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Ambiguities in the interpretation of both single-crystal and powder diffraction data can lead to wrong conclusions concerning the structure analysis of layered chalcogenides with interesting physical properties and potential applications. This is illustrated for binary and Pb-doped phases of the homologous series (Sb2)k(Sb2Te3)m. Almost homometric structure models for 39R-Sb10Te3 [R\bar 3m, a = 4.2874 (6), c = 64.300 (16) Å, R1 = 0.0298] have been derived from initial structure solutions and crystal chemical considerations. The variation of the electron density on certain positions may further reduce the differences between the calculated diffraction patterns of non-congruent structure models as exemplified by the new compound 33R-[Sb0.978(3)Pb0.022(3)]8Te3 [R\bar 3m, a = 4.2890 (10), c = 75.51 (2) Å, R1 = 0.0615]. Both compounds are long-range ordered, and in either case both `almost homometric' models can be refined equally well on experimental data sets. The models can only be distinguished by chemical analysis, as reasonable atom assignments lead to different compositions for each model. Interestingly, all structure solution attempts led to the wrong models in both cases. In addition, it is shown that stacking disorder of characteristic layers may lead to powder diffraction patterns that can be misinterpreted in terms of three-dimensional randomly disordered almost isotropic structures with a simple α-Hg-type basic structure.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0021889810032644/db5086sup1.cif
Contains datablocks hr, mnspl152_b_richtig

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0021889810032644/db5086sup2.hkl
Structure factors for decaantimony tritelluride

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0021889810032644/db5086sup3.hkl
Structure factors for Pb-doped antimony telluride

Computing details top

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

(hr) decaantimony tritelluride top
Crystal data top
Sb10Te3Dx = 6.627 Mg m3
Mr = 1600.30Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 1040 reflections
Hall symbol: -R 3 2"θ = 4–24°
a = 4.289 (1) ŵ = 21.87 mm1
c = 75.51 (2) ÅT = 293 K
V = 1202.9 (5) Å3Irregular polyhedron, metallic_dark_grey
Z = 30.08 × 0.06 × 0.01 mm
F(000) = 1998
Data collection top
Stoe IPDS
diffractometer
375 independent reflections
Radiation source: fine-focus sealed tube195 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.097
oscillation scansθmax = 26.0°, θmin = 2.4°
Absorption correction: multi-scan
Progam XPREP, from equivalents
h = 54
Tmin = 0.269, Tmax = 0.989k = 55
2811 measured reflectionsl = 9389
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: none
R[F2 > 2σ(F2)] = 0.062 w = 1/[σ2(Fo2) + (0.010P)2 + 5.P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.123(Δ/σ)max < 0.001
