Preparing the datasheet in tabular form, we have
Line
2h(°)
h(°)
sin h
sin
2 h
Common factor (c.f)
N ¼
sin
2 h
c:f
hkl
1
38.2
19.1
0.327
0.107
3
111
2
44.4
22.2
0.378
0.143
4
200
3
64.6
32.3
0.534
0.285
8
220
4
77.4
38.7
0.625
0.390
0.0356
11
311
5
81.6
40.8
0.653
0.426
12
222
6
98.0
49.0
0.755
0.570
16
400
7
110.6
55.3
0.822
0.676
19
331
8
115.0
57.5
0.843
0.711
20
420
From the values of N, the unknown cubic metal is found to have fcc structure.
All hkl values are provided in the last column of the table.
Example 2 Determine the (hkl) and 2h values of the first four lines on the powder
patterns obtained by using CuKa radiation of wavelength 1.54 Å corresponding to a
simple cubic structure with a = 4 Å.
Solution Given: k = 1.54 Å, simple cubic structure with a = 4 Å, (hkl) and 2h
values of the first four lines = ?
We know that the Bragg’s equation is given by
2d sin h ¼ nk
ðiÞ
For a cubic structure, the relationship between interplanar spacing “d” and lattice
parameter “a” is
Table 9.4 Datasheet in tabular form for determining hkl values
Line
h(°) = S/4
sin h
sin
2 h
Common factor (c.f)
N ¼
sin
2 h
c:f
(hkl)
1
2
3
…
Table 9.5 Datasheet in
tabular form for determining
lattice parameter a
Line
h (°)
d(Å)
N ¼
sin
2 h
c:f
ffiffiffiffi
N
p
a ¼ d
ffiffiffiffi
N
p
1
2
3
…
9.1 Steps in Crystal Structure Determinations
341