Scaled Equation of State and Critical Exponents in Magnets and Fluids

A systematic analysis in the context of the scaled equation of state has been made of available experimental data in the critical region of a number of ferromagnets [Gd, CrBr₃, La0.5{Sr}0.5$Co${O}₃$, Ni (two independent sets of data)] and fluids (C${O}₂$, ${He}⁴$, Xe) with the following assumed form for $h(x)=H{M}^{{-}1}{|M|}^{1{-}{δ}}$: $h(x)={E}₁[{(x+{x}₀)}{{x}₀}]{{1+{E}₂{[{(x+{x}₀)}{{x}₀}]}^{2{β}}}}^{{[{β}({δ}{-}1){-}1]}{2{β}}}$ where $h(x)$ is a scaling function, $x=t{|M|}^{{-}{1}{{β}}}$, $t={(T{-}{T}c)}{{T}c}$, and $x={-}{x}₀$ is the phase boundary. A nonlinear, least-squares method was used to simultaneously determine the six parameters (${β}$, ${δ}$, ${T}c$, ${x}₀$, ${E}₁$, ${E}₂$). Agreement between the proposed form for $h(x)$ and the experimental data was found. For both the magnets and fluids, we find that ${δ}{≈}4.4$; for the magnets ${β}{≈}0.37$ and for the fluids ${β}{≈}0.35$. Reasons for the considerably different values reported elsewhere for these exponents in the materials Cr${O}₂$ and YFe${O}₃$ are discussed.