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 (Sb
2)
k(Sb
2Te
3)
m. Almost homometric structure models for 39
R-Sb
10Te
3 [
Rm,
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 33
R-[Sb
0.978(3)Pb
0.022(3)]
8Te
3 [
Rm,
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
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
Sb10Te3 | Dx = 6.627 Mg m−3 |
Mr = 1600.30 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 1040 reflections |
Hall symbol: -R 3 2" | θ = 4–24° |
a = 4.289 (1) Å | µ = 21.87 mm−1 |
c = 75.51 (2) Å | T = 293 K |
V = 1202.9 (5) Å3 | Irregular polyhedron, metallic_dark_grey |
Z = 3 | 0.08 × 0.06 × 0.01 mm |
F(000) = 1998 | |
Data collection top
Stoe IPDS diffractometer | 375 independent reflections |
Radiation source: fine-focus sealed tube | 195 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.097 |
oscillation scans | θmax = 26.0°, θmin = 2.4° |
Absorption correction: multi-scan Progam XPREP, from equivalents | h = −5→4 |
Tmin = 0.269, Tmax = 0.989 | k = −5→5 |
2811 measured reflections | l = −93→89 |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary 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 = 1.71 | Δρmax = 3.19 e Å−3 |
375 reflections | Δρmin = −3.55 e Å−3 |
22 parameters | Extinction correction: SHELXL, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
0 restraints | Extinction 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 | x | y | z | Uiso*/Ueq | |
Te1 | 0.0000 | 0.0000 | 0.0000 | 0.0375 (12) | |
Sb1 | 0.6667 | 0.3333 | 0.02808 (5) | 0.0383 (9) | |
Te2 | 0.3333 | 0.6667 | 0.05018 (3) | 0.0256 (9) | |
Sb2 | 0.0000 | 0.0000 | 0.07986 (4) | 0.0284 (8) | |
Sb3 | 0.6667 | 0.3333 | 0.10044 (3) | 0.0206 (8) | |
Sb4 | 0.3333 | 0.6667 | 0.13116 (4) | 0.0298 (9) | |
Sb5 | 0.0000 | 0.0000 | 0.15135 (3) | 0.0258 (9) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Te1 | 0.0235 (15) | 0.0235 (15) | 0.066 (3) | 0.0118 (8) | 0.000 | 0.000 |
Sb1 | 0.0284 (10) | 0.0284 (10) | 0.058 (2) | 0.0142 (5) | 0.000 | 0.000 |
Te2 | 0.0240 (11) | 0.0240 (11) | 0.0288 (19) | 0.0120 (5) | 0.000 | 0.000 |
Sb2 | 0.0242 (11) | 0.0242 (11) | 0.0368 (18) | 0.0121 (5) | 0.000 | 0.000 |
Sb3 | 0.0218 (9) | 0.0218 (9) | 0.0181 (16) | 0.0109 (5) | 0.000 | 0.000 |
Sb4 | 0.0216 (12) | 0.0216 (12) | 0.046 (2) | 0.0108 (6) | 0.000 | 0.000 |
Sb5 | 0.0225 (11) | 0.0225 (11) | 0.032 (2) | 0.0113 (6) | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Te1—Sb1i | 3.260 (2) | Te2—Sb1ix | 2.986 (3) |
