Space Symmetry, Space Groups

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Space symmetry, Space groups - Space groups are the product of possible combinations of symmetry operations including translations. - There exist 230 different space groups in 3-dimensional space - Comparing to point groups, space groups have 2 more symmetry operations (table 1). These operations include translations. Therefore they describe not only the lattice but also the crystal structure. Table 1: Additional symmetry operations in space symmetry, their description, symmetry elements and Hermann-Mauguin symbols. symmetry H-M description symmetry element operation symbol screw 1. rotation by 360°/N screw axis NM (Schraubung) 2. translation along the axis (Schraubenachse) 1. reflection across the plane glide glide plane 2. translation parallel to the a,b,c,n,d (Gleitspiegelung) (Gleitspiegelebene) glide plane Glide directions for the different gilde planes: a (b,c): translation along ½ a or ½ b or ½ c, respectively) (with ,, cba = vectors of the unit cell) n: translation e.g. along ½ (a + b) d: translation e.g. along ¼ (a + b), d from diamond, because this glide plane occurs in the diamond structure Screw axis example: 21 (N = 2, M = 1) 1) rotation by 180° (= 360°/2) 2) translation parallel to the axis by ½ unit (M/N) Only 21, (31, 32), (41, 43), 42, (61, 65) (62, 64), 63 screw axes exist in parenthesis: right, left hand screw axis Space group symbol: The space group symbol begins with a capital letter (P: primitive; A, B, C: base centred I, body centred R rhombohedral, F face centred), which represents the Bravais lattice type, followed by the short form of symmetry elements, as known from the point group symbols. The symmetry elements are ordered according to the viewing directions in the respective crystal system (table 2). Some space groups have only one viewing direction, so their symbols are short (P4, P21/c...), others have up to 3 viewing directions and therefore a longer symbol (P4/mmm, I4/mcm, Pmmm…). Table 2: Viewing directions of the 7 crystal systems. position in the symbol triclinic monoclinic orthorhombic tetragonal trigonal hexagonal cubic 1. ― b a c c c ‹a› 2. ― b ‹a› ‹a› ‹a› ‹111› 3. ― c ‹110› ― ‹210› ‹110› ‹...›: ... and symmetry equivalent directions, respectively Literature: W. Borchardt-Ott, Kristallographie, 7th ed. Springer-Verlag, Berlin, Heidelberg, 2009. U. Müller, Anorganische Strukturchemie, 6th ed. Vieweg+Teubner, Wiesbaden, 2008. A. R. West, Basic Solid State Chemistry, 2nd ed. John Wiley & Sons LTD, Chichester, 2004. http://ruby.chemie.uni-freiburg.de/Vorlesung/Vorlagen/methoden_II_24.pdf Î (compact overview of space groups, bravais lattices and viewing directions, only 1 page) http://www.uni-leipzig.de/~minkrist/pdf/IMKM_Kristallographie_2.pdf http://chemkrist2009.uni-freiburg.de/Vortraege/englert_2.pdf http://img.chem.ucl.ac.uk/sgp/LARGE/sgp.htm http://cst-www.nrl.navy.mil/lattice/spcgrp/ .

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I`mt`qx1/00Lhmdq`knesgdLnmsg9Rbnkdbhsd This month’s mineral, scolecite, is an uncommon zeolite from India. Our write-up explains its origin as a secondary mineral in volcanic host rocks, the difficulty of collecting this fragile mineral, the unusual properties of the zeolite-group minerals, and why mineralogists recently revised the system of zeolite classification and nomenclature. OVERVIEW PHYSICAL PROPERTIES Chemistry: Ca(Al2Si3O10)A3H2O Hydrous Calcium Aluminum Silicate (Hydrous Calcium Aluminosilicate), usually containing some potassium and sodium. Class: Silicates Subclass: Tectosilicates Group: Zeolites Crystal System: Monoclinic Crystal Habits: Usually as radiating sprays or clusters of thin, acicular crystals or Hairlike fibers; crystals are often flattened with tetragonal cross sections, lengthwise striations, and slanted terminations; also massive and fibrous. Twinning common. Color: Usually colorless, white, gray; rarely brown, pink, or yellow. Luster: Vitreous to silky Transparency: Transparent to translucent Streak: White Cleavage: Perfect in one direction Fracture: Uneven, brittle Hardness: 5.0-5.5 Specific Gravity: 2.16-2.40 (average 2.25) Figure 1. Scolecite. Luminescence: Often fluoresces yellow or brown in ultraviolet light. Refractive Index: 1.507-1.521 Distinctive Features and Tests: Best field-identification marks are acicular crystal habit; vitreous-to-silky luster; very low density; and association with other zeolite-group minerals, especially the closely- related minerals natrolite [Na2(Al2Si3O10)A2H2O] and mesolite [Na2Ca2(Al6Si9O30)A8H2O]. Laboratory tests are often needed to distinguish scolecite from other zeolite minerals. Dana Classification Number: 77.1.5.5 NAME The name “scolecite,” pronounced SKO-leh-site, is derived from the German Skolezit, which comes from the Greek sklx, meaning “worm,” an allusion to the tendency of its acicular crystals to curl when heated and dehydrated.
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