J. CHEM. SOC. FARADAY TRANS., 1994, 90(18), 2653-2662 31P and IH Powder ENDOR and Molecular Orbital Study of a Cog3- -Ion in X-Irradiated Carbonate containing Hydroxyapatitest Peter D. Moens," Freddy J. Callens1 and Paul F. Matthys Laboratory of Crystallography and Study of the Solid State, Krijgslaan 28161, B-9000 Gent, Belgium Ronald M. Verbeeck Laboratory for Analytical Chemistry, Krijgslaan 281612,B-9000 Gent, Belgium An X-irradiated synthetic carbonate-containing apatite powder is examined with EPR and ENDOR. At low micro- wave powers, the room-temperature EPR spectrum contains a major contribution of a signal with g values: g, = 2.0045, gy= 2.0034 and g, = 2.0014. In a related l3C-enriched sample, the radical was shown to exhibit a hyperfine interaction with one carbon nucleus.The l3C hyperfine tensor values are: A, = 263MHz, A,, = 263 MHz and A, = 423 MHz. The radical is assigned to a co33-molecular ion. It is demonstrated by means of CNDO/II and INDO calculations that by lowering the symmetry of the Co,,- ion from C,, to C,, an orthorhombic g tensor can be obtained. However, the deviation from axial symmetry for the 13C hyperfine tensor is so small that it is not measurable on a powder specimen. The thus-calculated spin-Hamiltonian parameters are in very good qualitative and quantitative agreement with the experimental ones, adding strong evidence for the assign- ment of the observed signal to a Co,,-radical. At low temperatures, both 31P and 'H ENDOR spectra are recorded for different settings of the magnetic field (i.e.when the magnetic field is swept through the EPR CO,,- spectrum). By a careful analysis of the ENDOR powder spectra using computer simulations based on the 'orientation-selection ' principle, a detailed model for the C033- ion could be proposed. In this way, it is established unambiguously that the co,3-ion substitutes for a phosphate group in the hydroxyapatite lattice, with a vacancy on the nearest hydroxy-group site. In addition, some deductions can be made about the substitution mechanism according to which the precursor of the COS3- radical (i.e.a carbonate ion) is incorporated into the apatitic lattice. Hydroxyapatite, Ca,o(PO,),(OH),, forms the basic mineral of calcified tissues such as bone, dental enamel and renal stones.These biological apatites, however, contain some impuiity ions among which carbonate is the most important. As tnere exists a correlation between the amount and the location of the carbonate ions in the hydroxyapatite lattice, and the demineralization process of these calcified tissues,'*2 a study of the incorporation of C032-into hydroxyapatite is of value from a medical point of view. Two valuable tools for studying the magnetic properties of carbonate ions located in the apatite lattice are electron para- magnetic resonance (EPR) and electron nuclear double res- onance (ENDOR). However, as both techniques are able to detect only paramagnetic radicals and as the carbonate ion itself is not paramagnetic, the apatite samples have to be irra- diated in order to create paramagnetic species.In the past decades, biological as well as synthetically pre- pared carbonated apatites have been studied intensively with EPR.3-18 After X-or y-irradiation, the EPR spectra observed in the biological apatites consist of an asymmetric signal around g = 2.00. In synthetic apatite powder, not enriched in the isotopes 13C and/or 170, a very similar EPR signal was observed, indicating that related species were formed upon irradiation. Already from the earliest measurements, it became clear that the observed EPR signal was composite, i.e. it consisted of several contributions arising from radicals differing in their molecular structure (0-,03-,CO,-, co33-, ...) and location [hydroxy group (A site), phosphate (B site) and surface site allocation].As the EPR signals of the different radicals overlap considerably, the overall EPR spec- trum is very complex. Deducing the spin-Hamiltonian parameters of the different contributing signals from such ~~ t This paper was presented at the 27th International ESR Con-ference at the University of Wales, Cardiff, 21st-25th March, 1994. ++ Senior Research Associate of the NFSR (Belgium). complex spectra is not a trivial task. It was only very recently that a multivariate statistical method was proposed for ade- quate decomposition of the complex EPR powder spectra observed in X-irradiated carbonated hydroxyapatites. Moreover, the synthetically prepared hydroxyapatite speci- mens offer the possibility of enriching the samples in the iso- topes I3C and/or 170.In this way, valuable information about the identity and the electronic structure of the different paramagnetic species can be obtained. Once the spin-Hamiltonian parameters of the distinct rad- icals are determined, it is in principle possible to deduce the nature of the radicals, e.g. by comparing the experimentally obtained spin-Hamil tonian parameters with those resulting from the literature or from theoretical calculations. That it is not a straightforward task to identify the radicals unam-biguously is illustrated by the contradictory conclusions drawn by several research groups concerning the radical responsible for the most intense and stable signal in both bio- logical and synthetic hydroxyapatites.This radical is charac- terized by the following g values: g, = 2.0030, g, = 1.9970, g, = 2.0015, while the values for the 13C hyperfine tensor are A, = 459 MHz, A, = 445 MHz and A, = 557 MHz. Some authors assigned it to a C0,- radi~al,".'