NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 250 (2006) 17–23 www.elsevier.com/locate/nimb

Radiation effects in lanthanum pyrozirconate A. Chartier

a,*

, J.-P. Crocombette b, C. Meis c, W.J. Weber d, L.R. Corrales

a

d

d

CEA-Saclay, DEN/DPC/SCP/LM2T, Baˆt. 450 Sud, 91191 Gif-Sur-Yvette, France b CEA-Saclay, DEN/DMN/SRMP, Baˆt. 520, 91191 Gif-Sur-Yvette, France c CEA-Saclay, INSTN, 91191 Gif-Sur-Yvette, France Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA Available online 9 June 2006

Abstract The present paper reviews recent results on radiation resistance of lanthanum pyrozirconate La2Zr2O7 obtained through molecular dynamic simulations using empirical potentials. Detailed studies of displacement cascades carried out with a 6 keV U4+ cation, representing the a-recoil nucleus, have shown only point-defects formation, Frenkel pairs and cation antisites, indicating that in this material amorphization does not occur by a direct impact mechanism. In a more enhanced simulation study, the consequences of point-defect accumulation have been analyzed. The results show that cation Frenkel pair accumulation is the driving force for lanthanum zirconate amorphization. It is demonstrated that under cation Frenkel pair accumulation, the crystal undergoes a transition from the pyrochlore to the disordered fluorite structure, with the oxygen atoms simply rearranging around cations and next to the amorphous state. Consequently, these results provide atomic-level interpretation to experimental observations of a two-step phase transition under irradiation. Ó 2006 Elsevier B.V. All rights reserved. PACS: 61.80.Az; 61.80.Jh; 61.82.Ms Keywords: Pyrochlore; Radiation effects; Molecular dynamic; Point defects; Phase transition; Amorphization

1. Introduction Zirconate pyrochlores are considered as pertinent inert matrices for industrial- and military-grade plutonium incineration [1,2]. Indeed, many of their physicochemical properties are quite relevant for use in reactors. Some of these are the low neutron cross-section of Zr, the ease with which actinide ions are incorporated [3], and the high resistance of zirconate pyrochlore toward radiation damage. Rare-earth zirconate pyrochlore A2Zr2O7 with A = Gd, Er, Nd, Sm [4–6] have shown very high radiation resistance, remaining crystalline up to high doses (7.0 dpa) even at a very low temperature (25 K) and undergoing a radiation-induced transition to the disordered fluorite structure. The only exception known among zirconate pyrochlores is the lanthanum pyrozirconate (La2Zr2O7) *

Corresponding author. Tel.: +33 1 6908 3168; fax: +33 1 6908 9221. E-mail address: [email protected] (A. Chartier).

0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.04.079

which, after transiting to the disordered fluorite structure, becomes amorphous at low temperatures for doses around 1–2 dpa [6–8]. However, according to recent experiments [6,7], the La2Zr2O7 pyrochlore under irradiation initially shows a disordering in the oxygen sublattice under irradiation where the oxygens are randomly distributed between the two 8b and 48f oxygen sites and the native oxygen vacancy is in the 8a site. That stage is followed by a transition to the disordered fluorite phase of the pyrochlore where cations and anions are randomly distributed in their sublattices, respectively. Finally, at doses above 5.5 dpa at room temperature, the lanthanum pyrozirconate becomes amorphous. Despite a great number of experiments and simulations that have been devoted to the understanding of radiationinduced amorphization in pyrochlore, the involved mechanisms have remained unclear (see [9] for a full review). Direct-impact mechanism for amorphization has been suggested for titanate pyrochlores, while amorphization driven

