19F MAS NMR Investigation of Strontium Substitution Sites in Ca2+

Mar 27, 2008 - shift of 79.6 ppm is assigned to fluoride ions in the center of a triangle of Ca2Sr ions (the so-called Ca(2) ..... rather than shieldi...
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J. Phys. Chem. C 2008, 112, 6165-6172

6165

19F

MAS NMR Investigation of Strontium Substitution Sites in Ca2+/Sr2+ Fluorapatite Solid Solutions Gyunggoo Cho,†,# Chung-Nin Chau,‡ and James P. Yesinowski*,†,§ Department of Chemistry, Michigan State UniVersity, East Lansing, Michigan 48823-1322, Osram SylVania Products Incorporated, Hawes Street, Towanda, PennsylVania 18848, and Chemistry DiVision, NaVal Research Laboratory, Washington, District of Columbia 20375-5342 ReceiVed: December 4, 2007; In Final Form: January 31, 2008

The partial replacement of Ca2+ by Sr2+ in the fluorapatite lattice results in additional peaks in the 19F MAS NMR spectra at 9.4 T other than the main resonance of Ca10F2(PO4)6 at 64.0 ppm (from hexafluorobenzene). The assignment of these peaks to specific structural configurations is possible in the sample containing the least strontium, with a composition of Ca8.97Sr1.03F2(PO4)6. The solid-solution character of this sample is established by the observation of spectral spin diffusion between various peaks in the SPARTAN (selective population anti-z and rate of transfer to adjacent nuclei) experiment. Calculations based upon modeling the 19F chemical shift tensor show that this process is facilitated for most crystallites by the close approach of two peaks’ resonances during the rotor cycle. A peak and set of spinning sidebands with an isotropic chemical shift of 79.6 ppm is assigned to fluoride ions in the center of a triangle of Ca2Sr ions (the so-called Ca(2) sites occurring as Ca3F in the fluorapatite lattice). Smaller chemical shift perturbations observed by deconvolution of two shoulders at 61.2 and 58.8 ppm on the main 64.0 ppm resonance are assigned to a Ca3F configuration that has, respectively, either one or multiple Sr2+ neighbors in the adjacent Ca(2) sites. Quantitative peak intensity measurements relative to the main 64 ppm resonance of both the 79.6 ppm peak as well as the deconvoluted peaks separately indicate that Sr2+ ions preferentially occupy the Ca(2) site at a level 23% greater than that expected for random substitution in the above solid solution. A sample having the composition Ca4.95Sr5.05F2(PO4)6 has a qualitatively similar site preference and has peaks assigned to Ca2SrF at 70 ppm, CaSr2F at 87 ppm, and Sr3F at 105 ppm.

Introduction Nuclear magnetic resonance spectroscopy offers a unique means of observing local order in disordered solid materials, including solid solutions. The broad static NMR line width typical of powder samples, which arises from dipolar interactions and chemical shift anisotropy (CSA), obscures identification of individual peaks having different chemical shielding environments in many solids of interest. Since spinning the sample rapidly at the “magic-angle” of 54.7° (MAS NMR) averages out these anisotropies and results in sharp peaks at each isotropic chemical shift, MAS NMR is extremely useful for the structural study of solids having multiple environments about a given atom. For example, cation ordering in solid solutions of a (Ga,In)P semiconductor alloy was studied using 31P MAS NMR and peak deconvolution,1 and 19F MAS NMR has been used to unambiguously determine the site of antimony substitution in fluorapatites doped with low levels of Sb(III).2 Since the 19F chemical shift of the fluoride anion is very sensitive to the cations to which it is bound, increasing from 64.0 to 97.2 to 184.8 ppm in the series calcium, strontium, and barium fluorapatite,3 in this study we have used high-speed 19F MAS NMR to study local order in solid solutions of calcium/ * To whom correspondence should be addressed. E-mail: yesinowski @ nrl.navy.mil. Fax: (202) 767-0594. † Michigan State University. ‡ Osram Sylvania Products Incorporated. § Naval Research Laboratory. # Current address: Bio MR Research Center, 804-1 Yangcheong-Ri, Ochang-Eup, Cheongwon-Gun, Chungbuk 363-883, Korea.

strontium fluorapatite, Ca10-xSrxF2(PO4)6. These materials, when appropriately doped with luminescent ions such as Sb(III), have potential applications as halophosphate phosphors. They also represent a model for strontium incorporation into the closely related calcium hydroxyapatite structure, which is a prototype for (but in most cases not the actual) mineral found in bone and teeth.4 In fact, both stable and radioactive isotopes of strontium have been used to trace calcium pathways in the body and as markers for bone mineralization (references in ref 5). Strontium-calcium fluorapatite glass ceramics are of interest as biomedical implants.6 Furthermore, calcium/strontium fluorapatites occur naturally in apatite deposits and may serve as hosts for radioactive 90Sr contamination.7 In the present study we have assigned 19F MAS NMR peaks to specific bonding arrangements and investigated site preferences when Sr2+ (ionic radius 112 pm)8 substitutes for Ca2+ (ionic radius 99 pm)8 in the fluorapatite lattice. From single-crystal X-ray diffraction studies of calcium fluorapatite it is known that there are two types of calcium ions in the structure, four Ca(1) and six Ca(2).4,9 Fluoride ions are surrounded by three Ca(2) ions in an equilateral triangle perpendicular to the c-axis. Viewing down the c-axis shows successive equilateral triangles of Ca(2) ions that are rotated by 60° with respect to each other, i.e., each triangle is staggered with respect to the one above and below. The Ca(1) ions form columns located at the middle of a large equilateral triangle of three fluoride ions, with each Ca(1) ion midway between two of these large fluoride triangles. A number of studies of the

