Solid State Nuclear
Elsevier
Science
Mugnetic
Publishers
Resonance,
73
1 (1992) 73-83
B.V.. Amsterdam
Dipolar 31P NMR spectroscopy of crystalline inorganic phosphorus compounds David Lathrop, Deanna Franke, Robert Maxwell, Thomas Tepe, Robert Flesher, Zhengming Zhang and Hellmut Eckert &pcrr.fmerif of Chrmistry, Uric ,ersity of’ California, Sarm Barbartr. C.-l Y.?lOb, USA (Received
20 January
1992; accepted
23 January
1991)
Abstract
The ability of the 90”-t,-180” pulse sequence to produce accurate dipole-dipole coupling information in solids is investigated. To this end, the experimental “P spin echo decays are measured for eighteen crystalline phosphides and phosphorus chalcogenides and compared with simulations, based on the known internuclear distances in these compounds. The experimental results are generally found accurate in compounds where the dominant contribution to the dipole-dipole coupling arises from nuclei in structurally inequivalent sites with large chemical shift anisotropies. For this situation, the quantum mechanical “flip-flop“ term in the dipolar Hamiltonian is suppressed and the dipole-dipole coupling is entirely heteronuclear in character. All of those compounds that do not obey this condition show accelerated spin echo decays due to a fractional contribution of the flip-flop term and possibly incomplete refocusing of chemical shift terms on the time scale of the experiment. The results confirm on an empirical basis that the spin echo NMR technique can provide accurate dipole-dipole coupling information (and thus distance distributions) in disordered solids and glasses, h’er~~rl.~:
phosphides:
solid state NMR; dipolar
coupling
Introduction
Solid state NMR has proven to be a powerful tool for addressing a wide variety of structural questions in disordered materials such as glasses and ceramics. Its usefulness stems from the presence of internal interactions, which reflect the local chemical environment and which produce perturbations to the main Zeeman interaction. Among the various types of local interactions, the magnetic dipole-dipole coupling is of special significance, because it is the only one that is calculable from first principles on the basis of struc-
to: Dr. H. Eckert, Department of Chemistry, of California, Santa Barbara, Goleta. CA 93106,
Correspomknce
University USA.
0976-704o/Y?/sl)S.O~
80 1981 - Elsevier
Science
Publishers
tural data. Experimental techniques that can accurately extract such dipole coupling information are therefore of key interest. Previous investigations have indicated that the measurement of Hahn spin echo intensity as a function of evolution time holds considerable promise in this regard. For example, spin echo NMR has been used to examine and derive detailed atomic distribution models for phosphorus atoms dispersed in amorphous hydrogenated silicon [l-31, phosphorus and fluorine in silica glass [4,5], and phosphorus atoms in a number of covalent non-oxidic glasses [6-121. Various scattered applications to crystalline model compounds have produced good agreement between experimental and calculated dipolar couplings in some cases [7,13,141 and dramatic disagreement in certain other cases [7,15,161.
B.V. All rights reserved
74
D. Lathrop et al. /Solid State Nucl. Magn. Reson. ! (I 9921 73-83
In this contribution we present a comprehensive database that characterizes the ability of “P spin echo NMR to measure accurate homodipolar 31P-3’P couplings in inorganic phosphorus compounds. The discussion of the results shows that success and failure of this technique can generally be predicted from the spin dynamics of the compound in question and that the technique should be generally applicable to glasses and other disordered systems.
