research papers
The novel structure of the δ1 phase in the cobalt–zinc system was determined by single-crystal X-ray diffraction. The structure features fused double icosahedra linked by edge- and face-sharing. The δ1-CoZn7.8 structure is incommensurately modulated along the columnar b direction. The extent of the linear pentagonal antiprismatic intergrowth is limited to a maximum of two overlapping icosahedra because of geometric demands and radii relations. Even this limited fusion of icosahedra leads to strain that is believed to be the origin of the structural modulation. The compound was synthesized using a centrifugation-aided filtration method which yielded single crystals grown on cobalt pieces in a zinc-rich melt. The (3 + 1)-dimensional superspace group is F2/m(0β0)s0 and the modulation wavevector was determined to q = 0.234b*. The partial amorphization of the sample when subjected to mechanical grinding is an indication of a metastable structure. The incommensurability of the structure may be seen as an ordered pinning of phasons.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768103019694/sn5001sup1.cif | |
Graphic Interchange Format (GIF) image https://doi.org/10.1107/S0108768103019694/sn5001sup2.gif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768103019694/sn5001sup3.hkl |
Computing details top
Data reduction: X-RED: Data Reduction Program, Stoe and Cie, (1996); program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).
(global) top
Crystal data top
CoZn7.8 | F(000) = 1006 |
Mr = 568.90 | Dx = 3.854 (2) Mg m−3 |
Monoclinic, F2/m(0β0)s0† | Mo Kα radiation, λ = 0.71069 Å |
q = 0.23370b* | Cell parameters from 2026 reflections |
a = 9.030 (2) Å | θ = 2.9–48.4° |
b = 4.338 (1) Å | µ = 20.29 mm−1 |
c = 12.511 (3) Å | T = 293 K |
β = 89.90 (3)° | Tabular, metallic |
V = 490.1 (2) Å3 | 0.08 × 0.05 × 0.02 mm |
