Introduction

Most experiments are carried out under conditions of constant temperature and pressure. On the other hand, standard molecular dynamics (MD) simulations integrate the Newtonian equations of motion in an MD cell of fixed volume, $V$. The conserved quantity is the total energy $E$. Assuming particle conservation these situations are described by the microcanonical ($N$,$V$,$E$), canonical ($N$,$V$,$T$), isobaric-isenthalpic ($N$,$P$,$H$) and isobaric-isothermal ($N$,$P$,$T$) ensembles.

Using fundamental statistical mechanics one can show that the averages obtained from canonical and microcanonical ensembles differ by a factor of the order of $1/\sqrt{N}$. In the case of macroscopic systems one can neglect this difference and it indeed vanishes at the thermodynamic limit. Nevertheless one has to keep in mind this result is strictly valid for systems at equilibrium.

The systems which can be investigated by typical MD simulations are way smaller than real ones. In our particular case the system contains about 600 particles. From the relation mentioned above the averages computed in the microcanonical and the canonical ensembles should differ by approximately four per cent.

The objective of this project is to study nucleation from the vapor phase in metallic systems. In experiments rare gases are used to cool down the system. This is to be compared with the techniques to control the kinetic energy - that is to set the temperature - available for MD simulations. In the next section we will discuss the theory and implementation of several approaches developed throughout the last twenty years as well as compare and illustrate their aptitude to sample the various ensembles. Due to the existing structure of the code used we give an short overview in chap.4 of the two integration schemes involved, namely the Gear predictor-corrector algorithm and the Verlet integrator. Afterwards the calculation of energies and forces with the EAM and Lennard-Jones potentials is surveyed. The configuration of our simulations is described in section chap.6. chap.7 summarizes the results and their interpretation. Finally we will discuss the deficiencies of our approach and possible improvements.