A theory of localized and nonlocalized adsorption is given by applying the virial expansion theorem to the second layer. Anab initiocalculation of the thermodynamic functions is carried out for the system of helium on an argon crystal. The gashyphen;solid interaction potential is calculated using lattice summation. The periodic potential along the directions parallel to the solid surface is described by a polynomial phgr;n(xsol;d)sol;V0equals; 1minus;1minus;(2xsol;d)2nwithin a site spacingd, whereV0is the height of potential barrier andnis an integer to be determined from the minimum potential surface. The values ofnused for the first and second layers in the present work are 7 and 4, respectively. The second virial coefficient under the external potential is very well approximated by that of the two dimensional gas in free space. The Boyle temperature is 16.3deg;K for the system which is close to the experimental temperatures (10ndash;20deg;K) of Ross and Steele. The deviation from the ideality due to the second virial coefficient is small in the experimental temperature ranges; in the isosteric heat, the contribution coming from the second virial coefficient is less than 10percnt; of the total heat. The theory is in excellent agreement with experiment of Ross and Steele.
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