10.1021/jp7114498 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/27/2008

6166 J. Phys. Chem. C, Vol. 112, No. 15, 2008 intensities of X-ray powder diffraction lines of Ca/Sr hydroxyapatites have concluded that Sr2+ preferentially occupies Ca(2) sites.10,11 An opposing conclusion was reached in an EXAFS study of Ca/Sr hydroxyapatite prepared by aqueous coprecipitation without heating, which concluded that Sr2+ at low levels went exclusively into the Ca(1) sites.5 Studies of Ca/Ba and Sr/Ba fluorapatites by X-ray powder diffraction demonstrated a preference of the larger ion for the Ca(2) sites, especially for the former system, and the results were shown to be independent of thermal treatment and type of quenching.12 Thermodynamic arguments explaining the counterintuitive preference of larger ions for the Ca(2) site, which is smaller than the Ca(1) site, have been given.10,13 A single-crystal X-ray diffraction study of a mineral sample of Sr/Ca fluorapatite showed a strong preference of Sr2+ for the Ca(2) site.14 There was also a slight displacement of the fluoride ions from their pseudospecial positions on the 63 axis, and two types of Ca(1) sites could be distinguished as well. For fluorapatite glass ceramics 19F MAS NMR and Rietveld X-ray analyses of the same samples gave contradictory results;6 the conclusion from NMR that Sr prefers the Ca(I) site disagrees with the results of previous studies as well and may be due to poor resolution, limitations in the data analysis, and the glass ceramic nature of the sample. A singlecrystal X-ray diffraction study of a number of synthetic Sr/Ca chlorapatite samples showed a preference of Sr2+ for the Ca(2) site;15 in these chlorapatites the chloride anion position is shifted toward the midpoint between the planes containing the triangle of metal cations because of the larger size of the chloride visa´-vis fluoride anion. After presenting our experimental results, we will first discuss the assignment of peaks in the 19F MAS NMR spectra of a 9/1 Ca/Sr solid solution in terms of primary nearest-(cation)neighbor effects and site preferences. We will then make assignments based on secondary next-nearest-(cation)-neighbor effects that yield consistent conclusions about the strontium site preference. Next follows a detailed discussion of the mechanisms and significance of the spin-diffusion experiments. Finally, the previous conclusions will allow primary assignments to be made for a 5/5 Ca/Sr solid solution and conclusions to be drawn about strontium site preferences in this sample. Experimental Section Two samples of calcium/strontium fluorapatite solid solutions were synthesized with approximate Ca/Sr molar ratios of 9:1 and 5:5. The 9:1 Ca/Sr sample was made by reacting a mixture of finely powdered CaHPO4, CaCO3, and SrF2 with a molar Ca/Sr ratio of 9.04 for the starting materials at 1150 °C for 2 h. The product was analyzed to have 33.32% Ca and 8.40% Sr (molar Ca/Sr ) 8.67) and on this basis was assigned the formula Ca8.97Sr1.03F2(PO4)6. The 5:5 Ca/Sr sample was made by reacting a mixture of finely powdered SrHPO4, CaCO3, CaHPO4, and CaF2 with a molar Ca/Sr ratio of 1.00 for the starting materials at 1150 °C for 2 h. It was analyzed to contain 14.63% Ca and 32.61% Sr (molar Ca/Sr ) 0.98) and on this basis was assigned the formula Ca4.95Sr5.05F2(PO4)6. The high-temperature conditions of formation, together with the close agreement between initial and final Ca/Sr ratios and the absence of any nonapatitic fluorine resonances in the MAS spectra, rule out the possibility of any significant extent of carbonate or hydroxyl substitutions in the apatite lattice in these samples. Also, the 19F MAS NMR spectrum of a Ca10F2(PO4)6 sample prepared at high temperature showed only a sharp single peak and no perturbed peak positions as would be expected for carbonate or hydroxyl.2 The 19F MAS NMR spectra were acquired at 376 MHz on a 9.4 T Varian Associates VXR-400 spectrometer. A high-speed

Cho et al.

Figure 1. 19F MAS NMR spectra of Ca8.97Sr1.03F2(PO4)6 spinning at (a) 8.23 and (b) 10.87 kHz. The star symbol (f) indicates center bands, and the remaining peaks are spinning sidebands. 19F

MAS NMR probe from Doty Scientific with 5 mm o.d. rotors and Vespel caps was used. The spinning speed was measured with a fiber optic detector and was constant to within (10 Hz during acquisitions. Calcium fluorapatite was used as a secondary chemical shift reference (64.0 ppm with respect to hexafluorobenzene at 0 ppm). The π/2 pulse length was 4.0 µs, and relaxation delays were sufficiently long to avoid saturation of the signals due to long spin-lattice relaxation times of several minutes. The SPARTAN (selective population anti-z and rate of transfer to adjacent nuclei) pulse sequence was used to measure spectral spin diffusion (cross-relaxation) in the 19F MAS NMR spectrum.2 In this experiment, the center band and associated sidebands were selectively inverted by a DANTE pulse train equivalent to a π-pulse for on-resonance spins, and consisting of 12 15° (2 µs) pulses given at the same point of each rotor cycle (i.e., rotor-gated synchronization). After a variable mixing period in which spin diffusion occurs in the absence of applied rf, a nonselective π/2 read pulse (12 µs) was given with alternated phases to cancel out imperfections in the DANTE pulse train that resulted in incomplete inversion of magnetization at the carrier frequency. Deconvolution of the individual peaks was performed using the Varian VNMR 3.2 software. Results The 19F MAS NMR spectrum of Ca8.97Sr1.03F2(PO4)6 spinning at 8.23 kHz is shown in Figure 1a. It is difficult to obtain the isotropic chemical shift and spinning sideband intensities associated with a given center band from a single spectrum at a fixed spinning speed due to the overlap of the center band of one peak with a sideband from another. However, since the sidebands are spaced at integral multiples of the spinning frequency from the center band, we can differentiate between the center band of one peak and a sideband from another peak with a different isotropic chemical shift simply by increasing the spinning speed. In this way, three isotropic chemical shifts in the Ca8.97Sr1.03F2(PO4)6 sample (Figure 1b) can be obtained at 64, 79.6, and 97 ppm. (Note that the peak at 64 ppm has an upfield shoulder, whose peak deconvolution is discussed below.) The overlap of center band and sideband peaks makes it difficult to obtain reliable integral intensities of individual peaks in the

