Crystal Ography
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2.1 , , , , , . . , , . .. , , . . , .. , . , , , , . , , , . (. 2.1).
. 2.1: () . .
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, . , , : 1) : , . 2) : , . : , . , , :
, , . 3) : ( ) ( ), . 4) : (, ). , , . , , ( ).
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(, ) . , . , . , . , , , , , . , . Hay, 1784, , . , , , (. 3 ). , , , , .. , . Hay, , , .
- , : , . , , , , , . , . ,
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, . (. 2.2,). ( ) . , , . , ( , m ) - .
. 2.2: (m, ). . 2.2: ( .) , .
, . , . , , , . (. 2.3). . , , . , . , - , 2/ . , 2. (. 2.4).
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. 2.3: (i). .
. 2.4: , 2, 3, 4 6 , . , . , 5 6. ( ) () . , 1.
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1: . (: 1, 2, 3, 4, 6 ) , .
: 6 . 2 = 60 6
: 4 .
2 = 90 4
: 3 . 2 = 120 3
: 2 .
2 = 180 2
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(. 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
.
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()
()
. 2.6: () 1 ( 1 ), 360 . () 2 ( 2 ) 180 . (m) 2 .
, , , . , . , (low symmetry). , (high symmetry). , : 6 4, 3 ... , , .
. 2.7: ( ). , , .
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, , . 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
.
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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 . (, ) , . , . , , , , .
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. 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
