Structures and phase transitions of the A₇PSe₆ (A = Ag, Cu) argyrodite-type ionic conductors. II. β- and γ-Cu₇PSe₆

The crystal structures of two of the three polymorphic forms of the Cu₇PSe₆ argyrodite compound are determined by means of single-crystal X-ray diffraction. In the high-temperature form, at 353 K, i.e. 33 K above the first phase transition, γ-Cu₇PSe₆ crystallizes in cubic symmetry, space group F43m. The full-matrix least-squares refinement of the structure leads to the residual factors R  = 0.0201 and wR = 0.0245 for 31 parameters and 300 observed independent reflections. In the intermediate form, at room temperature, β-Cu₇PSe₆ crystallizes again in cubic symmetry, but with space group P2₁3. Taking into account a merohedric twinning, the refinement of the β-Cu₇PSe₆ structure leads to the residual factors R  = 0.0297 and wR  = 0.0317 for 70 parameters and 874 observed, independent reflections. The combination of a Gram–Charlier development of the Debye–Waller factor and a split model for copper cations reveals the possible diffusion paths of the d¹⁰ species in the γ-Cu₇PSe₆ ionic conducting phase. The partial ordering of the Cu⁺ d¹⁰element at the phase transition is found in concordance with the highest probability density sites of the high-temperature phase diffusion paths. A comparison between the two Cu₇PSe₆ and Ag₇PSe₆ analogues is carried out, stressing the different mobility of Cu⁺ and Ag⁺ and their relative stability in low-coordination chalcogenide environments.

Computing details

Figures

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Crystal data

Cu7PSe6	Dx = 6.105 Mg m^−3
Mr = 949.56	Ag Kα radiation, λ = 0.56090 Å
Cubic, P213	Cell parameters from 34 reflections
Hall symbol: P 2ac 2ab 3	µ = 18.63 mm^−1
a = 10.1080 (4) Å	T = 293 K
V = 1032.75 (12) Å^3	Sphere, metallic lustre
Z = 4	0.09 mm (radius)
F(000) = 1688

Data collection

Siemens P4 diffractometer	Rint = 0.057
θ scans	h = ?→?
Absorption correction: spherical ?	k = ?→?
Tmin = 0.112, Tmax = 0.136	l = ?→?
10070 measured reflections	3 standard reflections every 60 min
1627 independent reflections	intensity decay: <1%
874 reflections with I > 3.0σ(I)

Refinement

Refinement on F	w = 1/[σ^2|Fo| + (0.016|Fo|)^2]
R[F^2 > 2σ(F^2)] = 0.030	(Δ/σ)max < 0.0001
wR(F^2) = 0.032	Δρmax = 1.89 e Å^−3
S = 0.80	Δρmin = −1.14 e Å^−3
874 reflections	Extinction correction: Type I, Gaussian (Becker \& Coppens, 1974)
70 parameters	Extinction coefficient: 0.1056 (4)

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

	x	y	z	Uiso*/Ueq
P	0.7485 (2)	0.7485	0.7485	0.0103 (2)
Se1a	0.87477 (9)	0.87477	0.87477	0.0148 (2)
Se1b	0.37079 (11)	0.37645 (11)	0.88083 (10)	0.0134 (3)
Se2	0.23601 (11)	0.23601	0.23601	0.0210 (2)
Se3	0.49079 (12)	0.49079	0.49079	0.0221 (2)
Cu1	0.0720 (3)	−0.0892 (3)	−0.2696 (3)	0.0463 (6)
Cu2a	0.0024 (9)	0.0034 (9)	0.2795 (2)	0.059 (2)
Cu2b	0.0636 (11)	0.0578 (8)	0.2639 (8)	0.032 (2)
Cu3	0.3608 (5)	0.3608	0.3608	0.199 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P	0.0103 (4)	0.0103	0.0103	−0.0002 (9)	−0.0002	−0.0002
Se1a	0.0148 (4)	0.0148	0.0148	−0.0026 (4)	−0.0026	−0.0026
Se1b	0.0132 (5)	0.0145 (5)	0.0124 (5)	−0.0029 (4)	−0.0018 (3)	−0.0026 (3)
Se2	0.0210 (4)	0.0210	0.0210	0.0022 (4)	0.0022	0.0022
Se3	0.0221 (4)	0.0221	0.0221	0.0041 (4)	0.0041	0.0041
Cu1	0.0316 (9)	0.0495 (11)	0.0579 (11)	−0.0029 (8)	0.0025 (8)	0.0003 (10)
Cu2a	0.077 (5)	0.080 (5)	0.0213 (9)	0.056 (4)	0.010 (2)	0.005 (2)
Cu2b	0.036 (4)	0.032 (3)	0.028 (3)	0.005 (3)	0.004 (3)	−0.003 (2)
Cu3	0.199 (5)	0.199	0.199	−0.088 (3)	−0.088	−0.088