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by point-defect accumulation has been proposed for zirconate pyrochlores [9]. In the present paper, we review some recent results [10– 12] obtained using atomistic simulations that give microscopic insights on the processes that drive the zirconate pyrochlore toward amorphization under irradiation. After a brief presentation of the pyrochlore and fluorite crystallographic structures, we give the methodology followed to set up relevant empirical interatomic potentials for radiation damages studies. The three model structures of reference – pyrochlore, fluorite and amorphous states – are then constructed, which will be considered as reference states for the rest of the study. The numerical study of radiationinduced phase transition is presented in the last section. It includes displacement cascades (DCs) simulations and a disorder-induced phase transition. 2. Pyrochlore, fluorite and amorphous structures La2Zr2O7 pyrochlore is an ordered form of the cubic MO2 fluorite-like arrangement of atoms. Cations build an fcc network with La and Zr lying along the opposite diagonals of the faces of the cube. The oxygen sublattice is cubic with an intrinsic vacancy surrounded by Zr atoms in such a way that LaO8 and ZrO6 polyhedra are formed [13,14]. Conversely, in the disordered fluorite structure, cations as well as anions are randomly distributed in their sublattices. This leads, on average, to LaO7 and ZrO7 polyhedra and to an occupation of 7/8th of the oxygen sites. As a by-product, the body-centered site of the fcc cation sublattice, which is also the only interstitial site, becomes another equivalent origin with respect to which all cations can be translated, without any modification of the structure. Herein, sensible tests on the number and nature of oxygen vacancies and cations neighbors have been applied in order to identify the pyrochlore and disordered fluorite structure. Disorder in the oxygen sublattice is calculated by counting the occupation numbers. For the disordered fluorite state, this number should be 7/8th on average for all the oxygen sites; whereas it is zero for the intrinsic vacancy and one for the occupied oxygen sites in pyrochlore. To calculate the disorder in the cation sublattice, the ˚ ) must be contype of second neighboring cations (at 5.4 A sidered. The use of the first cation neighbors is irrelevant since there are four heteroatomic and four homoatomic neighbors in both ordered and disordered states. In pyrochlore, the second neighbor cations are entirely heteroatomic, while in disordered fluorite half are homoatomic and half are heteroatomic. Those second nearest-neighbor criteria are translated as an order parameter (OP), such that OPðnÞ ¼

jn  nðfluoÞj ; jnðpyroÞ  nðfluoÞj

where n is the number of heteroatomic second (next) nearest neighbors for cations. Thus, for OP = 0, the structure is fluorite, which corresponds to 64 cation exchanges out of 128 for each A and B cation sublattice. Cation interstitials

˚ cation–cation can be evidenced by the occurrence of 2.7 A distances. This order parameter is used to distinguish only pyrochlore from the disordered fluorite structure. Pyrochlore, disordered fluorite and amorphous states have also been identified using the energy differences between them. The radial distribution function (RDF) is used to identify the amorphous state from the two other states. 3. Generation and evaluation of empirical potentials 3.1. Empirical potentials [10] Most early theoretical studies dedicated to radiation resistance of pyrochlore have been performed using empirical potentials [10–12,15,16,5,17–20]. The main strength of these potentials is their simplicity that allows large-scale (in time and size) simulations. In addition, they have to reproduce the properties of the perfect crystal, as well as other properties far from the equilibrium crystalline order (such as Frenkel pair and cation antisite formation energies) that could arise during the displacement cascades. Consequently, they have to be carefully established and must compare satisfactorily with all the available experimental data. Among pyrochlores, only few of them (lanthanum, yttrium, gadolinium pyrozirconate) have been extensively studied experimentally and exhibit a sufficient number of physical properties [9] for that purpose. A complementary way to get some relevant properties, not available in the experimental data, is to use ab initio calculations [10]. In this way, equilibrium properties (structural parameters, elastic constants, etc.) and point-defect formation energies (Frenkel pairs or antisites) [10,21] can be obtained by first principles calculations and used to refine the empirical potentials. Furthermore, ab initio studies [10,21–23] may also provide some interesting insights on the nature of cation oxygen bonds. In the present case, La–O and Zr–O bonds have been revealed as being mainly ionic [10]. This allowed us to use Coulomb potentials (with formal charges), complemented by short-range Buckingham potentials, to describe interactions between anions and cations in La2Zr2O7 [11]. We have followed a three-step procedure during the fitting of the potential parameters (using the GULP code [24]: (i) a first fit is obtained upon some experimental and ab initio calculated properties at equilibrium (structural parameters, elastic constants, bulk modulus); and (ii) with the established potentials, other physical properties are calculated and compared with experimental data (e.g. thermal expansion and thermal conductivity) and ab initio values (e.g. AS formation energies). If the comparisons are satisfactory, then the potential optimization procedure stops at that level; if not, then (iii) the first step (i) is repeated again in order to get a new set of potentials and so on. As a result, a quite satisfactory set of empirical potentials (Table 1) has been obtained, appropriate for the study of ordered and disordered La2Zr2O7 [11,12].

