NEUTRON SCATTERING

           

               Neutron scattering is the technique of choice for condensed matter investigations in general because thermal/cold neutrons are a non-invasive probe; they do not change the investigated sample since they do not deposit energy into it.

Neutron diffraction

Principles of diffraction:

The scattering of rays from crystalline materials produces a diffraction pattern, if it satisfies the Braggs condition the pattern contains information about the atomic arrangement within the crystal.

Figure 1 is a geometrical interpretation of Braggs’ law. Diffraction can be implemented using different radiation: X-rays, neutrons, electrons, muons etc. The diffraction pattern is a product of the unique crystal structure of a material.

                     

                                          Figure 1. Geometrical interpretation of Braggs’ law

How a neutron interacts with matter??

Neutron diffraction is a non-destructive technique that is used to probe the atomic and/or magnetic structure of a material. Diffraction occurs when the neutrons interact with the atomic nuclei of the material. It is the electrical neutrality of the neutrons that makes it deeply penetrating into matters well beyond the surface of a sample. The extent to which a neutron interacts with the nuclei is termed as cross section. Neutron cross section is the effective area presented by a nucleus to an incident neutron and is measured in “barn”!!! (1 barn =10^-24 cm²)

Pros and Cons of X-ray and Neutron Diffraction

X-rays interact with electrons in the material via electromagnetic force, while neutrons interact with the nucleus via the very short-range strong nuclear force. Thus neutrons can penetrate much more deeply than that X-rays. In scattering, cross-section meant to identify the effective area presented by a nucleus/atom to an incident neutron/electron.Figure 2 shows the cross section comparison between neutrons and X-rays.

The atomic scattering power decreases with increasing scattering angle with X-rays, while it remains approximately constant with angle if we use neutrons. Atomic scattering power varies directly with atomic number in case of X-rays. With neutrons, there is no direct dependence of atomic number with the interaction strength. This difference is extremely useful because elements adjacent on the periodic table cannot be distinguished by X-rays but can have largely different neutron scattering lengths:   for   example aluminium and   silicon have   almost identical X-ray scattering factors, but have different neutron scattering lengths, which gives more precise identification.

Moreover, light atoms such as lithium and hydrogen that are practically invisible to X-rays, have larger neutron detectability in presence of elements with much large atomic number. Another interesting difference is the ability of neutrons to distinguish between isotopes of the same atomic species: for eg: hydrogen and deuterium have identical X-ray scattering factors but largely different neutron scattering lengths.

Perhaps the major challenge in the neutron scattering experiments is the large neutron scattering cross-section of hydrogen, an element commonly found in the electrolyte of the batteries. The dominant portion of this scattering is incoherent and isotropic, and results in a large contribution to the background, significantly reducing the signal-to-noise ratio in structural studies. This problem can be mitigated by substituting hydrogen with deuterium, which has a far smaller incoherent neutron scattering cross-section.

                                 

Figure 2. Comparison of scattering strength between X-Rays and neutrons for few elements (left) and interaction of x-rays and neutrons with the atoms (right).