Materials Science: Unit I: Crystallography
Directions in Crystal
It is always useful to have a convention or standardized procedure to specify the directions in a crystal.
DIRECTIONS IN CRYSTAL It is always useful to have a convention or standardized procedure to specify the directions in a crystal. The procedure of finding the directions inside the crystal is explained below. 1. Consider any lattice point that lies on the line as origin. 2. Write down the position vector of the next nearest point on the line in terms of the fundamental translation vector 3. Now the components of position vector Let us apply this procedure to find the directions of OP, OQ and OR of an orthorhombic unit cell (a ≠ b ≠ c; α = β = γ = 90°) in Figure 1.26 taking 'O' as origin. Position vector of OP = ⸫ r1 = 1; r2 = 1; r3 = 1 ⸫ Direction of OP is represented by [111] Position vector of OQ = ⸫ r1 = 1; r2 = 0; r3 = 0 ⸫ Direction of OP is represented by [100] Position vector of OR = ⸫ r1 = 1; r2 = 0; r3 = 1 ⸫ Direction of OP is represented by [101] It should be understood that the directions [222], [333], [444], [n r1 n r2 n r3] will all coincide with [1 1 1]. In such cases the lowest combination of integers i.e., [1 1 1] is used to specify the direction. If any of the integers is negative, for example - 3, it should be written as 3 which is read 3 bar. Given three integers of a direction, a family of directions with different possible combinations of them, both positive and negative, is represented with brackets of the type < >. For example, a family of directions such as [132], [312], [123], 
of the unit cell of the crystal, say, 
along the three directions of a, b, c are r1, r2, r3 respectively. Then the crystal direction is denoted by [r1 r2 r3].
(a) Direction of OP
(b) Direction of OQ
(c) Direction of OR
etc., is represented by <132>.
Materials Science: Unit I: Crystallography : Tag: : - Directions in Crystal
Materials Science: Unit I: Crystallography
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Materials Science
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