Theory Calculation of dipole-dipole couplings
While the influence of isolated pairs and clusters of few spins upon the NMR lineshape can be calculated rigorously, the problem becomes far more complex when larger numbers of spins are involved. In these cases the homonuclear dipole coupling is usually expressed in terms of a statistical property, the dipolar second moment MZd. This number can be calculated from internuclear distances dij by the van Vleck theory, which predicts for a polycrystalline material M,,(hom)
= 3/.5(/_~/47r)*1(1+
x Cd,
or M,,(inhom)
= 4/15( pa/4~)~1(
x zdLT6 i#j
I + l)y4h2N-’
(lb)
where y, I and N are the gyromagnetic ratio, the spin quantum number and the number of nuclei under observation, and d,, is the internuclear distance. For a discussion of homonuclear interactions, eqn. (la) is the appropriate one if these interactions dominate the rate of the free induction decay (and concomitantly the width of the spectrum). If this condition holds, the line-broadening is termed “homogeneous”. On the other hand, eqn. (lb) is the appropriate one to use if the dipolar coupling occurs between nuclei whose chemical shift difference (in Hz) is larger than the magnitude of the dipole-dipole coupling, a
situation that often prevails if line-broadening due to chemical shift inequivalence or heterodipolar interactions is dominant. In this case, the quantum mechanical (“flip-flop”) term in the dipolar Hamiltonian does not contribute to the dipolar interaction, resulting in the smaller prefactor (4/E) of eqn. (lb). This situation corresponds to the case of “inhomogeneous broadening”. Obviously, a situation with a prefactor between 3/5 and 4/15 is conceivable in a powder, if there is spectral overlap between dipolarly coupIed nuclei at some orientations, but none at other orientations. To give an estimate of the prefactor in such a case, it is necessary to locate the chemical shift tensor principal axis systems for the interacting nuclei, to compare the resonance frequency difference of these nuclei with the dipole-dipole coupling all over the 0,~$ space, and to evaluate the corresponding statistics. Such work necessitates single crystals, which are often not available. A further limitation to distance analyses from M,, values arises from the anisotropy AJ of indirect, electron-coupled dipole-dipole interactions, which also contribute to the experimental second moments, but are not included in eqns. (la) and (lb). For lighter nuclei, the assumption M2ilJ < M,, is usually correct. If this assumption is not fulfilled, however, the second moments loose their structural significance, as no reliable calculational approaches exist for A.7. Measurement of dipole-dipole couplings
A variety of sophisticated NMR techniques are available for the selective measurement of homonuclear dipole-dipole interactions. For magnetically non-dilute systems, a simple spin echo pulse sequence (90”-t,-180”) has been widely used to great advantage [l-14]. In principle, this sequence refocuses transverse magnetization decay due to all interactions linear in 1, (i.e., chemical shift anisotropy and heteronuclear dipole couplings), resulting in a spin echo at the time 2t,. In the simplest case, the intensity of the spin echo is attenuated only by homonuclear dipole couplings during the evolution time 2t,.
D. Luthrop
et al/Solid
For an isolated two-spin system this echo decay Z/I, is described by:
z(2ti)/Z[]=
ccos
a,jtl>
(2)
where a;, = $h( 1 - 3 cos2e)rj;”
(3)
and (> denotes averaging over all orientations 8 of the dipolar vector in the magnetic field. In the case of multiple pairwise interactions, we must write instead: I( 2r,)/Z,
= n
(cOS
U;jt,
>
j
(4)
The dipolar oscillations are smoothed out and the resulting decay very often resembles a Gaussian:
WWb, = ew -
75
State Nucl. Magn. Reson. I (1992) 73-83
[Prl)2h.12d/2]
(5)
Equation (5) defines a semilogarithmic plot of normalized echo height Llersus (2t,)*, which affords a convenient measurement of the second moment characterizing the homonuclear dipolar interactions. In many cases, however, the Gaussian decay shape can only be viewed as a crude approximation. It is important to note that the assumption of complete refocusing of chemical shift terms [and hence the applicability of eqn. (5)] is only valid in the limit t, -0. This is a consequence of the fact that during t, the density matrix evolves under the combined influence of the dipolar Hamiltonian (- 3Z,,Z,, - Z,Z,) and the chemical shift Hamiltonian (- I,), which do not commute. In reality, however, eqn. (5) is often a very good approximation over a wide range of evolution times, if the interacting nuclei have a chemical shift difference that is large compared to the dipole-dipole coupling. In such a situation the zero-quantum (flip-flop) spin transitions are quenched, allowing the dipolar Hamiltonian to be truncated to the commuting Zz1Z,2 term. Since it is difficult to make quantitative predictions in this regard on theoretical grounds, this question will be addressed experimentally in the present study on a wide range of model compounds.
Finally, the spin echo technique yields unsatisfactory results if the observe-nuclei I are coupled to nuclei S whose spin states undergo fluctuations on the time scale of the experiment. Such fluctuations could arise either from strong S-S dipole-dipole couplings or from a strong interaction of the S nuclei with the lattice (fast relaxation). In such cases, the heterodipolar Z-S interaction is only incompletely refocused and hence makes a contribution to the experimentally measured spin echo decay [l]. Since this effect would complicate the discussion further, we eliminate it here by choice of the range of compounds under study.
