Phys Chem Minerals (1991) 18:91-105

PHYSlCS(CHEMISTRY (MINERALS 9 Springer-Verlag1991

Evolution of the Distortion of Perovskites Under Pressure: An EXAFS Study of BaZrO3, SrZrO3 and CaGeO3 D. Andrault and J.P. Poirier

D6partement des G6omat~riaux,Institut de Physiquedu Globe de Paris, 4 Place Jussieu, F-75252 Paris Cedex 05, France Received July 9, 1990 / AcceptedMarch 30, 1991

Abstract. We have investigated the evolution of the distortion of several oxide perovskites with increasing pressure, using EXAFS in the diamond anvil cell. Cubic perovskite BaZrO3 remains cubic up to 52 GPa. Orthorhombic perovskite CaGeO3 becomes less distorted as pressure increases, becomes tetragonal at about 12 GPa and evolves toward cubic structure, still not obtained at 23 GPa. The distortion of orthorhombic perovskite SrZrO3 first increases with pressure up to 8 GPa, then decreases until the perovskite becomes cubic at 25 GPa. The results are interpreted in terms of a systematics, relating the distortion to the ratio f of the volumes of the AO12 dodecahedron and the BO6 octahedron, and to the compressibilities of the polyhedra. For cubic perovskites, f = 5 , which may correspond to a situation where the compressibilities of octahedra and dodecahedra are equal. The behavior of SrZrO~ offers a clue to predict the evolution of the distortion of MgSiO3 at lower mantle pressures. It is suggested that the increase in distortion experimentally observed at lower pressures should stop above about 10 GPa, and the distortion decrease until the perovskite undergoes ferroelastic transitions to tetragonal and cubic phases, at pressures possibly below the pressure at the core-mantle boundary.

Introduction

It is now currently accepted that (Mg, Fe)SiO 3 with perovskite structure is the dominant phase in the Earth's lower mantle. However, despite an increasing number of studies (e.g. Navrotsky and Weidner 1989), its properties are far from being well known, especially at the pressures of the lower mantle. Indeed, even the crystallographic structure of (Mg, Fe)SiO3 at great depths is not known with certainty. Depending on the size of the ions, pressure and temperature, perovskites can depart from the ideal cubic structure and distort into tetragonal, orthorhombic,

monoclinic or rhombohedral structures; the ferroelastic transitions between the various distorted structures are often displacive. The mantle perovskite (Mgo.9 Feo.1)SiO3, as well as pure MgSiO3, synthesized at high pressure in diamond-anvil cells or large-volume multianvil apparatus is metastable when brought at ambient pressure, it has an orthorhombic structure (space group Pbmn) (Yagi et al. 1978). Single-crystal X-ray diffraction studies up to 9.6 GPa at room temperature (Kudoh et al. 1987) have shown that the distortion increases with pressure, as the compression of the unit cell is controlled by the tilting of the SiO 6 octahedra. Temperature acts in the other direction, the distortion decreasing as temperature increases up to 400 K at ambient pressure (Ross and Hazen 1989). However, powder X-ray diffraction studies up to 100 GPa at room temperature (Knittle and Jeanloz 1987) have not evidenced any change in the degree of distortion, all lattice parameters decreasing uniformly with pressure. Ab initio calculations (Wolf and Bukowinski 1985) and lattice dynamics (Hemley et al. 1987) theoretical studies predict an increase of the distortion with pressure, in contradiction with the suggestion of Yagi et al. (1978) based on analog systematics. Molecular dynamics simulations either support the viewpoint that distortion increases with increasing pressure (Matsui 1988) or the opposite viewpoint, predicting a transition to the cubic phase at high pressures (Wall et al. 1986; Kapusta 1990). Although there are contradictory opinions on the effect of pressure on the distortion, experiments and theories alike, all predict a decrease in distortion with increasing temperature toward a cubic phase at high temperature. Samples of MgSiO 3 perovskite prepared at 26 GPa and 1600~ brought metastably to room temperature and ambient pressure and examined in transmission electron microscopy, were seen to be heavily twinned, which suggests that the stable phase in the conditions of synthesis may have been cubic and may have gone through phase transitions as pressure and temperature decreased (Wang et al. 1990).

