, , , 0.5 3.0 Å, .
( ) a0 . . , ( ). .
, , (cosa - cosa0), , (h) l, . 2a.
(cosa - cosa0) = hl (1)
, h, h £ l/2, .
, b, . , , .. :
(cosa - cosa0) = hl (2)
b(cosb - cosb0) = kl
, . :
(cosa - cosa0) = hl
b(cosb - cosb0) = kl (3)
c(cosg - cosg0) = ll,
, b, , ; h, k, l , 0, 1, 2,. , , a, b, g a0, b0, g0 .
(1), (2), (3) -, - .
(3) , (x, y, z). (3) h, k, l , . , (. 5), , , b, , . , ?
. 5. .
(3) , b, . a0, b0, g0 , , l . , , : a, b g, . . a, b, g . , , a, b, g :
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cos2a + cos2b + cos2g = 1. (4)
cos2a + cos2b + cos2g = (5)
, 4 , . , : . , .. , , a, b, g, - (3). , :
1) ;
2) ;
3) .
, . (3) (4) (5) , .
a0, b0, g0, .
, , , 2- , , .. (~10-3 ) ( ), . , , (3), .
, , . () , , ( ). . d , , (hkl), . (hkl) ( ) , h , b k , l . a = b = c. . . s, p, q, 1. h = 1/s, k = 1/p, l = 1/q (. 6).
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: (- ) ( ).
2 000, ½ ½ ½. . . , 8 , , .
. 6. (hkl): h = 1/s, k = 1/p, l = 1/q. |
8 , , 8 , , , 1/8 . 8, , , , . ½ ½ ½ .
) | ) |
. 7. (110) (111) () () .
4 . , . 6 , , , 3 ½ ½ 0, ½ 0 ½ 0 ½ ½ (. 7).
, .. . , . , , .
, , . , Index.exe, BASA.
, , . ( 10-5 ) . , , . , , , . d, , ( ), θ. D , , (. . 8) D = ab + bc = 2d×sinθ. , D , . . :
2dsinθ = nλ, (6)
n = 1, 2, 3- .
. 8. - .
(6) . . . (6) . d/n = l/2sinθ, κ l , θ . (6) n , n- d d/n. d/n = dhkl, (hkl) , (hkl) n - .
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(. 9), - . : ~1011. (I) d1 . . 9, 2θ1 -. - , . (, I'), d1, - 2θ1, , -. I' . , - , d1 ,
4θ1, , -, .
. 9. .
, , , ( d (6)). 4θ, .
, .
, , , (. 10).
, , .
. 10. , .
, : (4) (6), ( , ). . , dhkl, (6), * . JCPDS (International Centre of Powder Diffraction Data) , .
, , . , ..
a = b = c = d(h2+k2+l2)1/2 (7).
(7) . . ,
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, (8)
:
. (9)
, , 90.
, a, b, c α, β, γ, V , N, , :
ρ = Nm/V, (10)
m (m = A ... = 1.6610-24 , ( ), ... ), V = 310-24 3.
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* : .