By Robert Crispin Evans
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M. 4 4 (1) x,y,z (5) fS,! (2) Ht,jJ,z+! ,y,U! I+! ,z+! Okl: k+1 =2n hkO: h=2n hOO: h =2n OkO: k=2n 001: I =2n Special: as above, plus f,l.! l,U! f,z+! b O,O,! l,O hkl: h+I,k=2n a 0,0,0 I,O,! l,! ,! '=!. )(Pmmn); [2jPcm a(2b'= b)(Pba m); [2jPbm a(2e'= e)(Pbcm) Space-group symbol: The space-group symbol (upper left corner) always begins with a capitalletter, giving the Bravais lattice type. 2 for point groups. Next are given the (now obsolete) Schoenflies symbol, the crystal dass (point group) and the crystal system.
2). New rotoinversion axes do arise, however, on the coupling of 3-, 4-, and 6-fold axes with an inversion center to give the new 3-, 4- and 6-axes. For example, the operation of a 4-axis ("bar four" or "four bar" axis), which is characteristic of a tetrahedron distorted along a 2-fold axis, is shown in Fig. 2. g. a ligand molecule, is rotated by the coupled 4-fold axis through 90° to 2. The molecule in this position is not observed, but after inversion, its mirror image at 3 iso Another operation of the 4-fold axis places the molecule at 4, which again is not observed, but a further inversion leads to a molecule at 5.
To show this, a symbol is written either 3m 1 or 31m, where the "I" means 00 symmetry. Unfortunately in the literature "3m" alooe is sometimes written, making it unclear which of these distinct possibilities is meant. __ I / ~~ ____ ~~ ____ b ~~_m I Fig. 4. Alternative symmetry directions in trigonal and hexagonal crystal classes shown for the case of symmetries 3m I (Ieft) and 31 m (right). 46 CRYSTAL SYMMETRY This abbreviation is, however, permissible for R -lattices, where symmetry along [210) is never possible.