4624
J. Phys. Chem. 1993, 97,4624-4627
Double-Rotation NMR,,Magic Angle Spinning NMR, and X-ray Diffraction Study of the Structure of Aluminum Molybdate G. W. Haddix,' M. Narayana, and S. C . Tang Shell Development Company, Houston, Texas 77251- I380
Y. wu Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599 Received: November 9, 1992; In Final Form: February 8, 1993
An 27AlN M R study of aluminum molybdate (A12(M00&) has been carried out. Using the double-rotation technique (DOR), the residual line broadening observed in magic angle spinning (MAS) that is caused by second-order quadrupolar interactions is completely removed. The four inequivalent aluminum resonances, as predicted from the space group symmetry obtained from X-ray and neutron powder diffraction data, are clearly revealed by NMR. Moreover, additional structure in the DOR spectrum may be indicative of further inequivalency in the unit cell that is not discernible by powder diffraction methods. Tentative assignments of the observed aluminum resonances are given.
Introduction
Experimental Section
Magic angle spinning (MAS) has become a routine NMR technique in modern analytical laboratories. It enables collection of reasonably high resolution spectra for many solid materials. Normal MAS can average out many interactions experienced by a nucleus such as chemical shift anisotropy and weak dipolar interactions, thus producing sharp lines that can be interpreted ina fashionsimilar tothat of liquid-stateNMRspectra. However, normal MAS quite often cannot average out quadrupolar interactions experienced by spin > '12 nuclei. This severelylimits the ability to identify, in the solid state, molecular functionalities which involve quadrupolar nuclei. The effect of various static interactions on NMR spectra can often be calculated using time-dependent perturbation theory. It is often found that, to first order, the quadrupolar interaction is too large to easily observe even with today's modern solid-state NMR spectrometers. For half-integer nuclei, this is not such a great problem, as most of thechemical informationcan be obtained from the part of the spectrum which is not subjected to first-order broadening (i.e., the central transition, m1 = '12 to -'/2). This situation has thus enabled a variety of useful MAS experiments to be carried out on the central transitions of quadrupolar nuclei in many important systems. Unfortunately, to second order, the central transition (as for other transitions) is subject to fielddependent frequency shift and spectral broadening (powder averaging), which normal MAS cannot average to zero. The point of double-rotation(DOR) NMR is to remove the anisotropic part (line-broadening part) of the second-order quadrupolar interaction by rendering it time dependent via the simultaneous rotation of the sample about two axes of specificdirection relative to the Zeeman static field.' Aluminum molybdate (A12(M004)3) is a compound of interest to the catalyst community. It is often believed to form in Mocontaining hydrotreating catalysts utilizing A1203supports. The number of peaks observed in a MAS spectrum of A12(Mo04)3is fewer than the number of inequivalent AI atoms observed by diffraction techniques, thus indicating that MAS spectra include line-broadening mechanisms which compromise the ability to observe chemically distinct A1 centers. It is demonstrated here that the recently developed DOR method dramatically improves resolution in the 27Alspectrum of A12(Mo04)3, resulting in good agreement with the number of distinct A1 centers arrived at via diffraction methods.
The sample used was obtained from Alfa Chemicals and has a stated purity of 99%. 27AIDOR and MAS measurements were made on this sample at 4.7 T (52 MHz) on a Bruker MSL-200 using a simple pulse and acquire sequence. Measurements at 9.4 T (104 MHz) were performed on a Varian Unity 400. All spectra are referenced to aqueous AlC13 (hexaaquo aluminum ion) at 0 ppm. MAS measurements were made using 5-mm rotorequipped probes from Doty Scientific at a spin rate of 10 kHz. A DOR NMR probe described previously2 was used for all DOR measurements. Samples were typically spun at rotation rates of 5 and 1 kHz for the inner and outer rotors, respectively. The same DOR probe was retuned for operation at both fields. The number of scans required to acquire adequate signal-tonoise DOR spectra was typically about 500 scans. The recycle delay was set to 1 s and 10-ps 90' pulses were set on AlC13(aq). Pulses of 2 ps were used on the A12(Mo04)samples ( ~ 6 for 0 ~ the central transition). Powder XRD was performed on a Philips APD1700 diffractometer. Asimulationof theXRD powder patternof A12(M0O4)3 (monoclinic) was performed using the program POWD12.3 The crystal structure was represented on a Silicon Graphics IRIS4D/80 workstation running the molecular simulations program, Polygraf. The atom coordinates were derived assuming P 2 1 / a space group symmetry. Partial charges associated with atoms surrounding A1 sites were also calculated using Polygraf. Estimates of the field gradient tensor were made using these partial charges along with the atomic coordinates. A MatLab program on a Macintosh I1 computer was used for estimation of the principal components of the field gradient tensor.
