Radiation Scattering Experiments on Fluids

Abstract

The scattering of radiation by condensed matter may be related to the distribution of atomic positions if the wavelength of the radiation is of the order of magnitude of the interatomic spacing. If a beam of radiation falls on a target and wavelets scattered by different atoms have similar amplitudes and phases, then the scattered waves will interfere and the target will act as a diffraction grating. In this case the distribution of scattered intensity contains information on the distribution of atoms, and the spectrum of energy transfers on scattering contains information on atomic motion. The general principles behind this field, and the distribution functions themselves will be described.

Almost any kind of radiation may be used for such experiments — electromagnetic (X-rays, γ-rays, light); electrons; neutrons etc. Differences arise due to the differences in the scattering properties of single atoms for each kind of radiation. These differences will be summarized and discussed. It will be shown that neutrons have the simplest scattering properties since they are scattered by a ‘point’ nucleus which is the atoms centre of mass also. In addition they do not alter the quantum state of the nucleus, in contrast to electromagnetic radiation and electrons which may alter an atoms quantum state and hence lead to complicated corrections when the atom is treated as the scattering centre. These two features simplify the relationship between the distribution of atomic (centre of mass) positions and the pattern of scattered radiation in the case of neutron scattering. An alternative methods is to discuss the scattering of electromagnetic radiation in terms of the electrons as the scattering centres. In this case the quantum state of the scatterer is not changed and the whole of the scattered intensity may be used in the interpretation: this case will be discussed also.

The experiments fall into two classes: first there are experiments in which only the angular distribution of the scattered beam and the scattered intensity are determined, and secondly those in which the angular distibution for both the intensity and the energy transfer is measured. In the former experiments the intensity is related to a static structure factor S(Q), and in the latter it is related to a dynamic structure factor S(Qω), where ħ Q and ħω are the momentum and energy transferred to the target in the scattering process. If the incident and scattered wave vectors and energies are denoted by (k _o, k) and (E_o, E) respectively, then ħ Q = k _o − k and ħω = E_o − E. These structure factors atr the most useful for studying liquids and will be discussed in this paper.

A variety of cases will be considered. The application of these methods to atomic liquids, including metals, and particularly to simple molecular liquids will be described. With the help of typical results the study of static and dynamic correlation functions will be reviewed briefly. A very wide range of the variables Q and ω, will be shown to be needed for the complete study of these liquids. Some introductory remarks on the variety of experimental and interpretative methods open to the investigator will be included as well.