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MTLE2100 Structure of Engineering Materials,
Homework #5
Answer
1.
Predict the xray diffraction peak positions (2
θ
) for the
first four (smallest angle) peaks corresponding to (001),
(100), (101) and (110) for a tetragonal crystal with a =
2.300A, c= 2.500A,
λ
= 1.54A.
d
hkl
= a/
√
h
2
+ k
2
+l
2
(a/c)
2
d
hkl
= a/
√
h
2
+ k
2
+l
2
(a/c)
2
sin
θ
2
θ
(
°
)
(001)
2.300/(a/c)
=2.500
Å
0.308
35.9
(100)
2.300/
√
1
2
=2.300
Å
0.3348
39.1
(101)
2.300/
√
1
2
+ 1
2
(a/c)
2
=1.693
Å
0.4549
54.1
(110)
2.300/
√
1
2
+ 1
2
= 1.626
Å
0.474
56.5
2.
Transmitted intensity of xray is given by
I = I
0
exp (
μ
t)
and transmittance is given by I/I
0
= exp (
μ
t), where t is
thickness of the specimen and
μ
is the linear absorption
coefficient.
Scattered intensity, I
s
, by small inclusions in a solid
is proportional to both thickness and transmission, i.e.
I
s
= I
0
k t exp (
μ
t)
where k is a proportionality constant.
Obtain the scattered intensity normalized by the maximum
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 Spring '08
 Tomozawa

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