Size effect of the guest cation on the AlO₄ framework in aluminate sodalite-type oxides M₈[Al₁₂O₂₄](SO₄)₂ (M = Sr²⁺ and Ca²⁺) in the I43m phase

Sr₈[Al₁₂O₂₄](SO₄)₂ (SAS) and Ca₈[Al₁₂O₂₄](SO₄)₂ (CAS) are members of the aluminate sodalite-type oxides with the general chemical formula M₈[Al₁₂O₂₄](XO₄)₂ (M²⁺ is the guest cation and XO₄²⁻ is the guest anion). To discuss the role of the guest cations (M²⁺ = Sr²⁺ and Ca²⁺) on the rotation of AlO₄ in the oxygen tetrahedral framework in the I43m phase, the crystal structure parameters and the probability density function of the guest ions in SAS and CAS have been investigated via synchrotron radiation X-ray powder diffraction by considering Gram–Charlier expansions. The interatomic distances between the M²⁺ and O²⁻ ions evaluated from the maximum positions in the probability density distribution are almost equal to the sum of the ideal ionic radii of the M²⁺ and O²⁻ ions. This result suggests that the geometry of the AlO₄ tetrahedral framework and the fluctuation of the guest ions are mainly caused by steric effects between the M²⁺ and O²⁻ ions.

Computing details

cakcium aluminate sulfate (CAS-850K)

Crystal data

Al12Ca8O32S2	F(000) = 604.0007
Mr = 1220.52	Dx = 2.585 Mg m^−3
Cubic, I43m	Synchrotron radiation, λ = 0.775119(1) Å
a = 9.220676 (7) Å	T = 850 K
V = 783.95 (1) Å^3	white
Z = 1	cylinder, 24 × 0.2 mm

Data collection

Large Debye-Scherrer camera, BL02B2, SPring-8 diffractometer	Data collection mode: transmittion
Radiation source: synchrotron	Scan method: Stationary detector
Specimen mounting: powder in a glass capillary

Refinement

Rp = 0.006	Profile function: pseudo-Voigt
Rwp = 0.010	31 parameters
Rexp = 0.004	0 restraints
RBragg = 0.038	0 constraints
R(F) = 0.046	(Δ/σ)max = −0.047
R(F^2) = 0.0986	Background function: manual background
9800 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ca	0.20798 (6)	0.20798 (6)	0.20798 (6)	0.061796
S	0.000000	0.000000	0.000000	0.067126
Al	0.250000	0.500000	0.000000	0.019116
O1	0.15379 (11)	0.15379 (11)	0.44811 (11)	0.034267
O2	0.0754 (13)	0.0754 (13)	0.0754 (13)	0.305112

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ca	0.0618 (5)	0.0618 (5)	0.0618 (5)	0.0329 (5)	0.0329 (5)	0.0329 (5)
S	0.0671 (8)	0.0671 (8)	0.0671 (8)	0	0	0
Al	0.0134 (4)	0.0220 (3)	0.0220 (3)	0	0	0
O1	0.0270 (4)	0.0270 (4)	0.0488 (8)	0.0081 (6)	0.0025 (4)	0.0025 (4)
O2	0.305 (4)	0.305 (4)	0.305 (4)	−0.103 (3)	−0.103 (3)	−0.103 (3)

Geometric parameters (Å, º)

Ca—O1	2.324 (1)	Al—O1^i	1.739 (1)
Ca—O2	2.12 (1)	S—O2	1.20 (1)
O1^i—Al—O1^ii	118.68 (7)	O2—S—O2^iv	110 (1)
O1^i—Al—O1^iii	105.07 (4)

Symmetry codes: (i) y, z, x; (ii) y, −z+1, −x; (iii) −x+1/2, −y+1/2, z−1/2; (iv) −x, −y, z.

cakcium aluminate sulfate (SAS-850K)

Crystal data

Al12O32S2Sr8	F(000) = 748.0010
Mr = 1600.85	Dx = 3.155 Mg m^−3
Cubic, I43m	Synchrotron radiation, λ = 0.775119(1) Å
a = 9.444949 (5) Å	T = 850 K
V = 842.56 (1) Å^3	white
Z = 1	cylinder, 24 × 0.2 mm

Data collection

Large Debye-Scherrer camera, BL02B2, SPring-8 diffractometer	Data collection mode: transmittion
Radiation source: synchrotron	Scan method: Stationary detector
Specimen mounting: powder in a glass capillary

