  The formation, growth, structure and cluster size distribution (CSD)
properties in a two-dimensional system of particles interacting with
Lennard-Jones (LJ) potential under controlled cooling condition have been
studied using Monte-Carlo (MC) method considering modified Metropolis algorithm
to introduce realistic thermal motion of the particles. The system, initially
at relatively higher temperature Ti, undergoes temperature reduction following
exponential law with decay constant a to a lower temperature Tf and
subsequently reaches equilibrium. The equilibrium phase configuration depends
strongly on the number density c of particles and a. The root mean square
particle displacement in the final equilibrium phase shows maximum value for a
= ac ~ 10-3 for all c. The CSD properties obtained at a = 10-3 shows a sharp
peak in the lower cluster size region for low c. The peak shifts towards higher
cluster size for lower a. The CSD fits well with a modified Gamma distribution
function. All of the particles in the system form a single cluster when c is
larger than a critical value cc (~0.5). A compact well-defined ordered
structure is obtained for c > cc and a << ac.
