Strain relaxation and order–disorder phase transition in irradiated MgAl₂O₄

Abstract

MgAl₂O₄ spinel is widely studied in many fields of material science because of its variety of interesting properties and potential applications. The influence of cation disorder on the physical properties of MgAl₂O₄ makes understanding of the effects related to this disorder particularly important. It is known that, upon ion irradiation at low temperature, MgAl₂O₄ undergoes an order–disorder phase transition followed by amorphization. This paper reports a combined high resolution X-ray diffraction and transmission electron microscopy study elucidating the linkage between this phase transition and irradiation-induced elastic strain. Irradiations were carried out on 〈110〉 and 〈111〉-oriented single crystals of MgAl₂O₄ at T = 77 K with 600 keV Xe ions over a wide range of doses. The data suggests that the beginning of the order–disorder phase transition coincides with the beginning of strain relaxation. This result indicates that the volume of the new phase is slightly smaller than that of the unirradiated spinel. The dose at which the phase transformation occurs is found to be dependent on the crystal orientation, which can be attributed to both elastic and crystallographic properties.

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Introduction

MgAl₂O₄ is an extensively investigated material in several fields of material science because of a variety of interesting physical properties and potential uses. Thus during recent years, spinel has generated interest for optical applications. Cobalt doped MgAl₂O₄ is a promising Q-switch material.^1–3 Excellent transmittance in the infra-red (IR) range makes MgAl₂O₄ suitable for use as a material for IR windows in optical devices. This application motivates research into obtaining transparent polycrystalline MgAl₂O₄ ceramics.⁴ The properties of MgAl₂O₄ in the visible range⁵ make it promising for use in light emitting diodes.⁶ On the other hand, MgAl₂O₄ was a decades-long focus in nuclear material science due to its high radiation tolerance, especially as a waste form and as an inert nuclear fuel matrix.⁷

MgAl₂O₄ displays varying degrees of Mg–Al antisite disorder. The degree of disorder has an effect on the physical properties of this material. Thus, it affects the optical absorption of MgAl₂O₄ doped with transition metals.⁵ Cation disorder was found to determine the exceptional radiation stability of MgAl₂O₄ within different irradiation regimes.^7–9 It was found, by means of transmission electron microscopy (TEM), that, at low temperature, ion irradiated MgAl₂O₄ undergoes a disordering phase transition^8,9 that takes place prior to amorphization. The transition from ordered (defective) spinel (lattice parameter 8.08 Å, space group Fd3̄m) to a disordered structure (lattice parameter is about half of that of spinel, space group Fm3̄m) is easily indicated by the disappearance of the spinel (220) and (111) reflections, which results in fewer allowed spots in diffraction patterns.^8,9 The phase transition occurs by cation disordering when Mg and Al move to octahedral sites, while anions preserve a cubic close packed (ccp) arrangement. The new phase has the rock-salt structure and occurs during cryo-temperature irradiations in either stoichiometric or non-stoichiometric spinels.^8–10 A similar spinel ↔ rock-salt phase transition has been observed in magnesium chromium,¹¹ lithium manganese and lithium iron spinels, which are extensively studied due to their use in electrochemistry.¹²

Irradiation with energetic particles often results in a metastable state because of the large quantity of defects. The excess energy, especially the elastic energy due to irradiation-induced elastic strain, is the origin of the radiation-induced structural and microstructural modifications. The objective of the present study is to identify the changes in the structure of MgAl₂O₄ spinel single crystals with strain evolution over a wide dose range. This was performed by irradiating 〈111〉 and 〈110〉-oriented MgAl₂O₄ single crystals with doses equivalent to 0.3–28 dpa (displacements per atom) that were subsequently characterized by X-ray diffraction (XRD) that probes elastic strain variation in ion-irradiated materials (see e.g.ref. 13–17). Transmission Electron Microscopy analysis was also performed to identify microstructural and structural changes upon irradiation.

