J. CHEM. SOC. FARADAY TRANS., 1994, 90(11), 1501-1506 Normal and Anomalous Positronium States in Ionic and Molecular Solids investigated via Magnetic Field Effects T. Goworek,? A. Badia and G. Duplatre" Laboratoire de Chimie Nucleaire, CNRS/lN2P3 and Universite Louis Pasteur, Centre de Recherches Nucleaires, B.P.20,67037Strasbourg Cedex 2,France ~ ~~~ An external magnetic field (B) is applied in positron lifetime spectroscopy and Doppler broadening (DBARL) experiments to derive information on the positronium (Ps) state in solid matrices. The solids investigated are thorium phosphate and a molecular matrix, p-terphenyl, doped with either 0.5% anthracene or 1.5% chrysene to produce extrinsic defects of sufficient concentration and size to allow Ps formation. In thorium phosphate at zero field, the triplet Ps (0-Ps) pick-off lifetime is short (700 ps), reflecting annihilation in rather small (0.105 nm) free volumes of the lattice.This lifetime rises to 1160 and 1440 ps in p-terphenyl doped with pyrene and anthracene, respectively, reflecting annihilation in microvoids of 0.19-0.23 nm radius, which corresponds roughly to the size of a naphthalene molecule. The variations of the parameter R and of the 0-Ps (rn = 0) magnetic substrate lifetime with B in thorium phosphate are 'anomalous', requiring the use of two fitting parameters. The first parameter is the contact density affecting the hyperfine splitting, with a low value (q = 0.22) denoting an expand- ed Ps wavefunction. For the second fitting parameter, two possibilities exist: either a contact density affecting the Ps singlet state (p-Ps) lifetime, q' = 0.36, distinct from q, or a p-Ps pick-off lifetime (390ps) different from that of 0-Ps (700 ps).Analysis of the DBARL data shows that the second hypothesis is unlikely. By contrast, the magnetic field effects in doped p-terphenyl are 'normal', with a single fitting parameter, q = 0.80and 0.83,for anthracene and pyrene as dopants, respectively. After penetrating matter, the positron (e') can form a bound state with one of the electrons (e-) it has released by ionis- ation of the medium at the end of its track.' This bound state, positronium (Ps), possesses two spin states, triplet (ortho-positronium, 0-Ps) and singlet (para-positronium, p-Ps) . In matter, the positron in the latter state is annihilated essentially with its bound electron, in an intrinsic mode, while in the case of 0-Ps it is annihilated mainly in an extrinsic mode, termed 'pick-off ',with an electron from the surround- ing molecules.Positronium has been increasingly used during the past decade as a probe for determining various physico- chemical properties of matter.' In solids, and more specifi- cally in molecular solids, Ps appears to be a unique tool for investigating defects, whether intrinsic or not. Therefore, a quantitative expression has been established,'*2 correlating the 0-Ps lifetime with the size of those microvoids of the solid matrix in which 0-Ps is annihilated. The relative amount, or intensity, of 0-Ps formed is most generally correlated to the concentration of defects: no Ps is formed in solids where no free spaces are present, or if these are too small. Fruitful applications of Ps as a probe demand a good knowledge of its properties.These are most commonly assessed by using positron annihilation lifetime spectroscopy (LS), which delivers the lifetimes and intensities of the various positron states. To complement this, angular correlation or Doppler broadening of the annihilation radiation lineshape (DBARL) techniques give access to the intensities of the posi- tron states and to the momentum distributions of the annihi- lating e+/e- pairs, which also depend on the immediate surroundings of e+ and Ps. Combining these two classes of independent techniques (e.g.LS and DBARL) is very impor- tant to characterize the various processes in Ps chemistry, particularly regarding the reactions of solutes involved either at the moment of Ps formation or thereafter.3 However, the information derived from these techniques may not be suffi- cient. Therefore, many properties of Ps have remained poorly known, such as the triplet to singlet formation ratio, the p-Ps t On leave of absence from Instytut Fizyki UMCS, Lublin, Poland. pick-off process and the existence of excited or distorted Ps states. A convenient way to gain information on the Ps wave-function, and thereby shed some light on the above unknowns, is to apply an external magnetic field (B).3The mixing of the rn = 0 substates of Ps induced by B provokes