where h A and h B are two diffracting angles associated with the principal diffracting
planes h A k A l A
f
gand h B k B l B
f
g , respectively.
Case I From Table 9.1, we observe that the first two principal diffracting planes for
bcc structure are (110) and (200). Substituting the indices of these planes in the
above equation, we obtain
sin
2
h A
sin
2
h B
¼
1
2
þ 1
2
þ 0
2
2 2 þ 0
2
þ 0
2
¼ 0:5
Thus, if the crystal structure of the unknown cubic metal is bcc, the ratio of
sin
2
h values corresponding to the two principal diffracting planes will be 0.5.
Case II From Table 9.1, we observe that the first two principal diffracting planes
for fcc structure are (111) and (200). Substituting the indices of these planes in the
above equation, we obtain
Table 9.1 Miller indices of diffracting planes for cubic structures
P
h
2 þ k
2 þ l
2
À
Á
{hkl} planes
h
2 þ k
2 þ l
2
À
Á
Diffracting {hkl} planes
sc
bcc
fcc
dc
1
{100}
1
2 þ 0
2 þ 0
2
ð
Þ
100
–
–
–
2
{110}
1
2 þ 1
2 þ 0
2
ð
Þ
110
110
–
–
3
{111}
1
2 þ 1
2 þ 1
2
ð
Þ
111
–
111
111
4
{200}
2
2 þ 0
2 þ 0
2
ð
Þ
200
200
200
–
5
{210}
2
2 þ 1
2 þ 0
2
ð
Þ
210
–
–
–
6
{211}
2
2 þ 1
2 þ 1
2
ð
Þ
211
211
–
–
7
…
…
…
…
…
…
8
{220}
2
2 þ 2
2 þ 0
2
ð
Þ
220
220
220
220
9
{221}
2
2 þ 2
2 þ 1
2
ð
Þ
221
–
–
–
10
{310}
3
2 þ 1
2 þ 0
2
ð
Þ
310
310
–
–
11
{311}
3
2 þ 1
2 þ 1
2
ð
Þ
311
–
311
311
12
{222}
2
2 þ 2
2 þ 2
2
ð
Þ
222
222
222
–
13
{320}
3
2 þ 2
2 þ 0
2
ð
Þ
320
–
–
–
14
{321}
3
2 þ 2
2 þ 1
2
ð
Þ
321
321
–
–
15
…
…
…
…
…
…
16
{400}
4
2 þ 0
2 þ 0
2
ð
Þ
400
400
400
400
17
{410}
4
2 þ 1
2 þ 0
2
ð
Þ
410
–
–
–
18
{411}
4
2 þ 1
2 þ 1
2
ð
Þ
411
411
–
–
19
{331}
3
2 þ 3
2 þ 1
2
ð
Þ
331
–
331
331
20
{420}
4
2 þ 2
2 þ 0
2
ð
Þ
420
420
420
–
338
9 Determination of Crystal Structure Parameters