Experimental

MgAl₂O₄ single crystals of 〈111〉 and 〈110〉 orientations (manufactured by Union Carbide and MTI, respectively) were irradiated with 600 keV Xe ions at 77 K. Ion irradiations were carried at the Ion Beam Materials Laboratory (IBML) at Los Alamos National Laboratory (LANL) using a Danfysik 200 kV research implanter. The flux during implantation was kept below 10¹² Xe cm⁻² s⁻¹ (<0.003 dpa s⁻¹) to minimize potential beam heating effects. The samples were tilted 7° relative to the incidence beam direction in order to avoid ion channeling. Simulation of the Xe–spinel interactions was performed using the SRIM program.³⁴ The samples are designated by the maximum deposited damage dose (see Table 1). Values of implanted Xe ion fluences were verified by Rutherford Backscattering Spectrometry (RBS) measurements that were also performed at the IBML.

Table 1 Fluences determined by RBS measurements and corresponding maximum damage estimated by SRIM code

Crystal orientation	Maximum dose [dpa]	Fluence [Xe cm^−2]
〈111〉	0.3	1.1 × 10^14
	1.5	5.5 × 10^14
	3	1.1 × 10^15
	7	2.6 × 10^15
	9	3.5 × 10^15
〈110〉	0.3	1 × 10^14
	1.5	5.3 × 10^14
	3	1 × 10^15
	5	2.0 × 10^15
	7	2.6 × 10^15
	9	3.5 × 10^15
	12	4.4 × 10^15
	19	7.4 × 10^15
	28	1.1 × 10^16

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XRD measurements (see Fig. 1–3) were performed at the Institute for Fundamental Electronics (IEF – Orsay, France) using a Philips X'Pert PRO MRD diffractometer equipped with a standard Cu tube. An intense and monochromatic beam was obtained by using a multilayer mirror behind the tube followed by a four-crystal monochromator (4xGe220) in an asymmetric configuration. The resulting primary-beam divergence was ∼18 arcsec (0.005°). Symmetric θ–2θ scans and reciprocal space maps (RSMs) were recorded in the vicinity of the (444) (2θ–82.677°) and (440) (2θ–65.236°) Bragg reflections; asymmetric reflections (e.g. (444) for (110)-oriented crystals) were also probed. A detector slit, for RSMs, or a three-bounce crystal analyzer (3xGe220), for θ–2θ scans, was used to further limit the detector acceptance.

The notations used in Fig. 1–3a are based on ref. 18: (i) K_N and K_∥ are the normal (out-of-plane) and parallel (in-plane) components of the scattering vector K (2sinΘ/λ), respectively; (ii) H_(hkl) refers to the reciprocal lattice vector for the (444) or (440) reflections; (iii) q_N is defined as K_N–H_(hkl) and represents the deviation from the reciprocal lattice vector (which is sometimes called the reduced scattering vector); (iv) (−q_N/H_(hkl)) is equal to the elastic strain in the direction normal to the surface of the irradiated samples; (v) (ΔK_∥/H_(hkl)) indicates the width (here in degrees) of the reciprocal lattice point in the transverse direction.

TEM analysis (see Fig. 4–8) was performed at the Electron Microscopy Laboratory at LANL using a FEI Tecnai F30 operated at 300 kV. The samples were measured at room temperature. Cross-sectional samples were made by tripod polishing and subsequent Ar ion milling to electron transparency. Diffraction patterns and images were recorded under the conditions indicated in the figure captions. For selected area diffraction (SAD) patterns, the projected aperture size was 268 nm.

Results and discussion

Damage build-up determined by XRD measurements

XRD patterns obtained from 〈110〉-oriented spinel single crystals are shown in Fig. 1a. The patterns exhibit typical features observed for low-energy ion-irradiated materials.^14,16 First, an intense and sharp Bragg peak originating from the unirradiated, bulk part of the crystals is visible. This peak is due to the fact that the X-ray penetration depth (tenths of microns) is much larger than the irradiated layer thickness (<300 nm) and it is used as an internal strain gauge. Second, in the patterns measured on irradiated samples, an additional interference signal that comes from the irradiated layer is observed. This signal is on the low-angle wing of the curves, which indicates expanded lattice spacing in the direction perpendicular to the crystal surface. This signal has a shape that clearly evolves with the dose. A fringe pattern is observed as the dose increases up to 3 dpa. It has been shown that this pattern is due to the presence of a strain which changes with distance from the surface. Several approaches were developed in order to model the strain depth profile.^19–23 Fitting results will be presented in the following section. However, it should be noted that the maximum value of strain in the irradiated layer can be obtained already from these patterns, since the maximal strain corresponds to the most distant fringe from the main Bragg peak. In the present case (i.e. for the 〈110〉 orientation), this level reaches nearly 2% at 7 dpa. Note, however, that at 5 dpa, a significant change in the XRD pattern shape is observed. A hump appears at ∼0.25% strain level while the fringe pattern starts to smooth out. At 19 dpa, the fringes totally vanish and only the hump remains with a minor shift in position.