Z = 2 |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, 1/2+x4; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, 1/2−x4; (5) x1, 1/2+x2, 1/2+x3, x4; (6) −x1, 1/2+x2, 1/2−x3, 1/2+x4; (7) −x1, 1/2−x2, 1/2−x3, −x4; (8) x1, 1/2−x2, 1/2+x3, 1/2−x4; (9) 1/2+x1, x2, 1/2+x3, x4; (10) 1/2−x1, x2, 1/2−x3, 1/2+x4; (11) 1/2−x1, −x2, 1/2−x3, −x4; (12) 1/2+x1, −x2, 1/2+x3, 1/2−x4; (13) 1/2+x1, 1/2+x2, x3, x4; (14) 1/2−x1, 1/2+x2, −x3, 1/2+x4; (15) 1/2−x1, 1/2−x2, −x3, −x4; (16) 1/2+x1, 1/2−x2, x3, 1/2−x4. |
Data collection top
STOE IPDS diffractometer | 2026 independent reflections |
Radiation source: X-ray tube | 1095 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.075 |
θ–2θ scans | θmax = 48.4°, θmin = 2.9° |
Absorption correction: numerical from crystal shape | h = −10→10 |
Tmin = 0.263, Tmax = 0.724 | k = 0→5 |
8488 measured reflections | l = 0→14 |
Refinement top
Refinement on F | 104 parameters |
R[F2 > 2σ(F2)] = 0.062 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.069 | (Δ/σ)max = 0.0002 |
S = 2.92 | Δρmax = 4.98 e Å−3 |
2026 reflections | Δρmin = −4.53 e Å−3 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | ||
Co | −0.16084 (16) | −0.3052 (4) | 0.0879 (2) | 0.0105 (4) | |
Zn1 | −0.21276 (11) | 0 | 0.09149 (9) | 0.0174 (3) | |
Zn2 | 0.41599 (17) | 0 | 0.02151 (12) | 0.0215 (5) | |
Zn3 | 0.27052 (14) | 0 | 0.23105 (11) | 0.0136 (4) | |
Zn4 | 0.07312 (9) | 0 | 0.09012 (7) | 0.0146 (3) | |
Zn5 | −0.43014 (9) | 0 | 0.21472 (7) | 0.0140 (3) |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
Co | 0.0060 (7) | 0.0193 (9) | 0.0064 (7) | −0.0114 (6) | −0.0023 (6) | 0.0028 (6) |
Zn1 | 0.0160 (5) | 0.0225 (6) | 0.0138 (6) | 0 | 0.0030 (5) | 0 |
Zn2 | 0.0378 (9) | 0.0081 (7) | 0.0187 (8) | 0 | −0.0074 (7) | 0 |
Zn3 | 0.0136 (6) | 0.0148 (7) | 0.0126 (6) | 0 | −0.0028 (5) | 0 |
Zn4 | 0.0160 (5) | 0.0152 (5) | 0.0126 (5) | 0 | −0.0005 (4) | 0 |
Zn5 | 0.0183 (5) | 0.0097 (5) | 0.0140 (5) | 0 | 0.0032 (4) | 0 |
Geometric parameters (Å, º) top
Average | Minimum | Maximum | |
Co—Coi | 2.6 (5) | 2.6 (5) | 2.6 (5) |
Co—Zn1ii | 2.7 (4) | 2.7 (5) | 2.8 (3) |
Co—Zn1iii | 2.66 (18) | 2.7 (2) | 2.66 (14) |
Co—Zn2iv | 2.9 (2) | 2.83 (15) | 2.9 (3) |
Co—Zn2v | 2.77 (17) | 2.74 (13) | 2.8 (2) |
Co—Zn3vi | 2.65 (18) | 2.63 (13) | 2.7 (2) |
Co—Zn4ii | 3.8 (3) | 3.8 (2) | 3.8 (4) |
Co—Zn4 | 2.5 (2) | 2.52 (15) | 2.6 (3) |
