Crystal Ography

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2.1 , , , , , . . , , . .. , , . . , .. , . , , , , . , , , . (. 2.1).

. 2.1: () . .

46

, . , , : 1) : , . 2) : , . : , . , , :

, , . 3) : ( ) ( ), . 4) : (, ). , , . , , ( ).

47

(, ) . , . , . , . , , , , , . , . Hay, 1784, , . , , , (. 3 ). , , , , .. , . Hay, , , .

- , : , . , , , , , . , . ,

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, . (. 2.2,). ( ) . , , . , ( , m ) - .

. 2.2: (m, ). . 2.2: ( .) , .

, . , . , , , . (. 2.3). . , , . , . , - , 2/ . , 2. (. 2.4).

49

. 2.3: (i). .

. 2.4: , 2, 3, 4 6 , . , . , 5 6. ( ) () . , 1.

50

1: . (: 1, 2, 3, 4, 6 ) , .

: 6 . 2 = 60 6

: 4 .

2 = 90 4

: 3 . 2 = 120 3

: 2 .

2 = 180 2

51

(. 2.5). , , , . , .. 2 , .

. 2.5: 4 , 4 2 , 5 (m).

, , . , , ( ). ( ). , , , , . , (proper rotation), , (improper rotation). (1, 2, 3, 4, 6) (m). 1/m, 2/m, 3/m, 4/m 6/m, . , 1 (. 2.6), 2 (. 2.6) , , 6 3/m. , 1 , 2 6

.

52

()

()

. 2.6: () 1 ( 1 ), 360 . () 2 ( 2 ) 180 . (m) 2 .

, , , . , . , (low symmetry). , (high symmetry). , : 6 4, 3 ... , , .

. 2.7: ( ). , , .

53

, , . 4, 3, 2, (. 2.7) . , , , . . . . , , , .. , , , , . , 6 , .

, , , 32 . 32 (point group). . , . , , : . , . . , . , , . ( 32 ) . . 32 . ,

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-, . , , . , 1. -, , . - - . . ( ), x, y, z a, b, c ( ) . . .. 4 . , 90 z, x, a , y, b = a (. 2.8). , , x y . , , z, . c/a z x y, a/b = 1, . , ( a=bc) .

. 2.8: (a, b = a, c) 4 (, z). . .1

.

55

32 ( , ) , . . , , (. 2). 1, , , . .

2:

. 2, , . , , - /3 a, b, (a+b).

1

, . , .

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32 , . , -. . , , , ( ), ( ) . , , , . . , , . : + = =

, . . . , , . (. 2.9). , , . , , . , . , ,

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, .

()

()

. 2.9: () () . ab.

. , 5 6 . 2.10 . (, ) , . , . , , , , .

58

. 2.10: . , , 2, 3, 4 6 , . , .

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, 1, T, a, b, c:T = n1a + n2b + n3c

ni . , a b c ab. () 2 . ( ) r r:r = r + T = r + n1a + n2b + n3c

( r, r ) () r, n1, n2, n3. , a, b, c . ( ), , ni. , . , a, b, c, , , r, r n1, n2, n3 (. . 2.11). , ni, , . (.. ) a, b, c, . , 90, , . , .

1 2

.

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. 2.11: c (n1, n2, n3) = (2, 3, 5). a, b, c . , . , . , .., , , , , (. , ). . , () . , , , (unit cell). a, b, c (. 2.12). , . 1, ( : primitive unit cell), . , a(bc). . 2.13. , , , . . , . () , 1/8 , .1

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. 2.12: . a, b, c a, b, c . , , . .

. 2.13: (Primitive) (Non-Primitive) . (P) . .

, 1 , . . , (, .) .

1

, , . , , , , .

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BRAVAIS , 2, , , , . . , , , , ( 32 ). ( ). , , .

(centering) (.. 4 , 1.10). , . , , 1. . , . , : (face centered, F): .

1

. , . , , (, ). - -.

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(body centered, I): . - (side base end- centered, C): . . (. ). , ( ) , .

. Bravais. 3 . 2.14 , , , .

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3 ( , ) () ( ) (P, R)* (I, F, C)*

() ()

a=b=c a===90 a=b ===90 ===90 a=b, ==90 =120 a=b=c ==90