92

Whether (Mg, Fe)SiO3 perovskite in the lower mantle is orthorhombic, tetragonal or cubic is therefore a moot point: even if pressure and temperature work in the same sense, are they high enough to induce a transition to a higher symmetry phase in the lower mantle, and if they work in opposite senses, which one predominates? The question is far from trivial since ferroelastic displacive phase transitions in the lower mantle, although they would not induce seismic discontinuities, could still be responsible for a drop in shear modulus reflected in the anomalous variation in shear velocity relative to longitudinal velocity, seen by seismic tomography in the lower mantle (Yeganeh-Haeri et al. 1989). It seems therefore obvious that one would need experimental investigations of the effect of temperature and pressure on the distortion of oxide perovskites in general and MgSiO3 in particular. Despite its merits, powder X-ray diffraction is not accurate enough and also not local enough to yield detailed informations on the variations of distortion, especially if they are small. One needs to be able to determine, not lattice parameters but all the various interionic distances, in order to follow the distortion of the coordination polyhedra; this can be done with single-crystal Xray diffraction, but only at pressures lower than about 10 GPa. The only technique so far that allows the determination of interionic distances on powders at high pressures, is the Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy, using the synchrotron radiation from particle storage rings: the oscillations of the absorption spectrum close to the absorption edge of one type of ions gives information on the distances between these ions and their neighbors (e.g. Calas et al. 1984, 1987; Brown et al. 1988; Brown and Parks 1989). Due to technical difficulties, no investigations have been done so far at high pressures and high temperatures simultaneously. High-pressure experiments have to be done in diamond-anvil cells and the X-ray beam must go through the diamonds where it suffers a non-negligible absorption, especially at low energies. It is therefore almost impossible to use the absorption edge of elements lighter than cobalt or nickel, which is indeed unfortunate since it precludes the investigation of (Mg, Fe)SiO3 under pressure (at the Fe K edge, for instance, 3 mm of diamond would reduce the intensity of the X-ray beam by 99.9%). However, the investigation of other oxide perovskites, with various ion sizes, may be very rewarding and provide a firm basis to the extrapolations based on analog systematics. We have therefore investigated the distortion of cubic BaZrO a and orthorhombic SrZrO3 and CaGeO3 perovskites up to 52 GPa at room temperature, at the storage ring DCI of L U R E (Orsay).

Experimental Procedure Barium zirconate BaZrO3 and strontium zirconate SrZrO3 perovskites are stable at room temperature and ambient pressure, they were synthesized at the Laboratoire de Chimie Appliqu6e, University of Orsay. Calcium germanate CaGeO3 perovskite is a high-

.g

o

..0


5, the perovskites are generally hexagonal. For f < 5, the perovskites are distorted from the ideal structure by tilting of the octahedra, they usually are orthorhombic or tetragonal. We can obtain some qualitative information about the evolution of the distortion with pressure by using the empirical relation between the volume and the "bulk modulus" of the polyhedra (Hazen and Finger 1986):

Vd~ Kp d 3

Vdod

= ~d 3( G e - G e ) - - 34 td~3( G e - O) "

The angle of tilt ~ was calculated using the relation: __cos d(Ge-

Ge)/

"

The angle of tilt of the octahedra decreases as pressure increases (Fig. 9), which implies that the distortion of the perovskite also decreases; it does not, however, decrease smoothly and there seems to be a slight discontinuity in the curve e(P) in a range of pressure about 12.5 GPa. The curves of the bond lengths versus pressure (Fig. 9) exhibit the same feature. As the error bars are small (• due to the good quality of the fits and the good reproducibility of the results, the discontinuity might be real. The evolution of the distance d(G~-oe) under pressure is directly related to the bulk compression of the lattice and allows the determination of the bulk modulus of the perovskite CaGeO3. However, assuming the discon-

7.5 Mbar ~3

S 2 Z cZ a -

where K v is the bulk modulus of the polyhedron, experimentally determined, as we have seen above, from the compression curve of the appropriate bond lengths; d is the average cation-anion distance, Zc and Z, are the cation and anion charges, respectively, and S 2 is an empirical term related to the relative ion• of the bonds. In the case of A 2 +B 4 +0 3 perovskites, we easily derive the relation: K aod

R

Vo~t __ R

Vdod f

Ko,t where: R

5 S~od

41//So t

is a function of the relative ionicities of the bonds. We see that if f = R, the compressibility of the octahedra is the same as that of the dodecahedra.

