Structural transformation of Sb-based high-speed phase-change material

Matsunaga, T.; Kojima, R.; Yamada, N.; Kubota, Y.; Kifune, K.

doi:10.1107/S0108768112039961

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Structural transformation of Sb-based high-speed phase-change material

T. Matsunaga, R. Kojima, N. Yamada, Y. Kubota and K. Kifune

The crystal structure of a phase-change recording material (the compound Ag_3.4In_3.7Sb_76.4Te_16.5) enclosed in a vacuum capillary tube was investigated at various temperatures in a heating process using a large Debye–Scherrer camera installed in BL02B2 at SPring-8. The amorphous phase of this material turns into a crystalline phase at around 416 K; this crystalline phase has an A7-type structure with atoms of Ag, In, Sb or Te randomly occupying the 6c site in the space group. This structure was maintained up to around 545 K as a single phase, although thermal expansion of the crystal lattice was observed. However, above this temperature, phase separation into AgInTe₂ and Sb–Te transpired. The first fragment, AgInTe₂, reliably maintained its crystal structure up to the melting temperature. On the other hand, the atomic configuration of the Sb–Te gradually varied with increasing temperature. This gradual structural transformation can be described as a continuous growth of the modulation period γ.

Keywords: chalcogenide compounds; homologous structure; modulated layer structure; phase change; AIST.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768112039961/dk5006sup1.cif Contains datablocks global, I, II, III, IV, V
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112039961/dk5006Isup2.rtv Contains datablock I
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112039961/dk5006IIsup3.rtv Contains datablock II
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112039961/dk5006IIIsup4.rtv Contains datablock III
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112039961/dk5006IVsup5.rtv Contains datablock IV
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768112039961/dk5006Vsup6.rtv Contains datablock V

B-IncStrDB reference: 6732EXfQbW

Computing details top

Program(s) used to refine structure: Jana2000 (Petricek, Dusek & Palatinus, 2000) for (IV), (V). Software used to prepare material for publication: Jana2000 (Petricek, Dusek & Palatinus, 2000) for (IV), (V).

Figures top

(I) top

Crystal data top

Ag_0.034In_0.037Sb_0.764Te_0.165	Z = 3
M_r = 122	F(000) = 1834
Trigonal, R3m(00γ)00†	D_x = 6.709 Mg m⁻³
q = 1.500000c*	? radiation, λ = 0.41873 Å
a = 4.3037 (5) Å	T = 545 K
c = 5.6452 (6) Å	?, ? × ? × ? mm
V = 90.55 (2) Å³

Data collection top

2θ_min = 5.5°, 2θ_max = 31.5°, 2θ_step = 0.01°

Refinement top

R_p = 0.020	56 parameters
R_wp = 0.029	0 restraints
R_exp = 0.030	12 constraints
R(F) = 0.013	Weighting scheme based on measured s.u.'s
χ² = 0.960	(Δ/σ)_max = 7.061
2601 data points	Background function: 36 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Crystal data top

Ag_0.034In_0.037Sb_0.764Te_0.165	V = 90.55 (2) Å³
M_r = 122	Z = 3
Trigonal, R3m(00γ)00†	? radiation, λ = 0.41873 Å
q = 1.500000c*	T = 545 K
a = 4.3037 (5) Å	?, ? × ? × ? mm
c = 5.6452 (6) Å

Data collection top

2θ_min = 5.5°, 2θ_max = 31.5°, 2θ_step = 0.01°

Refinement top

R_p = 0.020	2601 data points
R_wp = 0.029	56 parameters
R_exp = 0.030	0 restraints
R(F) = 0.013	(Δ/σ)_max = 7.061
χ² = 0.960

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Sb1	0	0	0	0.0296 (6)	0.764
Te1	0	0	0	0.0296 (5)	0.165
Ag1	0	0	0	0.0296 (5)	0.034
In1	0	0	0	0.0296 (5)	0.037

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Sb1	0.0229 (5)	0.0229 (5)	0.0431 (14)	0.0114 (2)	0	0
Te1	0.0229 (5)	0.022892	0.0431 (14)	0.011446	0	0
Ag1	0.0229 (5)	0.022892	0.0431 (14)	0.011446	0	0
In1	0.0229 (5)	0.022892	0.0431 (14)	0.011446	0	0

