Synchrotron X-ray study of Er3Al5O12 and Yb3Al5O12 garnets

Etschmann, B.; Streltsov, V.; Ishizawa, N.; Maslen, E.N.

doi:10.1107/S0108768100019923

Synchrotron X-ray study of Er₃Al₅O₁₂ and Yb₃Al₅O₁₂ garnets

B. Etschmann, V. Streltsov, N. Ishizawa and E. N. Maslen

Structure factors for Er₃Al₅O₁₂ and Yb₃Al₅O₁₂ garnets were measured using focused synchrotron X-radiation, with λ = 0.7500 (2) and 0.7000 (2) Å, respectively. The difference electron density maps for Er₃Al₅O₁₂ and Yb₃Al₅O₁₂ were similar, as expected. This was attributed to the 4f electrons being shielded, which reduces their effectiveness in chemical bonding and the relative position of the rare-earth atoms in the periodic table. The symmetry of the difference electron density around the rare-earth atoms was found to reflect that of the cation geometry, emphasizing the importance of second nearest-neighbor interactions. This is consistent with the view that oxide-type structures may be regarded as a packed array of cations with anions in the interstices.

Keywords: synchrotron; garnets; electron density.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100019923/os0064sup1.cif Contains datablocks global, Er3Al5O12, Yb3Al5O12
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768100019923/os0064Er3Al5O12sup2.hkl Contains datablock Er3Al5O12
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768100019923/os0064Yb3Al5O12sup3.hkl Contains datablock Yb3Al5O12

Computing details top

For both compounds, data reduction: Xtal DIFDAT ADDREF SORTRF ABSORB; program(s) used to solve structure: Xtal; program(s) used to refine structure: Xtal CRYLSQ; molecular graphics: Xtal; software used to prepare material for publication: Xtal BONDLA CIFIO.

Figures top

(Er3Al5O12) top

Crystal data top

Al₅Er₃O₁₂	D_x = 6.382 Mg m⁻³
M_r = 828.68	Synchrotron radiation, λ = 0.7500 (2) Å
Cubic, Ia3d	Cell parameters from 14 reflections
Hall symbol: -I 4bd 2ab 3	θ = 77.4–81.1°
a = 11.9928 (2) Å	µ = 32.72 mm⁻¹
V = 1724.89 (9) Å³	T = 293 K
Z = 8	Rectangular plate, light_red
F(000) = 2920	0.02 × 0.02 × 0.01 mm

Data collection top

BL14A diffractometer	866 reflections with F > 3σ(F)
Radiation source: synchrotron	R_int = 0.09
Si(111) monochromator	θ_max = 57.4°, θ_min = 4.4°
ω/2θ scans	h = −26→26
Absorption correction: analytical (alcock, 1974) Alcock (1974)	k = −26→26
T_min = 0.41, T_max = 0.66	l = −26→26
38377 measured reflections	6 standard reflections every 94 reflections
866 independent reflections	intensity decay: 1%

Refinement top

Refinement on F	0 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F² > 2σ(F²)] = 0.022	(Δ/σ)_max = 0.001
wR(F²) = 0.028	Δρ_max = 2.1 e Å⁻³
S = 3.10	Δρ_min = −4.8 e Å⁻³
866 reflections	Extinction correction: Zachariasen, Eq22 p292 "Cryst. Comp." Munksgaard 1970
16 parameters	Extinction coefficient: 0.35 (7)x10⁴
0 restraints

Crystal data top

Al₅Er₃O₁₂	Z = 8
M_r = 828.68	Synchrotron radiation, λ = 0.7500 (2) Å
Cubic, Ia3d	µ = 32.72 mm⁻¹
a = 11.9928 (2) Å	T = 293 K
V = 1724.89 (9) Å³	0.02 × 0.02 × 0.01 mm

Data collection top

BL14A diffractometer	866 reflections with F > 3σ(F)
Absorption correction: analytical (alcock, 1974) Alcock (1974)	R_int = 0.09
T_min = 0.41, T_max = 0.66	6 standard reflections every 94 reflections
38377 measured reflections	intensity decay: 1%
866 independent reflections

