“…With the bulk thermodynamic database, at the annealing temperature of 500 °C, the equilibrium p O 2 of reactions and () are 7.15 × 10 –6 and 5.37 × 10 –13 Torr, respectively (Figure S3). In fact, as we are dealing with a nanoscale material, a surface energy term should be considered as an excess energy term to the bulk thermodynamic data. − By inverse calculation of the Gibbs free energy from the database of nanoscale copper oxide, , as described in more detail in Supporting Information (Table S1), the equilibrium p O 2 for the reduction of CuO to Cu 2 O is 2.4 × 10 –3 Torr, and that for the reduction of Cu 2 O to Cu is 1.1 × 10 –5 Torr at the temperature of 500 °C. From the calculated phase boundary conditions of p O 2 for each copper oxide, we established the p O 2 values for the experiment to the Cu 2 O-stable condition: 250 and 50 μTorr, and to the Cu-stable condition: 10 and 1 μTorr, and the annealing time is controlled to 1, 3, 6, and 12 h at each p O 2 to consider the reaction kinetics.…”