Synchronization of trajectories in canonical molecular-dynamics simulations: Observation, explanation, and exploitation

For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simulation, the Langevin thermostat and the Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] thermostat, we observe, as have others, synchronization of initially independent trajectories in the same potential basin when the same random number sequence is employed. For the first time, we derive the time dependence of this synchronization for a harmonic well and show that the rate of synchronization is proportional to the thermostat coupling strength at weak coupling and inversely proportional at strong coupling with a peak in between. Explanations for the synchronization and the coupling dependence are given for both thermostats. Observation of the effect for a realistic 97-atom system indicates that this phenomenon is quite general. We discuss some of the implications of this effect and propose that it can be exploited to develop new simulation techniques. We give three examples: efficient thermalization (a concept which was also noted by Fahy and Hamann [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)]), time-parallelization of a trajectory in an infrequent-event system, and detecting transitions in an infrequent-event system.

Efficient annealing of radiation damage near grain boundaries via interstitial emission

Although grain boundaries can serve as effective sinks for radiation-induced defects such as interstitials and vacancies, the atomistic mechanisms leading to this enhanced tolerance are still not well understood. With the use of three atomistic simulation methods, we investigated defect-grain boundary interaction mechanisms in copper from picosecond to microsecond time scales. We found that grain boundaries have a surprising "loading-unloading" effect. Upon irradiation, interstitials are loaded into the boundary, which then acts as a source, emitting interstitials to annihilate vacancies in the bulk. This unexpected recombination mechanism has a much lower energy barrier than conventional vacancy diffusion and is efficient for annihilating immobile vacancies in the nearby bulk, resulting in self-healing of the radiation-induced damage.

Machine learning bandgaps of double perovskites

The ability to make rapid and accurate predictions on bandgaps of double perovskites is of much practical interest for a range of applications. While quantum mechanical computations for high-fidelity bandgaps are enormously computation-time intensive and thus impractical in high throughput studies, informatics-based statistical learning approaches can be a promising alternative. Here we demonstrate a systematic feature-engineering approach and a robust learning framework for efficient and accurate predictions of electronic bandgaps of double perovskites. After evaluating a set of more than 1.2 million features, we identify lowest occupied Kohn-Sham levels and elemental electronegativities of the constituent atomic species as the most crucial and relevant predictors. The developed models are validated and tested using the best practices of data science and further analyzed to rationalize their prediction performance.

Radiation-induced amorphization resistance and radiation tolerance in structurally related oxides

Ceramics destined for use in hostile environments such as nuclear reactors or waste immobilization must be highly durable and especially resistant to radiation damage effects. In particular, they must not be prone to amorphization or swelling. Few ceramics meet these criteria and much work has been devoted in recent years to identifying radiation-tolerant ceramics and the characteristics that promote radiation tolerance. Here, we examine trends in radiation damage behaviour for families of compounds related by crystal structure. Specifically, we consider oxides with structures related to the fluorite crystal structure. We demonstrate that improved amorphization resistance characteristics are to be found in compounds that have a natural tendency to accommodate lattice disorder.

Structure and segregation of dopant–defect complexes at grain boundaries in nanocrystalline doped ceria

Σ5 twist grain boundary plane in doped ceria with dopant–defect complexes.

Structure and mobility of defects formed from collision cascades in MgO

We study radiation-damage events in MgO on experimental time scales by augmenting molecular dynamics cascade simulations with temperature accelerated dynamics, molecular statics, and density functional theory. At 400 eV, vacancies and mono- and di-interstitials form, but often annihilate within milliseconds. At 2 and 5 keV, larger clusters can form and persist. While vacancies are immobile, interstitials aggregate into clusters (In) with surprising properties; e.g., an I4 is immobile, but an impinging I2 can create a metastable I6 that diffuses on the nanosecond time scale but is stable for years.

Direct transformation of vacancy voids to stacking fault tetrahedra

Defect accumulation is the principal factor leading to the swelling and embrittlement of materials during irradiation. It is commonly assumed that, once defect clusters nucleate, their structure remains essentially constant while they grow in size. Here, we describe a new mechanism, discovered during accelerated molecular dynamics simulations of vacancy clusters in fcc metals, that involves the direct transformation of a vacancy void to a stacking fault tetrahedron (SFT) through a series of 3D structures. This mechanism is in contrast with the collapse to a 2D Frank loop which then transforms to an SFT. The kinetics of this mechanism are characterized by an extremely large rate prefactor, tens of orders of magnitude larger than is typical of atomic processes in fcc metals.