Fig. 1 θ–2θ scans recorded in the vicinity of (a) (440) and (b) (444) diffraction peaks from MgAl₂O₄ 〈110〉 and 〈111〉-oriented single crystals, respectively. A change in diffraction pattern between 3 and 5 dpa (a) and 1.5 and 3 dpa (b) indicates the onset of an order–disorder radiation induced phase transition.

Fig. 1b displays XRD patterns for the 〈111〉-oriented crystals. Here, a double Bragg peak is observed from the unirradiated part of crystals. This finding suggests the presence of two regions with slightly different compositions (no such double-peak has been observed in rocking-curves). It has been verified that this peculiarity did not have any effect on the overall behavior upon irradiation. Actually, the XRD patterns exhibit the same evolution as that observed for the 〈110〉-oriented crystals. However, two important differences are observed. First, the most significant change in the XRD pattern shape appears at a significantly lower dose. This transition is observed between 1.5 and 3 dpa on the 〈111〉 orientation whereas it is detected between 3 and 5 dpa for the 〈110〉 orientation. Second, the maximum strain level produced in the irradiated layer amounts to ∼0.8% (instead of ∼2% for the 〈110〉 orientation). This latter finding is consistent with the fact that MgAl₂O₄ is an elastically anisotropic material,²⁴ with the [110] direction softer than the [111] one. Such a crystallographic irradiation-dependent response was reported previously for yttria-stabilized c-ZrO₂, MgO^25,26 and Al₂O₃.²⁷

Earlier studies demonstrated that the damage accumulation in irradiated spinels occurs in two steps. The first transition was attributed to the formation of a metastable disordered rock-salt structure and the second one to amorphization.⁸ The present work, which investigates a wide range of doses, demonstrates that damage actually accumulates in three steps. This statement holds for both crystalline orientations. The first two stages of the damage build-up, which will be called the low-dose range and intermediate-dose range, are described in detail in the following sections. The third step that occurs in the high-dose range is ascribed to amorphization of the irradiated crystals. A similar three-step process has been shown using channeling measurements in 150 keV Cs-irradiated spinel crystals.²⁸

Damage build-up description

Low-dose range. In this range (below 3 dpa for 〈110〉 and 1.5 dpa for 〈111〉-oriented crystals), the magnitude of the elastic strain as deduced from XRD measurements increases with irradiation dose (Fig. 1). This result suggests that the strain is closely related to the formation of irradiation-induced defects. A simulation of the XRD curves corresponding to this low-dose range has been carried out by using GID_sl software.¹⁹ This software does not take into account diffuse scattering by defects and by lattice distortions around them which was shown to improve fit accuracy.²⁹ A representative example is given in Fig. 2a. Although the agreement is not perfect between the simulated XRD and the data due to the very complex structure of the experimental pattern, the number, position and width of the fringes have been well reproduced. This simulation was performed using the strain depth profile plotted in Fig. 2b. The maximum strain level was found to be ∼0.8% for the 〈111〉-oriented crystal irradiated to 1.5 dpa, a value which agrees with the value determined from observation of XRD pattern. The shape of this profile appears to be similar to the displacement damage (so-called dpa) distribution predicted by SRIM. This finding suggests that, in the low-dose range, the strain develops via the formation of non-interacting irradiation defects.

Fig. 2 (a) Measured diffraction profile from a 〈111〉-oriented crystal irradiated to the dose of 1.5 dpa (no phase transition) and fitting with the strain profile shown in (b). The shape of the strain profile is very close to that predicted by SRIM modeling. The thickness of the damaged layer determined from the TEM image is 200–210 nm.

