The reconstruction and the phase transition are discussed on the (111)
surfaces of Si and Ge by the use of the lattice gas model on a triang
ular net. A Monte Carlo simulation calculation is carried out of the l
attice gas model. It is shown that the characteristic diffuse scatteri
ng of electrons in the (1x1) phase of Ge(111) can be reproduced by the
model. Moreover, the underlying mechanism is discussed in terms of pa
rticle arrangements divided into irregular hexagon-like (2x2) domains
which yield the diffuse patterns in the (1x1) phase. For the Si(111) s
urface, on the other hand, the calculation concludes the absence of st
acking faults in the (1x1) state. The interrelation between the recons
tructions of the surfaces is also discussed.