Parallel replica dynamics with a heterogeneous distribution of barriers: Application ton-hexadecane pyrolysis

Parallel replica dynamics simulation methods appropriate for the simulation of chemical reactions in molecular systems with many conformational degrees of freedom have been developed and applied to study the microsecond-scale pyrolysis of n-hexadecane in the temperature range of 2100-2500 K. The algorithm uses a transition detection scheme that is based on molecular topology, rather than energetic basins. This algorithm allows efficient parallelization of small systems even when using more processors than particles (in contrast to more traditional parallelization algorithms), and even when there are frequent conformational transitions (in contrast to previous implementations of the parallel replica algorithm). The parallel efficiency for pyrolysis initiation reactions was over 90% on 61 processors for this 50-atom system. The parallel replica dynamics technique results in reaction probabilities that are statistically indistinguishable from those obtained from direct molecular dynamics, under conditions where both are feasible, but allows simulations at temperatures as much as 1000 K lower than direct molecular dynamics simulations. The rate of initiation displayed Arrhenius behavior over the entire temperature range, with an activation energy and frequency factor of E(a) = 79.7 kcal/mol and log A/s(-1) = 14.8, respectively, in reasonable agreement with experiment and empirical kinetic models. Several interesting unimolecular reaction mechanisms were observed in simulations of the chain propagation reactions above 2000 K, which are not included in most coarse-grained kinetic models. More studies are needed in order to determine whether these mechanisms are experimentally relevant, or specific to the potential energy surface used.

Multifidelity Information Fusion with Machine Learning: A Case Study of Dopant Formation Energies in Hafnia

Cost versus accuracy trade-offs are frequently encountered in materials science and engineering, where a particular property of interest can be measured/computed at different levels of accuracy or fidelity. Naturally, the most accurate measurement is also the most resource and time intensive, while the inexpensive quicker alternatives tend to be noisy. In such situations, a number of machine learning (ML) based multifidelity information fusion (MFIF) strategies can be employed to fuse information accessible from varying sources of fidelity and make predictions at the highest level of accuracy. In this work, we perform a comparative study on traditionally employed single-fidelity and three MFIF strategies, namely, (1) Δ-learning, (2) low-fidelity as a feature, and (3) multifidelity cokriging (CK) to compare their relative prediction accuracies and efficiencies for accelerated property predictions and high throughput chemical space explorations. We perform our analysis using a dopant formation energy data set for hafnia, which is a well-known high-k material and is being extensively studied for its promising ferroelectric, piezoelectric, and pyroelectric properties. We use a dopant formation energy data set of 42 dopants in hafnia-each studied in six different hafnia phases-computed at two levels of fidelities to find merits and limitations of these ML strategies. The findings of this work indicate that the MFIF based learning schemes outperform the traditional SF machine learning methods, such as Gaussian process regression and CK provides an accurate, inexpensive and flexible alternative to other MFIF strategies. While the results presented here are for the case study of hafnia, they are expected to be general. Therefore, materials discovery problems that involve huge chemical space explorations can be studied efficiently (or even made feasible in some situations) through a combination of a large number of low-fidelity and a few high-fidelity measurements/computations, in conjunction with the CK approach.

Irradiation-induced grain growth and defect evolution in nanocrystalline zirconia with doped grain boundaries

Grain boundaries are effective sinks for radiation-induced defects, ultimately impacting the radiation tolerance of nanocrystalline materials (dense materials with nanosized grains) against net defect accumulation. However, irradiation-induced grain growth leads to grain boundary area decrease, shortening potential benefits of nanostructures. A possible approach to mitigate this is the introduction of dopants to target a decrease in grain boundary mobility or a reduction in grain boundary energy to eliminate driving forces for grain growth (using similar strategies as to control thermal growth). Here we tested this concept in nanocrystalline zirconia doped with lanthanum. Although the dopant is observed to segregate to the grain boundaries, causing grain boundary energy decrease and promoting dragging forces for thermally activated boundary movement, irradiation induced grain growth could not be avoided under heavy ion irradiation, suggesting a different growth mechanism as compared to thermal growth. Furthermore, it is apparent that reducing the grain boundary energy reduced the effectiveness of the grain boundary as sinks, and the number of defects in the doped material is higher than in undoped (La-free) YSZ.

