In this work, we studied a few surface super-structures using reflection high-energy positron diffraction (RHEPD). We found that the RHEPD pattern from the Si(111)-7×7 surface exhibits different features from that of electron diffraction. The difference is explained as a strong thermal diffuse scattering of positrons at the first surface layer. We also studied the phase transition of the Si(111)-√3×√3-Ag surface. We found that the surface sensitive diffraction spots exhibit peculiar temperature dependences. Based on theoretical considerations, we interpreted the temperature dependences in terms of the order-disorder phase transition. Furthermore, we succeeded in determining a unique structure of the Si(111)-√21×√21-Ag surface.1 Introduction One important aspect in the interactions between high-energy positrons and matter is the negligibly small correlation effect. Therefore, the diffraction processes of high-energy positrons are described mainly using the Hartree-Fock (crystal) potential. Strictly to say, the scattering cross sections and hence atomic form factors for positrons and electrons are different due to the different phase shifts of the scattered waves. In high-energy region, however, the lowest-order Born approximation is adequate. Therefore, the crystal potential for positrons may be close to the absolute value of that for electrons. The crystal potential for positrons is thus positive. Consequently, a positron beam is totally reflected at the first surface layer when small enough incident angles. The total reflection never occurs in the case of electrons. The reflection high-energy positron diffraction (RHEPD) is suited to study the surface properties without any disturbances from the bulk [1].Using the electro-magnetic lenses we developed a positron beam, which is more coherent as compared to the previous beam [2]. This leads to the successful observation of the fractional order diffraction spots. In this article, we report the difference in positron and electron diffraction patterns. As the applications of RHEPD, we also report the observation of the phase transition of the Si(111)-√3×√3-Ag which is still under the debate [3][4][5][6][7] and the determination of the structure of the Si(111)-√21×√21-Ag [8][9][10][11].