Dynamic Properties of Solid Ammonium Cyanate - The Journal of

Sep 11, 2008 - Gin Keat Lim , Kotaro Fujii , Kenneth D. M. Harris , and David C. Apperley. Crystal Growth & Design 2011 11 (12), 5192-5199. Abstract |...
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J. Phys. Chem. C 2008, 112, 15870–15879

Dynamic Properties of Solid Ammonium Cyanate Arnaud Desmedt,†,‡,§ Simon J. Kitchin,| Kenneth D. M. Harris,*,⊥ Franc¸ois Guillaume,*,† Rik R. Tykwinski,# Mingcan Xu,⊥ and Miguel A. Gonzalez∇ UniVersite´ de Bordeaux, Groupe de Spectroscopie Mole´culaire, Institut des Sciences Mole´culaires, UMR CNRS 5255, 351 Cours de la Libe´ration, F-33405 Talence, France, Hahn-Meitner Institute, BENSC, Glienickerstrasse 100, D-14109 Berlin, Germany, School of Chemistry, UniVersity of Birmingham, Edgbaston, Birmingham B15 2TT, England, School of Chemistry, Cardiff UniVersity, Park Place, Cardiff CF10 3AT, Wales, Department of Chemistry, UniVersity of Alberta, Edmonton, Alberta T6G 2G2, Canada, and Institut Laue-LangeVin, 6 Rue Jules Horowitz, BP 156, F-38042, Grenoble Cedex 9, France ReceiVed: May 14, 2008; ReVised Manuscript ReceiVed: June 25, 2008

Ammonium cyanate is well-known to undergo a solid-state reaction to form urea. Knowledge of fundamental physicochemical properties of solid ammonium cyanate is a prerequisite for understanding this solid-state chemical transformation, and this paper presents a comprehensive study of the dynamic properties of the ammonium cation in this material. The techniques usedsincoherent quasielastic neutron scattering (QENS) and solid-state 2H NMR spectroscopysprovide insights into dynamic properties across a complementary range of time scales. The QENS investigations (carried out on a sample with natural isotopic abundances) employed two different spectrometers, allowing different experimental resolutions to be probed. The 2H NMR experiments (carried out on the deuterated material ND4+OCN-) involved both 2H NMR line shape analysis and 2H NMR spin-lattice relaxation time measurements. The results of both the QENS and 2H NMR studies demonstrate that the ammonium cation exhibits reorientational dynamics across a wide temperature range, and several dynamic models (based on knowledge of the crystal structure of ammonium cyanate) were considered in this work. It is found that a tetrahedral jump model for the dynamics of the ammonium cation provides the best description for both the QENS and 2H NMR data, and there is excellent agreement between the values of activation parameters established from these two experimental approaches, with estimated activation energies of 22.6 ( 2.1 kJ mol-1 from QENS and 21.9 ( 1.0 kJ mol-1 from 2H NMR spin-lattice relaxation time measurements. The wider implications of the results from this work are discussed. 1. Introduction In 1828, Friedrich Wo¨hler1a observed, while attempting to prepare ammonium cyanate [NH4+OCN-] by a number of different routes, that urea [OC(NH2)2] was formed instead. Subsequently, in 1830, Wo¨hler and Liebig1b were successful in preparing solid ammonium cyanate and demonstrated that, under appropriate conditions, this material undergoes a solid-state reaction to produce urea. These discoveries played a seminal role in the history of chemistry, as the reaction from ammonium cyanate to urea represented the first direct evidence that an inorganic material can be converted to an organic substance. Subsequently, this reaction has received much attention, both in aqueous solution and in the solid state,2 although most experimental studies have focused on the reaction in solution. Details of the reaction in the solid state remain sparse, although the recent determination of the crystal structure of ammonium cyanate3,4 has opened up new opportunities for exploring the solid-statereaction(forexample,usingcomputationaltechniques5,6). * To whom correspondence should be addressed. E-mail: HarrisKDM@ cardiff.ac.uk (K.D.M.H.); [email protected] (F.G.). † Universite ´ de Bordeaux. ‡ BENSC. § Present address: Universite ´ de Bordeaux. | University of Birmingham. ⊥ Cardiff University. # University of Alberta. ∇ Institut Laue-Langevin.

In spite of the importance of understanding structural properties of ammonium cyanate in the solid state, structure determination by single-crystal X-ray diffraction was precluded by the fact that this material can only be prepared as a microcrystalline powder. Structure determination was only carried out relatively recently from powder X-ray diffraction data,3 which established the positions of the non-hydrogen atoms, but could not reliably distinguish the orientation of the ammonium cation. Subsequent powder neutron diffraction studies4 were necessary to establish details of the hydrogen bonding arrangement, as discussed below. The structure is tetragonal with space group P4/nmm. The nitrogen atom of the ammonium cation resides at the center of a nearly cubic local arrangement of oxygen and nitrogen atoms (from cyanate anions), which occupy alternate corners of the “cube”. Two plausible orientations of the ammonium cation may be proposed, in one case forming four N-H · · · O hydrogen bonds and in the other case forming four N-H · · · N hydrogen bonds (Figure 1). Powder neutron diffraction studies4 on the deuterated material ND4+OCN- (actually ca. 77-81% 2H; see section 2.1) definitively support the structure with N-D · · · N hydrogen bonding, with no detectable extent of disorder between the N-D · · · O and N-D · · · N hydrogen bonding arrangements. Thus, Rietveld refinement calculations for a structural model comprising both orientations of the ammonium cation with fractional occupancies converge (within experimental errors) toward a situation with zero occupancy of the hydrogen (deuterium) atoms in sites corresponding to N-D · · · O hydrogen bonding and 100% occupancy in sites

10.1021/jp8042889 CCC: $40.75  2008 American Chemical Society Published on Web 09/11/2008

Dynamic Properties of Solid Ammonium Cyanate

Figure 1. The crystal structure of ammonium cyanate showing the two possible hydrogen bonding arrangements: (A) with the ammonium cation forming four N-H · · · N hydrogen bonds to four nitrogen atoms, or (B) with the ammonium cation forming four N-H · · · O hydrogen bonds to four oxygen atoms. The hydrogen bonds are shown as thin black lines. Neutron diffraction studies4 indicate that hydrogen bonding arrangement A exists in the crystal structure.

