Defect chemistry of doped bixbyite oxides

Solid State Sciences 9 (2007) 588e593 www.elsevier.com/locate/ssscie

Defect chemistry of doped bixbyite oxides Mark R. Levy a, Christopher R. Stanek b, Alexander Chroneos a,c, Robin W. Grimes a,* a

Department of Materials, Imperial College London, London SW7 2BP, UK b Los Alamos National Laboratory, Los Alamos NM 87545, USA c Institute of Microelectronics, NCSR Demokritos, Aghia Paraskevi 15310, Greece Received 19 January 2007; accepted 20 February 2007 Available online 14 March 2007

Abstract Activated bixbyite oxides (e.g. Eu:Lu2O3) are being considered as radiation detectors. In an attempt to improve their optical efficiency and decrease afterglow, these compounds have been doped with aliovalent cations. Here, atomistic scale computer simulation has been used to predict the defect processes associated with the solution of extrinsic divalent and tetravalent ions. These calculations provide a mechanistic framework through which it is possible to identify how specific doping schemes modify the populations of defects that could influence scintillator performance. A change in solution site preference is predicted for both divalent and tetravalent solutions as a function of dopant and host lattice cation radii. Ó 2007 Elsevier Masson SAS. All rights reserved. PACS: 61.66.Fn; 61.72Bb; 61.72Ji; 81.05Je; 84.60.Dn Keywords: Defect energies; Atomistic simulation; Oxides; Rare earth; Bixbyite; Scintillators

1. Introduction Due to their high light output, materials based on sesquioxides (R2O3 where R is the rare earth cation (PreLu), Y, Sc or In) are being considered as potential radiation detectors [1]. In the case of these materials, the scintillation mechanism relies upon an activator that is a second cation, which is substituted into the host lattice. A promising example is Eu3þ doped Lu2O3 [1e4]. Optimum scintillator materials are prompt, bright and dense. A material is prompt if the response to irradiation is quick, with the light output decreasing rapidly once the incident radiation has terminated (short afterglow). A further consideration is that the material is transparent so that the light emitted is not scattered before it reaches the electronics component of the detector. Unfortunately, materials such as Lu2O3 suffer from afterglow effects, which are governed by point defects [4]. Lu2O3 is, however, exceptionally dense

* Corresponding author. Tel.: þ44 0 207 594 6730. E-mail address: [email protected] (R.W. Grimes). 1293-2558/$ - see front matter Ó 2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2007.02.009

(9.39 g cm3) and bright (on the order of Tl:CsI [4]) and is thus ideally suited to medical imaging applications such as positron emission tomography (PET) [4] where afterglow time is less critical. In general, the efficiency of scintillator materials is significantly reduced by electron (e) and hole (hþ) traps which slowdown the rate of eehþ recombination or compete as non-radiative centres [5]. A variety of defects can act as traps, in particular point defects within the crystal lattice. It is, however, possible to introduce species into the lattice in order to reduce the concentration of deleterious trap centres and hence optimise optical properties [6]. For example, it has been proposed that oxygen vacancies (V ¨ gereVink notation O in Kro [7]) are the predominant electron trap sites in LuxY1xAlO3 (LuYAP) [8]. Having identified the performance limiting defect, it is possible to consider processes that decrease the concentration of these deleterious oxygen vacancies. In particular, Zr4þ has been incorporated into materials such as LuAlO3 and YAlO3 because oxygen interstitial defects ðO00i or O0i Þ are simultaneously introduced as charge compensating species [6,9]. These interstitial ions will combine with the oxygen

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vacancies through the oxygen Frenkel equilibrium (reaction (1)), thereby suppressing the oxygen vacancy concentration [10].

