49Ti Solid-State NMR Study of Layered Titanium Phosphates at

Publication Date (Web): May 13, 2009. Copyright ... Spies Within Metal-Organic Frameworks: Investigating Metal Centers Using Solid-State NMR. Peng He ...
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J. Phys. Chem. C 2009, 113, 10029–10037

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A 47/49Ti Solid-State NMR Study of Layered Titanium Phosphates at Ultrahigh Magnetic Field Jianfeng Zhu,† Nick Trefiak,‡ Tom K. Woo,‡ and Yining Huang*,† Department of Chemistry, The UniVersity of Western Ontario, London, Ontario, Canada N6A 5B7, and Department of Chemistry, UniVersity of Ottawa, Ottawa, Ontario, Canada K1N 6N5 ReceiVed: February 10, 2009; ReVised Manuscript ReceiVed: April 23, 2009

Layered titanium phosphates (TiPs) have many potentially important applications in ion exchange, catalysis, intercalation, and sorption. Characterization of metal local environments by solid-state 47/49Ti NMR has been difficult due to many unfavorable 47/49Ti NMR properties. In this work, we have directly characterized the local structures around Ti in several representative layered TiPs, including R-, β-, and γ-TiP, by examining the 47/49Ti static NMR spectra of these materials at an ultrahigh magnetic field of 21.1 T. The 47/49Ti chemical shielding and electric field gradient (EFG) tensors have been extracted from spectral analysis. The observed 47/49 Ti spectra are mainly determined by the second-order quadrupolar interactions. The quadrupole coupling constants (CQ) are sensitive to the distortion of the TiO6 octahedron in this series of layered TiPs. Quantum mechanical calculations have been performed on several model clusters as well as periodic systems. The results indicate that, in addition to the oxygens in the first coordination sphere of Ti, the atoms in the second and third coordination spheres and beyond also have significant effects on the EFG at the metal center, and this long-range effect contributes substantially to the CQ. A relationship between observed CQ and the Ti-O bond length distortion parameter appears to exist, and this empirical correlation is also confirmed by theoretical calculations. Using sodium-exchanged R-TiP (R-Na-TiP) with an unknown structure as an example, we show that the 47/49Ti NMR spectra can provide partial information on the local environment of the metal center. For this material, the ion exchange does not affect the Ti local environment significantly. It appears that the layer in R-TiP is more robust compared to that of the zirconium analogue. Introduction Layered metal phosphates, MPs (M ) Zr, Ti, Mo, Nb, V, Mg, Hf), have many important applications in the areas of ion exchange, intercalation, catalysis, sorption, protonic conductors, solar energy storage, and crystal engineering.1 As a key member of the MP family, layered titanium phosphates (TiPs) have received much attention in the last two decades due to their potential applications in the areas of ion exchange,2 catalysis,3 photochemistry,4 electrochemistry,5 and pharmaceuticals.6 The most important layered titanium phosphates are the R- and γ-phases. The R-Ti(HPO4)2 · H2O (denoted R-TiP) was first synthesized in 1967 by Alberti et al.7 The ion-exchange and intercalation behaviors of R-TiP have been widely studied,8 including ion exchange toward alkali, alkaline earth,9 and transition-metal ions10 and intercalations of various amines, such as alkyl amines,11 aromatic amines,12 and heterocyclic amines.13 The γ-Ti(PO4)(H2PO4) · 2H2O (denoted γ-TiP)14 was synthesized shortly after the discovery of R-TiP. Its ion-exchange and intercalation properties have been studied.8 β-TiP is the dehydrated phase of the γ-TiP.15 Besides the R-, γ-, and β-TiP, a number of titanium phosphates with layered structures have also been reported.16-18 In recent years, several amineintercalated layered titanium phosphates have been synthesized directly using the amines as organic templates.19-21 Characterization is important because understanding the relationship between the properties of the materials and their * Corresponding author. E-mail: [email protected]. Phone: 519-661-2111, ext 86384. Fax: 519-661-3022. † The University of Western Ontario. ‡ University of Ottawa.