~-'~ while others assigned it to a co33-This ambiguity is radi~al.'*~-~*l~~'~*~~ mainly due to the large isotropic 13C hyperfine interaction, typical for both types of radical. In the present study, a radical with spin-Hamiltonian parameters g, = 2.0045, g, = 2.0034, gz = 2.0014 and I3C hyperfine tensor values A, = 263 MHz, A, = 263 MHz, A, = 423 MHz, is observed in an X-irradiated carbonate- containing synthetic hydroxyapatite specimen.By means of theoretical calculations using two semi-empirical self-consistent field Hartree-Fock methods viz. the CNDO/II and the INDO method,21 the radical will be unambiguously iden- tified as co33-.In order to explain the orthorhombic char- acter of the g tensor, it has to be assumed that the molecular symmetry is lowered from C,, to C,, probably owing to the surrounding hydroxyapatite lattice. As a result of the theo- retical calculations, it will be proven that the stable and intense EPR signal observed in most apatite specimens cannot be identified as a Co,,-radical and hence has to be ascribed to a CO, -radical. Often, the nature of the different radicals is not of prime interest, but rather the location of the carbonate groups in the hydroxyapatite lattice.A way of obtaining such informa- tion is via the location of the paramagnetic centres derived from the carbonate ions upon irradiation. If the correspond- ing EPR signals have appropriate saturation characteristics, the interaction of the radicals with the surrounding nuclei can be studied quite profitably with ENDOR. With this tech- nique, it is, in principle and within certain approximations, possible to determine the type and the location of the inter- acting nucleus in the g tensor axes frame. Hence, detailed information about the environment of the paramagnetic centre can be obtained and thus the location of the species under study can be deduced. Up till now, there have been only a few reported cases where ENDOR was used to probe the location of the carbonate-derived radicals in irradiated hydroxyapatites.Sato7 recorded a structureless proton ENDOR signal in X-irradiated powdered human tooth enamel while monitoring the anisotropic C0,-EPR signal. Van Willigen et al.’ per-formed ENDOR measurements on the CO, -signal observed in human tooth enamel blocks. These authors detected a broad 31Psinglet and a ‘H doublet from which they deduced that the 31P and the ‘H nuclei had to be separated from the paramagnetic centre by at least 0.6 and 0.9 nm, respectively. From this they concluded that the C0,-radical had to be located at the surface of the apatite crystallites. Note that both authors erroneously ascribed the paramagnetic species to a Co,,-radical instead of to the C0,-ion.In two very recent publication^,^^,^^ the well known isotropic signal at g = 2.0007, attributed to CO,-, was investigated with ENDOR in synthetic apatite, synthetic monohydrocalcite and natural calcite (coral). From the ENDOR experiments, it could be deduced that the C0,-radical had to be located in the ‘occluded water’, i.e. a remnant of the aqueous solution from which the samples were precipitated, trapped between the crystallites. In conclusion, only radicals at the surface of the apatite crystallites or in the occluded water have been located with ENDOR so far. No firm evidence has yet been presented for radicals located in the bulk of the apatite crys- tallites, i.e. radicals located at a hydroxy-group site (A site) or at a phosphate site (B site).In this paper, ENDOR evidence will be presented for a CO,,-radical located at a phosphate site, with a vacancy on the nearest hydroxy-group site. Furthermore, we will be able to draw some conclusions about the substitution mechanism according to which the precursor of the Co,,-radical is incorporated into the hydroxyapatite lattice. To our know- ledge, this is the first time that the location of a carbonate-derived radical in the hydroxyapatite lattice has been determined unequivocally. Orientation-selection Principle in Powder ENDOR General Theory The different aspects of EPR powder spectra are well estab- li~hed.~~-,~In powder systems a large number of crystallites are randomly distributed, each crystallite still behaving like a monocrystal. As a result, the main axes of the crystallites (and hence also the molecular axes of the paramagnetic defects) can have any arbitrary orientation with respect to the mag- netic field vector.Although the magnetic field has a constant 3. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 direction in experimental practice, it is more convenient to assume that the magnetic field vector can have any arbitrary orientation in a certain molecular axes frame, the latter remaining fixed. For the cases to be considered in this paper, the electronic Zeeman interaction is the dominant term in the spin Hamiltonian and thus the coordinate system in which the g tensor is diagonal is an appropriate reference system.This is illustrated in Fig. 1. The EPR spectra of polycrystalline materials reflect a ‘powder’ average of all molecular orientations (each molecu- lar orientation being defined by a set of 8 and 4 values) with respect to the applied magnetic field. Every single molecular orientation has one or more contribution to the EPR powder spectrum, depending on the values of MI and M;. This can readily be seen from the following equation which holds for