A typical reciprocal space map (RSM) characteristic of crystals in the low-dose range is displayed in Fig. 3a. Such a figure depicts the scattered intensity (in logarithmic scale) in the vicinity of a given Bragg reflection. The intense signal – grey colour on the map – observed at the coordinates of the unstrained material signal corresponds to the undisturbed part of the samples probed by X-rays. Also visible on the map in Fig. 3a is a spreading of the scattered intensity along the K_N direction in the region of higher lattice parameter (positive −q_N/H₍₄₀₀₎ values), which is obviously consistent with XRD curves presented in Fig. 1. This signal arises from the scattering of the X-ray beam by the irradiated layer. More interestingly, it should be noted that the scattered intensity is confined to a small K_∥ region, even around the reflection corresponding to the damaged layer. This result strongly suggests that defects at the origin of the strain are of small dimensions (point defects or small defect clusters), i.e. no significant defect clustering occurred, which is consistent with previously reported results on e.g. irradiated zirconia.^13,15

Fig. 3 Reciprocal space mapping (RSM) on a 〈110〉 crystal irradiated to (a) 0.3 dpa; (b) 5 dpa, symmetric scan; (c) 5 dpa, asymmetric scan.

TEM analysis of samples irradiated within the low-dose region revealed that no order–disorder phase transition has taken place (see Fig. 4).

Fig. 4 Selected area diffraction patterns of [112] zone axes: (a) 〈111〉 crystal irradiated to 1.5 dpa and (b) unirradiated areas. No indication of order–disorder phase transition.

Intermediate-dose range. First, it is important to highlight that, in the intermediate dose-range, the formation of the disordered (i.e. rock-salt) structure is clearly observed, as evidenced by the fading of (220) spinel reflections in the electron diffraction pattern displayed in Fig. 5 and 6. Second, in this range, the magnitude of the strain does not increase with the irradiation dose. On the contrary, there is a gradual strain relaxation that is indicated by the disappearance of the fringe pattern and by the shift of the XRD signal corresponding to the irradiated layer towards the peak of the pristine (undamaged, unstrained) crystal (see Fig. 1). The RSM displayed in Fig. 3b (〈110〉-oriented crystal irradiated to 5 dpa) does not exhibit any sign of lateral broadening with respect to maps recorded at low dose (Fig. 3a). This observation, which holds for both crystalline orientations, indicates that the strain relief is not due to the formation of extended defects such as dislocations, as was previously observed in e.g. irradiated Zirconia.^13,15 Furthermore, asymmetric RSMs (a typical example is displayed in Fig. 3c) indicates that even after phase transformation the strain is still located only along the normal direction (no in-plane strain is observed).¹⁸ This finding indicates that there is no strain relaxation at the irradiated/pristine interface.

Fig. 5 Selected area diffraction patterns of [011] zone axes: (a) 〈111〉 crystal irradiated to 3 dpa and (b) unirradiated areas. The start of an order–disorder phase transition is manifested in the fading of the (220) spinel reflection.

Fig. 6 TEM microdiffraction patterns. 〈110〉 crystal implanted to 12 dpa. (a) Irradiated region and (b) from bulk unirradiated areas. Faded (220) reflections indicate that the defected spinel phase is still present in tiny amounts within the disordered phase. [001] zone axes.

In the intermediate dose range, XRD patterns cannot be fitted with the SRIM-predicted dpa profile (nor with the Xe distribution). This is mainly because the XRD curves corresponding to this dose range are characterized by the appearance of a hump at the left side of the main Bragg peak. It is found that the hump appears near the peaks which are allowed and which are forbidden in the disordered phase (i.e. (222) and (220) spinel reflections). Therefore it does not originate from the new disordered phase, but it has to be related to defective (ordered) spinel. Indeed, the defective spinel phase is still present within the irradiated layer. Electron microdiffraction patterns (Fig. 6) demonstrate that (220) reflections, which should be absent in the disordered phase, did not vanish entirely. This finding is confirmed by TEM dark-field images recorded with (220) reflection, that show presence of spinel phase, especially in the near-surface region (see Fig. 7). The result is in agreement with previous high resolution TEM studies in which domains of untransformed spinel with a size of about 5 nm in diameter³⁰ were seen. This defective spinel phase persists up to very high doses (e.g. 19 and 28 dpa for 〈110〉-oriented crystals). At ≥19 dpa TEM shows that the irradiated layer splits into three parts (see Fig. 8). The near-surface layer and the layer close to the bulk are single crystal and transformed into the disordered phase. However, the near-surface layer still has a residual ordered spinel phase. The embedded layer appears to be amorphous (or a mixture of amorphous zones and polycrystalline disordered-phase regions). A similar microstructure was previously reported in 〈111〉-oriented spinel implanted with 180 keV Xe to the dose of 15 and 30 dpa.³⁰

