Atomic Cluster Expansion for Quantum-Accurate Large-Scale Simulations of Carbon.

We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parametrized from an exhaustive set of important carbon structures over extended volume and energy ranges, computed using density functional theory (DFT). Rigorous validation reveals that ACE accurately predicts a broad range of properties of both crystalline and amorphous carbon phases while being several orders of magnitude more computationally efficient than available machine learning models. We demonstrate the predictive power of ACE on three distinct applications: brittle crack propagation in diamond, the evolution of amorphous carbon structures at different densities and quench rates, and the nucleation and growth of fullerene clusters under high-pressure and high-temperature conditions.

Role of pre-ordered liquid in the selection mechanism of crystal polymorphs during nucleation.

We investigate the atomistic mechanism of homogeneous nucleation during solidification in molybdenum employing transition path sampling. The mechanism is characterized by the formation of a pre-structured region of high bond-orientational order in the supercooled liquid followed by the emergence of the crystalline bulk phase within the center of the growing solid cluster. This precursor plays a crucial role in the process as it provides a diffusive interface between the liquid and crystalline core, which lowers the interfacial free energy and facilitates the formation of the bulk phase. Furthermore, the structural features of the pre-ordered regions are distinct from the liquid and solid phases and preselect the specific polymorph that nucleates. The similarity in the nucleation mechanism of Mo with that of metals that exhibit different crystalline bulk phases indicates that the formation of a precursor is a general feature observed in these materials. The strong influence of the structural characteristics of the precursors on the final crystalline bulk phase demonstrates that for the investigated system, polymorph selection takes place in the very early stages of nucleation.

Identification of a multi-dimensional reaction coordinate for crystal nucleation in Ni3Al.

Nucleation during solidification in multi-component alloys is a complex process that comprises competition between different crystalline phases as well as chemical composition and ordering. Here, we combine transition interface sampling with an extensive committor analysis to investigate the atomistic mechanisms during the initial stages of nucleation in Ni3Al. The formation and growth of crystalline clusters from the melt are strongly influenced by the interplay between three descriptors: the size, crystallinity, and chemical short-range order of the emerging nuclei. We demonstrate that it is essential to include all three features in a multi-dimensional reaction coordinate to correctly describe the nucleation mechanism, where, in particular, the chemical short-range order plays a crucial role in the stability of small clusters. The necessity of identifying multi-dimensional reaction coordinates is expected to be of key importance for the atomistic characterization of nucleation processes in complex, multi-component systems.

Experimental and Theoretical Investigation on Phase Formation and Mechanical Properties in Cr-Co-Ni Alloys Processed Using a Novel Thin-Film Quenching Technique.

The Cr-Co-Ni system was studied by combining experimental and computational methods to investigate phase stability and mechanical properties. Thin-film materials libraries were prepared and quenched from high temperatures up to 700 °C using a novel quenching technique. It could be shown that a wide A1 solid solution region exists in the Cr-Co-Ni system. To validate the results obtained using thin-film materials libraries, bulk samples of selected compositions were prepared by arc melting, and the experimental data were additionally compared to results from DFT calculations. The computational results are in good agreement with the measured lattice parameters and elastic moduli. The lattice parameters increase with the addition of Co and Cr, with a more pronounced effect for the latter. The addition of ∼20 atom % Cr results in a similar hardening effect to that of the addition of ∼40 atom % Co.

Fast diffusion mechanism in Li4P2S6 via a concerted process of interstitial Li ions.

The synthesis of Li superionic conductor Li7P3S11 may be accompanied by the formation of a detrimental Li4P2S6 phase due to a high mixing sensitivity of precursor materials. This phase exhibits a poor ionic conductivity whose origins are not fully understood. Recently Dietrich et al. investigated the energetics of Li ion migration in Li4P2S6 with nudged elastic band (NEB) calculations. The observed large migration barrier of 0.51 eV for purely interstitial diffusion leads to an interpretation of the low ionic conductivity by kinetic limitations. Based on ab initio molecular dynamics simulations (AIMD) we propose a new and energetically much more favorable diffusion path available to interstitial Li ion charge carriers that has not been considered so far. It consists of a concerted process in which a second lithium atom is pushed out from its equilibrium lattice position by the diffusing lithium ion. A detailed analysis with NEB calculations shows that the energy barrier for this concerted diffusion is only 0.08 eV, i.e. an order of magnitude lower than the previously reported value for purely interstitial diffusion. Therefore, the observed low ionic conductivity of Li4P2S6 is likely not originating from kinetic limitations due to high diffusion barriers but rather from thermodynamic reasons associated with a low concentration of free charge carriers. We therefore expect that increasing the charge carrier concentration by doping is a viable design route to optimize the ionic conductivity of this material.

Atomistic insight into the non-classical nucleation mechanism during solidification in Ni.