systems with S = 4and is correct to first order: Here, B is the Bohr magneton, A(8,4) is the hyperfine coup- ling of the unpaired electron with a nucleus belonging to the radical and A”(&4) is the hyperfine coupling with the nucleus not part of the paramagnetic species (superhyperfine coupling).g is the effective g value, vEPR is the microwave frequency and h is Planck’s constant. The g and A values are calculated as:27 (3) with a similar expression for the superhyperfine tensor. In eqn. (2) and (3), hi (i = 1-3) denote the direction cosines of the magnetic field vector in the g tensor axes frame. Eqn. (1) together with (2) and (3) indeed reveal that every molecular orientation has several contributions to the EPR powder spectrum. For ENDOR, the situation is different, as during the ENDOR experiment the magnetic field is kept fixed to a certain value. One has to perform the inverse calculation, i.e. to find the molecular orientations that are in resonance for a lgz7I /I n * I 0“ \ i -I I I \ Fig. 1 Definition of the different polar angles describing the mag- netic field vector and the direction of the interacting nucleus in the g tensor axes frame J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 given value of B,,,. The sets of (8, 4) values corresponding to for the superhyperfine tensors), the field direction [h,, h, , h3] a B,,, value can be calculated using a computer. In this way, and the field magnitude B,, as well as on the position of the it becomes clear that the applied magnetic field makes a8, (I,tensor axes frame gnucleus in the and t#)N, see Fig. 1). selection in the molecular orientations contributing to the ENDOR spectrum. The 'orientation-selection' principle was first suggested by Rist and Hyde28 and forms the basis of the interpretation of powder ENDOR spectra.Once the molecular orientations, selected by a given mag- netic field value, are determined, the nuclear resonance fre- quencies can be calculated. To first order, one has:27 ~VNM, = K(Ms) (4) with and PN and gN denote the nuclear magneton and the nuclear g factor (assumed to be isotropic), respectively. B, is the reson- ance field value and Ms the electronic quantum number. In powder ENDOR, usually the superhyperfine interaction is of interest. Hence, one has to use the tensor A" in eqn. (5). The matrix A" is the sum of the isotropic (A:,,) and the aniso- tropic superhyperfine interactions (A:). Assuming that the anisotropic interaction between the electron and nuclear spins is governed by a pure dipole-dipole interaction, one can write : where = & 47r (y) is a constant for each type of nucleus (3'P, 16.02 MHz; 'H, 39.78 MHz). ri (i = 1-3) denote the direction cosines describ- ing the direction of the interacting nucleus in the g tensor axes from (rl = cos 4Nsin ON, r2 = sin 4Nsin ON, r3 = cos ON), see also Fig.1. The distance between the nuclear and electron spins is r. When the g tensor anisotropy is small compared with the average g value, the electron and nuclear spins are quantized nearly along the same direction (the direction of the applied field) and hence eqn. (7) simplifies to: SUNA"(y) = -(3 cos2 y -1) + AYSOr3 y being the angle between the direction of the applied mag- netic field and the direction connecting the electron and nuclear spins.The final expression for the ENDOR frequencies is obtained by substituting eqn. (5) and (6)in eqn. (4).By doing so, one obtains in frequency units: with bN gN BOv, = -h Eqn. (9) shows that the ENDOR frequencies depend on the electronic g values, the type of nucleus (aNin the expressions As both B, and [h,, h,, h3] vary when the magnetic field is swept through the EPR powder spectrum, the ENDOR fre- quencies will also vary with the magnetic field. As the ENDOR frequencies depend on the position and type of the interacting nucleus, they give information not only on the electronic but also on the geometrical structure of the species studied. This method is called 'ENDOR crystallography' and is based entirely on the assumption that the anisotropic hyperfine coupling is purely dipolar.,' In many cases, the interacting nuclei are located far away from the paramagnetic centre and hence the dipolar inter- action becomes small. When it becomes smaller than the ENDOR linewidth, the ENDOR spectrum will consist of one or more isotropic resonances centred around the nuclear Zeeman frequency, depending on whether an isotropic hyper- fine splitting is present or not.This phenomenon is called distant ENDOR.30 A more profound outline of the theory of powder ENDOR can be found in the articles of Hoffman et ul.,31,32Hurst et ~l.,~~Henderson et and Greiner et u1.35,36as well as in the recent review article of Huttermann.37 From this point, we will consider only the cases relevant for this paper: systems with very small g tensor anisotropy [(gl -g3)/gavd O.OOl] exhibiting only superhyperfine interaction (and no hyperfine interaction).The ENDOR powder spectra observed in such systems were discussed in some detail by Moen~.