changes in the LS spectra that can be analysed and quantified through equations involving the contact density parameter (q)which expresses the electron density, I $(0)12,at the posi- tron in matter (subscript m) with respect to that in vacuum (subscript v; q = 1 in vacuo): This density influences both the value of the hyperfine split- ting, AE, and the decay rate constants of p-Ps (A:) and o-Ps (A:), in the absence of magnetic field.However, if excited states of Ps are present (L # 0), with non-spherical wavefunc- tions, the contact density parameter affecting AE can be dif- ferent from that affecting the As (denoted v'):~ (3) A; = q2, + Ap3 % Ap3 (4) where As = 8 and At = 0.007 ns-' are the intrinsic p-Ps and 0-Ps decay rate constants, respectively; Apl and Lp3 are the pick-off decay rate constants for p-Ps and 0-Ps, respectively which are usually considered to be the same.In the pure liquids studied up to now, whether polar or non-polar, Ps appears to behave normally, with 0.6 < q < 1, which corresponds to a Ps atom that is slightly swollen com- pared with its size in vacu~m.~?~ In solids, in contrast, the results are complex. In many mat rice^,^-^ ranging from ionic KC1, with a rather short 0-Ps lifetime (ri = 0.68 ns),' to molecular octadecane (T: = 1.5 n~)~and polymeric Teflon, with a long 0-Ps lifetime (r: = 4.15 ns),8 the contact density parameter has values similar to those in liquids. However, in a variety of solids, strongly anomalous variations in the LS parameters are observed, particularly at low B, which have been quantitatively described and explained in various ways.Therefore, in a series of polymers, the data are interpreted by supposing that there exist two types of Ps atoms in the solid, presumably corresponding to two different sites or regions of the lattice^:^" the 'normal' type, with q > 0.6, gives a contri- bution ranging from about 100% in Teflon' down to 65% in terfane;8 while the 'anomalous' species is strongly affected by B, with q as low as 0.1 and even 0.05, in isotactic poly- pr~pylene.~In naphthalene, fitting of the data requires the use of two distinct, rather low contact density parameters, affecting the hyperfine splitting and the intrinsic decay rate constant, respectively.lo Finally, whereas quite normal q values are found in some polycrystalline organic scintil- lators," much stronger magnetic field effects are observed in others,12 which are not quantified and are tentatively explained by the interaction of the nascent Ps atoms with the magnetic moments of radiolytic species produced in the posi- tron spur. Note that the role of the contact density parameters, q and q', is not restricted to magnetic field effects.Together with A,,, they intervene in the expression of the p-Ps decay rate constant in matter, eqn. (3), and therefore in the expressions for the various intensities ; consequently, they should affect the experimental results of all positron annihilation tech- niques : LS, DBARL, three-quantum annihilation, etc.Note that the increase in p-Ps lifetime implicit in eqn. (3) for q' < 1 was never observed experimentally. Considering that the factors governing the above parameters are far from under- stood, and the complete lack of an experimental estimate of Apl, the aim of this paper is to gain more information of Ps behaviour, via magnetic field effects, in a variety of solid matrices. These include an ionic compound in which the pick-off lifetime is expected to be short, and molecular com- pounds, previously studied in the absence of field,l3?l4 doped with smaller molecules in order to produce extrinsic defects of sufficient concentration and size to allow Ps formation and reasonably long pick-off lifetimes ; thorium phosphate, for which preliminary results have been presented at the last Positron and Positronium Chemistry Workshop (PPC4)l and p-terphenyl doped with either 0.5 wt.% anthracene or 1.5 wt.