现代结构分析方法-8.ppt

倒易点阵、正点阵与衍射
S0/l= k0
S/l= k
ghkl
(hkl)
000
相机长度
Rhkl
b
a
正交点阵沿c轴投影
a
b
c
a
b
c
入射束
d100
d110
7 衍射图标定相;取向 单晶衍射图的产生与标定
When is q small (electron diffraction), Rd=lL=diffraction constant, the reflection sphere cuts a 2D reciprocal plane.
Indexing: the plane normal [uvw] and at least one low index spot (hkl) (normally two spots), with hu+kv+lw=0.
S0/l= k0
S/l= k
ghkl
(hkl)
000
相机长度
Rhkl
[-101]
(101)
(010)
Plot the fcc [110] diffraction pattern
1) The zone axis [uvw] is perpendicular to all the plane indices (hkl) so that hu+kv+lw=0.
2) Distinctions of an fcc lattice: all even or odd (like 111, 200, 311, 220, etc.)
3) R1+R2=R3, and R1×R2=[UVW], R1 and R2 being the two short vectors
4) Fix R1 (if a and Ll are given then R1 is a known value) and draw R2, cosR1^R2=(h1*h2+k1*k2+l1*l2)/ (N1N2); R12/R22=N1/N2
5) All the other spots are determined by n1*R1+n2*R2=Rn
h1k1l1
h2k2l2
h3k3l3
R1
R2
h1k1l1=
-111
N
hkl
cp
bcc
fcc
1
100
100
2
110
110
110
3
111
111
111
4
200
200
200
200
5
210
210
6
211
211
211
8
220
220
220
220
º
h2k2l2=
1-11
h3k3l3=002
indexing using PDF files
a) Choose three spots such as R3=h3k3l3, R1=h1k1l1, R2=h2k2l2.
b) di=Ll/Ri, d1=Ll/R1= d2= {111}, R3=Ll/R3=3/={200}.
c) h3k3l3= h1k1l1 + h2k2l2: {111}+{111}={200}(111)+(1-1-1)=(200),
(111)^(1-1-1)=º
d) [uvw] = R1×R2= R1×R3= R3×R2=[01-1]
h1k1l1
h2k2l2
h3k3l3
[uvw]
R1
R2
R1=R2=, R1^R2=º. Ll= nm*mm.
indexing using PDF files
a) Choose three spots such as R3=h3k3l3, R1=h1k1l1, R2=h2k2l2.
b) di=Ll/Ri, d1=Ll/R1= {200}, R2 = R3=Ll/R2={311}.
c) h3k3l3= h1k1l1 + h2k2l2: {200}+{311}={311}(200)+(-113)=(113),
(200)^(-113)=º
d) [uvw] = R1×R2= R1×R3= R3×R2=[0-31]
R1
R2
R3
R1= mm, R2 = R3= mm, R1^R2=º. Ll= nm*mm.
PARAMETERS
A= B= C= Å
AF= BT= GM=
NUVW= 3 NSY= 1 NL= 1
SY: 1-CUBIC; 2-TETRA; 3-ORTH; 4-HEX;