~~ In the following two paragraphs, a short outline will be given of the methodology for analysing ENDOR powder spectra of species with very small g tensor anisotropy. The computer program for simulating ENDOR powder spectra will be discussed below. Systems with an Axial g Tensor When dealing with systems with an axial g tensor, the direc- tion of the magnetic field vector in the g tensor axes frame is determined only by the polar angle 8.Thus, when the mag- netic field has a value B(8), only those crystallites for which the angle between the direction of the applied magnetic field and the gllaxis is equal to 8, will be in resonance. For some field positions, one obtains 'single crystal-like' ENDOR powder spectra, comparable to those of an oriented single crystal. The angle 8 can easily be calculated using the follow- ing equation : with where B, is the magnitude of the applied magnetic field. When the g tensor anisotropy is small compared with the average g value, the difference between eqn. (7) and (8) is neg- ligible and hence, eqn. (8) can be applied to obtain good initial estimates for Aiso, r and 8,. Indeed, from eqn. (8), it follows that the largest splitting is found when the magnetic field vector is parallel to the axis connecting the electron and nucleus (y = 0O)assuming A:,~z O or A:,, < O and geaN/r3z I 2AYsOI.In this way, an estimate for 8, can be obtained using eqn. (11): the field value for which the largest splitting is found in the ENDOR powder spectrum gives the value for 8, (as 8 = 8, when the magnetic field is parallel to the axis con- necting the interacting nucleus and the paramagnetic radical). From eqn. (8), it follows that: gaNy = 0"-+ Av1 = AFs0+ 2 -r3 (13) gaNy = 90" +Av, = AEo --r3 or Avl + 2Av,A? 3 (1 5)1so = where Avl is the splitting measured in the ENDOR powder spectrum corresponding to y = o",whereas Av2 is the split- ting corresponding to y = 90".The two unknown variables Arso and r can be readily obtained from eqn. (15) and (16). The signs of the splittings, however, are not a priori known: they have to be determined using simulation^.^^ When A:& < 0 and g, aN/r3< I2ArS01, the largest splitting is observed for y = 90" corresponding to the situation in which the largest splitting is measured along the direction perpendicular to the axis connecting the electron and the nucleus. However, cases with such large negative Aim values have not occurred so far in the literature. The values for the parameters A&,, r and 8, obtained using the method described above are used as initial estimates in the simulation of the ENDOR powder spectra, using a self- written computer program (see below).By varying the three parameters independently and comparing the simulated spectra with the experimental ones, the set of parameters giving the best agreement between experimental and simu- lated spectra, for all field settings, are retained as the real ones. Systems with an Orthorhombic g Tensor In systems with an orthorhombic g tensor, the 4 and 4N angles are also relevant. In cases with a small g tensor anisot- ropy, however, it has been shown that one can still determine rough initial estimates for the parameters Aiso, r and 8, by assuming an axial g tensor.38 The thus-obtained values, together with the 4, parameter then have to be optimized by an iterative procedure. In the simulations, of course, an orthorhombic g tensor is used.Powder ENDOR Simulation (PENSI) Program In order to simulate ENDOR powder spectra for systems with S = 4,I = 0 and I" = 4, a program was developed using the formulae given above. The input parameters include the frequencies, v1 and v,, between which the ENDOR powder spectra will be calculated, the spectral resolution, Av, the principal g tensor values, the position and the type of the interacting nucleus in the g tensor axis frame (r, ON, &), the isotropic superhyperfine splitting, the homogeneous EPR linewidth, rEpR, the ENDOR linewidth, rEND, and the lineshape (Lorentzian or Gaussian). Then, eqn. (1) is calculated for 0 < 8 < 71 and 0 d # < 271. All the thus-calculated B values (two for each molecular orientation) are stored in the matrices BREsland BREs2 of which the column and the row numbers correspond to the values of 8 and 4, respectively. The field value, B,,,, for which the ENDOR powder spec- trum has to be calculated, is used as an input parameter, assuming that vE~R= 9.47 GHz. Using the homogeneous EPR linewidth as the FWHM, a Lorentzian is constructed J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 with mean B,,,. All the elements of the matrices BREs1 and BRES2 are weighted with this Lorentzian and are given a cor- responding amplitude. Only the sets of orientations, (8, 4),, for which the amplitude is greater than or equal to 0.05, are retained. For the sets of molecular orientations (8, 4), thus selected, the ENDOR frequencies are calculated using eqn.(9), making use of eqn. (7) for the superhyperfine coupling (thus allowing for orthorhombic g tensors). Centred on these resonance fre- quencies, a lineshape (Lorentzian or Gaussian) is placed with linewidth rEND. The final ENDOR powder spectrum is obtained by summing up all of the calculated ENDOR spectra for the selected molecular orientations with their cor- responding weight factor. Finally, the ENDOR powder spec- trum is displayed and can be stored on disk. If applicable, another ENDOR powder spectrum can be calculated for another field value with the same input parameters. In this way, the matrices BREs1 and BREs2 need not to be calculated afresh. The PENSI program was run on an HP-Apollo 423 work- station. The calculation of one ENDOR powder spectrum for typically 200 abscissa points takes ca.5 min. Materials and Methods Materials The sample studied in this paper was prepared according to .