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Table 1 Comparison between experimental [25–32] and calculated data for the La2Zr2O7 pyrochlore using a static minimization method at constant pressure La2Zr2O7 ˚ 3) V (A q (g cm3) B (GPa) C11 (GPa) C12 (GPa) S300 K (J/mol K) a (106 K1) D700 K (106 m2 s1) vL (m s1) DG300 K (eV/atom)

Exp. [25–32]

P

F

A

315.4 6.024 175–191a 335a 120a 240 7.0–9.1 0.85

315.4 6.024 191.4 338 118 208 6.24 1.05 7487 0.000

311.2 (1.3%) 6.105 184.6 (3.6%) 331 (2.1%) 112 (5.1%) 394 7.48

341.6 (+8.3%) 5.562 122.1 (36.2%) 191 (43.5%) 75 (36.4%) 402.6

7360 0.092

5857 0.35

The P, F and A sets represent perfect pyrochlore, disordered fluorite (in both cation and anion sublattices) and amorphous states, respectively. Changes of values for fluorite and amorphous states, compared to pyrochlore, are indicated in percentages in parenthesis. Calculations have been done with the GULP code [24]. a Ab initio values from [10].

3.2. Simulating fluorite and amorphous phases Various disordered fluorite and amorphous states of La2Zr2O7 were generated with the optimized set of empirical potentials. They can be considered as generic tests for the potentials, but they will also be used as references for the rest of the study. Their relative stability has to be well described in order to ensure valid results for displacement cascades. For example, inversion of relative stabilities between the amorphous state and the perfect pyrochlore could lead to unphysical amorphization even during lowenergy displacement cascades. Our model of the disordered fluorite phase was generated in a 704 atom–cell by a random inversion of half of the cations (64 out of 128) of each type (A or B type) resulting in ASs configurations. This randomization is meant to closely represent the defect fluorite structure irrespective of a possible reminiscent cationic order. No oxygen sublattice disorder was introduced. Oxygen ions spontaneously relaxed

Fig. 1. Partial and total radial distribution function (RDF) for the amorphous quenched pyrochlore. The total RDF is mainly flat for ˚ , only La–O and Zr–O polyhedrons show sharp distances greater than 4 A peaks, reduced by around 10% compared with the crystalline pyrochlore structure.

during the molecular dynamics (MD) run toward their more stable positions, depending on their environment. A fully disordered fluorite structure was obtained as evidenced by the order parameters analysis (see inset in Fig. 1) and the partial radial distribution functions. A more detailed description will be given below. The calculated physical properties quoted in Table 1 have been obtained by averaging each value over a set of 10 different configurations using a static minimization procedure [24]. The average volume for the disordered fluorite is found to be lower than the volume for the perfect pyrochlore structure by roughly 1%. We have no experimental observation for La2Zr2O7 but this contradicts what has been observed in Gd2Zr2O7 where the volume is slightly increased by +0.1% when transitioning from the ordered to the disordered structure [33]. Conversely, it has been observed that the pyrochlore to fluorite transformation shows no evidence of lattice strain in Gd2Ti2O7 [34], which indicates no swelling of the grain. The bulk modulus of La2Zr2O7 is decreased in the disordered fluorite state, in agreement with experimental results obtained on Gd2Zr2O7 [35]. The Gibbs free-energy difference between ordered pyrochlore and disordered fluorite at room temperature is 0.092 eV/atom. The value of less than 0.1 eV/ atom is in accordance to that determined by Helean et al. [36] in other zirconate pyrochlores. This free-energy value can also be compared with the value of 0.096 eV/atom obtained for the difference between the normal and inverse structures of MgAl2O4 [37]. The amorphous state was obtained by quenching the perfect pyrochlore from 6000 K toward 300 K with a cooling rate of 30 K/ps. The total radial and partial distribution functions have been plotted in Fig. 1. Results show that short-range order is maintained in the simulated amorphous phase so that La–O and Zr–O distances still appear ˚ . These on the RDF figure with lengths of around 2.1–2.2 A distances are roughly 10% less than the average value of ˚ in perfect pyrochlore, in agreement with experiments 2.4 A done by Lumpkin [38] where a decrease of 7% for M–O has been observed between amorphous and crystalline natural