101 For the case of ideal cubic perovskites, f = 5. If R < 5, the dodecahedra are more compressible than the octahedra, i.e. the volume of the dodecahedra decreases relatively faster than that of the octahedra as pressure increases, which can be achieved only by tilting of the octahedra, hence the structure becomes orthorhombic or tetragonal as pressure is applied. If R > 5, the structure would tend to become hexagonal (more favorable for large cations in the dodecahedral sites and small cations in the octahedral sites). If R = 5, the perovskite remains cubic. For the case of distorted orthorhombic perovskites, f < 5, the compressibilities of the octahedra and of the dodecahedra are equal for R = f < 5. If R

55

50

I

0

,

10

I

20

,

/

30

~

I

40

,

50

Pressure (GPa)

Fig. 11. SrZrO3: Compression curve of the unit cell. The equation of state is fitted only to the experimentalpoints above 8 GPa

of the SrOt2 dodecahedron in the cubic strontium perovskite SrTiO3, equal to 49.62]~ 3 (Samara 1966); we will therefore assume that Vdod= 49.62 ~3. The actualdodecahedron volume is larger than the ideal volume by almost 20%, the extra volume is taken up by further tilting of the octahedra, as pressure increases, until the compressibilities of the polyhedra become the same; the tilt angle then decreases until the structure becomes cubic. The compression curve of the unit cell of strontium zirconate is given by that of the Z r - Z r bond (Fig. 11); fitting an equation of state of Birch-Murnaghan to the whole curve would yield an unusually low bulk modulus (Ko = 60 GPa) with an unusually high value of K'0 (K~ = 10). This anomalous behavior is due to the large contribution of the distortion of the dodecahedra at low pressures. If we use in the fit only the experimental points above about 8 GPa, when the distortion decreases and both types of polyhedra are uniformly compressed, we obtain a bulk modulus Ko=360+_ 10 GPa, with K~=4. The volume of the unit cell, extrapolated at atmospheric pressure, from the high-pressure portion of the compression curve, is found to be V0= 64 + 1.5 ~. It is interesting to note that this value is close to that of the ideal (fictive) unit cell volume of SrZrO3 at atmospheric pressure: V~ = V~od+ Vo~o~;if we take for the ideal volume of the dodecahedron that of SrOt2 in SrTiO3, equal to 49.6 ~3 and for the ideal volume of the octahedron, that of ZrO6 in BaZrO 3, equal to 12.3 ]~3, we find V~=62 ~3.

Calcium Germanate The compression curves of the polyhedra are rather similar and the angle of tilt of the octahedra decreases, indicating a decrease of the distortion with increasing pressure. The volume of the dodecahedron at atmospheric pressure (Vdoa = 42.6 .~3) is very close to the ideal volume estimated to be 41~3, there is no extra dodecahedral volume to take up and the distortion does not have to increase first, as in the case of SrZrO3. At about

102 12 GPa, the compression curves possibly exhibit a discontinuity. This behavior could be interpreted as a progressive decrease of the orthorhombic distortion, leading to a phase transition toward a tetragonal structure at about 12 GPa. The tetragonal structure, in turn, would evolve toward a cubic structure, by becoming less and less distorted as pressure increases. However, we have not found evidence for the transition to cubic perovskite at pressures up to 23 GPa. We may note that Liu et al. (1990) give X-ray diffraction evidence for a decrease of the tilting of GeO6 octahedra with increasing temperature in the range 25250 ~ C for metastable CaGeO3 at atmospheric pressure, followed by an orthorhombic to tetragonal transition at 250 ~ C.

