Real structure of Ge₄Bi₂Te₇: refinement on diffuse scattering data with the 3D-ΔPDF method

Metastable Ge₄Bi₂Te₇ is highly disordered; the average structure corresponds to the rocksalt type. The diffraction pattern shows diffuse streaks interconnecting Bragg reflections along all cubic 〈111〉 directions. These streaks exhibit satellite-like maxima and arise from vacancy ordering in non-periodically spaced defect layers. The atom layers near these vacancy layers are displaced with respect to the average structure: they tend to form α-GeTe-type double layers. The three-dimensional difference pair distribution function (3D-ΔPDF) method yields quantitative information on the distribution of defect layer spacings, which peaks at a value corresponding to Ge₃Bi₂Te₆ building blocks. The cation distribution along with the displacement of the atom layers is refined as well, using a least-squares approach. Bi concentrates on cation positions next to the vacancy layers.

Computing details

Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

(I)

Crystal data

Bi1.09Ge2.37Te4	Synchrotron radiation, λ = 0.47686 Å
Mr = 910.23	Cell parameters from 410 reflections
Cubic, Fm3m	θ = 3.9–20.1°
a = 6.055 (2) Å	µ = 14.63 mm^−1
V = 222.0 (2) Å^3	T = 293 K
Z = 1	Octahedron, metallic_dark_grey
F(000) = 374	0.10 × 0.09 × 0.08 mm
Dx = 6.807 Mg m^−3

Data collection

Heavy duty (Huber) diffractometer	47 reflections with I > 2σ(I)
oscillation scans	Rint = 0.036
Absorption correction: multi-scan SADABS	θmax = 24.2°, θmin = 3.9°
Tmin = 0.53, Tmax = 0.79	h = −7→10
1161 measured reflections	k = −8→8
49 independent reflections	l = −10→8

Refinement

Refinement on F^2	1 restraint
Least-squares matrix: full	Primary atom site location: model
R[F^2 > 2σ(F^2)] = 0.016	Secondary atom site location: none
wR(F^2) = 0.019	w = 1/[σ^2(Fo^2) + (0.0052P)^2 + 0.0547P] where P = (Fo^2 + 2Fc^2)/3
S = 1.35	(Δ/σ)max < 0.001
49 reflections	Δρmax = 0.66 e Å^−3
7 parameters	Δρmin = −1.74 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2sigma(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ge1	0.0228 (4)	0.0228 (4)	0.0228 (4)	0.0298 (10)	0.0740 (8)
Bi1	0.0228 (4)	0.0228 (4)	0.0228 (4)	0.0298 (10)	0.0340 (5)
Te2	0.5000	0.5000	0.5000	0.02721 (18)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.0298 (10)	0.0298 (10)	0.0298 (10)	0.0026 (4)	0.0026 (4)	0.0026 (4)
Bi1	0.0298 (10)	0.0298 (10)	0.0298 (10)	0.0026 (4)	0.0026 (4)	0.0026 (4)

Geometric parameters (Å, º)

