Determine the Miller-Bravais direction indices of the basal plane of the
The Miller-Bravais direction indices of the basal plane of the vectors originating at the center of the lower basal plane and existing at the midpoints between the principal planer axes.
Answer to Problem 56AAP
The Miller-Bravais Direction indices of the vector OA is
The Miller-Bravais Direction indices of the vector OB is
The Miller-Bravais Direction indices of the vector OC is
The Miller-Bravais Direction indices of the vector OD is
The Miller-Bravais Direction indices of the vector OE is
The Miller-Bravais Direction indices of the vector OF is
Explanation of Solution
The coordinates of intercept
Directions OA is
Directions OB is
Directions OC is
Directions OD is
Directions OE is
and directions OF is
Conclusion:
Direction vector originating at the centre of the lower basal plane and ending at the end point of the upper basal plane for a Hexagonal closed packed unit cell.
Figure below represent the Hexagonal closed packed unit cell.
Figure-(1)
In the figure-(1) closed packing is Hexagonal closed packing and the direction vector of the planes are shown in figure-1. Here, the originating vector at the centre of the lower basal plane and ending at the end point of the upper basal plane for a Hexagonal closed packed unit cell is defined in the figure-(1).
Miller-Bravais direction Indices for the directions is tabulated below.
Direction vectors | Co-ordinates of intercepts | Reciprocal of intercept | Miller-Bravais Direction indices |
OA | |||
OB | |||
OC | |||
OD | |||
OE | |||
OF |
Thus, the Miller-Bravais Direction indices of the vector OA is
Thus, the Miller-Bravais Direction indices of the vector OB is
Thus, the Miller-Bravais Direction indices of the vector OC is
Thus, the Miller-Bravais Direction indices of the vector OD is
Thus, the Miller-Bravais Direction indices of the vector OE is
The Miller-Bravais Direction indices of the vector OF is
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Chapter 3 Solutions
Foundations of Materials Science and Engineering
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