# Εισαγωγή στην κρυσταλλογραφία

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Αντιστοιχεί και συμπληρώνει τις σελίδες 32 - 37 , 52-56 των σημειώσεων ΓΕΝΙΚΗ ΟΡΥΚΤΟΛΟΓΙΑ του κου Α. Βγενόπουλου. Εισαγωγή στην κρυσταλλογραφία. Συμμετρία και κρυσταλλικά συστήματα. Ηλίας Χατζηθεοδωρίδης 2003/2007 /2011. - PowerPoint PPT Presentation

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2003/2007/2011 32-37, 52-56 . . internet C. Klein, Mineral Science, 22nd Edition, Wiley.

Hay, (.. ) :, .. H2O , (CO3)2-, (SiO4)4-, (PO4)3- , Ca2+, Mg2+, Fe2+, Fe3+ ; , . () . 1=1 1+2 = 2+1 + 1+1=2, 1+1+1=3, 1+2=3 10=0, 11=1, 22=4 . = ,

M.C. Escher

(1898-1972)

M.C. Escher

M.C. Escher

M.C. Escher (fractals)

7

32 : - (point groups) (, , ) () . (7) / } 7 32 point groups a b c 901 = 1-= 1--b-c-a+a+b+ca0b0c0 a b c = = 90 90 2 = 12m=m2/m = I, 1A2, m-b-c-a+a+b+cb0a0c0 a b c = = = 90222 = 3A2mm2 = 1A2, 2m2/m 2/m 2/m = I, 3A2, 3m-b-c-a+a+b+c=90=90=90c0b0a0 a = b ca = = = 904 = 1A44- = 1A-44/m = I, 1A4, m422 = 1A4, 4A24mm = 1A4, 4m4-2m = 1A-4, 2A2, 2m4/m 2/m 2/m = I, 1A4, 4A2, 5m-b-c-a+a+b+c=90=90=90c0b0a0 () a1 = a2 = a3 = c1=2=3 =120 = = 903 = 1A33- = 1A-3 (i+1A3)32 = 1A3, 3A23m = 1A3, 3m3-2/m = 1A-3 (=i+1A3), 3A2, 3m-c+a1+b+c=120=90=90a1c0+a2+a3a2a3 a1= (a2b)=a3 c0 1= 2= 3 =120 = = 906 = 1A66- = 1A-6 (=1A3 + m)6/m = I, 1A6, m622 = 1A6, 6A26mm = 1A6, 6m6-m2 = 1A-6 (=1A3+m), 3A2, 3m6/m 2/m 2/m = I, 1A6, 6A2, 7m-c+a1+b+c=120=90=90a1c0+a2+a3ba2a3 () a = b = ca = = = 90-b-c-a+a+b+c=90=90=90c0b0a06/m2/m2/m = i, 1A6, 6A2, 7m23 = 3A2, 4A32/m3 = 3A2, 3m, 4A3432 = 3A4, 4A3, 6A24 3m = 3A4, 4A3, 6m4/m32/m = 3A4, 4A3, 6A2, 9m_____

90 i , , . i. , .

m.

, . 90 .18018012012012090909090606060606060 (2) (3) (4) (6) 360, , . ( ) , . . . -.4im 21801804909090903120120120- (1, 2, 3, 4, 6) .

1, 2, 3, 4 6._ _ _ _ _i 11_m2 2_ 5, 7

5 !

Al-Pd-Re 5 Roger Penrose: - (1984)

12345 () : 6, 4, 3, 2, 1, 6, 4, 3, 2 = m, 1 = i_ _ _ _ _ . 10 , 1. : (1, 2, 3, 4 6)

- (1, 2, 3, 4 6)

, 32 , 32 ._ _ _ _ _ 32 (-) 32 point groups

32 32 - ( )

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Bravais .

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Bravais

, (primitive cells), ( ), ( ).

.

Bravais:

, ( 8 ). , 8 1/8 = 1 , . Bravais:

14 : .

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HRTEM

- (space groups) 32 - (point groups) 14 Bravais 230 - (space groups). () :

: : : 230 -

32 (crystal class) - (space group), 230. . .1 ( Hay) +2+csp+b+a+1+2+1+2+12 ( Bravais) ( ) AABCAABC

A= = = 1.4466

55

B= = = 1.0665

542

C= = = 0.8063

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