~the method originally proposed by Legeros et ~ 1 According ~ to this method lg of commercial Mallinckrodt AR grade monetite, CaHPO,, was hydrolysed in 1 1 of Na,CO, solu-tion (0.250 mol 1-') at 95"C.15-17 The suspension was con- tinuously and thoroughly stirred for 5 h, and precautions were taken to prevent CO, contamination from the atmo- sphere. The precipitate was then filtered off and washed thor- oughly with hot distilled water. After drying at 400 "C under vacuum until constant weight, the solid was analysed for its Ca, P and CO, content.Calcium was determined by com- plexometric titration with EDTA after separation of the phosphate. Phosphorus was analysed as phosphate using a slight modification of the spectrophotometric method of Brabson et aL4' Carbonate was determined by coulometric titration of the CO, evolved from an acidified aqueous solu- tion of the apatite. The sample contained 35.64 (kO.07) wt.% Ca, 12.38 (k0.02) wt.% P, 4.11 (k0.02) wt.% Na and 21.0 (&0.4) wt.% CO, . The X-ray diffraction pattern and the IR spectrum show sharp and well resolved peaks, characteristic of crystalline solids. The X-ray pattern is typical of an apatite, and no extraneous peaks other than for apatitic could be found. In the IR spectrum, absorptions around 872 (k0.8),1417 (k2.5) and 1470 (f4.7) cm-' indicate that the CO,,- ions occupy Po4,-lattice sites (B-type CO,),.Methods The EPR spectra were recorded using a Bruker ESP300 X-band spectrometer, with a maximum power of 200 mW. The magnetic field was modulated at 100 kHz with a peak-to-peak amplitude of 0.5 x lop4 T. All of the EPR spectra were normalized to the same frequency, i.e. 9.47 GHz, and hence can be directly compared. The magnetic field was measured using a Bruker NMR035M Gaussmeter. With this equipment it is possible to measure accurately the relative positions of the EPR signals present. Small shifts in the magnetic field positions down to 0.1 x T can be detected. For absolute g value determi- nation, a calibration using the g standard DPPH at 0.1 mW (g = 2.0036) was performed.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 ENDOR spectra were recorded on the same spectrometer equipped with a Bruker ESP353E ENDOR/TRIPLE exten- sion (EN374 RF amplifier with a maximum power of 200 W, EN525 Schomandl synthesizer and an ER033M field-frequency lock unit). The best ENDOR signals were obtained with a microwave power of 0.2mW (27 dB) and 200 W radio frequency (RF) power (0 dB). The modulation depth was set to l00kHz and ten scans of 81 s each were run for each ENDOR spectrum. The irradiation of the sample was performed using a tung- sten anti-cathode Philips X-ray tube, operated at 60 kV and 40 mA, for 10 min, which corresponds to a dose of 13.2 kGy.Experimental Results EPR Results The sample studied in this paper was originally part of a series of ten samples, each having a different carbonate content (ranging from 8.12 to 21.0 wt.%). After X-irradiation, the samples exhibit strong resonances in the region around g = 2.00.'5-17 At low microwave powers (P < 0.1 mW), it has been shown that the observed EPR peaks exhibit contri- butions of several ~igna1s.l~ The two most important ones were labelled Z1 and A2'. The contribution to the overall 'low-power" spectra of the Z1 and A2' signals increases with increasing carbonate content of the samples as does the 21 : A2' ratio. As the sample studied in this paper has an extremely high carbonate content (21.0 wt.%), the low-power EPR spectrum exhibits mainly a contribution of the Z1 signal, with a small contamination of the A2' signal.Fig. 2 shows the EPR spectrum recorded at 0.01 mW, in which the Z1 and A2' signals are indicated. For the purpose of this paper, only the Z1 signal is of inter- est and hence we will restrict ourselves to this signal. The g values of the Z1 signal are obtained from a spectral decom- position of the observed 12C EPR spectra.17 The 13C hyper- fine tensor is obtained from a least-squares fit of the signal observed in a 13C-enriched ~amp1e.l~ In this way, one obtains: g, = 2.0045, gy = 2.0034, g, = 2.0014, A, = 263 MHz, A = 263 MHz and A, = 423 MHz. The computer fits of the 15C and 13C lineshapes are shown in Fig. 3 and 4, respectively.The Z1 signal remains visible down to 4 K, whereas the A2' signal is visible only at temperatures >50 K. In this way, the Z1 signal is found to be quite isolated at low temperatures. ". \\ 3370 3390 t3/10-4 T Fig 3 Computer fitting of the "C lineshape of the Z1 signal" ENDOR Results In order to obtain sufficient microwave saturation, the speci- men has to be cooled. The ENDOR resonances are visible from 4 K up to 80 K, with an optimum detection tem-perature of 8 K. Fortunately, at 8 K, the EPR powder spec- trum is not composite, i.e. only the Z1 signal contributes to the spectrum. In this way, it is ensured that the ENDOR res- onances are due to only one paramagnetic species. A typical ENDOR spectrum is shown in Fig. 5.As can be seen from this figure, the ENDOR spectrum consists of three peaks, centred around the nuclear Zeeman frequency of 3260 3510 q10-4 T Fig. 4 Computer fitting of the 3C lineshape of the Z1 signal" A2' iI,J , , , 0 3 0 1 20 t3/10-~T v/MHz 0.01 mW EPR spectrum recorded at room temperature. The Fig. 5 Typical ENDOR powder spectrum recorded at 8 K. For the different components are indicated in the figure. experimental conditions, see text. 23Na,31Pand 'H, respectively. ENDOR powder spectra are recorded for nine different magnetic field settings within the EPR powder envelope. It transpired that the 23Na hyperfine interaction is