, , , , .
, , . a×cosa - a×cosa0 (.2.7). , , S0 S. 1, S0 - , S - . a×cos a×1 - a×cosa0×1 = (a [ S - S0 ]). , , ..
(a [ S - S0 ]) = ml. (2.24 )
, :
(b [ S - S0 ]) = nl, (c [ S - S0) = pl. (2.24 )
l, :
(2.25)
- m, n p, H, ,
H = m a *+ n b * + p c *. (2.26)
, a, b ,
(2.27)
(2.26) (2.27), :
(S - S0)/l = H (2.28)
3 . , (2.28) a, b c .
. . , (. 2.10).
.2.10. .
. , - O, , (. ). , . . .2.10 . , S0. , . ( O) S0 /l, - A. 1/l, .. | S0 |=1. A 1/l. . .
, , , . , , M OAM. OA + AM = OM. OM , H, OA = S0 /l
|
|
AM S0 /l = H (2.29)
(2.28) , AM, 1/l, S. , :
S /l S0 /l = H (2.30)
. . , . , , S /l. , a, b, c l , , . , , , , .. , a, b, c. , , . , 2/l. l . H, , . , ( l£ 2d),
| H |< 2/l. (2.31)
l=2Å, | H |=1/d <1Å. , d >1Å 1 Å, .
[[ HKL ]] . (hkl) H (.2.11).
. 2.11. .
, (hkl). H (hkl), OAM, . , S0 (hkl), (hkl) . (hkl) , , .
, , . , . - . , , .
-
|
|
, , d, .. (.2.12).
. 2.12. - .
S0 q (hkl), S q (hkl). 1, 2, 3... (hkl). , , 1- 2, 3 .. . , nl. 2.12. AB + BC = 2AB = 2d sinq. , ,
2d sinq = nl, (2.32)
d - , n=1, 2, 3....
-. q, , ; n - .
- () . . , . . ,
nl/2d = sinq £ 1 nl£2d. (2.33)
. - n, , , .
- (2.32) , n,
2(dhkl / n) sinq = l. (2.34)
dhkl / n , (HKL) . , :
dhkl / n=dHKL, (2.35)
H, K, L - .
, , , , , . p, h=1/pa=1/pdhkl
H= 1/pdHKL=n/dhkl H= nh.
= nk,
L=nl. (2.36)
H, K, L . (HKL) - :
2dHKL×sinq=l. (2.37)
. ..
(2.37), , (HKL), ( ) n. n n .
, (001) d001 4l. 2d001×sinq=4l (2d001/4)sinq=l. (001) , d/4=d¢ 2d004×sinq=l, d¢=d004. , (001) , 4l, (004) l. , 4.