Te1—Sb1 | 3.260 (2) | Sb2—Sb3iii | 2.923 (2) |
Te1—Sb1ii | 3.260 (2) | Sb2—Sb3 | 2.923 (2) |
Te1—Sb1iii | 3.260 (2) | Sb2—Sb3v | 2.923 (2) |
Te1—Sb1iv | 3.260 (2) | Sb3—Sb2vi | 2.923 (2) |
Te1—Sb1v | 3.260 (2) | Sb3—Sb2viii | 2.923 (2) |
Sb1—Te2vi | 2.986 (3) | Sb4—Sb5ix | 2.908 (2) |
Sb1—Te2vii | 2.986 (3) | Sb4—Sb5viii | 2.908 (2) |
Sb1—Te2 | 2.986 (3) | Sb4—Sb5 | 2.908 (2) |
Sb1—Te1vi | 3.260 (2) | Sb5—Sb4vii | 2.908 (2) |
Sb1—Te1viii | 3.260 (2) | Sb5—Sb4v | 2.908 (2) |
Te2—Sb1iii | 2.986 (3) | | |
| | | |
Sb1i—Te1—Sb1 | 180.00 (10) | Te2—Sb1—Te1vi | 173.40 (12) |
Sb1i—Te1—Sb1ii | 82.26 (7) | Te1—Sb1—Te1vi | 82.26 (7) |
Sb1—Te1—Sb1ii | 97.74 (7) | Te2vi—Sb1—Te1viii | 92.79 (3) |
Sb1i—Te1—Sb1iii | 97.74 (7) | Te2vii—Sb1—Te1viii | 173.40 (12) |
Sb1—Te1—Sb1iii | 82.26 (7) | Te2—Sb1—Te1viii | 92.79 (3) |
Sb1ii—Te1—Sb1iii | 180.00 (10) | Te1—Sb1—Te1viii | 82.26 (7) |
Sb1i—Te1—Sb1iv | 82.26 (7) | Te1vi—Sb1—Te1viii | 82.26 (7) |
Sb1—Te1—Sb1iv | 97.74 (7) | Sb1iii—Te2—Sb1ix | 91.80 (11) |
Sb1ii—Te1—Sb1iv | 82.26 (7) | Sb1iii—Te2—Sb1 | 91.80 (11) |
Sb1iii—Te1—Sb1iv | 97.74 (7) | Sb1ix—Te2—Sb1 | 91.80 (11) |
Sb1i—Te1—Sb1v | 97.74 (7) | Sb3iii—Sb2—Sb3 | 94.38 (10) |
Sb1—Te1—Sb1v | 82.26 (7) | Sb3iii—Sb2—Sb3v | 94.38 (10) |
Sb1ii—Te1—Sb1v | 97.74 (7) | Sb3—Sb2—Sb3v | 94.38 (10) |
Sb1iii—Te1—Sb1v | 82.26 (7) | Sb2vi—Sb3—Sb2 | 94.38 (10) |
Sb1iv—Te1—Sb1v | 180.00 (10) | Sb2vi—Sb3—Sb2viii | 94.38 (10) |
Te2vi—Sb1—Te2vii | 91.80 (11) | Sb2—Sb3—Sb2viii | 94.38 (10) |
Te2vi—Sb1—Te2 | 91.80 (11) | Sb5ix—Sb4—Sb5viii | 95.03 (9) |
Te2vii—Sb1—Te2 | 91.80 (11) | Sb5ix—Sb4—Sb5 | 95.03 (9) |
Te2vi—Sb1—Te1 | 173.40 (12) | Sb5viii—Sb4—Sb5 | 95.03 (9) |
Te2vii—Sb1—Te1 | 92.79 (3) | Sb4vii—Sb5—Sb4v | 95.03 (9) |
Te2—Sb1—Te1 | 92.79 (3) | Sb4vii—Sb5—Sb4 | 95.03 (9) |
Te2vi—Sb1—Te1vi | 92.79 (3) | Sb4v—Sb5—Sb4 | 95.03 (9) |
Te2vii—Sb1—Te1vi | 92.79 (3) | | |
Symmetry codes: (i) −x, −y, −z; (ii) −x+1, −y, −z; (iii) x−1, y, z; (iv) −x+1, −y+1, −z; (v) x−1, y−1, z; (vi) x+1, y, z; (vii) x, y−1, z; (viii) x+1, y+1, z; (ix) x, y+1, z. |
Crystal data top
Pb0.18Sb7.82Te3 | Dx = 6.677 Mg m−3 |
Mr = 1371.89 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 841 reflections |
Hall symbol: -R 3 2" | θ = 4–27° |
a = 4.2874 (6) Å | µ = 23.64 mm−1 |
c = 64.300 (16) Å | T = 293 K |
V = 1023.6 (3) Å3 | Irregular polyhedron, metallic_dark_grey |
Z = 3 | 0.18 × 0.10 × 0.08 mm |
F(000) = 1707.5 | |
Data collection top
Stoe IPDS diffractometer | 462 independent reflections |