Nucleation is a key step during crystallization, but a complete understanding of the fundamental atomistic processes remains elusive. We investigate the mechanism of nucleation during solidification in nickel for various undercoolings using transition path sampling simulations. The temperature dependence of the free energy barriers and rate constants that we obtain is consistent with the predictions of classical nucleation theory and experiments. However, our analysis of the transition path ensemble reveals a mechanism that deviates from the classical picture of nucleation: the growing solid clusters have predominantly non-spherical shapes and consist of face-centered-cubic and random hexagonal-close-packed coordinated atoms surrounded by a cloud of prestructured liquid. The nucleation initiates in regions of supercooled liquid that are characterized by a high orientational order with structural features that predetermine the polymorph selection. These results provide atomistic insight not only into the nucleation mechanism of nickel but also into the role of the preordered liquid regions as precursors for crystallization.

Collective Atomic Displacements during Complex Phase Boundary Migration in Solid-Solid Phase Transformations.

The A15 to bcc phase transition is simulated at the atomic scale based on an interatomic potential for molybdenum. The migration of the phase boundary proceeds via long-range collective displacements of entire groups of atoms across the interface. To capture the kinetics of these complex atomic rearrangements over extended time scales we use the adaptive kinetic Monte Carlo approach. An effective barrier of 0.5 eV is determined for the formation of each new bcc layer. This barrier is not associated with any particular atomistic process that governs the dynamics of the phase boundary migration. Instead, the effective layer transformation barrier represents a collective property of the complex potential energy surface.

Thermodynamic and kinetic solid-liquid interface properties from transition path sampling.

We perform transition path sampling simulations to determine two of the key quantities in solidification, the solid-liquid interface energy and velocity, in a Lennard-Jones system. Our approach is applicable to a wide range of temperature and pressure conditions, at the melting temperature and out-of-equilibrium. We show that small system sizes are sufficient for good values of interface energies and velocities. The transition path sampling method thus offers an attractive and robust alternative for the evaluation of solid-liquid interface properties.

Atomistically Informed Extended Gibbs Energy Description for Phase-Field Simulation of Tempering of Martensitic Steel.

In this study we propose a unified multi-scale chemo-mechanical description of the BCT (Body-Centered Tetragonal) to BCC (Body-Centered Cubic) order-disorder transition in martensitic steel by adding the mechanical degrees of freedom to the standard CALPHAD (CALculation of PHAse Diagrams) type Gibbs energy description. The model takes into account external strain, the effect of carbon composition on the lattice parameter and elastic moduli. The carbon composition effect on the lattice parameters and elastic constants is described by a sublattice model with properties obtained from DFT (Density Functional Theory) calculations; the temperature dependence of the elasticity parameters is estimated from available experimental data. This formalism is crucial for studying the kinetics of martensite tempering in realistic microstructures. The obtained extended Gibbs energy description opens the way to phase-field simulations of tempering of martensitic steel comprising microstructure evolution, carbon diffusion and lattice symmetry change due to the ordering/disordering of carbon atoms under multiaxial load.

Martensitic transformation between competing phases in Ti-Ta alloys: a solid-state nudged elastic band study.

A combined density functional theory and solid-state nudged elastic band study is presented to investigate the martensitic transformation between ߠ→ (α″, ω) phases in the Ti-Ta system. The minimum energy paths along the transformation are calculated and the transformation mechanisms as well as relative stabilities of the different phases are discussed for various compositions. The analysis of the transformation paths is complemented by calculations of phonon spectra to determine the dynamical stability of the ß, α″, and ω phase. Our theoretical results confirm the experimental findings that with increasing Ta concentration there is a competition between the destabilisation of the α″ and ω phase and the stabilisation of the high-temperature ß phase.

Non-collinear magnetism with analytic Bond-Order Potentials.

The theory of analytic Bond-Order Potentials as applied to non-collinear magnetic structures of transition metals is extended to take into account explicit rotations of Hamiltonian and local moment matrix elements between locally and globally defined spin-coordinate systems. Expressions for the gradients of the energy with respect to the Hamiltonian matrix elements, the interatomic forces and the magnetic torques are derived. The method is applied to simulations of the rotation of magnetic moments in α iron, as well as α and ß manganese, based on d-valent orthogonal tight-binding parametrizations of the electronic structure. A new weighted-average terminator is introduced to improve the convergence of the Bond-Order Potential energies and torques with respect to tight-binding reference values, although the general behavior is qualitatively correct for low-moment expansions.

Vacancy mobility and interaction with transition metal solutes in Ni.

Interaction of Re, Ta, W and Mo solutes with vacancies and their diffusion in fcc Ni is investigated by density-functional theory in combination with kinetic Monte Carlo simulations. Interaction energies are calculated for the first six neighbor shells around the solutes and a complete set of diffusion barriers for these shells is provided. Further, diffusion coefficients for the four elements in Ni as well as for vacancies in the presence of these elements are calculated. The calculated solute diffusion coefficients based on our ab initio data are found to compare favorably to experimental values. The mobility of the vacancies as a key factor in dislocation climb is only minimally influenced by the solute atoms within the dilute limit.

