1. http://en.wikipedia.org/wiki/Solid_state_physics
http://www.msm.cam.ac.uk/doitpoms/tlplib/miller
_indices/intro.php
: http://www.matter.org.uk/diffraction/sitemap.htm
.
:
1

2. .
.
A(3,0,0),B(0,2,0),C(0,0,1) A,B,C
( )
. (3,2,1)
:
.1
a, b , c
2

3. 2
(hkl )
.
x=3a ,y=2b,z=1c
x/a=3,y/b=2,z/c=1
(6) 1/ 3:1/ 2:1/ 1
6 3 2 2/ 6:3/ 6:6/ 6
.(236) h=2,k=3,l=6
.
:
( y k
( k )
3

4. 4

5. 5

6. :
Miller Indices
All lattice planes and lattice
directions are described by a
mathematical description known
as a Miller Index. This allows
the specification,
investigation, and discussion of
specific planes and directions
of a crystal. In the cubic
lattice system, the direction
[hkl] defines a vector direction
normal to surface of a
particular plane or facet. The
Miller Indices h,k,l are defined
as follows:
6

7. . A,B,C .1
. 1/A,1/ B,1/ C .2
D .3
.
h=D/A , k=D/ B , l=D/ C : .4
A=1/ 2 ,B=2 , C=1/ 3: 3:
1/A:1/ B:1/ C=1/ 1/ 2:1/ 2:1/ 1/ 3=2/ 1:1/ 2:3/ 1 :
D=2 2
(hkl)=(416) h=D/A=4 , k=D/ B=1 , l=D/ C=6
7

8. [hkl]
:
8

9. 9

10. 10

11. {110} {hkl}
[011],[01-1],[-101],[101],[10-1],[110],[-110],[-1-10],[-
.10-1],[1-10]
.10-1],[1-10]
<hkl>
: <1
<1 1 0 >
[ -1 0 1 ] ,[ 1 0 -1 ] ,[ 1 0 1 ] ,[ 1 -1 0 ] ,[ -1 1 0 ] ,[ 1 1 0 ]
11

12. :
h1h2 k1k2 l1l 2
cos 1 1
( h12 k12 2 2 2
l ) ( h2
1
2
k2 2 2
l )
2
12

13. d
: (hkl)
1
d
h2 k2 l2
a2 b2 c2
when a b c then
a
d
h2 k2 l2
13

14. ( x1,x2,x3,z
x1,x2,x3
z 120
-
(1,2,3,4)
D=12 (1/ 1:1/ 2:1/ 3:1/ 4)
(hkli)=(12,6,4,3)
14

15. 15