Other A2 + B 4 +03 Perovskites - SrTiO 3 is cubic at atmospheric pressure and room temperature, it was studied by Brillouin scattering and X-ray diffraction up to 21 GPa (Fischer et al. 1989) and was found to exhibit a transition from cubic to tetragonal at about 6GPa; a recent study by EXAFS under pressure up to 18 GPa, showed that the tetragonal distortion was very slight and that the compression of the tetragonal phase was almost identical for the various polyhedra (Bonello 1989). - CaTiO 3 is orthorhombic at atmospheric pressure and room temperature, it was studied by X-ray diffraction under pressure up to 14 GPa at room temperature (Xiong et al. 1986). It becomes hexagonal at 11 GPa; the angle of tilt of the octahedra, calculated from the data, decreases as pressure increases, suggesting that tetragonal and cubic phases probably appear before the hexagonal phases; however, the distortion of the orthorhombic phase being already quite small, it is impossible to distinguish it from more symmetrical phases. - CaSiOa is an unquenchable high pressure phase, it has been prepared at pressures higher than 15 GPa and studied by X-ray diffraction at room temperature and pressures up to 96 GPa by Tarrida and Richet (1989). It was found to remain cubic at all pressures investigated. This is in agreement with the lattice dynamics calculations of Wolf and Bukowinski (1987), who find that the cubic phase should be stable to at least 70 GPa. Ab initio calculations (Hemley et al. 1987) predict that cubic CaSiOa should become unstable at about 100 GPa. - Hexagonal perovskite-like compounds with ABO 3 formula differ from cubic perovskites by the hexagonal close packed (hcp) stacking of some or all of the AO3 layers, instead of the cubic close packed (ccp) stacking characteristic of cubic perovskites. Complete hcp stacking of AO3 layers implies that the BO6 octahedra share opposite faces with their neighbors, forming unidimensional chains and causes the distance between B cations to be smaller than in cubic perovskites. Hexagonal perovskite-like structures are thus favored in the case of large A cations and small B cations. The ratio f = Vaoa/Voctis thus larger than 5. According to the proportion of ABO 3 layers that are in hcp or ccp stacking,

various structures can be found (Muller and Roy 1974): in the BaNiO 3 structure all layers are hcp; in the BaRuOa structure, two thirds of the layers are hcp and one third is ccp; in the high-T BaMnO3 structure, one half of the layers is hcp and one half is ccp; in the hexagonal BaTiO3 structure, one third of the layers is hcp and two thirds are ccp. The density of the structures increases and the ratio f decreases from the BaNiOa to the perovskite structure, and there is evidence for phase transitions to the denser structures (lower f ) as pressure increases: BaMnO3, which has the BaNiO3 structure at atmospheric pressure, transforms to the BaRuO3 structure at about 3 GPa and to the high BaMnO 3 structure at about 9 GPa (Syono et al. 1969). SrMnO3, which has the high BaMnO3 structure at atmospheric pressure, transforms to the hexagonal BaTiO3 structure at 5 GPa (Syono et al. 1969). BaRuO 3 transforms to the high BaMnO3 structure at 1.5GPa, then to the hexagonal BaTiO3 structure at 3 GPa; the same sequence of transitions is obtained at ambient pressure by substituting Sr to Ba and even goes to the perovskite structure for 95% substitution (Longo and Kafalas 1968).

Magnesium Silicate Perovskite Knittle and Jeanloz (1987) measured the lattice parameters of (Mgo.88, Feo.12)SiO3 perovskite at several pressures between 25 and 127 GPa, by powder X-ray diffraction in the diamond-anvil cell. They found that, within experimental error, the ratios of the lattice parameters b/a and c/a remained identical to those of the perovskite quenched to zero pressure; they concluded that there was no change in the degree of distortion of the orthorhombic structure over the pressure range of the mantle. Kudoh et al. (1987), however, made an accurate study of the crystal structure of single crystals of MgSiO3 by four-circle X-ray diffractometry, under hydrostatic conditions in the diamond-anvil cell up to 9.6 GPa, they found that the ratio b/a increases while c/a decreases, with increasing pressure; pressure distorts the dodecahedra, moving the coordination of Mg in the direction of 8-fold rather than 12-fold coordination. They concluded that the unit cell compression is controlled mainly by the tilting of the relatively rigid octahedra. A systematics approach, based on the idea that the degree of distortion is an increasing function of the ratio of the size of the BO 6 octahedron to that of the A cation: d(B-o)/RA = (RB -b Ro)/RA, led Yagi et al. (1978) to suggest that MgSiOa should become less distorted as pressure increases. O'Keefe et al. (1979), however, contended that the degree of distortion is related not to the ratio used by Yagi et al. (1978) but to the ratio of the sizes of the octahedron and of the dodecahedron: d(~_o)/d(A_o) and that the distortion of the perovskites should increase with pressure. Theoretical ab initio calculations generally concur in predicting that the distortion of MgSiO 3 increases with pressure; the investigations were conducted up to 2.5 GPa (Matsui 1988), 30 GPa (Wolf and Bukowinski 1985), 150 GPa (Wolf and Bukowinski 1987), 200 GPa