Bond lengths (Å)

P—Se1a	2.210 (2)	Cu2a—Se1b	2.382 (7)
P—Se1b	2.199 (2)	Cu2a—Se1b	2.423 (7)
Cu3*—Se2	2.2636 (11)	Cu1*—Se2	2.4849 (11)
Cu3*—Se3	2.1971 (12)	Cu1*—Se1a	2.5056 (9)
Cu2b*—Cu2a	0.833 (9)	Cu1*—Se1b	2.5246 (10)
Cu1*—Cu2b*	2.416	Cu1*—Se3	2.5667 (12)
Cu1*—Cu2a	2.855 (8)	Cu2b*—Se1b	2.4357 (11)
Cu1*—Cu2a	2.865 (8)	Cu2b*—Se1b	2.5253 (11)
Cu2b*—Cu2b*	2.928	Cu2b*—Se2	2.5310 (11)
Cu2b*—Cu2a	2.954 (8)	Cu2b*—Se3	2.6203 (12)
Cu2a—Se3	2.326 (3)

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Crystal data

Cu7PSe6	Dx = 6.096 Mg m^−3
Mr = 949.56	Mo Kα radiation, λ = 0.71073 Å
Cubic, F43m	Cell parameters from 25 reflections
Hall symbol: F -4 2 3	µ = 35.32 mm^−1
a = 10.113 (1) Å	T = 353 K
V = 1034.3 (3) Å^3	Sphere, metallic lustre
Z = 4	0.07 mm (radius)
F(000) = 1688

Data collection

Enraf-Nonius CAD-4 diffractometer	300 reflections with I > 3.0σ(I)
ω–θ scans	Rint = 0.034
Absorption correction: spherical ?	h = ?→?
Tmin = 0.045, Tmax = 0.088	k = ?→?
1726 measured reflections	l = ?→?
368 independent reflections

Refinement

Refinement on F	w = 1/[σ^2|Fo| + (0.015|Fo|)^2]
R[F^2 > 2σ(F^2)] = 0.020	(Δ/σ)max < 0.0001
wR(F^2) = 0.025	Δρmax = 0.69 e Å^−3
S = 1.09	Δρmin = −0.76 e Å^−3
300 reflections	Extinction correction: Type I, Gaussian (Becker \& Coppens, 1974)
31 parameters	Extinction coefficient: 0.172 (8)

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

	x	y	z	Uiso*/Ueq
P	0.75	0.75	0.75	0.0098 (2)
Se1	0.87576 (5)	0.87576	0.87576	0.01623 (7)
Se2	0.25	0.25	0.25	0.0330 (2)
Se3	0.5	0.5	0.5	0.0273 (2)
Cu1	0.0787 (8)	0.0787	0.2673 (6)	0.0511 (10)
Cu2	0.016 (3)	0.016	0.2757 (8)	0.068 (10)
Cu3	0.1286 (8)	0.1286	0.3714	0.243 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P	0.0098 (3)	0.0098	0.0098	0	0	0
Se1	0.01622 (12)	0.01622	0.01622	−0.00362 (7)	−0.00362	−0.00362
Se2	0.0330 (4)	0.0330	0.0330	0	0	0
Se3	0.0273 (4)	0.0273	0.0273	0	0	0
Cu1	0.0479 (14)	0.0479	0.057 (2)	0.004 (2)	−0.0008 (12)	−0.0008 (12)
Cu2	0.09 (2)	0.09	0.030 (3)	0.06 (2)	−0.019 (9)	−0.019
Cu3	0.24 (2)	0.24	0.24	−0.101 (10)	−0.101	−0.101

Bond lengths (Å)

P—Se	2.2028 (5)	Cu2*—Se1	2.373 (5)
Cu3—Se2	2.127 (8)	Cu1*—Se1	2.4982 (5)
Cu3—Se3	2.252 (8)	Cu1*—Se3	2.5611
Cu2*—Se3	2.2279	Cu1*—Se2	2.5800