S = 1.71Δρmax = 3.19 e Å3
375 reflectionsΔρmin = 3.55 e Å3
22 parametersExtinction correction: SHELXL, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraintsExtinction coefficient: 0.00057 (7)
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s 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 > σ(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 (Å2) top
xyzUiso*/Ueq
Te10.00000.00000.00000.0375 (12)
Sb10.66670.33330.02808 (5)0.0383 (9)
Te20.33330.66670.05018 (3)0.0256 (9)
Sb20.00000.00000.07986 (4)0.0284 (8)
Sb30.66670.33330.10044 (3)0.0206 (8)
Sb40.33330.66670.13116 (4)0.0298 (9)
Sb50.00000.00000.15135 (3)0.0258 (9)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Te10.0235 (15)0.0235 (15)0.066 (3)0.0118 (8)0.0000.000
Sb10.0284 (10)0.0284 (10)0.058 (2)0.0142 (5)0.0000.000
Te20.0240 (11)0.0240 (11)0.0288 (19)0.0120 (5)0.0000.000
Sb20.0242 (11)0.0242 (11)0.0368 (18)0.0121 (5)0.0000.000
Sb30.0218 (9)0.0218 (9)0.0181 (16)0.0109 (5)0.0000.000
Sb40.0216 (12)0.0216 (12)0.046 (2)0.0108 (6)0.0000.000
Sb50.0225 (11)0.0225 (11)0.032 (2)0.0113 (6)0.0000.000
Geometric parameters (Å, º) top
Te1—Sb1i3.260 (2)Te2—Sb1ix2.986 (3)
Te1—Sb13.260 (2)Sb2—Sb3iii2.923 (2)
Te1—Sb1ii3.260 (2)Sb2—Sb32.923 (2)
Te1—Sb1iii3.260 (2)Sb2—Sb3v2.923 (2)
Te1—Sb1iv3.260 (2)Sb3—Sb2vi2.923 (2)
Te1—Sb1v3.260 (2)Sb3—Sb2viii2.923 (2)
Sb1—Te2vi2.986 (3)Sb4—Sb5ix2.908 (2)
Sb1—Te2vii2.986 (3)Sb4—Sb5viii2.908 (2)
Sb1—Te22.986 (3)Sb4—Sb52.908 (2)
Sb1—Te1vi3.260 (2)Sb5—Sb4vii2.908 (2)
Sb1—Te1viii3.260 (2)Sb5—Sb4v2.908 (2)
Te2—Sb1iii2.986 (3)
Sb1i—Te1—Sb1180.00 (10)Te2—Sb1—Te1vi173.40 (12)
Sb1i—Te1—Sb1ii82.26 (7)Te1—Sb1—Te1vi82.26 (7)
Sb1—Te1—Sb1ii97.74 (7)Te2vi—Sb1—Te1viii92.79 (3)
Sb1i—Te1—Sb1iii97.74 (7)Te2vii—Sb1—Te1viii173.40 (12)
Sb1—Te1—Sb1iii82.26 (7)Te2—Sb1—Te1viii92.79 (3)
Sb1ii—Te1—Sb1iii180.00 (10)Te1—Sb1—Te1viii82.26 (7)
Sb1i—Te1—Sb1iv82.26 (7)Te1vi—Sb1—Te1viii82.26 (7)
Sb1—Te1—Sb1iv97.74 (7)Sb1iii—Te2—Sb1ix91.80 (11)
Sb1ii—Te1—Sb1iv82.26 (7)Sb1iii—Te2—Sb191.80 (11)
Sb1iii—Te1—Sb1iv97.74 (7)Sb1ix—Te2—Sb191.80 (11)
Sb1i—Te1—Sb1v97.74 (7)Sb3iii—Sb2—Sb394.38 (10)
Sb1—Te1—Sb1v82.26 (7)Sb3iii—Sb2—Sb3v94.38 (10)
Sb1ii—Te1—Sb1v97.74 (7)Sb3—Sb2—Sb3v94.38 (10)
Sb1iii—Te1—Sb1v82.26 (7)Sb2vi—Sb3—Sb294.38 (10)
Sb1iv—Te1—Sb1v180.00 (10)Sb2vi—Sb3—Sb2viii94.38 (10)
Te2vi—Sb1—Te2vii91.80 (11)Sb2—Sb3—Sb2viii94.38 (10)
Te2vi—Sb1—Te291.80 (11)Sb5ix—Sb4—Sb5viii95.03 (9)
Te2vii—Sb1—Te291.80 (11)Sb5ix—Sb4—Sb595.03 (9)
Te2vi—Sb1—Te1173.40 (12)Sb5viii—Sb4—Sb595.03 (9)
Te2vii—Sb1—Te192.79 (3)Sb4vii—Sb5—Sb4v95.03 (9)
Te2—Sb1—Te192.79 (3)Sb4vii—Sb5—Sb495.03 (9)
Te2vi—Sb1—Te1vi92.79 (3)Sb4v—Sb5—Sb495.03 (9)
Te2vii—Sb1—Te1vi92.79 (3)
Symmetry codes: (i) x, y, z; (ii) x+1, y, z; (iii) x1, y, z; (iv) x+1, y+1, z; (v) x1, y1, z; (vi) x+1, y, z; (vii) x, y1, z; (viii) x+1, y+1, z; (ix) x, y+1, z.