corresponding to N-D · · · N hydrogen bonding (across the temperature range from 14 to 288 K investigated in the neutron diffraction study). Although the crystal structure determined from neutron diffraction data gives a well-defined ordered time-averaged structure, it is important to consider the possibility that dynamic processes may occur in this material. Indeed, the reorientational dynamics of ammonium cations in a wide range of other materials have been studied previously by experimental and computational techniques.7 In the case of ammonium cyanate, it is also relevant to consider whether the onset of the solidstate chemical transformation to produce urea might be triggered by the occurrence of an appropriate dynamic process of the ammonium cation. With these motivations, we report here a comprehensive study of the dynamic properties of the ammonium cation in solid ammonium cyanate, focusing on solid-state 2H NMR spectroscopy (on the deuterated material, denoted ND4+OCN-) and incoherent quasielastic neutron scattering (on the material with natural isotopic abundances, denoted NH4+OCN-). As demonstrated previously,8 the combination of these two techniques is a powerful strategy for probing dynamic properties of organic materials, as together they allow molecular motions to be studied across a wide range of characteristic time scales. Relevant results from a previous computational study9 of energy barriers for reorientation of the ammonium cation in ammonium cyanate are also considered in the context of the dynamic models discussed here. 2. Experimental Details 2.1. Sample Preparation. Ammonium cyanate was prepared by an adaptation of the ion exchange procedure reported by Dieck and co-workers.10 In the present work, the reaction was conducted under normal laboratory conditions in standard dry glassware under a nitrogen atmosphere rather than in a drybox as described in ref 10. Et2O was distilled from sodium/ benzophenone ketyl, and CH3CN was distilled from CaH2 immediately prior to use. Briefly, anhydrous NEt4OCN (5.16 g, 30.0 mmol) was dissolved in dry CH3CN (15 mL) and stirred under a positive pressure of N2 until dissolved. In a separate round-bottom flask (100 mL), anhydrous NH4SCN (2.28 g, 30.0 mmol) was dissolved in CH3CN (40 mL) and stirred under a

J. Phys. Chem. C, Vol. 112, No. 40, 2008 15871 positive pressure of N2 until dissolved (slight heating can be used to facilitate this process). The NEt4OCN solution was poured into the NH4SCN solution at ambient temperature, resulting in the immediate formation of a white precipitate. This heterogeneous mixture was stirred under a positive pressure of N2 for ca. 20 min, and the precipitate was collected on a fine fritted filter (under a stream of N2) by suction filtration. While still on the fritted funnel, the precipitate was washed with CH3CN (2 × 35 mL) and then Et2O (2 × 25 mL). The resulting solid was dried under vacuum (ca. 1 mmHg) for 30 min, and then stored in a sealed vial at -78 °C to minimize the transformation to urea (yield, 1.6 g, 89%). Deuterated ammonium cyanate was prepared by the same method, using NEt4OCN and ND4SCN (Aldrich). The deuteration level of the product was estimated, by electron impact ionization mass spectrometry of a sample converted to urea, to be ca. 77%. A sample from the same batch of deuterated ammonium cyanate was used in our previous powder neutron diffraction study.4 In the Rietveld analysis of the neutron diffraction data, refinement of the 1H/2H occupancies led to an estimate of the deuteration level (ca. 81%) in close agreement with the value determined by mass spectrometry. 2.2. Quasielastic Neutron Scattering Experiments. For the quasielastic neutron scattering (QENS) experiments, a powder sample of ammonium cyanate (with natural isotopic abundances) was placed in a flat aluminum container (sealed with indium wire). The angle between the incident beam and the plane of the sample holder was 45°. To minimize the effects of multiple scattering, a sample thickness of less than 0.2 mm was used, such that the transmitted intensity was about 90% of the intensity of the incident beam. High-resolution (HR) QENS spectra were recorded on the back-scattering spectrometer IN1611a at the Institut LaueLangevin (Grenoble, France) using the Si(111) monochromator and analyzers (λo ) 6.27 Å; energy resolution ∆E ≈ 1 µeV). Given the scattering angles covered by the analyzers, the momentum-transfer values (pQ) probed correspond to Q in the range of 0.2-1.9 Å-1. The first stage of our experiments was to record a “fixed window scan”, involving measurement of the elastic scattering as a function of temperature, with the sample heated from 1.6 to 330 K over 13.5 h and then from 330 to 340 K over 1.5 h (the data collection time per spectrum was 3 min). After these measurements, a fresh sample was used to record full HR-QENS spectra (data collection time ca. 8 h) at 2 K (to determine the instrumental resolution function) and then at 220, 253, 282, and 305 K for subsequent spectral analysis. To probe faster components of motion, QENS spectra were recorded using the time-of-flight (ToF) spectrometer NEAT11b at the Berlin Neutron Scattering Centre of the Hahn-Meitner Institute (Berlin, Germany). The scattering angles (2θ) on this instrument are in the range of 13-136°, and two different energy resolutions were used: ∆E ) 90 µeV (λo ) 5.1 Å) and ∆E ) 30 µeV (λo ) 8.1 Å). The data acquisition times for the ∆E ) 90 µeV and ∆E ) 30 µeV resolutions were 7 and 15 h, respectively, and the spectra were recorded (in order of increasing temperature) at 253, 267, 282, and 293 K for ∆E ) 30 µeV resolution, and at 267 and 282 K for ∆E ) 90 µeV resolution. A fresh sample of ammonium cyanate was used at the start of the experiments at each resolution. Analysis of Bragg peaks (i.e., elastic coherent contributions to the scattered intensity) confirmed that no urea was formed during the acquisition of the QENS spectra. The raw data were corrected for detector efficiency and sample-geometry dependent attenuation, and the background