too small for discussion. Hence, only the angular variations of the 31P and the 'H interactions are studied in detail.' P Interaction Fig. 6 shows the angular variation of the 31Pinteraction. The most prominent feature is the broad and intense line centred on the nuclear Zeeman frequency of 31Pand which is assign- ed to the distant ENDOR signal. Fortunately, two small doublets (indicated by 1 and 2 in the figure) are also observed. We will confine our attention to these two doub- lets. The resonances of doublet 1 exhibit the largest splitting for g = 2.0043 (xgx). The splitting decreases only slightly with increasing g value and the smallest splitting is observed for g = 2.0018 (x9,). Following the procedure described above, Av, can be estimated from the ENDOR powder spec- trum at g = 2.0043 (largest splitting corresponding to y = 0), whereas Av, is obtained from the spectrum at g = 2.0018.Using an axial approximation for the g tensor (gl= 2.0045, g,, = 2.0014), one obtains 8,= 90", r = 0.40 nm and A:, = J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 g= 2.0024 5 7 v/M Hz Fig. 7 Theoretical angular variation for the resonances of doublet 1. For the values of the different parameters used in the simulation, see text. MHz, r = 0.49 (0.02) nm, 8, = 25" (k20").The value for 4, has almost no effect on the simulated spectra. The values of the other parameters are the same as those used in the simu- -0.23 MHz. The 4, value cannot be estimated from the lation of the resonances of doublet 1. The simulated spectra are shown in Fig. 9.experimental spectra.Using these values as input parameters in the PENS1 program, the following results were obtained The rather broad ENDOR lines of both doublets 1 and 2 suggest that several, not completely equivalent nuclei contrib- ute to the ENDOR spectrum. after some iterations: Ai, = -0.22 (L0.02) MHz, r = 0.39 + 90" ( fSo) and 4, = 30" (& lo"),rEPR= 0.5( f0.01)nm,8, x lov4T and rEND = 60 kHz. The theoretical angular varia- tion thus obtained, is shown in Fig. 7. From this figure, it can 'H Interactionbe seen that more than two resonances are present. The two outer (and strongest) resonances have the same dependence In contrast to the ENDOR spectra of the 31Pinteraction, the 'H resonances do not exhibit any resolvable anisotropic on the selected field value as the resonances of doublet 1; the other resonances are most probably obscured by the matrix ENDOR signal.Fig. 8 shows the experimental ENDOR powder spectra together with the simulated ones for three different field set- tings. The agreement between theory and experiment i.e. the reproduction of the resonance positions and intensities is satisfactory. The resonances of doublet 2 allow only a qualitative description as they are largely hidden under the matrix ENDOR signal. They become visible at g x 2.0034. The largest splitting is observed for g x 2.0025, corresponding to 8, x 30" (in an axial approximation for the g tensor). The fact that the angular variation cannot be followed completely results in an only roughly determined 8,.The value for 4N cannot be estimated at all. The spectra for doublet 2 are best simulated using the following parameters: Aiso= -0.1 (k0.1) 5 7 v/MHz v/M Hz Fig. 8 Comparison between the experimental and simulated 31P Fig. 6 Angular variation of the 31Phyperfine interaction. The ENDOR powder spectra for the resonances of doublet 1, for three doublets 1 and 2 are indicated in the figure. different magnetic-field settings J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 CT 0 n zw v/M Hz Fig. 9 Theoretical angular variation for the resonances of doublet 2. For the values of the different parameters used in the simulation, see text. hyperfine interaction. This is depicted in Fig. 10, where the two ENDOR spectra recorded for different magnetic field values are shown.The linewidth of the 'H ENDOR reson- ances is 140 kHz. As no anisotropic hyperfine splitting is observed (although carefully searched for), it has to be con- cluded that the splitting is smaller than the observed ENDOR linewidth. In this way, the distance between the paramagnetic centre and the nearest proton can be estimated to be at least 0.8 nm. Discussion The two most important features to be discussed are the nature and the site allocation of the Z1 radical. They will be treated separately. I%I i Y Y.LL 1 13 16 v/M Hz Fig. 10 'H interaction measured for the Z1 signal for two different magnetic-field settings at 8 K Nature of the Observed Species The EPR results reveal that the Z1 signal exhibits hyperfine interaction with one carbon nucleus and hence, the radical responsible for the observed signal must contain one carbon atom.Possible candidates are CO-, CO,-, CO,-and CO,, -molecular ions. The large isotropic 13C hyperfine interaction (Aiso= 316.3 MHz) excludes the CO,- ion, as this ion is characterized by a very small (and negative) 13C iso- tropic hyperfine value (Ais,,z -40 MHz).~'-~, On the same basis, the CO- ion can be excluded.44 Both the C0,- and Co3,-ions have large isotropic 13C hyperfine coupling con- stants and thus can be assigned to the Z1 radical. The free Co,,-ion has a pyramidal structure with C,, symmetry exhibiting axial spin-Hamiltonian parameter^.^^.^' Theoreti-cally, both the gL and the gll values should be larger than ge, with gL > glr,whereas for the 13C hyperfine tensor All > A,.However the C0,- ion has C,, symmetry giving rise to orthorhombic g and A tensor^.