Refinement top

R[F² > 2σ(F²)] = 0.022	16 parameters
wR(F²) = 0.028	0 restraints
S = 3.10	Δρ_max = 2.1 e Å⁻³
866 reflections	Δρ_min = −4.8 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Er	0.12500	0.00000	0.25000	0.00322 (3)
Al(1)	0.00000	0.00000	0.00000	0.00272 (18)
Al(2)	0.37500	0.00000	0.25000	0.0032 (2)
O	−0.03039 (6)	0.05124 (7)	0.14915 (6)	0.00309 (19)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Er	0.00218 (3)	0.00374 (2)	0.00374 (2)	0.00000	0.00000	0.000811 (17)
Al(1)	0.00272 (18)	0.00272 (18)	0.00272 (18)	−0.00003 (10)	−0.00003 (10)	−0.00003 (10)
Al(2)	0.0016 (3)	0.0040 (2)	0.0040 (2)	0.00000	0.00000	0.00000
O	0.00272 (18)	0.0040 (2)	0.00253 (19)	0.00004 (14)	0.00036 (14)	0.00025 (14)

Geometric parameters (Å, º) top

Er—O	2.3051 (7)	Er—Er	3.6720 (1)
Er—Oⁱ	2.3051 (7)	Er—Er	3.6720 (1)
Er—Oⁱⁱ	2.3051 (7)	Er—Al(2)^viii	3.6720 (1)
Er—O	2.3051 (7)	Er—Al(2)^vii	3.6720 (1)
Er—O	2.4287 (8)	Er—Al(2)	3.6720 (1)
Er—Oⁱⁱⁱ	2.4287 (8)	Er—Al(2)	3.6720 (1)
Er—O^iv	2.4287 (8)	Al(1)—O^ix	1.9261 (7)
Er—O^v	2.4287 (8)	Al(1)—O^x	1.9261 (7)
Er—Al(2)ⁱ	2.9982 (1)	Al(1)—O^xi	1.9261 (7)
Er—Al(2)	2.9982 (1)	Al(1)—O^iv	1.9261 (7)
Er—Al(1)^vi	3.3521 (1)	Al(1)—O^viii	1.9261 (7)
Er—Al(1)	3.3521 (1)	Al(1)—O	1.9261 (7)
Er—Al(1)ⁱⁱ	3.3521 (1)	Al(2)—O	1.7686 (7)
Er—Al(1)	3.3521 (1)	Al(2)—O^xii	1.7686 (7)
Er—Er^vii	3.6720 (1)	Al(2)—Oⁱ	1.7686 (7)
Er—Er^viii	3.6720 (1)	Al(2)—O^xiii	1.7686 (7)

O—Er—O	67.76 (3)	O^ix—Al(1)—O^iv	180.0000
O—Er—Oⁱ	72.11 (3)	O—Al(2)—Oⁱ	100.18 (3)
O—Er—Oⁱⁱⁱ	73.78 (3)	O—Al(2)—O^xii	114.30 (4)
O—Er—O^iv	94.96 (3)	O—Al(2)—O^xiii	114.30 (4)
O—Er—Oⁱⁱ	111.95 (3)	O—Al(2)—Er	50.09 (2)
O—Er—O^v	124.85 (2)	O—Al(2)—Er^xii	129.91 (2)
O—Er—O	158.97 (3)	O—Al(2)—Er^xiv	81.11 (2)
O—Er—Al(2)	36.054 (18)	O—Al(2)—Er^xv	132.72 (3)
O—Er—Al(2)ⁱ	143.946 (19)	O—Al(2)—Er	107.52 (3)
O—Er—Al(1)	33.812 (18)	O—Al(2)—Er	34.43 (3)
O—Er—Al(1)^vi	96.186 (18)	Al(2)ⁱ—O—Al(1)	130.21 (4)
O—Er—Al(1)ⁱⁱ	97.07 (2)	Al(2)ⁱ—O—Er	93.85 (3)
O—Er—Al(1)	126.87 (2)	Al(2)ⁱ—O—Er^viii	121.25 (4)
O^ix—Al(1)—O^x	86.55 (3)	Al(1)—O—Er	104.43 (3)
O^ix—Al(1)—O^xi	86.55 (3)	Al(1)—O—Er^viii	100.02 (3)
O^ix—Al(1)—O^viii	93.45 (3)	Er—O—Er^viii	101.71 (3)
O^ix—Al(1)—O	93.45 (3)

