISF, Ao(Q)]is the ratio of the elastic to the total (elastic +quasielastic) intensity in the incoherent scattering spectrum. Ao(Q)=Bo(Q)/(Bo(Q)+JF(Q,a)da) =Bo(Q)for normalised S(Q,w) (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,w). Scattering vector magnitudes Qel corresponding to Bragg scattering (diffraction giving a coherent elastic contribution) by the sample were determined from XRD data.In experi-ments using IN6, spectra from detectors ‘contaminated’ by Bragg scattering were simply ignored. In experiments using IN13, Ao(Q)(EISF) values at Qel ‘contaminated’!y coherent scattering (Qel=3.198, 3.524, 3.840, 4.134, 5.072 A) were cor- rected following Richardson et ~1.~~3’~ IN 13 Spectra Spectra at 105 and 115 K were found to have Qel-independent half-widths for the quasielastic (Lorentzian) component, con- E 0 , , , 2, , , 4, ,>1 3, 56 Fig. 4 Empirical EISF obtained on IN13 for ( NH4)0,24H,,03Mo03at 115 K. Vertical lines denote error bars. Solid lines show the predicted variations of EISF with Qelfor a range of possible reorientations (see text) of all of the NH; ions present.sistent with broadening originating in a reorientational motion (of NH:).14 Quasielastic broadening was small at 105 K, and spectra at 115 K were therefore used to extract Ao(Q) (the EISF). The intensities of the broadened components remained low, and this combined with the scatter in the individual spectra to give considerable (but unsystematic) scatter in the half-widths. In evaluating the empirical EISF (Fig. 4) spectra were fitted with the half-width for the Lorentzian fixed at the mean value (7 peV). IN6 Spectra Quasielastic broadening was observed at all temperatures. At each temperature the half-width for the quasielastic (Lorentzian) component was found to be QJndependent, consistent with broadening originating in a reorientational motion (of NH:).I4 The temperature dependence of half- widths was slight, but they did increase with temperature.Empirical EISF us. Qelplots showed a temperature dependence of Ao(Q),this being illustrated in Fig. 5. Consideration of Common Features The various spectra observed for both compounds have the following features in common: (i) Quasielastic broadening originating in reorientation of constitutional NH: is observed over a remarkably large temperature range. This is evidence for facile reorientation within the interlayer region of the SI-MOO, host (Fig. 1). (ii) Empirical EISF us. Qel plots show a temperature dependence.‘Theoretical’ variations of EISF with Qel can be calculated for various classical models of KHT ion jumping between different orientations within an essentially static host matrix (see below and Fig. 4). Empirical EISF values are higher than the corresponding ‘theoretical’ ones, indicating a higher elastic contribution in the empirical spectra. The compound in this study will have incomplete filling of NH,f sites in the interlayer region of the x-MOO, host framework (Fig. 1). Fig. 6 shows a projection (onto the y= 0.25 plane) of the interlayer region in the ammonium molyb- denum bronze, (NH4)o~24Ho~o,Mo0,,in this study [assuming the Cmcm space group of the parent orthorhombic Ho,27Mo0, to be retained on reaction with NH,(g)].Projection of the terminal O(3) atoms (Fig. 1)definFs an approximately square grid [a=3.840( 2) A, c =3.725(1)A]. A possible location for the ammonium ions would be in sites in cavities defined by four O(3) atoms (two from a layer above y=0.25 and two from the layer below), which are at the centres of the ‘squares’ J. MATER. CHEM., 1994, VOL. 4 in the projection of Fig. 6 and are of type 4c in Cmcm. The stoichiometry would then require 0.24 of these sites to be occupied. The local environment (and reorientatioiial barrier) for any given NH,f would then depend on how many neigh- bouring cavities were filled (assuming random occupation, this would range from zero to eight), each different arrange- ment causing a different perturbation of the layerv (and local vibrations of them) and a different electrostatic (NH;-NH;) contribution.Those (higher barrier) ions reonenting too slowly to produce discernible quasielastic broadening would give rise to purely 'elastic' scattering. The temperature depen- dence of the EISF may therefore result from a