Having established the performance of the method for the chemical ordering optimization of particles with a fixed shape, we next turn to exploring ensembles of different shapes. In order to generate a large ensemble of stable single-metal particle shapes, we reuse the BH algorithm whereby an element 'X' is introduced as a placeholder for an empty fcc lattice site. We carry this optimization out for Pt particles of 140 atoms and recalculate the most stable structures for Au. We find more than 200 structures within a 1.0 eV energy range for Pt ( 1.4 eV for Au), and that the truncated octahedron (TO) is the global minimum for both metals. For every shape, a separate training set consisting of 100 randomly ordered structures with evenly spaced compositions is calculated at the EMT level of theory and used for fitting the parameters of our energy model (E coor CNi for CN i = 6, 7, 8, 9, 12 and E bond 0,0 , E bond 0,1 , E bond 1,1 , and a term accounting for variable composition). We then optimize the chemical ordering for every particle of the ensemble and for every composition, circumventing the difficulty of optimizing both shape and ordering at the same time. In order to speed up the ordering optimization at each composition, we feed the solution for the particle Au n Pt 140-n as the starting guess for the next previous composition (Au n+1 Pt 139-n ). This allows performing the ∼ 30k global optimizations required to find the global minimum for every shape and stoichiometry. The lowest-energy chemical orderings found for every shape and composition result in a minimum-energy hull for every shape in the ensemble, illustrating the evolution of the mixing energy within that shape as a function of composition. The mixing energy (also referred to as excess energy) represents the propensity of two metals to form bimetallic particles instead of monometallic ones, and is calculated as