Engineering Physics

3.2 Distance of separation between successive hkl planes

The separation between successive parallel planes in rectangular axes crystal system can be extracted easily. Let us consider a rectangular [cartesian] coordinate system with origin ‘0’at one of the lattice points. Let (hkl) be the Miller indices of a plane ABC, which makes intercepts OA, OB and OC on X, Y and Z axes, respectively as shown Fig 3.4. A normal to this plane from the origin passes through a point N in the plane ABC, such that ON = d₁. This normal makes α′, β′ and γ′ angles with X, Y and Z-axes, respectively. Since the plane segments ‘a’ into ‘h’ equal parts, b into k equal parts and c into l equal parts, then the intercepts OA, OB and OC are such that:

where a, b, c are ...