structures is crucial for developing new applications and for improving their performance in current uses. However, for MPs, it is usually difficult to obtain suitable crystals for single-crystal X-ray diffraction studies. As such, structural determinations for many layered MP derivatives have been attempted from much more limited powder X-ray diffraction data. This situation is particularly true for the layered TiPs. For the three most important TiPs (R-, γ-, and β-phase), the structures of R- and β-TiP were proposed on the basis of the powder X-ray and neutron diffraction data.15,22 The structure of the γ-phase was only partially resolved.22 For many ion-exchanged and intercalated derivatives, the problem becomes more severe due to the reduced crystallinity during the ion exchange or the insertion of guest species. Solid-state NMR is a complementary technique to X-ray diffraction. Indeed, 31P and 1H MAS NMR have been successfully used to characterize various layered TiPs and their derivatives.18,19,20b,21,23 However, the titanium environments in these materials have never been directly probed by 47/49Ti solidstate NMR. This is due to the difficulties resulting from the nuclear properties of titanium: (i) The two NMR-active Ti isotopes, 47Ti (spin I ) 5/2) and 49Ti (spin I ) 7/2), both have small gyromagnetic ratios (γ) and are qualified as low-γ nuclei (the resonance frequencies are only 22.547 and 22.552 MHz at 9.4 T for 47Ti and 49Ti, respectively). (ii) They both also have low natural abundances (7.28% for 47Ti and 5.51% for 49Ti). The combination of (i) and (ii) leads to very low intrinsic detection sensitivity. (iii) The two isotopes both have moderately large quadrupole moments (Q) with a ratio of Q(49Ti)/Q(47Ti) being 0.818.24a The large 49Ti and 47Ti quadrupole moments

10.1021/jp901235w CCC: $40.75  2009 American Chemical Society Published on Web 05/13/2009

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usually result in a strong second-order quadrupolar interaction with nonspherical electric field gradients (EFGs), which gives rise to the broad powder patterns of the central transitions. Furthermore, since the width of the central transition depends on a factor of Q2[I(I + 1) - 3/4]/γ[2I(2I - 1)]2,24b the smaller spin I and the larger Q of 47Ti compared to those of 49Ti lead to a much broader 47Ti signal (ca. 3.52 times of the width of 49 Ti), making it more difficult to observe. (iv) 47Ti and 49Ti have very similar gyromagnetic ratio values, resulting in a very small frequency difference (for example, the frequency separation is only about 10 kHz even at 21.1 T). As a result, more often than not, the signals of the 47Ti and 49Ti arising from the same site are observed in the same spectrum with the central transition of 49Ti being nested within that of 47Ti. All these unfavorable NMR characteristics make observation of the broad solid-state 47/49 Ti spectra very difficult. Despite these difficulties, 47/49Ti solid-state NMR has been successfully applied to a number of inorganic compounds, such as TiO225 and MTiO3 (M ) Ba2+, Pb2+, Ca2+, Mg2+, etc.).26,27 Recently, ultrahigh field magnets have become increasingly accessible. The sensitivity enhancement techniques, such as quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) and related sequences,28,29 have been developed for quadrupolar nuclei. High-field NMR reduces the effects of second-order quadrupolar broadening and increases the population difference of the central transition, therefore, enhancing the sensitivity. In the present study, the local environments of the titanium centers in several representative TiPs, including R-, γ-, and β-TiP, have been directly probed using solid-state 47/49Ti static Hahn-echo and QCPMG NMR at ultrahigh field of 21.1 T. Chemical shielding (CS) and electric field gradient (EFG) tensor parameters of 49Ti were extracted from the spectra. Theoretical calculations were also performed on model clusters of varying size and periodic structures to assist in explaining the experimental results. Relationships between the NMR parameters and local structure around Ti were examined, and the results were used to obtain partial information regarding the Ti local coordination environment of Na+-ion-exchanged R-TiP (R-NaTiP) with unknown structure. Experimental Section Synthesis. R-TiP was synthesized using titanium dioxide and phosphoric acid.30 Specifically, 2 g of TiO2 was mixed with 50 mL of H3PO4 (85%) and refluxed at boiling in a three-neck round-bottom flask overnight. Thirty milliliters of water was then added to this solution, and the mixture was refluxed for 3 more days. The precipitate was recovered by filtration and washed with water. The product was dried at room temperature. γ-TiP was prepared by hydrothermal treatment of amorphous titanium phosphate.15 The amorphous titanium phosphate was first prepared as described by Alberti et al.7 A mixture containing 12.5 g of TiCl4 and 215 mL of 2 M HCl aqueous solution was prepared and then added dropwise to 200 mL of 1.25 M H3PO4 solution at room temperature. The mixture was then stirred for 24 h to allow precipitation. The resulting solids were filtered, washed with water to pH 3-3.5, and dried at ambient conditions. γ-TiP was then prepared as follows: Three grams of amorphous titanium phosphate was stirred in 60 mL of H3PO4 (85%) for 24 h; the mixture was then sealed in an autoclave and heated at 200 °C for 48 h. After the reaction was quenched in cold water, the solids were isolated by filtration and washed with water. β-TiP was obtained by dehydration of the γ-phase at 190 °C