(II) top

Crystal data top

Sb_0.89Te_0.11	Z = 3
M_r = 122.4	F(000) = 800
Trigonal, R3m(00γ)00†	D_x = 6.716 Mg m⁻³
q = 1.551587c*	? radiation, λ = 0.41873 Å
a = 4.29686 (13) Å	T = 293 K
c = 5.67590 (19) Å	?, ? × ? × ? mm
V = 90.75 (1) Å³

Data collection top

2θ_min = 5.5°, 2θ_max = 42.1°, 2θ_step = 0.01°

Refinement top

R_p = 0.021	68 parameters
R_wp = 0.030	0 restraints
R_exp = 0.030	4 constraints
R(F) = 0.016	Weighting scheme based on measured s.u.'s
χ² = 1.000	(Δ/σ)_max = 5.113
3661 data points	Background function: 36 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: March & Dollase

Crystal data top

Sb_0.89Te_0.11	V = 90.75 (1) Å³
M_r = 122.4	Z = 3
Trigonal, R3m(00γ)00†	? radiation, λ = 0.41873 Å
q = 1.551587c*	T = 293 K
a = 4.29686 (13) Å	?, ? × ? × ? mm
c = 5.67590 (19) Å

Data collection top

2θ_min = 5.5°, 2θ_max = 42.1°, 2θ_step = 0.01°

Refinement top

R_p = 0.021	3661 data points
R_wp = 0.030	68 parameters
R_exp = 0.030	0 restraints
R(F) = 0.016	(Δ/σ)_max = 5.113
χ² = 1.000

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Sb1	0	0	0	0.0116 (3)	0.887
Te1	0	0	0	0.0116 (3)	0.113

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Sb1	0.0123 (2)	0.0123 (2)	0.0101 (7)	0.00614 (12)	0	0
Te1	0.0123 (2)	0.012285	0.0101 (7)	0.006143	0	0

(III) top

Crystal data top

AgInTe₂	Z = 4
M_r = 477.9	F(000) = 800
Tetragonal, I42d	D_x = 6.092 Mg m⁻³
Hall symbol: I -4;2bw	? radiation, λ = 0.41873 Å
a = 6.4275 (3) Å	T = 293 K
c = 12.6089 (9) Å	?, ? × ? × ? mm
V = 520.91 (5) Å³

Data collection top

2θ_min = 5.5°, 2θ_max = 42.1°, 2θ_step = 0.01°

Refinement top

R_p = 0.021	68 parameters
R_wp = 0.030	0 restraints
R_exp = 0.030	4 constraints
R(F) = 0.016	Weighting scheme based on measured s.u.'s
χ² = 1.000	(Δ/σ)_max = 5.113
3661 data points	Background function: 36 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Crystal data top

AgInTe₂	V = 520.91 (5) Å³
M_r = 477.9	Z = 4
Tetragonal, I42d	? radiation, λ = 0.41873 Å
a = 6.4275 (3) Å	T = 293 K
c = 12.6089 (9) Å	?, ? × ? × ? mm

Data collection top

2θ_min = 5.5°, 2θ_max = 42.1°, 2θ_step = 0.01°

Refinement top

R_p = 0.021	3661 data points
R_wp = 0.030	68 parameters
R_exp = 0.030	0 restraints
R(F) = 0.016	(Δ/σ)_max = 5.113
χ² = 1.000

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

	x	y	z	U_iso*/U_eq
Ag1	0	0	0.5	0.0289 (13)*
In1	0	0	0	0.0289 (13)*
Te2	0.252 (11)	0.25	0.125	0.0289 (13)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
?	?	?	?	?	?	?

(IV) top

Crystal data top

Sb_0.87Te_0.13	Z = 3
M_r = 122.5	F(000) = 1841
Trigonal, R3m(00γ)00†	D_x = 6.598 Mg m⁻³
q = 1.56522c*	X-ray radiation, λ = 0.41853 Å
a = 4.3181 Å	T = 773 K
c = 5.7267 Å	?, ? × ? × ? mm
V = 92.47 Å³

