Work-biased path-sampling calculations of chemical potentials: Principles and applications to uranium oxide

We present the work-biased path-sampling scheme to calculate chemical potentials in atomic scale simulations. This scheme is based on a series of chained insertion and deletion paths from N to N + 1 to N atom systems, the sampling being performed on the paths themselves rather than on the final configurations. Equations for parallel path generations as well as geometrically biased insertions or deletions are presented. We then present two applications of our approach for the uranium dioxide crystal. The first is a test case validation of our approach for the insertion of a Xe atom in UO2. The second explores the relationship between cluster structure stability and oxygen chemical potential in overstoichiometric UO2+x oxide as a function of temperature from 800 to 2000 K and composition, from UO2 to UO2.16, using two different empirical potentials. We find that the evolution of the oxygen chemical potential is irregular, with dips for specific numbers of added oxygen atoms. Five oxygen clusters are stable at 800 K and are associated with strong dips in the chemical potential values. At intermediate temperatures, clusters of four and five oxygen atoms compete in stability. They become unstable at the highest temperatures, and the evolution of the chemical potential is then monotonous with composition.