Fig. 7 Two-beam condition imaging of the 〈110〉 crystal irradiated to 12 dpa: (a) dark field image formed with the spinel (440) reflection. This reflection exists in both the ordered and disordered phase; (b) dark field image with the spinel (220) reflection. This reflection is present in the ordered phase only. The image shows that the irradiated layer contains an ordered phase (appears bright), especially in the near-surface region (to the left of the blue line).

Fig. 8 19 dpa sample: bright field cross-sectional TEM image on a 〈110〉-oriented crystal. The whole irradiated layer is transformed into a disordered phase, some inclusions of the ordered phase may be present.

Damage accumulation interpretation

During the irradiation process atomic displacements are created by nuclear collisions resulting in the formation of point defects or small defect clusters. Accumulation of point defects induces volume expansion and, consequently, in-plane compressive stress in irradiated material.³¹ As a result, a tensile strain develops along the normal direction of irradiated crystals.¹⁸ This strain increases with the fluence in the low-dose range. At higher fluences a disordered (i.e. rock-salt) phase appears. It is known that the disordered phase arises from a randomized cation redistribution on octahedral sites of Mg and Al.³⁰ Irradiation-induced defects are “frozen-in” at cryogenic temperature. Furthermore, it is demonstrated here that the phase transition only occurs after an incubation dose. Therefore, it appears that the phase transformation process takes place by a reorganization of defects formed in the first irradiation stage. This defect rearrangement seems to occur inhomogeneously over the entire irradiated volume, as suggested by the remaining islands of untransformed material. This result is consistent with the phase transition process occurring within collision cascades. It is noteworthy that entropy increase due to disordering cannot be a key factor in the stabilization of the new phase because previous work³² revealed that the rock-salt phase reverts to the ordered spinel structure after annealing for 52 days at 1100 °C.

Since the phase transformation appears to be concomitant with the strain (and stress³¹) relaxation, it indicates that these phenomena are related. The question that arises is whether strain relaxation is a cause or a consequence of the order–disorder phase transition. The fact that no mechanism of typical plastic relaxation (e.g. interface dislocations, amorphization) has been observed suggests that strain relaxation is rather a consequence of phase transformation. The fact that compressive stress is relieved implies that the new (disordered) phase has a smaller volume than that of the ordered (defective) spinel. In other words, transition from strained (defective) spinel to rock-salt phase induces a slight shrinkage of the unit cell. However, one should remember that the rock-salt phase does not appear at the same dose, hence not at the same strain level, for the two studied crystalline orientations. Actually, the phase transition occurs at lower doses when the crystal is oriented along the stronger direction, i.e. along the direction that exhibits smaller maximum deformation, i.e. the [111] direction. The presence of elastic energy accelerates the phase transformation.

Another reason for disordering anisotropy could lie in structure-related effects. In order to form the rock-salt phase in MgAl₂O₄ the Mg and Al need to be displaced from tetrahedral to octahedral sites via ion collisions. The simplified way to represent this process can be described in Kröger–Vink notations as following:

Therefore two factors can have an impact on the efficiency of the rock-salt phase formation: (i) the availability and configuration of these sites in a chosen crystallographic direction; (ii) the attraction force between two charged species that are created. Intuitively the latter works against stabilization of the rock-salt phase because attraction force favors recombination.