Experimental Table 1 provides an overview of the samples investigated. Published standard literature procedures were employed for their synthesis, and their identity and purity was confirmed by melting point (DuPont 912 DSC), liquid state NMR spectroscopy (where possible), and X-ray powder diffraction (Scintag diffractometer). Literature references on the preparation and crystal structures of the compounds under study have been included in Table 2. In the case of GaP and InP, commercial samples (Gap, Alfa, purity 99.999%, InP, Strem, purity 99.999%) were investigated. “P Spin echo NMR experiments were carried out at 121.65 MHz on a General Electric GN-300 spectrometer, and a probe from Doty Scientific. The spectrometer frequency was carefully adjusted to minimize resonance offset effects. Typical acquisition parameters were: dwell time, l-2 ps; 90” pulse length, 5-7 ps; relaxation delays, 1 h; 1 scan. I,,, the spin echo intensity at 2t, = 0, was determined by Gaussian extrapolation. Spin echo intensities at short evolution times are corrected for the weak feedthrough signal arising from imperfect 180” pulses. Second moments were calculated from the crystallographic information available (see Table 2), using all the distances to other phosporus atoms within lo-30 A. Further characterization was carried out by magic-angle spinning (MAS NMR) spectroscopy at 121.65 or 202.47 MHz (using both General Electric GN-300
76
D. Luthrop et nl. /Solid
and GN-500 spectrometers), equipped with a 5 mm high-speed spinning probe from Doty Scientific. Typical conditions were: 4.5 pus 90” pulse and 10 min recycle delays, 16 scans. Isotropic chemical shifts (LWW 85% H,PO,) were measured from the MAS centerband positions, while the anisotropic shift parameters were determined from the spinning sideband intensities using the method of Herzfeld and Berger [17]. These data
TABLE
1
“‘P Chemical shift parameters (Lwsus 85% H,PO,) of solid phosphides and phosphorus chalcogenides under study Compound
PA” “-P&J,
P-P&d2 a-P,Se,12 SiP
ZnP,
CdP2 Cu,PSe, AgPS, Ag,P,S,,
CdGeP, ZnGePz CdSiP,
6,,, a 233.7 140.5 120.4 111.7 95.8 81.9 111.9 112.8 51.6 49.7 125.0 214.0 142.3 120.9 130 110.5 - 143.6 - 152.6 - 232.8 -236.1 - 239.7 -51.0 - 58.5 - 162.8 - 117.1 - 56.6 - 84.6 64.4 103.3 101.1 91.9 - 32.2 - 60.3 - 131.4
a +0.2 ppm. a Estimated error:
+5 ppm.
6 11 b
8z2 b
103
285
- 65 26 2 35 6 -49 -44 -57 -55
186 95 67 76 82 137 115 106 94
-45 164 40 220 not measurable not measurable 9 157 -96 133 - 199 - 142 - 196 - 159 -301 - 239 - 290 - 227 - 293 - 230 -150 -41 -175 -44 - 262 - 160 - 268 -124 -174 -89 -113 - 82.5 - 139 135 89 105 50 116 54 88 -80 -33 -94 -61 -176 - 134
6 33 h
313 301 240 266 177 158 248 267 106 110
TABLE
State Mtcl. Mqw.
Re~on. I (1992) 7.i-S.7
2
Comparison of experimental and calculated “P NMR second moments (in units of 10h rad’/s’; estimated experimental error + 10%) for solid crystalline phosphorus compounds Compound
ref.
PA
26 26 26 21 28 29 30. 30 31 32 33,34 30 35 37 38 36 36 36
exp.
