Abstract
A simplified method of calculating the diffraction patterns of crystals showing mistake broadening is outlined, and used to correct three results published by Wilson in 1943. Wilson’s model 3 (mistakes on {110} planes) is extended in the light of probable differences of the energy of interfaces between domains of different types. The apparent particle sizes obtained, when differences in interfacial energy are ignored, are:
formistakes
on
{
100
}
planes
3
N
1
2
/
2
(
h
+
k
+
l
)
δ
;
formistakes
on
{
110
}
planes
3
(
2
N
)
1
2
/
4
(
2
h
+
k
)
δ
;
formistakes
on
{
111
}
planes
3
(
3
N
)
1
2
/
8
h
δ
if
h
≥
k
+
l
,
3
(
3
N
)
1
2
/
4
(
h
+
k
+
l
)
δ
if
h
<
k
+
l
;
where
δ
is the probability of a mistake per unit length,
h, k, l
are the positive values of the indices of reflexion arranged in the order
h
≥
k
≥ 1, and
N
=
h
2
+
k
2
+
l
2
. When differences in interfacial energy are taken into account the apparent particle size for mistakes on {100} planes becomes
2
N
1
2
/
{
2
(
h
+
k
+
l
−
u
)
δ
′
+
(
h
+
k
+
l
+
u
)
δ
′
′
}
,
where
u
is the impaired index, and that for mistakes on {110} planes becomes
(
2
N
)
1
2
/
{
4
h
δ
′
+
2
(
h
+
k
)
δ
′
′
}
when
(
2
N
)
1
2
/
{
2
(
h
+
k
)
δ
′
+
(
3
h
+
k
)
δ
′
′
}
when
k
or
l
is the unpaired index. All {111} interfaces have the same energy in AuCu
3
, so the expressions for mistakes on {111} planes are not altered.
Reference10 articles.
1. Bragg W. L. 1940 Proc. Phys.
2. Hirabayashi M. 1959 Soc.52 105-109.
3. J .Phys. Soc. Ja 14 262-273.
4. On the Anti-Phase Domain Structure of the Ordered Phase CuAu3
5. Phys;Lifschitz I. M.;Z. Sowjet.,1937
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