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₂, −x₁, x₃, x₄; (4) −x₁+x₂, −x₁, x₃, x₄; (5) x₁, x₁−x₂, x₃, x₄; (6) −x₁+x₂, x₂, x₃, x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₂, x₁, −x₃, −x₄; (10) x₁−x₂, x₁, −x₃, −x₄; (11) −x₁, −x₁+x₂, −x₃, −x₄; (12) x₁−x₂, −x₂, −x₃, −x₄; (13) 2/3+x₁, 1/3+x₂, 1/3+x₃, x₄; (14) 2/3−x₂, 1/3+x₁−x₂, 1/3+x₃, x₄; (15) 2/3−x₂, 1/3−x₁, 1/3+x₃, x₄; (16) 2/3−x₁+x₂, 1/3−x₁, 1/3+x₃, x₄; (17) 2/3+x₁, 1/3+x₁−x₂, 1/3+x₃, x₄; (18) 2/3−x₁+x₂, 1/3+x₂, 1/3+x₃, x₄; (19) 2/3−x₁, 1/3−x₂, 1/3−x₃, −x₄; (20) 2/3+x₂, 1/3−x₁+x₂, 1/3−x₃, −x₄; (21) 2/3+x₂, 1/3+x₁, 1/3−x₃, −x₄; (22) 2/3+x₁−x₂, 1/3+x₁, 1/3−x₃, −x₄; (23) 2/3−x₁, 1/3−x₁+x₂, 1/3−x₃, −x₄; (24) 2/3+x₁−x₂, 1/3−x₂, 1/3−x₃, −x₄; (25) 1/3+x₁, 2/3+x₂, 2/3+x₃, x₄; (26) 1/3−x₂, 2/3+x₁−x₂, 2/3+x₃, x₄; (27) 1/3−x₂, 2/3−x₁, 2/3+x₃, x₄; (28) 1/3−x₁+x₂, 2/3−x₁, 2/3+x₃, x₄; (29) 1/3+x₁, 2/3+x₁−x₂, 2/3+x₃, x₄; (30) 1/3−x₁+x₂, 2/3+x₂, 2/3+x₃, x₄; (31) 1/3−x₁, 2/3−x₂, 2/3−x₃, −x₄; (32) 1/3+x₂, 2/3−x₁+x₂, 2/3−x₃, −x₄; (33) 1/3+x₂, 2/3+x₁, 2/3−x₃, −x₄; (34) 1/3+x₁−x₂, 2/3+x₁, 2/3−x₃, −x₄; (35) 1/3−x₁, 2/3−x₁+x₂, 2/3−x₃, −x₄; (36) 1/3+x₁−x₂, 2/3−x₂, 2/3−x₃, −x₄.

Data collection top

2θ_min = 3.02°, 2θ_max = 30.5°, 2θ_step = 0.02°

Refinement top

R_p = 0.020	Profile function: Pseudo-Voigt
R_wp = 0.029	59 parameters
R_exp = 0.024	Weighting scheme based on measured s.u.'s
R(F) = 0.030	(Δ/σ)_max = 0.628
χ² = NOT FOUND	Background function: 36 Legendre polynoms
1375 data points	Preferred orientation correction: none

Crystal data top

Sb_0.87Te_0.13	V = 92.47 Å³
M_r = 122.5	Z = 3
Trigonal, R3m(00γ)00†	X-ray radiation, λ = 0.41853 Å
q = 1.56522c*	T = 773 K
a = 4.3181 Å	?, ? × ? × ? mm
c = 5.7267 Å

Data collection top

2θ_min = 3.02°, 2θ_max = 30.5°, 2θ_step = 0.02°

Refinement top

R_p = 0.020	χ² = NOT FOUND
R_wp = 0.029	1375 data points
R_exp = 0.024	59 parameters
R(F) = 0.030	(Δ/σ)_max = 0.628

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Sb1	0	0	0	0.03832 (14)	0.870
Te1	0	0	0	0.03832 (12)	0.130

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Sb1	0.03681 (14)	0.03681 (14)	0.0413 (3)	0.01841 (7)	0	0
Te1	0.03681 (14)	0.03681	0.0413 (3)	0.018405	0	0

