Beam Intamotions with Materials 8 Atoms
EJSEVIER
Ion-beam-induced amorphization of LaPO, and ScPO, A. Meldrum a**, L.A. Boatner b, L.M. Wang a, R.C. Ewing a a Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, NM 87131-l 116, USA b Oak Ridge National Laboratory, Oak Ridge, TN 378314056,
USA
Abstract LaPO, and ScPO, were irradiated by a 1.5 MeV Krf ion beam using the HVEM-tandem Facility at Argonne National Laboratory. The ion-beam-induced amorphization was investigated over a temperature range of 20 to 570 K and the degree of amorphization was determined in-situ by monitoring the gradual loss of electron diffraction maxima. Subsequent high-resolution TEM analysis revealed the development of an amorphous phase. LaPO, and ScPO, were found to have activation energies for irradiation-enhanced annealing of 0.02 and 0.11 eV, attributed to diffusion-driven epitaxial recrystallization. The critical temperatures of amorphization were found to be 365 and 540 K, respectively. Both materials recrystallized under electron irradiation. These results suggest that the phosphates are generally less sensitive to ion-beam irradiation over a wide temperature range than are their silicate structure analogues and that the zircon structure-type has a higher energy barrier to recrystallization than the related monazite structure-type.
1. Introduction Radiation effects in ABO, materials having the monazite (P2 ,/n, 2 = 4) and zircon (14,/amd, Z = 4) structure-types have recently been the subject of a renewed level of interest because of the potential application of these materials as waste forms for high-level nuclear waste [l-3] and as storage media for excess weapons plutonium [4], respectively. The monazite and zircon structure-type materials have a high physical and chemical durability and have been demonstrated to accommodate greater than 20 wt.% simulated waste and actinide elements [5,6]. Naturally occurring ABO, minerals having the monazite or zircon structure (A = Ln, AC, Zr, Y, Hf, Pb; B = P, Si, where Ln = lanthanides and AC = actinides) are important in U-Pb and Th-Pb geochronology because of their high actinide content [7,8]. Natural monazite [(Ln, Th)PO,] can contain more than 17 wt.% ThO,, in some cases corresponding to more than 8 displacements per atom (dpa) over 2 to 3 billion years, due to the decay of 232Th, but it almost invariably remains crystalline. Xenotime (YPO,: zircon structure) is also usually reported to be crystalline in nature, although it typically contains only l-5 wt.% ThO, + UO, - roughly equivalent to 1-2 dpa over a similar time span. Natural zircon (ZrSiO,), on the other hand, is frequently metamict (amorphous) despite containing less than 0.5 wt.% total radionuclides (O-O.5
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dpa). Recent work [9] has confirmed that natural samples of monazite and zircon show a greatly different response to heavy-ion irradiation. The monazite and zircon structure-types are related in that both consist of chains of edge-sharing eight-fold (zircon) or nine-fold (monazite) A-site polyhedra and BO, tetrahedra parallel to c [lo,1 I] (Fig. 1). Each AO, or AO, polyhedron shares edges with other A-site polyhedra, linking the polyhedron-tetrahedron chains in the ab plane. The larger radius of the A-site cation in monazite requires an increase in the coordination number, the result of which is a distortion of the structure which involves a rotation of the tetrahedra and a shift of the (100) plane by 0.22 nm along [OlO][ 121.This reduces the symmetry from 14, /amd to P2 ,/n. The BO, tetrahedra in both minerals are isolated; they do not share edges or comers with other BO, tetrahedra. Synthetic LaPO, and ScPO, are important monazite and zircon structure-type end-members [ 10,111 that are used in the present work to investigate the effects of structure and composition on the temperature-dependent amorphization of these materials. The use of synthetic starting materials ensures that the effects of impurities on damage accumulation are minimized. The present results will be compared to the currently available data for naturally occurring monazite, xenotime, and zircon. Previous work on the response of the orthophosphates to heavy particle irradiation is limited. Karioris et al. [13] irradiated monazite and several related phases with 3 MeV Krf ions at ambient temperature. They found that monazite amorphized at a dose of less than 5 x lOI ions/cm*,
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sections showed that monazite is easily damaged. Subsequently, Meldrum et al. [9] have demonstrated that monazite has a low activation energy for irradiation-enhanced annealing (0.04 eV).
