Perturbation theory is applied to calculate the dielectric constant of a dipolar hard sphere fluid. The results seem to be fairly good. However, this conclusion can only be stated tentatively because of uncertainties in the computer simulation estimates of the dielectric constant of this fluid.

In evaluating the critical properties of lattice spin systems in the real-space renormalization-group theory we use the cluster variation method. A configuration in the transformed system is constrained and the probability of occurrence of this configuration is calculated both in the transformed system and in the original system. By equating the two probabilities and forming ratios of two such equalities (for two or more constrained configurations) the fixed point of the renormalization transformation is evaluated. The method can avoid the trouble due to different singularities in the original and transformed systems, and hence can obviate the possible development of spurious singularities in the transformation at low temperatures. The two-dimensional triangular Ising model is treated with numerical results comparable with those obtained by the cluster treatment of Niemeijer and van Leeuwen who used more and larger cluster types than those we introduce.

Grand partition function methods are used to generate formal perturbation theory expressions systematically through fifth order for the Helmholtz free energy (A) and through third order for the angle-averaged two-body radial distribution function of a system of hard spheres perturbed by embedded electric dipoles. Integrating as required over all dipole orientations causes most terms in these expressions to vanish such that numerical evaluation for the first time of the fourth-order contribution to A appears to be feasible using the Monte Carlo method. This work is in progress.

ADVERTISEMENT RETURN TO ISSUEPREVLetterNEXTHeat capacity of monatomic solidsCharles E. Hecht Cite this: J. Chem. Educ. 1973, 50, 6, 448Publication Date (Print):June 1, 1973Publication History Received3 August 2009Published online1 June 1973Published inissue 1 June 1973https://doi.org/10.1021/ed050p448.3RIGHTS & PERMISSIONSArticle Views523Altmetric-Citations1LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (681 KB) Get e-Alertsclose Get e-Alerts

The partition function method proposed by Feynman for pure liquid ${\mathrm{He}}^{4}$ and previously extended to treat pure liquid ${\mathrm{He}}^{3}$ by Kikuchi is here applied to liquid mixtures of ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$. The variation of the $\ensuremath{\lambda}$ point with mole fraction ${\mathrm{He}}^{3}$, the isotopic phase separation curve, and the excess functions of mixing are discussed. The theoretical $\ensuremath{\lambda}$ line is interpreted as a cooperative boson transition and follows the experimental results closely up to ${X}_{3}=0.5$ irrespective of the effective mass of the ${\mathrm{He}}^{3}$ atoms while above ${X}_{3}=0.5$ the $\ensuremath{\lambda}$ temperatures are too high. An asymmetric isotopic phase separation is found in the mixtures at temperatures below a critical temperature that depends slightly on further assumptions in the model but which is of the correct order of magnitude (1\ifmmode^\circ\else\textdegree\fi{}K). The phase separation is due to the quantum dynamical effects as opposed to the purely statistical effects arising out of the different inherent symmetries of the wave functions for ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$. The calculated excess Gibbs free energies of mixing become positive in "time" to effect the phase separation but are less positive than the experimental values and are in fact of the wrong sign above 1\ifmmode^\circ\else\textdegree\fi{}K. The calculated excess entropies of mixing are much too positive. The model used assumes zero excess volumes of mixing.