tzmperature- dependent distribution of NH: ions. Low activation barriers, as evident for NH: in this study, are commonly associated with the occurrence of non-classical phenomena (e.g. tunnelling). In the high-temperature limit large fluctuations in the potential barrier (due to interactions of rotations with thermal lattice vibrations) can even result in the observation of non-Arrhenius behaviour [such as the decreasing half-width of the quasielastic component at the highest temperatures in our study of (NH4)o.22W037].As discussed above, the variations in the half-widths for the quasielastic broadenings point to the observation of reorien- tational motions. A dissociation of NH:, in which hydrogen would transfer to a neighbouring terminal oxygen of the MOO, layers of the host, might also be thought possible. Those H-atom sites are, however, not those occupied by H in the parent hydrogen bronze (Fig. 1). Such a dissociation has been detected by 'H NMR in the related bronze (NH4),W0,,15716 in which the dissociation leads to long-range translation of the H that has transferred. That motion is strongly activated and at a timescale that would not give rise to quasielastic broadenings discernible with available instru- mentation (i.e.broadenings would be very much less than the instrumental resolutions). A similar dissociative mechanism, if present in the bronze in this study, would (1) not lead to broadening analysable as a reorientation (a rapid translational -0.0 0.5 1:O 1.5 2.0 2.5 motion of H would ensue as in the interlayer region in the bronze H1.,Mo03'), (ii) not lead to the weak temperature a&-' dependence of the observed broadenings and (iii) not give Fig.5 Temperature dependence of the empirical EISF obtained on broadenings discernible in the experimental temperature IN6 for the (NH,)o,,,Ho,03M003.Data correspond to measurements range. at (top-to-bottom) 295,200 and 151 K.Solid lines show the predicted variations of EISF with Qel for a range of possible reorientations (see text) of all of the NH; ions present. Data Analysis Reorientation of Ammonium Ions Reorientational motions of the NHZ ion have been studied in a large range of compounds using various spectroscopic techniques, e.g. ref. '2*17-20 . Neutron studies support the description of the NH,' ion as tetrahedral with an N-H0 bond length of 1.1A, as determined in NH,ReO, by neutron diffraction.21 Classical reorientation of the ammonium ion t 0 0 involves jumping between different orientations within the potential due to an essentially static environment. In contrast, the non-classical case with low barriers in the high-fC0 temperature limit is treated as rotational difi~sion,~'.~~ ions being taken to perform continuous small-angle rotations.Several literature studies of NH; reorientation are relevant to the further treatment of data in this study. Skold and 0 t 0 Dahlborgl7 studied NH4C1 and detected quasielastic broaden- ing (mean residence time on a site, qes=2 x 10-I2 s at 180 "C),rv 0 but they were unable to distinguish between two types of rotation (a two-fold jump about a C2 axis or a three-fold Fig. 6 Projection of the O(3) atoms neighbouring the interlayer rotation about a C3axis); the scattering laws for these models region in the a-MOO, structure (Fig. 1) onto the plane y=O.25. Filled circles represent atoms from the layer above, and open circles those over the Qel range studied are similar. Livingstone et ~1.'~ from the layer below.Dots represent 'cavity' sites that might be detected a dominant rotational mechanism of four-fold reori- (see text). entation (z,,, =3 x lo-'' s at 373 K) about a C'' axis in NH,Br. occupied by NH; in (NH4)o~,4Ho~03Mo03 J. MATER. CHEM., 1994, VOL. 4 A study of NH,ReO, by Richardson and HowardL2 in the temperature range 120<T/K <300 observed three-fold rotation. Studies of the layered solid protonic conductor NH: p-alumina24-26 observed 44% of the NH: ions under- going three-fold reorientation (z,,, = s at 395 K) about a C, axis. Those ions not observed rotating were said to be strongly hydrogen bonded in other sites and not free to rotate (a ‘static fraction’).In our own study of NH: in the h-WO, framework7 (in the ammonium tungsten bronze (NH4)0.22W03 and the hexagonal polytungstate [(NH,)zO],~,,,WO,) it