Co—Zn4vii | 2.53 (18) | 2.52 (13) | 2.6 (2) |
Co—Zn4viii | 3.8 (3) | 3.8 (4) | 3.8 (2) |
Co—Zn4iv | 2.7 (2) | 2.7 (3) | 2.71 (16) |
Co—Zn5 | 2.9 (2) | 2.92 (15) | 2.9 (3) |
Co—Zn5ix | 2.73 (17) | 2.70 (12) | 2.8 (2) |
Co—Zn5x | 4.0 (3) | 3.9 (4) | 4.0 (2) |
Co—Zn5xi | 2.7 (2) | 2.7 (3) | 2.79 (16) |
Coi—Co—Zn1ii | 171 (6) | 171 (5) | 172 (7) |
Coi—Co—Zn1ix | 95 (5) | 95 (5) | 95 (5) |
Coi—Co—Zn1iv | 72 (6) | 72 (7) | 73 (5) |
Coi—Co—Zn1xi | 72 (6) | 72 (7) | 72 (5) |
Coi—Co—Zn1iii | 112 (9) | 110 (11) | 114 (7) |
Coi—Co—Zn1xii | 34 (4) | 33 (4) | 35 (4) |
Coi—Co—Zn2viii | 137 (7) | 137 (7) | 137 (7) |
Coi—Co—Zn2iv | 63 (7) | 62 (8) | 63 (6) |
Coi—Co—Zn2v | 109 (9) | 109 (10) | 109 (7) |
Coi—Co—Zn3vi | 111 (9) | 111 (7) | 111 (11) |
Coi—Co—Zn4ii | 146 (6) | 145 (5) | 146 (7) |
Coi—Co—Zn4 | 59 (8) | 58 (9) | 60 (6) |
Coi—Co—Zn4vii | 112 (9) | 112 (11) | 113 (7) |
Coi—Co—Zn4viii | 141 (6) | 140 (7) | 141 (5) |
Coi—Co—Zn4iv | 61 (8) | 60 (6) | 61 (9) |
Coi—Co—Zn5ii | 136 (6) | 136 (5) | 136 (7) |
Coi—Co—Zn5 | 63 (7) | 63 (9) | 63 (6) |
Coi—Co—Zn5ix | 109 (9) | 108 (7) | 110 (11) |
Coi—Co—Zn5x | 138 (6) | 137 (5) | 140 (7) |
Coi—Co—Zn5xi | 61 (8) | 59 (6) | 63 (9) |
Coi—Co—Zn5iii | 101 (7) | 100 (8) | 101 (6) |
Zn1ii—Co—Zn1ix | 94 (5) | 94 (5) | 94 (5) |
Zn1ii—Co—Zn1iv | 116 (6) | 116 (8) | 116 (5) |
Zn1ii—Co—Zn1xi | 104 (5) | 104 (4) | 105 (7) |
Zn1ii—Co—Zn1iii | 65 (7) | 64 (5) | 67 (9) |
Zn1ii—Co—Zn1xii | 142 (5) | 141 (3) | 143 (6) |
Zn1ii—Co—Zn2viii | 37 (4) | 37 (4) | 37 (4) |
Zn1ii—Co—Zn2iv | 110 (7) | 110 (5) | 111 (9) |
Zn1ii—Co—Zn2v | 79 (8) | 79 (11) | 79 (6) |
Zn1ii—Co—Zn3vi | 65 (7) | 64 (5) | 65 (9) |
Zn1ii—Co—Zn4ii | 43 (4) | 42 (5) | 44 (3) |
Zn1ii—Co—Zn4 | 130 (9) | 129 (7) | 131 (11) |
Zn1ii—Co—Zn4vii | 59 (7) | 58 (5) | 60 (9) |
Zn1ii—Co—Zn4viii | 44 (4) | 44 (5) | 44 (3) |
Zn1ii—Co—Zn4iv | 123 (8) | 122 (11) | 124 (6) |
Zn1ii—Co—Zn5ii | 36 (3) | 36 (2) | 36 (4) |
Zn1ii—Co—Zn5 | 109 (7) | 108 (5) | 109 (8) |
Zn1ii—Co—Zn5ix | 78 (8) | 77 (10) | 78 (6) |
Zn1ii—Co—Zn5x | 44 (4) | 43 (5) | 46 (3) |
Zn1ii—Co—Zn5xi | 120 (8) | 119 (10) | 122 (6) |
