X-ray resonant single-crystal diffraction technique, a powerful tool to investigate the kesterite structure of the photovoltaic Cu₂ZnSnS₄ compound

Cu/Zn disorder in the kesterite Cu₂ZnSnS₄ derivatives used for thin film based solar cells is an important issue for photovoltaic performances. Unfortunately, Cu and Zn cannot be distinguished by conventional laboratory X-ray diffraction. This paper reports on a resonant diffraction investigation of a Cu₂ZnSnS₄ single crystal from a quenched powdered sample. The full disorder of Cu and Zn in the z = 1/4 atomic plane is shown. The structure, namely disordered kesterite, is then described in the space group.

S1. Experimental

S1.1. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1.

S2. Results and discussion

Computing details

Data collection: unknown; cell refinement: unknown; data reduction: unknown; program(s) used to solve structure: unknown; molecular graphics: unknown.

Figures

(I)

Crystal data

Cu2S4SnZn	Z = 2
Mr = 439.4	F(000) = 404
Tetragonal, I42m	Dx = 4.553 Mg m^−3
Hall symbol: I -4 2	? radiation, λ = 0.66842 Å
a = 5.4353 (1) Å	µ = 12.84 mm^−1
c = 10.8464 (3) Å	T = 293 K
V = 320.43 (1) Å^3	0.08 × 0.05 × 0.05 mm

Data collection

Radiation source: synchrotron	Rint = 0.088
Absorption correction: empirical (using intensity measurements) ?	θmax = 34.7°, θmin = 3.5°
Tmin = 0.91, Tmax = 1.10	h = −6→8
5275 measured reflections	k = −9→9
449 independent reflections	l = −18→18
449 reflections with I > 2σ(I)

Refinement

Refinement on F^2	2 constraints
R[F^2 > 2σ(F^2)] = 0.029	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0016I^2)
wR(F^2) = 0.074	(Δ/σ)max = 0.004
S = 1.60	Δρmax = 1.39 e Å^−3
449 reflections	Δρmin = −2.17 e Å^−3
15 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 1900 (150)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Cu_2a	0	0	0	0.01903 (16)
Cu_4d	0	0.5	0.25	0.01688 (13)	0.5
Zn_4d	0	0.5	0.25	0.01688 (13)	0.5
Sn_2b	0	0	0.5	0.01077 (9)
S	0.75608 (10)	0.24393 (10)	0.12788 (5)	0.0112 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu_2a	0.0194 (2)	0.0194 (2)	0.0183 (3)	0	0	0
Cu_4d	0.0170 (2)	0.0170 (2)	0.0166 (3)	0	0	0
Zn_4d	0.0170 (2)	0.0170 (2)	0.0166 (3)	0	0	0
Sn_2b	0.01111 (15)	0.01111 (15)	0.01008 (17)	0	0	0
S	0.0114 (3)	0.0114 (3)	0.0108 (4)	0.00056 (18)	−0.00023 (13)	0.00023 (13)

Geometric parameters (Å, º)

Cu_2a—S^i	2.3322 (6)	Zn_4d—S^i	2.3344 (5)
Cu_2a—S^ii	2.3322 (6)	Zn_4d—S^v	2.3344 (5)
Cu_2a—S^iii	2.3322 (6)	Zn_4d—S^vi	2.3344 (5)
Cu_2a—S^iv	2.3322 (6)	Zn_4d—S^vii	2.3344 (5)
Cu_4d—Zn_4d	0	Sn_2b—S^viii	2.4080 (6)
Cu_4d—S^i	2.3344 (5)	Sn_2b—S^ix	2.4080 (6)
Cu_4d—S^v	2.3344 (5)	Sn_2b—S^x	2.4080 (6)
Cu_4d—S^vi	2.3344 (5)	Sn_2b—S^vii	2.4080 (6)
Cu_4d—S^vii	2.3344 (5)
S^i—Cu_2a—S^ii	107.01 (2)	S^v—Zn_4d—S^vii	108.781 (19)
S^i—Cu_2a—S^iii	110.713 (19)	S^vi—Zn_4d—S^vii	110.86 (2)
S^i—Cu_2a—S^iv	110.713 (19)	S^viii—Sn_2b—S^ix	109.658 (19)
S^ii—Cu_2a—S^iii	110.713 (19)	S^viii—Sn_2b—S^x	109.378 (18)
S^ii—Cu_2a—S^iv	110.713 (19)	S^viii—Sn_2b—S^vii	109.378 (18)
S^iii—Cu_2a—S^iv	107.01 (2)	S^ix—Sn_2b—S^x	109.378 (18)
Zn_4d—Cu_4d—S^i	0	S^ix—Sn_2b—S^vii	109.378 (18)
Zn_4d—Cu_4d—S^v	0	S^x—Sn_2b—S^vii	109.658 (19)
Zn_4d—Cu_4d—S^vi	0	Cu_2a^xi—S—Cu_4d^xi	110.70 (2)
Zn_4d—Cu_4d—S^vii	0	Cu_2a^xi—S—Cu_4d^xii	110.70 (2)
S^i—Cu_4d—S^v	110.86 (2)	Cu_2a^xi—S—Zn_4d^xi	110.70 (2)
S^i—Cu_4d—S^vi	108.781 (19)	Cu_2a^xi—S—Zn_4d^xii	110.70 (2)
S^i—Cu_4d—S^vii	108.781 (19)	Cu_2a^xi—S—Sn_2b^xiii	108.34 (2)
S^v—Cu_4d—S^vi	108.781 (19)	Cu_4d^xi—S—Cu_4d^xii	110.81 (2)
S^v—Cu_4d—S^vii	108.781 (19)	Cu_4d^xi—S—Zn_4d^xi	0.0 (5)
S^vi—Cu_4d—S^vii	110.86 (2)	Cu_4d^xi—S—Zn_4d^xii	110.81 (2)
Cu_4d—Zn_4d—S^i	0	Cu_4d^xi—S—Sn_2b^xiii	108.09 (2)
Cu_4d—Zn_4d—S^v	0	Cu_4d^xii—S—Zn_4d^xi	110.81 (2)
Cu_4d—Zn_4d—S^vi	0	Cu_4d^xii—S—Zn_4d^xii	0.0 (5)
Cu_4d—Zn_4d—S^vii	0	Cu_4d^xii—S—Sn_2b^xiii	108.09 (2)
S^i—Zn_4d—S^v	110.86 (2)	Zn_4d^xi—S—Zn_4d^xii	110.81 (2)
S^i—Zn_4d—S^vi	108.781 (19)	Zn_4d^xi—S—Sn_2b^xiii	108.09 (2)
S^i—Zn_4d—S^vii	108.781 (19)	Zn_4d^xii—S—Sn_2b^xiii	108.09 (2)
S^v—Zn_4d—S^vi	108.781 (19)

Symmetry codes: (i) x−1, y, z; (ii) −x+1, −y, z; (iii) y, −x+1, −z; (iv) −y, x−1, −z; (v) −x+1, −y+1, z; (vi) y−1/2, −x+3/2, −z+1/2; (vii) −y+1/2, x−1/2, −z+1/2; (viii) x−1/2, y−1/2, z+1/2; (ix) −x+1/2, −y+1/2, z+1/2; (x) y−1/2, −x+1/2, −z+1/2; (xi) x+1, y, z; (xii) −x+1/2, y−1/2, −z+1/2; (xiii) x+1/2, y+1/2, z−1/2.