Parameterized electronic description of carbon cohesion in iron grain boundaries.

We employ a recently developed iron-carbon orthogonal tight-binding model in calculations of carbon in iron grain boundaries. We use the model to evaluate the properties of carbon near and on the Σ5 (3 1 0)[0 0 1] symmetric tilt grain boundary (GB) in iron, and calculations show that a carbon atom lowers the GB energy by 0.29 eV/atom in accordance with DFT. Carbon segregation to the GB is analyzed, and we find an energy barrier of 0.92 eV for carbon to segregate to the carbon-free interface while segregation to a fully filled interface is disfavored. Local volume (via Voronoi tessellation), magnetic, and electronic effects are correlated with atomic energy changes, and we isolate two different mechanisms governing carbon's behavior in iron: a volumetric strain which increases the energy of carbon in interstitial α iron and a non-strained local bonding which stabilizes carbon at the GB.

Modelling the lattice dynamics in Si(x)Ge(1-x) alloys.

The development of simplified models for the simulation of thermodynamic and thermal transport properties in random alloys is of great importance. In this paper we show how a simple second nearest neighbour model can reliably capture the lattice dynamics of Si(x)Ge(1-x) alloys. The model parameters are extracted from DFT-calculated force constant matrices for pure Si, pure Ge and the Si0.5Ge0.5 ordered alloy. We extract the nearest neighbour contributions directly from density functional theory, whereas effective interactions are obtained for the second nearest neighbour contributions. We demonstrate how the thermal properties, including the expansion coefficient, can be reliably reproduced and that the model is transferable to random Si(x)Ge(1-x) alloys.

Environmental tight-binding modeling of nickel and cobalt clusters.

Tight-binding models derived from density functional theory potentially provide a systematic approach to the development of accurate and transferable models of multicomponent systems. We introduce a systematic methodology for environmental tight binding in which both the overlap and environmental contributions to the electronic structure are included. The parameters of the model are determined directly from ab initio considerations, thus providing a formal conceptual link to density functional approaches. In order to test the validity of the approach, the model is applied to small clusters of Ni and Co, whose electronic structure is largely determined by the interplay of tightly bound d-valent states and the disperse s-states. We numerically illustrate that it is essential to include environmental contributions in the tight-binding approach in order to reliably reproduce the electronic structure of such clusters.

High throughput density functional investigations of the stability, electronic structure and thermoelectric properties of binary silicides.

The structural stabilities of binary Mg-X (X = Si, Ge, Sn) and 4d transition metal silicides Mo-Si and Ru-Si are investigated. The convex hulls of stable alloys are in overall good agreement with the known experimental phase diagrams. It is shown how the Si-rich Ru-Si structures have band gaps at the Fermi-level and how the Ru(2)Si(3) structure is stabilized compared to the corresponding Fe(2)Si(3) structure. We discuss the band structure of Ru(2)Si(3) and show how the anisotropic band masses lead to favorable calculated thermoelectric properties.

Tight-binding simulation of transition-metal alloys.

In order to perform atomistic simulations of steel, it is necessary to have a detailed understanding of the complex interatomic interactions in transition metals and their alloys. The tight-binding approximation provides a computationally efficient, yet accurate, method to investigate such interactions. In the present work, an orthogonal tight-binding model for Fe, Mn and Cr, with the explicit inclusion of magnetism, has been parameterized from ab initio density-functional calculations.

Cluster expansions in multicomponent systems: precise expansions from noisy databases.

We have performed a systematic analysis of the numerical errors contained in the databases used in cluster expansions of multicomponent alloys. Our results underscore the importance of numerical noise in the determination of the effective cluster interactions and in the expansion determination. The relevance of the size of and information contained in the input database is highlighted. It is shown that cross-validatory approaches by themselves can produce unphysical expansions characterized by non-negligible, long-ranged coefficients. A selection criterion that combines both forecasting ability and a physical limiting behavior for the expansion is proposed. Expansions performed under this criterion exhibit the remarkable property of noise filtering. A discussion of the impact of this unforeseen characteristic of the cluster expansion method on the modeling of multicomponent alloy systems is presented.

Ordering and magnetism in Fe-Co: dense sequence of ground-state structures.

We discover that Fe-Co alloys develop a series of ordered ground-state structures in addition to the known CsCl-type structure. This new set of structures is found from a combinatorial ground-state search of 1.5 x 10(10) bcc-based structures. The energies of the searched bcc structures are constructed with the cluster expansion method from few first-principles calculations of ordered Fe-Co structures. The set of new ground-state structures is explained from the decay behavior of the cluster expansion coefficients which allows us to identify a simple geometric motif common to all structures. The appearance of these FeCo superstructures offers a broader view of the ordering reactions in bipartite-lattice based binary alloys.