Zhu et al. for 20 h. The R-Na-TiP was prepared by titration of R-TiP (suspended in water) with 0.1 M (NaOH + NaCl) solution to neutral.9a The identity of the synthesized materials was confirmed by comparing their powder XRD patterns (Supporting Information, Figure S1) with those reported in the literature.15,22 Powder XRD measurements were performed on a Rigaku rotating anode diffractometer (45 kV/160 mA) using graphite-monochromated Co KR radiation with a wavelength of 1.7902 Å. The XRD patterns were recorded within the range 5° e 2θ e 65° with 10°/min step width. NMR Measurement. 47/49Ti NMR spectra were acquired at 21.1 T on a 900 MHz Bruker Avance II spectrometer at the National Ultrahigh-Field NMR Facility for Solids in Ottawa, Canada. The operating frequency was 50.8 MHz. A 7.0 mm home-built single-channel wide-line NMR probe was used. The observed 47/49Ti spectra were referenced against a secondary standard that is a concentrated solution of Cp2TiCl2 in CH2Cl2 by setting the 49Ti resonance of Cp2TiCl2 to -773 ppm relative to 49Ti in neat, liquid TiCl4.31 The 49Ti and 47Ti chemical shifts reported in the text are both referenced to Cp2TiCl2 solution (i.e., set both 49Ti and 47Ti peaks to -773 ppm). 47/49 Ti static spectra were also acquired by using the Hahnecho32 sequence with a 90° refocusing pulse (π/2-τ-π/2-τacq). A π/2 pulse width of 6.5 µs, corresponding to a selective π/2 pulse width of 1.6 µs for 49Ti central transition, was calibrated on the concentrated Cp2TiCl2/CH2Cl2 solution. Note that the tip angle for 47Ti would be only 3π/8 due to the I dependence of the selective pulse. A recycle delay of 1.0 s and a τ of 50 µs were used. The number of scans collected was between 28 000 and 75 800. The echo was collected prior to the echo maximum and shifted to ensure that the free induction decay (FID) used in Fourier transformation begins exactly at the echo maximum. 47/49 Ti static QCPMG spectra were acquired using the conventional QCPMG pulse sequence,28 which provides a better sensitivity than that of the regular static Hahn-echo experiments. The selective π/2 pulse width was 1.6 µs, and the recycle delay was 1.0 s. The interpulse and interacquisition delays were set to τ1 ) τ2 ) τ3 ) τ4 ) 60 µs. The acquisition time (τa) for each echo was adjusted to obtain spikelet separations (1/τa) of 1920 Hz for R-TiP, 892 Hz for γ- and β-TiP, and 3100 Hz for R-Na-TiP in the frequency spectrum. The number of MeiboomGill (MG) loops was varied to ensure the acquisition of the full free induction decay. Piecewise spectra were acquired by increasing or decreasing the transmitter frequency. The offsets of the transmitter frequency were set as a multiple of spikelet separation to make sure that the spikelets can be added up for each subspectrum. Approximately 13 500 scans were collected for each piece. The subspectra with different frequency offsets were co-added in frequency scale (hertz). The resulting spectrum was then treated and referenced as a single spectrum. All the spectral simulations were carried out with the DMfit software package33 and the WSOLIDS1 software package.34 The experimental error for each measured parameter was determined by visual comparison of experimental spectra with simulations. The parameter of concern was varied bi-directionally starting from the best-fit value, and all other parameters were kept constant, until noticeable differences between the spectra were observed. Calculations of EFG Tensors. The calculations of EFG tensors of 47/49Ti in the TiPs were performed using Gaussian 03 program35 on SHARCNET (www.sharcnet.ca).36 To make the calculation practical, simplified molecular clusters containing

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Figure 1. The structures of (A) R-TiP, (B) γ-TiP, and (C) β-TiP. The coordinates of H atoms in (A) and (B) and O coordinates in water molecules in (B) were not determined and, therefore, are not shown.

the structural units of interest were used. Two types of model complexes, including Ti(OH)62- and Ti(PO4)6Hnm- (n is equal to 6, 12, and 8 and m is equal to 8, 2, and 6 for R-, β-, and γ-TiP, respectively), were examined. The model complexes were constructed according to the available crystal structure data of the corresponding TiPs,15,22 and no further optimization was performed. The clusters were terminated with OH groups, an approach widely used in ab initio calculations of 27Al EFG tensors in periodic solids, such as zeolites.37 The terminal H atoms are either H atoms in the P-OH group or replacing P or Ti atoms connected to the O atoms in the third coordination spheres. The number of H atoms varies for different TiPs because the H coordinates in the P-OH groups in R- and γ-TiP are not determined, and therefore, these H atoms are not included in the clusters. The calculations were carried out using the restricted Hartree-Fock (RHF) method. This method was shown by several researchers38 to give better EFG predictions than the hybrid density functional theory (DFT). To examine the basis set dependence, several expanded all-electron basis sets,39 including 3F(4333/43/4), 3F(5333/53/5), 5F(4333/43/4), and 5F(5333/53/5), were applied to Ti. Basis set 6-311G** was applied to the atoms other than Ti. The calculated EFGs (Vxx, Vyy, Vzz) were converted to the quadrupole coupling constant (CQ) and asymmetry parameter (ηQ) according to the following definition: |Vxx| e |Vyy| e |Vzz|, CQ ) (eVzzQ/h) × 9.71736 × 1021 (Hz), and ηQ ) (Vxx-Vyy)/ Vzz, where e is the electric charge, Q is the nuclear quadrupole moment [Q(47Ti) ) 3.02 × 10-29 m2 and Q(49Ti) ) 2.47 ×

