MCE 230_ F10_lec_7 - Multiply by 2   1 2 z y x a c b...

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MCE 230 – Materials Science Fall 2010 Lecture - 7
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Crystalline Structure
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Crystallographic Directions The length of the vector in terms of the lattice parameters (a, b, c) If not integer: multiply by a number to get the smallest integer values. If negative: use bar on top If not passing through the origin: translate and maintain parallelism
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Crystallographic Directions z y x O Direction : vector passing through the origin [u v w] u: projection along the x-axis v: projection along the y axis w: projection along the z axis
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z y x a c b If the direction is not passing through the origin: translate to the origin and maintain parallelism. 1/2   1 0 2 Head - Tail H (1,1,0) T (0,1,1/2) (1,1,0) - (0,1,1/2) = (1,0,-1/2)
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Unformatted text preview: Multiply by 2   1 2 z y x a c b Head - Tail H (1,0,1) T (0,1,1) (1,0,1) - (0,1,1) = (1,-1,0)   1 1 Directional indices for hexagonal unit cell • Find projections for a1 axis (u’), a2 axis (v’) and z axis (w’) u’ = 1, v’=1 and w’=1 • Use the following relations: u= 1/3 (2u’- v’) v= 1/3 (2v’- u’) t= - (u + v) w= w’ • u=1/3 , v=1/3, t=-2/3 & w=1 • multiply by a number to get smallest integer --- u=1, v=1, t=-2 & w=3 • the direction is [uvtw] -------- [1123] u’ = 1 , v’= 1 & w’=1/3 u= 1/3(2*1-1) = 1/3 Multiply by 3   1 2 11 v= 1/3(2*1-1) = 1/3 t= -(1/3+1/3) = -2/3 1/3c...
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This note was uploaded on 12/05/2010 for the course MECHANICAL mce 230 taught by Professor Bassildrass during the Fall '10 term at American University of Sharjah.

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MCE 230_ F10_lec_7 - Multiply by 2   1 2 z y x a c b...

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