15872 J. Phys. Chem. C, Vol. 112, No. 40, 2008 was subtracted using the measurement for the empty sample container. The data were normalized to the elastic scattering of vanadium and transformed to an energy scale. Several detectors were grouped together in order to improve the statistical accuracy, and Bragg peaks were removed from the experimental data. All of these procedures were carried out using the INX software12a for the ToF-QENS data and the SQW software12b for the HR-QENS data. Data analysis was carried out using the program NEMO.13 2.3. 2H NMR Spectroscopy. All solid-state 2H NMR experiments were carried out on a Chemagnetics CMX-Infinity 300 spectrometer (2H frequency, 46.080 MHz) using a Chemagnetics nonspinning probe (5 mm coil). 2H NMR line shapes of powder samples of deuterated ammonium cyanate were recorded in the temperature range 123-290 K using the standard quadrupole echo pulse sequence:14 (π/2)φ-τ-(π/2)φ(π/2-τ′-acquirerecycle, with τ ) 30 µs. An eight-step phase cycle was used, and the 90° pulse duration was 2.0 µs. At each temperature, the recycle delay used was at least five times the largest value of 〈1/T1〉p-1, where 〈1/T1〉p-1 denotes the powder-average 2H NMR spin-lattice relaxation time. Simulations of 2H NMR line shapes were carried out using the program EXPRESS (an updated version of the program MXQET15). Powder-average 2H NMR spin-lattice relaxation times 〈1/T1〉p-1 were measured between 123 and 290 K using a saturation recovery pulse sequence with quadrupole echo detection: [τd-(π/ 2)x]n-τr-(π/2)φ-τ-(π/2)φ(π/2–τ′-acquire-recycle. The number of 90° pulses used for saturation was typically n ) 36-48, with τd ) 400 µs, τ ) 30 µs, and τ′ < τ. The variable relaxation delay τr was increased geometrically according to τr ) to[10(N-1)/10], where N is the delay number and to is the value of the first delay (i.e., τr ) to for N ) 1). 3. Dynamic Models 3.1. Specification of Models. The tetrahedral (Td) point group symmetry of the ammonium cation and the location of this cation within a local environment that presents the opportunity to form either four N-H · · · O hydrogen bonds or four N-H · · · N hydrogen bonds (see Figure 1) give rise to several plausible dynamic models discussed below. Models A-C involve motions that preserve a single type of hydrogen bonding arrangement (e.g., only N-H · · · N hydrogen bonds), whereas models D and E allow the ammonium cation to populate both the N-H · · · N and N-H · · · O hydrogen bonding arrangements during the motion. 3.1.1. Model A. The ammonium cation has three 2-fold rotation axes (i.e., the bisectors of each H-N-H bond angle), and this model involves 180° jumps about one of these 2-fold axes (see Figure 2). Starting from the orientation with four N-H · · · N hydrogen bonds, such jumps take the ammonium cation into an equivalent orientation with four N-H · · · N hydrogen bonds. 3.1.2. Model B. The ammonium cation has four 3-fold rotation axes (i.e., along each N-H bond), and this model involves 120° jumps about one of these 3-fold axes (see Figure 2). Again, starting from the orientation with four N-H · · · N hydrogen bonds, such jumps take the ammonium cation into an equivalent orientation with four N-H · · · N hydrogen bonds. We note that one N-H bond (collinear with the axis of rotation) remains fixed during this motion. 3.1.3. Model C. This model is a four-site tetrahedral jump model, in which each hydrogen atom of the ammonium cation visits all four sites (corresponding to the four N-H · · · N hydrogen bonds) with equal probability during the time scale

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Figure 2. Symmetry axes of the ammonium cation. The lighter and darker hydrogen atoms correspond to the relative orientations of the ammonium cation in the two different hydrogen bonding arrangements.

of the measurement. This situation could be achieved by different types of local jump, either (i) by individual jumps of the type discussed above for model B (i.e., 3-fold 120° jumps about a single N-H bond), but with the N-H bond that serves as the rotation axis changing such that each of the four N-H bonds serves as the rotation axis with equal probability during the time scale of the measurement; (ii) by individual jumps of the type discussed for model A above (i.e., 180° jumps about a 2-fold axis of the ammonium cation), but with the 2-fold axis that serves as the rotation axis changing such that each 2-fold axis of the ammonium cation serves as the rotation axis with equal probability during the time scale of the measurement; or (iii) by a combination of the 3-fold and 2-fold jumps discussed in (i) and (ii). 3.1.4. Model D. This model comprises 90° jumps about a single 2-fold axis of the ammonium cation and leads to interconversion of the N-H · · · N and N-H · · · O hydrogen bonding arrangements (see Figure 2). This model is equivalent to jumps of each hydrogen atom between four equivalent sites equally spaced on a circle (the plane of which is perpendicular to the 2-fold axis), with the diameter of the circle equal to the H · · · H distance in the ammonium cation. 3.1.5. Model E. This model also involves interconversion between the N-H · · · N and N-H · · · O hydrogen bonding arrangements, and is an eight-site jump model in which all hydrogen atoms of the ammonium cation visit all eight sites (i.e., for both the N-H · · · N and N-H · · · O hydrogen bonding arrangements) with equal probability during the time scale of the measurement. Thus, each hydrogen atom visits each of the eight corners of a cube during the motion, with the diagonal of the cube equal to twice the N-H bond length. This model implies that there should be equal populations of the N-H · · · N and N-H · · · O hydrogen bonding arrangements, although the model may clearly be generalized to allow for different populations of the N-H · · · N and N-H · · · O hydrogen bonding arrangements. 3.2. Preliminary Assessment of Dynamic Models. A fundamental requirement of proposed models for dynamic processes in crystalline solids is that the time average of the dynamic process should be compatible with the experimental crystal structure determined from diffraction-based studies. As discussed above, powder neutron diffraction studies4 indicate that there is no observable population of hydrogen/deuterium sites corresponding to the orientation of the ammonium cation with N-H · · · O hydrogen bonding. On this basis, both models D and E are incompatible with the experimental crystal structure as both models imply that there is a nonzero population of