19F

MAS NMR of Sr2+ Substitution in Fluorapatite

Figure 2. Deconvolution of peaks near 64 ppm from the spectrum in Figure 1b.

spectrum. From the spectrum in Figure 1b only the integrated intensity of the center band and sidebands of the 79.6 ppm peak can be reliably measured, since the center bands and sidebands of the other two peaks overlap. The integrated intensity of the center band and sidebands of the 79.6 ppm peak relative to the total integral intensity in Figure 1b is 29%. The deconvoluted spectrum of the center band peaks near 64 ppm and also of the peak near 51 ppm due to the -1 sideband of the 79.6 ppm peak of Figure 1b is shown in Figure 2. It is apparent from the spectrum that at least three peaks are present in the asymmetric 64 ppm peak, and good agreement with the experimental spectrum was obtained by summing three deconvoluted peaks with different fractions of Gaussian and Lorentzian line shapes. The justification for using slightly different line shapes is not only the good agreement with the experimental spectrum obtained using a minimum number of peaks (three) but also the reasonable expectation that longer-range unresolved effects of Sr2+ substitution on the 19F shifts might be expected to produce Gaussian distributions of shifts with different widths. The Gaussian fractions of the deconvoluted peaks I and II are 0.88, and that of peak III is 0.68. The half-height line widths of peaks I, II, and III are 454, 536, and 758 Hz, respectively. The chemical shifts of peaks I, II, and III are 64.0, 61.2, and 58.8 ppm, respectively. The percentages of the integral intensity of deconvoluted peaks I, II, and III are 45.4%, 37.3%, and 17.4%, respectively. The deconvolution of the -1 sideband near 51 ppm is only approximate and was made only to estimate the effects of the “tail” of the distribution upon the main deconvolution of the 64 ppm peaks. Figure 3 shows a series of 19F MAS NMR spectra at a spinning speed of 10.87 kHz of Ca8.97Sr1.03F2(PO4)6 obtained with the SPARTAN pulse sequence and mixing times for spin diffusion ranging from 0.1 to 30 s. The expanded portion of the spectra shows the 64 and 79.6 ppm center band peaks and the -1 sideband of the latter. The transmitter offset (carrier) in this experiment was set to invert the 64 ppm peak (peak I in the deconvolution spectrum of Figure 2), leaving the other peaks unperturbed. Since the pulses in the DANTE train are repeated every rotor period, the sidebands of this 64 ppm peak are also inverted. As the mixing time increases, the intensities of adjacent peaks (both the upfield shoulders of the 64 ppm peak as well as the peak at 79.6 ppm and its -1 sideband near 51 ppm) decrease while the center band (and sidebands, not shown) of the 64 ppm peak goes from being inverted to having a positive intensity. This recovery is rapid compared to the 19F spin-lattice

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Figure 3. 19F MAS NMR spin-diffusion experiments on Ca8.97Sr1.03F2(PO4)6 using the SPARTAN pulse sequence, spinning at 10.87 kHz. The peak at 64.0 ppm was inverted and can be seen continuously recovering in the overlaid spectra for the various mixing times of 0.1, 1, 3, 6, 9, 12, 15, 18, 21, 24, and 30 s.

Figure 4. 19F MAS NMR spectra of Ca4.95Sr5.05F2(PO4)6 spinning at (a) 8.25 and (b) 10.30 kHz. The f indicates center bands; the remaining peaks are spinning sidebands.

relaxation time T1 of 101 s measured with an inversionrecovery pulse sequence; all peaks in the spectrum have the same T1. The 19F MAS NMR spectra of Ca4.95Sr5.05F2(PO4)6 at two different spinning speeds are shown in Figure 4. The center bands are better resolved at the higher spinning speed (Figure 4b), and have isotropic chemical shifts of 69.7, 86.8, and 104.5 ppm. Reliable integrated peak intensities could not be obtained from these spectra due to the overlap between center bands and spinning sidebands of other peaks. Discussion We will discuss the assignment of peaks in the 19F MAS NMR spectra of the 9/1 Ca/Sr solid solution by first considering the primary effects of strontium substitution in nearest-neighbor environments. Evidence for a strontium site preference based upon the integrated intensities of peaks will be given. Subsequently the secondary effects of next-nearest-neighbor substitu-

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Cho et al. TABLE 1: Calculated Probabilities of Configurations A-D in Ca8.97Sr1.03F2(PO4)6 (Figure 5), for Both Random Substitution and a 23% Preference of Sr2+ Ions for the Ca(2) Sites, and Comparison with the Experimental 19F MAS NMR Integrated Intensity probability, probability, 23% preference random configuration substitution (%) Ca(2) site (%) A B C D total

72.1 24.9 2.9 0.1 100.0

66.5 29.0 4.2 0.2 99.9

integrated MAS NMR peak intensity a 29.0% (79.6 ppm)b a a 100.0

a Integrals for individual peaks were not reliable because of weakness and overlaps, but the combined integrated intensity of peaks A, C, and D by difference is 100.0% - 29.0% ) 71.0%. b Includes the first two pairs of spinning sidebands.