103 v dod l Voct

5,5 ~

SrMnO3 10 CaTiOa 20 i 7 i ~ E v ' q ' ~ ' - ~ - L i I [ Z i ] I ', ; ~ 5,0 . ~ C a G e O 3 ~ "ftf'''~ SrY~rZrO3 -"

:

;

CaSiO3 30 BaZrQ3 40 I L I i [ 12J a I I Z [ ~ . .-''''" ~'lgSiO3- " Pressure (GPa)

/

4.0

.''

-"

3.5

(Hemley et al. 1987). Molecular dynamics simulation up to 10 GPa (Matsui et al. 1988) confirm the increase of distortion with pressure. Wall et al. (1986) investigated the sensitivity to interatomic potentials of computer simulations of the structure of MgSiO3, based on energy minimization; the potential which best models the properties of MgSiO 3 predicts that the angle of tilt of the octahedra, hence the distortion, should first increase with pressure, then decrease with increasing pressure above about 100 GPa; by 200 GPa, the cubic phase should be more stable than the orthorhombic phase.

Speculations We can now gather our experimental results and the results found in the literature, concerning oxide perovskites, in a plot of the ratio f = Vdo~/Vootversus pressure (Fig. 12). The general picture is that, as pressure increases, hexagonal perovskites ( f > 5) undergo a series of phase transitions toward structures with lower values of the ratio f that should eventually lead to the cubic perovskite structure at high enough pressure; cubic perovskites ( f = 5) stay cubic and some distorted perovskites ( f < 5 ) orthorhombic at room temperature and atmospheric pressure, decrease their distortion and tend to become cubic at high enough pressures ( f tends toward 5). However, there seems to be notable exceptions to the latter trend: for SrTiO3 and MgSiO3, the distortion increases with pressure in the experimental range (up to 10 GPa) and the ratio f slightly decreases; as we have seen, this behavior is often taken as a confirmation of some theoretical predictions of the effect of pressure on the distortion.

Fig. 12. Ratio f of the volume of the AO12 dodecahedron to the volume of the BO 6 octahedron as a function of pressure, for various ABO3 perovskites. For cubic perovskites, f=5; for hexagonal perovskites f > 5; for orthorhombic and tetragonal perovskites, f < 5. The values of f calculated from the data of Kudoh et al. (1987) for MgSiO3 perovskite are figured by stars. As pressure increases distorted perovskites tend to become cubic (see text for comment and sources)

The behavior of SrZrO3 is more interesting and we will use it as a basis for speculations on the behavior of MgSiO 3 at lower mantle pressure: the distortion of SrZrO3 perovskite first increases with pressure, goes through a maximum ( f goes through a minimum) then decreases and the structure eventually becomes cubic. We ascribed the increase in distortion at lower pressures to the fact that the volume of the SrO~2 dodecahedron at atmospheric pressure is larger than the ideal volume V~oa; pressure, then, first reduces the size of the dodecahedron by tilting of the octahedra until the extra dodecahedral volume disappears, the distortion can then decrease until the perovskite becomes cubic. For MgSiO3, we calculated the value of the ratio f at several pressures, from the data of Kudoh et al. (1987); we found f=4.281, 4.244, 4.232, 4.218, for P = 0 , 4, 6.7, 9.6 GPa respectively. The ideal volume of the dodecahedron: V,~od= 27_+ 2 ~3, was estimated from a linear empirical relation between the volume of the dodecahedron and the volume of the A cation (Fig. 13), using data culled from Muller and Roy (1974); a similar relation for oetahedra had been successfully used by Horiuchi et al. (1982). The volume of the magnesium cation (V~ag2+ = 9.2 ]~3), in turn, was estimated from another empirical linear relation between the size of the ions and their coordination, using data from Muller and Roy (1974). The ideal f ratio for MgSiO3 at atmospheric pressure is then found to be f~=3.5, smaller than the actual value f=4.3. AS in the case of SrZrO3, we find that there is an extra dodecahedral volume of about 20%, at atmospheric pressure, that must be taken up by further tilting of the octahedra, before the distortion can decrease. On the basis of our experimental data on SrZrOa

104

80 c s

70

"0

cO (D "O

o

60 9

50 '

O rO 13)

>

40

20

.I , .