Table 1 Lattice sites for ions in the bixbyite structure. x, y, z are dependent on the particular structure under consideration

00 OXO 4V O þ Oi

Species

Wycoff site

Position

RE (1) RE (2) O Interstitial (1) Interstitial (2) Interstitial (3)

8b 24d 48e 16c 24d 8b

1

ð1Þ 

⁄4 , 1⁄4 , 1⁄4 x, 0, 1⁄4 x, y, z 1/8, 1/8, 1/8 1⁄4 , 0, 1⁄4 ½, ½, 0

This approach is only effective if the extent to which e or hþ species are trapped by Zr4þ substitutional defects is substantially less than by the oxygen defects [10]. A similar study [11] has considered aliovalent doping of RE3Al5O12 (RE ¼ rare earth cations) garnets. However, the defect process behaviour in these materials is different to that in perovskites containing the same elements. Specifically for the garnets, it was found that tetravalent dopants are charge compensated by rare earth cation vacancies. This defect mechanism is decidedly unintuitive and defect engineering approaches that are successful in optimizing defect behaviour in the related perovskites do not translate across to other materials’ systems. Since the previously mentioned examples (in garnet and perovskite) demonstrate that the solution behaviour of aliovalent dopants is not intuitive, here we consider the energies and structures associated with the accommodation of divalent and tetravalent dopants over a range of bixbyite oxides. We employ static lattice, atomic scale computer simulation, which has proved successful for studying intrinsic processes in the same materials [12] and dopant processes in Y2O3 [13] (the present results correlate well). The systematic study of aliovalent dopant solution energies, as a function of dopant or host lattice cation radius, allows us to identify key trends in dopant behaviour. This improved fundamental understanding of aliovalent defect structures will aid in optimizing this class of material.

following layer consists exclusively of octahedral about the 24d position. Of particular relevance to the optical properties, the 24d site is noncentrosymmetric (C2) whereas the 8b site is centrosymmetric (S6). Therefore the electronic characteristics of cations residing at these two sites differ so that the preferential doping of one or other of the two sites will produce different electrical or magnetic properties [16]. For scintillator applications it is desirable that the activator ion reside predominantly at the 24d site. In fact, for Eu electric dipole electronic transitions are forbidden if the site is centrosymmetric [17]. The bixbyite structure is also able to accommodate ions at three distinct interstitial sites: 16c, 24d and 8b (see Table 1). The local environments of the interstitial sites are again different, and although all are 6-fold coordinated by oxygen ions, the 8b and 24d sites are 6-fold coordinated by cations, while the 16c site is only tetrahedrally coordinated by cations. Furthermore, despite the apparent similarity in the coordinations of the 8b and 24d interstitial sites, they are subject to different distortions from ideal octahedral. Previous work identified the 16c site was occupied by oxygen interstitial ions [13].

1.1. Crystallography

2. Methods

At room temperature, all the sesquioxides considered here exhibit the cubic bixbyite, C-type rare earth structure [14], space group Ia3 (206) [15]. Within this structure, there are two non-equivalent octahedral cation positions, 24d and 8b (see Fig. 1) with oxygen ions occupying only 48e position (see Table 1). The cation sites are arranged such that they create consecutive (100) layers with the first layer composed of RO6 octahedral around 24d and 8b positions, while the

The calculations performed in this work are based upon a classical Born-like description of an ionic crystal lattice [18,19]. The interatomic forces acting between ions are resolved into two components: a long-range columbic, summed via the Ewald method [20], and a short-range pair-wise interaction, modelled using parameterized Buckingham pair poten˚. tials [21] and summed directly up to a cut-off value of 18 A The lattice energy is then given by,

EL ¼

XX j>i

Fig. 1. The 8b (left) and 24d (right) cation sites with their associated oxygen ions.

"

!#   qi qj rij Cij þ Aij exp  4p30 rij rij rij6

ð2Þ

where Aij, rij and Cij are adjustable short-range parameters, 30 is the permittivity of free space, and rij is the interionic separation between ions i and j of charge qi and qj, respectively. The perfect lattice is defined by tessellating the unit cell throughout space using boundary conditions defined by the crystallographic lattice vectors. The lattice is relaxed to zero strain at constant pressure by varying the ion positions and the unit cell dimensions, according to a NewtoneRaphson energy minimisation procedure.