Figure 5. Modes of primary substitution of Sr2+ ions in the three nearest-neighbor Ca(2) sites of Ca/Sr fluorapatite solid solutions (the hexad crystal c-axis is perpendicular to the plane of the triangles).

tion of strontium for calcium will be shown to account for the deconvolution peaks, whose intensities provide further confirmation of the deduced strontium site preference. Both of these assignments will be useful in understanding the spin-diffusion results obtained with the SPARTAN sequence, which will be discussed next. Finally, we will assign peaks in the spectrum of the 5/5 Ca/Sr solid solution considering only the primary effects of strontium substitution in nearest-neighbor environments. Primary Effects of Nearest-Neighbor Strontium. Differences in the chemical bonds between a fluoride anion and either a calcium or a strontium cation give rise to significant differences in the 19F chemical shifts. The fluoride ions in Ca8.97Sr1.03F2(PO4)6 can have any of the four different primary chemical bonding environments depicted in Figure 5. These differ only in the number of Sr2+ ions replacing some or all of the three Ca(2) ions that surround the fluoride ion in an equilateral triangle. Since the structure of A represents the local fluoride ion environment in Ca10F2(PO4)6, whose 19F shift is 64.0 ppm, we assign the peaks whose isotropic chemical shifts are near 64 ppm to the primary bonding arrangement A. The isotropic chemical shifts of structures B and C in Figure 5 can be predicted by assuming that the shielding components from individual cation to fluoride anion bonds are additive, as discussed in ref 16. In that approach, which is based upon the work of Gagarinskii and Gabuda,17 the 19F chemical shift differences for different alkaline earth fluorapatites are viewed as arising from different contributions to the paramagnetic term in the Ramsey equation for chemical shielding, the diamagnetic term remaining nearly constant for a negatively charged fluoride anion. The paramagnetic term arises from the overlap of cation and anion orbitals, and by considering the measured chemical shift anisotropies of the fluorapatites it can be broken down into angular-dependent contributions from both σ- and π-bonding, with coefficients aσ and aπ, respectively. Structure B in Figure 5 has two Ca-F and one Sr-F bonds, whereas structure C has one Ca-F and two Sr-F bonds. The isotropic chemical shifts of B and C predicted using the calculated values16 (vide infra) of aπ and aσ for Ca10F2(PO4)6 and Sr10F2(PO4)6 are 75.1 and 86.1 ppm, respectively. Neither value matches exactly the isotropic chemical shift of the peak at 79.6 ppm in Figure 1. However, since the peak at 79.6 ppm is the first one observed downfield from the main 64 ppm peak, we can assign it to

structure B (Sr1Ca2F) in Figure 5. The fact that the experimental shift of structure B is 4.5 ppm downfield of the predicted value is not unreasonable in view of the neglect of effects of nextnearest-neighbor interactions and/or lattice distortions discussed below. Whether the very weak peak at 97 ppm (whose relative intensity is difficult to estimate) arises from structure C or D in Figure 5 cannot be decided with certainty, since the latter assignment could be made assuming that a stronger peak due to structure C is concealed by overlap with the downfield sideband of the 64 ppm peak in Figure 1. However, even though this latter assignment also seems to agree with the 97.8 ppm shift obtained from Sr10F2(PO4),3 we think it more likely on the basis of intensity arguments (see Table 1 below) and nearestneighbor shift arguments (see the assignments of the peaks for the Ca4.95Sr5.05F2(PO4)6 sample given below) that the 97 ppm peak arises from structure C. Site Preferences. The degree of any possible preference of Sr2+ ions for the Ca(2) site in Ca/Sr fluorapatite solid solutions can be studied by using both fully resolved peaks in the 19F MAS NMR spectrum as well as from peak deconvolution of overlapping peaks. There are two different types of calcium ions in Ca10F2(PO4)6. Since there are four Ca(1) ions and six Ca(2) ions in the unit cell, we can rewrite the formula of Ca8.97Sr1.03F2(PO4)6 as Ca(2)6xSr(2)6yCa(1)4x′Sr(1)4y′F2(PO4)6 (6x + 4x′ ) 8.97 and 6y + 4y′ ) 1.03, and x + y ) x′ + y′ ) 1). Since the fluoride ions are bonded to Ca(2) and Sr(2) ions, the primary chemical shift of the fluoride ion depends upon the number of Ca(2) and Sr(2) ions to which it is bonded. The fractional integrated areas of the peaks corresponding to the configurations in Figure 5 (i.e., the integrated intensity of a center band plus associated sidebands relative to the total integrated intensity of all peaks) are represented by the following equations:

A ) x3 B ) 3x2y C ) 3xy

(1)

2

D ) y3 where (A + B + C + D) ) (x + y)3 ) 1.0. If the strontium ions substitute randomly for calcium ions in Ca8.97Sr1.03F2(PO4)6, i.e., if x ) x′ and y ) y′, the integrated intensity of B calculated from eq 1 would be 24.9%. The experimental value is 29%, which implies values for x and y of 0.873 and 0.127, respectively. Thus, the experimental integrated intensity of peak B indicates an approximately 23% [(0.127 0.103)/0.103] site preference of a Sr2+ ion for the Ca(2) site in