10-29 m2],40 and h is Planck’s constant. The constant of 9.71736 × 1021 in the equation is due to Vzz being calculated in atomic units. First-principles calculations based on plane-wave pseudopotential density functional theory were also conducted using the CASTEP (version 4.3)41 program. The calculations were performed using ultrasoft pseudopotentials generated from the “on-the-fly” method42 implemented within the CASTEP. The generalized gradient approximation (GGA) PBE43 exchangecorrelation functional was used. A plane-wave cutoff energy of 550 eV was applied to all three TiPs. For k-point sampling, 3 × 5 × 2, 1 × 4 × 5, and 5 × 4 × 2 Monkhorst-Pack (MP) grids, corresponding to 9, 6, and 10 k-points, were used for R-, β-, and γ-TiP, respectively. Geometry optimization was not performed due to the size of periodic systems. Results and Discussion r-TiP. The layered structure of R-TiP is shown in Figure 1A. Each layer consists of one TiO6 octahedron sheet sandwiched by two sheets of PO4 tetrahedra. Each TiO6 octahedron is linked to six PO4 tetrahedra by sharing oxygen atoms. Each PO4 tetrahedron is connected to three TiO6 octahedra, with the fourth oxygen bonded to a hydrogen atom to form an OH group. The OH groups are oriented perpendicular to the layers and form hydrogen bonds with water molecules in the interlayer space. The crystal structure indicates that there is only one Ti lattice site,22 suggesting one signal in the NMR spectrum. The powder XRD pattern of synthesized R-TiP (Supporting Informa-

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Figure 2. (A-E) Piecewise 47/49Ti static QCPMG spectra of R-TiP at 21.1 T (50.76 MHz), with the offset of the transmitter frequency indicated on each spectrum. The spectral width of each piece is 500 kHz. (F) The co-added 47/49Ti spectrum. The simulated spectra when considering (G) both the CQ and CSA, (H) CQ only, and (I) CSA only. The spectra were referenced against the 49Ti peak of Cp2TiCl2 solution (which is -773 ppm from neat TiCl4 liquid).

tion, Figure S1A) is consistent with those reported in the literature,22,30 confirming the identity of the R-TiP. In addition, an interlayer distance of 7.4 Å was estimated according to the XRD pattern, in good agreement with the literature value of 7.6 Å. The attempt to acquire a 47/49Ti QCPMG spectrum of R-TiP at 9.4 T failed, and therefore, the experiments were performed at 21.1 T. The static Hahn-echo experiments were first attempted but were also unsuccessful. Thus, the QCPMG technique had to be applied. Because the central transitions of 49Ti and 47Ti are quite broad, a total of five piecewise frequency-stepped subspectra (Figure 2, spectra A-E) were obtained. The individually acquired segments were Fourier transformed and summed to produce the full powder spectrum (Figure 2, spectrum F). The co-added spectrum shows a strong signal with a distinct line shape from -20 to -85 kHz (-400 to -1600 ppm) superimposed on a weaker and much broader pattern from 50 to -200 kHz (500 to -4000 ppm). The strong signal with a width of 65 kHz is assigned to the 49Ti isotope and the broad signal to the 47Ti isotope. Simulations were conducted using the DMfit software33 and the WSOLIDS1 program.34 The strong line shape was first fitted using the following 49Ti parameters (Table 1): the isotropic chemical shift (δiso) ) -820 ppm, span (Ω) ) 300 ppm, skew (κ) ) 1.0, CQ ) 14.3 MHz, ηQ ) 0.05, and the Euler angles (R, β, γ) ) (0, 70, 0). Using the nuclear quadrupole moment ratio between 49Ti and 47Ti, the quadrupolar coupling constant

