Determination of the critical exponentηby neutron and light scattering from a binary liquid mixture

Light-scattering and small-angle neutron scattering data obtained for an isobutyric acid deuterium oxide mixture of critical composition are combined to determine the value of the critical exponent $\eta$. The neutron scattering experiments are performed at momentum-transfer values $Q$ between 0.015 and 0.21 ${\mathrm{\AA }}^{-1\mathrm{}}$. Experimental correlation scaling functions $g_{\mathrm{expt}}\mathrm{}\left(x\right)\mathrm{}$ are composed of scattering patterns with $x$ ranging from 2 to 270. $g_{\mathrm{expt}}\mathrm{}\left(x\right)\mathrm{}$ is fitted with two adjustable independent parameters by the Fisher-Langer approximation and the asymptotic correlation scaling function. In this way a value of $\eta =0.0858\mathrm{}\pm 0.0263$ is obtained.