Bond lengths (Å) top

	Average	Minimum	Maximum
Sb1—Sb1ⁱ	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1ⁱⁱ	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1ⁱⁱⁱ	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1^iv	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1^v	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1^vi	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Te1ⁱ	3.1483 (6)	2.8798 (9)	3.4307 (9)
Sb1—Te1ⁱⁱ	3.1483 (6)	2.8798 (9)	3.4307 (9)
Sb1—Te1ⁱⁱⁱ	3.1483 (6)	2.8798 (9)	3.4307 (9)
Sb1—Te1^iv	3.1491 (6)	2.8804 (9)	3.4316 (9)
Sb1—Te1^v	3.1491 (6)	2.8804 (9)	3.4316 (9)
Sb1—Te1^vi	3.1491 (6)	2.8804 (9)	3.4316 (9)

Symmetry codes: (i) x₁−1/3, x₂−2/3, x₃+1/3, x₄; (ii) x₁−1/3, x₂+1/3, x₃+1/3, x₄; (iii) x₁+2/3, x₂+1/3, x₃+1/3, x₄; (iv) x₁−2/3, x₂−1/3, x₃−1/3, x₄; (v) x₁+1/3, x₂−1/3, x₃−1/3, x₄; (vi) x₁+1/3, x₂+2/3, x₃−1/3, x₄.

(V) top

Crystal data top

Sb₂O₃	Z = 16
M_r = 291.5	F(000) = 1841
Cubic, Fd3m	D_x = 5.442 Mg m⁻³
Hall symbol: -F 4vw;2vw;3	X-ray radiation, λ = 0.41853 Å
a = 11.2471 Å	T = 773 K
V = 1422.71 Å³	?, ? × ? × ? mm

Data collection top

2θ_min = 3.02°, 2θ_max = 30.5°, 2θ_step = 0.02°

Refinement top

R_p = 0.020	Profile function: Pseudo-Voigt
R_wp = 0.029	59 parameters
R_exp = 0.024	Weighting scheme based on measured s.u.'s
R(F) = 0.030	(Δ/σ)_max = 0.628
χ² = NOT FOUND	Background function: 36 Legendre polynoms
1375 data points	Preferred orientation correction: none

Crystal data top

Sb₂O₃	Z = 16
M_r = 291.5	X-ray radiation, λ = 0.41853 Å
Cubic, Fd3m	T = 773 K
a = 11.2471 Å	?, ? × ? × ? mm
V = 1422.71 Å³

Data collection top

2θ_min = 3.02°, 2θ_max = 30.5°, 2θ_step = 0.02°

Refinement top

R_p = 0.020	χ² = NOT FOUND
R_wp = 0.029	1375 data points
R_exp = 0.024	59 parameters
R(F) = 0.030	(Δ/σ)_max = 0.628

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

	x	y	z	U_iso*/U_eq
Sb2	0.88704 (13)	0.88704 (13)	0.88704 (13)	0.0264 (14)*
O1	0.188 (2)	0	0	0.0264 (14)*

Bond lengths (Å) top

Sb2—O1ⁱ	1.986 (10)	O1—O1^viii	2.99 (2)
Sb2—O1ⁱⁱ	2.936 (16)	O1—O1^ix	2.979 (8)
Sb2—O1ⁱⁱⁱ	2.936 (16)	O1—O1^x	2.99 (2)
Sb2—O1^iv	1.986 (10)	O1—O1^xi	2.979 (8)
Sb2—O1^v	2.936 (16)	O1—O1^xii	2.99 (2)
Sb2—O1^vi	1.986 (10)	O1—O1^xiii	2.979 (8)
O1—O1^vii	2.979 (8)	O1—O1^xiv	2.99 (2)

Symmetry codes: (i) −x+1, −y+1, z+1; (ii) −x+5/4, z+3/4, y+3/4; (iii) y+3/4, −x+5/4, z+3/4; (iv) −z+1, −x+1, y+1; (v) z+3/4, y+3/4, −x+5/4; (vi) −y+1, z+1, −x+1; (vii) −y+1/4, x−1/4, z−1/4; (viii) z, x, y; (ix) y+1/4, −x+1/4, z+1/4; (x) −z, −x, y; (xi) z+1/4, −y−1/4, x−1/4; (xii) y, z, x; (xiii) z+1/4, y+1/4, −x+1/4; (xiv) −y, z, −x.