Symmetry codes: (i) −x+1/4, −z+1/4, −y+1/4; (ii) x, −y, −z+1/2; (iii) z, −x, −y+1/2; (iv) z, x, y; (v) −z+1/4, −y+1/4, −x+1/4; (vi) −y+1/4, −x+1/4, −z+1/4; (vii) y, −z, −x+1/2; (viii) y, z, x; (ix) −z, −x, −y; (x) −y, −z, −x; (xi) −x, −y, −z; (xii) x+1/2, y, −z+1/2; (xiii) x+1/2, −y, z; (xiv) y+1/2, −z, x; (xv) y+1/2, z, −x+1/2.

(Yb3Al5O12) top

Crystal data top

Al₅O₁₂Yb₃	Synchrotron radiation, λ = 0.7000 (2) Å
M_r = 846.02	Cell parameters from 14 reflections
Cubic, Ia3d	θ = 56.0–75.1°
Hall symbol: -I 4bd 2ab 3	µ = 30.95 mm⁻¹
a = 11.9386 (4) Å	T = 293 K
V = 1701.6 (3) Å³	Dodecahedron, colourless
Z = 8	0.05 × 0.05 × 0.05 mm
D_x = 6.605 Mg m⁻³

Data collection top

BL14A diffractometer	788 reflections with F > 3σ(F)
Radiation source: synchrotron	R_int = 0.089
Si(111) monochromator	θ_max = 50.0°, θ_min = 4.1°
ω/2θ scans	h = −26→26
Absorption correction: analytical (alcock, 1974) Alcock (1974)	k = −26→26
T_min = 0.29, T_max = 0.35	l = −26→26
34089 measured reflections	6 standard reflections every 94 reflections
788 independent reflections	intensity decay: 1%

Refinement top

Refinement on F	0 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F² > 2σ(F²)] = 0.022	(Δ/σ)_max = 0.0001
wR(F²) = 0.031	Δρ_max = 2.2 e Å⁻³
S = 3.45	Δρ_min = −3.6 e Å⁻³
765 reflections	Extinction correction: Zachariasen, Eq22 p292, Cryst. Comp., Munksgaard 1970
16 parameters	Extinction coefficient: 0.49 (5)x10⁴
0 restraints

Crystal data top

Al₅O₁₂Yb₃	Z = 8
M_r = 846.02	Synchrotron radiation, λ = 0.7000 (2) Å
Cubic, Ia3d	µ = 30.95 mm⁻¹
a = 11.9386 (4) Å	T = 293 K
V = 1701.6 (3) Å³	0.05 × 0.05 × 0.05 mm

Data collection top

BL14A diffractometer	788 reflections with F > 3σ(F)
Absorption correction: analytical (alcock, 1974) Alcock (1974)	R_int = 0.089
T_min = 0.29, T_max = 0.35	6 standard reflections every 94 reflections
34089 measured reflections	intensity decay: 1%
788 independent reflections

Refinement top

R[F² > 2σ(F²)] = 0.022	16 parameters
wR(F²) = 0.031	0 restraints
S = 3.45	Δρ_max = 2.2 e Å⁻³
765 reflections	Δρ_min = −3.6 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Yb	0.12500	0.00000	0.25000	0.00317 (3)
Al(1)	0.00000	0.00000	0.00000	0.0029 (2)
Al(2)	0.37500	0.00000	0.25000	0.0028 (3)
O	−0.02991 (8)	0.05185 (8)	0.14966 (8)	0.0028 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Yb	0.00201 (3)	0.00375 (2)	0.00375 (2)	0.00000	0.00000	0.00069 (2)
Al(1)	0.0029 (2)	0.0029 (2)	0.0029 (2)	−0.00006 (14)	−0.00006 (14)	−0.00006 (14)
Al(2)	0.0020 (3)	0.0032 (2)	0.0032 (2)	0.00000	0.00000	0.00000
O	0.0027 (2)	0.0039 (2)	0.0018 (2)	0.0002 (2)	0.0002 (2)	0.0005 (2)

