In a paper published in the journal Nature Communications, researchers introduced deep carbon nanotube 22 (DeepCNT-22) to drive molecular dynamics simulations and reveal the atomic-level mechanisms of CNT formation. They discovered that the tube-catalyst interface was highly dynamic, with significant fluctuations in the CNT-edge's chiral structure, challenging the idea of continuous spiral growth.
A sketch-map consisting of 22,975 structures where each colored dot represents an individual atomic configuration (structure). The position of each dot is determined by principal component analysis of the learned descriptors of the structures and its color indicates the corresponding energy of the structure. Examples of atomic configurations from different regions of the sketch map are shown to provide insight into the diversity of the data set. Here orange and grey spheres represent Fe and C atoms, respectively. Image Credit: https://www.nature.com/articles/s41467-024-47999-7
Instead, the team found that defects formed stochastically at the interface but healed under low growth rates and high temperatures, allowing CNTs to grow defect-free. These insights, unobtainable through experiments, highlighted the power of machine learning force field (MLFF)-driven simulations in understanding CNT growth mechanisms.
Background
Past work has established CNTs as a prime example of low-dimensional materials with remarkable mechanical, thermal, electrical, and optical properties. However, achieving uniform properties over the entire length of CNTs is challenging due to chirality changes caused by defects during synthesis.
Catalytic chemical vapor deposition, particularly using iron catalysts, has become the leading method for CNT synthesis. Understanding the mechanisms of CNT nucleation and growth at the atomic level is crucial for producing long, defect-free CNTs. While experimental studies have provided valuable insights, a comprehensive atomic-level understanding still needs to be discovered.
Methods and Simulations
An initial set of structures was generated using various methods, including molecular dynamics (MD) driven by density functional tight binding (DFTB) and randomly perturbed structures and carbon allotropes from the GAP-20 dataset. This dataset was further refined using an active learning scheme, where the analysts trained an ensemble of MLFFs to drive MD simulations of single-walled CNT (SWCNT) growth.
Model deviation in force predictions identified unrepresented structures, which were then labeled and added to the dataset, repeating this process until the model deviation remained consistently low. Regardless of the generation method, all structures were labeled with energies and forces obtained via dispersion-corrected DFT calculations.
The initial dataset included structures from DFTB MD simulations of SWCNT nucleation from atomic carbon precursors on iron nanoparticle catalysts. DFTB, an extended two-center Hückel approximation to DFT, enabled dynamic simulations much faster than DFT while including electronic effects.
Simulations used self-consistent charge DFTB to compute quantum chemical potential energy and gradients. The extracted structures featured iron nanoparticles with surface-adsorbed carbon monomers and dimers, carbon chains, ring networks, and SWCNT-cap and tube-like structures.
High-energy structures from early MLFF versions were annealed with DFTB MD, and farthest point sampling identified which structures to label with DFT for the training data.
DFT calculations used the Vienna Ab initio simulation package (VASP) with a plane wave basis set and projector-augmented wave method, accounting for dispersion interactions. Calculations ensured high precision with specific parameters for energy cutoffs, convergence, smearing, and spin-polarization.
The MLFF, DeepCNT-22, built on the Deep Potential-Smooth Edition architecture, used a neural network to predict atomic energies, summing them to yield the structure's total energy. The training involved an embedding net and descriptor embedding net with specific neuron configurations, smooth cutoffs, and a fitting net. The loss function balanced energy and force errors, training for 300,000 batches using the Adam optimizer.
MD simulations of SWCNT growth were performed using LAMMPS with the deepmd pair style and DeepCNT-22 MLFF. The nsq algorithm constructed neighbor lists with specific cutoff and skin distances and simulations operated in the NVT ensemble with a Nosé-Hoover chain thermostat. Equations of motion were integrated with a 2.0 fs timestep, with initial velocities scaled to the growth temperature.
Carbon atoms were introduced individually at a controlled rate within a spherical deposit region centered on the iron catalyst. The researchers recentered to maintain the catalyst's central position and simulation data was recorded every 2 ps for subsequent analysis.
MLFF Development Challenges
MLFFs have emerged as a powerful method for modeling materials at experimental lengths and timescales. These methods involve training machine learning models on extensive datasets of atomic configurations labeled with energies, forces, and virials, which are calculated using first-principal methods like DFT. Once trained, MLFFs can predict physical quantities and drive atomistic simulations with the computational efficiency of empirical force fields while maintaining the accuracy of DFT or beyond-DFT methods.
However, a significant challenge in developing MLFFs is creating high-quality, diverse datasets for training. The DeepCNT-22 dataset addresses this by including structures relevant to single-walled carbon nanotube (SWCNT) growth, demonstrated through a sketch-map representation that highlights the diversity and quality of the learned descriptors.
DeepCNT-22 drove MD simulations, revealing a five-phase SWCNT growth process that achieves defect-free tubes even at high rates with effective defect healing. The study explored growth conditions' influence and proposed a defect-free CNT length prediction model, emphasizing growth parameter optimization. Tube-catalyst interface dynamics highlighted configurational entropy's role in edge configuration determination and stochastic interface defect occurrence.
Conclusion
To sum up, MLFFs presented a potent avenue for modeling materials with precision and efficiency, leveraging extensive datasets labeled with atomic configurations. The DeepCNT-22 dataset exemplified this approach, demonstrating its capacity to encompass diverse structures crucial for SWCNT growth. The study unveiled a comprehensive understanding of the SWCNT growth process through meticulous training and simulation, achieving defect-free outcomes even at high rates.
Moreover, insights into the influence of growth conditions on defect formation and healing provided valuable guidelines for optimizing CNT production. The analysis of tube-catalyst interface dynamics underscored the role of configurational entropy, offering profound implications for future material design and synthesis endeavors.
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