Dynamic Properties of Solid Ammonium Cyanate hydrogen/deuterium sites corresponding to N-H · · · O hydrogen bonding. In the limit in which the population of the N-H · · · O hydrogen bonding arrangement is zero, model D becomes equivalent to model A and model E becomes equivalent to model C. Energetic aspects of the reorientation of the ammonium cation in crystalline ammonium cyanate have been investigated previously using DFT techniques.9 These studies considered (i) rotation about a single (fixed) N-H bond of the ammonium cation, which is analogous to the type of rotation in model B, and (ii) rotation about a 2-fold axis of the ammonium cation (specifically the 2-fold axis parallel to the crystallographic 4j axis), which is analogous to the type of rotation in models A and D. Relative to the energy of the structure with the ammonium cation in the N-H · · · N hydrogen bonding arrangement, the computed energy barriers were 34.8 kJ mol-1 for rotation of type (i) and 42.6 kJ mol-1 for rotation of type (ii), suggesting that rotation of type (i) should be favored over rotation of type (ii). Starting from the N-H · · · N hydrogen bonding arrangement, the energy profile for rotation of type (ii) has a local minimum at 90° rotation (corresponding to the N-H · · · O hydrogen bonding arrangement) before returning to the N-H · · · N hydrogen bonding arrangement at 180° rotation. The DFT calculations indicate that the N-H · · · O hydrogen bonding arrangement is higher in energy than the N-H · · · N hydrogen bonding arrangement by ca. 24.4-26.0 kJ mol-1 (depending on details of the computational technique). Given the magnitude of this energy difference (for which the Boltzmann distribution predicts a population ratio N(N-H · · · O)/N(N-H · · · N) of only ca. 3 × 10-5 at 290 K), rotation of type (ii) would not be expected to involve a significant population of the N-H · · · O hydrogen bonding arrangement (as indeed observed in the crystal structure determined from powder neutron diffraction data). Finally, we note that DFT calculations9 for rotation of type (i) suggest that the ammonium cation is displaced by ca. 0.21 Å along the direction of the fixed N-H bond (i.e., the rotation axis), such that this N-H · · · N hydrogen bond is shortened (strengthened), while the other three N-H · · · N hydrogen bonds are lengthened (weakened). Clearly this displacement serves to lower the energy barrier for rotation. Such translational displacements are not detected by the 2H NMR techniques discussed here but may in principle be observed by QENS, provided the displacement occurs on an appropriate time scale. However, the relatively small magnitude of the displacement inferred from the DFT study is such that it would be accessible from QENS data only through measurement of the Debye-Waller factor. 4. Data Analysis, Results, and Discussion 4.1. Quasielastic Neutron Scattering. 4.1.1. Background. For the sample of ammonium cyanate with natural isotopic abundances used in the QENS experiments, the main contribution to the QENS spectra arises from incoherent scattering by 1H nuclei in the ammonium cation, thus allowing the ammonium dynamics to be probed. The reduced QENS spectra Sexp(Q,ω) recorded as a function of momentum transfer pQ and energy transfer pω are related to the scattering law S(Q,ω) by the following equation:16,17

Sexp(Q, ω) ) F(Q)e-pω⁄2kTS(Q, ω) X R(Q, ω) + B(Q) (1) where F(Q) is the scaling factor [the Q dependence of which arises from the Debye-Waller factor associated with vibrational components of the motion of the 1H nuclei (i.e., e-Q2〈u2〉, where

J. Phys. Chem. C, Vol. 112, No. 40, 2008 15873 〈u2〉 is the mean square displacement in the isotropic approximation)], e-pω/2kT is the detailed balance factor, S(Q,ω) is the scattering law for the dynamic process, and B(Q) is the background term (represented by a straight line as the energy window considered is fairly small) due to the inelastic contributions (incoherent and coherent) within the quasielastic region. The function R(Q,ω) represents the experimental energy resolution. On the time scale accessible by the ToF-QENS and HRQENS experiments, no long-range translational diffusion should contribute to the scattering function, and only short-range translational diffusion is observable via the Debye-Waller factor, as noted above. It follows that only reorientational motions are expected to contribute to the scattering law S(Q,ω) of the QENS spectra. Thus, the scattering law may be written as the superposition of an elastic peak plus Lorentzian functions: n

S(Q, ω) ) A0(Q) δ(ω) +

∑ Aj(Q) Lj(ω) j)1

n

with

∑ Aj(Q) ) 1

(2)

j)0

where Ao(Q) is the elastic incoherent structure factor (EISF) giving the amplitude of the elastic term, which is represented by δ(ω). The EISF provides information about the geometry of the reorientational motion of the ammonium cation. The Lorentzian functions Lj(ω) represent the quasielastic contributions, with amplitudes given by the structure factors Aj(Q). The half-width at half-maximum height (denoted HWHM) of each Lorentzian function provides information about the characteristic time of the reorientational motion. The number of Lorentzian functions (n) depends on the model considered to describe the reorientational motion, as discussed below. In eq 1, the theoretical scattering law S(Q,ω) is convoluted with the experimental energy resolution function R(Q,ω), allowing comparison with the experimental QENS spectra. The width (denoted ∆E) of the energy resolution function establishes the accessible time scale on which a given motion is observable in the experimental QENS spectra so that the energy resolution ∆E acts as a time filter on the scattering law. For example, if the dynamic process can be decomposed into different localized diffusive motions, then to a first approximation each localized diffusive motion will give rise to a quasielastic component characterized by one of the Lorentzian functions in eq 2. The HWHM of a given quasielastic component is denoted ∆j, and we consider three cases: (a) ∆j > 10 µeV, (b) ∆j ≈ 1 µeV, and (c) ∆j , 1 µeV. In case (a), the quasielastic broadening is too large in comparison with the accessible energy-transfer window of the HR-QENS spectrometer and will be subsumed into the flat background of the HR-QENS spectra. On the other hand, such components of motion will be resolved in the ToF-QENS spectra. In case (b), the motion will be observed in the HRQENS spectra, as the quasielastic broadening is of the same order as the energy resolution. However, this quasielastic broadening is narrower than the instrumental resolution function on the ToF-QENS spectrometer and will give rise to apparent elastic scattering in the ToF-QENS spectra. Case (c) represents the limiting case as ∆j is significantly smaller than the highest energy resolution (i.e., ∆E ≈ 1 µeV for the HR-QENS spectrometer), and thus only apparent elastic scattering will be observed in both the HR-QENS and ToF-QENS experiments. Thus, investigations using both the ToF-QENS and HR-QENS spectrometers allow motions across a broad range of time scales

15874 J. Phys. Chem. C, Vol. 112, No. 40, 2008

Figure 3. Fixed window scan recorded for ammonium cyanate between 1.6 and 340 K on the HR-QENS spectrometer (IN16) with an instrumental resolution of 1 µeV. The dashed lines indicate the three temperature regions discussed in the text.

