Crystal symmetry. (a) two fold (diad ) 2. (b) three fold (triad ) 3. (c) four fold (tetrad ) 4. (d) six fold (hexad ) 6. mirror
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1 MS2041 leture ntes fr edutinl purpses nly III Crystl symmetry 3-1 Symmetry elements (1) Rttin symmetry () tw fld (did ) 2 () three fld (trid ) 3 () fur fld (tetrd ) 4 (d) six fld (hexd ) 6 (2) Refletin (mirrr) symmetry m LH RH mirrr (3) Inversin symmetry (enter f symmetry) RH LH
2 MS2041 leture ntes fr edutinl purpses nly (4) Rttin-Inversin xis = Rtte y 360,then invert. n () ne fld rttin inversin ( 1) () tw fld rttin inversin ( = mirrr symmetry = m 2 ) () inversin trid ( 3 ) = Othedrl site in n thedrn Nte: 3
3 MS2041 leture ntes fr edutinl purpses nly (d) inversin tetrd ( 4 ) = tetrhedrl site in tetrhedrn (e) inversin hexd ( 6 ) Hexgnl lse-pked (hp) lttie
4 MS2041 leture ntes fr edutinl purpses nly 3-2 Furteen Brvis lttie strutures Cnstrut Brvis ltties frm symmetril pint f view D lttie 3 types f symmetry n e rrnged in 1-D lttie (1) mirrr symmetry (m) (2) 2-fld rttin (2) (3) enter f symmetry ( ) D lttie Tw wys t repet 1-D 2-D (1) mintin 1-D symmetry
5 MS2041 leture ntes fr edutinl purpses nly (2) destry 1-D symmetry () Retngulr lttie (, 90 ) Mintin mirrr symmetry m Symmetry elements in retngulr lttie Unit ell, 90
6 MS2041 leture ntes fr edutinl purpses nly () Center Retngulr lttie ( Mintin mirrr symmetry m, 90 ) Symmetry elements in enter retngulr lttie Unit ell
7 MS2041 leture ntes fr edutinl purpses nly Rhmus ell (Primitive unit ell), 90 () Prllelgrm lttie (, 90 ) Destry mirrr symmetry Symmetry elements in prllelgrm lttie Unit ell
8 MS2041 leture ntes fr edutinl purpses nly (d) squre lttie (, 90 ) Symmetry elements in squre lttie Unit ell (e) hexgnl lttie (, 120 ) Symmetry elements in hexgnl lttie Unit ell
9 MS2041 leture ntes fr edutinl purpses nly D lttie : 7 systems,14 Brvis ltties Strting frm prllelgrm lttie, 90 (1)Trilini system 1-fld rttin (1), 90 lttie enter symmetry t lttie pint s shwn ve whih the mleule is istrpi ( 1 )
10 MS2041 leture ntes fr edutinl purpses nly (2) Mnlini system, 90 ne did xis (nly ne xis perpendiulr t the drwing plne mintin 2-fld symmetry in prllelgrm lttie) (1) Primitive mnlini lttie (P ell) Primitive mnlini lttie (P ell) (2) Bse entered mnlini lttie B-fe entered mnlini lttie
11 MS2041 leture ntes fr edutinl purpses nly The send lyer inident t the middle f the first lyer,nd mintin 2-fld symmetry Nte: ther wys t mintin 2-fld symmetry A-fe entered mnlini lttie If releling lttie rdintin x y x y then A-fe entered mnlini lttie = B-fe entered mnlini lttie (3) Bdy entered mnlini = Bse entered mnlini S mnlini hs tw types 1. Primitive mnlini 2. Bse entered mnlini
12 MS2041 leture ntes fr edutinl purpses nly (3) Orthrhmi system, did xes (1) Derived frm retngulr lttie (, 90 ) t mintin 2 fld symmetry The send lyer superpses diretly n the first lyer () Primitive rthrhmi lttie () B- fe entered rthrhmi = A -fe entered rthrhmi
13 MS2041 leture ntes fr edutinl purpses nly () Bdy-entered rthrhmi (I- ell) (2) Derived frm entered retngulr lttie (, 90 ) () C-fe entered Orthrhmi C- fe entered rthrhmi = B- fe entered rthrhmi
14 MS2041 leture ntes fr edutinl purpses nly () Fe-entered Orthrhmi (F-ell) (4) Tetrgnl system, 90 One tetrd xis strting frm squre lttie (, 90 ) (1) mintin 4-fld symmetry
15 MS2041 leture ntes fr edutinl purpses nly () Primitive tetrgnl lttie First lyer Send lyer () Bdy-entered tetrgnl lttie First lyer Send lyer (5) Hexgnl system One hexd xis, 90, 120 strting frm hexgnl lttie (, 90 )
16 MS2041 leture ntes fr edutinl purpses nly (1) mintin 6-fld symmetry Primitive hexgnl lttie (2) mintin 3-fld symmetry Rhmhedrl lttie, 90
17 MS2041 leture ntes fr edutinl purpses nly (6) Cui system, 90 4 trid xes ( trid xis=ue dignl ) Cui is speil frm f Rhmhedrl lttie Cui system hs 4 trid xes mutully inlined lng ue dignl () 90 Primitive ui, 90 () 60 Fe-entered ui, 60 2 regulr tetrhedrl
18 MS2041 leture ntes fr edutinl purpses nly () 109 Bdy-entered ui, 109
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