19F

MAS NMR of Sr2+ Substitution in Fluorapatite

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Ca8.97Sr1.03F2(PO4)6. Table 1 shows the probabilities calculated for the various configurations assuming either random substitution or a 23% preference of the Sr2+ ions for the Ca(2) site. In terms of the distribution coefficient K expression used by Heijligers et al. to characterize site preferences in Sr/Ca hydroxyapatites,11 a 23% site preference of Sr2+ for the Ca(2) site corresponds to a constant K ) 0.493 (K ) 1 for no site preference). This value reflects a somewhat larger degree of ordering than the value reported by Heijligers et al. (for hydroxyapatites) of K ) 0.85 ( 0.09, which they concluded did not depend significantly upon composition.11 However, this latter conclusion is at odds with another X-ray powder diffraction study of Ca/Sr hydroxyapatites, in which the degree of ordering was observed to decrease with increasing Sr content.10 Using the “degree of order” parameter σ defined in this latter work, the 23% site preference we have determined corresponds to σ ) 0.35, which is somewhat less than the extrapolated value σ ≈ 0.6 anticipated from this latter work. The 23% site preference we obtain is close to the 19% preference measured by X-ray diffraction for a Sr7.3Ca2.7F2(PO4)6 single-crystal sample14 but smaller than the almost complete ordering deduced from other X-ray single-crystal studies.7 It is impossible at present to know what the quantitative discrepancies above are due to. However, the important qualitative conclusion is that both X-ray powder diffraction and our 19F MAS NMR results indicate a preference of Sr2+ for the Ca(2) site in the apatite lattice, casting some doubt upon a more limited NMR study of ceramic glasses6 that arrived at the opposite conclusion. Secondary Effects of Next-Nearest-Neighbor Strontium. The 19F MAS NMR peaks in Figure 1b are asymmetric and broad, but it is not immediately obvious whether this is due to perturbations from strontium ions substituted in Ca(1) sites or from strontium ions in the next-nearest-neighbor Ca(2) sites. We now consider how to resolve this question, with reference to the deconvoluted peaks around 64 ppm. From the crystal structure of calcium fluorapatite, a single Sr2+ ion substituting in a Ca(1) site would potentially perturb six fluoride ions in an equivalent fashion, whereas a Sr2+ ion substituting in a nextnearest-neighbor Ca(2) site perturbs two fluoride ions (those above and below the triangular plane containing the Sr2+ substitution). Thus, Sr2+ ions in Ca(1) sites perturb 3-fold more fluoride ions than those in next-nearest-neighbor Ca(2) sites and cannot account for the significant 45.4% relative intensity of the deconvoluted peak at 64.0 ppm if this peak is plausibly assumed to arise from fluorine nuclei unaffected by Sr2+ substitution. We are therefore led to the conclusion that the chemical shift perturbations responsible for the three deconvoluted peaks around 64 ppm will depend on the number of strontium ions at the next-nearest-neighbor Ca(2) sites. The schematic arrangements of the metal cations neighboring a fluorine atom resonating near 64 ppm are shown in Figure 6. The fractional integrated intensities of peaks arising from the individual configurations in Figure 6 are then given by the following equations:

I ) x6 II ) 6x5y

(2)

III ≈ 1 - I - II (y , x) Since the probability of substitution of more than two Sr2+ ions in Ca8.97Sr1.03F2(PO4)6 is low, configuration III in eq 2 represents essentially the sum of the probabilities of having g2 Sr2+ ions in Ca(2) sites. The comparison of the deconvoluted integrated

Figure 6. Modes of secondary substitution of Sr2+ ions in the six nextnearest-neighbor Ca(2) sites of Ca/Sr fluorapatite solid solutions. The middle equilateral triangle in each configuration represents the observed Ca3F group resonating near 64 ppm, and the triangles above and below it (along the c-axis, see Figure 5 caption), although parallel, are drawn tilted for clarity. Configuration II has one Sr2+ ion either in a top triangle (as shown) or in a bottom triangle (not shown). Two Sr2+ ions in the configuration III are either both in a top triangle or a bottom triangle (not shown), or one each in both triangles (as shown).

TABLE 2: Calculated Probabilities of Configurations I-III in Ca8.97Sr1.03F2(PO4)6 (Figure 6), for Both Random Substitution and a 23% Preference of Sr2+ Ions for the Ca(2) Sites, and Comparison with the Experimental Deconvoluted Peak Intensities intensities of probability, probability, 23% preference deconvoluted peaks random near 64 ppm (%) configuration substitution (%) Ca(2) site (%) I II III total

52.1 35.9 12.0 100.0

45.6 38.3 16.1 100.0

45.4 37.3 17.3 100.0

intensities of the peaks near 64 ppm and the integrated intensities calculated both for random substitutions of Sr2+ ions and for a 23% preference of strontium ions for the Ca(2) site is summarized in Table 2. The predictions for a 23% site preference (x ) 0.873 and y ) 0.127) are significantly closer to the deconvolution data than those assuming random substitution. The half-height line widths of the deconvoluted peaks are broader than those of pure calcium and strontium fluorapatite (respectively, 130 Hz at 10.56 kHz and 365 Hz at 10.20 kHz spinning speeds16). Since strontium ions substituted in the Ca(1) sites appear to have a much smaller perturbing effect on the 64 ppm peak compared to that of strontium ions substituted in the next-nearest-neighbor Ca(2) sites, we believe that the main effect of strontium ions in the Ca(1) sites is to produce a slight increase in the half-height line widths of deconvoluted peaks corresponding to different arrangements of the Sr2+ ions in the six Ca(1) sites that “surround” a given fluorine nucleus. Spin Diffusion between Peaks. The above assignments and conclusions about substitutional site preferences are predicated upon the assumption that the additional 19F MAS NMR peaks due to the effects of strontium incorporation arise from perturbed fluoride ions in the same lattice, rather than in any separate phase. That this is the case is suggested by the equality of T1 values for all the peaks: if as in a previous 19F MAS NMR study of doped fluorapatites it is assumed that spin-lattice