If viewed along the [110] or [111] direction, MgAl₂O₄ has different arrangements of tetrahedral and octahedral sites. Along [110], both types of crystallographic sites form rows that consist of only one site type (for convenient visualization see ref. 33). In contrast, along the [111] direction there are both types of crystallographic sites. Therefore, the process of cation mixing into octahedral sites along this direction will be more efficient. Once displaced, an atom can migrate within a row of edge-to-edge connected octahedra by one or two bonding units (mobility is limited at low temperature) increasing charge separation and thus contributing to the stabilization of the new phase. The preference of the (111) orientation to disorder could be reflected in different number of defects relative to the (110) orientation. Indeed, previous studies of MgO²⁶ and Al₂O₃ߙ²⁷ showed that the defect production rate upon irradiation varies significantly between crystallographic orientations. MgAl₂O₄ would therefore be an obvious candidate material for further evaluation of this effect.

Conclusions

This work demonstrates how order–disorder phase transformation in MgAl₂O₄ is related to relaxation of irradiation-induced elastic strain. The behavior of 〈111〉 and 〈110〉-oriented MgAl₂O₄ spinel single crystals under irradiation in the nuclear energy-loss regime has been investigated in a wide dose range by XRD and TEM. Owing to dramatic changes in the XRD patterns with fluence, two steps in the damage build-up are detailed (a third step ascribed to amorphization has been previously evidenced^8,30). At the low dose, XRD measurements strongly suggest that small irradiation-induced defect clusters are formed and an in-plane elastic compressive stress is developed as a consequence. Consequently normal tensile strain develops and its level increases with the fluence. At a given transition dose (between 3 and 5 dpa for the 〈110〉 and 1.5 and 3 dpa for the 〈111〉 orientations), the XRD patterns change drastically. This change is a signature of the onset of the order–disorder phase transition, namely from the spinel to rock-salt structure, that is clearly revealed by the TEM analysis. The appearance of the new phase is a cause of the concomitant partial relaxation of normal tensile strain, which implies a volume change. It is demonstrated that the volume of the new phase is slightly smaller than that of irradiated spinel. Finally, the dose at which this transition takes place is found to be dependent on the crystallographic orientation. It is shown that both elastic properties and crystal structure might be at the origin of this dependence.

Acknowledgements

The author wants to thank V. Kaganer from the Paul Drude Institute for Solid State Electronics, Germany for helpful comments and suggestions, Y. Wang and I. O. Usov from LANL for their help with RBS measurements, R. Dickerson from LANL for his help with TEM, J. Zhang and E. Fu from LANL for their help with irradiations, Y. Feldman from Weizmann Institute of Science, Israel for his help with preliminary measurements, S. Stepanov from Argonne National Laboratory, USA for his help with X-ray Server. XRD measurements on the Panalytical diffractometer have been performed at the nanocenter CTU-IEF-Minerve that is partially funded by the “Conseil Général de l'Essonne”. The LANL portion of this work was sponsored by the FCR&D, LDRD and Basic Energy Science of the US Department of Energy Office.