2. Experimental
a
T kb
Fig. 1.Comparison of the structures of ScPO, (A) and LaPO, (B), using the data from Refs. [IO,1 11. In SePO,, the smaller A-site cations are I-coordinated, and the SiO, tetrahedra are symmetrical. The presence of larger A-site cations distorts the zircon (ScPO,) structure by rotating, distorting, and shifting the tetrahedra and introduces a ninth oxygen into the coordination sphere of the metal cation, producing the monazite (LapO,) structure-type (B). The larger size of the AO, polyhedronreduces the amount of void space and correspondingly increases the density of the monazite stmcture. The void spaces between groups of four tetrahcdra in (A) form channels parallel to c, an important consideration in the development of collision cascades.
as compared to over 2 X 10” ions/cm’ for ThO,, and concluded that monazite is not “resistant” to radiation damage. According to Karioris et al. [14] the damage cross
Synthetic crystals of LaPO, and &PO, were grown using a flux technique [3] in which lanthanum or scandium oxide was combined with lead hydrogen phosphate and heated to 1360°C in a platinum crucible. The system was held at this temperature for several days, cooled at IT per hour to 9OO”C,and then rapidly quenched to room temperature. Single crystals of the orthophosphate were then removed from the Pb,P,O, flux by boiling in nitric acid for four weeks. The sample composition was subsequently checked by Energy Dispersive Spectrometry (EDS), and X-ray diffraction analysis confirmed the monazite and zircon structure-types. The single crystals were cut perpendicular to the c-axis using a diamond saw. Samples were then thinned and ion milled to perforation using 4 keV Ar+ ions. The materials were irradiated 10” off the [OOl] zone axis by 1.5 MeV Krf ions using the HVEM-tandem Facility at Argonne National Laboratory. This facility consists of a modified Kratos/AEZI EM7 high-voltage electron microscope connected to a 2 MeV tandem ion accelerator. Irradiations were performed over the temperature range 20-570 K. The dose rate was 3.4 X lOI ionscmB2s-‘. Dose-rate effects were monitored by repeating some irradiations at 1.7 X lOI ions cm-2s-1. The effect of ion energy on the amorphization of ScPO, was investigated by repeating the experiments using an 800 keV ion beam. Amorphization was observed in-situ by the loss of electron diffraction maxima (Fig. 2). During irradiation the electron beam was turned off to avoid the effects of electron irradiation. Subsequent thermal anneals with in-situ transmission-electron microscopy (TEM) were performed in a JEOL 2000FX microscope at the University of New Mexico.
Fig. 2. I3ectron diffraction patterns monitoring the degree of amorphization in ScPO, at room temperature: unirradiated (A), 6.8 x IOk ions/cm’ (B), 1.4 X 1Ol4 ions/cm* (0, and 2.05 X lOI4 ions/cm2 (D). Beam direction is parallel to [Ool].
I. FUNDAMENTALS/BASICS
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3. Results and discussion
ScPO, was amorphized at temperatures from 20 to 533 K (Table 1). At 570 K, amorphization was not achieved after a dose of 5 X 10I5 ions/cm’. LaPO, could not be amorphized at 3.50 K after a similar dose. The amorphization of LaPO, in particular was retarded in the presence of the electron beam, so irradiations were done with limited intermittent use of the electron beam. ScPO, showed a similar, although significantly less pronounced, effect. Variations in beam flux from 1.7 to 3.4 X 10” ions cm-‘s- ’ did not cause a noticeable change in critical amorphization dose, although the results of Koike et al. [I51 for the irradiation of CuTi did show a weak dependence on dose rate. Subsequent to irradiation, samples of each material were thermally annealed to compare the ease of annealing in the absence of the ion beam. Three samples of each material were annealed to account for sample-to-sample variations in thickness and shape. Thermal annealing showed that LaPO, recrystallized epitaxially from the thick edges of the TfZM foil at 300°C within one hour. Amorphous &PO, showed no reaction after being held at
Table 1 Critical amorphization dose at various temperatures for ScPO, and LaPO,. A large number of data points were collected for ScPO, using 1500 keV ions in order to check for the presence of two annealing stages, as documented in zircon. Displacements per atom were calculated based on density values of 3.71 and 5.12 g/cm3 for ScPO, and LaPO.,, respectively. TRIM-95 calculations (full cascades) were used to determine displacements per ion at 100 nm depth, n.a. indicates that the sample was not amorphized Material
T [K]
Ions/cm*
@a
SCPO, 1500 keV
25 100 200 303 373 403 433 463 512 510
1.45E+ 1.45E+ 1.62E+ 2.05E + 2.91E+ 3.08E + 3.76E+ 4.62E + 1.37E+ n.a.