0022-3654/93/2091-4624%04.00/0
Results and Discussion Shown in Figure 1 is a representation of the crystallinestructure of A12(Mo04)3. A recent neutron powder diffraction crystal structure refinement of A12(Mo04)3 indicates the structure is monoclinic and is a member of space group P21/a.4 Another study reached a similar conclusion but also stated that A12(Mo04)3 can also exist in an orthorhombic form (Pnca) at temperatures in excess of 200 OC.5 XRD of the sample examined here reveals the structure to be monoclinic. The monoclinic structure has 16 A1 per unit cell, with four magnetically inequivalent A1 types. Thus, one would expect four resonances in the NMR spectrum. 0 1993 American Chemical Society
Structure of Aluminum Molybdate
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4625
Figure 1. Crystalline (unit cell) structure of monoclinic A12(Mo0&.
,'
' ''
L' ' ' ' b '
'
'-k]
''
li5'
''
:A'
' ipk
b) g.4T
I""I""I""I""I""I""I""I""I""I 5 0 -5 -10 -15 -20
Ill 1 A"b) 9.4T
5 -25
30
ppm
Figure 2. Z7Al MAS spectra: (a) collected at 4.7 T and (b) collected at 9.4 T.
The orthorhombic form has only one type of A1 center, thus predicting one resonance. The normal MAS spectrum taken at 4.7 T (Figure 2a) shows two poorly resolved peaks. In fact, the peaks are so poorly resolved that one cannot rule out that the MAS spectrum is a powder pattern arising from the second-order quadrupolar interaction from 'a single A1 center. MAS at a higher field (Figure 2b) results in apparently two well-resolved peaks. Clearly, MAS methods are incapable of resolving the four different A1 types present in this sample. Under DOR at 4.7 T (Figure 3a), two peaks are clearly resolved, with the downfield peak being just noticeably split. This demonstrates the advantage of DOR over MAS and also demonstrates that second-order quadrupolar anisotropy is the dominant line-broadening mechanism remaining in the MAS spectrum. Turning finally to the DOR spectrum collected at 9.4T (Figure 3b), there are four clearly resolved peaks in the spectrum. This confirms the presence of the monoclinic form with its four inequivalent sites as predicted by XRD. In addition, if one examines the resonances of the 9.4-T DOR spectrum carefully
o
4
-IO
-15
20
-25
-30
ppm
Figure 3. *'AI DOR spectra: (a) collected at 4.7 T and (b) collected at 9.4 T.
(Figure4),it appearsthat thepeaksarenot necessarilysymmetric. A tentative interpretation of this is that there is probably some amorphous fraction present, or perhaps the point group symmetry at some A1 centers is somewhat less than the overall space group symmetry. Lattice strain, or a high concentration of lattice defect sites (such as Fe3+or other trivalent cation occupying an A1 site), may distort the lattice enough to introduce some additional inequivalence as far as NMR is concerned. If this is true, then it appears DOR will be useful for looking at minor defects in crystalline materials. The frequency separation between isotropicresonances in DOR spectra is generally governed by the chemical shift interaction and the second-order quadrupolar interaction. The isotropic chemical shift (in hertz) is a direct linear function of the external magnetic field, while the isotropic second-order quadrupolar interaction is inversely related to the applied fields6 The strength of this inverse relationship is governed by the strength of the quadrupolar interaction. The second-order isotropicquadrupolar shift is only exactly calculableif the quadrupolar couplingconstant ( W Q ) and asymmetry parameter ( q ) are known for the nucleus in question. The form of the second-order isotropic quadrupolar
4626 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
Haddix et al.