was necessary to invoke a ‘static fraction’ of NH,f ions, this arising from the temperature- dependent defect structures associated with incomplete filling of NH: sites (in the hexagonal tunnels of the h-W03 host). Variations in the scattering law at low temperature were consistent with a classical description of jump reorientation of NHZ (interchanging three or four of the H-atom positions) of a fraction of the ions present. At higher temperatures non- classical behaviour was detected (half-widths for the quasielas- tic components in scattering spectra decreased at the highest temperatures), this arising from interactions of rotations with lattice modes, and spectra were then treated using the isotropic rotational diffusion model.Reorientational Models Jump reorientations of NH; can be discussed in terms of jumping of H-atoms between equivalent sites on a circle (following Barnes2’). For a population reorientating about a single axis the scattering law is then in the form of eqn. (2) and (3) (convoluted with the instrumental resolution function) with (4) where B,(Qr)=N-’z0[2Qr sin(np/N)] cos(2nnp/N) (5) j,(x)=(sin x)/x for a powder sample, r is the radius (of gyration) of the circle, N is the number of sites and z,= z1sin2(~/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 qesby z,,, =z1[1-cos (2n/N)] (6) In the case of observation of distinct reorientating and static populations (e.g.rotation of NH: about a single ionic C3 axis does not move 25% of the H present) the predicted EISF [&(Q)] for QENS spectra is simply related to AFt(Q) appro-priate to the dynamic population [calculated via eqn. (2) and (4)] is given by +,rot) (7)A,(Q) =[patic +prot~;~t(~)]/(pstatic where Paticand Protare the (relative) magnitudes of the static and rotating populations. The case of uniaxial rotational diffusion corresponds to the limiting behaviour as N+m. The scattering law for isotropic rotational diffusionz3 (no preferred orientation) has the form of eqn.(2) (convoluted with the instrumental resolution function) with where B,(Qr)=(2n+ MXQr). (9) jn(x)is a spherical Bessel fuction of order n, r is the radius of gyration (of the sphere on which H atoms move), T,’= n(n+ 1)D, and Dr is the rotational diffusion coefficient. The series in eqn. (8) is rapidly convergent (higher terms are negligible) except for large radii of gyration. In seeking to characterise the motion leading to quasielastic broadening, and to avoid any preconceptions derived from a hypothesis of the structure (as yet undetermined) of this ammonium bronze, the following reorientations of guest NH; (within the layered a-MOO, host) have been considered. Model A: Three-fold reorientation about a single ionic C, axis (an NH bond) or two-fold reorientation about a Czaxis. The computed EISF variations for these two possibilities are indistinguishable. Model B: Reorientation moving all H atoms to equivalent positions.This is achieved either by jump reorientation occurring about all four ionic C3 axes or by two-fold reorientation about ionic C2axes (bisecting the bond angles). Model C: Four-fold reorientation about one or more ionic C2 axes. The H atoms visit the eight corners of a cube in this model. Model D: Uniaxial rotational diffusion about an ionic C3 axis (model A with N-co). Model E: Isotropic rotational diffusion. The corresponding ‘theoretical’ EISF us. Qel variations are shown in Fig. 4. Comparison of Model and Experimental EISFs IN13 Spectra Fig.4 allows comparison of the empirical EISFs with the empirical data as obtained on IN13 at 115 K. As discussed above, empirical EISF values are higher than the correspond- ing ‘theoretical’ values, indicating a higher elastic contribution in the empirical spectra. This is attributable to the occurrence of ‘static’ (higher barrier) ions reorienting too slowly to produce discernible quasielastic broadening and is a conse-quence of incomplete filling of cavity sites (see above). Modification of any of models A-E to include the presence of some ‘static’ ions raises the calculated EISF towards the IN13 values and the effects of such modifications are shown in Fig. 7. Models A and B, which both involve reorientations of order <3, remain inadequate to explain the observed EISF variation.The variations across the