The X-ray scattering behavior of molecular fluids

Citation

Morrison, Paul Frederick (1972) The X-ray scattering behavior of molecular fluids. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/R17M-GP28. https://resolver.caltech.edu/CaltechTHESIS:06062016-090735912

Abstract

The Steele-Pecora equation describing the x-ray scattering behavior of molecular fluids has been investigated. Several molecular scattering factor coefficients, molecular distribution functions for chlorine according to the Percus-Yevick theory,and intensity functions for chlorine have been evaluated using orthonormal expansion methods.

Molecular scattering factors for H₂, N₂, LiH, and HF have been obtained as spherical harmonic expansions. The coefficients of the expansions and corresponding gas scattering intensities have been evaluated using both the molecular orbital and isolated atom approaches, and significant differences have been found to exist between the two methods. Chlorine scattering factor coefficients were calculated for the isolated atom approximation only. Expressions for the two-centered Gaussian scattering integral coefficients were derived, and the harmonic expansion technique was shown to be a practical method of calculation.

The Percus-Yevick equation was solved for chlorine by an extension of the Hankel transform method of Chen and Steele. Chlorine was represented by an appropriate two-centered Lennard -Jones potential, the σ-and ɛ parameters having been determined from second virial data. Higher order expansions of f(R₁R₂), C(R₁R₂), and H(R₁R₂) were used here than in previous work as well as a more complete representation of the product of two harmonic series. Pair correlation functions were obtained over the density range ρ* = 0.1 to 1.2 for T* = 0.75, 1.00, and 1.30. It was concluded that the first two expansion coefficients of f(R₁R₂), C(R₁R₂), and H(R₁R₂) were sufficient to obtain accurate pair correlation functions over this range of states. For certain states, use of the more complete product expression reduced the error in g₀₀₀ by several percent. Evidence for a chlorine critical point was obtained in the vicinity of (ρ*,T*) = (0.65, 0.70).

A version of the Steele-Pecora equation suitable for use with diatomic molecules was derived. Substitution of the chlorine scattering factor coefficients and Percus-Yevick distribution functions into this equation led to the determination of total scattered intensity functions expressed as sums of gas scattering, spherical, and angular intensity contributions. The angular contributions were shown to be experimentally significant in the regions of the first and second peaks at high densities (ρ*1.2). Temperature was shown to have only a slight effect on total intensity. g₀₀₀, g₂₀₀, and g₂₂₀ were found to be the principal contributors to the intensity.

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