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The adjustable parameters of the Buckingham potential were derived using a multi-structure fitting procedure [22,23] as described elsewhere [24,25]. The polarisability of oxygen ions is accounted for via the shell model of Dick and Overhauser [26]. In order to model the effect of a charged defect on the lattice, a multi-region approach is adopted in which the lattice is partitioned into concentric, spherical regions centered on the defect. The region immediately surrounding the defect is termed region I, in which all ions are explicitly relaxed, subject to forces described by the interatomic potentials. Surrounding this is region IIa in which the forces between the ions are determined via a dielectric continuum approximation and all ions are relaxed in a single step. The interaction energies between the ions in interfacial region IIa and region I are, however, calculated explicitly. Beyond region IIa is the outer region IIb, which is a point charge array and provides the Madelung field of the remaining lattice; the response energy for this region is determined using the MotteLittleton approximation [27]. Calculations were carried out using the GULP code [28]. Defect energies are presented as a function of defect or host cation radii either two dimensionally in graphs or in three dimensions as composition maps. To generate the map contours, it is necessary to interpolate values between the discreet compositions for which specific calculations are carried out [29]. The contours are displayed over the component cation radii [30] surface. This surface is formed by ordering the host cation radii along the x-axis and the dopant cation radii along the yaxis to generate a grid of compositions for which simulations have been carried out.

charge compensation. The predicted energies for the solution of A3þ ions from their associated oxides (A2O3) into the host (R2O3) lattices (via Eq. (3)) are presented in Fig. 2. A2 O3 þ 2RXR 52AXR þ R2 O3

ð3Þ

Fig. 2 shows that when the isovalent dopant is larger than the host cation, it has a preference for the 8b site (indicated by filled circles). Conversely, when the dopant is smaller, it will reside on the 24d site (indicated by open circles). The energy preference to occupy one site rather than another increases from practically zero, when the host and dopant cations are of similar size, to 0.38 eV per ion when there is a large size mismatch between the host and dopant cation. The change in preference is related to the symmetries and differences in metaleoxygen distances exhibited by the two sites (see Fig. 1). For the 8b site, all six metaleoxygen bonds are of equal length (see Table 2 and Fig. 1) whereas the 24d site has two bonds that are shorter than in the 8b site, two the same, and two larger (the average being almost the same). The smaller dopant is readily accommodated in a site with shorter bonds whereas for a larger dopant, this quickly causes greater strain. This observation establishes the pure size preference effect. (A more in-depth analysis of the implications for scintillator performance is given by Stanek et al. [31], where, for example, ions such as Eu3þ are shown to occupy both 24d and 8b sites.) What follows is a consideration of aliovalent dopant preferences (and solution energies), where the charge of the dopant ion will also influence the accommodation process. 3.2. Divalent ion solution

3. Results 3.1. Trivalent (isovalent) ion solution Since trivalent dopant ions are isovalent with respect to the host lattice ions they replace, as dopants, they do not require

Divalent cations (M2þ) can be accommodated at either 24d or 8b trivalent lattice sites. The necessary charge compensation can be provided by either an oxygen vacancy (Eq. (4)), a dopant interstitial (Eq. (5)) or a host lattice cation interstitial (Eq. (6)).

Fig. 2. Internal energies for dopant A3þ solution in host rare earth oxides, R2O3, with the bixbyite structure.

