The in-plane structures of the Si(111)-√3×√3-Ag surface at both room temperature (RT) and 50 K are determined by synchrotron X-ray diffraction. The honeycomb chained triangle model with strongly anisotropic thermal vibrations of Ag atoms is preferred over the inequivalent triangle (IET) model at RT. On the other hand, at 50 K, the IET model better explains the experimental results. Not only ordinary Bragg reflection peaks but also broad reflection peaks are observed below the phase transition temperature of T_c=150±4 K accompanied by the formation of the twin IET structure. The critical exponent β obtained from the broad peaks is 0.27±0.03, that is not explained by simple two-dimensional order-disorder transition models. The temperature dependence of the Bragg intensities also supports a displacive transition.