14 14 14 14 14 14 14 14 15
0.182067 0.182067 0.203486 0.257035 0.364134 0.385553 0.471232 0.57833 1.71357 n.a.
SCPO, 800 keV
25 303 373 423
1.98E+ 2.75E+ 4.38E + 8.758+
14 14 14 14
0.415 0.574113 0.913361 1.826722
25 50 100 303 350
1.2E+ 14 1.37E+ 14 1.54E+ 14 1.03E+ 15 n.a.
0.193699 0.22137 0.249042 1.660278 n.a.
LaPO, 1500 keV
7
0
200
400
600
800
1000
Temperature (K)
Fig. 3. Temperature dependence of the critical amorphization dose for LaPO, (squares), &PO, (tilled triangles: 800 keV Kr z‘, open triangles: 1500 keV Kr+), natural monazite 191 (circles), and zircon [ 161 (diamonds). The data are fitted using a least-squares refinement for E,, D,, and ln(l/&r) for Eq. (1). The dotted line shows stage-l annealing in zircon, for which there is no critical temperature. For the purpose of comparison, the number of displacements per ion as a function of depth was taken from the TRIM-95 calculations at 100 nm, instead of 200, as in the original Ref. [ 161.The maximum error in the irradiations was determined to be * 0.08 dpa, although some errors are thought to be smaller; for consistency an error of iO.08 dpa is used for all data points. Data points for temperatures at which complete amorphization could not be. achieved (Table I) are not shown. One data point for monazite at 3.6 dpa is also not plotted.
this temperature for four hours: to anneal at comparable times (1 h), the temperature was raised to 400°C. The critical amorphization dose (0,) is shown as a function of temperature in Fig. 3. Doses were converted into dpa using TRIM-95 (Table 1: full cascades, specimen thickness = 100 nm) using the theoretical density obtained from the X-ray diffraction analysis. Ed was assumed to be 20 eV for both materials. Only single-stage annealing was recognized in both structure-types. Weber et al. 1161,based on an earlier model by Morehead and Crowder [17], showed that the activation energy for irradiation-enhanced annealing (E,) could be calculated assuming that recrystallization occurs over a short time span (7) and acts to reduce the volume of each displacement cascade. Under these assumptions, they showed that the critical amorphization dose can be related to an activation energy for irradiation-enhanced annealing by ln(1 -De/D)
= ln(l/@r)
- EJkT,
(1)
where De is the critical amorphization dose at 0 K (no annealing), 4 is the ion flux, u is the amorphization cross section, and k is Boltzmann’s constant. Activation energies were obtained by calculating the slope of a In(l Do/D) vs. l/kT curve on an Arrhenius plot, in which the value of Do was visually estimated by drawing a curve on the D, vs. T graph. The critical amorphization temperature
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(T,: the temperature above which amotphization by 1.5 MeV Krf ions cannot be induced), can be derived from Eq. (1): G = E,/[k
In(W
(2)
in which In( l/&zr) is obtained from the y-intercept on the Arrhenius plot. Close examination of Eq. (1) shows that the calculated activation energy is highly sensitive to the value chosen for D,, and is directly dependent not only on c, but on the degree of curvature on the DC vs. T plot. Values of E, can change by 50 to 100% for only small changes in D,. In order to obtain a meaningful curve in Fig. 3, the parameters E,, D,, and ln( 1/&rr) were determined based on a least-squares refinement of the experimental data using Eq. (1). In this way, the activation energies for LaPO, and &PO, were calculated to be 0.02 and 0.11 eV. The critical amorphization temperatures were found to be 365 and 540 K, respectively. This solution to the Weber equation has the advantage that all data points contribute to the value taken for D,; thus, this is a more consistent way of comparing different materials. The value of E, for irradiation-enhanced epitaxial recrystallization in zircon (0.3 1 eV [ 161)is apparently almost an order of magnitude higher than for the dozen or SO other materials for which such data are available (E, values range from 0.02 eV for stage-l annealing in zircon f16] and for stage-2 annealing of LaPO., (this study), to 0.13 eV for stage-2 in coesite [ 181). Using the above method, E, for stage 2 annealing in zircon was recalculated to be 0.16 eV, bringing this value more in line with the results for other materials. For consistency, the E, and T, for monazite were recalculated from the results of Meldrum et al. [9] to be 0.04 eV and 440 K, respectively. The form of Eq. (1) with the values obtained from the least-squares refinement is shown in Fig. 3 with the actual data points for LaP04, ScPO,, monazite, and zircon. The activation energies for LaPO, and ScPO, are attributed to diffusion-driven, irradiation-enhanced, epitaxial recrystallization within displacement cascades (stage-2 annealing). A separate initial annealing stage, as documented for zircon [16], was not observed. The activation energy for LaPO, is identical to that found for stage-l annealing in zircon, attributed to close-pair recombination. However, for reasons outlined in Ref. [9], close-pair recombination is unlikely to completely account for the entire annealing process. The low activation energy for irradiation-enhanced annealing of LaPO, is consistent with its ease of recrystallization under the electron beam. Both materials required higher temperatures for epitaxial recrystallization in the absence of the ion beam. The E, for scandium phosphate is significantly higher than for LaPO,, indicating that the zircon structure is more difficult to anneal. This explains why minerals having the monazite structure-type [e.g., monazite and huttonite (monoclinic IT&O,)] are almost invariably crystalline in
