ABSTRACT
Fingerprint distances, which measure the similarity of atomic environments, are commonly calculated from atomic environment fingerprint vectors. In this work, we present the simplex method that can perform the inverse operation, i.e., calculating fingerprint vectors from fingerprint distances. The fingerprint vectors found in this way point to the corners of a simplex. For a large dataset of fingerprints, we can find a particular largest simplex, whose dimension gives the effective dimension of the fingerprint vector space. We show that the corners of this simplex correspond to landmark environments that can be used in a fully automatic way to analyze structures. In this way, we can, for instance, detect atoms in grain boundaries or on edges of carbon flakes without any human input about the expected environment. By projecting fingerprints on the largest simplex, we can also obtain fingerprint vectors that are considerably shorter than the original ones but whose information content is not significantly reduced.
ABSTRACT
Stabilization of different morphologies of iso-material native/non-native heterostructures is important for electron-hole separation in the context of photo-electrochemical and opto-electronic devices. In this regard, we explore the stabilities of different morphologies of rutile ("native", ground state phase) and anatase ("non-native" phase) TiO2 heterostructures through (1) seed-mediated growth and (2) a thermally induced arrested phase transition synthesis protocol. Furthermore, the experimental results are analyzed through a combination of Density Functional Tight Binding (DFTB) and Finite Element Model (FEM) methods. During the seed-mediated growth, anatase is grown over a polydispersed and polycrystalline rutile core through thermal treatment yielding core-shell, Janus and yolk-shell iso-material heterostructures as observed from HRTEM. The arrested phase transition of anatase to rutile at different annealing temperatures yields rutile crystals in the subsurface region of the anatase and rutile/core-thin anatase/shell heterostructures but does not yield a Janus structure. Small particles that can be modeled via DFTB computations suggest that: (1) a heterostructure of the rutile/core-anatase/shell is energetically more stable than the anatase/core-rutile/shell or any other Janus configuration, (2) the off-centered rutile/core-anatase shell is more favorable to the mid-centered rutile/core-anatase shell and (3) Janus heterostructures can be stabilized when the mass ratio of the rutile seed to anatase overgrowth is high. FEM simulations, performed to evaluate the importance of stress relaxation in bicrystalline materials without defects, suggest that Janus structures can be stabilized in larger particles. The present studies add to the heuristics available for synthesizing iso-material heterostructures.
ABSTRACT
Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster LJ_{38}, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C_{60} and C_{20}H_{20}, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.