M.R. Levy et al. / Solid State Sciences 9 (2007) 588e593 Table 2 Equilibrium bond distances in Dy2O3 from oxygen to the host cation and oxygen to aliovalent dopants Site

Dopant

˚) Oxygen bond length (A 1

2

3

4

5

6

Mean

8b

Perfect Ca2þ Zr4þ

2.29 2.43 2.11

2.29 2.43 2.11

2.29 2.43 2.11

2.29 2.43 2.11

2.29 2.43 2.11

2.29 2.43 2.11

2.29 2.43 2.11

24d

Perfect Ca2þ Zr4þ

2.22 2.28 2.06

2.22 2.28 2.06

2.29 2.45 2.10

2.29 2.45 2.10

2.35 2.52 2.18

2.35 2.52 2.18

2.29 2.42 2.11

˚. Lattice parameter ¼ 10.633 A

2MO þ 2RXR þ OXO 52M0R þ V O þ R2 O3

ð4Þ

3MO þ 2RXR 52M0R þ M i þ R2 O3

ð5Þ

3MO þ 3RXR 53M0R þ R þ R2 O3 i

ð6Þ

For all host lattices, the lowest solution energy is the mechanism described by Eq. (4), i.e. via the formation of oxygen vacancies (a similar preference was observed for analog perovskites [32] and garnets [11]). The extent to which Eq. (4) is preferred over Eq. (5) or (6) is a function of host lattice and dopant, with energy preference values ranging from only 0.06 eV for a large host lattice cation with small divalent dopant, to 2.23 eV for a small host lattice cation with a large divalent dopant. As a consequence of Eq. (4) being preferred, there is an equilibrium between the concentrations of oxygen interstitials and oxygen vacancies (through the anion Frenkel equilibrium, Eq. (1)), divalent cation solution will influence the oxygen interstitial concentration. It is therefore important to know which divalent dopant exhibits the lowest solution energy in a given host as this will result in the host being able to accept the highest dopant concentration and therefore the highest concentration of oxygen vacancies. As shown in Fig. 3 for bixbyite oxides with the largest lattice cations, i.e.

591

Nd2O3, Sm2O3 and Eu2O3, the divalent ion with the lowest energy is Sr2þ. For Sc2O3 (which has the smallest lattice cation considered here) the lowest solution energy is for Cd2þ. All other sesquioxides show a preference for solution of Ca2þ (although in a majority of these cases, the difference between Cd2þ and Ca2þ is small). Another important concern is the cation lattice site at which divalent dopant solution is preferred. As discussed earlier, the two cation host lattice sites provide different distorted octahedral environments. In Fig. 3, open circles once again indicate preference for solution at the 24d site, and closed circles preferred solution on the 8b site. It is thus clear that smaller dopants prefer to reside on the 24d lattice site, as was the case for isovalent doping. Furthermore, the change in site preference from 24d to 8b occurs at almost exactly the same dopant:host radius ratio as for isovalent doping, i.e. 1, (compare to Fig. 2). The preferred solution site therefore seems to be governed completely by the dopant cation size mismatch to the host cation. However, as the dopant is divalent there is a charge difference as well as a cation size mismatch. Accommodating a divalent ion at a trivalent lattice site should cause the lattice to expand slightly (since the coordinating O2 ions are less strongly attracted by M2þ substituted ions than by host R3þ ions) and thereby lead to a crossover at a slightly smaller radius ratios. This has certainly been observed in other systems [33]. Nevertheless, such a reduction in crossover radius is not predicted. The reason stems from the asymmetrical response (ionic relaxation) of the lattice due to the inclusion of a dopant at the 24d site compared to the symmetric response at the 8b site (see Table 2). In particular, the expansion (increase in bond length) of the two shortest oxygen ions associated ˚ ) than the expansion with the 24d site is much smaller (0.06 A ˚ and 0.17 A ˚ ). Effecof the other four longer bonds (0.16 A tively, the 24d site has not expanded very much and therefore will only accommodate up to the same size of ion before the ˚ for all ions) becomes more expanded 8b site (by 0.14 A preferred.

