Anomalous Liquid-Solid Transformation of Helium-Three

The present paper is devoted to the study of the anomalous liquid-solid phase transformation of ${\mathrm{He}}^3$. By allowing the phase boundary lines of the liquid and solid volumes to have singular pressure derivatives, the melting pressure minimum and the boundary volume line maximas of the liquid and solid occur at two different temperatures. This leads to smooth variations of the anomalous isobars and isochores of the liquid, insuring a single minimum to the isobaric expansion coefficients, in qualitative agreement with data available at the present time. The transformation of a normal family of isotherms into an anomalous one, and vice versa, either on a phase transformation or within a pure phase will be clarified. The geometry of the state surface, on the basis of the stated assumptions, will be shown to justify the existence of thermal anomalies of the cubic solid ${\mathrm{He}}^3$ over a finite extension of this phase well beyond its boundary line.