Zhu et al. of 47Ti (CQ) was calculated to be 17.3 MHz. Figure 2, spectra G-I, shows clearly that, to better simulate the observed spectrum, chemical shift anisotropy (CSA) needs to be included. Observing a large 47Ti CQ of 14.3 MHz is likely due to the fact that the TiO6 octahedron has a large O-Ti-O angle distortion with a range from 84.58 to 94.81° (average ) 89.96°) and a large Ti-O bond length variation from 1.911 to 2.062 Å. The value of ηQ is 0.05, implying that the Vzz component can be approximately viewed as the unique component of the EFG tensor. γ-TiP. Figure 1B shows the structure of γ-TiP. Different from R-TiP, each layer of γ-TiP consists of two sheets of TiO6 octahedra sandwiched by three sheets of PO4 tetrahedra. Each TiO6 octahedron is connected to four phosphate groups (PO43-) and two dihydrogen phosphate groups (H2PO4-). The remaining two oxygen atoms in H2PO4- group bind to the protons to form OH groups, which point into the interlayer space. These OH groups are hydrogen bonded to the water molecules. There is also only one Ti site22 and, therefore, one 47/49Ti signal in the NMR spectrum. The powder XRD pattern of synthesized γ-TiP (Supporting Information, Figure S1C) is consistent with those reported in the literature.22 The interlayer distance of 11.6 Å obtained is identical to the literature value. Both the 47/49Ti static Hahn-echo and QCPMG spectra of γ-TiP were acquired and are shown in Figure 3. The overall spectral width of the 47/49Ti resonance is much narrower than that of R-TiP, allowing a static Hahn-echo spectrum to be obtained as well. The QCPMG spectrum shows two almost resolved signals: a strong and narrower signal at high frequency corresponding to 49Ti and a weak and broad pattern at low frequency due to 47Ti. The near separation between the 47Ti and 49 Ti signals suggests that the Ti site must have a relatively small CQ. It is noted that, for the QCPMG spectra, although the signal is narrow, piecewise acquisition (Figure 3, spectra A-C) is still necessary to obtain a correct line shape for simulation. The oscillation of the spikelets in each subspectrum is due to the fact that a finite excitation pulse of 1.6 µs was used in the experiment rather than an infinite pulse, as shown by Larsen and co-workers.28 Fitting the strong signal (Figure 3, spectrum D) yielded the following 49Ti parameters (Table 1): δiso ) -1130 ppm, CQ ) 4.9 MHz, and ηQ ) 0.9. The 47Ti CQ was calculated to be 5.92 MHz. These parameters, together with the ηQ (which is the same as in 49Ti), were then used to calculate the broad 47Ti powder pattern. The spectrum can be well-fitted using only one set of 47/49 Ti quadrupolar parameters without CSA, indicating that the Ti site must have a very small CSA. Observing a 49Ti CQ of 4.9 MHz that is much smaller than that of R-TiP (14.3 MHz) is probably due to a smaller Ti-O bond length distribution (1.961-2.018 Å) since the O-Ti-O angles range from 85.65 to 95.19° with an average of 90.01°, similar to that of R-TiP. β-TiP. If the water molecules between the layers of the γ-TiP are removed by gentle dehydration, the β-phase is obtained. This phase can slowly change back to the γ-phase if it is exposed to air at ambient conditions. Thus, their structures are very similar (Supporting Information, Figures S1B and S1C) except for a smaller interlayer distance in β-TiP due to the absence of the interlayer water molecules. An interlayer distance of 9.18 Å is estimated according to the XRD pattern, consistent with the reported value of 9.15 Å. Both the 47/49Ti static Hahn-echo and QCPMG spectra were obtained (Figure 4). The spectra are similar to those of γ-TiP with two patterns due to 49Ti and 47Ti being almost separated. Careful inspection of the spectrum shows that both patterns are

Solid-State NMR Study of Layered Titanium Phosphates TABLE 1: Parameters Used to Simulate

Ti NMR Spectra of r-, γ-, β-, and r-Na-TiPa

47/49

R-TiP 49

δiso (ppm)d Ω (ppm)e κf CQ(MHz)g ηQh R (deg) β (deg) γ (deg)

Ti

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γ-TiPc 47

Ti

b

-820 ( 20 -820 300 ( 40 1.0 ( 0.2 14.3 ( 0.5 17.3 0.05 ( 0.05 0 ( 20 70 ( 5 0i

49

Ti

-1130 ( 20 4.9 ( 0.2 0.9 ( 0.1

R-Na-TiP

β-TiPc 47

Ti

b

-1130

5.92

49

47

Ti

-1130 ( 20

Ti

b

-1130

4.0 ( 0.2 0.8 ( 0.1

4.83

49

Ti

47

Tib

-800 ( 20 -800 300 ( 40 -0.5 ( 0.2 13.5 ( 0.5 16.3 0.20 ( 0.05 0 ( 20 30 ( 5 0 ( 20

a The CS tensor is described by three principal components ordered such that σ11 e σ22 e σ33. The EFG tensor is described by three principal components ordered such that |Vxx| e |Vyy| e |Vzz|. b The CQ values of 47Ti are calculated according to those of 49Ti; the 47Ti chemical shift was referenced against the 47Ti peak of Cp2TiCl2 solution (-773 ppm from neat TiCl4 liquid). c CSA is not included for γ- and β-TiP. d δjj ) (σiso,ref - σjj)106/(1 - σiso,ref) ≈ σiso,ref - σjj, where jj ) 11, 22, or 33 and δiso ) (δ11 + δ22 + δ33)/3. e Ω ) δ11 - δ33. f κ ) 3(δ22 - δiso)/Ω. g CQ ) eQVzz/h. h ηQ ) (VxxsVyy)/Vzz. i The spectrum is not sensitive to the Euler angle γ for R-TiP.