Refinement

Rp = 0.008	Profile function: pseudo-Voigt
Rwp = 0.015	31 parameters
Rexp = 0.004	0 restraints
RBragg = 0.029	0 constraints
R(F) = 0.032	(Δ/σ)max = −0.047
R(F^2) = 0.0294	Background function: manual background
9700 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Sr	0.22472 (5)	0.22472 (5)	0.22472 (5)	0.058139
S	0.000000	0.000000	0.000000	0.067130
Al	0.250000	0.500000	0.000000	0.015304
O1	0.15715 (10)	0.15715 (10)	0.48364 (18)	0.030590
O2	0.0768 (16)	0.0768 (16)	0.0768 (16)	0.354681

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sr	0.0581 (4)	0.0581 (4)	0.0581 (4)	0.0405 (3)	0.0405 (3)	0.0405 (3)
S	0.067 (9)	0.067 (9)	0.067 (9)	0	0	0
Al	0.0202 (5)	0.0129 (3)	0.0129 (3)	0	0	0
O1	0.0232 (5)	0.0232 (5)	0.0454 (8)	0.0136 (6)	0.0038 (5)	0.0038 (5)
O2	0.355 (6)	0.355 (6)	0.355 (6)	−0.102 (5)	−0.102 (5)	−0.102 (5)

Geometric parameters (Å, º)

Sr—O1	2.607 (2)	Al—O1^i	1.731 (1)
Sr—O2	2.42 (2)	S—O2	1.26 (2)
O1^i—Al—O1^ii	119.12 (7)	O2—S—O2^iv	110 (1)
O1^i—Al—O1^iii	104.87 (3)

Symmetry codes: (i) y, z, x; (ii) y, −z+1, −x; (iii) −x+1/2, −y+1/2, z−1/2; (iv) −x, −y, z.

cakcium aluminate sulfate (SAS-1100K)

Crystal data

Al12O32S2Sr8	F(000) = 748.0010
Mr = 1600.85	Dx = 3.117 Mg m^−3
Cubic, Im3m	Synchrotron radiation, λ = 0.774493(1) Å
a = 9.483220 (6) Å	T = 1100 K
V = 852.84 (2) Å^3	white
Z = 1	cylinder, 24 × 0.2 mm

Data collection

Large Debye-Scherrer camera, BL02B2, SPring-8 diffractometer	Data collection mode: transmittion
Radiation source: synchrotron	Scan method: Stationary detector
Specimen mounting: powder in a glass capillary

Refinement

Rp = 0.022	Profile function: pseudo-Voigt
Rwp = 0.033	25 parameters
Rexp = 0.022	0 restraints
RBragg = 0.034	0 constraints
R(F) = 0.032	(Δ/σ)max = −0.046
R(F^2) = 0.0396	Background function: manual background
12683 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Sr	0.250000	0.250000	0.250000	0.101901
Al	0.250000	0.500000	0.000000	0.021725
S	0.000000	0.000000	0.000000	0.106242
O1	0.1581 (2)	0.1581 (2)	0.5000 (2)	0.037026
O2	0.08155 (2)	0.08155 (2)	0.08155 (2)	0.400738	0.5000

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sr	0.1019 (7)	0.1019 (7)	0.1019 (7)	0.0735 (7)	0.0735 (7)	0.0735 (7)
S	0.1062 (16)	0.1062 (16)	0.1062 (16)	0	0	0
Al	0.0236 (10)	0.0208 (5)	0.0208 (5)	0	0	0
O1	0.0293 (8)	0.0293 (8)	0.0525 (13)	0.0229 (10)	0	0
O2	0.401 (6)	0.401 (6)	0.401 (6)	0.008 (3)	0.008 (3)	0.008 (3)

Geometric parameters (Å, º)

Sr—O1	2.672 (2)	Al—O1^i	1.734 (2)
Sr—O2	2.7669 (2)	S—O2	1.3395 (2)
O1^i—Al—O1^ii	119.7 (1)	O2—S—O2^iv	109.47 (2)
O1^i—Al—O1^iii	104.63 (1)	O2—S—O2^v	70.53 (2)

Symmetry codes: (i) y, z, x; (ii) y, −z+1, −x; (iii) −x+1/2, −y+1/2, −z+1/2; (iv) −x, y, −z; (v) −x, y, z.