Chemistry Reference
In-Depth Information
t
s
n
s
s
0
z
h
s
0
h
z
d
V
z
d
V
t
n
z
(
a
)
(
b
)
FIGURE 6.13 Absorption correction of flat slab: (a) reflection; (b) transmission.
distance z from the sample surface is given as
z
1
cos h
þ
1
cos z
t ¼
ð6
:
58Þ
The transmission coefficient is given as [17,32]
1
cos h
þ
1
cos z
1 exp
mt
A ¼
ð6
:
59Þ
cos z
cos h
þ1
m
where h is the angle between the incident beam and the normal of the sample surface
and z is the angle between the diffracted beam and the sample normal. In absorption
correction for conventional diffractometers, the incident beam, sample normal, and
diffracted beam are typically within the same plane. It is common in the absorption
equation to use sin(uw) in place of cosh and sin(u þ w) in place of cos z, where w is
the tilt angle which reduces the incident angle to a value below the Bragg angle u.For
two-dimensional X-ray diffraction, the incident beam, sample normal and diffracted
beam are not necessarily in the same plane, so it is more convenient to use cosh and
cos z in the equation. For a thick plate with negligible transmission, the above
equation becomes
cos h
m cos hþ cos z
ð6
:
60Þ
A ¼
ð
Þ
For two-dimensional X-ray diffraction, there is a single incident beam direction at
a time, but various diffracted beam directions simultaneously. The unit vectors of the
incident beam, diffracted incident beam and the sample normal, respectively, are
given in Chapter 2 as
2
3
2
3
2
3
1
0
0
cos 2u
sin 2u sin g
sin 2u cos g
sin v cos c
cos v cos c
sin c
4
5
; s ¼
4
5
;
4
5
s
0
¼
and n ¼
ð6
:
61Þ
Then we have
cos h ¼s
0
n ¼ sin v cos c
ð6
:
62Þ