Figure 3. (A-C) Piecewise 47/49Ti static QCPMG spectra of γ-TiP at 21.1 T (50.76 MHz), with the offset of the transmitter frequency shown on each spectrum, (D) the co-added QCPMG spectrum, (E) the static Hahn-echo spectrum, and (F) the simulated spectrum. The spectra were referenced against the 49Ti peak of Cp2TiCl2 solution (which is -773 ppm from neat TiCl4 liquid).

slightly narrower than those of γ-TiP, suggesting a smaller CQ. Again, for the QCPMG spectra, stepwise acquisition had to be used to acquire the correct line shape despite the relatively narrow signal. 49 Ti parameters were extracted by fitting the signal at high frequency (Figure 4): δiso ) -1130 ppm, CQ ) 4.0 MHz, and ηQ ) 0.8 (Table 1). The corresponding 47Ti CQ is 4.83 MHz. These parameters were then used to calculate the 47Ti signal at low frequency. The fact that no CSA is needed for simulating the spectrum suggests a very small chemical shift interaction. The 49Ti NMR parameters are almost identical to those of γ-TiP except for a slightly smaller CQ. The similarity in their quadrupolar parameters is understandable due to their very similar structures. Perhaps a slightly smaller Ti-O bond length deviation for the β-phase is responsible for its slightly smaller CQ compared to that of the γ-phase. CQ versus Distortion of TiO6 Octahedra. To investigate the relationship between CQ and the distortion of the MO6 octahedra, several parameters have been suggested in the

Figure 4. (A, B) Piecewise 47/49Ti static QCPMG spectra of β-TiP at 21.1 T (50.76 MHz), with the offset of the transmitter frequency shown on each spectrum, (C) the co-added QCPMG spectrum, (D) the static Hahn-echo spectrum, and (E) the simulated spectrum. The spectra were referenced against the 49Ti peak of Cp2TiCl2 solution (which is -773 ppm from neat TiCl4 liquid).

literature for characterizing the degree of distortion around a metal center at an octahedral site. The commonly used parameters are the shear strain Ψ and the longitudinal strain R suggested by Ghose and Tsang,44 which define the distortion in O-M-O bond angle and M-O bond length, respectively 12

ψ)

∑ |tan(θi - θ0)|

(1)

i)1

where the sum runs over the actual O-Ti-O angles θi and θ0 is the ideal value (90°) and 6

R)

∑ |ln(li/l0)|

(2)

i)1

where li is the observed Ti-O bond length and l0 is the “ideal” Ti-O bond length, a perfect octahedron with bond length l0 having the same volume as the “real” octahedron. Linear correlations between CQ and these distortion parameters have

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Figure 6. Clusters used to calculate the EFG tensors. H atoms are omitted for clarity in (B).

Figure 5. Correlation between the measured CQ with (A) the shear strain Ψ and (B) the longitudinal strain R.

been reported for some inorganic materials containing MgO6,45 ZnO6,46 AlO6,47 ZrO6,48 and TiO6 octahdra.27 From the crystal structures, the shear strain values are 0.567, 0.318, and 0.658 and the longitudinal strain values are 0.148, 0.0663, and 0.0388 for the Ti sites in R-, γ-, and β-TiP, respectively. The CQ values decrease with decreasing longitudinal strain R from R-, to γ-, and to β-TiP, as expected. On the other hand, the R- and β-TiPs with very different 47/49Ti CQ values have very similar angular distortion parameters, Ψ. Figure 5 shows the plots of the CQ values of the three compounds against the distortion parameter (noting that the origin was also included assuming that a perfect TiO6 octahedron will give a CQ of zero). The points in the plot of CQ against the angular distortion parameter (Figure 5A) are scattered. However, an approximate linear correlation between CQ and bond-length distortion parameter, R, appears to exist (Figure 5B)

CQ(MHz) ) 96.0R - 0.26

(3)

It seems that the distortion of the bond length contributes significantly to CQ. Theoretical Calculations. Since the above-mentioned empirical relationship is only based on a few points, it is necessary to verify the trend by theoretical calculations. The work by Padro et al. established good empirical correlations of 49Ti CQ with both angular and bond-length distortion parameters for several MTiO3 (M ) Ba2+, Pb2+, Ca2+, Mg2+, etc.) compounds.27 However, those relationships do not apply to the TiPs in this study. It appears that the TiP systems are more complicated, and the nature of the atoms and their positions in the second and third coordination spheres and beyond may also make contributions to CQ, which cannot be neglected. For these reasons, a series of ab initio calculations were carried out on two model clusters with different sizes, Ti(OH)62- and Ti(PO4)6Hnm- (n and m vary for different TiPs; see the Experimental Section for details), which were formed by