Fig. 3. Internal energies for M2þ dopant ion solution (via Eq. (4)) in rare earth host oxides, R2O3, with the bixbyite structure.

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3.3. Tetravalent ion solution In an attempt to reduce the concentration of oxygen vacancies, there has been an experimental study in which YAlO3 was doped with Zr4þ [6]. In order to consider the equivalent process in bixbyite oxides, solution reactions for the process of tetravalent doping are reported below in Eqs. (7)e(9) (although Eqs. (7) and (8) are related through the intrinsic Schottky and oxygen Frenkel reactions). 000

3MO2 þ 4RXR 53MR þ VR þ 2R2 O3

ð7Þ

2MO2 þ 2RXR 52MR þ O00i þ R2 O3

ð8Þ

1 1 MO2 þ O2 ðNÞ þ RXR 5MR þ O0i þ R2 O3 ð9Þ 4 2 Solution energies corresponding to these mechanisms were calculated for Zr4þ, Ce4þ and Ti4þ. It was found that, by a considerable margin, the lowest energy solution process for these tetravalent dopants is achieved through O interstitial defect compensation (Eq. (9)) where the oxygen interstitial ion always occupies the 16c site. Results corresponding to Eq. (9) are presented in Fig. 4. Energies for the solution via Eq. (8), the next most favourable mechanism, vary between 0.95 eV for a large host lattice with a small dopant, to 1.66 eV for a small host lattice with a large dopant. It is evident (from Fig. 4) that the oxygen interstitial mediated solution reaction energies become negative for a series of compounds; however, these data assume solution of an oxygen molecule as an isolated species ðO2 ðNÞÞ whereas, of course, it should proceed from the gas ðO2 ðgÞÞ. Thus, some estimate of the effect of the chemical potential of oxygen gas should be taken into consideration. At an effective solution temperature of 1000 K and (partial) pressure of oxygen gas of 1 atm, this term will be 2.4 eV per O2 [34], which would drive all solution reactions just positive. Solution of tetravalent species would thus result in only small concentrations, driven (as is usually

the case) by the defect configurational entropy. The extent of solution is beyond the present calculations but would follow the trend shown in Fig. 4. This is discussed in more depth by Grimes et al. [34]; for an example of the corresponding equation of chemical equilibrium, see Schmalzreid [35]. From Fig. 4 it can be concluded that the lowest energies are for the solution of Zr4þ, followed by Ce4þ and then Ti4þ for all bar Sc2O3 where the solution energy of Ti4þ is lower than Ce4þ (although cerium and titanium could conceivably be incorporated as Ce3þ and Ti3þ, thus lowering their incorporation energies, and subsequently oxidised to the tetravalent charge state). It is also interesting to note that the minima in the solution energies occur at host lattice cation radii proportionate with the ionic radius of the dopant, i.e. the minimum solution energy for Ti4þ occurs with the lowest host cation radius, followed by Zr4þ at intermediate host radii and Ce4þ solution is most easily accommodated in oxides with the largest host cations. Finally, as with the solution of di- and trivalent species, there is also a change in cation solution site preference for tetravalent incorporation; again smaller dopants are more readily accommodated onto a 24d lattice site. Indeed, Ti4þ always substitutes onto the 24d site; Zr4þ substitutes at the 24d site for all rare earths oxides calculated here (LueNd) but at 8b in the smaller In2O3 and Sc2O3 host lattices; Ce4þ only substitutes onto the 24d site for rare earth oxides with host cation radii greater than Gd3þ. Significantly, the swap over from the 24d to 8b site occurs at a larger host cation radius than the corresponding dopant radius. This is a consequence of the lattice contraction around the M4þ cation decreasing the effective size of the solution site. Table 2 shows the average con˚ and traction for both the 8b and 24d sites which is 0.18 A furthermore the contraction is nearly symmetric (that is, all tetravalent dopanteoxygen bonds contract by the same amount for both sites) quite different to the situation for divalent ion substitution, where the expansion was asymmetric. For tetravalent substitution the swap therefore does occur at a larger host radius than is the case with trivalent dopants. 4. Conclusions