Ge1—Te2^i	2.896 (2)	Te2—Ge1^vi	2.896 (2)
Ge1—Te2^ii	2.896 (2)	Te2—Bi1^vii	2.896 (2)
Ge1—Te2^iii	2.896 (2)	Te2—Bi1^viii	2.896 (2)
Te2—Bi1^iv	2.896 (2)	Te2—Bi1^ix	2.896 (2)
Te2—Bi1^v	2.896 (2)	Te2—Bi1^x	2.896 (2)
Te2—Bi1^vi	2.896 (2)	Te2—Ge1^xi	2.896 (2)
Te2—Ge1^iv	2.896 (2)	Te2—Ge1^xii	2.896 (2)
Te2—Ge1^v	2.896 (2)
Te2^i—Ge1—Te2^ii	95.34 (9)	Ge1^v—Te2—Bi1^ix	84.66 (9)
Te2^i—Ge1—Te2^iii	95.34 (9)	Ge1^vi—Te2—Bi1^ix	5.47 (10)
Te2^ii—Ge1—Te2^iii	95.34 (9)	Bi1^vii—Te2—Bi1^ix	7.75 (14)
Bi1^iv—Te2—Bi1^v	84.40 (10)	Bi1^viii—Te2—Bi1^ix	90.131 (5)
Bi1^iv—Te2—Bi1^vi	84.40 (10)	Bi1^iv—Te2—Bi1^x	5.47 (10)
Bi1^v—Te2—Bi1^vi	84.40 (10)	Bi1^v—Te2—Bi1^x	84.66 (9)
Bi1^iv—Te2—Ge1^iv	0.00 (9)	Bi1^vi—Te2—Bi1^x	89.869 (5)
Bi1^v—Te2—Ge1^iv	84.40 (10)	Ge1^iv—Te2—Bi1^x	5.47 (10)
Bi1^vi—Te2—Ge1^iv	84.40 (10)	Ge1^v—Te2—Bi1^x	84.66 (9)
Bi1^iv—Te2—Ge1^v	84.40 (10)	Ge1^vi—Te2—Bi1^x	89.869 (5)
Bi1^v—Te2—Ge1^v	0.00 (9)	Bi1^vii—Te2—Bi1^x	90.131 (5)
Bi1^vi—Te2—Ge1^v	84.40 (10)	Bi1^viii—Te2—Bi1^x	84.40 (10)
Ge1^iv—Te2—Ge1^v	84.40 (10)	Bi1^ix—Te2—Bi1^x	95.34 (9)
Bi1^iv—Te2—Ge1^vi	84.40 (10)	Bi1^iv—Te2—Ge1^xi	5.47 (10)
Bi1^v—Te2—Ge1^vi	84.40 (10)	Bi1^v—Te2—Ge1^xi	89.869 (5)
Bi1^vi—Te2—Ge1^vi	0.0	Bi1^vi—Te2—Ge1^xi	84.66 (9)
Ge1^iv—Te2—Ge1^vi	84.40 (10)	Ge1^iv—Te2—Ge1^xi	5.47 (10)
Ge1^v—Te2—Ge1^vi	84.40 (10)	Ge1^v—Te2—Ge1^xi	89.869 (5)
Bi1^iv—Te2—Bi1^vii	84.66 (9)	Ge1^vi—Te2—Ge1^xi	84.66 (9)
Bi1^v—Te2—Bi1^vii	89.869 (5)	Bi1^vii—Te2—Ge1^xi	84.40 (10)
Bi1^vi—Te2—Bi1^vii	5.47 (10)	Bi1^viii—Te2—Ge1^xi	90.131 (5)
Ge1^iv—Te2—Bi1^vii	84.66 (9)	Bi1^ix—Te2—Ge1^xi	90.131 (5)
Ge1^v—Te2—Bi1^vii	89.869 (5)	Bi1^x—Te2—Ge1^xi	7.75 (14)
Ge1^vi—Te2—Bi1^vii	5.47 (10)	Bi1^iv—Te2—Ge1^xii	89.869 (5)
Bi1^iv—Te2—Bi1^viii	84.66 (9)	Bi1^v—Te2—Ge1^xii	5.47 (10)
Bi1^v—Te2—Bi1^viii	5.47 (10)	Bi1^vi—Te2—Ge1^xii	84.66 (9)
Bi1^vi—Te2—Bi1^viii	89.869 (5)	Ge1^iv—Te2—Ge1^xii	89.869 (5)
Ge1^iv—Te2—Bi1^viii	84.66 (9)	Ge1^v—Te2—Ge1^xii	5.47 (10)
Ge1^v—Te2—Bi1^viii	5.47 (10)	Ge1^vi—Te2—Ge1^xii	84.66 (9)
Ge1^vi—Te2—Bi1^viii	89.869 (5)	Bi1^vii—Te2—Ge1^xii	90.131 (5)
Bi1^vii—Te2—Bi1^viii	95.34 (9)	Bi1^viii—Te2—Ge1^xii	7.75 (14)
Bi1^iv—Te2—Bi1^ix	89.869 (5)	Bi1^ix—Te2—Ge1^xii	84.40 (10)
Bi1^v—Te2—Bi1^ix	84.66 (9)	Bi1^x—Te2—Ge1^xii	90.131 (5)
Bi1^vi—Te2—Bi1^ix	5.47 (10)	Ge1^xi—Te2—Ge1^xii	95.34 (9)
Ge1^iv—Te2—Bi1^ix	89.869 (5)

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