Exploring the configuration space of elemental carbon with empirical and machine learned interatomic potentials

Abstract

We demonstrate how the many-body potential energy landscape of carbon can be explored with the nested sampling algorithm, allowing for the calculation of its pressure-temperature phase diagram. We compare four interatomic potential models: Tersoff, EDIP, GAP-20 and its recently updated version, GAP-20U. Our evaluation is focused on their macroscopic properties, melting transitions, and identifying thermodynamically stable solid structures up to at least 100 GPa. The phase diagrams of the GAP models show good agreement with experimental results. However, we find that the models’ description of graphite includes thermodynamically stable phases with incorrect layer spacing. By adding a suitable selection of structures to the database and re-training the potential, we have derived an improved model — GAP-20U+gr — that suppresses erroneous local minima in the graphitic energy landscape. At extreme high pressure nested sampling identifies two novel stable structures in the GAP-20 model, however, the stability of these is not confirmed by electronic structure calculations, highlighting routes to further extend the applicability of the GAP models.

Neural-network force field backed nested sampling: Study of the silicon p−T phase diagram

“…For the three pressures we ran using 64 atoms, at 4 and 10 GPa the melting temperature decreases by around 100 K; at 16 GPa almost no shift appears. A similar trend was recently observed in a NS study of carbon, where the finite-size effect almost diminished above a pressure of 100 GPa [12].…”

“…The successful use of neural-network force fields together with nested sampling adds to the growing field of calculating phase diagrams using machine-learned force fields [12,50,51]. Despite their success, machine-learned force fields still heavily rely on the quality, size, and diversity of the training datasets to deliver accurate and reliable results.…”

“…With the emergence of efficient machine-learned force fields (MLFFs), the sampling of potential energy surfaces (PESs) at a level of accuracy similar to the underlying ab initio method becomes affordable for NS. In this context, it has been applied in conjunction with Gaussian approximation potentials and moment tensor potentials to predict the thermodynamic behavior of carbon [12], platinum [13], and AgPd [14] alloys.…”

Experiment-Driven Atomistic Materials Modeling: A Case Study Combining X-Ray Photoelectron Spectroscopy and Machine Learning Potentials to Infer the Structure of Oxygen-Rich Amorphous Carbon

“…The problems with empirical potentials have been widely stated and will not be commented on here in detail. This includes detailed comparisons of their performance against the Gaussian approximation potential (GAP) framework used here, even for the case of simulating disordered carbon materials specifically. − In brief, these potentials cannot accurately reproduce the PES except for in those regions of configuration space for which they were optimized. They are usually parametrized for specific materials and can fail spectacularly, or even catastrophically (“blow up”, in jargon), when configurations are out of the scope of the fit.…”

Surface phase diagrams from nested sampling

“…NS was first introduced in Bayesian statistics, 41,42 and was later adopted by various research fields 43 and adapted to sample the PES of atomic-scale systems. 40,44,45 The power of NS has been demonstrated in studying various systems, including the formation of clusters, 46,47 calculation of the quantum partition function, 48 sampling transition paths, 49 as well as computing the pressure-temperature phase diagram for various metals, alloys, and model potentials, [50][51][52][53][54] which often identified previously unknown stable solid phases.…”