6170 J. Phys. Chem. C, Vol. 112, No. 15, 2008 relaxation most likely takes place via spin diffusion to trace paramagnetic impurities,2 then the existence of spin diffusion between the various peaks must necessarily imply a significant dipolar coupling between the different types of fluoride ions and correspondingly close spatial proximity. A more definitive proof that the fluorine nuclei of the peaks at 64.0, 61.2, 58.8, and 79.6 ppm belong to the same phase rather than phasesegregated regions is offered by the SPARTAN results (Figure 3). Spin diffusion is the transfer of Zeeman magnetization between two nearby spins by a spin flip-flop process.18 Spectral spin diffusion between two peaks at widely different frequencies generally will not occur at a significant rate.19 However, under MAS conditions two peaks with widely separated isotropic chemical shifts, and highly anisotropic chemical shifts, can have identical instantaneous transition frequencies (Zeeman plus chemical shift at a particular orientation of the crystallite, vide infra for effects of dipolar couplings) at some point in a rotor period. This condition appeared to be met and to facilitate spectral spin diffusion in Sb(III)-doped fluorapatites, but direct proof was not possible in that case since the chemical shielding tensors at the dopant sites were not accurately known.2 The spin system in the present study is somewhat more favorable in this respect, and we will now attempt to demonstrate by calculating frequencies of the pair of inequivalent spins in a given crystallite during each part of a rotor cycle that spin diffusion between the 64.0 and 79.6 ppm peaks is facilitated by a closer instantaneous approach of their frequencies. A spin Hamiltonian under MAS conditions can be transformed from the chemical shift principal axis system (PAS) of each crystallite to a reference frame fixed on the rotor.20 The MAS Hamiltonian for the chemical shift PAS becomes periodic with respect to the rotation period, the detailed shape and amplitude depending upon both the chemical shielding tensor (CSA and asymmetry parameter) as well as the crystallite orientation with respect to the rotor axis. Although eq 4 of ref 20 conveniently requires only two of the three Euler angles to calculate instantaneous frequencies for the two tensors, it can yield incorrect results if the arctangents of expressions, which have two values differing by 180°, are not properly chosen (there is also a misplaced curly bracket in the expression). We therefore used eq 1 of the same reference, which requires all three Euler angles R, β, γ (note that there is also a mistake in this expression: the factor of (3/2)1/2 should be replaced by unity). Note also that the “reduced anisotropy”21 δ is defined there and elsewhere as σ33 - 1/3Tr(σ), where σ refers to a chemical shift rather than shielding tensor despite the normal convention. It is also important to recognize in applying eq 1 that the ordering of the three chemical shift components must be such that the reduced anisotropy δ has the largest absolute value,21 which may or may not be consistent with an order beginning with σ11 as the highest frequency (furthest downfield). Figure 3 demonstrates the existence of spin diffusion between the (inverted) peak at 64.0 ppm and the well-separated peak at 79.6 ppm. The CSA and asymmetry parameter of the peak at 64 ppm are known from previous work.16,22 Thus, we need to know the CSA and asymmetry parameter of the peak at 79.6 ppm and the orientation of its chemical shift PAS in order to predict its instantaneous frequency. We assume that configuration B of Figure 5, which is strictly speaking an isosceles triangle because of the slightly larger ionic radius of the Sr2+ ion, has the fluoride and calcium ions in the same positions as in configuration A and consequently has all three M2+-F-M2+ angles equal to 120°. The largest chemical shift tensor compo-

Cho et al. nent δ11 is obtained when the external magnetic field is perpendicular to the triangle in configuration B (note that this is the most downfield or highest frequency value and, hence, is a chemical shift rather than shielding component, as discussed elsewhere23). Since the three principal shift components δ11, δ22, δ33 are along orthogonal axes, δ22 and δ33 are in the plane of the triangle. The smallest chemical shift component δ33 is obtained when the external magnetic field is parallel to a Sr-F bond. From the equations in ref 16, which are based on those in ref 17, the chemical shift tensor components δ11, δ22, and δ33 of configuration B in Figure 5 can be represented by

δ11 ) δ(90°)(Sr) + δ(90°)(Ca) + δ(90°)(Ca) ) 2aσ(Ca) + aσ(Sr)

(3)

δ22 ) δ(90°)(Sr) + δ(30°)(Ca) + δ(30°)(Ca) ) (1/2)aσ(Ca) + (3/2)aπ(Ca) + aσ(Sr)

(4)

δ33 ) δ(0°)(Sr) + δ(120°)(Ca) + δ(120°)(Ca) ) (3/2)aσ(Ca) + (1/2)aπ(Ca) + aπ(Sr)

(5)

Here δ(θ)(M) refers to the chemical shift due to the paramagnetic shielding term when the magnetic field makes an angle θ with respect to the M-F bond axis. For a given cation M, the σ-bonding contribution to δ(θ) is aσ sin2(θ), and the π-bonding contribution is aπ cos2(θ).17 The predicted values of the shift tensor components δ11, δ22, and δ33 for the peak at 79.6 ppm (configuration B in Figure 5) obtained using aπ and aσ values for Ca-F and Sr-F bonds from ref 16 are equal to 137, 51.4, and 36.9 ppm, respectively. The isotropic shift calculated from these three predicted component values and used in the following calculations is 75.1 ppm, which is not too far from the observed shift. For completeness we will give the respective aπ and aσ values calculated in ref 16 for both Ca fluorapatite (81.7 ( 0.1 ppm, 24.6 ( 0.3 ppm) and Sr fluorapatite (97.6 ( 0.6 ppm, 26.0 ( 1.2 ppm). These values were obtained from a 19F MAS NMR moments analysis of the axially symmetric chemical shift tensors of the two pure compounds referenced to the theoretical free fluoride ion shift,24 which yielded respective δperp and δparallel values of (159.5 ( 0.2 ppm, 245.0 ( 0.5 ppm) for Ca fluorapatite and (185.4 ( 1.1 ppm, 292.8 ( 1.9 ppm) for Sr fluorapatite. (The chemical shift values relative to the C6F6 reference used in this paper can be obtained by simply subtracting 124.0 ppm.) The calculated reduced anisotropy δ and asymmetry parameter η of this 75.1 ppm peak (corresponding to the experimental 79.6 ppm peak) are 61.9 ppm and 0.234. These compare to the corresponding values used for the 64 ppm peak (calcium fluorapatite) of 57.0 ppm and 0 (which corresponds to a span of 85.5 ppm, within a couple of ppm of the slightly different values reported for calcium fluorapatite2,16,22). (Note that the spinning sidebands of the 79.6 ppm peak are more intense relative to the center band than those of the 64 ppm peak, as qualitatively expected.) The above approach enabled us to predict the 19F chemical shift tensor of configuration B in the crystallographic frame. Attempts to obtain merely the three components of the shift tensor from a Herzfeld-Berger graphical analysis of spinning sideband intensity patterns suffered from the known difficulties25 in extracting reliable values when the asymmetry parameter is small, as it is in the present case. Furthermore, the (small) dipolar couplings present and the presence of peak overlaps also limit the accuracy. The shift tensor components calculated in the preceding paragraph did successfully reproduce the semiquan-

