A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials

Abstract

We present an evolutionary algorithm which predicts stable atomic structures and phase diagrams by searching the energy landscape of empirical and ab initio Hamiltonians. Composition and geometrical degrees of freedom may be varied simultaneously. We show that this method utilizes information from favorable local structure at one composition to predict that at others, achieving far greater efficiency of phase diagram prediction than a method which relies on sampling compositions individually. We detail this and a number of other efficiency-improving techniques implemented in the genetic algorithm for structure prediction code that is now publicly available. We test the efficiency of the software by searching the ternary Zr-Cu-Al system using an empirical embedded-atom model potential. In addition to testing the algorithm, we also evaluate the accuracy of the potential itself. We find that the potential stabilizes several correct ternary phases, while a few of the predicted ground states are unphysical. Our results suggest that genetic algorithm searches can be used to improve the methodology of empirical potential design.

Ab initio prediction of the Li5Ge2 Zintl compound

“…An ab initio structure search was performed using the GASP code [11][12][13] to explore the low-energy structures of the Li-Ge phase diagram. It uses a grand-canonical genetic algorithm to find structures, which minimize the formation energy with respect to elemental Li and Ge for all compositions between those two endpoints.…”

“…The Li-Ge binary phase diagram is created from the computed formation energies using the convex hull construction [11]. The voltage curve describing the potential of a Li/Ge anode as a function of lithium content with respect to Li/Li + was computed from the energies of the ground state phases [20,21].…”

“…This allows us to predict the voltage characteristics and charge capacity of a germanium anode. Furthermore, we search the phase diagram using the Genetic Algorithm for Structure and Phase Prediction (GASP) code [11][12][13]. This search identifies a structure with composition Li 5 Ge 2 which does not appear in previous phase diagrams but which we predict to be thermodynamically stable with respect to all competing phases at low temperature.…”

Prediction of two‐dimensional materials by the global optimization approach

“…Wang et al and Glass et al used the negative of the ab initio total energy of the locally optimized structure as fitness value. Differently, Tipton et al normalized the fitness in the context of its generation. In particular, an organism with an objective function of value k is assigned a fitness f given by where a and b are the objective function values of the worst and best structures in the current generation, respectively.…”

“…Tipton et al directly compare atomic positions to identify duplicate structures in the population . During the search, two separate lists of previously observed structures are maintained.…”