Fig. 4. Internal energies for M4þ solution (via Eq. (9)) in rare earth host oxides, R2O3, with the bixbyite structure. The radii of the respective M4þ cations ˚ , Zr4þ ¼ 0.72 A ˚ and Ce4þ ¼ 0.87 A ˚. are: Ti4þ ¼ 0.605 A

In previous work [12], simulation studies identified the oxygen Frenkel reaction (i.e. reaction (1)) as the lowest energy intrinsic defect process in bixbyite oxides. Part of the reason that this was the favoured process is the existence of a large 16c interstitial lattice site. Thus, oxygen interstitial defects will be present in these undoped oxides, and may act as hole traps. This could explain results obtained by van Schaik et al. [36], who by doping Lu2O3 with Ca2þ, observed an improvement in scintillation properties. In this case, it was assumed that the divalent dopant is accompanied by charge compensating oxygen vacancies; these will combine with the oxygen interstitial defects through the Frenkel equilibrium thereby reducing the overall oxygen interstitial concentration. Of course, this process is only effective if the substitutional cations do not trap hþ as efficiently as oxygen interstitials. The results of the present study are consistent with this model, in that solution of divalent cations is predicted to be

M.R. Levy et al. / Solid State Sciences 9 (2007) 588e593

energetically most favourably compensated by forming oxygen vacancies rather than by cation interstitial ions. Furthermore, the simulations show that Ca2þ will have a lower solution energy compared to alternative divalent dopants of larger or smaller radius. Also, we predict that for Lu2O3, Ca2þ will occupy the 8b site rather than the 24d site and thus not be in competition with rare earth activator ions for 24d sites. From the point of view of scintillator properties, rare earth activator ions on the 8b site are not effective (as electric dipole transitions are forbidden). However, for most combinations of host lattice and activator, a fraction of activator ions are likely to reside on the 8b site [31]. Thus, any occupation of the active 24d site by cations other than activator ions should be avoided. If the dopant cations fill 8b sites, it is likely that more activator cations will reside on the 24d site than if there was no divalent dopant. In this regard, the results for all divalent substitutional ions are of significance as only certain combinations of dopant and host lattice result in the preferential occupation of the 8b site (see Fig. 3). Further experimental studies will improve the understanding of the simultaneous solution behaviour of dopants and activators in bixbyite oxides. In previous studies of perovskites, tetravalent dopants (in particular Zr4þ) were introduced into host lattices in an attempt to improve scintillator performance. In those perovskites, intrinsic oxygen vacancies are considered deleterious but can be reduced in concentration, through the Frenkel equilibrium, by biasing the oxygen interstitial concentration (since tetravalent dopants are compensated by O2 interstitial ions). In the case studied here, of bixbyite hosts, it is predicted that tetravalent doping is not compensated by O2 interstitials ðO00i Þ but by O interstitials ðO0i Þ. Furthermore, the internal energy of Zr4þ solution is predicted to be quite low, certainly much lower than that for the intrinsic Frenkel reaction. It is therefore very easy to over dope with Zr4þ which would result in a significant concentration of O0i which can act as electron traps. Also, if O ions move into the intrinsic oxygen vacancy sites to form positively charged OO they would clearly also act as effective electron traps. Tetravalent doping should therefore be treated with caution in bixbyite. Finally, as with divalent doping, tetravalent substitution can occur at either the 24d or 8b sites depending on the dopanthost cation combination. Again, given that it is desirable for the activator ion to be substituted onto the 24d site, it follows that it is desirable to choose a dopant which will be preferentially accommodated at the 8b site. Acknowledgements Computing resources were provided by the MOTT2 facility (EPSRC Grant GR/S84415/01) run by the CCLRC eScience Centre. Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396.

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