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pyrochlore samples. The O–O peak can still be distinguished, along with the very weak next-neighbor cation– ˚ ; see Fig. 1). Note that the latter cation peak (around 4 A was not observed by Greegor et al. [39–42] in amorphous natural samples. Long-range order is removed for longer ˚ , showing distances: the total RDF is nearly flat above 4 A no distinguishing structural features, in agreement with the experimental RDF obtained by Krivokoneva and Sidorenko [43] on fully metamict natural samples. The cell has then been relaxed using the static minimization energy method. Present calculations show a swelling of 8.3%, in close agreement with the experimental values of 5–10%, which depend on accumulation dose in gadolinium titanate [44]. The bulk modulus shows a 36% decrease compared with the pyrochlore, in accordance with experiments [44]. The calculated Gibbs free-energy difference between the crystalline pyrochlore and the amorphous states at 300 K is 0.35 eV/atom, which is higher than the stored energy (0.1–0.14 eV/atom) released during recrystallization of natural metamict pyrochlores [38]. In summary, the present empirical potential can reproduce quite satisfactorily the crystalline pyrochlore, disordered fluorite and amorphous states of the lanthanum pyrozirconate. Calculated properties for those three phases will be used as references in the following. 4. Radiation resistance evaluation 4.1. Displacement cascades [11] Molecular dynamics simulation of displacement cascades have been performed by imparting 6 keV of kinetic energy to a uranium atom along a given crystallographic direction (see [11] for details) in the perfect pyrochlore at 350 K. The accelerated ion loses its kinetic energy by ballistic collisions within the crystalline matrix. At the very beginning of the cascade, the instantaneous temperature calculated over the supercell exhibits a very fast decrease as illustrated in Fig. 2. The highest number of displaced atoms (for La, Zr and oxygen) is then observed at around 0.3 ps along with a relative minimum of the instantaneous temperature. It corresponds to the end of the ballistic collision phase. The potential energy acquired by the displaced atoms is then released through a fast recovery processes, leading to a relative increase of the instantaneous temperature. Heat and mechanical shock waves appear and travel throughout the bulk back to the displacement cascades area because periodic boundary conditions (PBC) are used. Those heat and mechanical waves can unphysically interact with the displacement cascades area [45,46] and drastically modify the final results. Numerical methods [46,47] have been developed in order to reduce the self-interaction caused by the PBC. A sufficiently large simulation box, with a thermal bath applied at the borders, is an alternative method that is used in the present work to handle such effects. In the simulation box employed here, the mechanical shock wave needs about 1.7 ps to come

˚ ) and instantaFig. 2. Number of displaced atoms (by more than 1.5 A neous temperature evolution averaged over four supercells during single event displacement cascades along different crystallographic directions. The temperature decreases as a function of time (for t > 2 ps) towards 350 K, since a 350 K thermal bath is applied at the borders.

back to the damaged area according to the sound wave velocity (Table 1). The characteristic time for the heat wave – evaluated from the heat diffusion coefficient (see Table 1) – to reach the border is around 2 ps. This time scale represents twice the time (1.0 ps) needed for all the ballistic displacements caused by the cascades to occur (see Fig. 2). The number of defects then stabilizes (for t > 2.0 ps) and the instantaneous temperature of the supercell slowly decreases toward the thermal bath applied at 350 K (see Fig. 2). During the cascades, the relative number of displaced lanthanum, zirconium, or oxygen atoms is related to their threshold displacement energies (see Table 2). Thus, more oxygen atoms are displaced than cations, and twice as many lanthanum atoms are displaced than zirconium atoms at 0.3 ps. After a few picoseconds (7.5 ps), only 10% of the maximum displaced atoms during the cascades stabilize as point defects; the rest of them recover to equivalent crystallographic sites. The oxygen atoms mainly move to the intrinsic vacancy 8a site to reconstruct the close shell around the AS. Twice as many lanthanum FPs than zirconium FPs are observed at 7.5 ps, as suggested by their formation energies (see Table 2) 5.4 and 14.2 eV, respectively. This La/Zr FP ratio will be used in the following simulations to mimic point-defect accumulation caused by cascades overlap. We also observed that twice as many ASs are produced compared with FPs, which is an early indication that La2Zr2O7 pyrochlore transitions first to the fluorite structure under irradiations. That can again be related to the AS formation energy of 2.4 eV, which is smaller than the FP formation energies. Note that the formation energies slightly converge to smaller value for AS (1.32 eV) and to a single value for cation FP (around 8 eV) as the structure transitions toward the disordered fluorite state. This does not affect the relative stability of the FP compared with AS.