PAS, P,S,,, a-P$31* P-P,S$z a-P,Se,I, GaP InP SiP CdP, ZnP, BPO, Cu,PSe, AgPS, Ag,P,S,, CdGeP, ZnGeP, CdSiP,
R
MU
29.4 19.0 9.9 35.5 33.8 36.4 20.7 21.0 14.5 67.0 73.5 10.6 1.10 9.8 2.1 15.0 18.4 19.4
talc. 33.6 18.8 7.0 34.9 34.3 32.6 13.5 8.7 14.0 56.8 67.9 5.7 0.82 6.7 2.0 11.2 13.7 12.3
0.88 1.01 1.41 1.02 0.99 1.12 1.53 2.41 1.04 1.18 1.08 1.86 1.34 1.46 1.05 1.34 1.34 1.58
are reported following the convention a,, > & > 6 11’
256 380
Results and discussion 224 295 -90 - 103 - 158 - 191 -196 38 43 -66 41 93 -5x 197 115 137 135 15 -26 -84
31PMAS NMR Since knowledge of the chemical shift characteristics is important in the context of the present study, all of the compounds were characterized by 3’P MAS NMR. Chemical shift data on crystalline phosphides have been particularly scarce [7,18-211 and the data published here (Table 1) represent so far the largest compilation of anisotropic chemical shift data for crystalline phosphides. Unfortunately, j’P chemical shifts in solids are generally rather poorly understood and for the range of phosphides investigated here we have found no satisfactory empirical correlations with local geometries. Thus, it is generally not possible to assign individual resonances to the individual sites present in a given crystal structure with certainty. Nevertheless, some tentative as-
D. Lafhrvp
et rrl. /Solid
71
State Mtcl. Magn. Reson. 1 (1992) 73-X.1
published and discussed by us [3,22,23] and others [24,25]. CdP, (JCPDS card #22-127) crystallizes in the tetragonal space group P4,22. The structure is based on infinite P-P-P chains with Cd atoms inserted in between [32]. All the P atoms have distorted tetrahedral coordination with two P and two Cd nearest neighbors. There are two crystallographically inequivalent P sites, which differ slightly in the degree of distortion of the P tetrahcdra. The “P MAS NMR spectrum shows two
signments can be made, based on the correlations of geometrical parameters with experimental trends observed in chemical shift anisotropies and MAS NMR linewidths. In the following, we will give a brief discussion of the MAS NMR spectra for the compounds CdPi, ZnPz, SIP, cyPJS,12, AgPS,, and Ag,P,S,,, which are reported here for the first time. The “P MAS NMR spectra of these compounds are summarized in Fig. 1. The “P MAS NMR spectra of the remaining compounds in Table 1 have been previously
200
,OO
0
-100
pm
24)
d
11‘
r.
58
wm
Fig. 1. “P MAS NMR spectra of selected phosphorus compounds (spinning speeds in parentheses): CdP, (5.07 kHz), P-ZnP, (9.04 kHz), SiP (4.85 kHz), wP,S,I~ (8.22 kHz), AgPS, (3.34 kHz). Ag,P,S,, (3.13 kHz). Central bands are indicated by the symbol d. All of the spectra were recorded at _ 121.65 MHz (7.05 T), except for P-ZnP2 and SIP, which were measured at 202.49 MHz ( 11.7 T).
78
well-resolved resonances with substantial chemical shift anisotropies. The large chemical shift difference between the two P sites is somewhat surprising in view of the small structural differences. /I-ZnP, (JCPDS card #24-1463) crystallizes in the monoclinic space group P2,/c. There are four crystallographically distinct phosphorus atoms, all of which have distorted tetrahedral coordination environments. The structure initially reported by Hegyi et al. [33] differs significantly from that of its homologue CdP,. In that report, the P(1) site is bonded to three P atoms and one Zn, whereas the P(2)-P(4) sites are coordinated to two P and two Zn atoms. While earlier NMR results on /3-ZnP, were interpreted in terms of these sites [20], the structure was subsequently re-investigated by Fleet and Mowles [34]. Based on a considerably improved R factor these authors concluded that the local structures of all of the four P atoms are characterized by two P and two Zn neighbors. The MAS NMR spectrum shows that three of these sites are clearly resolved. One of the resonances is shifted significantly upfield (by more than 100 ppm) from the remaining three resonances. This observation, the reasons for which are not clear at the present time, should not be taken as support of the Hegyi structure, since ‘rP chemical shifts in phosphides are quite unpredictable. SiP (JCPDS card #29-1133) crystallizes in the monoclinic space group Cmc2,. There are six inequivalent P sites, all of which are coordinated to three silicon atoms [31]. There are also six inequivalent Si sites, all of which have distorted tetrahedral environments with one Si-Si and three Si-P bonds. The 31P MAS NMR spectrum resolves the resonances of five of the six inequivalent P atoms. The two remaining sites are essentially indistinguishable by NMR, even at a field strength of 11.7 T. The crystal structure of SIP reveals that two of the six P sites have decidedly different local environments from the others. Specifically, the P(3) and P(6) sites differ significantly from the remaining sites both in the average P-Si bond lengths and the average P-Si-X (X = P or Si) bond angles. Average P-Si bond lengths (in A> are: P(l), 2.2775; P(2), 2.2760; P(3),
