Searching for iron nanoparticles with a general-purpose Gaussian approximation potential

Abstract

We present a general-purpose machine learning Gaussian approximation potential (GAP) for iron that is applicable to all bulk crystal structures found experimentally under diverse thermodynamic conditions, as well as surfaces and nanoparticles (NPs). By studying its phase diagram, we show that our GAP remains stable at extreme conditions, including those found in the Earth's core. The new GAP is particularly accurate for the description of NPs. We use it to identify new low-energy NPs, whose stability is verified by performing density functional theory calculations on the GAP structures. Many of these NPs are lower in energy than those previously available in the literature up to N atoms = 100. We further extend the convex hull of available stable structures to N atoms = 200. For these NPs, we study characteristic surface atomic motifs using data clustering and low-dimensional embedding techniques. With a few exceptions, e.g., at magic numbers N atoms = 59, 65, 76, and 78, we find that iron tends to form irregularly shaped NPs without a dominant surface character or characteristic atomic motif, and no reminiscence of crystalline features. We hypothesize that the observed disorder stems from an intricate balance and competition between the stable bulk motif formation, with bcc structure, and the stable surface motif formation, with fcc structure. We expect these results to improve our understanding of the fundamental properties and structure of low-dimensional forms of iron and to facilitate future work in the field of iron-based catalysis.

Strategic sampling with stochastic surface walking for machine learning force fields in iron's bcc–hcp phase transitions

“…This is related to the lack of highenergy region data used in the tting, although we use the SSW sampling method to avoid this problem. This phenomenon is not unique to our model; the PES calculated by Jana et al 46 used Dragoni's GAP potential 28 and Mendelev's EAM potential 60 also exhibit similar behavior. The low weight of transition state structures in the tting process, owing to their small proportion in the dataset, contributes to the challenges in accurately capturing their energy during the tting process.…”

“…At the time of our research, publicly available datasets specically focused on the structures formed by the Fe element were not identied. However, subsequent to our research work, we came across a recent paper 46 that provides a dataset on iron clusters. Regrettably, there remains a lack of available data on the bulk structure, which is directly relevant to our work.…”

“…Therefore, in Fig. 6(b), we present a failed schematic representation of the 60 Dragoni's GAP potential 28 and the latest Jana's TurboGAP potential 46 with the same structures based on our MLFF PES. The dashed line represents the barrierless prediction using MLFF trained without SSW data.…”

“…Fig.6(a)IS, TS, FS structures and (b) reaction energy profile along the Fe bcc-to-hcp phase transition pathway the double-ended surface walking trajectories from bcc to hcp phase, calculated by our MLFF, DFT, Mendelev's EAM potential,60 Dragoni's GAP potential28 and the latest Jana's TurboGAP potential46 with the same structures based on our MLFF PES. The dashed line represents the barrierless prediction using MLFF trained without SSW data.…”

Computational understanding of the coalescence of metallic nanoparticles: a mini review

“…Besides the above empirical potentials, machine learning (ML) potentials have also been developed with the rapid development of artificial intelligence technology. 43–46 For example, neural network ML potentials developed from the DeepMD-kit package (deep potentials), which are trained from a database constructed with first-principles calculations, have been demonstrated to be accurate in predicting the structural and dynamic properties of Au, 47 Ti, 48 and Fe 49 metals, and the AgAu 50 alloy. Besides, ML potentials trained using the Gaussian approximation potential framework or the spectral neighbor analysis potential approach have also proven to possess excellent accuracy.…”