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nature; whereas, zircon-structure minerals [e.g., zircon and tborite (tetragonal ThSiO,)] are frequently partially or completely amorphous. The barrier to recrystallization is, therefore, lower in the monazite structure.-type (within the phosphates chemistry is apparently less important, based on initial results for GdPO, and LuPO,). The ease of recrystallization is often related to diffusion in the thermal spike [17] or to bulk diffusion enhanced by radiolysis or knock-on events [19]. Why these differences should be so pronounced in amorphous phosphates having similar chemistry requires further research on the structure and diffusion in amorphous materials. Structurally, in the absence of annealing, displacement cascades in monazite are probably smaller than in zircon because of the lower symmetry (less channeling and no linear collision sequences (LCS) in monazite. [ZOl). However, the defect density must then be lower in the zircon structure-type because of the enhanced energy loss through ionization thought to occur via channeling and LCS. Work is ongoing to determine the amorphization process (directly in cascades or as a result of one or more cascade overlaps) in the monazite and zircon structure-types. The structural topology criterion [21] predicts that the monazite structure-type should be slightly harder to amorphize, because of the larger number of vertices in the AO, relative to the AO, polyhedron, although this criterion obviously fails to account for chemical variations (e.g., ScPO, vs. ZrSiO,). On an atomic scale, the amorphization dose is dependent to a large degree on the amount of epitaxial recrystallization along the edges of each displacement cascade and on the size of the cascades. Apparently, the transition from the amorphous phase to the monazite structure occurs more easily than the transition to the zircon structure. At any given temperature, the time constant, 7, may be larger in the monazite structure, so that the material can recrystallize to a greater extent before the damage is “frozen” in place. Qualitatively, the calculated energy transferred to recoil atoms for LaPO, (120 eV/ion) and ScPO, (117 eV/ion) in combination with the chemical similarities between these materials suggests that the value of o, the amorphization cross section, is similar. If this is true, the relative magnitude of T can also be obtained from the irradiation data. The least squares solution for ln(bar) predicts an approximately five times larger time constant for LaPO,, consistent with its greater ease of annealing. Initial results on the electron-irradiation of amorphous LaPO,, ScPO, and ZrSiO, indicate that these materials will recrystallize to a polycrystalline assemblage, even at a low electron-beam energy (80 keV). The crystallites have the same composition as the original material, except zircon, which recrystallizes to ZrO, + amorphous SiO,. The dose required to recrystallize LaPO, is an order of magnitude less than for ScPO,, and almost two orders of magnitude less than for ZrSiO,. Although the recrystallization process is different, these data are consistent with the 1.FUNDAMENTALS/BASICS
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low calculated annealing activation energy for LaPO, and further indicate the unusual ease of the amorphous-tocrystalline transition in the monazite structure-type. The general progression from low to high E,, and T, values from LaPO, through natural monazite to ScPO, is readily apparent. Zircon, however, appears to show markedly different behavior: a) two stages of annealing are identified, b) zircon has a critical temperature of amorphization well over double that for isostructural ScPO,, and c) D, for zircon is twice that of the other three materials. In zircon, stage-l annealing was attributed to close-pair recombination, proposed to be effectively instantaneous and complete at temperatures above 300 K (T, = m>1161.If this type of stage-l annealing is present in the otthophosphates, it was not observed within experimental error. The low critical amorphization temperature of ScPO, relative to zircon is indicative of the ease of recrystallization in the phosphates, consistent with