Figure 4. QENS spectra recorded for ammonium cyanate on the HRQENS spectrometer (IN16, λo ) 6.27 Å, ∆E ) 1 µeV) at 220 (squares), 253 (triangles), and 282 K (circles), together with the resolution function (thin line). The momentum transfer is Q ) 1.9 Å-1, and all scattering laws have been normalized.

to be probed, ranging typically from nanosecond (HR-QENS) to picosecond (ToF-QENS) regimes. 4.1.2. Phenomenological Analysis. Figure 3 shows the intensities, averaged over all scattering angles, recorded in the fixed window scan on the HR-QENS spectrometer as a function of increasing temperature. These intensities include both the quasielastic and elastic components for energy transfer equal to zero. Because of the experimental energy resolution, motions occurring on a time scale significantly longer than ca. 10-9 s will give rise to “elastic-like” scattering in the HR-QENS experiment. From the fixed window scan, three temperature regimes are clearly identified. In the first regime, below ca. 200 K, all motions of the 1H nuclei are frozen in comparison with the time scale of the HR-QENS measurements, and the slight decrease of elastic intensity is due to the increasing amplitudes of external and internal vibrations of the ammonium cations (associated with the Debye-Waller factor) as temperature is increased. The second temperature regime, from ca. 200 to 320 K, is characterized by a decrease in the intensity of elastic scattering. This behavior is associated with the appearance of a quasielastic component with HWHM of the order of the energy resolution (ca. 1 µeV) in the HR-QENS experiment (see Figure 4). Thus, above 200 K, the ammonium cation undergoes reorientational motion on a time scale of ca. 10-9 s or shorter. This observation

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Figure 5. Experimental EISF determined from QENS spectra recorded at 282 K with ∆E ) 1 µeV (HR, IN16, λo ) 6.27 Å; filled circles), ∆E ) 30 µeV (ToF, NEAT, λo ) 8.1 Å; open circles), and ∆E ) 90 µeV (ToF, NEAT, λo ) 5.1 Å; crosses). The theoretical EISF for each dynamic model discussed in the text is also shown: models A and B (long dashed line), model C (thin continuous line), model D (short dashed line), and model E (dotted line). The multiple scattering corrected EISFs for models C and E are shown as the thick continuous line.

is confirmed by both the HR-QENS and ToF-QENS spectra, for which quasielastic broadening is clearly observed above ca. 240 K for ∆E ) 30 µeV and above ca. 260 K for ∆E ) 90 µeV. The QENS spectra have been analyzed first at a phenomenological level, with the HR-QENS and ToF-QENS data fitted by eqs 1 and 2 with n ) 1, yielding the experimental EISF Ao(Q). The EISF extracted at 282 K is shown in Figure 5, from which two main observations may be made. First, for the data recorded on the HR-QENS spectrometer, the limiting value of EISF in the low-Q region does not tend to a value of 1, which may be attributed to the effects of multiple scattering.16 Second, the EISF appears to depend on the energy resolution (with higher EISF at higher energy resolution; Figure 5), which may arise for one of the following reasons: (i) if reorientation of the ammonium cation occurs on a time scale of the order of ca. 10-9 s, this process is better resolved in the HR-QENS data and the apparent EISF measured with the ToF-QENS spectrometer will be greater than that measured with the HR-QENS spectrometer, or (ii) if the ammonium dynamics comprise at least two localized diffusive motions, one occurring on a time scale of the order of ca. 10-9 s (thus observable in the HRQENS experiments) and the other occurring on a time scale of the order of ca. 10-12 s (thus observable in the ToF-QENS experiments). As discussed below, situation (i) is applicable in the present case. The third temperature regime, above ca. 320 K, is associated with the chemical transformation from ammonium cyanate to urea. As seen in Figure 3, the elastic intensity decreases abruptly at 320 K, indicating that the ammonium cation gains reorientational and/or translational degrees of freedom. This behavior is then followed by an abrupt increase in the elastic intensity at 333 K, associated with the formation of urea. Indeed, it is known from independent studies that the dynamics of the urea molecules in solid urea18 occur on a time scale (of the order of ca. 10-6 s in the region of 333 K18g) that is significantly longer than the characteristic time scale of the HR-QENS experiment. Thus, solid urea should only contribute to the elastic peak in the HR-QENS measurements. The chemical transformation to

Dynamic Properties of Solid Ammonium Cyanate

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TABLE 1: Expression for the EISF for Each of the Dynamic Models Discussed in Section 3.1, Where jo(x) Is the Spherical Bessel Function of Zero Order and d Is the Nearest-Neighbour Distance between Hydrogen Atoms in the Ammonium Cation (d ≈ 1.6 Å) model A B C D E

EISF A0(Q) ) (1/2)[1 A0(Q) ) (1/2)[1 A0(Q) ) (1/4)[1 A0(Q) ) (1/4)[1 A0(Q) ) (1/8)[1 3j0(Qd)]