Geometric parameters (Å, º) top

Yb—Oⁱ	2.2887 (9)	Yb—Yb	3.6554 (2)
Yb—Oⁱⁱ	2.2887 (9)	Yb—Yb	3.6555 (2)
Yb—O	2.2887 (9)	Yb—Al(2)^viii	3.6554 (2)
Yb—O	2.2888 (9)	Yb—Al(2)^vii	3.6555 (2)
Yb—Oⁱⁱⁱ	2.4105 (10)	Yb—Al(2)	3.6555 (2)
Yb—O	2.4105 (10)	Yb—Al(2)	3.6556 (2)
Yb—O^iv	2.4105 (10)	Al(1)—O^ix	1.9243 (9)
Yb—O^v	2.4106 (10)	Al(1)—O^viii	1.9243 (9)
Yb—Al(2)ⁱ	2.9846 (2)	Al(1)—O^x	1.9243 (9)
Yb—Al(2)	2.9846 (2)	Al(1)—O^iv	1.9243 (9)
Yb—Al(1)^vi	3.3369 (1)	Al(1)—O^xi	1.9244 (9)
Yb—Al(1)	3.3369 (1)	Al(1)—O	1.9244 (9)
Yb—Al(1)ⁱⁱ	3.3369 (1)	Al(2)—O	1.7627 (9)
Yb—Al(1)	3.3369 (1)	Al(2)—O^xii	1.7627 (9)
Yb—Yb^vii	3.6554 (2)	Al(2)—Oⁱ	1.7627 (9)
Yb—Yb^viii	3.6554 (2)	Al(2)—O^xiii	1.7627 (9)