Experimental details

	(I)	(II)	(III)	(IV)
Crystal data
Chemical formula	Ag_0.034In_0.037Sb_0.764Te_0.165	Sb_0.89Te_0.11	AgInTe₂	Sb_0.87Te_0.13
M_r	122	122.4	477.9	122.5
Crystal system, space group	Trigonal, R3m(00γ)00†	Trigonal, R3m(00γ)00‡	Tetragonal, I42d	Trigonal, R3m(00γ)00§
Temperature (K)	545	293	293	773
Wave vectors	q = 1.500000c*	q = 1.551587c*	I -4;2bw	q = 1.56522c*
a, b, c (Å)	4.3037 (5), 4.3037 (5), 5.6452 (6)	4.29686 (13), 4.29686 (13), 5.67590 (19)	90, 90, 90	4.3181, 4.3181, 5.7267
α, β, γ (°)	90, 90, 120	90, 90, 120	520.91 (5)	90, 90, 120
V (Å³)	90.55 (2)	90.75 (1)	4	92.47
Z	3	3	800	3
Radiation type	?, λ = 0.41873 Å	?, λ = 0.41873 Å	–	X-ray, λ = 0.41853 Å
µ (mm⁻¹)	–	–	?	–
Specimen shape, size (mm)	?, ? × ? × ?	?, ? × ? × ?		?, ? × ? × ?

Data collection
Diffractometer	?	?	?	?
Specimen mounting	?	?	?	?
Data collection mode	?	?	?	?
Scan method	?	?	?	?
2θ values (°)	2θ_min = 5.5 2θ_max = 31.5 2θ_step = 0.01	2θ_min = 5.5 2θ_max = 42.1 2θ_step = 0.01	2θ_min = 5.5 2θ_max = 42.1 2θ_step = 0.01	2θ_min = 3.02 2θ_max = 30.5 2θ_step = 0.02

Refinement
R factors and goodness of fit	R_p = 0.020, R_wp = 0.029, R_exp = 0.030, R(F) = 0.013, χ² = 0.960	R_p = 0.021, R_wp = 0.030, R_exp = 0.030, R(F) = 0.016, χ² = 1.000	R_p = 0.021, R_wp = 0.030, R_exp = 0.030, R(F) = 0.016, χ² = 1.000	R_p = 0.020, R_wp = 0.029, R_exp = 0.024, R(F) = 0.030, χ² = NOT FOUND
No. of data points	2601	3661	3661	1375
No. of parameters	56	68	68	59
No. of restraints	0	0	0	?
(Δ/σ)_max	7.061	5.113	5.113	0.628

	(V)
Crystal data
Chemical formula	Sb₂O₃
M_r	291.5
Crystal system, space group	Cubic, Fd3m
Temperature (K)	773
Wave vectors	-F 4vw;2vw;3
a, b, c (Å)	90, 90, 90
α, β, γ (°)	1422.71
V (Å³)	16
Z	1841
Radiation type	–
µ (mm⁻¹)	?
Specimen shape, size (mm)

Data collection
Diffractometer	?
Specimen mounting	?
Data collection mode	?
Scan method	?
2θ values (°)	2θ_min = 3.02 2θ_max = 30.5 2θ_step = 0.02

Refinement
R factors and goodness of fit	R_p = 0.020, R_wp = 0.029, R_exp = 0.024, R(F) = 0.030, χ² = NOT FOUND
No. of data points	1375
No. of parameters	59
No. of restraints	?
(Δ/σ)_max	0.628

