The seventh blind test of crystal structure prediction: structure generation methods.

A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern.

Machine Learning Classification of Local Environments in Molecular Crystals.

Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of molecular crystals using learning models that employ either flexibly learned or handcrafted molecular representations. In the first case, we follow our earlier work on graph learning in molecular crystals, deploying an atomistic graph convolutional network combined with molecule-wise aggregation to enable per-molecule environmental classification.

Controlling crystallization: what liquid structure and dynamics reveal about crystal nucleation mechanisms.

Over recent years, molecular simulations have provided invaluable insights into the microscopic processes governing the initial stages of crystal nucleation and growth. A key aspect that has been observed in many different systems is the formation of precursors in the supercooled liquid that precedes the emergence of crystalline nuclei. The structural and dynamical properties of these precursors determine to a large extent the nucleation probability as well as the formation of specific polymorphs.

Geometric Deep Learning for Molecular Crystal Structure Prediction.

We develop and test new machine learning strategies for accelerating molecular crystal structure ranking and crystal property prediction using tools from geometric deep learning on molecular graphs. Leveraging developments in graph-based learning and the availability of large molecular crystal data sets, we train models for density prediction and stability ranking which are accurate, fast to evaluate, and applicable to molecules of widely varying size and composition. Our density prediction model, MolXtalNet-D, achieves state-of-the-art performance, with lower than 2% mean absolute error on a large and diverse test data set.

Practical guide to replica exchange transition interface sampling and forward flux sampling.

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results.

Template-Induced Precursor Formation in Heterogeneous Nucleation: Controlling Polymorph Selection and Nucleation Efficiency.

We present an atomistic study of heterogeneous nucleation in Ni employing transition path sampling, which reveals a template precursor-mediated mechanism of crystallization. Most notably, we find that the ability of tiny templates to modify the structural features of the liquid and promote the formation of precursor regions with enhanced bond-orientational order is key to determining their nucleation efficiency and the polymorphs that crystallize. Our results reveal an intrinsic link between structural liquid heterogeneity and the nucleating ability of templates, which significantly advances our understanding toward the control of nucleation efficiency and polymorph selection.

Interplay of structural and dynamical heterogeneity in the nucleation mechanism in nickel.

Gaining a fundamental understanding of crystal nucleation processes in metal alloys is crucial for the development and design of high-performance materials with targeted properties. Yet, crystallization is a complex non-equilibrium process and, despite having been studied for decades, the microscopic aspects that govern the crystallization mechanism of a material remain elusive to date. Recent evidence shows that the spatial heterogeneity in the supercooled liquid, characterised by extended regions with distinctive mobility and order, may be a key microscopic factor that determines the mechanism of crystal nucleation.

Trends in elastic properties of Ti-Ta alloys from first-principles calculations.

The martensitic start temperature () is a technologically fundamental characteristic of high-temperature shape memory alloys. We have recently shown [Chakraborty2016B224104] that the two key features in describing the composition dependence ofare the= 0 K phase stability and the difference in vibrational entropy which, within the Debye model, is directly linked to the elastic properties. Here, we use density functional theory together with special quasi-random structures to study the elastic properties of disordered martensite and austenite Ti-Ta alloys as a function of composition.

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.

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

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 NiAl. 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.

Mechanism of collective interstitial ordering in Fe-C alloys.

Collective interstitial ordering is at the core of martensite formation in Fe-C-based alloys, laying the foundation for high-strength steels. Even though this ordering has been studied extensively for more than a century, some fundamental mechanisms remain elusive. Here, we show the unexpected effects of two correlated phenomena on the ordering mechanism: anharmonicity and segregation.

Neural-Network-Based Path Collective Variables for Enhanced Sampling of Phase Transformations.

The investigation of the microscopic processes underlying structural phase transformations in solids is extremely challenging for both simulation and experiment. Atomistic simulations of solid-solid phase transitions require extensive sampling of the corresponding high-dimensional and often rugged energy landscape. Here, we propose a rigorous construction of a 1D path collective variable that is used in combination with enhanced sampling techniques for efficient exploration of the transformation mechanisms.

Maximum Likelihood Analysis of Reaction Coordinates during Solidification in Ni.

Understanding the underlying mechanism of crystal nucleation is a fundamental aspect in the prediction and control of materials properties. Classical nucleation theory (CNT) assumes that homogeneous nucleation occurs via random fluctuations within the supercooled liquid, that the structure of the growing clusters resembles the most stable bulk phase, and that the nucleus size is the sole reaction coordinate (RC) of the process. Many materials are, however, known to exhibit multiple steps during crystallization, forming different polymorphs.

Origin of Structural Modulations in Ultrathin Fe Films on Cu(001).

Employing ab initio calculations we demonstrate that the complex structural modulations experimentally observed in ultrathin Fe films on Cu(001) originate from Fe bulk phases that arise under extreme deformations. Specifically, we show that the structural modulations correspond to the motifs observed when transforming fcc Fe to bcc Fe in the Pitsch orientation relationship [(001)_{fcc}||(11[over ¯]0)_{bcc}]. The observed structural equivalence between surface and unstable bulk structures naturally explains the experimentally reported magnetic and structural transitions when going from low (two to four MLs) to intermediate (four to ten MLs) film coverages.

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.

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.

Comparison of minimum-action and steepest-descent paths in gradient systems.

On high-dimensional and complex potential energy surfaces, the identification of the most likely mechanism for the transition between local minima is a challenging task. Usually the steepest-descent path is used interchangeably with the minimum-energy path and is associated with the most likely path. Here we compare the meaning of the steepest-descent path in complex energy landscapes to the path integral formulation of a trajectory that minimizes the action functional for Brownian dynamics.

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.

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 β → (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 β, α″, and ω phase.

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.

Solid-state dimer method for calculating solid-solid phase transitions.

The dimer method is a minimum mode following algorithm for finding saddle points on a potential energy surface of atomic systems. Here, the dimer method is extended to include the cell degrees of freedom for periodic solid-state systems. Using this method, reaction pathways of solid-solid phase transitions can be determined without having to specify the final state structure or reaction mechanism.