+ + + + +

j0(Qd)] j0(Qd)] 3j0(Qd)] 2j0((2/2)Qd) + j0(Qd)] j0((6/2)Qd) + 3j0((2/2)Qd) +

ref 16 16 7b 16 16

urea reaches completion in less than 1 h between 333 K (i.e., the temperature at which the minimum elastic intensity is observed) and 340 K (i.e., the temperature at which the elastic intensity is characteristic of solid urea). 4.1.3. Modeling the QENS Data. The complete scattering law has been calculated for each dynamic model described in section 3, and the theoretical EISF for each model is given in Table 1. We note that models A and B lead to identical scattering laws, as a consequence of the fact that the jump distance is the same for 2-fold 180° jumps and 3-fold 120° jumps (in both cases, the jump distance is equal to the H · · · H distance in the ammonium cation) and the fact that one of the four 1H nuclei of the ammonium cation is immobile for the 3-fold 120° jump motion. These two motions are distinguished in terms of the definition of the HWHM (denoted ∆) for the quasielastic broadening, with ∆ ) 2k for the two-site 180° jump model A and ∆ ) 1.5k for the three-site 120° jump model B, where k denotes the jump rate of the motion. In Figure 5, the EISF extracted from the fits of the phenomenological approach is compared with each theoretical model. It is clear that models A, B, and D do not reproduce the experimental data, whereas the experimental EISF follows approximately the behavior of models C and E. However, the experimental EISF and the theoretical EISFs for these models are clearly different in the region of low-Q values, originating (as discussed above) from the effects of multiple scattering. For this reason, we have corrected the EISFs for both models C and E to take account of second scattering processes (following the procedure described for a flat sample container in previous papers16,19,20), leading to excellent agreement between the experimental EISF and the multiple-scattering corrected theoretical EISF for each model. The EISFs for models C and E differ only for Q values greater than ca. 2 Å-1 (as a consequence of the shorter jump distances that arise for the cubic jump model but not for the tetrahedral jump model). The same observation can also be made for a generalized version of model E with different populations for the two types of hydrogen bonding arrangement, which yields EISFs that vary between the EISF for model C (i.e., p ) 0) and the EISF for model E (i.e., p ) 0.5), where p denotes the fraction of N-H · · · O hydrogen bonding. Unfortunately, no experimental data are available beyond ca. 2 Å-1 as a consequence of the intrinsic characteristics of the neutron scattering spectrometers used in the present work. Thus, on consideration of the EISF alone, it is impossible to conclude whether model C or model E best reproduces the experimental data. However, the fact that neutron diffraction4 provides conclusive evidence for N-H · · · N hydrogen bonding, with no significant populations of N-H · · · O hydrogen bonding, implies that model E may be ruled out. The complete set of experimental data has been fitted using the scattering law for the tetrahedral jump model C, as shown

in Figure 6. There is clearly good agreement between experimental and theoretical scattering laws, although some differences are observed in the low-Q region of the HR-QENS data (the left-hand side of Figure 6). These differences are due to multiple scattering (which is negligible at medium- and large-Q values) and has not been taken into account in the fitting procedure. The jump rate (k) and the HWHM of the quasielastic broadening (∆) are related by ∆ ) 4k, allowing the jump rate to be established as a function of temperature. The temperature dependence of k, shown in Figure 7, is found to exhibit Arrhenius behavior:

k(T) ) koe-Ea⁄kBT

(3)

From fitting this equation to the values of k(T), the activation energy and preexponential factor are determined to be Ea ) 22.6 ( 2.1 kJ mol-1 and ko ) 20 ( 16 ps-1, respectively. Previous studies of ammonium dynamics in other materials7b have shown that multiple scattering effects give rise to underestimation of the jump rate by ca. 3-4% and the activation energy by ca. 2%, and in the present case such errors are subsumed into the values determined by fitting the Arrhenius equation. Finally, the Debye-Waller factors have been extracted from the HR-QENS data, and the values of mean square displacement 〈u2〉 are 0.05 ( 0.02 Å2 at 200 K, 0.08 ( 0.02 Å2 at 253 K, 0.08 ( 0.01 Å2 at 282 K, and 0.11 ( 0.01 Å2 at 305 K. While bearing in mind the isotropic approximation considered in extracting the mean square displacement, we note that these values are in reasonable agreement with the local translational displacement of ca. 0.21 Å (corresponding to a squared displacement of 0.044 Å2) that has been suggested,9 on the basis of DFT calculations, to be associated with the reorientational motion of the ammonium cation (see section 3.2). 4.2. 2H NMR Spectroscopy. 4.2.1. Background. Solid-state 2H NMR spectroscopy is a powerful technique for studying reorientational motions of molecules in solids21 and has been used to characterize the dynamic properties of a wide range of systems. Different aspects of 2H NMR yield different information on dynamic properties, and the two most commonly used techniques are 2H NMR line shape analysis and 2H NMR spin-lattice relaxation time measurements. For 2H nuclei in organic solids, the quadrupolar interaction is normally so large that other nuclear spin interactions are negligible in comparison. A polycrystalline powder sample containing a random distribution of crystal orientations gives rise to a characteristic 2H NMR “powder pattern” (often called a “Pake powder pattern”21). Analysis of this powder pattern allows quantitative determination of the quadrupole interaction parameters (the quadrupole coupling constant χ and the asymmetry parameter η) for the 2H nucleus. Because the quadrupole interaction parameters are influenced significantly when the 2H nucleus undergoes motion on an appropriate time scale (see below), the appearance of the 2H NMR powder pattern changes significantly depending on the rate and mechanism of the motion. When the 2H nucleus is static, or undergoes rates of motion lower than ca. 103 s-1 (the static/slow motion regime), the 2H NMR line shape for a powder sample has a characteristic shape that is independent of the rate and geometry of the motion. 2H NMR line shape analysis is particularly informative when the rate of motion is in the range 103 s-1 to 108 s-1 (the intermediate motion regime), as analysis of the 2H NMR line shape in this regime provides detailed information on the rate and mechanism of the dynamic process. For rates of motion higher than ca. 108 s-1 (the rapid motion regime), the actual

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Figure 6. Fits of the tetrahedral jump model (model C) to the experimental QENS spectra recorded at 282 K, showing various Q values at the three energy resolutions considered. Left: HR-QENS (IN16), λo ) 6.27 Å, ∆E ) 1 µeV. Middle: ToF-QENS (NEAT), λo ) 8.1 Å, ∆E ) 30 µeV. Right: ToF-QENS (NEAT), λo ) 5.1 Å, ∆E ) 90 µeV. The circles show the experimental spectra. The dotted straight line is the fitted linear background, and the Lorentzian-shaped dashed line is the fitted QENS component. The complete fitted scattering laws are shown as continuous lines (in the insets for the HR-QENS data).