19F

MAS NMR of Sr2+ Substitution in Fluorapatite

J. Phys. Chem. C, Vol. 112, No. 15, 2008 6171

Figure 7. Calculated variation in the instantaneous 19F chemical shifts (C6F6 reference) during a MAS rotor cycle of the 64.0 and 79.6 ppm peaks of the Ca8.97Sr1.03F2(PO4)6 solid solution for four different crystallite orientations represented by the given Euler angles relating the principal axis system (PAS) of the chemical shift tensors to the rotor. The top curve represents configuration A (Ca3F), the middle curve represents configuration B (SrCa2F), and the bottom curve is the difference. See text for modeling of the chemical shift tensor of the 79.6 ppm peak (configuration B) and other details.

titative features of the experimental sideband pattern, lending support to their use in the calculations of frequency modulations below. The predicted frequency modulations (as described several paragraphs above) of the 64 and 79.6 ppm peaks during one rotor cycle for four different initial crystallite orientations are shown in Figure 7. These predicted curves are typical of those from many other crystallite orientations (not shown) in revealing fairly close approaches, but no level-crossing, of the peaks corresponding to configurations A and B in Figure 5 during a part of the rotor cycle. (We note that the actual distances of closest approach may be larger than those shown by about 4.5 ppm, the difference between predicted and actual isotropic shifts of configuration B). In order to decide whether these close approaches are sufficient to lead to measurable spin diffusion, we need to consider the magnitude of various dipolar interactions. As can be seen from Figure 7, the closest approaches occur when configuration A (corresponding to the pure fluorapatite tensor) has a frequency slightly below 40 ppm, which corresponds to the perpendicular tensor component. In such orientations, the (perpendicular) homonuclear 19F-19F dipolar coupling between neighboring fluoride ions has a magnitude of ca. 2600 Hz, half of its maximal (parallel) value of 5234 Hz.2 From the observed triplet structure of the static low-field 19F NMR of single-crystal fluorapatite in the parallel orientation,26 we expect the perpendicular orientation also to show a triplet structure with peaks (3.6 kHz from the center peak. Since this corresponds to 10 ppm at our field strength, the result will be that energy-conserving spin diffusion should be permitted during close-approach portions of the rotor cycle. Full spin system density matrix calculations (such as those used for related

rotational resonance experiments) would be very involved, because of the presence of 19F-31P and 31P-31P dipolar couplings (2200 and 640 Hz maximum values, respectively2) and are beyond the scope of this study. The main conclusion of this analysis is that in a powder sample of Ca8.97Sr1.03F2(PO4)6 most crystallites will experience close approaches under MAS, resulting in the spin diffusion (or cross-relaxation) observed in Figure 3 between the 64.0 and 79.6 ppm peaks. In principle, rotational resonance experiments as first described by Andrew et al.27 could also be used to demonstrate cross-relaxation between the peaks at 64.0 and 79.6 ppm; however, the spinning speed necessary to achieve sideband overlap is insufficient to provide adequate spectral resolution. Such desirable higher spinning speeds could be retained by modifying the basic experiment by adding a weak rf during the exchange period to achieve the rotational resonance condition in the tilted rotating frame.28 Primary Effects of Nearest-Neighbor Strontium in 5/5 Ca/ Sr Fluorapatite. The above assignments and considerations help in the interpretation of the Ca4.95Sr5.05F2(PO4)6 solid-solution data in Figure 4. Although we cannot quantitatively determine the degree of site preference at this higher Sr composition due to the overlaps in the spectrum, for purposes of argumentation we can estimate it to be 20%, similar to the value determined above and close to the 19% preference measured by X-ray diffraction for a Sr7.3Ca2.7F2(PO4)6 sample.14 Doing so yields predicted relative intensities of the structures A, B, C, and D in Figure 5 of 4%, 23%, 44%, and 29%, respectively. The only plausible assignment of peaks that qualitatively agrees with these intensity predictions then has structure B at 70 ppm, C at 87 ppm, and D at 105 ppm (structure A is too weak to be seen).

6172 J. Phys. Chem. C, Vol. 112, No. 15, 2008 Note that a random substitution would give predicted relative intensities of structures A-D of 12%, 37%, 38%, and 13%, respectively, in sharp disagreement with what is observed. The fact that the peak assigned to structure D (Sr3F) is downfield (by 7 ppm) from the shift3 of Sr10F2(PO4)6 can be rationalized in terms of the secondary effects of strontium substitution at next-nearest-neighbor sites: the pure strontium fluorapatite has the most such neighbors, which produce an upfield shift relative to calcium in the same sites. The same consideration can also account for the fact that the Sr1Ca2F configuration (B in Figure 5) has a more upfield shift of 70 ppm in the 5/5 Ca/Sr sample vis-a´-vis the shift in the more calcium-rich 9/1 sample of 79.6 ppm. Lattice distortions in these solid solutions may also affect shifts. Conclusion Strontium ion substitution into the calcium fluorapatite lattice results in a number of completely or partly resolved peaks in the 19F MAS NMR spectra that can be assigned to specific bonding arrangements involving substitution at either nearestneighbor Ca(2) sites or next-nearest-neighbor Ca(2) sites on the hexad axis of the crystal. Substitution at the columnar Ca(1) sites appears to have a much smaller effect, resulting in broadening of the resonances. The utility of the SPARTAN pulse sequence in establishing the spatial proximity of the fluorine nuclei giving rise to these various peaks in the solid solution Ca8.97Sr1.03F2(PO4)6 has been demonstrated, and theoretical calculations based upon modeled chemical shielding tensors have rationalized the mechanism by which spectral spin diffusion can occur. A 23% preference of Sr2+ ions for Ca(2) sites in Ca8.97Sr1.03F2(PO4)6 was also deduced from quantitative intensity measurements in two separate cases, the nearestneighbor case and the next-nearest-neighbor case. The peak assignments and intensities of the spectrum from the Ca4.95Sr5.05F2(PO4)6 sample are also qualitatively consistent with this degree of site preference. The NMR results show the same general preference of the larger Sr2+ ion for the smaller Ca(2) site that has been observed by X-ray diffraction in fluorapatite14 and in hydroxyapatite.10,11 However, this conclusion is at variance with the Ca(1) site preference inferred from EXAFS data on precipitated hydroxyapatite containing trace strontium5 and with much less detailed 19F MAS NMR studies of glass ceramics.6 The highly sensitive 19F MAS NMR approach used in the present work could be applied to precipitated fluorapatite samples containing trace strontium to see whether kinetic effects may be responsible for the apparently different behavior in the former case. Acknowledgment. We are grateful to GTE Electrical Products Corporation for partial financial support of this work. J.P.Y. thanks Drs. Joel Miller and Christopher Klug (NRL) for helpful discussions on spin diffusion and Dr. Miller for