% chrysene.To derive more detailed information, both LS and DBARL were used. Experimental Materials Thorium phosphate was polycrystalline, prepared at high temperature' and compressed into self-supporting pellets of suficient thickness for complete absorption of the positrons. Briefly, synthesis of this compound was achieved by dis- solving thorium nitrate (from Rhbne Poulenc) in concen-trated phosphoric acid (from Merck), and then evaporating to dryness. The volatile residues were eliminated by heating the solid in an oven, at a rate of 1 K h-', and then keeping the temperature constant for 1 h, successively at 573 and 873 K.Thereafter, the samples were heated again, at the same rate, and kept for 6 h, successively at 1223 and 1573 K, with continual grinding. As established by various methods, including proton-induced X-ray emission (PIXE) and X-ray photoelectron spectroscopy (XPS), the stoichiometry of the final salt is Th,(PO,), . The molecular matrix, p-terphenyl, usually employed to prepare liquid scintillators, was from Nuclear Enterprises and was used as received. Preliminary LS measurements showed no detectable long-lived component in this compound. The dopants, pure grade from Aldrich, were further purified by J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 recrystallization. The preparation of the doped matrices has been described previ0us1y.l~ In the case of anthracene, the doped samples were in the form of single crystals grown from the vapour phase17 and cut in the primary cleavage plane, while with chrysene, they were polycrystalline, moulded directly from the melt in the form of pellets. Previous experi- ments have shown that no significant difference exists in the LS parameters between such polycrystalline samples and single crystals. l4 In either case, doping introduces defects in the p-terphenyl lattice, allowing for Ps formation, with the 0-Ps intensity increasing with dopant concentration, up to a saturation val~e.'~*'~The amounts of dopants, 0.5 wt.% anthracene and 1.5 wt.% chrysene, were thus chosen to corre- spond to the onset of saturation.Techniques The positron source consisted of ca. 1 MBq ',Na embedded between two thin Kapton foils, giving a source correction of 8%, and was sandwiched between two pieces of samples for LS and DBARL countings. The LS spectrometer, equipped with plastic scintillators and light guides, was specially designed for shielding the photomultipliers from the magnetic field.' The time resolution, as given by the full width at half maximum (FWHM) of the 6oCoprompt curve, was 380 ps. At B = 0, complementary measurements were made using spectrometers with resolutions of 310 ps (plastic scintillators) or 215 ps (BaF, scintillators).When the field is off, the LS spectra include three com- ponents of lifetimes zo (or decay rate constants, A! = l/zo) and intensities I?, where i = 1, 2 and 3, referring to p-Ps, free e+ and 0-Ps, respectively. At B # 0, the m = 0 substates of Ps are mixed, resulting in the appearance of four components: 0-Ps (rn = f1) remains unaffected, with a lifetime (z3 = 7:) and an intensity (I3 = 21:/3) independent of B, while p-Ps and 0-Ps (rn = 0), the latter with subscript i = 4, have con- stant intensities (Il = I, = 1:/3) but decay rate constants varying with B according to the following equations:19 A1 = (y'l: + A?)/(l + y2) (5) Ah = (y2A?+ Ai)/(l + y2) (6) with y = [(l + x')~', -1]/~; x = 0.027 56B(T)/q (7) In the presence of B, owing to the limited resolution of the spectrometer, the LS spectra cannot be analysed in terms of four components without fixing some parameters.Therefore, the z, values were derived by fixing some of the parameters as measured at zero field: T:, I, = 21:/3 and I, = Z:/3.576 To avoid such constraints, the LS data can, alternatively, be pre-sented in the form of parameter R, which is the ratio of the normalized areas (f) of the spectra in a specified time window (t,,tb),when the field is on and off: t, is chosen such that the contribution of the short-lifetime components is very small, and t,, at the limit of statistically significant counts.5s6 The experimental errors were within 40 ns for z4, and 0.013 for R. The DBARL data were collected using a hyperpure Ge detector with a resolution of 1.38 keV at 514 keV (85Sr photopeak). The data will be reported in the form of the FWHM of the experimental spectra: the error on FWHM was within 0.01 keV.The spectra can be deconvoluted using the resolution function, and resolved into Gaussian com-ponents, corresponding to the various positron states, with intensities ID and FWHMs Ti, where i denotes the same states as for the LS parameters.,' Correlations exist and can J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 be established quantitatively between the LS and DBARL intensities. All experiments were carried out at 294 K. Results and Discussion Thorium Phosphate Table 1 displays the LS parameters derived at B = 0 when using the BaF, scintillators.Within experimental error, these agree with those found using the two other spectrometers. It may be seen that z: is rather short, indicating that Ps is trapped in a small void of the lattice. Quantitatively, an