MAXIMUM ENTROPY DETERMINATION OF THE ELECTRON DISTRIBUTION OF THE Si(111) 7X7 SURFACE FROM X-RAY AND ELECTRON-DIFFRACTION DATA. C. A. M. Carvalho¹, A. Ghosh², I. K. Robinson², H. Hashizume³. ¹Dept. of Physics, Univ. Federal do Paranà, Brazil, ²Dept. of Phys., Univ. of Illinois, USA. ³Research Laboratory of Engineering Materials, Tokyo Institute of Technology, Japan.

The two-dimensional electron-density distribution of the Si(111) 7x7 surface has been calculated by the Maximum Entropy (ME) technique using X-ray and electron diffraction data. The maps clearly show all the 102 atoms of the Takayanagi dimer-adatom-stacking fault model. The atomic coordinates defined by the density maxima are in good agreement with those obtained by a standard crystallographic least-squares fit. It is shown that ME maps can give many more details than Fourier synthesis. A comparison between maps calculated using new X-ray data and maps using simulated data obtained from the DAS model shows some evidence of bonding that was absent in our previous work [C. Carvalho, H. Hashizume, A. W. Stevenson & I. K. Robinson: Physica B (in press)]. It is also shown that a high density level between adjacent atoms does not necessarily indicate valence charge redistribution.We discuss the reliability of the ME method and show that the calculation procedure must be continued to values of [[Chi]]²<1, differently from a standard fitting process. Doubts about the validity of the method [W. Jauch & A. Palmer: Acta Cryst. A49, 590 (1993); A50, 650 (1994)] are answered. The effect of data uncertainty in the resultant map is analysed and we propose a method to identify the features of the distributions that can be trusted. Results obtained from data sets with different numbers of reflections and data precision show that artifacts in the density distributions are caused by the data themselves and not the ME method, and that detailed information can be obtained with a relatively small number of precisely measured reflections. An example is shown where a map calculated from an X-ray data set with fewer reflections than an electron diffraction one in fact give better electron densities for the Si(111) 7x7 surface. The ME technique is promising to obtain detailed surface structure information.