Notes and references

1. K. V. Yumashev, I. A. Denisov, N. N. Posnov, P. V. Prokoshin and V. P. Mikhailov, Appl. Phys. B: Lasers Opt., 2000, 70, 179–184.
2. G. Karlsson, V. Pasiskevicius, F. Laurell, J. A. Tellefsen, B. Denker, B. I. Galagan, V. V. Osiko and S. Sverchkov, Appl. Opt., 2000, 39, 6188–6192.
3. J. E. Hellstrom, G. Karlsson, V. Pasiskevicius, F. Laurell, B. Denker, S. Sverchkov, B. Galagan and L. Ivleva, Appl. Phys. B: Lasers Opt., 2005, 81, 49–52.
4. M. Shimada, T. Endo, T. Saito and T. Sato, Mater. Lett., 1996, 28, 413–415.
5. C. Garapon, H. Manaa and R. Moncorgé, J. Chem. Phys., 1991, 95(8), 5501–5512.
6. K. Izumi, S. Miyazaki, S. Yoshida, T. Mizokawa and E. Hanamura, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 075111.
7. K. E. Sickafus, A. C. Larson, N. Yu, M. Nastasi, G. W. Hollenberg, F. A. Garner and R. C. Bradt, J. Nucl. Mater., 1995, 219, 128–134.
8. N. Yu, K. E. Sickafus and M. Nastasi, Philos. Mag. Lett., 1994, 70(4), 235–240.
9. R. Devanathan, K. E. Sickafus, N. Yu and M. Nastasi, Philos. Mag. Lett., 1995, 72(3), 155–161.
10. K. Sickafus, N. Yu, R. Devanathan and M. Nastasi, Nucl. Instrum. Methods Phys. Res., Sect. B, 1995, 106, 573–578.
11. Yu. G. Chukalkin, V. V. Petrov, R. Shtirts and B. K. Goshchitskii, Phys. Status Solidi A, 1985, 92, 347–354.
12. M. Thackeray, J. Am. Ceram. Soc., 1999, 82(12), 3347–3354.
13. S. Moll, L. Thomé, G. Sattonnay, A. Debelle, F. Garrido, L. Vincent and J. Jagielski, J. Appl. Phys., 2009, 106, 073509.
14. A. Debelle, A. Declémy, L. Vincent, F. Garrido and L. Thomé, J. Nucl. Mater., 2010, 396, 240–244.
15. A. Debelle, S. Moll, B. Décamps, A. Declémy, L. Thomé, G. Sattonay, F. Garrido, I. Jowik and J. Jagielsky, Scr. Mater., 2010, 63, 665–668.
16. A. Debelle, L. Thomé, D. Dompoint, A. Boulle, F. Garrido, J. Jagielski and D. Chaussende, J. Phys. D: Appl. Phys., 2010, 43, 455408.
17. A. Debelle, A. Boulle, F. Garrido and L. Thomé, J. Mater. Sci., 2011, 46, 4683–4689.
18. A. Debelle and A. Declémy, Nucl. Instrum. Methods Phys. Res., Sect. B, 2010, 268, 1460–1465.
19. (a) S. Stepanov and R. Forrest, J. Appl. Crystallogr., 2008, 41, 958–962; (b) http://x-server.gmca.aps.anl.gov/ .
20. U. Pietsch, V. Holý and T. Baumbach, High Resolution X-ray Scattering, Springler-Verlag, New York, USA, 2nd edn, 2004.
21. A. Boulle and A. Debelle, J. Appl. Crystallogr., 2010, 43, 1046–1052.
22. D. Shilo, E. Lakin and E. Zolotoyabko, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 205420.
23. D. Shilo, E. Lakin and E. Zolotoyabko, Appl. Crystallogr., 2001, 34, 715–721.
24. I. Suzuki, I. Ohno and O. L. Anderson, Am. Mineral., 2000, 85, 304–311.
25. I. Usov, P. N. Arendt, J. R. Groves, L. Stan and R. F. DePaula, Nucl. Instrum. Methods Phys. Res., Sect. B, 2005, 240, 661–665.
26. I. Usov, J. A. Valdez and K. E. Sickafus, Nucl. Instrum. Methods Phys. Res., Sect. B, 2011, 268, 288–291.
27. G. B. Krefft and E. P. EerNisse, J. Appl. Phys., 1978, 49(5), 2725–2730.
28. J. Jagielski and L. Thomé, Nucl. Instrum. Methods Phys. Res., Sect. B, 2007, 261, 1155–1158.
29. Y. Avrahami and E. Zolotoyabko, Nucl. Instrum. Methods Phys. Res., Sect. B, 1996, 120, 84–87.
30. M. Ishimaru, Y. Hirotsu, I. Afanasyev-Charkin and K. E. Sickafus, J. Phys.: Condens. Matter, 2002, 14, 1237–1247.
31. J. Jagielsky and L. Thomé, Vacuum, 2007, 81, 1352–1356.
32. I. Afanasyev-Charkin, R. M. Dickerson, D. W. Cooke, B. L. Benett, V. T. Gritsyna and K. E. Sickafus, J. Nucl. Mater., 2001, 289, 110–114.
33. http://www.chemtube3d.com/solidstate/_sync(28spinel).htm .
34. (a) J. F. Ziegler, J. P. Biersack and U. Littmark, The stopping and range of ions in matter, Pergamon, New York, vol. 2–6, 1985; (b) http://www.srim.org .

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Footnote

† Current address: Science Institute-University of Iceland, Dunhaga 3, Reykjavik, Iceland. E-mail: anna.kossoy@gmail.com, annaeden@hi.is; Fax: +354 552 8911; Tel: +354 694 8163

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