previous results on apatite (Ca,(PO,),F) [22], berlinite (AIPO,) [23], and monazite [9], which can be attributed to the lower rigidity of the PO, relative to SiO, tetrahedra in the amorphous matrix. If the amorphous phase can be compared to the glass, as suggested by a comparison of amorphization with ease of glass formation [24], then PO, tetrahedra are coordinated across only three comers (one double-bonded oxygen), as compared to four for the SiO, tetrahedra (no double bonds), and can therefore more easily reorient themselves in the recrystallization process. The apparent difference in D, could be a product of the assumed values for Ed. In order to shift the value of D, to the level for the other materials, zircon must have a significantly higher average displacement energy. Initial work suggested that Ed may show a positive linear correlation with melting temperature for many ceramics [25]. Monazite melts at 2150°C [l], but zircon undergoes solidstate decomposition at 16OO”C,suggesting that the large difference in D, is not related to the assumed values of E,,. Additionally, according to Pauling’s second rule [26], the tetrahedrally coordinated P-O bonds are stronger than the Si-0 bonds by a factor of 1.25, and are correspondingly shorter (average 1.534 A in monazite [ 121 and 1.623 A in zircon [27]). The higher strength for the P-O bond results in a higher displacement energy and a lower value for the calculated critical amorphization dose (in dpa) at a fixed ion fluence. Thus, the difference in D, is probably real, and occurs as a result of structure-type (affecting the cascade size and the amorphization mechanism through channeling and linear collision sequences), and chemical composition (weaker Si-0 bonds). The effect of chemical variation on the A-site is to retard the irradiation-enhanced annealing process. The acnvation energy and critical temperature of amorphization for natural monazite are significantly higher than for LaPO, (Fig. 3). This suggests that the presence of heavy impurity atoms (e.g., Ln, Th, Pb) in the natural phase retards the
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annealing process. Impurity elements in natural monazite, including radiogenic Pb, may inhibit the recrystallization process because many of these elements are not stable in the monazite structure-type. Similarly, pure ZrSiO, is expected to recrystallize more readily than naturally occurring zircon that is rich in impurity elements. The degree to which a particular impurity element retards the annealing process in these materials probably depends on the charge and radius mismatch on the A-site. The effect of lowering the ion energy from 1500 to 800 keV is to decrease the critical temperature of amorphization and to increase the amorphization dose even at low temperature (Fig. 3). 7’,‘,for ScPO, decreased from 540 to 470 K, and D, increased from 0.20 to 0.41 dpa. The cross section for nuclear collisions increases with decreasing energy, but the efficiency of damage production apparently decreases (possibly because of smaller cascades and lower defect survival). Thus, the net effect is that the material becomes more difficult to amorphize as the ion energy is decreased. This is reflected by the calculated decrease in the activation energy from 0.11 eV (1500 KeV Kr) to 0.09 eV (800 KeV Kr). 4. Conclusions Synthetic LaPO, and ScPO, were irradiated between 20 and 5 12 K by 1.5 MeV Kr+ ions. The critical amorphization dose was measured over this temperature range. Subsequent thermal anneals were completed in order to compare the temperature for thermal annealing with the critical amorphization temperature under irradiation. The Weber equation was used to determine the activation energies and critical temperatures, using a least-squares refinement method for three independent variables. We conclude: - LaPO, and ScPO, have activation energies of 0.02 and 0.11 eV, and critical temperatures of 365 and 540 K, respectively, attributed to irradiation-enhanced, diffusiondriven, epitaxial recrystallization. - Both materials were found to require temperatures higher than T, for thermal annealing. - LaPO, and ScPO, both recrystallized by a nucleation and growth method as a result of electron irradiation. - The monazite structure-type is more easily recrystallized during heavy-ion irradiation than the related higher symmetry zircon structure-type. Structurally, this is probably due to the effects of channeling and LCS in zircon and ScPO,. On the basis of chemistry, materials with phosphorous in the B-site as compared to silicon are more easily annealed because of the lower coordination across the PO, tetrahedron as a result of irradiation and the higher strength of the P-O bonds. - Chemical impurities (e.g., U, ?h,‘Pb) in the A-site, as seen in natural monazite and zircon, lead to a higher barrier to recrystallization. This is attributed to the instability of impurity atoms in the crystal structure.