D. Lathrop et al. /Solid
State Nucl. Magn. Reson. I (1992) 7.75$3
2.2619; P(4), 2.2706; P(5), 2.2702; and P(6), 2.2604. Average P-Si-X bond angles are: P(l), 108.06”; P(2), 108.02”; P(3), 111.25”; P(4), 107.36”; P(5), 107.35”; and P(6), 111.26”. This structural information corresponds very nicely to the 31P MAS NMR spectrum, in which two of the six resonances are shifted distinctly downfield from the others. On this basis it appears reasonable to assign these two resonances (at - 143.6 and - 152.7 ppm) to P(3) and P(6). Further assignments are currently not possible. a-PJ, Iz forms monomeric cage-molecules, consisting of two chemically inequivalent P atoms [27]. In contrast, only one single phosphorus site is visible in the “P MAS NMR spectrum. We explain this situation in terms of the strong nuclear electric quadrupolar interaction of the iodine atoms. It has been generally found that the lineshapes of spin-l/2 nuclei that are directly bonded to quadrupolar nuclei experiencing strong nuclear electric quadrupolar couplings cannot be narrowed effectively by magic-angle spinning, unless the quadrupolar nuclei are self-decoupling by rapid spin-lattice relaxation. In (Y-P,S,I, this broadening effect appears to be so strong that the resonance belonging to the iodine-bonded P atoms is essentially broadened into the baseline. Similar broadening effects (albeit less strong) have been observed previously in the solid state 31P MAS NMR spectra of p-P,S,I, [81 and in LYP,Se,I, t231. AgPS,. Single crystal X-ray studies confirm that the structure of AgPS, is based on dimeric PzSi- groups, corresponding to two PS3 tetrahedra sharing a common edge 1371. The P .. . P distance across this edge is unusually short (2.89 A). The “P MAS NMR spectrum shows an extremely wide spinning sideband pattern, revealing a large chemical shift anisotropy. This is understandable in view of the local phosphorus coordination, in which the wide range of S-P-S bond angles (93.7”-118”) testifies to extremely large distortion of the ideal tetrahedral geometry. Ag,P,,S,,. The structure of Ag,P$,, contains a P,S;- group and a PSZ- group [381. Accordingly, the spectrum shows three resonances (at 103.3, 101.1, and 91.9 ppm) in an approximate 1: 1: 1 ratio. We assign the first resonance to the
D. Lathrop et al. /Solid
State Nucl. Magn. Reson. I (1992) 73-83
Psi- group and the latter two to the two inequivalent P atoms of the P,Sgroup. This assignment is supported by the fact that these peaks have larger chemical shift anisotropies and are significantly broader than the 103.3 ppm peak. The larger anisotropies are expected due to the more distorted local geometry in the P,S$- group, whereas the broadening of the resonances is attributed to unresolved scalar spin-spin interaction across the sulfur bridge. Other compounds. The compounds CdSiPz, CdGeP,, and ZnGeP, crystallize in the tetragonal chalcopyrite structure (space group 142d). Each P atom is at the center of a slightly distorted tetrahedron comprised of two Cd(Zn) atoms and two Ge(Si) atoms. As expected from this fairly symmetric arrangement, the chemical shift anisotropies are relatively small and their precise measurement necessitates the use of low spinning MAS or static experiments. The same situation occurs in Cu,PSe,, in which the P atoms adopt a
79
near-tetrahedral coordination environment with selenium. In InP, GaP and BPO, the chemical shift anisotropies are zero within experimental error. Spin-echo NMR All of the compounds investigated here yield well-defined Hahn spin echoes at the expected time period 2t,. Over the range of delays studied, these echoes decay in an approximately Gaussian fashion. Figures 2-4 show the decays of the spin echo intensities as a function of evolution time 2t,, together with the simulations from the crystal structures, using eqns. (lb) and [5]. Table 2 compares experimental and calculated second moments, as well as the ratio R = M,,(exp)/ Mz,(calc). With respect to their behavior, we can clearly differentiate between two groups of compounds: those which show close agreement between experiment and calculation (Group I, 0.9 I
Fig. 2. 3’P Spin echo decays of selected phosphorus compounds: P4S5. P4S7, CI-P,S,I~, ,CP,S,I,. spin echo decays as calculated with eqns. (lb) and (5) from the respective crystal structures.