O···O^iv	2.6290 (13)	Al(1)^xvi···O^xlvi	6.6028 (10)
O···O^viii	2.6291 (13)	Al(1)^xvi···O	6.6028 (10)
O···Oⁱⁱ	2.6969 (13)	Al(1)^xvi···O^xlvii	6.6031 (11)
O···Oⁱⁱⁱ	2.8084 (14)	Al(1)^xvi···O	6.6031 (11)
O···O^ix	2.8107 (14)	Yb···O^xxvii	6.6581 (10)
O···O^x	2.8108 (14)	Yb···O	6.6581 (10)
O···O	2.9009 (14)	Yb···O	6.6582 (10)
O···O	2.9651 (14)	Yb···O	6.6583 (10)
O···O	2.9651 (14)	Yb···O^xlviii	6.6761 (10)
O···O	3.4689 (14)	Yb···O	6.6761 (10)
O···O	3.4689 (14)	Yb···O	6.6762 (10)
O···Oⁱ	3.7883 (14)	Yb···O	6.6762 (10)
O···O^xi	3.8487 (13)	Yb···O^xlix	6.7049 (10)
O···O^vi	3.8952 (14)	Yb···O	6.7049 (10)
O···O	4.0083 (13)	Yb···O	6.7049 (10)
O···O^xiv	4.0085 (14)	Yb···O^xlvi	6.7050 (10)
O···O^xv	4.1669 (14)	Al(2)···O	6.7318 (10)
O···O^v	4.1671 (14)	Al(2)···O	6.7318 (10)
Al(1)^xvi···O	5.9222 (10)	Al(2)···O	6.7318 (10)
Al(1)^xvi···O^xvii	5.9222 (10)	Al(2)···O	6.7320 (10)
Al(1)^xvi···O	5.9222 (10)	Al(2)···O^l	6.7606 (10)
Al(1)^xvi···O^xviii	5.9222 (10)	Al(2)···O	6.7606 (10)
Al(1)^xvi···O	5.9224 (10)	Al(2)···O	6.7607 (11)
Al(1)^xvi···O^xix	5.9224 (10)	Al(2)···O	6.7608 (11)
Al(1)^xvi···O^xx	5.9385 (10)	Yb···O^xviii	6.7919 (11)
Al(1)^xvi···O^xxi	5.9385 (10)	Yb···O	6.7919 (11)
Al(1)^xvi···O^xxii	5.9385 (10)	Yb···O	6.7921 (11)
Al(1)^xvi···O^xxiii	5.9385 (10)	Yb···O^li	6.7922 (11)
Al(1)^xvi···O^xxiv	5.9386 (10)	Al(1)^xvi···O	6.8004 (10)
Al(1)^xvi···O^xxv	5.9386 (10)	Al(1)^xvi···O	6.8004 (10)
Al(2)···O^xxvi	6.0053 (10)	Al(1)^xvi···O	6.8005 (10)
Al(2)···O^xiv	6.0054 (10)	Al(1)^xvi···O	6.8005 (10)
Al(2)···O	6.0054 (10)	Al(1)^xvi···O	6.8005 (10)
Al(2)···O^ix	6.0055 (10)	Al(1)^xvi···O	6.8005 (10)
Al(2)···O	6.0975 (10)	Yb···O	6.8202 (10)
Al(2)···O^xxvii	6.0975 (10)	Yb···O	6.8203 (10)
Al(2)···O	6.0978 (10)	Yb···O^lii	6.8203 (10)
Al(2)···O^xxviii	6.0978 (10)	Yb···O^liii	6.8205 (10)
Yb···O	6.1585 (10)	Al(1)^xvi···O^liv	6.8355 (11)
Yb···O^xxix	6.1585 (10)	Al(1)^xvi···O	6.8355 (11)
Yb···O	6.1585 (10)	Al(1)^xvi···O^liii	6.8356 (11)
Yb···O	6.1586 (10)	Al(1)^xvi···O	6.8356 (11)
Al(2)···O	6.2675 (10)	Al(1)^xvi···O^lv	6.8358 (11)
Al(2)···O^xxx	6.2675 (10)	Al(1)^xvi···O	6.8358 (11)
Al(2)···O	6.2676 (10)	Al(1)^xvi···O^lvi	6.8497 (10)
Al(2)···O	6.2677 (10)	Al(1)^xvi···O^li	6.8497 (10)
Al(1)^xvi···O^xxxi	6.2871 (10)	Al(1)^xvi···O^lvii	6.8498 (10)
Al(1)^xvi···O^xxxii	6.2871 (10)	Al(1)^xvi···O^xxvi	6.8498 (10)
Al(1)^xvi···O^xxxiii	6.2872 (10)	Al(1)^xvi···O^lviii	6.8498 (10)
Al(1)^xvi···O^xxxiv	6.2872 (10)	Al(1)^xvi···O^lix	6.8498 (10)
Al(1)^xvi···O^xxxv	6.2873 (10)	Al(2)···O	6.8581 (10)
Al(1)^xvi···O^xxxvi	6.2873 (10)	Al(2)···O^lx	6.8581 (10)
Al(2)···O^xxxvii	6.3342 (10)	Al(2)···O	6.8582 (10)
Al(2)···O	6.3342 (10)	Al(2)···O^xxiii	6.8584 (10)
Al(2)···O^xxxviii	6.3342 (10)	Yb···O^lxi	6.9170 (10)
Al(2)···O^xi	6.3344 (10)	Yb···O	6.9171 (10)
Yb···O	6.3504 (10)	Yb···O	6.9171 (10)
Yb···O^xxxix	6.3504 (10)	Yb···O^xxviii	6.9173 (10)
Yb···O	6.3505 (10)	Al(2)···O^lxii	6.9469 (11)
Yb···O^xl	6.3506 (10)	Al(2)···O	6.9470 (11)
Al(1)^xvi···O^xli	6.5313 (10)	Al(2)···O^li	6.9472 (11)
Al(1)^xvi···Oⁱⁱⁱ	6.5313 (10)	Al(2)···O	6.9473 (11)
Al(1)^xvi···Oⁱ	6.5313 (10)	Al(1)^xvi···O^v	7.0267 (10)
Al(1)^xvi···O^xlii	6.5313 (10)	Al(1)^xvi···O	7.0267 (10)
Al(1)^xvi···O^vi	6.5314 (10)	Al(1)^xvi···O^lx	7.0268 (10)
Al(1)^xvi···O^xliii	6.5314 (10)	Al(1)^xvi···O	7.0268 (10)
Yb···O	6.5988 (10)	Al(1)^xvi···O^lxiii	7.0269 (10)
Yb···O	6.5989 (10)	Al(1)^xvi···O	7.0269 (10)
Yb···O^xliv	6.5990 (10)	Yb···O^xix	7.0969 (10)
Yb···O	6.5990 (10)	Yb···O	7.0969 (10)
Al(1)^xvi···O	6.6028 (10)	Yb···O	7.0970 (10)
Al(1)^xvi···O^xlv	6.6028 (10)	Yb···O	7.0971 (10)