truncating the corresponding crystal structures (Figure 6). The calculation results are listed in Table 2. Ti(OH)62- is a TiO6 octahedron-based cluster. The calculated results of the Ti(OH)62- clusters are basis-set-dependent, but the CQ values calculated using different basis sets follow the same trend as the observed one; that is, R-TiP has the largest calculated CQ and β-TiP the smallest. As mentioned earlier, TiO6 octahedra in the TiPs have a similar degree of angular distortion but different distortions in the bond lengths. The abovementioned trend from the theoretical calculations confirms that Ti-O bond length distortion is indeed one of the major contributing factors to CQ. However, the calculations overestimate CQ for all three TiPs, especially for γ-TiP. This is probably due to contributions to CQ from the atoms in the second and third coordination spheres. To examine the long-range effect of the EFG and to improve the CQ calculations, larger clusters (Figure 6B), including P and O atoms in the second and third coordination spheres, were considered. The calculations again give the correct CQ trend as the observed one (i.e., a- > γ- > β-TiP), and the values approach the experimental ones with the improvement being particularly significant for the γ- and β-phases (Table 2). Calculations with the 3F(4333/43/4) basis set appear to give the best predictions of 47/49Ti CQ (Table 2). It is interesting to note that, for the large cluster, there is an approximate linear relationship between the longitudinal strain and the CQ values calculated with all the basis sets used (Supporting Information, Figure S2), whereas no such linear correlation exists for the small cluster (Supporting Information, Figure S3). This result indicates that the effect of the longitudinal strain is not simply localized to the immediate coordination about the metal center. CASTEP,41 a plane-wave-based density functional theory package capable of evaluating the electronic properties of periodic structures, was also applied. These results are also listed in Table 2. For R- and β-TiP, the CASTEP calculations give CQ values very similar to those obtained from model cluster calculations using Gaussian. The periodic DFT calculations of γ-TiP resulted in a metallic electronic structure with no band gap. EFG calculations in CASTEP are not implemented for metallic systems, and as a result, the CQ values for γ-TiP are not reported. Underestimation of the band gap in materials is a well-known deficiency of DFT calculations. Shown in Figure 7 are the calculated EFG eigenvectors from the CASTEP calculation for R- and β-TiP. In addition, the CSA of Ti in R-TiP was calculated using CASTEP. The calculation gives a span Ω of 243 ppm and a skew κ of 0.62, in reasonable agreement with the fitting values of 300 ppm and 1.0. Overall, the calculations on larger clusters (and periodic systems) do give better CQ values, suggesting that

Solid-State NMR Study of Layered Titanium Phosphates

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TABLE 2: Calculated 47Ti and 49Ti CQ Values of Different Clusters Using the Gaussian 03 and CASTEP Programs compounds R-TiP

[Ti(OH)6]

basis sets 2-

3F(4333/43/4) 3F(5333/53/5) 5F(4333/43/4) 5F(5333/53/5) 3F(4333/43/4) 3F(5333/53/5) 5F(4333/43/4) 5F(5333/53/5)

[Ti(PO4)6H6]8-

CASTEP experimental γ-TiP

[Ti(OH)6]2-

3F(4333/43/4) 3F(5333/53/5) 5F(4333/43/4) 5F(5333/53/5) 3F(4333/43/4) 3F(5333/53/5) 5F(4333/43/4) 5F(5333/53/5)

[Ti(PO4)6H8]6-

CASTEP experimental β-TiP

[Ti(OH)6]2-

[Ti(PO4)6H12]2-

3F(4333/43/4) 3F(5333/53/5) 5F(4333/43/4) 5F(5333/53/5) 3F(4333/43/4) 3F(5333/53/5) 5F(4333/43/4) 5F(5333/53/5)

CASTEP experimental

the nature and spatial arrangement of the atoms beyond the oxygen atoms in the first coordination sphere contribute significantly to the EFG at the Ti sites. r-Na-TiP. 47/49Ti NMR spectra can provide partial structural information for compounds with unknown crystal structure. This is important since the structures of many TiP derivatives are not known. To illustrate this point, R-Na-TiP (a Na+ ionexchanged R-TiP) with unknown structure was examined by 47/49 Ti NMR. The XRD pattern of R-Na-TiP (Supporting Information, Figure S1D) suggests that the overall layered structure was retained after ion exchange. The interlayer spacing is 8.34 Å, comparable to the value of 7.4 Å for the parent R-Ti(HPO4)2 · H2O.9a,b The 47/49Ti piecewise QCPMG spectra are shown in Figure 8. The line shape is very similar to that of R-TiP. The spectrum contains a strong, narrow pattern due to 49Ti superimposed on a weak, broad pattern originating from 47Ti. The narrow pattern can be well-simulated using a single 49Ti site

47

CQ (MHz) 19.8 23.5 23.0 26.9 18.1 22.5 21.9 26.9 16.3 17.3 20.0 21.6 21.3 23.9 8.27 10.2 11.2 14.0 NA 5.92 15.2 15.0 14.0 14.3 7.74 10.0 9.25 11.5 9.04 4.83