Radiation source: fine-focus sealed tube | 184 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.081 |
oscillation scans | θmax = 30.0°, θmin = 2.9° |
Absorption correction: numerical X-RED, X-SHAPE (Stoe, Darmstadt 2002) | h = −6→6 |
Tmin = 0.080, Tmax = 0.184 | k = −5→6 |
3739 measured reflections | l = −90→85 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Primary atom site location: structure-invariant direct methods |
R[F2 > 2σ(F2)] = 0.030 | Secondary 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 reflections | Δρmax = 1.17 e Å−3 |
19 parameters | Δρmin = −2.04 e Å−3 |
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 | x | y | z | Uiso*/Ueq | Occ. (<1) |
Te1 | 0.0000 | 0.0000 | 0.0000 | 0.0186 (8) | |
Sb1 | 0.3333 | 0.6667 | 0.03102 (5) | 0.0315 (7) | 0.911 (14) |
Pb1 | 0.3333 | 0.6667 | 0.03102 (5) | 0.0315 (7) | 0.089 (14) |
Te2 | 0.6667 | 0.3333 | 0.05790 (3) | 0.0186 (6) | |
Sb2 | 0.0000 | 0.0000 | 0.09485 (4) | 0.0202 (5) | |
Sb3 | 0.3333 | 0.6667 | 0.11874 (4) | 0.0185 (6) | |
Sb4 | 0.6667 | 0.3333 | 0.15475 (4) | 0.0160 (4) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Te1 | 0.0181 (12) | 0.0181 (12) | 0.0196 (11) | 0.0091 (6) | 0.000 | 0.000 |
Sb1 | 0.0239 (8) | 0.0239 (8) | 0.0466 (11) | 0.0120 (4) | 0.000 | 0.000 |
Pb1 | 0.0239 (8) | 0.0239 (8) | 0.0466 (11) | 0.0120 (4) | 0.000 | 0.000 |
Te2 | 0.0165 (9) | 0.0165 (9) | 0.0227 (8) | 0.0082 (5) | 0.000 | 0.000 |
Sb2 | 0.0165 (8) | 0.0165 (8) | 0.0276 (9) | 0.0082 (4) | 0.000 | 0.000 |
Sb3 | 0.0152 (9) | 0.0152 (9) | 0.0252 (8) | 0.0076 (4) | 0.000 | 0.000 |
Sb4 | 0.0126 (7) | 0.0126 (7) | 0.0229 (8) | 0.0063 (3) | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Te1—Pb1i | 3.179 (2) | Sb1—Te1vi | 3.179 (2) |
Te1—Sb1 | 3.179 (2) | Sb1—Te1viii | 3.179 (2) |
Te1—Sb1i | 3.179 (2) | Te2—Pb1iii | 3.019 (3) |
Te1—Pb1ii | 3.179 (2) | Te2—Sb1iii | 3.019 (3) |
Te1—Sb1iii | 3.179 (2) | Te2—Pb1ix | 3.019 (3) |
Te1—Sb1ii | 3.179 (2) | Te2—Sb1ix | 3.019 (3) |
Te1—Pb1iii | 3.179 (2) | Sb2—Sb3iii | 2.913 (2) |
Te1—Pb1iv | 3.179 (2) | Sb2—Sb3 | 2.913 (2) |
Te1—Pb1v | 3.179 (2) | Sb2—Sb3v | 2.913 (2) |
Te1—Sb1v | 3.179 (2) | Sb3—Sb2vi | 2.913 (2) |
Te1—Sb1iv | 3.179 (2) | Sb3—Sb2viii | 2.913 (2) |
Sb1—Te2vi | 3.019 (3) | Sb4—Sb4x | 2.912 (3) |
Sb1—Te2vii | 3.019 (3) | Sb4—Sb4xi | 2.912 (3) |
Sb1—Te2 | 3.019 (3) | Sb4—Sb4xii | 2.912 (3) |
| | | |
Pb1i—Te1—Sb1 | 180.00 (9) | Pb1i—Te1—Sb1iv | 84.81 (7) |
Sb1—Te1—Sb1i | 180.00 (9) | Sb1—Te1—Sb1iv | 95.19 (7) |
Pb1i—Te1—Pb1ii | 84.81 (7) | Sb1i—Te1—Sb1iv | 84.81 (7) |