Oⁱ—Yb—Oⁱⁱⁱ	67.98 (3)	O^ix—Al(1)—O^viii	180.0000
Oⁱ—Yb—O	72.19 (3)	O—Al(2)—Oⁱ	99.81 (4)
Oⁱ—Yb—O^iv	73.35 (3)	O—Al(2)—O^xii	114.51 (5)
Oⁱ—Yb—O^v	95.12 (3)	O—Al(2)—O^xiii	114.51 (5)
Oⁱ—Yb—O	111.70 (3)	O—Al(2)—Yb	49.91 (3)
Oⁱ—Yb—O	124.91 (3)	O—Al(2)—Yb^xiii	130.09 (3)
Oⁱ—Yb—Oⁱⁱ	159.39 (3)	O—Al(2)—Yb	34.20 (3)
Oⁱ—Yb—Al(2)	36.10 (2)	O—Al(2)—Yb^xxxix	81.45 (3)
Oⁱ—Yb—Al(2)ⁱ	143.90 (2)	O—Al(2)—Yb	107.53 (3)
Oⁱ—Yb—Al(1)^vi	33.95 (2)	O—Al(2)—Yb^xl	132.41 (3)
Oⁱ—Yb—Al(1)	96.13 (2)	Al(2)ⁱ—O—Al(1)	129.61 (6)
Oⁱ—Yb—Al(1)ⁱⁱ	127.10 (3)	Al(2)ⁱ—O—Yb	94.00 (4)
Oⁱ—Yb—Al(1)	96.86 (2)	Al(2)ⁱ—O—Yb^viii	121.54 (5)
O^ix—Al(1)—O^x	86.17 (4)	Al(1)—O—Yb	104.42 (4)
O^ix—Al(1)—O^xi	86.17 (4)	Al(1)—O—Yb^viii	100.07 (4)
O^ix—Al(1)—O^iv	93.83 (4)	Yb—O—Yb^viii	102.10 (4)
O^ix—Al(1)—O	93.83 (4)