full Qelrange are consistent with the higher order reorientations C (four-fold), D (uniaxial diffusion) or E (isotropic diffusion). The experimental data at low temperatures are thus consistent with a proportion of the NH; present undergoing motion describable as a high- order reorientation. In Fig. 7 this would correspond to static fractions of 52, 40 and 60% for C, D or E, respectively. Here, as in later discussion, ‘static H’ includes the residual hydrogen 0.4- I I I I 1 0 1 2 3 4 5 6 QedA-’ Fig.7 Modelling the empirical EISF obtained for (NH,)o,,,H,,o,MoO, at 115 K on IN13. The modified models are as follows (with static fractions in brackets): A (30%) (---), B (49%) (---), C (52%) (-), D (40%) (-**.-), E (60%) (-*-) present in hydroxy groups in intralayer sites (see discussion of IINS spectrum above).The 4c sites at the centres of the 'squares' in Fig. 6 (actually 'cavity' sites, see above) lie on a crystallographc C, axis. Considering the nearest-neighbour O(3)s only, a 90" jump of an NH: ion with its ionic C, axis coincident with the crystallographic axis would take the ion to an orientation very nearly equivalent to that before the jump (but not exactly equivalent as a#c); the C2 axis could thus define an approxi- mately four-fold reorientational barrier (characterised by two slightly different reorientational barriers). The absence of a C3 axis from the interlayer region could be taken as evidence against the model being a uniaxial diffusion of type D.It is tempting to assign the NH: to the 4c sites and thus to assign the motion as of type C at low temperature (rather than type E), but such an assignment is beyond the scope of the data. IN6 Spectra The Qel values accessed in the studies on IN6 were G2.1 A-'. Combination of the variations in 'theoretical' EISFs in this Qel range with the necessity to describe a proportion of the H present as static leads to the conclusion that modification of any of models A-E (using an appropriate choice of 'static fraction') could lead to a satisfactory fit to the data over such a narrow Qel range. As discussed above, the reorientational barriers are small in these compounds.IN6 spectra should be treated as in the high-temperature limit (i.e.with broadenings arising from non-classical reorientation which should be mod- elled as isotropic rotational diffusion). EISF data from IN6 can then be compared to the predictions of model E modified to incorporate a static fraction of ammonium ions. Visual fitting enabled evaluation of the static fractions as a function of temperature (see Table 1). Fig. 8 shows the corresponding empirical and (modified) theoretical EISFs as a function of temperature. It is expected that EISF41 as Qel+l. The observed small deviations from this behaviour arise from unavoidable incomplete removal of multiple scattering effects in data reduction, which affects empirical EISF values at low Qel.Modelling the Scattering Laws Empirical S (Q,o)data were fitted to a convolution of the instrumental resolution function with scattering laws of the form S(Q,O)=U~(~)+~S"~(Q,~) ( 10) In the case of spectra from IN13 the rotational scattering law Srot(Q,o)for reorienting ions was in the form of eqn. (2) and (3) as appropriate to model C (uniaxial four-fold reorien- tation). In these spectra U corresponds to combination of the elastic scattering arising from (i) 'static' hydrogen (proportion Table 1 Rotational diffusion coefficients for the NH,f ion in ( NH4)0.24H0.03M003 T,IK static H (%)a D,,lWV Dr/lO" Tad2 s-' 29 5 38 99 1.5 260 42 93 1.4 225 47 77 1.2 200 52 64 1.0 175 60 56 0.9 151 70 55 0.8 119 82b 8b 0.13b "Percentage of the total hydrogen 'static' (see text).bImprecise owing to the large static fraction and very narrow quasielastic broadening. J. MATER. CHEM., 1994, VOL. 4 0.0 1 0.0 0.5 -10.00.0 0.5 1.o 1.5 2.0 QejA-' Fig.8 Modelling the temperature-dependent empirical ETSFs obtained for (NH4)o~24Ho,o,Mo03on IN6. Data correspond to measurements at (top to bottom) 295, 200 and 151 K. The model EISFs correspond to isotropic rotational diffusion of NH; ions, with incorporation of the temperature-dependent 'static' tractions of (top to bottom) 38, 52 and 70% of the hydrogen present (Table 1). determined above) and (ii) Bragg scattering (at known