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Table 2 Average (minimum) threshold displacement energies hEdi (min Ed) and AS (AS) and Frenkel pairs (FP) formation energies (Ef) for pyrochlore (and fluorite in parenthesis) for all cations in La2Zr2O7 La

Zr

O

O (Exp. [48])

hEdi (min) eV Ef(AS) (eV) Ef(FP) (eV)

153 (53) 2.4 (!1.3) 5.4 (!8.8)

188 (68) 2.4 (!1.3) 14.2 (!7.2)

42 (7.0)

47

Atoms displaced at 0.3 s Point defects at 7.5 ps

150 19

82 14

755 66

Average number of maximum displaced atoms during 6 keV displacement cascades (DC) has been quoted for 0.3 ps. Number of point defects has been quoted at 7.5 ps.

In summary, single-event displacement cascades have revealed that only point defects are produced and that amorphization does not occur by a direct-impact mechanism in lanthanum zirconate pyrochlore. Point-defect accumulation in the structure plays a major role in the amorphization process, as will be investigated below. 4.2. Disorder-induced amorphization [12] Throughout the following, a series of independent calculations have been performed. For each calculation, starting from a defect-free cell, a given number of cation defects (FP or AS) is introduced in a randomly distributed manner in the simulation cell. The cell is then thermalized at 300 K at constant pressure during 4 ps. This prevents the atoms from being artificially accelerated when exposed to strong repulsive potentials resulting from the introduction of interstitials. An MD run of 18 ps is then performed, and the final structure is analyzed in terms of atomic configurations and internal energy. As before, oxygen disorder was not introduced. However, we checked that a complete randomization of the oxygen ions among 8a, 8b and 48f sites does not create any cation displacements nor induce amorphization. We first explore the transition of the pyrochlore structure toward the disordered fluorite structure by introducing different concentrations of ASs (%AS). For that purpose, 140 configurations have been randomly generated, sampling the number of AS from 0%, for the perfect pyrochlore structure, to 100% that corresponds to the disordered fluorite structure. For all configurations, no cation FPs appear during the simulation, and the resulting structures show only cation ASs. For a low percentage of AS introduced (less than 20%, corresponding to an average distance ˚ ), the ASs do not interact, and the between them of 20 A energy variation as a function of the %AS (see Fig. 3) closely follows a linear extrapolation of point-defect formation energy, which is 2.4 eV per AS. The oxygen atoms, consequently, hardly rearrange around the cations (see inset of Fig. 3), and the OP (oxygen) still equals one for low cation AS concentrations, i.e. OP (cation) = 0.9. Raising the number of ASs increases their self-interactions, and the formation energy slowly converges to an asymptotic value of 1.3 eV per AS. That makes the AS formation energy cost lower per AS as the structure approaches the fluorite state. The disorder that appears on the oxygen sub-

Fig. 3. Evolution of the pyrochlore to fluorite transition energy determined as a function of the percentage of ASs in the NVT ensemble. Black circles are MD calculations, while the open diamond corresponds to ab initio values obtained within periodic boundary conditions (PBC). The horizontal line is the average energy per atom for the fluorite cell. The long-dashed line indicates the linear extrapolation of the point-defect formation energy for ASs. Note that the ab initio AS formation energy [10] calculated using periodic boundary conditions in the primitive cell is very close to the present MD values. The inset shows the evolution of the oxygen order parameter (OP) as a function of the cation OP (see details in the text). Oxygen atoms spontaneously rearrange around cations.