Cho et al. discussions and analyses of spinning sideband patterns. This work was also supported in part by the Office of Naval Research. References and Notes (1) Tycko, R.; Dabbagh, G.; Kurtz, S. R.; Goral, J. P. Phys. ReV. B 1992, 45, 13452. (2) Moran, L. B.; Berkowitz, J. K.; Yesinowski, J. P. Phys. ReV. B 1992, 45, 5347. (3) Yesinowski, J. P. Nuclear Magnetic Resonance Spectroscopy of Calcium Phosphates. In Calcium Phosphates in Biological and Industrial Systems; Amjad, Z., Ed.; Kluwer Academic Publishers: Boston, MA, 1998; pp 103-143. (4) Elliott, J. C. Structure and Chemistry of the Apatites and Other Calcium Orthophosphates; Studies in Inorganic Chemistry 18; Elsevier Science: Amsterdam, 1994. (5) Rokita, E.; Hermes, C.; Nolting, H.-F.; Ryczek, J. J. Cryst. Growth 1993, 130, 543. (6) (a) Hill, R. G.; Stamboulis, A.; Law, R. V.; Clifford, A.; Towler, M. R.; Crowley, C. J. Non-Cryst. Solids 2004, 336, 223. (b) Hill, R. G.; Stamboulis, A.; Law, R. V. J. Dent. 2006, 34, 525. (c) Hill, R.; Calver, A.; Skinner, S.; Stamboulis, A.; Law, R. V. Key Eng. Mater. 2006, 309-311, 305. (7) (a) Hughes, J. M.; Cameron, M.; Crowley, K. D. Am. Mineral. 1991, 76, 1857. (b) Rakovan, J.F.; Hughes, J. M. Can. Mineral. 2000, 38, 839. (8) Handbook of Chemistry and Physics, 57th ed.; Weast, R. C., Ed.; CRC Press, Cleveland, OH, 1976-77. (9) Sudarsanan, K.; Mackie, P. E.; Young, R. A. Mater. Res. Bull. 1972, 7, 1331. (10) Khudolozhkin, V. O.; Urusov, V. S.; Tobelko, K. I. Geochem. Int. 1972, 9, 827. (11) Heijligers, H. J. M.; Driessens, F. C. M.; Verbeeck, R. M. H. Calcif. Tissue Int. 1979, 29, 127. (12) Khudolozkin, V. O.; Urusov, V. S.; Tobelko, K. I. Geochem. Int. 1973, 10, 266. (13) Urusov, V. S.; Khudolozkin, V. O. Geochem. Int. 1974, 11, 1048. (14) Pushcharovskii, D. Y.; Nadezhina, T. N.; Khomyakov, A. P. Kristallografiya 1987, 32, 891; SoV. Phys. Crystallogr. 1987, 32, 524. (15) Sudarsanan, K.; Young, R. A. Acta Crystallogr. 1980, B36, 1525. (16) Cho, G. NMR Investigations of Chemical Shielding, Structure, and Multiple-Quantum Dynamics of Apatites. Ph.D. Thesis, Department of Chemistry, Michigan State University, 1993. (17) Gagarinskii, V.; Gabuda, S. P. Zh. Strukt. Khim. 1970, 11 (5), 955 (Engl. Transl. p 897). (18) Abragam, A. The Principles of Nuclear Magnetism; Oxford University Press: London, 1961; Chapters V and IX. (19) Kubo, A.; McDowell, C. A. J. Chem. Soc., Faraday Trans. 1988, 84, 3713. (20) Raleigh, D. P.; Olejniczak, E. T.; Griffin, R. G. J. Chem. Phys. 1988, 89, 1333. (21) A useful discussion of the various conventions for describing chemical shift tensors can be found at: http://anorganik.uni-tuebingen.de/ klaus/nmr/index.php?p=conventions/conventions; Titled ‘Software Klaus Eichele’, accessed March 19, 2008. (22) Carolan, J. L. Chem. Phys. Lett. 1971, 12, 389. (23) Jameson, C. J. Solid State Nucl. Magn. Reson. 1998, 11, 265. (24) Andrew, E. R. Prog. Nucl. Magn. Reson. Spectrosc. 1972, 8, 1. (25) Clayden, N. J.; Dobson, C. M.; Lian, L. Y.; Smith, D. J. J. Magn. Reson. 1986, 69, 476. (26) Van der Lugt, W.; Caspers, W. J. Physica 1964, 30, 1658. (27) Andrew, E. R.; Bradbury, A.; Eades, R. G.; Wynn, V. T. Phys. Lett. 1963, 4, 99. (28) Takegoshi, K.; Nomura, K.; Terao, T. Chem. Phys. Lett. 1995, 232, 424.