Figure 7. Jump rates for the tetrahedral jump model (model C) determined from the QENS data. The continuous line represents the fitted Arrhenius equation. The symbols show the experimental values. Filled circles: HR-QENS (IN16), ∆E ) 1 µeV. Triangles: ToF-QENS (NEAT), ∆E ) 30 µeV. Open circles: ToF-QENS (NEAT), ∆E ) 90 µeV. The jump rate (cross symbol) reported at the highest temperature (324 K) was determined using the phenomenological fit of a short acquisition (1 h) ToF-QENS spectrum (NEAT, λo ) 5.1 Å, ∆E ) 90 µeV).

rate of motion cannot be established from 2H NMR line shape analysis, but information on the geometry and mechanism of the motion can nevertheless be obtained. 2H NMR line shape analysis is generally carried out by calculating the line shapes for proposed dynamic models, and finding the dynamic model

for which the set of calculated line shapes give rise to the best fit to the set of experimental line shapes recorded as a function of temperature. When the rate of motion is in the rapid regime with respect to 2H NMR line shape analysis, detailed dynamic information can still be obtained from measurement and analysis of the 2H NMR spin-lattice relaxation time (T1), which is particularly sensitive for studying dynamic processes with rates in the range 10-3ν to 103ν (where ν is the 2H Larmor frequency). 4.2.2. Analysis and Discussion. 2H NMR spectra recorded as a function of temperature for a polycrystalline sample of deuterated ammonium cyanate are shown in Figure 8. Although the 2H NMR line shape recorded at the lowest temperature studied (123 K) has some resemblance to a classical Pake powder pattern (characteristic of the slow/static motion regime), the presence of a small, relatively sharp component at the center of the spectrum and the fact that the intensity across the central region of the spectrum is higher than that in a static powder pattern, indicate that, even at this temperature, the dynamics of the ammonium cation has already entered the intermediate motion regime (rate of motion k > 103 s-1). On increasing temperature from 123 K, the intensity of the broad powder pattern decreases while the intensity of the sharp central component increases, such that at ca. 153 K and higher temperatures only the sharp central component is present. These changes in the spectrum as a function of temperature indicate clearly that the ammonium cation undergoes a dynamic process on the 2H NMR time scale, and the evolution of the line shape into a narrow Gaussian line at higher temperatures indicates

Dynamic Properties of Solid Ammonium Cyanate

Figure 8. Experimental 2H NMR line shapes recorded as a function of temperature for deuterated ammonium cyanate.

that the geometry of the motion is such that the quadrupole coupling constant is averaged to zero. Simulated 2H NMR line shapes for each of the dynamic models A-E are shown in Figure 9, as a function of the rate of motion ranging from the static/slow motion regime to the rapid motion regime. It is clear from visual comparison of the 2H NMR line shapes in Figures 8 and 9 that the motion of the ammonium cation is not described by dynamic models A or B. For model A, all deuteron sites in the ammonium cation are equivalent with respect to the dynamic process, and thus the 2H NMR line shape is described by the dynamics of a single deuteron, but the line shape does not take the form of a single Gaussian line for any jump rate within the intermediate and rapid motion regimes. For model B, one deuteron of the ammonium cation remains static, with the other three deuterons undergoing a three-site 120° jump motion. The 2H NMR line shape for this model comprises two components, one of which (for the single deuteron) gives rise to a static 2H NMR powder pattern at all temperatures, whereas the other (for the three deuterons) gives rise to a line shape that changes significantly through the intermediate motion regime, but again does not become a single Gaussian line for any jump rate within the intermediate and rapid motion regimes. Dynamic models for which the 2H NMR line shape is a single Gaussian line in the rapid motion regime include isotropic

J. Phys. Chem. C, Vol. 112, No. 40, 2008 15877 reorientation, a tetrahedral jump motion (model C), a motion comprising n-site 2π/n jumps about an axis for which the angle between this axis and the N-D bond is equal to the “magic angle” [cos-1(1/3)] provided n g 3 (e.g., model D, for which n ) 4), and a cubic jump motion (model E). Isotropic reorientation (for which each N-D bond of the ammonium cation has equiprobable orientations in all directions) is incompatible with the crystal structure of ammonium cyanate, for which the time-averaged description has well-defined orientations of the N-D bonds. Furthermore (as discussed in section 4.1 above), the four-site 90° jump model (model D) and the cubic jump model (model E) are also incompatible with the crystal structure of ammonium cyanate, as the time average of these models requires that both the N-H · · · O and N-H · · · N hydrogen bonding arrangements are populated. On the other hand, the tetrahedral jump motion (model C), in which each N-D bond of the ammonium cation has an equiprobable distribution of orientations toward the four corners of a tetrahedron, is fully compatible with the crystal structure of ammonium cyanate, as it is consistent with a situation in which the ammonium cation forms only N-H · · · N hydrogen bonding during the motion. For these reasons, comparison between experimental and simulated 2H NMR line shapes, together with knowledge of the time-averaged crystal structure, strongly favors the tetrahedral jump model for the dynamics of the ammonium cation. In principle, finding the simulated 2H NMR line shape that represents the best fit to the experimental 2H NMR line shape at each temperature within the intermediate motion regime allows the jump rate to be established as a function of temperature, thus allowing activation parameters to be assessed. However, the fact that the experimental 2H NMR line shape for ammonium cyanate is a single Gaussian line throughout most of the intermediate motion regime is such that the fitting process in this case is less discriminating than usual for establishing the jump rate that gives the best-fit line shape at each temperature (particularly as the width of the narrow Gaussian line in the spectrum is influenced by other factors, not just the motionally averaged quadrupole coupling constant). For this reason, our studies of 2H NMR spin-lattice relaxation time data, discussed below, provide a more reliable quantitative determination of activation parameters for the motion in this case. The temperature dependence of the powder-average 2H NMR spin-lattice relaxation time 〈1/T1〉p-1, determined across the temperature range from 123 to 290 K, is shown in Figure 10. Clearly 〈1/T1〉p-1 passes through a minimum at ca. 235 K, indicating that the correlation time τc at this temperature is τc ) ωo-1 ≈ 3.5 × 10-9 s. The temperature dependence of the experimental values of 〈1/T1〉p-1 has been fitted by an expression derived21c,22 for the tetrahedral jump model, and under the assumption that the temperature dependence of the jump rate exhibits Arrhenius behavior. The three fitted parameters in this expression are the static quadrupole coupling constant (χ), the activation energy (Ea), and the preexponential factor (τc°). As shown in Figure 10, the fitted theoretical expression is in excellent agreement with the experimental data, giving further support to the tetrahedral jump model in this system. The bestfit values obtained are χ ) 166 kHz, Ea ) 21.9 kJ mol-1 and ln(τc°/s) ) -31.3. The estimated fitting errors in Ea and ln(τc°/ s) are (1.0 kJ mol-1 and (0.8, respectively. In summary, both the 2H NMR line shape analysis and 2H NMR spin-lattice relaxation time measurements provide strong support for the tetrahedral jump model (model C). Furthermore, the activation energy and preexponential factor determined from

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Figure 9. Simulated 2H NMR line shapes calculated for models (a) A, (b) B, (c) C, (d) D, and (e) E, for values of jump rate (k) ranging from the slow/static motion regime to the rapid motion regime.

