Evolution of $\sqrt {31} \times \sqrt {31} R9^{\circ}$ surface of Al$_{2}$O$_{3}$(0001) generated in air

As reported by S. Baik et al\footnote{S. Baik, D. E. Fowler, J. M. Blakely, and R. Raj, J. Am. Ceram. Soc. 68(5), 281 (1985).} $\sqrt {31} \times \sqrt {31} R9^{\circ}$ surface of Al$_{2}$O$_{3}$(0001) can be generated by annealing at a high temperature in air. We reproduced this $\sqrt {31} \times \sqrt {31} R9^{\circ}$ surface and investigated surface structures with x-ray diffraction using synchrotron radiation at Advanced Photon Source and RHEED techniques. We also annealed this $\sqrt {31} \times \sqrt {31} R9^{\circ}$ surface in a UHV chamber until the superstructure disappeared and a new $\sqrt {31} \times \sqrt {31} R9^{\circ}$ surface was generated. We will compare the results to the previous x-ray diffraction experiments\footnote{G. Renaud, B. Villette, I. Vilfan, and A. Bourret, Phys. Rev. Lett. 73, 1825 (1994).} and recent AFM/DFT investigation.\footnote{J. V. Lauritsen, M. C. R. Jensen, K. Venkataramani, B. Hinnemann, S. Helveg, B. S. Clausen, and F. Besenbacher, Phys. Rev. Lett 103, 076103 (2009). } The UHV generated $\sqrt {31} \times \sqrt {31} R9^{\circ}$ surface also appeared to preserve the $\sqrt {31} \times \sqrt {31} R9^{\circ}$ symmetries as Pd films were deposited. However, the intensity ratios between superlattice peaks went through large changes.