The classical equation of state of gaseous helium, neon and argon

Source abstract

Abstract The deviations from the equation of state for perfect gases which are observed in all known gases result from the interactions of their constituent atoms or molecules. The excess pressures observed at all but the lowest temperatures show that the dominating factor is the strong repulsion between atoms at close renge, due to the interpentration of complete electron shells. Little is known about these repulsions, and that is readily summarized. Between atoms with spherically symmetrical distributions it is likely that the repulsive potential is accurately represented by a function P(r)e-r/p, (1) Where r is separation of the atomic nuclei and P(r) a polynomial in r. Quantum theoretical calculations made by Slater (1928) for helium atoms (with a closed shell of two electrons) and by Bleick and Mayer (1934) for neon atoms (with a closed shell of eight electrons) show that an adequate expression may sometimes be obtained if the polynomial is replaced by a constant. Some confirmation of this (though over a very restricted range of r) is given by Born and Mayer (1932) and Huggins (1937), whose work on ionic cubic crystals shows that their elastic properties are admirably correlated when the repulsive potential of two ions of rare gas type is represented by an exponential function be-r/p, with a range of about one atomic diameter.