separated pyramids of two types but mixture of facets, e.g., on the (211) facet a smaller (011) facet can occur.

Simulation of LEED patterns {#s5}
===========================

Low energy electron diffraction (LEED) experiments play an important role in investigation of structures and phase transitions of faceted surfaces [@mad94; @song95]. Very recently, Song et al. [@song95] where able to study LEED patterns of Pd/Mo(111) system in high temperatures up to 1200K. They demonstrated the existence of reversible planar/faceted phase transition with transition temperature different for heating cycles ($T\approx 870K$) and for cooling cycles ($T\approx 830K$).

![ LEED patterns of (a) disordered phase where spots are represented by squares and also spots of ideal bcc(111) surface (crosses) are shown, (b) faceted {211} phase where circles, diamonds, and triangles denote spots coming from diffraction on facets (121), (211), and (112), respectively. []{data-label="figure8"}](fig8){width="6cm"}

In this section we employee the BCCSOS model to analyze the temperature dependence of LEED patterns. The diffracted intensity is proportional, in the kinematic approximation, to the structure factor

$$S({\bf k}) = 
  {\left<  
    \left|        
      \sum\limits_{j} 
         {           
            \exp(i {\bf k  R}_j)                                                       
         }  
     \right|^2
   \right>},$$

where summing is over surface atoms, ${\bf k}= {\bf k}_f-{\bf 
k}_i$, and ${\bf k}_i$, ${\bf k}_f$ is the wave 