^'-^* The C0,- ion has very characteristic principal g tensor values, with gy z 1.997 (corresponding with the 0-0 axis). Because all g tensor values of the Z1 radical are quite dif- ferent from 1.997, this radical cannot be attributed to a C0,- ion. Thus, only the Co,,- ion is left as a possible candidate. The axial I3C hyperfine tensor strengthens this hypothesis. However, the Z1 radical exhibits an orthorhombic g tensor with one g tensor value somewhat lower than g,, in contrast with what would be expected. In order to elucidate this matter, theoretical calculations using two semi-empirical self-consistent field Hartree-Fock methods, viz.the CNDO/II and the INDO methods, were performed for the co33-molecular ion. The CNINDO program of Pople and Beveridge,' was adapted in order to calculate the g and A tensors. Only the I3C hyperfine tensor is reproduced as there are no experimental data available for the I7O hyperfine tensor. The g values are calculated using Stone's formula.49 In the theoretical calculations, three struc- tural parameters are varied independently: (1) the bond dis- tance, d, between the central carbon atom and the three oxygen atoms; (2) the distance, dl, between the carbon atom and the plane defined by the three oxygen atoms; (3) the bond angle, a,between two of the oxygen atoms [O(l) and 0(2)]. By varying a, the symmetry of the Co,,- ion is lowered from C,, to C,.The convention of the different molecular axes for the co,3-ion is as follows: the z axis is perpendicular to the plane of the three oxygen atoms, the y axis connects the two equivalent oxygen atoms (making an angle a), the x axis is perpendicular to both the y and the z axes. The results of the theoretical calculations are sum-marized in Table 1. Note that lowering the symmetry of the Co,,-ion from C,, to C, changes the g and A tensors from axial to orthorhombic. One principal g tensor value is around 2.0045, while the gy can vary between 2.0032 and 2.0043. However, the g, is somewhat lower than ge. On the other hand, the deviations from axial symmetry for the 13C Table 1 Results of the CNDO/II and INDO calculations for the C0,3- ion CNDO/II INDO 2.0045 (2.0041, 2.0046) 2.0044 2.0041 (2.0043, 2.0035) 2.0037 2.0022 (2.0023, 2.0020) 2.0020 286.9 (215, 485) 332.0 -52.0 (-44,-55) -56.5 -52.2 (-44,-55) -56.7 104.2 (88, 110) 113.2 Z1 radical (2.0042, 2.0046) 2.0045 (2.0042, 2.0032) 2.0034 (2.0023, 2.0016) 2.00 14 (216, 566) 316.0 (-60, -48) -53.0 (-60, -48) -53.0 (120, 92) 106.0 ~~ ~~ ~~ ~~~~ The geometry used in the calculations is: d = 0.1 19 nm, d, = 0.006 nm and a = 112" for CNDO/II; d = 0.1 14 nm, d, = 0.005 nm and a = 112" for INDO.The values in parenthese denote the limits between which the spin-Hamiltonian parameters vary when the molecular geometry is varied within the following regions: d, 0.110-0.121 nm; d,, 0.003-0.007 nm; c1, 110"-118" for CNDO/II; d, 0.110-0.1 15 nm; d,, 0.004-0.01 nm; a, 110"-118" for INDO.The hyperfine parameters are in MHz. 2660 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 \-*--@ \ \ @\ \ @--+--@ Q \ Q ances of doublet 1. The two NN 31P nuclei are situated in the mirror plane above and the mirror plane below the mirror plane in which the carbon nucleus of the co33-radical is situated (further indicated by the Co,,- mirror plane). The plane of the three oxygen atoms of the Co,,- radical (further denoted as the molecular plane) is oriented parallel with the hexagonal c axis of the hydroxyapatite crystallite, such that the two NN 31Pare lying in the molecular plane.The gx axis is assumed to be parallel with the hexagonal c 8, axis of the hydroxyapatite. In this way, the NN 31P nuclei is 90°, whereas the 4, angles for these two angle for the \ equivalent nuclei are ca. 30". All these data agree very well with the experimental ENDOR results for doublet 1. This model is depicted in Fig. 11. The eight next nearest neighbour (NNN) 31P nuclei are all situated at a distance of ca. 0.5nm:" four are situated in the co,3-mirror plane, two are situated in the mirror plane below and two in the mirror plane above the CO,,- mirror plane. The angles between the axis connecting the paramagnetic species and the distinct sur- rounding nuclei, and the gz axis of the co33-ion, vary between 10" and 50" for the different NNN nuclei when the above model for the co,3-is considered (see Fig.11). These data agree well with the data of doublet 2. The NN and the NNN 'P nuclei are indicated in Fig. 11 with indices 1 and 2, respectively. In view of the model described above, the NN 'H nucleus would have to be located at a distance of 0.35 nm, in contra- diction with the experimental ENDOR data. Moreover, the NNN protons, located at 0.50 nm, also seem to be removed. The question remains whether the hydroxy-group sites are occupied by vacancies or by carbonate ions (A-type carbonate). However, as no IR evidence is present for A-type carbonate ions in this ample,^' the hydroxy-group sites are probably occupied by vacancies.The 'H ENDOR data will be discussed in more detail in the next section. The ,'P ENDOR data strongly suggest a B-site allocation for the C0,3-ion. An A-site allocation for the radical can be ruled out as, in this case, the NN ,'P should be located at 0.35 nm," too small compared with the distance of 0.39 nm determined experimentally. In the case of an A-type ion, the NN 'H nuclei should be located at 0.34 nm. In addition, a strong correlation between the intensity of the EPR Z1 signal and