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by: Ashley Kunze


Ashley Kunze
GPA 3.61

R. Little

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R. Little
Class Notes
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This 5 page Class Notes was uploaded by Ashley Kunze on Thursday October 22, 2015. The Class Notes belongs to CHEM 227 at University of California Santa Barbara taught by R. Little in Fall. Since its upload, it has received 23 views. For similar materials see /class/226943/chem-227-university-of-california-santa-barbara in Chemistry and Biochemistry at University of California Santa Barbara.

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Date Created: 10/22/15
39 11c h edu MATERIALS ZlSCHEMISTRY 227 CRYSTALLOGRAPHY MATRL 218CHEM 227 Class IV Crystallography Ram Seshadri seshadrimrlucsbedu Lattices unit cells symmetry how crystallography simplifies the depiction of structures Most of the materials we deal with in this course are crystalline meaning that they are periodic at the atomic scale The unit Cell is repeated tiled many billions of times in every direction in order to obtain crystal The unit cell Tiled in the three directions 0 o 0 o Crystallography is the science that helps understand and perhaps even rationalize the atomicscale struc ture of crystalline materials This class is a quick review For a uick and comprehensible treatment of the subject see C Hammond The basics of crystallography and di raction TUCrOxford This is more than sufficient for the purpose of this course For a more advanced treatment see the edited book by C Giacovazzo An introduction to crystallography TUCrOxford o The crystal is built up by tiling the unit cell 0 The contents of the unit cell are atoms and molecules 0 The use of symmetry elements simplifies the description of the contents of the unit cell 39 in h edu MATERIALS ZlSCHEMISTRY 227 CRYSTALLOGRAPHY o In 1 D there are 7 line groups 7 the crystallography of frieze patterns Frieze n A band of painted or sculptured decoration More interestingly that member in the entablature of an order which comes between the architrave and cornice Also in extended sense 0 These line groups possess three different kinds of symmetry elements the mirrors m the twofold rotations 2 and the glides g They act on the motif to copy it within the unit cell unit cell A 7 p2mg AL 1 AL L 2 7 1 7 1 7 P mm The doted vertical lines mark the outlines of the unit cells 0 In going from 1D to 2D where there are now seventeen plane groups only one new concept is added 7 that of centering 0 There are 5 kinds of cells in 2D 7 the plane lattices 39 m h edu MATERIALS ZlSCHEMISTRY 227 CRYSTALLOGRAPHY square rectangular oblique centered rectangular hexagonal 0 There are 17 plane groups obtained by combining all the possible symmetry operations in 2D The oper ations are 2 3 and 4 fold rotations mirrors m glides g centering c Examples of plane groups L L cm I F p4gm V V 0 Sometimes it is useful to add another element of symmetry For example twocolor symmetry indi cated by a prime switches black to white and viceeversu These are called Shubnikov groups 39 in h edu MATERIALS ZlSCHEMISTRY 227 CRYSTALLOGRAPHY Shubnikov groups are useful when properties such as spin need to be overlaid over the normal crystal lographic symmetry What about 3D 7 We shall have mercifully little to say about the 230 space groups N W Ashcroft and N D Mermin Solid State Physics There are 14 lattices in 3D 7 the Bruvuis lattices The only new elements of symmetry on going from 2D to 3D are the screw axes See the handout for an illustration of what these are Crystallography simplifies the description of crystal structures The diamond structure Cubic closepacking of C atoms with C occupying some of the tetrahedral interstices Space Group ngm 227 u 356 A Atom Wyckoff letter Site symmetry 36 z y C 8n 13m 0 0 0 m h edu MATERIALS 218 CHEMISTRY 227 CRYSTALLOGRAPHY Faujasite The zeolitic SiO framework of this material is described by five atoms Space Group Fd3m 227 u 2456 A Atom Wyckoff letter Site symmetry x y 7 Si 192i 1 00364 01272 03029 01 192139 1 0 03864 06136 02 96g m 00012 00012 01447 03 96g m 00684 00684 03126 04 96g m 03257 03257 00288 gory Iquot quot 5 D xa vr I b q I I l I I 1 I g I A I t The SiO framework of the zeolite Faujasite The tetrahedra have Si at the center Approxi mately 640 atom positions are required to make this drawing


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