(mnspl152_b_richtig) top
Crystal data top
Pb0.18Sb7.82Te3Dx = 6.677 Mg m3
Mr = 1371.89Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 841 reflections
Hall symbol: -R 3 2"θ = 4–27°
a = 4.2874 (6) ŵ = 23.64 mm1
c = 64.300 (16) ÅT = 293 K
V = 1023.6 (3) Å3Irregular polyhedron, metallic_dark_grey
Z = 30.18 × 0.10 × 0.08 mm
F(000) = 1707.5
Data collection top
Stoe IPDS
diffractometer
462 independent reflections
Radiation source: fine-focus sealed tube184 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.081
oscillation scansθmax = 30.0°, θmin = 2.9°
Absorption correction: numerical
X-RED, X-SHAPE (Stoe, Darmstadt 2002)
h = 66
Tmin = 0.080, Tmax = 0.184k = 56
3739 measured reflectionsl = 9085
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.030Secondary atom site location: none
wR(F2) = 0.083 w = 1/[σ2(Fo2) + (0.039P)2]
where P = (Fo2 + 2Fc2)/3
S = 0.81(Δ/σ)max < 0.001
462 reflectionsΔρmax = 1.17 e Å3
19 parametersΔρmin = 2.04 e Å3
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s 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 > σ(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 (Å2) top
xyzUiso*/UeqOcc. (<1)
Te10.00000.00000.00000.0186 (8)
Sb10.33330.66670.03102 (5)0.0315 (7)0.911 (14)
Pb10.33330.66670.03102 (5)0.0315 (7)0.089 (14)
Te20.66670.33330.05790 (3)0.0186 (6)
Sb20.00000.00000.09485 (4)0.0202 (5)
Sb30.33330.66670.11874 (4)0.0185 (6)
Sb40.66670.33330.15475 (4)0.0160 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Te10.0181 (12)0.0181 (12)0.0196 (11)0.0091 (6)0.0000.000
Sb10.0239 (8)0.0239 (8)0.0466 (11)0.0120 (4)0.0000.000
Pb10.0239 (8)0.0239 (8)0.0466 (11)0.0120 (4)0.0000.000
Te20.0165 (9)0.0165 (9)0.0227 (8)0.0082 (5)0.0000.000
Sb20.0165 (8)0.0165 (8)0.0276 (9)0.0082 (4)0.0000.000
Sb30.0152 (9)0.0152 (9)0.0252 (8)0.0076 (4)0.0000.000
Sb40.0126 (7)0.0126 (7)0.0229 (8)0.0063 (3)0.0000.000
Geometric parameters (Å, º) top
Te1—Pb1i3.179 (2)Sb1—Te1vi3.179 (2)
Te1—Sb13.179 (2)Sb1—Te1viii3.179 (2)
Te1—Sb1i3.179 (2)Te2—Pb1iii3.019 (3)
Te1—Pb1ii3.179 (2)Te2—Sb1iii3.019 (3)
Te1—Sb1iii3.179 (2)Te2—Pb1ix3.019 (3)
Te1—Sb1ii3.179 (2)Te2—Sb1ix3.019 (3)
Te1—Pb1iii3.179 (2)Sb2—Sb3iii2.913 (2)
Te1—Pb1iv3.179 (2)Sb2—Sb32.913 (2)
Te1—Pb1v3.179 (2)Sb2—Sb3v2.913 (2)
Te1—Sb1v3.179 (2)Sb3—Sb2vi2.913 (2)
Te1—Sb1iv3.179 (2)Sb3—Sb2viii2.913 (2)
Sb1—Te2vi3.019 (3)Sb4—Sb4x2.912 (3)
Sb1—Te2vii3.019 (3)Sb4—Sb4xi2.912 (3)