TABLE I: Aluminum Site Assignments for A l u " Molybdate Based on Estimated Principal Components of tbe Field Gradient Tensor
-11.0
-11.5
-12.0
-12.5
-13.0
obsd shift at 4.7 T, ppm
true chemical shift, ppm
Aw!:~~~,,Hz
-11.38 -11.67 -13.50 -14.06
-13.30 -13.02 -16.06 -16.06
-9.45 -10.32 -10.94 -12.06
492 537 569 628
-
A W ! ~ ~ Hza , ~ , ~ , siteh 492 520 741 2093
2 3 1 4
Aw/:JcaIc W Q ~ (+ ~ q 2 / 3 ) , where WQ and q are estimated from calculations. The first value in this column agrees perfectly with experimental by definition, since the experimental data for this peak are used to determine a constant of proportionality. bSee Figure 5 for correspondence with structure.
1 " " 1 " " 1 ~ " ' 1 " " 1 " " 1 ~ " ' 1 " " 1 " " 1 " ' ~ 1 " ~ ' 1 -10.5
obsd shift at 9.4 T, PP*
-13.5
-14.0
wm
Figure 4. Blowup of spectra collected at 9.4 T: (a) MAS and (b) DOR.
follows:
shift is
w~~~=-""z-(,+~)(Z(Z+l)-2) 10 wo 4
(1)
where wQ = e2qQ/[2Z(2Z- l)h]
eq = rl = (V,,
v,,
(3)
- V,) / V,,
(4)
with
lVz2l2 IyJ 2 PXXl Here, Q is the nuclear quadrupole moment, a property of the nucleus in question. viare the principal components of the electric field gradient tensor at the nuclear site. As has been noted previously, given the above-mentioned interaction, improvements in resolution are achieved at lower fields if the quadrupolar interaction dominates and at higher fields if the chemical shift interaction dominates. Thus, the basic tenet of "higher fields are better" does not necessarily apply to DOR measurements. The resolution improvement available under DOR for the A12MOO,)^ system allows all A1 types to be clearly observed in a 1-D spectrum. The next task in such a study is to attempt to make an assignment of each resonance to a particular A1 site. This is not a simple exercise in this case. All four A1 centers are present in equal numbers in the unit cell, and we expect equal peak areas for each site. Thus, stoichiometryis useless as a means of assignment, and peak-to-site associationsmust be rationalized on structural grounds. The isotropic chemical shift and isotropic second-order quadrupolar interactions are both related to the electronic structure around the nucleus of interest. If spectra are plotted on a ppm scale, then the observed isotropic chemical shift values do not change with field. Looking in Figure 3, it is clear that all of the peaks shift upon the field change. This shift is due solely to the second-order quadrupolar interaction. Thus, we can focus on only the quadrupolar interaction Aw,!,2dcxpt = (#lo X wolo)
-
X WOhi)
(5)
where is the experimentally observed shift upon field change (in hertz); sl0 and shi are the observed shifts at the low and high fields, respectively (in ppm); and ool0and WOhi are the Larmor frequencies of the nucleus of interest at the low and high fields, respectively. The experimentally observed shifts on field change arising from the isotropic second-order quadrupolar interaction are shown for each peak in Table I. Such a shift upon field change is determined by the secondorder isotropic quadrupolar interaction and can be calculated as
By substituting A w ! : ~ ~for ~ Aw!:iCalc in eq 6, the quantity W Q ~ (1 + $/3) can be easily Jetermined (the remaining terms in eq 6 are constant for data taken at two known fields). Assuming 71 = 0 results in a value of WQ on the order of 0.15 MHz for all A1 sites. (The range of WQ based on all peaks and allowing 0 I71 5 1 is from 0.12 to 0.17 MHz.) Unfortunately, this is not tremendously helpful from an assignment standpoint. In this case, the dependence of the second-order isotropic shift on 71 is about the same as the dependence of WQ, since the WQ values in this case do not differ greatly from A1 site to A1 site. We can, in principle, determine a value for A ~ f 2 , , ~if ~we can reasonably estimate WQ and 9 (all other parameters are known). Since the relative positions of atoms in the lattice are known from the diffractiondata, one can estimate elements of the field gradient tensor around each site. This can be done by assuming that the electric field gradient at the site of interest is the sum of field gradients arising from point charges at fixed locationsaway from the site. The data necessary for this calculation are the Cartesian coordinates of atoms surrounding the site of interest (available from XRD) and partial chargesassociated with neighboringatoms that crudely represent the true electronic structure around the site (available from charge equilibration calculations on