49

CQ (MHz)

ηQ

16.2 19.2 18.8 22.0 14.8 18.4 17.9 22.0 13.3 14.3 16.4 17.6 17.4 19.5 6.77 8.37 9.12 11.4 NA 4.9 12.4 12.3 11.5 11.7 6.36 8.22 7.57 9.42 7.40 4.0

0.81 0.78 0.75 0.74 0.44 0.30 0.16 0.13 0.07 0.05 0.75 0.94 0.92 0.92 0.80 0.29 0.21 0.12 NA 0.90 0.90 0.95 0.96 0.93 0.81 0.56 0.63 0.63 1.00 0.80

with the following parameters (Table 1): δiso ) -800 ppm, Ω ) 300 ppm, κ ) -0.5, CQ ) 13.5 MHz, ηQ ) 0.20, and (R, β, γ) ) (0, 30, 0). The corresponding 47Ti parameters are given in Table 1. The simulated spectrum compares well with the observed one (Figure 8). The quadrupolar and CSA parameters are similar to those of R-TiP, indicating that the ion exchange has little effect on the environment of Ti within the layer. Using the CQ value of 49Ti and eq (3), the longitudinal strain R was calculated to be 0.143, which is very close to that of R-TiP, implying no major change in the Ti environment during the Na+ ion exchange. This result significantly differs from the situation for layered zirconium phosphates (ZrP). Layered R-ZrP with a single Zr site has the same lamellar structure as that of layered R-TiP. However, ion exchange with Na+ ions substantially affects the local environment of the Zr. For instance, the number of crystallogphically nonequivalent Zr site changes from one in R-Zr(HPO4)2 · H2O to two in R-Zr(NaPO4)2 · H2O. The CQ values for two Zr sites in R-Zr(NaPO4)2 · H2O are 7.8 and 6.6 MHz compared to 5.8 MHz for the Zr in the parent material, R-Zr(HPO4)2 · H2O.48 It appears that the layered structure of R-TiP is more robust than that in R-ZrP. Conclusions

Figure 7. EFG tensor orientations from CASTEP calculations for (A) R-TiP and (B) β-TiP showing only the first and second coordination spheres: Ti, blue; P, white; O, red.

In this work, 47/49Ti static NMR spectra of several representative TiPs at an ultrahigh magnetic field of 21.1 T were acquired using the QCPMG pulse sequence. For narrow signals in βand γ-TiP, 47/49Ti static Hahn-echo spectra were also obtained. The observed spectra allow for the extraction of NMR interaction tensors via spectral simulations. In this series of related layered TiPs, the quadrupole coupling constant is particularly sensitive to a distortion in bond length. An empirical relationship between CQ and the bond length distortion parameter appears to exist, and the trend was confirmed by theoretical calculations. The results of calculations on several related model clusters

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J. Phys. Chem. C, Vol. 113, No. 23, 2009

Zhu et al. References and Notes

Figure 8. (A-D) Piecewise 47/49Ti static QCPMG spectra of R-NaTiP at 21.1 T (50.76 MHz), with the offset of the transmitter frequency shown on each spectrum. (E) The co-added QCPMG spectrum and the simulated spectra when considering (F) both the CQ and CSA, (G) CQ only, and (H) CSA only. The spectra were referenced against the 49 Ti peak of Cp2TiCl2 solution (which is -773 ppm from neat TiCl4 liquid).

indicate that, for TiPs, the long-range effect of EFG at Ti is important and the atoms in second and third coordination spheres and beyond and their spatial arrangement contribute significantly to the observed 47/49Ti quadrupolar coupling constants. It was also demonstrated that the 47/49Ti spectra can provide partial information on the local structure of Ti in those TiP derivatives with unknown structures, which was exemplified by R-Na-TiP. Acknowledgment. Y.H. and T.K.W. acknowledge the financial support from NSERC of Canada for research grants and CFI for equipment grants. Funding from the Canada Research Chair program is also gratefully acknowledged. Access to the 900 MHz NMR spectrometer was provided by the National Ultrahigh-Field NMR Facility for Solids (Ottawa, Canada), a national research facility funded by the Canada Foundation for Innovation, the Ontario Innovation Trust, Recherche Que´bec, the National Research Council Canada, and Bruker BioSpin and managed by the University of Ottawa (http://www.nmr900.ca). We thank Drs. Terskikh and Pawsey for assistance in NMR experiments and Prof. Wasylishen for the software WSOLIDS1. Computing resources were made available by SHARCNET, Canada Foundation for Innovation, the Ontario Innovation Trust, and IBM of Canada. Supporting Information Available: Powder XRD data and figures showing correlation between the calculated CQ with the longitudinal strain R. This material is available free of charge via the Internet at http://pubs.acs.org.

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