Improved energy minimization of iron-carbon systems: on the influence of positioning interstitial atoms

We compare different optimization schemes for the energy minimization in iron-carbon single crystals, where either choosing an initial distribution of interstitial atoms is followed by a conjugate gradient algorithm, or a simulated annealing (SA) procedure is employed. As an alternative to random or so-called single-atom starting configurations, globally optimal interstitial sites with respect to a long-range potential for the carbon-carbon interaction are computed by exact methods of discrete optimization. A comparison of the mechanical properties of the corresponding systems reveals that the positioning scheme can have a large influence. The elastic properties of the crystals for initially randomly distributed carbon atoms show large fluctuations for different initial C interstitial positions. The solution by SA is superior but still causes significant deviations, while using the optimized configurations leads to an increased stiffness of the Fe-C system.