Non-uniform Solute Segregation at Semi-Coherent Metal/Oxide Interfaces

The properties and performance of metal/oxide nanocomposites are governed by the structure and chemistry of the metal/oxide interfaces. Here we report an integrated theoretical and experimental study examining the role of interfacial structure, particularly misfit dislocations, on solute segregation at a metal/oxide interface. We find that the local oxygen environment, which varies significantly between the misfit dislocations and the coherent terraces, dictates the segregation tendency of solutes to the interface. Depending on the nature of the solute and local oxygen content, segregation to misfit dislocations can change from attraction to repulsion, revealing the complex interplay between chemistry and structure at metal/oxide interfaces. These findings indicate that the solute chemistry at misfit dislocations is controlled by the dislocation density and oxygen content. Fundamental thermodynamic concepts – the Hume-Rothery rules and the Ellingham diagram – qualitatively predict the segregation behavior of solutes to such interfaces, providing design rules for novel interfacial chemistries.

Evidence for percolation diffusion of cations and reordering in disordered pyrochlore from accelerated molecular dynamics

Diffusion in complex oxides is critical to ionic transport, radiation damage evolution, sintering, and aging. In complex oxides such as pyrochlores, anionic diffusion is dramatically affected by cation disorder. However, little is known about how disorder influences cation transport. Here, we report results from classical and accelerated molecular dynamics simulations of vacancy-mediated cation diffusion in Gd₂Ti₂O₇ pyrochlore, on the microsecond timescale. We find that diffusion is slow at low levels of disorder, while higher disorder allows for fast diffusion, which is then accompanied by antisite annihilation and reordering, and thus a slowing of cation transport. Cation diffusivity is therefore not constant, but decreases as the material reorders. We also show that fast cation diffusion is triggered by the formation of a percolation network of antisites. This is in contrast with observations from other complex oxides and disordered media models, suggesting a fundamentally different relation between disorder and mass transport.Diffusion plays an important role in sintering, damage tolerance and transport. Here authors perform classical and accelerated molecular dynamics simulations of vacancy-mediated cation diffusion in Gd₂Ti₂O₇ pyrochlore and report non-monotonic evolution of cation diffusivity.

Radiation tolerance of nanocrystalline ceramics: insights from Yttria Stabilized Zirconia

Materials for applications in hostile environments, such as nuclear reactors or radioactive waste immobilization, require extremely high resistance to radiation damage, such as resistance to amorphization or volume swelling. Nanocrystalline materials have been reported to present exceptionally high radiation-tolerance to amorphization. In principle, grain boundaries that are prevalent in nanomaterials could act as sinks for point-defects, enhancing defect recombination. In this paper we present evidence for this mechanism in nanograined Yttria Stabilized Zirconia (YSZ), associated with the observation that the concentration of defects after irradiation using heavy ions (Kr⁺, 400 keV) is inversely proportional to the grain size. HAADF images suggest the short migration distances in nanograined YSZ allow radiation induced interstitials to reach the grain boundaries on the irradiation time scale, leaving behind only vacancy clusters distributed within the grain. Because of the relatively low temperature of the irradiations and the fact that interstitials diffuse thermally more slowly than vacancies, this result indicates that the interstitials must reach the boundaries directly in the collision cascade, consistent with previous simulation results. Concomitant radiation-induced grain growth was observed which, as a consequence of the non-uniform implantation, caused cracking of the nano-samples induced by local stresses at the irradiated/non-irradiated interfaces.

