Editor | Green Luo

Just like the fragrance of flowers that spreads in the wind and hits your face, the atoms and molecules in the material are also undergoing their "diffusion".

Dispersion in materials determines the dynamics of precipitation, new phase formation and microstructural evolution and strongly affects mechanical and physical properties. The inherent chemical complexity of materials with complex compositions poses challenges to atomic diffusion modeling and the formation of chemically ordered structures.

In this regard, researchers from the University of California have proposed a neural network dynamics (NNK) method for predicting atomic diffusion and the resulting microstructural evolution in materials with complex compositions.

The framework is based on efficient lattice structure and chemical characterization, combined with artificial neural networks, and is able to accurately predict all path-dependent migration barriers and single atom hopping. The scalable NNK framework provides a promising new avenue for exploring diffusion-related properties in a vast combinatorial space that hides extraordinary properties.

The related research was titled "Neural network kinetics for exploring diffusion multiplicity and chemical ordering in compositionally complex materials" and was published in "Nature Communications on May 9 "superior.

Material Diffusion and Modeling Challenges

Diffusion as atoms move from one location to another controls many important processes and behaviors, such as precipitation and phase nucleation.

In metals and alloys, the diffusion process is related to vacancies and point defects that mediate atomic jumping in the crystal lattice. Molecular dynamics (MD) modeling based on force fields or density functional theory can probe atomic diffusion mechanisms on nanosecond time scales, but microstructural changes caused by slow diffusion dynamics are often unobtainable.

kMC simulation method is a technique used to simulate diffusion-mediated structural evolution. In kMC simulations, due to the high computational cost of transition state search, key parameters are usually parameterized from the continuum model.

The emergence of compositionally complex alloys (CCAs), often referred to as high-entropy alloys, has brought about many interesting dynamic behaviors, including chemical short-range ordering, precipitation, segregation and radiative defect annihilation, which have not yet been Fundamentally understood and ultimately predicted. However, the chemical complexity in CCA brings new challenges to the modeling of diffusion-mediated processes.

The emergence of machine learning methods has demonstrated the potential to solve computationally complex problems in materials science involving nonlinear interactions and large-scale combinatorial spaces.

Regarding vacancy diffusion in alloys with complex compositions, an important key parameter is the diffusion energy barrier ΔE, which is the energy difference between the transition state and the initial energy minimum. Due to the atomic-scale compositional fluctuations and the presence of multiple diffusion directions in CCA, machine learning models are needed to accurately predict the vector properties, especially the diffusion path-related potential barriers.

Neural Network Dynamics Scheme

In this study, the researchers proposed a neural network dynamics (NNK) scheme to predict and simulate complex enrichment ( Diffusion-induced chemical and structural evolution in concentrated chemical environments.

Figure a below is a lattice structure and chemical representation in which the initial atomic configuration with vacancies is encoded into a numerical matrix or neuron diagram. The numbers (1, 2, and 3) represent the corresponding atom type, and 0 represents a vacancy. These vectorized numbers are then passed to the NNK model and used as input neurons.

NNK consists of artificial neural networks and neuron dynamics modules. The introduced neural network (with more than two hidden layers) aims to learn nonlinear interactions between input neurons (i.e. atoms and vacancies) and output diffusion energy barriers. Notably, this network only uses vacancies and their neighboring neurons as input, resulting in a low and constant computational cost without sacrificing accuracy.

The Neuron Dynamics module uses a kinetic Monte Carlo method to evolve diffusion dynamics using the available potential barriers associated with each diffusion path. With a single conversion of atomic configurations into neuron graphs, vacancy hopping and chemical evolution can be simulated by swapping two digits of the neuron graph. In this way, millions of gap jumps can be efficiently modeled, with each jump iteration involving the actions of only two neurons.

Exploring diffusion, chemical ordering in materials with complex compositions

The researchers used NNK and bcc NbMoTa as model systems to explore diffusion kinetics-mediated chemical ordering and The B2 phase forms and reveals the anomalous diffusion (diffusion multiplicity) inherent in CCA.

Discovered the existence of a critical temperature at which the order of B2 (the B2 unit cell has a simple bcc structure, consisting of two substances, Ta and Mo, ordered at the corners or center of the cube) reaches a maximum. The temperature dependence of chemical ordering is closely related to the underlying lattice hopping stochasticity.

At high temperatures close to the melting point, the diffusion jump eventually approaches a purely random process, corresponding to a low propensity for order formation. At low temperatures, lattice diffusion is dominated by the lowest barrier path, manifesting as directional hopping and limiting the nucleation of chemically ordered structures. At intermediate range critical temperatures, random and directional lattice hopping spread throughout the system, exhibiting the highest diffusional heterogeneity (multiplicity).

By tracking individual B2 clusters during the annealing process, it was found that their nucleation and growth are intermittent and non-uniform, accompanied by the reduction and annihilation of small clusters. This distinctive feature of the kinetic growth of the B2 structure was not captured by virtual thermodynamics-based modeling using random atom type exchange, which showed a more uniform growth.

These results highlight the complex and numerous kinetic pathways of CCA toward a stable state, in which many processes such as nucleation, annihilation, growth, and rearrangement of ordered structures interact and coordinate.

Neural networks trained on dozens of components demonstrate high performance on unseen components, revealing the entire ternary space of Nb-Mo-Ta. Since the design space for compositions is almost unlimited, compositionally complex materials formed by mixing multiple elements open up a new realm to be explored.

By directly linking multidimensional compositions to diffusion barrier spectra, NNK points a bright path toward exploring the vast compositional space of CCA, where extraordinary dynamical properties are hidden.

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