How do you proved the interplanar spacing for hexagonal crystal?

Answer 1

To prove the interplanar spacing for a hexagonal crystal, you can use Bragg's law and the geometry of the hexagonal lattice. The interplanar spacing (d) for planes characterized by Miller indices ((h, k, l)) can be derived using the formula:

[ d = \frac{a}{\sqrt{3}} \cdot \frac{1}{\sqrt{h^2 + hk + k^2}} ]

for the basal planes where (l = 0), and

[ d = \frac{c}{l^2} ]

for planes perpendicular to the c-axis. Here, (a) is the lattice parameter in the basal plane, and (c) is the height of the unit cell. By analyzing the geometry and applying these formulas, you can confirm the interplanar spacings for hexagonal crystals.