The solid curves are the expected
00
04
02
08
0.6
2t 1
I 0
(ms)
Sip, CdP,. P-ZnP2. The solid curves are the expected Fig. 3. “P Spin echo decays of selected phosphorus compounds: cu-P,Se,I,, spin echo decays as calculated with eqns. (lb) and (5) from the respective crystal structures. In the case of ZnP, results from two independent
data sets are shown (open and filled circles).
_.
(msj
Fig. 4. alP Spin echo decays of selected phosphorus compounds: P,S,,, spin echo decays as calculated with eqns. (lb) and (5) from the respective of an alternate calculation using eqns. (la) and (5).
20
1 0
00
2t,
St, BPO,,
(ms)
InP, Cu,PSe,.
crystal structures.
The solid curves
The dashed
are the expected
curve represents
the result
D. Lathrap
rr ul. /Said
State Nd.
Map.
Rrson.
I (19921 7.?-83
R 5 1.2) and those for which the experimental spin echoes decay somewhat more rapidly than predicted (Group II, R > 1.2). In principle, the situation needs to be discussed for each compound individually. TO this end, it is necessary to know the relative orientations of the chemical shift principal axis systems for the interacting nuclei. This requires detailed orientation-dependent measurements on single crystals, which are often not available. However, even in the absence of such data, the results presented here allow some generalizations: The compounds in Group I comprise P,S,, P,S,, aand P-P3S311. P,Se,12, SIP, CdP,, ZnPz, and Ag,P3S,,. All of these compounds have one feature in common: the major contribution to the i’P-3’P dipole-dipole couplings in them arises from interactions among chemically and crystallographically inequivalent -?‘P nuclei, which possess
(b)
1 2-
s\ /“\ [
/p\,/p’s
/s
Fig. 5. Molecular geometries of (a) the compound P,S,,, and (b) the dimeric P,Si- group in the compound AgPS,.
81
asymmetric chemical shift tensors with moderateto-large chemical shift anisotropies. This situation leads to the consequence that the chemical shift difference between the interacting nuclei is larger than the dipole-dipole coupling at most crystal orientations. Therefore, the flip-flop transitions can be considered to be largely quenched in these compounds. Thus, the spin dynamics in these compounds are such that the spin echo technique produces the result anticipated with eqn. (lb) from the crystal structure. By contrast, for all of the compounds in Group If the dipolarly interacting “‘P nuclei are crystallographically and chemically equivalent (or nearly so in the case of P,S,,,). Furthermore, the chemical shift anisotropies are in general moderately small or zero (except for P,S,,, and AgPS,, for which the shift tensors are close to axially symmetric). In fact, for the compounds BPO,, GaP, and InP, it would be expected that all of the interacting “‘P nuclei have identical resonance frequencies, regardless of crystallite orientation. In principle, the 90”~t,-180” pulse sequence should not produce an echo at all under such conditions, were it not for the magnetic inequivalences generated by the heteronuclear dipole-dipole couplings of “‘P to the quadrupolar nuclei and 11.1.115 i(1.11 B h9.71Ga, In in these compounds. However, the degree to which flip-flop transitions are quenched here is difficult to predict on theoretical grounds. Significant deviations between experimental and simulated data are also noticeable for Cu,PSe, and AgPS, as well as for the chalcopyrites CdGePz, ZnGeP,, and CdSiP,. Again, the dipole-dipole coupling is likely to be homogeneous at least for part of the crystal orientations in these cases and hence refocusing of chemical shift evolution may be incomplete. Obviously, the spin echo decay cannot function as a reliable source of structural information. For these cases, the use of the Carr-Purcell sequence is expected to give more accurate results, as demonstrated recently for tightly coupled twospin systems [39j. The compounds P,S ,() and AgPS, are of special interest. Although P,S,,, has four crystallographically inequivalent sites and a moderately large chemical shift anisotropy, these sites have
82