Sb1—Te23.019 (3)Sb4—Sb4xii2.912 (3)
Pb1i—Te1—Sb1180.00 (9)Pb1i—Te1—Sb1iv84.81 (7)
Sb1—Te1—Sb1i180.00 (9)Sb1—Te1—Sb1iv95.19 (7)
Pb1i—Te1—Pb1ii84.81 (7)Sb1i—Te1—Sb1iv84.81 (7)
Sb1—Te1—Pb1ii95.19 (7)Pb1ii—Te1—Sb1iv84.81 (7)
Sb1i—Te1—Pb1ii84.81 (7)Sb1iii—Te1—Sb1iv95.19 (7)
Pb1i—Te1—Sb1iii95.19 (7)Sb1ii—Te1—Sb1iv84.81 (7)
Sb1—Te1—Sb1iii84.81 (7)Pb1iii—Te1—Sb1iv95.19 (7)
Sb1i—Te1—Sb1iii95.19 (7)Pb1v—Te1—Sb1iv180.00 (9)
Pb1ii—Te1—Sb1iii180.00 (9)Sb1v—Te1—Sb1iv180.00 (9)
Pb1i—Te1—Sb1ii84.81 (7)Te2vi—Sb1—Te2vii90.48 (11)
Sb1—Te1—Sb1ii95.19 (7)Te2vi—Sb1—Te290.48 (11)
Sb1i—Te1—Sb1ii84.81 (7)Te2vii—Sb1—Te290.48 (11)
Sb1iii—Te1—Sb1ii180.00 (9)Te2vi—Sb1—Te1176.06 (12)
Pb1i—Te1—Pb1iii95.19 (7)Te2vii—Sb1—Te192.29 (3)
Sb1—Te1—Pb1iii84.81 (7)Te2—Sb1—Te192.29 (3)
Sb1i—Te1—Pb1iii95.19 (7)Te2vi—Sb1—Te1vi92.29 (3)
Pb1ii—Te1—Pb1iii180.00 (9)Te2vii—Sb1—Te1vi92.29 (3)
Sb1ii—Te1—Pb1iii180.00 (9)Te2—Sb1—Te1vi176.06 (12)
Pb1i—Te1—Pb1iv84.81 (7)Te1—Sb1—Te1vi84.81 (7)
Sb1—Te1—Pb1iv95.19 (7)Te2vi—Sb1—Te1viii92.29 (3)
Sb1i—Te1—Pb1iv84.81 (7)Te2vii—Sb1—Te1viii176.06 (12)
Pb1ii—Te1—Pb1iv84.81 (7)Te2—Sb1—Te1viii92.29 (3)
Sb1iii—Te1—Pb1iv95.19 (7)Te1—Sb1—Te1viii84.81 (7)
Sb1ii—Te1—Pb1iv84.81 (7)Te1vi—Sb1—Te1viii84.81 (7)
Pb1iii—Te1—Pb1iv95.19 (7)Pb1iii—Te2—Pb1ix90.48 (11)
Pb1i—Te1—Pb1v95.19 (7)Sb1iii—Te2—Pb1ix90.48 (11)
Sb1—Te1—Pb1v84.81 (7)Pb1iii—Te2—Sb1ix90.48 (11)
Sb1i—Te1—Pb1v95.19 (7)Sb1iii—Te2—Sb1ix90.48 (11)
Pb1ii—Te1—Pb1v95.19 (7)Pb1iii—Te2—Sb190.48 (11)
Sb1iii—Te1—Pb1v84.81 (7)Sb1iii—Te2—Sb190.48 (11)
Sb1ii—Te1—Pb1v95.19 (7)Pb1ix—Te2—Sb190.48 (11)
Pb1iii—Te1—Pb1v84.81 (7)Sb1ix—Te2—Sb190.48 (11)
Pb1iv—Te1—Pb1v180.00 (9)Sb3iii—Sb2—Sb394.76 (10)
Pb1i—Te1—Sb1v95.19 (7)Sb3iii—Sb2—Sb3v94.76 (10)
Sb1—Te1—Sb1v84.81 (7)Sb3—Sb2—Sb3v94.76 (10)
Sb1i—Te1—Sb1v95.19 (7)Sb2vi—Sb3—Sb294.76 (10)
Pb1ii—Te1—Sb1v95.19 (7)Sb2vi—Sb3—Sb2viii94.76 (10)
Sb1iii—Te1—Sb1v84.81 (7)Sb2—Sb3—Sb2viii94.76 (10)
Sb1ii—Te1—Sb1v95.19 (7)Sb4x—Sb4—Sb4xi94.83 (12)
Pb1iii—Te1—Sb1v84.81 (7)Sb4x—Sb4—Sb4xii94.83 (12)
Pb1iv—Te1—Sb1v180.00 (9)Sb4xi—Sb4—Sb4xii94.83 (12)
Symmetry codes: (i) x, y, z; (ii) x, y+1, z; (iii) x, y1, z; (iv) x+1, y+1, z; (v) x1, y1, z; (vi) x, y+1, z; (vii) x1, y, z; (viii) x+1, y+1, z; (ix) x+1, y, z; (x) x+5/3, y+1/3, z+1/3; (xi) x+5/3, y+4/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3.
 

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