Symmetry codes: (i) −x+1/4, −z+1/4, −y+1/4; (ii) x, −y, −z+1/2; (iii) −z+1/4, −y+1/4, −x+1/4; (iv) z, x, y; (v) z, −x, −y+1/2; (vi) −y+1/4, −x+1/4, −z+1/4; (vii) y, −z, −x+1/2; (viii) y, z, x; (ix) −y, −z, −x; (x) −z, −x, −y; (xi) −x, −y, −z; (xii) x+1/2, −y, z; (xiii) x+1/2, y, −z+1/2; (xiv) −y, z, x+1/2; (xv) −y, −z+1/2, x; (xvi) x+1/2, y+1/2, z+1/2; (xvii) −z+1/2, −x, y+1/2; (xviii) −x, y+1/2, −z+1/2; (xix) y+1/2, −z+1/2, −x; (xx) −z+1/4, −y+3/4, x+3/4; (xxi) z+3/4, y+1/4, −x+1/4; (xxii) −x+1/4, z+3/4, y+1/4; (xxiii) x+3/4, −z+1/4, −y+3/4; (xxiv) y+1/4, −x+1/4, z+3/4; (xxv) −y+3/4, x+3/4, −z+1/4; (xxvi) y+3/4, x+1/4, −z+1/4; (xxvii) −z+1/2, x+1/2, y; (xxviii) z+1/4, −y+1/4, x+3/4; (xxix) −z+3/4, −y+1/4, x+1/4; (xxx) y, −z+1/2, x+1/2; (xxxi) z+3/4, −y+3/4, x+1/4; (xxxii) −z+1/4, y+1/4, −x+3/4; (xxxiii) x+1/4, z+3/4, −y+3/4; (xxxiv) −x+3/4, −z+1/4, y+1/4; (xxxv) y+1/4, −x+3/4, −z+1/4; (xxxvi) −y+3/4, x+1/4, z+3/4; (xxxvii) x+3/4, z+1/4, −y+1/4; (xxxviii) −x, y, z+1/2; (xxxix) y+1/2, −z, x; (xl) y+1/2, z, −x+1/2; (xli) z+3/4, y+3/4, x+3/4; (xlii) x+3/4, z+3/4, y+3/4; (xliii) y+3/4, x+3/4, z+3/4; (xliv) −y+1/2, −z+1/2, −x+1/2; (xlv) x, −y+1/2, z+1/2; (xlvi) z+1/2, x, −y+1/2; (xlvii) −y+1/2, z+1/2, x; (xlviii) z, x+1/2, −y; (xlix) z+1/2, −x, y; (l) −z+1/2, −x+1/2, −y+1/2; (li) x+1/4, −z+1/4, y+3/4; (lii) −x+1/2, y, −z; (liii) −x+1/2, −y, z+1/2; (liv) −y, z+1/2, −x+1/2; (lv) z+1/2, −x+1/2, −y; (lvi) −x+3/4, z+3/4, −y+1/4; (lvii) −y+1/4, −x+3/4, z+3/4; (lviii) −z+1/4, y+3/4, x+1/4; (lix) z+3/4, −y+1/4, −x+3/4; (lx) −x, −y+1/2, z; (lxi) −z, x+1/2, −y+1/2; (lxii) −x+1/2, y+1/2, z; (lxiii) −y+1/2, z, −x.

Experimental details

	(Er3Al5O12)	(Yb3Al5O12)
Crystal data
Chemical formula	Al₅Er₃O₁₂	Al₅O₁₂Yb₃
M_r	828.68	846.02
Crystal system, space group	Cubic, Ia3d	Cubic, Ia3d
Temperature (K)	293	293
a (Å)	11.9928 (2)	11.9386 (4)
V (Å³)	1724.89 (9)	1701.6 (3)
Z	8	8
Radiation type	Synchrotron, λ = 0.7500 (2) Å	Synchrotron, λ = 0.7000 (2) Å
µ (mm⁻¹)	32.72	30.95
Crystal size (mm)	0.02 × 0.02 × 0.01	0.05 × 0.05 × 0.05

Data collection
Diffractometer	BL14A diffractometer	BL14A diffractometer
Absorption correction	Analytical (Alcock, 1974) Alcock (1974)	Analytical (Alcock, 1974) Alcock (1974)
T_min, T_max	0.41, 0.66	0.29, 0.35
No. of measured, independent and observed [F > 3σ(F)] reflections	38377, 866, 866	34089, 788, 788
R_int	0.09	0.089
(sin θ/λ)_max (Å⁻¹)	1.123	1.094

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.022, 0.028, 3.10	0.022, 0.031, 3.45
No. of reflections	866	765
No. of parameters	16	16
Δρ_max, Δρ_min (e Å⁻³)	2.1, −4.8	2.2, −3.6

Computer programs: Xtal DIFDAT ADDREF SORTRF ABSORB, Xtal CRYLSQ, Xtal BONDLA CIFIO.

