Question

Problem 3 The primitive basis vectors of a direct lattice for body centered cubic system are given by: $vec{a} = -frac{a}{2}hat{i} + frac{a}{2}hat{j} + frac{a}{2}hat{k}$ $vec{b} = frac{a}{2}hat{i} - frac{a}{2}hat{j} + frac{a}{2}hat{k}$ $vec{c} = frac{a}{2}hat{i} + frac{a}{2}hat{j} - frac{a}{2}hat{k}$ a) Find the volume of the primitive cell using the vector product ($V = |vec{a} cdot (vec{b} imes vec{c})|$)? b) Find the volume of the Unit cell using your answer of part (a)? c) Find the reciprocal lattice vectors $vec{a}^, vec{b}^ and vec{c}^*$? d) Find the reciprocal lattice vector $G_{hkl}$ which is perpendicular to the (220) plane? e) Find the d-spacing for the (220) planes using your answer of part (d)?

          Problem 3
The primitive basis vectors of a direct lattice for body centered cubic system are given by:
$vec{a} = -frac{a}{2}hat{i} + frac{a}{2}hat{j} + frac{a}{2}hat{k}$
$vec{b} = frac{a}{2}hat{i} - frac{a}{2}hat{j} + frac{a}{2}hat{k}$
$vec{c} = frac{a}{2}hat{i} + frac{a}{2}hat{j} - frac{a}{2}hat{k}$
a) Find the volume of the primitive cell using the vector product ($V = |vec{a} cdot (vec{b} 	imes vec{c})|$)?
b) Find the volume of the Unit cell using your answer of part (a)?
c) Find the reciprocal lattice vectors $vec{a}^*, vec{b}^* and vec{c}^*$?
d) Find the reciprocal lattice vector $G_{hkl}$ which is perpendicular to the (220) plane?
e) Find the d-spacing for the (220) planes using your answer of part (d)?

$Problem 3 The primitive basis vectors of a direct lattice for body centered cubic system are given by: veca = -fraca2hati + fraca2hatj + fraca2hatk vecb = fraca2hati - fraca2hatj + fraca2hatk vecc = fraca2hati + fraca2hatj - fraca2hatk a) Find the volume of the primitive cell using the vector product (V = |veca cdot (vecb imes vecc)|)? b) Find the volume of the Unit cell using your answer of part (a)? c) Find the reciprocal lattice vectors veca^*, vecb^* and vecc^*? d) Find the reciprocal lattice vector Ghkl which is perpendicular to the (220) plane? e) Find the d-spacing for the (220) planes using your answer of part (d)?$

Added by John C.

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