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₁+x₂, −x₁, x₃, x₄; (4) x₂, x₁, −x₃, −x₄; (5) x₁−x₂, −x₂, −x₃, −x₄; (6) −x₁, −x₁+x₂, −x₃, −x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₁−x₂, x₁, −x₃, −x₄; (10) −x₂, −x₁, x₃, x₄; (11) −x₁+x₂, x₂, x₃, x₄; (12) x₁, x₁−x₂, x₃, x₄; (13) x₁+2/3, x₂+1/3, x₃+1/3, x₄; (14) −x₂+2/3, x₁−x₂+1/3, x₃+1/3, x₄; (15) −x₁+x₂+2/3, −x₁+1/3, x₃+1/3, x₄; (16) x₂+2/3, x₁+1/3, −x₃+1/3, −x₄; (17) x₁−x₂+2/3, −x₂+1/3, −x₃+1/3, −x₄; (18) −x₁+2/3, −x₁+x₂+1/3, −x₃+1/3, −x₄; (19) −x₁+2/3, −x₂+1/3, −x₃+1/3, −x₄; (20) x₂+2/3, −x₁+x₂+1/3, −x₃+1/3, −x₄; (21) x₁−x₂+2/3, x₁+1/3, −x₃+1/3, −x₄; (22) −x₂+2/3, −x₁+1/3, x₃+1/3, x₄; (23) −x₁+x₂+2/3, x₂+1/3, x₃+1/3, x₄; (24) x₁+2/3, x₁−x₂+1/3, x₃+1/3, x₄; (25) x₁+1/3, x₂+2/3, x₃+2/3, x₄; (26) −x₂+1/3, x₁−x₂+2/3, x₃+2/3, x₄; (27) −x₁+x₂+1/3, −x₁+2/3, x₃+2/3, x₄; (28) x₂+1/3, x₁+2/3, −x₃+2/3, −x₄; (29) x₁−x₂+1/3, −x₂+2/3, −x₃+2/3, −x₄; (30) −x₁+1/3, −x₁+x₂+2/3, −x₃+2/3, −x₄; (31) −x₁+1/3, −x₂+2/3, −x₃+2/3, −x₄; (32) x₂+1/3, −x₁+x₂+2/3, −x₃+2/3, −x₄; (33) x₁−x₂+1/3, x₁+2/3, −x₃+2/3, −x₄; (34) −x₂+1/3, −x₁+2/3, x₃+2/3, x₄; (35) −x₁+x₂+1/3, x₂+2/3, x₃+2/3, x₄; (36) x₁+1/3, x₁−x₂+2/3, x₃+2/3, x₄.

‡ Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₁+x₂, −x₁, x₃, x₄; (4) x₂, x₁, −x₃, −x₄; (5) x₁−x₂, −x₂, −x₃, −x₄; (6) −x₁, −x₁+x₂, −x₃, −x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₁−x₂, x₁, −x₃, −x₄; (10) −x₂, −x₁, x₃, x₄; (11) −x₁+x₂, x₂, x₃, x₄; (12) x₁, x₁−x₂, x₃, x₄; (13) x₁+2/3, x₂+1/3, x₃+1/3, x₄; (14) −x₂+2/3, x₁−x₂+1/3, x₃+1/3, x₄; (15) −x₁+x₂+2/3, −x₁+1/3, x₃+1/3, x₄; (16) x₂+2/3, x₁+1/3, −x₃+1/3, −x₄; (17) x₁−x₂+2/3, −x₂+1/3, −x₃+1/3, −x₄; (18) −x₁+2/3, −x₁+x₂+1/3, −x₃+1/3, −x₄; (19) −x₁+2/3, −x₂+1/3, −x₃+1/3, −x₄; (20) x₂+2/3, −x₁+x₂+1/3, −x₃+1/3, −x₄; (21) x₁−x₂+2/3, x₁+1/3, −x₃+1/3, −x₄; (22) −x₂+2/3, −x₁+1/3, x₃+1/3, x₄; (23) −x₁+x₂+2/3, x₂+1/3, x₃+1/3, x₄; (24) x₁+2/3, x₁−x₂+1/3, x₃+1/3, x₄; (25) x₁+1/3, x₂+2/3, x₃+2/3, x₄; (26) −x₂+1/3, x₁−x₂+2/3, x₃+2/3, x₄; (27) −x₁+x₂+1/3, −x₁+2/3, x₃+2/3, x₄; (28) x₂+1/3, x₁+2/3, −x₃+2/3, −x₄; (29) x₁−x₂+1/3, −x₂+2/3, −x₃+2/3, −x₄; (30) −x₁+1/3, −x₁+x₂+2/3, −x₃+2/3, −x₄; (31) −x₁+1/3, −x₂+2/3, −x₃+2/3, −x₄; (32) x₂+1/3, −x₁+x₂+2/3, −x₃+2/3, −x₄; (33) x₁−x₂+1/3, x₁+2/3, −x₃+2/3, −x₄; (34) −x₂+1/3, −x₁+2/3, x₃+2/3, x₄; (35) −x₁+x₂+1/3, x₂+2/3, x₃+2/3, x₄; (36) x₁+1/3, x₁−x₂+2/3, x₃+2/3, x₄.

§ Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₂, −x₁, x₃, x₄; (4) −x₁+x₂, −x₁, x₃, x₄; (5) x₁, x₁−x₂, x₃, x₄; (6) −x₁+x₂, x₂, x₃, x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₂, x₁, −x₃, −x₄; (10) x₁−x₂, x₁, −x₃, −x₄; (11) −x₁, −x₁+x₂, −x₃, −x₄; (12) x₁−x₂, −x₂, −x₃, −x₄; (13) 2/3+x₁, 1/3+x₂, 1/3+x₃, x₄; (14) 2/3−x₂, 1/3+x₁−x₂, 1/3+x₃, x₄; (15) 2/3−x₂, 1/3−x₁, 1/3+x₃, x₄; (16) 2/3−x₁+x₂, 1/3−x₁, 1/3+x₃, x₄; (17) 2/3+x₁, 1/3+x₁−x₂, 1/3+x₃, x₄; (18) 2/3−x₁+x₂, 1/3+x₂, 1/3+x₃, x₄; (19) 2/3−x₁, 1/3−x₂, 1/3−x₃, −x₄; (20) 2/3+x₂, 1/3−x₁+x₂, 1/3−x₃, −x₄; (21) 2/3+x₂, 1/3+x₁, 1/3−x₃, −x₄; (22) 2/3+x₁−x₂, 1/3+x₁, 1/3−x₃, −x₄; (23) 2/3−x₁, 1/3−x₁+x₂, 1/3−x₃, −x₄; (24) 2/3+x₁−x₂, 1/3−x₂, 1/3−x₃, −x₄; (25) 1/3+x₁, 2/3+x₂, 2/3+x₃, x₄; (26) 1/3−x₂, 2/3+x₁−x₂, 2/3+x₃, x₄; (27) 1/3−x₂, 2/3−x₁, 2/3+x₃, x₄; (28) 1/3−x₁+x₂, 2/3−x₁, 2/3+x₃, x₄; (29) 1/3+x₁, 2/3+x₁−x₂, 2/3+x₃, x₄; (30) 1/3−x₁+x₂, 2/3+x₂, 2/3+x₃, x₄; (31) 1/3−x₁, 2/3−x₂, 2/3−x₃, −x₄; (32) 1/3+x₂, 2/3−x₁+x₂, 2/3−x₃, −x₄; (33) 1/3+x₂, 2/3+x₁, 2/3−x₃, −x₄; (34) 1/3+x₁−x₂, 2/3+x₁, 2/3−x₃, −x₄; (35) 1/3−x₁, 2/3−x₁+x₂, 2/3−x₃, −x₄; (36) 1/3+x₁−x₂, 2/3−x₂, 2/3−x₃, −x₄.

Computer programs: Jana2000 (Petricek, Dusek & Palatinus, 2000).

Selected bond lengths (Å) for (IV) top

	Average	Minimum	Maximum
Sb1—Sb1ⁱ	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1ⁱⁱ	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1ⁱⁱⁱ	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1^iv	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1^v	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Sb1^vi	3.1499 (14)	2.9339 (7)	3.3530 (8)
Sb1—Te1ⁱ	3.1483 (6)	2.8798 (9)	3.4307 (9)
Sb1—Te1ⁱⁱ	3.1483 (6)	2.8798 (9)	3.4307 (9)
Sb1—Te1ⁱⁱⁱ	3.1483 (6)	2.8798 (9)	3.4307 (9)
Sb1—Te1^iv	3.1491 (6)	2.8804 (9)	3.4316 (9)
Sb1—Te1^v	3.1491 (6)	2.8804 (9)	3.4316 (9)
Sb1—Te1^vi	3.1491 (6)	2.8804 (9)	3.4316 (9)

Selected bond lengths (Å) for (V) top

Sb2—O1ⁱ	1.986 (10)	O1—O1^viii	2.99 (2)
Sb2—O1ⁱⁱ	2.936 (16)	O1—O1^ix	2.979 (8)
Sb2—O1ⁱⁱⁱ	2.936 (16)	O1—O1^x	2.99 (2)
Sb2—O1^iv	1.986 (10)	O1—O1^xi	2.979 (8)
Sb2—O1^v	2.936 (16)	O1—O1^xii	2.99 (2)
Sb2—O1^vi	1.986 (10)	O1—O1^xiii	2.979 (8)
O1—O1^vii	2.979 (8)	O1—O1^xiv	2.99 (2)

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