sin
2
h A
sin
2
h B
¼
1
2
þ 1
2
þ 1
2
2 2 þ 0
2
þ 0
2
¼ 0:75
Thus, if the crystal structure of the unknown cubic metal is fcc, the ratio of sin
2
h
values corresponding to the two principal diffracting planes will be 0.75.
(b) X-ray Diffraction Methods
(i) Powder Method
The Bragg angle h and the distance between the pair of arcs S on the powder pattern
(Fig. 9.1) are related through
h ¼
S
4
The extinction rules for cubic crystals are provided in Table 9.2.
From these extinction rules, it is possible to derive the ratios of ðh
2
þ k
2
þ l
2
Þ
for allowed reflections in the following cubic lattices. They are given as:
Fig. 9.1 a Relation between Bragg angle and linear distance between pair of arcs b Schematic
powder pattern
9.1 Steps in Crystal Structure Determinations
339
2
h A
sin
2
h B
¼
1
2
þ 1
2
þ 1
2
2 2 þ 0
2
þ 0
2
¼ 0:75
Thus, if the crystal structure of the unknown cubic metal is fcc, the ratio of sin
2
h
values corresponding to the two principal diffracting planes will be 0.75.
(b) X-ray Diffraction Methods
(i) Powder Method
The Bragg angle h and the distance between the pair of arcs S on the powder pattern
(Fig. 9.1) are related through
h ¼
S
4
The extinction rules for cubic crystals are provided in Table 9.2.
From these extinction rules, it is possible to derive the ratios of ðh
2
þ k
2
þ l
2
Þ
for allowed reflections in the following cubic lattices. They are given as:
Fig. 9.1 a Relation between Bragg angle and linear distance between pair of arcs b Schematic
powder pattern
9.1 Steps in Crystal Structure Determinations
339