Crystallographic Directions • Cubic systems – directions are named based upon the projection of a vector from the origin of the crystal to another point in the cell.
• Conventionally, a right hand Cartesian coordinate system is used. – The chosen origin is arbitrary, but is always selected for the easiest solution to the problem.
Crystallographic Directions • Points within the lattice are written in the form h,k,l, where the three indices correspond to the fraction of the lattice parameters in the x,y,z direction.
Angle Between Directions • A=ui+vj+wk • B=u1i+v1j+w1k • A.B=|A||B|cosθ • Θ=cos{(uu1+vv1+ww1)/[(u2+v2+w2)1/2 (u12+v12+w12)1/2]} • Find angle between [011] and [001] directions
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Closed Pack Planes Highest density planes BCC FCC