lattice follows almost perfectly the disorder introduced for cations (for OP (cation) < 0.8), as can be seen in the inset of Fig. 1. Oxygen atoms are consequently driven by cation positions. This is consistent with the suggestion by Hess et al. [33] that in gadolinium pyrochlores, the pyrochlore to fluorite transition is mainly driven by cations. Based upon this, only cations will be considered in the following. In order to obtain a view of the early stage of radiation damage, different concentrations of randomly generated Frenkel pairs, up to 16% of the cations, were introduced in the perfect pyrochlore. To maintain the ratio of the remaining point defects observed in displacements cascades, twice as many lanthanum as zirconium FPs were introduced. No amorphization is observed up to 16% of Frenkel pairs. The energy difference per atom with the pyrochlore follows a three-step behavior as a function of the percentage of FPs inserted, as can be seen in Fig. 4. The energy rapidly increases from 0% to 7.8% with FP insertion. While the

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A. Chartier et al. / Nucl. Instr. and Meth. in Phys. Res. B 250 (2006) 17–23

Fig. 4. Energy differences (eV/atom) between the resulting states and the perfect pyrochlore as a function of the cation FP inserted in the pyrochlore structure.

energy per atom (Fig. 4) suggests that the fluorite structure is attained once the FPs introduced exceed 6%, the OP for cations of 0.7–0.8 (quoted in Fig. 5) indicates that the fluorite disorder is not yet stabilized. The rapid increase in the energy is caused instead by the high ratio of isolated FP atoms that remain at the end of simulations (see Fig. 5) and store roughly five times more energy per defect (average value 10 eV/FP, see Table 2) than ASs (2.4 eV/AS). For concentrations ranging from 0% to 7.8%, the introduction of more FPs results in fewer FPs remaining at the end of the simulations (see Fig. 5). For concentrations higher than 7.8% up to 12%, the energy stabilizes at the disordered fluorite energy, and FPs no longer remain at the end of the simulation. This can be explained by considering that for large initial concentrations, the interstitial–vacancy pairs are unstable as their distances become smaller than the recombination radius. From this, it can be deduced that the

Fig. 6. The energy difference (eV/atom) between the resulting states and the perfect pyrochlore as a function of the number of FPs inserted into the fluorite structure calculated at constant pressure. Filled open symbols denote crystalline amorphous states. Energies of the reference states are represented by lines.

˚ , which corresponds to recombination radius is about 8 A the third neighbor cation–cation distance. The energy begins to increase again for more than 12% FP insertion. From Fig. 5, the FP per cation concentration required to fully transform the pyrochlore (OP = 1) to the fluorite structure (OP = 0) can be estimated by extrapolation of the OP as a function of the FP introduced to be around 0.2 FP. Finally, we have put in evidence that under the increasing introduction of FPs, perfect pyrochlore transits first to the fluorite structure. To model the further evolution of pyrochlore under irradiation, different concentrations of randomly generated Frenkel pairs were introduced in the disordered fluorite structure. Results reported in Fig. 6 shows that the introduction of more than 10% FPs (with the same ratio between La and Zr FPs) in the disordered fluorite structure induces a transition to the amorphous state for some cases. Lower initial concentrations of FPs do not trigger the amorphization process. 5. Conclusion

Fig. 5. Remaining interstitials (after NPT simulations) as a function of the percentage of FP inserted in the perfect pyrochlore, as well as the cation order parameter, OP, induced by antisites. The percentages of interstitials and FPs are calculated as a function of the total number of cations (256) in the present cells used.

In view of these results, we can draw a complete picture of the processes taking place in zirconate pyrochlores under irradiation and provide an atomic-level interpretation of the three-step process for amorphization suggested by Lian et al. [6,7]. The oxygen atoms play little role in the order– disorder transitions, because the cation order parameter drives that of the oxygen atoms. The accumulation of FPs is the mechanism that drives zirconium pyrochlores toward amorphization following a two-step process: (1) a transition from the pyrochlore to the disordered fluorite that occurs for a ratio of about 0.2 FP per cation in La2Zr2O7 and with the continued production of more FPs and (2) amorphization of the disordered fluorite La2Zr2O7 takes place at a critical additional FP concentration of 0.1. In the

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