Practical Electron Microscopy and Database

Chapter/Index: Introduction | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | Appendix

I4₁/amd (141) Space Group

Table 3022. I41/amd (141) space group. Name in the International Tables for Crystallography I41/amd Lattice type I Patterson space group 139 Point group 4/mmm Crystal system Tetragonal Laue class 4/mmm Asymm 0 ≤ x ≤1/2 and 0 ≤ y ≤1/2 and 0 ≤ z ≤ 1/8 Number of symmetry operators 32 Symmetry (atomic coordinates) X, Y, Z; 1/2-X, 1/2-Y, 1/2+Z; -Y, 1/2+X, 1/4+Z; 1/2+Y, -X, 3/4+Z; 1/2-X, Y, 3/4-Z; X, 1/2-Y, 1/4-Z; 1/2+Y, 1/2+X, 1/2-Z; -Y, -X, -Z; -X, 1/2-Y, 1/4-Z; 1/2+X, Y, 3/4-Z; Y, -X, -Z; 1/2-Y, 1/2+X, 1/2-Z; 1/2+X, 1/2-Y, 1/2+Z; -X, Y, Z; 1/2-Y, -X, 3/4+Z; Y, 1/2+X, 1/4+Z; 1/2+X, 1/2+Y, 1/2+Z; -X, -Y, Z; 1/2-Y, X, 3/4+Z; Y, 1/2-X, 1/4+Z; -X, 1/2+Y, 1/4-Z; 1/2+X, -Y, 3/4-Z; Y, X, -Z; 1/2-Y, 1/2-X, 1/2-Z; 1/2-X, -Y, 3/4-Z; X, 1/2+Y, 1/4-Z; 1/2+Y, 1/2-X, 1/2-Z; -Y, X, -Z; X, -Y, Z; 1/2-X, 1/2+Y, 1/2+Z; -Y, 1/2-X, 1/4+Z; 1/2+Y, X, 3/4+Z Crystal examples ZnMn2O4, MgMn2O4 TiO2: a = 3.764 and c = 9.502 V52O64 Li2Mn2O4 (a = b = 5.6488 Å and c = 9.198 Å):     Atom x y z Site symmetry Wyckoff site and multiplicity Li1 0.0 0.7500 0.125 -4m2 4a Li2 0.0 0.0 0.0 2/m 8c Mn 0.0 0.0 0.5 2/m 8d O 0.0 0.4776 0.2493 m 16h   [010] anatase TiO2 [1] Figure 3022. Examples of indexed electron diffraction (or FFT) patterns of I41/amd (141) crystals.         [1] Ma, Xue Yan; Chen, Zhi Gang; Hartono, Sandy Budi; Jiang, Hai Bo; Zou, Jin; Qiao, Shi Zhang; Yang, Huagui, Fabrication of uniform anatase TiO2 particles exposed by {001} facets, Chemical Communications, 46(35), 6608, 2010. DOI: 10.1039/c0cc01473g.