Inelastic scatttering of neutrons or x rays by phonons Essay

Inelastic scatttering of neutrons or x rays by phonons - Essay Example The instrument used to measure this form of X ray scattering is called a TOF chopper spectrometers. Inelastic scattering essentially involves the interaction between neutron and phonons and the exchange of energy and momentum that takes place. The Inelastic Neutron Scattering can be represented by the following double differential equation ( Loong Chun, 2006) Here, the scattering function S (Q, E) is directly related to the space-time correlation functions that exist between particles or the space-time constraints of the particle itself. Coherent Inelastic Scattering This involves addition of both energy and momentum. A coherent scattering experiment provides details about the frequency and space configurations of 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 diffrac tion experiments provide information regarding the behaviour of quantum liquids. The speed of sound in water which is 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. ... Further the Born-Von Karman analysis provides 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-Crystal Mono-chromators and Choppers The INS instrument is capable of performing very precise measurements and calculating S (Q, E) to its absolute units. It is very critical to calculate 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 combin ing variable incident energy and fixed scattered energy. The coherent inelastic x ray spectrometer uses a mono-chromator of high energy that is utilized as the source. The analyzer is formed by a curved Si crystal. A nested crystal that is formed by a combination of Si (4 4 0)-(15 11 3) forms the mono-chromator. A Diced Silicon crystal of bending radius 6m with a combination of (18 6 0) forms the analyzer. The energy resolution obtained in this exercise is 2meV while the momentum transferred is 5A-1. The energy of the photons that are used to impact initially is in the range of 21.657 keV. (Loong Chun, 2006) Source: Phonon dispersion measurements in Berrylium along (0 0 ?) direction for the longitudinal phonons for ? values indicated for each spectrum,