Zn1ii—Co—Zn5iii | 82 (6) | 82 (7) | 82 (4) |
Zn1iii—Co—Zn1ii | 65 (7) | 64 (5) | 67 (9) |
Zn1iii—Co—Zn1ix | 112 (4) | 112 (4) | 112 (4) |
Zn1iii—Co—Zn1iv | 90 (3) | 90 (4) | 91 (2) |
Zn1iii—Co—Zn1xi | 142 (4) | 142 (5) | 142 (3) |
Zn1iii—Co—Zn1xii | 78 (5) | 77 (7) | 79 (4) |
Zn1iii—Co—Zn2viii | 38 (5) | 38 (5) | 38 (5) |
Zn1iii—Co—Zn2iv | 59 (3) | 58 (3) | 61 (2) |
Zn1iii—Co—Zn2v | 78 (5) | 76 (4) | 79 (7) |
Zn1iii—Co—Zn3vi | 116 (10) | 115 (7) | 116 (12) |
Zn1iii—Co—Zn4ii | 85 (8) | 84 (6) | 87 (10) |
Zn1iii—Co—Zn4 | 123 (5) | 122 (7) | 124 (4) |
Zn1iii—Co—Zn4vii | 60 (4) | 60 (5) | 61 (3) |
Zn1iii—Co—Zn4viii | 45 (5) | 44 (3) | 46 (6) |
Zn1iii—Co—Zn4iv | 68 (3) | 66 (4) | 70 (2) |
Zn1iii—Co—Zn5ii | 78 (7) | 78 (5) | 78 (8) |
Zn1iii—Co—Zn5 | 105 (4) | 104 (5) | 106 (3) |
Zn1iii—Co—Zn5ix | 129 (12) | 129 (14) | 130 (9) |
Zn1iii—Co—Zn5x | 109 (11) | 109 (8) | 110 (14) |
Zn1iii—Co—Zn5xi | 172 (12) | 172 (15) | 172 (9) |
Zn1iii—Co—Zn5iii | 37.9 (18) | 37 (2) | 39.1 (13) |
Zn2iv—Co—Zn2viii | 75 (5) | 75 (5) | 75 (5) |
Zn2iv—Co—Zn2v | 123 (5) | 122 (4) | 124 (6) |
Zn2iv—Co—Zn3vi | 105 (4) | 104 (6) | 106 (3) |
Zn2iv—Co—Zn4ii | 145 (8) | 145 (11) | 145 (6) |
Zn2iv—Co—Zn4 | 115 (12) | 113 (15) | 117 (9) |
Zn2iv—Co—Zn4vii | 58 (3) | 58 (4) | 59 (2) |
Zn2iv—Co—Zn4viii | 105 (5) | 105 (6) | 105 (4) |
Zn2iv—Co—Zn4iv | 69 (6) | 69 (7) | 69 (4) |
Zn2iv—Co—Zn5ii | 93 (4) | 92 (5) | 93 (3) |
Zn2iv—Co—Zn5 | 54 (4) | 54 (5) | 55 (3) |
Zn2iv—Co—Zn5ix | 171 (13) | 170 (9) | 171 (17) |
Zn2iv—Co—Zn5x | 143 (7) | 143 (9) | 144 (5) |
Zn2iv—Co—Zn5xi | 112 (11) | 111 (8) | 113 (14) |
Zn2iv—Co—Zn5iii | 79 (3) | 78 (4) | 80 (2) |
Zn2v—Co—Zn2viii | 94 (10) | 94 (10) | 94 (10) |
Zn2v—Co—Zn2iv | 123 (5) | 122 (4) | 124 (6) |
Zn2v—Co—Zn3vi | 127 (11) | 127 (8) | 128 (14) |
Zn2v—Co—Zn4ii | 44 (4) | 44 (6) | 45 (3) |
Zn2v—Co—Zn4 | 59 (3) | 59 (3) | 59 (2) |
Zn2v—Co—Zn4vii | 129 (12) | 129 (9) | 130 (15) |
Zn2v—Co—Zn4viii | 44 (4) | 43 (3) | 45 (5) |
Zn2v—Co—Zn4iv | 61 (3) | 60 (3) | 61 (2) |
Zn2v—Co—Zn5ii | 115 (11) | 115 (8) | 115 (13) |
Zn2v—Co—Zn5 | 172 (14) | 172 (17) | 173 (10) |
Zn2v—Co—Zn5ix | 61 (4) | 58 (5) | 65 (3) |
