Wavelength and Crystal Structure

The wavelength of X-rays can be determined from the Bragg’s equation, 2d sin θ = nλ …. (i). The lattice constant d for rock salt crystal can be calculated. One gram molecule of NaCl will contain N molecules where N is the Avogadro’s number. The number of molecules in one cm cube where ρ is the density. As a molecule has two atoms (Na and Cl), the total number of atoms per unit volume If the distance between the neighbouring atoms is d, the number of atoms in one cm length = 1/d and the number of atoms per unit volume = (1/d)²

= 2.814 × 10^-8 cm

Substituting the value of d and knowing θ for a particular order spectrum, the value of λ can be calculated. Similarly, knowing λ and θ for a particular order spectrum, the lattice constant can be determined. The crystal structure of various compounds has been studied and the different lattice constants for different planes have also been determined.

Miller evolved a system to represent a plane in a crystal by three numbers known as Miler Indices. The place BHFC is 1, 0, 0 plane and the distance between two such parallel planes is d₁₁₀. The plane BGD is 1, 1, 1 plane and the distance between two such parallel planes is d₁₁. The distances d₁₀₀, d₁₁₀, d₁₁₁ have been verified in the case of crystals of rock salt and KCl with the help of Bragg’s experiment using the equation 2d sin θ = nλ.

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