expression has been derived correlating the 0-Ps decay rate constant, A:, to the radius (R,) of the presumably spherical microvoids in which Ps is annihilated:'*2 A:/ns-' = 211 -RJR, + (1/2n)sin(2nRv/R,)] (8) where R,/nm = R, + 0.166. In the present case, with 2: = 1/0.7 ns-', the radius of the largest free space in the thorium phosphate lattice is thus expected to be R, = 0.105 nm. As no crystallographic data are yet available for thorium phos- phate, it is not possible to compare R, with effective sizes of the free spaces in this lattice.The decrease with B of both R and z4, as shown in Fig. 1, is as expected from eqn. (5)-(7) : increasing B progressively decreases z4 and removes 1/3 of the integral of counts from the time window (la, tb). Several hypotheses (noted h) were considered to fit the data, based on eqn. (3) and (4): (hl) a 1.0 0.9 R 0.8 > 2.74 9 2 2.73 z 2.72 Fig. 1 Variations of parameter R (a),0-Ps (rn = 0) lifetime, zJns (O),and FWHM/keV of the DBARL line (a)with magnetic field intensity, B/T, in thorium phosphate. The broken lines are calculated on the hypothesis of a single fitting parameter [(hl) in Table 11, and the solid lines, on the hypothesis of two fitting parameters C(h2) or (h3) in Table 11.Error bars are given on the figure. single fitted parameter is used, with q = q', and the pick-off lifetimes for o-Ps and p-Ps are supposed to be the same, zpl = zp3 = z:; (h2) and (h3) two fitting parameters are involved, with either q # q' and rpl = zY3= z: or q = q' and zpl # zp3.Note that as far as the variations with B of R and z4 are concerned, (h2) and (h3) correspond to the same fitting, as parameters q' and zpl appear as a sum in eqn. (3). The resulting values are given in Table 1, together with the ensuing standard deviations, cR and cZ4.With the simplest hypothesis (hl), usually valid in most cases reported, the stan- dard deviations, c,, = 40 ps and uR = 0.021, compare reason- ably well with the experimental errors, 40 ps and 0.013, respectively.However, the fitting is such that for both R and z4 the calculated variations with B (broken lines in Fig. 1) appear systematically below the experimental plots at low field intensity and above at high B. Furthermore, trial calcu- lations show that q x 0.35 is the optimum value to give the lowest average slopes of the variations. For these reasons, (hl) does not appear to be realistic and the better standard deviations obtained with either (h2) or (h3), which lead to excellent agreement with the shapes of the experimental plots (solid lines in Fig. l), are more acceptable. However, as stressed above, which of these two hypotheses is correct cannot be decided from the LS data alone. As is usual in all liquids previously studied,*' a small broad component, with intensity (4 +_ 0.3)% and r = (7.1 & 0.2) keV, was present in the deconvoluted DBARL spectra at all values of B.This component is poss- ibly attributable to the annihilation of energetic positrons or, alternatively, may correspond to some contribution of core electrons in the annihilation of the various positron states; it is implicitly taken into account in all treatments of the data that follow. Owing to the limited resolution of the DBARL apparatus and to the mediocre value of I: in thorium phosphate (Table l),it appears difficult to derive significant results when resolv- ing the deconvoluted spectra into four components (including the broad component) without fixing some parameters.Therefore, the 15 spectra obtained at B = 0 were first analysed by fixing the free positron intensity, such as I: = (100 -41:/3). This led to a very reproducible value of r2= (2.74 +_ 0.02) keV. Other possibilities were explored which all led to very similar results, thus giving confidence in the above value. Therefore, the average values found after each fitting run for the remaining parameters were fixed, successively for rl and I?. At each run, the DBARL parameters were very similar to those obtained at the last run, with all parameters fixed except r3,the values of which are given in Table 1 (the intensities are corrected for the broad component). The variation of FWHM with B calculated using the data in Table 1 is in excellent agreement with the experimental plot (solid line in Fig.1). The values of r resemble those usually obtained in liquids." In particular, rl is much higher than 0.23 keV, the value expected for thermalized free Ps atoms at 294 K,6 indi-cating that Ps is effectively trapped in a microvoid of the lattice. Note that the use of a single parameter corresponding to the pick-off process, r3,implies that the momentum dis- tributions from pick-off annihilation of both o-Ps and p-Ps Table 1 Experimental LS and DBARL parameters for thorium phosphate at B = 0, and parameters derived from the fitting of the variations of both R and z4 with B [q, q' and zpl, according to hypotheses (hl), (h2) and (h3)] together with the resulting standard deviations (a); time windows, t, = 1.6 ns, t, = 5 ns r;/PS 4/PS 1; (%) 1: ("0) 1: (Yo) F1/keV r,/kev r,/kev 322 f 10 700+ 17 22.7 f1.2 4.5 -t 0.5 25.8 k 1.3 0.88 f0.1 2.74 t-0.02 1.95 f0.03 (hl) = 0.32 & 0.02; oT4= 40PS;oR= 0.021.