# The battle between Energy and Entropy: Molecular Dynamics and Free Energies

F. Eriksson,
M. Kjelltoft,
O. Larsson,
and
M. Svensson

Bachelor′s Thesis
(2014)

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The purpose of this report was to illustrate the procedure of calculating a binary phase diagram. In this study, the investigated system was the titanium-tungsten alloy of different compositions at 0 Pa.

The phase diagram of Ti-W alloys is difficult to experimentally determine due to a slow solid-solid transition. To bypass this problem, Molecular Dynamics (MD) simulations were employed using MEAM (Modified Embedded-Atom Method) spline, and CDIP (Composition-Dependent Interatomic Potential) potentials.

Two different simulation methods were used. The direct method simulated a two-phase coexistence of the alloy, which was used to determine the melting lines. For the solid-solid transitions two types of λ-integration were used and compared. These methods are referred to as the multishot and singleshot method in this report.

The direct method was successful and a phase diagram of the high temperature region of the Ti-W alloy was constructed. Issues encountered with the method included a minor energy drift that indicated that the system was not entirely equilibrated as well as difficulties to accurately determine the composition between liquid and solid.

The λ-integration was not so successful. From the beginning the idea was to calculate the phase transitions in the entire solid region but this was abandoned due to time limits. Instead the phase transition for the pure Ti system was calculated and the results compared to the 2012 Master thesis by Tommy Andersson. Unfortunately, his results couldn’t be replicated and we suspect some kind of systematic error. However, the ordinary MD-simulations that were run in order to determine the parameters for the λ-integration went well. It showed that a great deal of information can be computed with low effort by ordinary MD-simulations.