*Incoherent inelastic neutron scattering (IINS)*

The vibrational interactions between a molecule and an electromagnetic radiation can be described by a simple harmonic oscillator model. In terms of vibrations, a molecule is equivalent to a system of weakly coupled harmonic oscillators. The decomposition of coupled harmonic oscillators into a collection of independent oscillators is known as a normal mode expansion and the independent oscillators are called *normal modes*. These normal modes are defined as modes of vibration where the respective atomic motions of the atoms all reach their maximum and minimum displacements at the same time. These normal modes can be expressed in terms of bond stretches and angle deformation. The vibration frequencies of these modes are characteristic of a molecule and this property is used in vibrational spectroscopies to characterize a sample.

Whereas coherent inelastic neutron scattering can be used for the study of collective excitations in single-crystals, such as **phonons** and **magnons**, incoherent inelastic neutron scattering probes the local environment of the scattering atom and is complementary to the optical techniques of infrared and Raman spectroscopies. This vibrational neutron spectroscopy yields information both on the local structure and on the sample dynamics, e.g. diffusion mechanisms. IINS resembles Raman scattering with photons replaced by neutrons but with no neutron selection rules.

#### References

J.L. Koenig, *Spectroscopy of polymers*, Elsevier, 1999, 2^{nd} edition.

D.J. Bower and W.F. Maddams, *The vibrational spectroscopy of polymers*, Cambridge University Press, 1989.