very similar isotropic chemical shifts in the MAS NMR experiment. The shift tensors for all of these sites are close to being axially symmetric, with the principal axes oriented along the P=S double bonds. The four angles 8 these axes make with the magnetic field direction (and hence the resonance frequencies of the corresponding phosphorus nuclei) are inter-related by the architecture of the P,S,, molecule (see Fig. 5a1. For instance, if the molecule is oriented with one P=S axis parallel to the magnetic field (6’ = 0% the other three P=S axes are all oriented at approximately 19= 109.5”. Thus, these three P atoms have almost identical resonance frequencies, and hence zero-quantum (flip-flop) transitions are allowed among them. There are a multitude of other crystal orientations where at least two P atoms have a difference in resonance frequencies that is comparable to, or less than, the strength of the dipole-dipole coupling. For all of these orientations, the flip-flop term contributes to the dipolar Hamiltonian and hence causes the spin echo to decay more rapidly than expected from eqn. (lb). Similar, albeit less definite reasoning probably applies to the compound AgPS,. In this compound a major contribution to the dipole-dipole coupling arises from the chemically equivalent P atoms constituting the P,Si- dimeric unit (Fig. 5b). In th e absence of single crystal NMR data the orientation of the chemical shift tensor relative to the symmetry elements of this unit is not known. It is worth noting, however, that the chemical shift tensor for this compound is close to being axially symmetric. This increases the probability that the neighboring 31P nuclei have identical resonance frequencies. For instance, if one assumed that the principal axis of the chemical shift tensor coincides with the C, axis of the P,Sigroup, the two 31P nuclei would have approximately the same resonance frequency at any given crystal orientation.
Conclusions The ability of the Hahn spin echo technique to serve as a reliable source of structural information requires that the flip-flop term in the dipolar
D. Lathrop et al. /Solid State Nucl. Magn. Resort. I (1992) 73-83
Hamiltonian is quenched due to a large chemical shift difference between the interacting nuclei at the large majority of crystal orientations. The results of the present study show that for 3’P spin echo NMR at moderately high magnetic field strengths (7.05 T), this condition is usually fulfilled if the major contribution to the dipole-dipole couplings arises from interactions among crystallographically and chemically inequivalent phosphorus sites. Asymmetric 3’P chemical shift tensors, moderately large chemical shift anisotropies (> 100 ppm), and high operating magnetic field strengths work in favor of attaining this limit. The fact that excellent agreement between the experimental and calculated spin echo decays is observed in such cases, also suggests that the second moment contribution from indirect 3’P31P spin-spin coupling is generally negligible compared to the direct contribution (at least within the experimental error of the measurement). For glasses, we expect that neighboring spins are rendered chemically inequivalent due to small variations in local geometries. Even more importantly, the lack of long-range order will result in random mutual orientations of the chemical shift tensor axis systems of interacting nuclei. Therefore, the spin dynamics in glasses are expected to mimick those discussed for the compounds of Group I. Based on the results discussed here, we can thus predict that 31P spin echo NMR, when applied to glasses and other phosphorus-containing disordered systems will generally produce accurate and thus structurally significant dipole-dipole coupling information. Structural topics that pose exciting prospects for future applications of 31P spin echo NMR include: phase separation processes in glasses (particularly phosphate of phosphorus into glasses * 1, incorporation molecular sieve structures and the dispersion of phosphorus oxides on catalyst surfaces.
*
Although the thophosphates perform well presence of (meta-, pyro-
chemical shift anisotropies of inorganic orare rather small, the method is expected to in phosphate glasses, due to the simultaneous chemically inequivalent phosphorus species and orthophosphate groups) in these glasses.
D. Lathrop et al. /Solid
X3
Slate Nucl. Magn. Reson. 1 (1992) 73-83
Acknowledgments This research was supported by the National Science Foundation, grant DMR 89-13738 and the UCSB Academic Senate. Acknowledgment is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial funding of this project. The authors thank Mr. David Schmidt and Ms. Kesha Banks for technical assistance, Mr. Christopher Hudalla for providing the sample of CdSiP, and Mr. Robert Shibao and Dr. Regina Francisco for fruitful discussions.
16 M. Mortimer, E.A. Moore, DC. Apperley and G. Oates. Chem. Phys. Letr., 138 (1987) 209. 17 J.H. Herzfeld and A.E. Berger. J. Chem. Phys., 73 (1980)
6021. 18 T.A. Vanderah and R.A. Nissan. J. Phys. Gem. (1988) 1335. 19 R.A. Nissan and T.A. Vanderah, J. Phys. Gem.
Solids. 49 Solids, 50
(1989) 347.