(h2), (h3) q = 0.22 _+ 0.06; h(2) q' = 0.36 & 0.06;(h3) zPl = 390 f50 PS;or4= 17 PS; oR= 0.010. are the same; the limited resolution of DBARL does not allow one to seek differences between these distributions. The intensity for intrinsic annihilation, I?, is significantly lower than @3, showing that a large portion, ca. 40%, of p-Ps is annihilated via pick-off: this is expected on the basis of eqn. (3), which predicts that if q’ [or q, on hypothesis (hl)] is low, the contribution from pick-off can become important. Whereas the LS data do not allow (h2) and (h3) to be distin- guished, the DBARL results should provide the information by considering the following equations : for (h2) I? = (W3)~’&h’4 + Ap3) (9) for (h3) I? = (m3)q&/(v&+ Jpl) (10) From these expressions, and the data in Table 1, the expected values for I? are 4.8% and 2.9% for (h2) and (h3), respec- tively.By comparison with the value of 4.5% derived from the experimental spectra, it appears that (h2), which implies a similar value for the pick-off lifetimes of p-Ps and 0-Ps and distinct values for q and q’, is more likely than (h3). p-Terphenyl as a Matrix Table 2 collects the LS parameters obtained for the doped p-terphenyl samples. It may be seen that these are very similar with either dopant.The 0-Ps intensities, at about 20%, both represent the values obtained at saturation, when the dopant concentration is increased. The 0-Ps lifetimes and intensities in both mixtures are in excellent agreement with previous determinations. l4*I8 In accordance with the increase of I! with dopant concentration, the lifetimes are long enough to indicate that Ps is effectively trapped in those defects introduced by the dopant molecules. Thus, from eqn. (8), a spherical void of the size of a whole benzene molecule, with a radius of 0.14 nm, would lead to a lifetime of 855 ps only. In the present case, it is expected that anthracene and chrysene should introduce defects of roughly the size of a naphthalene molecule.The latter is not spherical, but two estimates of the size of such a defect can be obtained by con- sidering the distances from the centre of symmetry of the molecule to the farthest (0.252 nm) or second-farthest (0.185 nm) carbon atoms: from eqn. (8), the corresponding 0-Ps life- times are 1660 ps and 1120 ns, respectively. The values in Table 2 are effectively within these limits, as are several others for a variety of dopants in p-ter~henyl,’~ which were found to range between 1110 ps with a-benzopyrene to 1620 ps with phenanthrene. The linear shape of anthracene appears to allow a better insertion of this molecule into the p-terphenyl lattice, with 7; closer to the value corresponding to the largest possible void, than chrysene which produces defects of a smaller size reflecting some geometrical hin- drance.When applying B, with either anthracene or chrysene as dopants, both R and z4 decrease (Fig. 2 and 3) in a much smoother way than in thorium phosphate. Quantitatively, these variations are described very well using a single fitting J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 R -0.8 I 1 1 I I 0 05 1.0 1.5 B/T Fig. 2 Variations of parameter R (0)and 0-Ps (rn = 0) lifetime, zJns (O),with magnetic field intensity, B/”, in solid p-terphenyl doped with 0.5% anthracene. The broken and solid lines are calcu- lated on the hypothesis of a single parameter, q = 1 and q = 0.80 (Table 2), respectively. Error bars are given in the figure. parameter, q.The derived values are given in Table 2, together with the standard deviations, which compare well with the experimental errors; consequently, the resulting cal- culated curves (solid lines in Fig. 2 and 3) show excellent agreement with the experimental plots. By contrast with thorium phosphate and numerous liquids previously studied, it was not possible to resolve the DBARL spectra into components. A reason for this failure is that the momentum distributions of the free annihilation (r,)and -1.0 -0.9 R -0.8 I I 0 0.5 1.o 1.5 B/T Fig. 3 Variations of parameter R (a)and 0-Ps (rn = 0) lifetime, rJns (O), with magnetic field intensity, BIT, in solid p-terphenyl doped with 1.5%chrysene. The broken and solid lines are calculated on the hypothesis of a single parameter, q = 1 and q = 0.83 (Table 2), respectively.Error bars are given in the figure. Table 2 Experimental LS parameters for p-terphenyl doped with either anthracene (0.5 wt.