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- Lowering the ion energy increases the critical amorphization dose and decreases q and E,.
Acknowledgements
The authors thank E. Ryan, S. Ockers, and L. Funk (HVEM-Tandem Facility, Argonne National Laboratory) for their assistance with the irradiations. This work was supported by the Office of Basic Energy Sciences, DOE (grant # DE-FGO3-93ER45498). A.M. acknowledges financial support through a scholarship from les Fonds pour la Formation de Chercheurs et 1’Aide ‘a la Recherche (FCAR, Quebec).
References [l] L.A. Boamer, G.W. Beah, M.M. Abraham, C.B. Finch, P.G. Huray and M. Rappaz, in: Scientific Basis for Nuclear Waste Management, Vol. 2, ed. C.J.M. NOI~~NP Jr. (Plenum, New York, 1980) p. 289. [2] L.A. Boamer, M.M. Abraham and M. Rappaz, in: Scientific Basis for Nuclear Waste Management, Vol. 3. ed. J.G. Moore (Plenum, New York, 1981) p. 181. [3] L.A. Boatner and B.C. Sales, in: Radioactive Waste Forms For the Future, eds. W. Lutze and R.C. Ewing (Elsevier, Amsterdam, 1988) p. 495. [4] R.C. Ewing, W. Lutze and W.J. Weber, J. Mater. Res. 10 (1995) 243. 151 B.C. Sales, C.W. White and L.A. Boatner, Nuclear and Chemical Waste Management 4 (1983) 281. [6] C. Keller, Nukleonik 5 (1963) 41. [7] R.R. Parrish, Can. J. Earth Sci. 27 (1990) 1431. [S] L. Heaman and R.R. Parrish, in: MAC Short Course on Radiogenic Isotope Systems, Vol. 19, eds. L. Heaman and
165
J.N. Ludden (Mineralogical Association of Canada, Toronto, 1991) p. 59. [91 A. Meldrum. L.M. Wang and R.C. Ewing, Nucl. Instr. and Meth. B 116(1996)220. [lOI D.F. Mullica, W.O. Milhgan, D.A. Grossie. G.W. Beall and L.A. Boamer, Inorg. Chim. Acta 95 (1984) 23 1. bll W.O. Milhgan, D.F. Mullica, G.W. Beall and L.A. Boamer, Inorg. Chim. Acta 60 (1982) 39. 1121 Y. Ni, J.M. Hughes and A.N. Mariano, Am. Min. 80 (1995) 21. 1131 F.G. Karioris, K. Appaji Gowda and L. Car& Radiat. Eff. Lest. 58 (1981) 1. 1141 F.G. Karioris, K. Appaji Gowda, L. Cartz and J.C. Labbe, J. Nucl. Mater. 108 & 109 (1982) 748. [I51 J. Koike, P.R. Okamoto and L.E. Rehn. J. Mater. Res. 4 (1989) 1143. 1161 W.J. Weber, R.C. Ewing and L.M. Wang, J. Mater. Res. 9 (1994) 688. 1171F.F. Morehead, Jr. and B.L. Crowder, Radiat. Eff. 6 (1970) 27. 1181 W.L. Gong, L.M. Wang, R.C. Ewing and J. Zhang, Phys. Rev. B 54(1996) 1. 1191 F.W. Clinard and L.W. Hobbs, in: Physics of Radiation Effects in Crystals, eds. R.A. Johnson and A.N. Grlov (Elsevier, Amsterdam, 1986) p. 387. DO1 M.T. Robinson, Phys. Rev. B 27 (1983) 27. Dl L.W. Hobbs, Nucl. Instr. and Meth. B 91 (1994) 30. w L.M. Wang, M. Cameron, W.J. Weber, K.D. Crowley and R.C. Ewing, in: Hydroxyapatite and Related Materials. eds. P.W. Brown and B. Constantz (CRC Press, Boca Raton, 1994) p. 243. b31 N. Bordes and R.C. Ewing, Mater. Res. Sot. Symp. Proc. 373 ( 1995) 395. k41 S.X. Wang, L.M. Wang and R.C. Ewing, Mater. Res. Sot. Symp. Proc., in press. [251 W.L. Gong, personal communication. [261 L. Pauling, J. Am. Chem. Sot. 51 (1929) 1010. k71 R.M. Hazen and L.W. Finger, Am. Mineral. 64 (1979) 1%.
1. FUNDAMENTALS/BASICS