EBK PRINCIPLES OF ELECTRIC CIRCUITS
10th Edition
ISBN: 9780134880068
Author: Buchla
Publisher: VST
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Finding crystallographic direction
Z
pt. 2
head
pt. 1:
៩
Example 2:
pt. 1 x₁ = a, y₁ = b/2, z₁ = 0
pt. 2 x2=-a, y₂ = b,
Z₂ = c
-a-a b-b/2
c-0
a
b c
tail
=> -2, 1/2, 1
Multiplying by 2 to eliminate the fraction
-4,1,2 => [412] where the overbar represents a
negative index
families of directions
Crystallographic planes
Crystallographic planes are denoted by Miller indices.
5b
Algorithm for Miller indices
1. Read off intercepts of plane with axes in
terms of a, b, c
2. Take reciprocals of intercepts
3. Reduce to smallest integer values
4. Enclose in parentheses, no commas.
353
1/3 1/5 1/3
535
(535)
In the cubic system, a plane and a
direction with the same indices are
orthogonal. E.g. [100] direction is
perpendicular to (100) plane.
Correspondingly, [123] direction is
perpendicular to (123) plane.
[2,3,3]
Plane intercepts axes at 3a, 2b, 2c
2
11 1
Reciprocal numbers are:
3'2'2
b.
Indices of the plane (Miller): (2,3,3)
2
a
Indices of the direction: [2,3,3]
X
(200)
(100)
(110)
(111)
(100)
Indices of crystallographic plane can be found from cross product of indices of
any two non-parallel directions in this plane.
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