, , , . .
, , , , .
, . , , .
:
1) .
2) , .
.1.10. [[ mnp ]].
. 1.10 . m, n, p R x, y, z. , . .
, - . , , . [[ mnp ]] [[ ]].
x¢=x+ m a
y¢=y+ n b (1.1)
z¢=z+ p c
, , , , m, n, p.
.1.11. [ m n p ].
, m, n, p , (.1.11). , R
R= m a+ n b+ p c. (1.2)
m, n, p .
1) , .
2) , m, n, p.
3) , .. .
, , , , , [100], [111], [102]. (.1.11).
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[ mnp ], , . , [ mnp ] x, y, z :
(1.3)
[ m 1 n 1 p 1] [ m 2 n 2 p 2]. j :
cos j =cos a 1×cos a2 + cos b1 ×cos b2 + cos g1 ×cos g2 (1.4)
(1.3) cos j (1.4),
(1.5)
. , , (.1.12). .
.1.12. (hkl).
A, B, C.
+ + = G (1.6)
: G ; x = ma, y = nb, z = pc - . m = x/a, n = y/b, p = z/c,
= G
a/A, b/B, c/C ,
: : = h: k: l (1.7)
R ( , ), : R = h, R = k, R = l : m(h/R) + n(k/R) + p(l/R) = G mh + nk + pl = N, N=GR .
N 1. , , , mh + nk + pl = 0, :
mh + nk + pl = 1 (1.8)
h, k, l, , . , . h,k,l , . (h k l) .. [[000]].
, .
1). : a, b/2, c/3 .. A=a, B=b/2, C=c/3. . , , ( ). , .. (1,2,3).
2). : , : a/2, b, c (2,1,1).
, , .
: (2,0,1). , : 1/2, ¥, 1. .
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, , ( ). h, k, l , . (111), (222), (333) (.1.12). , , , -, , -, , .. (111).
- , , (H, K, L),
H=qh; K=qk; L=ql, (1.9)
q - .
, (333) .1.12. , (hkl) (HKL) , .
, . . , (100), (010), (001), (0 0), ( 00), (00 ) - 6 . (110) 12 ..
. , (100) 6. .1.1
1.1
hkl h¹k¹l | hk 0 h¹k | hkl h=k | ||||
.
4- . (hkil). , , - (.1.13). x, y, u , a, b, d ., () z, x y. , , , 120. , , .
, , . i . :
i = (h + k) (1.10)
. , . , (.1.13) . (100), (010), ( ) .. . . 1, 2, 3 (.1.13) ( ), ( ), ( ) .. , .
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. 1.13. .