20 M.A. Ryan. M.W. Peterson, D.L. Williamson. J.S. Frey, G.E. Maciel and B.A. Parkinson, J. Mater. Sot., 2 (1987) 528.
21 T.M. Duncan, R.F. Karlicek. W.A. Bonner and F.A. Thiel. J. Phys. Chem. Solids, 45 (1984) 389. 22 H. Eckert, C.S. Liang and G.D. Stucky, J. Phys. Chem., 93 (1989) 452. 23 D. Lathrop and H. Eckert, J. Phys. Chem., 93 (1989) 7895. 24 R.K. Harris. P.J. Wilkes, P.T. Wood and J.D. Woolins. J. Chem. Sot., Dalton Trans., (1989) 809.
References 1 J.A. Reimer and T.M. Duncan, Phys. Rw. B, 27 (1983) 4895. 2 J.B. Boyce and S.E. Ready, Phys. Rev. B, 38 (1988) 11008.
3 S. Hayashi. K. Hayamizu, S. Yamasaka, A. Matsuda and K. Tanaka, Phys. Rec. B, 38 (1988) 31. 4 DC. Douglass, T.M. Duncan, K.L. Walker and R. Csencsits, J. Appl. Phys., 58 (1985) 197. 5 T.M. Duncan, D.C. Douglass, R. Csencsits and K.L. Walker, J. Appl. Phys., 60 (1986) 130. 6 H. Eckert, Angew. Chem. AWL,.Mater., 101 (1989) 1763. 7 D. Lathrop and H. Eckert, J. Am. Chem. Sot., 111 (1989) 3536. 8 M. Tullius, D. Lathrop and H. Eckert, J. Phys. Chem., 94 (1990) 2145. 9 H. Eckert, D. Franke, D. Lathrop, R. Maxwell and M. Tullius, Mater. Res. Sot. Symp. Proc.. 172 (1990) 193. 10 D.R. Franke and H. Eckert. J. Phys. Chem., 95 (1991) 331. 11 D. Lathrop and H. Eckert, Phys. Rer. B, 43 (1991) 7279. 12 D. Franke. R. Maxwell, D. Lathrop and H. Eckert. J. Am. C’hem. Sot., 113 (1991) 4822. 13 M. Engelsberg and R.E. Norberg, Phys. Rer. B, 5 (1972) 3395. 14 N. Boden, M. Gibb, Y.K. Levine and M. Mortimer, J. Magn. Reson., 16 (1974) 471. 15 W.W. Warren and R.E. Norberg, Phys. Rer.. 154 (1967) 727.
25 T. Bjorholm and H. Jacobsen, J. Am. Chem. Sot.. 113 (1991) 27. 26 A. Vos. R. Othof, F. Van Bolhuis and R. Botterweg. Acta Ctystallogr., 19 (1965) 864.
27 D. Wright and B. Penfold, Acta Crystallogr., 12 (1959) 455. 28 G. Hunt and A. Cordes, Inorg. Chem., 10 (1971) 1935. 29 R. Blachnik, G. Kurz and U. Wickel. Z. Naturforsch. Teil B. 39 (1984) 778.
30 R.W.G. Wyckoff, Crystal Structures, 2nd edn., Interscience, New York, 1963. 31 T. Wadsten, Chem. Ser., 8 (1974) 63. 32 J.G. White, Acfa Crystallogr., 18 (1965) 217; J. Manolikas, J. Van Tendeloo and S. Amelinckx, Phys. Status Solidi A. 97 (1986) 87.
33 I.J. Hegyi, E.E. Loebner, E.W. Poor, Jr. and J.G. White, J. Phys. Chem. Solids, 24 (1963) 333.
34 M.E. Fleet and T.A. Mowles, Acta Crystallogr. Sect. C, 40 (1984) 1778.
35 J. Garin and E. Parthe, Acta Ctystullogr. Sect. E, 28 (1972) 3672.
36 H. Pfister, Acta Crystallogr., 11 (1958) 221. 37 P. Toffoli, P. Khohadad and N. Rodier, Acta Crystallogr. Sect. B, 34 (1978) 3561.
38 P. Toffoli, P. Khohadad and N. Rodier, Acfa Cryslallogr. Sect B. 38 (1982) 2374.
39 M. Engelsberg (1990) 393.
and C.S. Yannoni.
J. Magn. Reson., 88