clusters of atoms surrounding the site of interest). Given this, we can estimate the principal components of the field gradient tensor, determine values for WQ and 7, and ultimately find an estimate for Aw,!s2dcalcvia eq 6. These can then be compared to the experimentally determined Aw!f,)expt. In this fashion, peak-tosite associations can be made. Due to the rather large unit cell for monoclinic A12(Mo04)3, it is not possible to perform the charge equilibration on the entire unit cell in a reasonable amount of time. We confined the charge equilibration calculations to (A106)(MoO&H18 clusters representing the four sites. We tried several estimates of the components of the field gradient tensor involving contributions from first-nearest-neighboroxygens,up to contributionsincluding third-nearest-neighbor oxygen, and averaging partial charges for atom types around each site. Uncertainty related to the determinedpartial charges,and more fundamentallyto thevalidity of the point charge treatment, makes it difficult to calculate a meaningful absolute AU[:,)~~,. For example, in calculating Aw!:JCalc directly from the partial charges and atom coordinates, we typically get values on the order of a few hertz. Obviously, these are off by about 2 orders of magnitude when compared to AW{;J,,~~. Given this obvious inadequacy, we are forced to attempt assignment based on the relative order of A W ~ ~ J (or ~,~, equivalently W Q Z ( ~ + 92/3)). Here we have chosen to use the A w ! ; , ~ ~data ~ ~ for the furthest downfield peak to determine a
Structure of Aluminum Molybdate
The Journal of Physical Chemistry, Vol. 97, NO. 18, 1993 4627 ments. This exampleserves to point out difficultiesthat are likely to arise in assignment of DOR spectra in the absence of prior information about OQ and 7.
Slte X3
Conclusions See X4
x
DOR NMR has been applied to a sampleof Al*(MoO&. The result supports the conclusion that the structure is monoclinic. Tentative assignments of the observed resonances to the four A1 sites have also been given. It is clear that the DOR approach will make solid-state NMR a more easily interpretable technique for crystalline structural studies, although spectral assignment difficulties may arise. Furthermore, the sensitivity of the quadrupolarinteraction to thecrystal structure may enableNMR to add to what is already known about crystal structure from diffraction techniques.
Site #2
Figure 5. Inequivalent A106 octahedra of the monoclinic AI*(MoO& unit cell.
+
constant that can be multiplied by the calculated O Q ~1( $/3) values for the other sites to give an estimate of A U ~ ~ ~ ,This ~,,. results in a value for Ao!:~,,, that is at least comparable to A o ~ ~ ~ , , Such ~ , . values are shown in Table I. This is admittedly a crude approach, but it should be noted that the relative order of oQ2(1 $/3) values is insensitiveto how many shells of nearest neighbors are used in the point charge treatment. Placing the estimates of AO::,),~,~ for each site in the same order as the experimentally observed Ao!ZeXpt allows an attempt at assignment. Shown in Table I are the assignments of the observed peaks under DOR to specific sites based on the preceding treatment. (Figure 5 shows the four inequivalent AI06 octahedra excised from a unit cell.) We are reasonably confident that the two upfield (Figure 3b) peaks are due to sites 1 and 4, while the downfield peaks are due to sites 2 and 3, although a more refined calculation would perhaps lend more credibility to these assign-
+
Acknowledgment. We thank Prof. Alexander Pines for use of the DOR probe developed at the University of California, Berkeley. We also thank Dr. W.Mason Skiff of Shell Development Co. for assistance with partial charge calculations. Y. Wu is supported by the National Science Foundation under contract DMR-9 122992. References and Notes (1) Samoson, A.; Lippmaa, E.; Pines, A. Mol. Phys. 1988, 65,1013. (2) Wu, Y.;Sun, 8. Q.;Pines, A.; Samoson, A.; Lippmaa, E. J . Magn. Reson. 1990,89, 297.
(3) Smith, D. K.; Holomany, M. A. A FORTRAN IV Program for Calculating X-ray Powder Diffraction Patterns-Version 12. The Pennsylvania State University Department of Geosciences, April 1986. (4) Harrison, W. T. A.; Cheetham, A. K.; Faber, J. Jr. J . Solid Srare Chem. 1988, 76,328. (5) Sleight, A. W.; Brixner, L. H. J. Solid State Chem. 1973, 7, 172. (6) Cohen, M. H.;Reif, F.QuadrupoleEffectsinNMRStudiesofSolids. In Solid Stare Physics; Seitz, Turnbull, Eds.; Academic Press: New York, 1957; Vol. 5 , p 321.
