Determination of Crystal Structures

Max von Laue proposed that crystals could diffract X-rays due to their periodic atomic arrangement.

X-rays, having about 100-picometer wavelength similar to internuclear distances in molecules, interact with electrons, enabling structure determination using an X-ray diffractometer.

Later, it was furthered by William and Lawrence Bragg, considering an ordered array of atoms in lattice planes separated by a distance d. If two waves of monochromatic X-rays hit the crystal, one wave is reflected from an atom in the first lattice plane and the second from an atom in the second lattice plane.

When hit at a random angle, it results in destructive interference, producing no detectable diffracted X-rays. On the other hand, when hit at a specific angle, constructive interference leads to measurable diffracted X-rays.

This constructive interference happens if the additional distance traveled by the second wave equals a multiple of the wavelength, expressed as 2d sin θ_B.

This equation is known as Bragg's law of diffraction, which relates X-ray wavelength, crystal lattice spacing, and incidence angle.

Bragg's law allows for different diffraction orders, each corresponding to integral values of n.