# Inelastic Scattering of Neutrons or Xrays by Phonons

The phonons can be quantified as the vibrations of ions in their respective positions of equilibrium. The experiment manages in measuring the static and dynamic factors of both the core electrons and the electrons located in the outer periphery. These x-ray diffraction experiments provide information regarding the behaviour of quantum liquids. The speed of sound in water which is a function of its temperature can be ascertained using this experiment. Further density variations of fluids with temperature changes and the corresponding arrangements of ions structurally also form part of the inelastic scattering process. (Loong Chun, 2006)Coherent x-ray scattering provides output about the dynamic structure factor. The method of measuring phonon involves relating the momentum to the inter-atomic distance. This transferred energy due to the highly excited ions provides a measure of the energy of phonons. The phonon energy is measured in terms of momentum transferred. Further, the Born-Von Karman analysis provides a relationship between force constants and the dispersions. (Loong Chun, 2006) Dispersion curves thus plotted using this relation provide information regarding the phonon density. This is critical in measuring thermodynamic specifics like vibration entropy and specific heat of materials. ( Loong Chun, 2006)The INS instrument is capable of performing very precise measurements and calculating S (Q, E) to its absolute units. It is very critical to calculating the total energy interaction that occurs when scattering takes place. An energy filter placed at a certain collimated solid angle is used to allow these low energy scattered neutrons to pass through it. (Veenendaal M van et al, 2010)This utilizes two methods to assess the process. One involves a direct geometry which utilizes a combination of fixed incident energy and variable scattered energies. The other uses inverse geometry combining variable incident energy and fixed scattered energy.