,

10

12

8

Ca Sr , tl , , . , 14

16

18

.

~ , 20

Ba J . 22

24

Volume of the A cation (,~3)

Fig. 13. Empirical plot of the volume of the AOlz dodecahedron as a function of the volume of the A cation for CaGeO3, SrZrO3 and BaZrO3. The plot is used to estimate the ideal volume of the MgO12 dodecahedron

behavior is interpreted in terms of the elimination, at low pressures, of an extra dodecahedral volume above the ideal volume for the strontium cation, by tilting of the octahedra. The evolution of the distortion of SrZrO 3 with pressure provides a clue for predicting the behavior of the perovskite MgSiO 3 at lower mantle pressures: we suggest that the increase of the distortion experimentally observed at low pressures might disappear above 10 G P a and that the perovskite would then become less and less distorted as pressure increases, possibly going through an orthorhombic-tetragonal transition and a tetragonalcubic transition in the lower mantle. The ferroelastic transitions might cause a decrease in certain elastic constants and be responsible for the anomalous variation in shear velocity (d In VJd In Vp= 2) in the lower mantle as suggested by Yeganeh-Haeri et al. (1989). The effect of the high temperatures of the lower mantle would be additive to that of pressure and favor the evolution toward cubic structure.

Acknowledgments. We perovskite, of K u d o h et aI. (1987) data on MgSiO3, and of the systematics relating the ratio of dodecahedral to octahedral volumes to the pressure, we suggest that the distortion of MgSiO 3 perovskite, while further increasing at pressures lower than 10 GPa, might go through a maximum for a pressure may be not much higher than 10 GPa, and decrease until it becomes tetragonal, then cubic. F r o m the trend exhibited by the plot f(P) (Fig. 12), the pressure at which the silicate perovskite may become cubic is probably not lower than 30 G P a but might be anywhere between 30 G P a and 100 G P a or even higher. Our suggestion independently agrees with the identical one, made on different grounds by Wall et al. (1986). The idea that the transition might occur for lower mantle pressures ( P < 135 GPa) is buttressed by the observation of numerous twins in perovskite quenched from 26 GPa (Wang et al. 1990) and by the fact that the transition toward cubic perovskites is favored by high temperature.

Conclusion We have investigated the evolution of distortion with pressure by EXAFS, in cubic perovskite BaZrO3 and orthorhombic perovskites SrZrO3 and CaGeO3; the results are consistent with a systematics, based on the literature, embodied in a plot of the ratio of the volume of the AO12 dodecahedron and the volume of the BO6 octahedron as a function of pressure. According to this systematics, cubic perovskites, with an ideal value of the ratio, equal to 5, should remain cubic; distorted orthorhombic or tetragonal perovskites, however, with a value of the ratio smaller than 5, should tend to become cubic as pressure increases and the compressibility of the polyhedra becomes comparable. BaZrO3, cubic, does indeed stay cubic and CaGeO3, orthorhombic, becomes less distorted as pressure increases. The case of SrZrO3 is more interesting since its distortion first increases with pressure, then decreases until the perovskite becomes cubic above 25 GPa. This

are deeply indebted to A. Fontaine and J.P. Iti6, who introduced us to LURE and helped us with the apparatus they had set up. We thank G. Calas and A. Manceau for letting us use their program of data processing by Fourier transform and C. Sotin for help with the inversion program. BaZrO 3 and SrZrO3 perovskites were kindly donated by A. Revcolevschi. We gratefully acknowledge the synthesis of CaGeO3 perovskite by F. Guyot at the Stony Brook High Pressure Laboratory which is jointly supported by the NSF Division of Earth Sciences (Grant EAR86-07105) and the State University of New York at Stony Brook. G. Calas, A. Fontaine, F. Guyot, J.P. Iti6, R.C. Liebermann, M. Madon, A. Manceau, J. Peyronneau, provided much help in the course of numerous fruitful discussions. The contribution of Prof. K. Langer and of an anonymous referee is gratefully acknowledged. This work was partly supported by CNRS (URA734); it is IPG contribution n~1165.

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