the integrated IR absorption at 873 cm-' (typical for B-type carbonate), was observed in a series of related samples." Hence, the Z1 Co3,-radical is located at a B site, substituting for a phosphate group. The positions of the NN protons, however, still remain to be elucidated.Substitution Mechanism of the Precursor of the Coj3-Radical Returning to the basic question, viz. the location of the car- bonate ions and how the latter are incorporated in the hydroxyapatite lattice, one has to try to establish a corre-lation between a certain suggested substitution mechanism for the carbonate ions and the signal height of a certain EPR signal in a series of related samples. In our case, the Z1 signal is attributed to a B-type radical, and hence, we have to look for substitution mechanisms accounting for B-type substitut- ions. A possible mechanism is the one originally suggested by Labarthe et al. :52 Ca2+ +PO4,-+OH--V, +C03'-+V,, V, denotes a vacancy on an x site.According to this mecha- nism, one Po4,-ion is substituted by one C0,2- ion, with the loss of a Ca2+ and an OH- from the immediate vicinity. This situation is depicted in Fig. 11, i.e. a B-type radical with a vacancy on a Ca2+-OH- site. Furthermore, as the sample \ t3 Q\ o @OH c OP(Z=-~/~) 1/4, Z=3/4)~P(z= Fig. 11 Model of the C033-radical in the hydroxyapatite lattice. The nuclei with z = t are situated in the C033-mirror plane, whereas the nuclei with z = -iand z = $ are lying in the mirror planes below and above the C0,3-mirror plane, respectively. hyperfine tensor are so small that they are not measurable for powder systems. All these observations are in very good agreement with the experimental data, qualitatively and even quantitatively.Hence there can be no doubt about the nature of the Z1 radical, i.e. it is a co,3-radical. The distortion from C,, to C, symmetry most probably arises from the sur- rounding hydroxyapatite lattice. Consequently it is evident that the intense and stable EPR signal observed in X-irradiated human tooth enamel (with one g value of 1.997)cannot possibly be ascribed to a co33-radical, but has to be identified with a C0,- ion. However, many authors have made the wrong assignment. Site Allocation of the Paramagnetic Species Whereas the nature of the paramagnetic radical results from the EPR measurements, the location of the co,3-radical can be deduced from the ENDOR data. A detailed descrip- tion of the crystal structure of hydroxyapatite is given by Kay et al.O In our opinion, the ENDOR data can be explained only when the Co,,-ion is located at a B site, i.e. substituting for a phosphate group, since the distance from a B site radical to the nearest neighbour, (NN) phosphorus nuclei is 0.40 nm, as was derived from neutron diffraction experiments," com-pared with 0.39 nm determined experimentally for the reson- 1.E Y J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 studied in this paper has a large amount of carbonate ions, relative to the number of phosphate groups (for this sample, the ratio is ca. 1 : lS1),it is highly probable that one or more of the six phosphate ions situated around the hexagonal c axis in the mirror planes above and below the CO,,-mirror plane are also substituted by a carbonate ion with the accom- panying creation of a vacancy on a hydroxy-group site.In this way, the nearest proton can be located far from the para- magnetic centre (r > 0.84nm), in agreement with the experi- mental data. In addition, a detailed physical and chemical analysis of a series of related samples revealed that the B-type carbonate ions were mainly incorporated by means of the above-mentioned substitution mechani~m.~ Fig. 12 shows the contribution of the above-mentioned mechanism (as determined from the chemical analysis) plotted against the amplitude of the Zl EPR signal for a series of related samples, showing a positive correlation. Hence, it has to be concluded that the CO,,-ion is located on a B site with a vacancy on the NN hydroxy-group site.Conclusion The EPR signal observed in an X-irradiated synthetic car- bonate containing hydroxyapatite powder is assigned to a CO,,-molecular ion. This defect is characterized by the fol- lowing g tensor, g, = 2.0045, g,, = 2.0034, g, = 2.0014, and 13C hyperfine coupling tensor, A, = 263 MHz, A, = 263 MHz, A, = 423 MHz. The co,3-ion normally exhibits C,, symmetry and hence should have axially symmetric spin- Hamiltonian parameters. However, by lowering the sym- metry of the Co,,-radical from C,, to C,, an orthorhombic g tensor can be obtained, whereas the deviation from axial symmetry for the hyperfine tensor is negligible. The spin- Hamiltonian parameters of a deformed Co,,-ion with low symmetry were calculated using both the CNDO/II and the INDO methods, yielding results in very good qualitative and even quantitative agreement with the experimental findings.The lowering of the symmetry of the molecular ion most probably results from the incorporation of the radical in the hydroxyapatite lattice. In order to establish the site allocation of the Co,,-ion in the hydroxyapatite lattice, ENDOR studies were performed. At low temperatures, ENDOR resonances due to interactions with 23Na, ,'P and 'H nuclei were observed. The experimen- tal ,'P powder ENDOR spectra could be interpreted in terms of two sets of nuclei; the interactions with the NN as well as with the NNN phosphorus nuclei were resolved. 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