Zn2v—Co—Zn5x | 83 (7) | 82 (9) | 84 (5) |
Zn2v—Co—Zn5xi | 109 (5) | 107 (6) | 110 (3) |
Zn2v—Co—Zn5iii | 45 (2) | 42.9 (15) | 48 (3) |
Zn3vi—Co—Zn4ii | 85 (8) | 84 (6) | 85 (10) |
Zn3vi—Co—Zn4 | 120 (5) | 118 (4) | 121 (7) |
Zn3vi—Co—Zn4vii | 60 (4) | 60 (5) | 60 (3) |
Zn3vi—Co—Zn4viii | 108 (11) | 108 (8) | 109 (14) |
Zn3vi—Co—Zn4iv | 171 (13) | 171 (10) | 172 (16) |
Zn3vi—Co—Zn5ii | 38 (4) | 37 (3) | 38 (5) |
Zn3vi—Co—Zn5 | 59 (3) | 58 (3) | 59 (2) |
Zn3vi—Co—Zn5ix | 74 (5) | 71 (4) | 78 (7) |
Zn3vi—Co—Zn5x | 45 (4) | 43 (3) | 46 (6) |
Zn3vi—Co—Zn5xi | 65 (3) | 65 (4) | 66 (2) |
Zn3vi—Co—Zn5iii | 146 (12) | 146 (14) | 147 (9) |
Zn4ii—Co—Zn4 | 87 (5) | 85 (4) | 89 (6) |
Zn4ii—Co—Zn4vii | 102 (11) | 102 (14) | 102 (8) |
Zn4ii—Co—Zn4viii | 41 (3) | 41 (2) | 41 (4) |
Zn4ii—Co—Zn4iv | 104 (5) | 103 (7) | 105 (4) |
Zn4ii—Co—Zn5ii | 74 (6) | 74 (4) | 75 (8) |
Zn4ii—Co—Zn5 | 143 (8) | 142 (6) | 143 (10) |
Zn4ii—Co—Zn5ix | 45 (5) | 43 (6) | 46 (3) |
Zn4ii—Co—Zn5x | 41 (3) | 40 (4) | 41 (2) |
Zn4ii—Co—Zn5xi | 103 (5) | 102 (7) | 104 (4) |
Zn4ii—Co—Zn5iii | 75 (4) | 74 (3) | 75 (5) |
Zn4—Co—Zn4ii | 87 (5) | 85 (4) | 89 (6) |
Zn4—Co—Zn4vii | 171 (14) | 169 (19) | 172 (10) |
Zn4—Co—Zn4viii | 103 (5) | 102 (4) | 104 (6) |
Zn4—Co—Zn4iv | 60 (5) | 60 (7) | 60 (4) |
Zn4—Co—Zn5ii | 151 (7) | 149 (5) | 153 (9) |
Zn4—Co—Zn5 | 114 (12) | 113 (15) | 115 (9) |
Zn4—Co—Zn5ix | 59 (3) | 59 (2) | 59 (4) |
Zn4—Co—Zn5x | 100 (5) | 98 (4) | 102 (6) |
Zn4—Co—Zn5xi | 59 (5) | 58 (4) | 59 (6) |
Zn4—Co—Zn5iii | 86 (3) | 85 (2) | 87 (4) |
Zn4vii—Co—Zn4ii | 102 (11) | 102 (14) | 102 (8) |
Zn4vii—Co—Zn4 | 171 (14) | 169 (19) | 172 (10) |
Zn4vii—Co—Zn4viii | 85 (8) | 85 (10) | 86 (6) |
Zn4vii—Co—Zn4iv | 119 (5) | 118 (6) | 120 (4) |
Zn4vii—Co—Zn5ii | 34 (4) | 34 (5) | 35 (3) |
Zn4vii—Co—Zn5 | 57 (3) | 57 (2) | 57 (4) |
Zn4vii—Co—Zn5ix | 126 (12) | 125 (8) | 128 (15) |
Zn4vii—Co—Zn5x | 86 (8) | 85 (10) | 86 (6) |
Zn4vii—Co—Zn5xi | 116 (5) | 116 (4) | 117 (6) |
Zn4vii—Co—Zn5iii | 98 (5) | 97 (7) | 100 (4) |
Zn4viii—Co—Zn4ii | 41 (3) | 41 (2) | 41 (4) |
Zn4viii—Co—Zn4 | 103 (5) | 102 (4) | 104 (6) |
