Determination of the Argon Intermolecular Pair Potential from Distribution Functions Measured by X-ray Diffraction from Fluid Argon

Citation

Karnicky, Joseph Francis (1974) Determination of the Argon Intermolecular Pair Potential from Distribution Functions Measured by X-ray Diffraction from Fluid Argon. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/htpg-c668. https://resolver.caltech.edu/CaltechTHESIS:07212021-212145639

Abstract

X-ray diffraction experiments were carried out on fluid argon at a temperature of -100°C and densities of .0824 g/cm³, .1331 g/cm³, .2087 g/cm³, and .3111 g/cm³. The measurements of the state at .2087 g/cm³ were repeated to establish reproducibility. The methods used to obtain the experimental quantities and to subsequently analyze the data included significant improvements over previous investigations.

The data from each experiment at the three higher densities were analyzed to obtain a set of structure factors which were Fourier transformed to obtain sets of direct correlation functions and radial distribution functions. The Percus-Yevick equation was applied to these distribution functions to obtain the effective intermolecular potential from each experiment. These potentials were corrected for three-body effects to give four estimates of the argon pair potential, and a final estimate which is the precision weighted average of the four seperate estimates.

The characteristics of these potentials, with error limits determined by a perturbation analysis of the uncertainties in the experimental quantities, are:

state 1- n = .2087 g/cm³, σ = 3.401 ± .038 A°, ∈ = 143.2 ± 10.2 °K, r_min = 3.89 ± .09 A°.

state 1R- n = .2087 g/cm³, σ = 3.402 ± .035 A°, ∈ = 149.9 ± 10.2 °K, r_min = 3.87 ± .07 A°.

state 2- n = .3111 g/cm³, σ = 3.375 ± .0233 A°, ∈ = 146.6 ± 6.8 °K, r_min = 3.87 ±.05 A°.

state 3- n = .1331 g/cm³, σ = 3.379 ± .050 A°, ∈ = 145.1 ± 16.0 °K, r_min = 3.83 ± .13 A°.

average u(r)- σ = 3.389 ± .015 A°, ∈ = 146.3 ± 4.9 °K r_min = 3.86 ± .05 A°.

Physical quantities were calculated from the average potential and agreed with the experimental values for the second virial coefficient of argon and the vibrational transition energies of the argon dimer, as well as the theoretical long range dispersion potential.

The range of densities studied was not large enough to allow direct determination of three-body forces. Methods are suggested whereby information about nonadditive forces could be derived from the combination of the results of these experiments with the results of previous x-ray experiments or with third virial coefficient data.

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