%)or chrysene (1.5 wt.%), and fitting parameter (q) for the variations of both R and r4 with B together with the resulting standard deviations (a), time windows, t, = 2.4 ns, t, = 9 ns for anthracene and t, = 2.4 ns, t, = 7 ns for chrysene dopant z:/PS r;lPs 1; (%) q %JPS OR anthracene 313 -t 4 1438 _+ 15 19.9 -t 0.2 0.80 f 0.02 22 0.009 chry sene 317 f 3 1160+ 13 22.5 0.3 0.83 f 0.02 22 0.008 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 pick-off (r,)components appear to be very close and thus cannot be resolved owing to the limited resolution of the DBARL apparatus.Furthermore, even when fixing rl to 0.97 keV (the value found in p-terphenyl doped with anthracene by angular correlation measurements18) the intensity of the narrow component, I:, is found to be slightly negative. This may reflect the fact that Gaussian functions are not adequate to describe the momentum distributions in this doped matrix. As in thorium phosphate (Fig. l), the variations of FWHM with B (not reported) show a smooth decrease, confirming the increase in the proportion of the Ps narrow component, with annihilation occurring in an intrinsic way owing to the mixing of states. Origin of the Anomalous States of Ps in Solids From Tables 1 and 2, it appears that doped p-terphenyl belongs to the class of solids in which Ps behaves normally, while in thorium phosphate it behaves anomalously.Except for those compounds in which the existence of two distinct Ps trapping sites is s~spected,~*' anomalous magnetic quenching effects have been found only in naphthalene" and in some organic polycrystalline scintillators. l2 In the latter case, the authors emphasize that the magnetic quenching is regular, when comparison is possible, in amorphous samples com- pared with that of the crystalline phases. They conclude that crystallinity is a necessary, although not sufficient, condition to observe anomalous effects, a conclusion which would hold for the present results. However, the explanation proposed,' based on possible magnetic interactions between Ps and radiolytic products in the positron spur, does not appear likely.In particular, it is difficult to see how the nature of the triplet states formed at the end of the positron track could differ (for long enough to affect Ps via magnetic interactions) in amorphous and polycrystalline samples of a specified com- pound. In the following, two different possibilities are exam- ined and discussed. As suggested by those cases where more than one type of Ps seems to be present,'.' a possible alternative to the above hypothesis is the existence of a distribution of the contact density parameter. In the case of naphthalene for instance, it has been shown, by comparing the activation energy of Ps formation in this matrix and the sublimation energy, that those sites at which 0-Ps is annihilated do not correspond to intrinsic vacancies, in contrast to what is found in a number of plastic molecular solids.2' As is the case in solid poly- mers,' Ps is possibly formed and decays in the natural free volumes of the naphthalene lattice.At a specified tem-perature, these free volumes are not of a constant size and thermal movements of the molecules in the lattice can give rise to a distribution of void sizes and, consequently, of Ps lifetimes and contact densities. Such lifetime distributions have been claimed to be found in a variety of However, the corresponding experimental LS spectra are well fitted using a single 0-Ps lifetime; this implies that most prob- ably only a very broad distribution of q will make it neces- sary to distinguish between q and u' in eqn.