Zn4viii—Co—Zn4vii | 85 (8) | 85 (10) | 86 (6) |
Zn4viii—Co—Zn4iv | 80 (4) | 79 (6) | 82 (3) |
Zn4viii—Co—Zn5ii | 78 (6) | 77 (8) | 78 (5) |
Zn4viii—Co—Zn5 | 142 (7) | 142 (9) | 142 (5) |
Zn4viii—Co—Zn5ix | 84 (7) | 82 (9) | 85 (6) |
Zn4viii—Co—Zn5x | 75 (6) | 74 (8) | 76 (5) |
Zn4viii—Co—Zn5xi | 143 (7) | 142 (10) | 144 (5) |
Zn4viii—Co—Zn5iii | 40.5 (19) | 40 (2) | 40.5 (15) |
Zn4iv—Co—Zn4ii | 104 (5) | 103 (7) | 105 (4) |
Zn4iv—Co—Zn4 | 60 (5) | 60 (7) | 60 (4) |
Zn4iv—Co—Zn4vii | 119 (5) | 118 (6) | 120 (4) |
Zn4iv—Co—Zn4viii | 80 (4) | 79 (6) | 82 (3) |
Zn4iv—Co—Zn5ii | 146 (7) | 144 (9) | 148 (5) |
Zn4iv—Co—Zn5 | 113 (11) | 113 (8) | 114 (14) |
Zn4iv—Co—Zn5ix | 110 (5) | 108 (6) | 112 (4) |
Zn4iv—Co—Zn5x | 143 (7) | 142 (9) | 144 (5) |
Zn4iv—Co—Zn5xi | 110 (11) | 108 (8) | 112 (14) |
Zn4iv—Co—Zn5iii | 41 (2) | 40 (3) | 42.0 (17) |
Zn5—Co—Zn5ii | 73 (4) | 73 (3) | 73 (5) |
Zn5—Co—Zn5ix | 120 (5) | 117 (3) | 123 (6) |
Zn5—Co—Zn5x | 103 (5) | 102 (3) | 104 (6) |
Zn5—Co—Zn5xi | 68 (5) | 68 (4) | 69 (7) |
Zn5—Co—Zn5iii | 134 (5) | 132 (6) | 135 (4) |
Zn5ix—Co—Zn5ii | 92 (8) | 90 (5) | 94 (10) |
Zn5ix—Co—Zn5 | 120 (5) | 117 (3) | 123 (6) |
Zn5ix—Co—Zn5x | 41 (4) | 39 (3) | 43 (5) |
Zn5ix—Co—Zn5xi | 59 (3) | 59 (2) | 60 (3) |
Zn5ix—Co—Zn5iii | 106 (5) | 105 (7) | 108 (4) |
Zn5x—Co—Zn5ii | 51 (4) | 51 (3) | 51 (5) |
Zn5x—Co—Zn5 | 103 (5) | 102 (3) | 104 (6) |
Zn5x—Co—Zn5ix | 41 (4) | 39 (3) | 43 (5) |
Zn5x—Co—Zn5xi | 77 (4) | 77 (6) | 78 (3) |
Zn5x—Co—Zn5iii | 114 (8) | 114 (10) | 114 (6) |
Zn5xi—Co—Zn5ii | 103 (5) | 103 (6) | 103 (3) |
Zn5xi—Co—Zn5 | 68 (5) | 68 (4) | 69 (7) |
Zn5xi—Co—Zn5ix | 59 (3) | 59 (2) | 60 (3) |
Zn5xi—Co—Zn5x | 77 (4) | 77 (6) | 78 (3) |
Zn5xi—Co—Zn5iii | 145 (7) | 143 (5) | 146 (9) |
Symmetry codes: (i) x1, −x2, x3, −x1/2; (ii) x1, x2−1, x3, x4; (iii) −x1−1/2, −x2−1/2, −x3, −x4; (iv) −x1, −x2, −x3, −x4; (v) −x1+1/2, −x2−1/2, −x3, −x4; (vi) −x1, −x2−1/2, −x3+1/2, −x4; (vii) x1−1/2, x2−1/2, x3, x4; (viii) −x1, −x2−1, −x3, −x4; (ix) x1+1/2, x2−1/2, x3, x4; (x) −x1−1/2, −x2−1, −x3+1/2, −x4; (xi) −x1−1/2, −x2, −x3+1/2, −x4; (xii) −x1−1/2, −x2+1/2, −x3, −x4. |