angles). Spectra were initially fitted individually as a function of Qel, yielding residence times zreS of (1.5 k0.5)x f 0-l' s (105 K) and (7.0f4.0) x 10-l' s (115 K).Fig. 9 present.; representative final fits (z,,, fixed to mean values) of S(Q,w) iks a function of Qel.The fits are satisfactory. In the case of spectra from IN6, the rotational scattering law Srot(Q,w)for reorienting ions was in the form of eqn. (2) and (8), as appropriate to isotropic rotational diffusion of reorienting ions (model E). In these spectra U corresponds solely to the elastic scattering from 'static' ions (proportion determined above). Spectra were initially fitted individually as a function of Qel,yielding the T-dependent mean rotational diffusion coefficients D,given in Table 1. Representative final fits (D,fixed to mean value at each T)of S(Q.w) as a function of eeland T are given in Fig.10. The fits are satisfactory. Discussion Temperature dependence of EISFs might be taken as evidence of a simple change in reorientational mechanism. The situation in these systems is, however, considerably more complex, with J. MATER. CHEM., 1994, VOL. 4 i ‘*-. 4.28 o 0.28 0.56i’Ii 1i ,_ic 1 -0.28 0 0.28 0.56 / . . . . . . .__... -* --\ -0.28 0 0.28 0.56-Fig. 9 Fitso to the scattering law S(Q,o)obtained on IN13 for (NH,)o,,,Ho,03Mo0, at (a) 105 and (b)115 K and (left to right) Qel = 1.29, 2.47, 4.13, 5.07 A-*. Solid lines show the fits to the data (+). Dashed lines separate the elastic and the quasielastic (broadened) components.a ‘static fraction’ evident in the low-temperature (IN13) spectra assigned to jump reorientation. The reorientational barrier for a probe NH: ion will be sensitive to the detailed local environment. The temperature dependence of the EISF is consequent on the non-stoichiometry of this system and is explicable in terms of a temperature-dependent distribution of ammonium ions in the interlayer region. If the ‘cavity’ sites of type 4c are used, this would correspond to a T-dependence of the relative populations of NH: with 0, 1, 2, 3, 4,5, 6, 7 and 8 nearest-neighbour cavities occupied. In this study and to a first approximation: (i) ions with no neighbouring cavity filled will all have similar barriers, (ii) the barriers will differ for each pattern of filling of neighbouring cavities. This system therefore presents complex theoretical problems.This study has yielded information concerning purely reori- entational motions of NH:. ‘H NMR detected two additional motions in the related bronze (NH4)xW03,15’16 these being a hopping of NH: between cavities in that material [a mechan- ism for changing the defect structure in both that material and in (NH4)o,24Ho~o,Mo0,] and a high-temperature (dissoci- ative) self-diffusion of H (discussed earlier). Those motions were very much slower in (NH,),WO, than the reorientations probed in this study and, assuming that similar timescales for such motions apply in (NH4)o~24Ho~o,Mo0,, would not give rise to quasielastic broadenings discernible with available instrumentation (i.e. broadenings would be very much less than the instrumental resolutions). Conclusions The IINS vibrational spectrum confirms the presence of NH; (in the interlayer region of the a-MOO, host) and J.MATER. CHEM.. 1994, VOL. 4 ated with the partial filling of NH; sites is suggested. Such behaviour would result in a distribution of activation barriers, lower barrier ions giving rise to discernible broadenings in quasielastic neutron scattering spectra S(Q,o) over a wide temperature range. Reorientational barriers associated with observed NH; ion reorientations in this material are low. Quasielastic neutron scattering spectra [S(Q,o]at low tem- perature are consistent with reorientation about a barrier of order >3 for a fraction of the NH: ions present, and have been treated assuming a four-fold barrier.Spectra at higher temperatures are treated using the isotropic rotational diffusion model for those ions giving rise to quasielastic broadening, such a diffusion being consequent. in the high- temperature limit, on interaction of rotations of low energy barrier with lattice modes. We thank the Institut Laue-Langevin for access to spec-trometers INlBeF, IN6 and IN13. 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