(2) and (3). To assess the validity of the present hypothesis, LS spectra involving a contact density distribution were simulated for various field strengths, up to 1.7 T, and subsequently analysed in the same way as the experimental spectra. The spectra were calculated using LS parameters similar to those obtained with thorium phosphate. The distributions were normalized Gaussians of specified maximum (11') and FWHM, truncated on the lower side, at q 2 0.01. As illus- trated in Table 3, the resulting analyses show that even with an extremely broad distribution, the simulated spectra are quite well described by a single fitting parameter, q.The Table 3 Fitting parameter (q) and resulting standard deviations (uR,orjfor the variations of both R and r4 with B from simulated spectra with a Gaussian distribution (qo, FWHM) of the contact density parameter FWHM ~~~~~ 0.6 0.2 0.60 O.OO0 0 0.6 0.62 0.003 4 1.4 0.79 0.006 7 0.3 0.1 0.29 0.001 1 0.3 0.25 0.004 5 1.o 0.58 0.011 12 1.4 0.69 0.009 11 necessity for two fitting parameters as encountered in the case of thorium phosphate cannot therefore be taken as indicative of the presence of a distribution of the contact density parameter due to some distribution in the size of the lattice sites. Although theory predicts that q should be different from 21' in the case of an excited state of Ps,~it is likely that the corre- sponding formalism, expressed through eqn. (2), (3) and (5)-(7), would give satisfactory results when describing any Ps wavefunction suficiently distorted compared with the spher- ical ground-state function.Distortion of the Ps atoms can be provoked by local conditions within the solid matrices. From the wealth of data accumulated, two situations are found: (i) presence of local fields with non-spherical geometries and (ii) existence of free spaces of sufficient volume to allow Ps for-mation and survival, but of shapes significantly different from spherical. The first case relates to ionic crystals. It is amazing that Ps does exist in such tightly packed lattices as that of Kcl.'~~~In this matrix, the largest space available corre- sponds to the tetrahedral sites circumscribed by four C1- anions.With a radius of 0.0845 nm, these sites would give an 0-Ps lifetime of 627 ps [eqn. (S)], which agrees well with the values of 7: = 628 ps24 or 680 ps' found experimentally, thus confirming that Ps in pure KCl is not annihilated in intrinsic vacancies. As T! in thorium phosphate is very close to the latter value, a similar conclusion holds. The difference in the liability to magnetic field effects in the two solids is therefore ascribable to a non-spherical electric field present in the free sites in thorium phosphate, because of the asymmetry in the balance of charges in the Th4+ and PO:-ions, in contrast to KCl which presents a regular arrangement of alternating monopositive and mononegative charges.In the case of naphthalenelo and other molecular com- pounds,I2 the existence of distorted Ps atoms should find explanation in the shape of the free spaces in which Ps is annihilated : most probably, if the voids available are of sufi-cient volume to allow Ps formation but of a shape signifi- cantly different from spherical (like rods), the latter may impose a distorted wavefunction on Ps. Conclusion The present results confirm that the Ps states in solids can be diverse, resulting in either normal or anomalous effects of an external magnetic field. In the 'normal' matrices studied here (p-terphenyl doped with either anthracene or chrysene molecules) Ps is created and is annihilated in extrinsic defects introduced by the dopants : approximating these defects to spheres with a radius similar to that of a naphthalene mol- ecule leads to a quantitatively good agreement with the experimental pick-off lifetime of 0-Ps, z: .Anomalous mag- netic field effects are found in ionic thorium phosphate, although the value for 7: is close to that found in another ionic lattice, KC1, in which normal magnetic effects have been J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 observed. This difference of behaviour is attributed to a dif- ference in the symmetry of the static electric field in those voids where Ps is annihilated in the lattices, which would be more spherical in the case of KCl than of thorium phosphate.It is suggested that, more generally, distortion of the Ps wave-function from spherical will occur, and therefore result in anomalous field effects, whenever local conditions are favour- able: such conditions can result not only from the electrical field, in the case of ionic crystals, but also from specific geo- metrical constraints, in the case of molecular solids. It would be rewarding to verify these hypotheses by examining a larger variety of solids, particularly molecular compounds, to gain information on Ps and thereby enlarge its applicability as a probe of the physico-chemical properties of matter. The authors thank C. Merigou and M. 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