Thermodynamic Relationships at the Tricritical Point inHe3-He4Mixtures

Abstract

An analysis is made of the $\ensuremath{\lambda}$ transition, the phase-separation transition, and the relation between the two, for mixtures of liquid $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$. Stability conditions require that ${C}_{x}$ (specific heat at constant $x$, where $x$ is the mole fraction ratio $\frac{{x}_{4}}{{x}_{3}}$ of $^{4}\mathrm{He}$ to $^{3}\mathrm{He}$) be less than a certain value, or, equivalently, that ${(\frac{\ensuremath{\partial}{\ensuremath{\mu}}_{4}}{\ensuremath{\partial}x})}_{T}$ be positive ${\ensuremath{\mu}}_{4}$ is the chemical potential of $^{4}\mathrm{He}$). The phase separation occurs when these conditions are violated. The changes in these quantities appear to occur gradually rather than suddenly, as supposed earlier by one of us. The evidence indicates that there is no real critical singularity at the tricritical point. It then seems reasonable to expand thermodynamic functions about each side of the tricritical point separately, and by thermodynamic arguments the relations between the critical exponents $\ensuremath{\beta}$ (for the coexistence curve) and $\ensuremath{\delta}$ (for the critical isotherm) can be obtained and compared with observations.