Interplanar Distance Calculation in Different Crystal Systems
How can we calculate the interplanar distance (dhkl) in different crystal systems?
What are the relationships for calculating the distance between crystal surfaces (dhkl) and Miller's coefficients for the following crystal structures: • cubic crystal system • Quaternary crystal system • Hexagonal crystal system • rhombic crystal based monoclinic crystal system • Triclinic crystal system?
Interplanar Distance Calculation:
The interplanar distance (dhkl) in different crystal systems can be calculated using Miller's indices (hkl). This calculation varies among systems, with differing complexities from relatively straightforward for cubic and hexagonal systems to more involved for rhombic, monoclinic, quaternary, and triclinic systems.
The distance between parallel crystal surfaces, also termed as the interplanar distance (dhkl), can be calculated using Miller's indices (hkl) depending on the crystal system in question. In the cubic crystal system, the interplanar distance can be given by the formula: dhkl = a / √(h^2 + k^2 + l^2) where 'a' denotes the lattice parameter and 'h', 'k', and 'l' are the Miller indices.
For a hexagonal crystal system, the formula modifies to: dhkl = c / √(h^2 + k^2 + h*k + l^2/c^2) where 'c' is the height of the hexagonal unit cell.
On the other hand, in a rhombic crystal based monoclinic system, the distance between crystal planes is more complex to calculate as it involves more parameters of the unit cell and is dependent on the crystallographic angles.
As for the quaternary crystal system and triclinic crystal system, the interplanar distance calculation involves the complete metric tensor of the crystal lattice.