The role of surfaces, chemical interfaces, and disorder on plutonium incorporation in pyrochlores

Pyrochlores, a class of complex oxides with formula A2B2O7, are one of the candidates for nuclear waste encapsulation, due to the natural occurrence of actinide-bearing pyrochlore minerals and laboratory observations of high radiation tolerance. In this work, we use atomistic simulations to determine the role of surfaces, chemical interfaces, and cation disorder on the plutonium immobilization properties of pyrochlores as a function of pyrochlore chemistry. We find that both Pu(3+) and Pu(4+) segregate to the surface for the four low-index pyrochlore surfaces considered, and that the segregation energy varies with the chemistry of the compound. We also find that pyrochlore/pyrochlore bicrystals A2B2O7/A2'B2'O7 can be used to immobilize Pu(3+) and Pu(4+) either in the same or separate phases of the compound, depending on the chemistry of the material. Finally, we find that Pu(4+) segregates to the disordered phase of an order/disorder bicrystal, driven by the occurrence of local oxygen-rich environments. However, Pu(3+) is weakly sensitive to the oxygen environment, and therefore only slightly favors the disordered phase. This behavior suggests that, at some concentration, Pu incorporation can destabilize the pyrochlore structure. Together, these results provide new insight into the ability of pyrochlore compounds to encapsulate Pu and suggest new considerations in the development of waste forms based on pyrochlores. In particular, the phase structure of a multi-phase pyrochlore composite can be used to independently getter decay products based on their valence and size.

Competing kinetics and he bubble morphology in W

The growth process of He bubbles in W is investigated using molecular dynamics and parallel replica dynamics for growth rates spanning 6 orders of magnitude. Fast and slow growth regimes are defined relative to typical diffusion hopping times of W interstitials around the He bubble. Slow growth rates allow the diffusion of interstitials around the bubble, favoring the biased growth of the bubble towards the surface. In contrast, at fast growth rates interstitials do not have time to diffuse around the bubble, leading to a more isotropic growth and increasing the surface damage.

Efficient Ab initio Modeling of Random Multicomponent Alloys

We present in this Letter a novel small set of ordered structures (SSOS) method that allows extremely efficient ab initio modeling of random multicomponent alloys. Using inverse II-III spinel oxides and equiatomic quinary bcc (so-called high entropy) alloys as examples, we demonstrate that a SSOS can achieve the same accuracy as a large supercell or a well-converged cluster expansion, but with significantly reduced computational cost. In particular, because of this efficiency, a large number of quinary alloy compositions can be quickly screened, leading to the identification of several new possible high-entropy alloy chemistries. The SSOS method developed here can be broadly useful for the rapid computational design of multicomponent materials, especially those with a large number of alloying elements, a challenging problem for other approaches.

Diffusion of Ge below the Si(100) surface: theory and experiment

We have studied diffusion of Ge into subsurface layers of Si(100). Auger electron diffraction measurements show Ge in the fourth layer after submonolayer growth at temperatures as low as 500 degrees C. Density functional theory predictions of equilibrium Ge subsurface distributions are consistent with the measurements. We identify a surprisingly low energy pathway resulting from low interstitial formation energy in the third and fourth layers. Doping significantly affects the formation energy, suggesting that n-type doping may lead to sharper Si/Ge interfaces.

Role of antisite disorder on preamorphization swelling in titanate pyrochlores

Ion irradiation experiments and atomistic simulations were used to demonstrate that irradiation-induced lattice swelling in a complex oxide, Lu2Ti2O7, is due initially to the formation of cation antisite defects. X-ray diffraction revealed that cation antisite formation correlates directly with lattice swelling and indicates that the volume per antisite pair is approximately 12  Å3. First principles calculations revealed that lattice swelling is best explained by cation antisite defects. Temperature accelerated dynamics simulations indicate that cation Frenkel defects are metastable and decay to form antisite defects.

The effects of cation-anion clustering on defect migration in MgAl2O4

Magnesium aluminate spinel (MgAl2O4), like many other ceramic materials, offers a range of technological applications, from nuclear reactor materials to military body armor. For many of these applications, it is critical to understand both the formation and evolution of lattice defects throughout the lifetime of the material. We use the Speculatively Parallel Temperature Accelerated Dynamics (SpecTAD) method to investigate the effects of di-vacancy and di-interstitial formation on the mobility of the component defects. From long-time trajectories of the state-to-state dynamics, we characterize the migration pathways of defect clusters, and calculate their self-diffusion constants across a range of temperatures. We find that the clustering of Al and O vacancies drastically reduces the mobility of both defects, while the clustering of Mg and O vacancies completely immobilizes them. For interstitials, we find that the clustering of Mg and O defects greatly reduces O interstitial mobility, but has only a weak effect on Mg. These findings illuminate important new details regarding defect kinetics relevant to the application of MgAl2O4 in extreme environments.