Figure 10. Temperature dependence of the powder-average 2H NMR spin-lattice relaxation time 〈1/T1〉p-1 for deuterated ammonium cyanate. The fitted line is the best fit to the experimental data using the theoretical expression for 〈1/T1〉p-1 for the tetrahedral jump model (model C).

the 2H NMR spin-lattice relaxation time measurements are in excellent agreement (within experimental errors) with the corresponding values determined from the QENS data (section 4.1.3): Ea ) 22.6 ( 2.1 kJ mol-1 and ko ) 20 ( 16 ps-1 [the latter corresponding to a value of ln(τc°/s) ) -30.6]. 5. Concluding Remarks The results reported in this paper demonstrate that the combination of 2H NMR and QENS techniques is a powerful approach for probing dynamic properties of solid ammonium cyanate, leading to the assignment of the dynamic properties of the ammonium cation as a tetrahedral jump model. There is excellent quantitative agreement in the activation parameters for this motion established independently from each of these techniques. Several different models for the dynamic properties of the ammonium cation in ammonium cyanate were considered

in this work, and in more general terms, the paper provides a critical assessment of the relative abilities of 2H NMR and QENS to distinguish these different dynamic models. As discussed above, under some circumstances [for example, in specific regimes of time scale or in certain regions of the spectral data (e.g., the momentum-transfer range in the case of QENS)] it is not always possible to distinguish certain dynamic models, which further emphasizes the necessity of utilizing both the 2H NMR and QENS techniques in combination, and in each case utilizing data recorded across a wide temperature range (and hence a wide range of motional time scales). Another factor that has been important in distinguishing the different dynamic models for ammonium cyanate relies on the requirement that the time average of a dynamic process occurring in a crystalline solid should be compatible with the experimental crystal structure determined from diffraction-based studies. For ammonium cyanate, an accurate description of the crystal structure across a wide temperature range has been established previously from powder neutron diffraction (including reliable information on the positions of the hydrogen atoms of the ammonium cation), and the availability of this structural information has served as a valuable additional constraint in the assessment of different dynamic models. Aspects of the reorientational motion of the ammonium cation in ammonium cyanate have also been explored previously by DFT calculations.9 The results obtained for one of the reorientational processes considered in that work (rotation about a single fixed N-H bond) may be compared to the experimental results obtained in the present work, as this motion (which populates only the N-H · · · N hydrogen bonding arrangement) may well represent the type of individual jump that gives rise to the overall tetrahedral jump model observed. While the activation energies for the tetrahedral jump model obtained from our QENS (22.6 ( 2.1 kJ mol-1) and 2H NMR (21.9 ( 1.0 kJ mol-1) studies are in excellent agreement with each other, we note that they are significantly lower than the computed energy

Dynamic Properties of Solid Ammonium Cyanate barrier (34.8 kJ mol-1) for rotation about a single N-H bond in the DFT study. This difference may reflect the fact that the DFT calculations did not consider relaxation of the remainder of the crystal structure during the reorientation of the ammonium cation (which should lead to overestimation of the energy barrier in the DFT calculations). We also note that the reorientational motions of neighboring ammonium cations in the experimental system may be correlated with each other, which will clearly also influence the energy barrier for the reorientational motion. The experimental techniques employed in the present work probe the dynamics of individual ammonium cations and therefore cannot distinguish whether the motions of neighboring ammonium cations are correlated or uncorrelated, but nevertheless the activation parameters determined from the experimental data will clearly be influenced by the extent of correlation that exists. In principle, the extent of correlation may be investigated by appropriate computational techniques, although the DFT calculations carried out previously did not include a systematic investigation of this issue. Clearly this aspect of the dynamic properties of ammonium cyanate remains an interesting area for future investigation. Acknowledgment. We are grateful to Professor Jack Dunitz for valuable discussions on this work. The Berlin Neutron Scattering Centre (Hahn-Meitner Institute, Berlin, Germany) and the Institut Laue-Langevin (Grenoble, France) are thanked for the provision of beam time for QENS experiments. We are grateful to Cardiff University and the University of Birmingham for financial support of the solid-state NMR studies and Dr. Zhongfu Zhou for help in this aspect of the work. We thank the European Commission for funding (to A.D.) under the sixth Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures [Contract No. RII3-CT-2003-505925 (NMI3)]. References and Notes (1) (a) Wo¨hler, F. Poggendorff’s Ann. Phys. Chem. 1828, 12, 253. (b) v Liebig, J.; Wo¨hler, F. Ann. Phys. Leipzig, Ser. 2 1830, 20, 369. (2) Shorter, J. Chem. Soc. ReV. 1978, 77, 21. (3) Dunitz, J. D.; Harris, K. D. M.; Johnston, R. L.; Kariuki, B. M.; MacLean, E. J.; Psallidas, K.; Schweizer, W. B.; Tykwinski, R. R. J. Am. Chem. Soc. 1998, 120, 13274. (4) MacLean, E. J.; Harris, K. D. M.; Kariuki, B. M.; Kitchin, S. J.; Tykwinski, R. R.; Swainson, I. P.; Dunitz, J. D. J. Am. Chem. Soc. 2003, 125, 14449. (5) Tsipis, C. A.; Karipidis, P. A. J. Am. Chem. Soc. 2003, 125, 2307. (6) Me´reau, R.; Desmedt, A.; Harris, K. D. M. J. Phys. Chem. B 2007, 111, 3960. (7) (a) Lotsch, B. V.; Schnick, W.; Naumann, E.; Senker, J. J. Phys. Chem. B 2007, 111, 11680. (b) Jalarvo, N.; Desmedt, A.; Lechner, R. E.; Mezei, F. J. Chem. Phys. 2006, 125, 184513. (c) Tripadus, V.; Gugiu, M.;

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