Sb1—Te1—Pb1ii | 95.19 (7) | Pb1ii—Te1—Sb1iv | 84.81 (7) |
Sb1i—Te1—Pb1ii | 84.81 (7) | Sb1iii—Te1—Sb1iv | 95.19 (7) |
Pb1i—Te1—Sb1iii | 95.19 (7) | Sb1ii—Te1—Sb1iv | 84.81 (7) |
Sb1—Te1—Sb1iii | 84.81 (7) | Pb1iii—Te1—Sb1iv | 95.19 (7) |
Sb1i—Te1—Sb1iii | 95.19 (7) | Pb1v—Te1—Sb1iv | 180.00 (9) |
Pb1ii—Te1—Sb1iii | 180.00 (9) | Sb1v—Te1—Sb1iv | 180.00 (9) |
Pb1i—Te1—Sb1ii | 84.81 (7) | Te2vi—Sb1—Te2vii | 90.48 (11) |
Sb1—Te1—Sb1ii | 95.19 (7) | Te2vi—Sb1—Te2 | 90.48 (11) |
Sb1i—Te1—Sb1ii | 84.81 (7) | Te2vii—Sb1—Te2 | 90.48 (11) |
Sb1iii—Te1—Sb1ii | 180.00 (9) | Te2vi—Sb1—Te1 | 176.06 (12) |
Pb1i—Te1—Pb1iii | 95.19 (7) | Te2vii—Sb1—Te1 | 92.29 (3) |
Sb1—Te1—Pb1iii | 84.81 (7) | Te2—Sb1—Te1 | 92.29 (3) |
Sb1i—Te1—Pb1iii | 95.19 (7) | Te2vi—Sb1—Te1vi | 92.29 (3) |
Pb1ii—Te1—Pb1iii | 180.00 (9) | Te2vii—Sb1—Te1vi | 92.29 (3) |
Sb1ii—Te1—Pb1iii | 180.00 (9) | Te2—Sb1—Te1vi | 176.06 (12) |
Pb1i—Te1—Pb1iv | 84.81 (7) | Te1—Sb1—Te1vi | 84.81 (7) |
Sb1—Te1—Pb1iv | 95.19 (7) | Te2vi—Sb1—Te1viii | 92.29 (3) |
Sb1i—Te1—Pb1iv | 84.81 (7) | Te2vii—Sb1—Te1viii | 176.06 (12) |
Pb1ii—Te1—Pb1iv | 84.81 (7) | Te2—Sb1—Te1viii | 92.29 (3) |
Sb1iii—Te1—Pb1iv | 95.19 (7) | Te1—Sb1—Te1viii | 84.81 (7) |
Sb1ii—Te1—Pb1iv | 84.81 (7) | Te1vi—Sb1—Te1viii | 84.81 (7) |
Pb1iii—Te1—Pb1iv | 95.19 (7) | Pb1iii—Te2—Pb1ix | 90.48 (11) |
Pb1i—Te1—Pb1v | 95.19 (7) | Sb1iii—Te2—Pb1ix | 90.48 (11) |
Sb1—Te1—Pb1v | 84.81 (7) | Pb1iii—Te2—Sb1ix | 90.48 (11) |
Sb1i—Te1—Pb1v | 95.19 (7) | Sb1iii—Te2—Sb1ix | 90.48 (11) |
Pb1ii—Te1—Pb1v | 95.19 (7) | Pb1iii—Te2—Sb1 | 90.48 (11) |
Sb1iii—Te1—Pb1v | 84.81 (7) | Sb1iii—Te2—Sb1 | 90.48 (11) |
Sb1ii—Te1—Pb1v | 95.19 (7) | Pb1ix—Te2—Sb1 | 90.48 (11) |
Pb1iii—Te1—Pb1v | 84.81 (7) | Sb1ix—Te2—Sb1 | 90.48 (11) |
Pb1iv—Te1—Pb1v | 180.00 (9) | Sb3iii—Sb2—Sb3 | 94.76 (10) |
Pb1i—Te1—Sb1v | 95.19 (7) | Sb3iii—Sb2—Sb3v | 94.76 (10) |
Sb1—Te1—Sb1v | 84.81 (7) | Sb3—Sb2—Sb3v | 94.76 (10) |
Sb1i—Te1—Sb1v | 95.19 (7) | Sb2vi—Sb3—Sb2 | 94.76 (10) |
Pb1ii—Te1—Sb1v | 95.19 (7) | Sb2vi—Sb3—Sb2viii | 94.76 (10) |
Sb1iii—Te1—Sb1v | 84.81 (7) | Sb2—Sb3—Sb2viii | 94.76 (10) |
Sb1ii—Te1—Sb1v | 95.19 (7) | Sb4x—Sb4—Sb4xi | 94.83 (12) |
Pb1iii—Te1—Sb1v | 84.81 (7) | Sb4x—Sb4—Sb4xii | 94.83 (12) |
Pb1iv—Te1—Sb1v | 180.00 (9) | Sb4xi—Sb4—Sb4xii | 94.83 (12) |
Symmetry codes: (i) −x, −y, −z; (ii) −x, −y+1, −z; (iii) x, y−1, z; (iv) −x+1, −y+1, −z; (v) x−1, y−1, z; (vi) x, y+1, z; (vii) x−1, 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. |