Diffraction Techniques.

INTRODUCTION

When an electromagnetic radiation (Fig 1) reach a sample, different effects can occur :

- absorption; fluorescence; phosphorescence

- refraction (change in the direction)

- scattering (deflection from the initial direction)

elastic (Rayleigh) scattering (energy remains unchanged)

inelastic (Compton) scattering (frequency is changed)

Fig 1. Electromagnetic spectrum (and type of excitation that give rise to each region)

Whereas SPECTROSCOPIES probe energy levels, from which structure is inferred, SCATTERING experiments explore electron distributions directly.

A characteristic property of waves is that they interfere with each other (Fig. 2). Interference between waves was demonstrated by Thomas Young at the beginning of the nineteenth century.

Diffraction occurs when the dimensions of the diffracting object are comparable to the wavelength of the radiation.

Fig. 2 Interference between waves.
1) Waves reinforce each other when they are in phase (constructive interference (a)) while they tend to cancel each other out when they are out of phase (destructive interference (b)).

Fig. 2 Interference between waves.
2) The spreading of light at an aperture (single slit (a), two slits close together (b) or further apart (c)) gives a diffraction pattern. Only for some directions, the waves reinforce each other. Note the reciprocity relationship between the distance between the apertures and the positions of the diffracted beams.

Just like visible light can be diffracted by very small objects, X rays are diffracted by electrons, and neutrons are diffracted by the nuclei of atoms. The physical explanation given for diffraction by atoms is this : when X-rays hit an atom, the rapidly oscillating electric field of the radiation sets the electrons of the atom into oscillation about their nuclei. This oscillation has the same frequency as that of the incident radiation (coherent/elastic scattering). In a periodic arrangement of atoms, the diffusion (continuum of emitted radiation) of waves becomes diffraction (a discrete number of directions) Fig. 3.

Fig. 3 In a periodic arrangement of atoms, the diffusion (continuum of emitted radiation) of waves becomes diffraction (only a discrete number of directions are conserved).

All the techniques described here make use of the property of diffraction of waves by objects with dimensions similar to the wavelength of the waves.

- X Rays have wavelengths comparable to bond lengths in molecules and spacing of atoms in crystals (about 1 Å)

- Electrons moving at about 20 000 km/s (after acceleration through about 4 kV) have wavelengths ~ 40 pm and may be diffracted by molecules, surfaces, and thin films of solids

- Neutrons generated in a nuclear reactor, and slowed tp thermal velocityes, have also wavelengths ~ 40 pm.

In this respect, one of the most useful applications of elastic scattering is the technique of X-ray diffraction, in which X-rays (wavelength ~ 1 Å) scattered by individual atoms in crystalline sample interfere with one another to give a characteristic pattern of intensities. This pattern can be interpreted in terms of location of atoms in the molecule (molecular structure).

Neutron and electron diffraction bear close similarities to X-ray diffraction, but provide complementary information.

Abel A. Colmenares E.
17.810.847
CRF