Selected geometric parameters (Å, º) for (Er3Al5O12) top

Er—Oⁱ	2.3051 (7)	Er—Erⁱⁱⁱ	3.6720 (1)
Er—Oⁱⁱ	2.4287 (8)	Al(1)—O^iv	1.9261 (7)
Er—Al(2)	2.9982 (1)	Al(2)—O^v	1.7686 (7)
Er—Al(1)	3.3521 (1)

O—Er—O	67.76 (3)	O—Al(2)—O^vi	100.18 (3)
O—Er—O^vi	72.11 (3)	O—Al(2)—O^xi	114.30 (4)
O—Er—O^vii	73.78 (3)	O—Al(2)—Er	50.09 (2)
O—Er—O^viii	94.96 (3)	O—Al(2)—Er^xi	129.91 (2)
O—Er—Oⁱ	111.95 (3)	Al(2)^vi—O—Al(1)	130.21 (4)
O—Er—Oⁱⁱ	124.85 (2)	Al(2)^vi—O—Er	93.85 (3)
O—Er—O	158.97 (3)	Al(2)^vi—O—Er^x	121.25 (4)
O—Er—Al(2)	36.054 (18)	Al(1)—O—Er	104.43 (3)
O—Er—Al(2)^vi	143.946 (19)	Al(1)—O—Er^x	100.02 (3)
O^ix—Al(1)—O^iv	86.55 (3)	Er—O—Er^x	101.71 (3)
O^ix—Al(1)—O^x	93.45 (3)

Symmetry codes: (i) x, −y, −z+1/2; (ii) −z+1/4, −y+1/4, −x+1/4; (iii) y, −z, −x+1/2; (iv) −x, −y, −z; (v) x+1/2, −y, z; (vi) −x+1/4, −z+1/4, −y+1/4; (vii) z, −x, −y+1/2; (viii) z, x, y; (ix) −z, −x, −y; (x) y, z, x; (xi) x+1/2, y, −z+1/2.

Selected geometric parameters (Å, º) for (Yb3Al5O12) top

Yb—Oⁱ	2.2887 (9)	Yb—Ybⁱⁱⁱ	3.6554 (2)
Yb—Oⁱⁱ	2.4105 (10)	Al(1)—O^iv	1.9244 (9)
Yb—Al(2)	2.9846 (2)	Al(2)—O^v	1.7627 (9)
Yb—Al(1)	3.3369 (1)

O^vi—Yb—Oⁱⁱ	67.98 (3)	O—Al(2)—O^vi	99.81 (4)
O^vi—Yb—O	72.19 (3)	O—Al(2)—O^xi	114.51 (5)
O^vi—Yb—O^vii	73.35 (3)	O—Al(2)—Yb	49.91 (3)
O^vi—Yb—O^viii	95.12 (3)	O—Al(2)—Yb^xi	130.09 (3)
O^vi—Yb—O	111.70 (3)	Al(2)^vi—O—Al(1)	129.61 (6)
O^vi—Yb—O	124.91 (3)	Al(2)^vi—O—Yb	94.00 (4)
O^vi—Yb—Oⁱ	159.39 (3)	Al(2)^vi—O—Yb^xii	121.54 (5)
O^vi—Yb—Al(2)	36.10 (2)	Al(1)—O—Yb	104.42 (4)
O^vi—Yb—Al(2)^vi	143.90 (2)	Al(1)—O—Yb^xii	100.07 (4)
O^ix—Al(1)—O^x	86.17 (4)	Yb—O—Yb^xii	102.10 (4)
O^ix—Al(1)—O^vii	93.83 (4)

Symmetry codes: (i) x, −y, −z+1/2; (ii) −z+1/4, −y+1/4, −x+1/4; (iii) y, −z, −x+1/2; (iv) −x, −y, −z; (v) x+1/2, −y, z; (vi) −x+1/4, −z+1/4, −y+1/4; (vii) z, x, y; (viii) z, −x, −y+1/2; (ix) −y, −z, −x; (x) −z, −x, −y; (xi) x+1/2, y, −z+1/2; (xii) y, z, x.

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