Critical scattering function in a binary fluid mixture: A study of sodium-deuteroammonia solution at the critical concentration by small-angle neutron scattering

Small-angle neutron scattering experiments have been performed on the Na-ND₃ mixture of critical composition. Neutrons are very sensitive to the fluctuations of concentration in this system (high contrast). This allowed good statistics for a reasonable counting time, typically 0.5% at each value of the momentum transfer q for a 40-min run. Momentum transfers q between 0.008 and 0.067 A^-1 were investigated with the chosen experimental setup. Using several approximations of the scattering function at small x=q{ξ}, and after very careful data correction, the correlation length {ξ} has been determined with a good precision (2% for {ξ}300 A{}). The experimental scaling function g(q{ξ}) was then fitted in the whole x range using different approximate equations discussed in literature. A value of the critical index {η}=0.030±{}0.0015 was thus found with a precision not yet obtained from experiments. A lower limit for the validity of the scaling hypothesis is given for the first time: 2-{η}-{γ}/{ν}{≤}0.002. These results reconcile neutron scattering results with those obtained with light scattering and are in favor of renormalization-group-theory predictions for the three-dimensional Ising model.