Improving the reliability of machine learned potentials for modeling inhomogeneous liquids.

Development of an interatomic potential for Fe-He by neural network

The accuracy of classical physical property predictions using molecular dynamics simulations is determined by the quality of the interatomic potentials. Here we introduce a training approach for empirical interatomic potentials (EIPs) which is well suited for capturing phonons and phonon-related properties. Our approach is based on direct comparisons of the second- and third-order irreducible derivatives (IDs) between an EIP and the Born-Oppenheimer potential within density functional theory (DFT) calculations. IDs fully exploit space group symmetry and allow for training without redundant information. We demonstrate the fidelity of our approach in the context of ThO2and UO2, where we optimize parameters of an embedded-atom method potential in addition to core-shell interactions. Our EIPs provide thermophysical properties in good agreement with DFT and outperform widely utilized EIPs for phonon dispersion and thermal conductivity predictions. Reasonable estimates of thermal expansion and formation energies of Frenkel pairs are also obtained.

A new empirical interatomic potential for Si-Ge alloy system is proposed based on the Khor--Das Sarma universal interatomic potential for tetrahedrally bonded materials. We modify the Khor--Das Sarma potential and check its validity by calculating the elastic constants of Si and Ge using the homogeneous-deformation method. The feasibility for applying this potential to binary systems is tested by investigating pressure-induced phase transitions associated with isotropic compression and tetragonal distortion. The new empirical potentials for Si, Ge, and Si-Ge are used to calculate thermodynamic properties such as lattice parameters, bond lengths, and excess energies for Si-Ge superlattices. The calculated results are shown to be in good agreement with available experimental data. We also calculate the phonon dispersion for bulk Si. The newly obtained empirical potentials for Si, Ge, and Si-Ge should be useful for investigating Si-Ge binary systems.

Germanium telluride (GeTe) is an important functional material that has been attracting extensive research attention. Challenges such as phase transition processes and crystallization of amorphous GeTe cannot yet be accurately calculated using ab initio molecular dynamics because of the time limitations of density functional theory calculations. Molecular dynamics simulation using empirical potentials can address the aforementioned issues. However, their accuracy relies on the validity of the empirical interatomic potential. With the advancement of computational methodologies within materials science and engineering, machine learning potentials (MLPs) have garnered substantial interest. In this paper, we review the applications of MLPs, including neural network potential, Gaussian approximation potentials, and neuroevolution potential, in studying the phonon properties of GeTe. Our focus includes the crystallization of amorphous GeTe, the mechanisms underlying structural phase transitions, and thermal conductivity. These advancements can offer valuable guidance for the utilization of GeTe in advanced thermal management and contribute to the exploration of MLPs in phonon physics.

Sintering of alumina nanoparticles is of interest both from the view of fundamental research as well as for industrial applications. Atomistic simulations are tailor-made for understanding and predicting the time- and temperature-dependent sintering behaviour. However, the quality and predictability of such analysis is strongly dependent on the performance of the underlying interatomic potentials. In this work, we investigate and benchmark four empirical interatomic potentials and discuss the resulting properties and drawbacks based on experimental and density functional theory data from the literature. The potentials, which have different origins and formulations, are then used in molecular dynamics (MD) simulations to perform a systematic study of the sintering process. To analyse the results, we develop a number of tailored data analysis approaches that are able to characterise and quantify the sintering process. Subsequently, the disparities in the sintering behaviour predicted by the potentials are critically discussed. Finally, we conclude by providing explanations for the differences in performance of the potentials, together with recommendations for MD sintering simulations of alumina.

Polarized and depolarized interaction-induced light scattering spectra at room temperature (294.5±1) K have been used for deriving the empirical multiparameter Morse–Morse–Morse–spline–van der Waals interatomic potential. These new data of scattering are accurate enough to permit for the first time a reliable determination of the interatomic potential of the gaseous helium as a function of the interatomic separation. The potential parameters describing the location and depth of the attractive well are given by ε = 11.2±0.015 K,

Graphene is an elementary unit for various carbon based nanostructures. The recent technological developments have made it possible to manufacture hybrid and sandwich structures with graphene. In order to model these nanostructures in atomistic scale, a compatible interatomic potential is required to successfully model these nanostructures. In this article, an interatomic potential with modified cut-off function for Tersoff potential was proposed to avoid overestimation and also to predict the realistic mechanical behavior of single sheet of graphene. In order to validate the modified form of cut-off function for Tersoff potential, simulations were performed with different set of temperatures and strain rates, and results were made to compare with available experimental data and molecular dynamics simulation results obtained with the help of other empirical interatomic potentials.

The properties of large vacancy clusters, containing from 10 to 40 vacancies, were investigated for copper using an interatomic potential derived from the pseudopotential method. The stacking fault energy of copper was calculated to be 65.3 mJ m-2 for a potential cut-off radius of 8.5155 AA, which is in good agreement with the experimental value of approximately 70 mJ m-2. For longer cut-off radii, however, the calculated stacking energy decreased and became negative. It is suggested that this results from the analytical fit of the numerically calculated interatomic potential being inaccurate at relatively long interatomic radii. Using the cut-off radius of 8.5155 AA, the minimum energy configurations of hexagonal and triangular vacancy platelets of 10 or more vacancies were determined, and it was found that they collapsed into hexagonal faulted loops and stacking fault tetrahedra, respectively. This agrees with X-ray diffuse scattering experiments in which loops of this size have been observed, and with previous calculations for copper using empirical interatomic potentials. The calculated displacement field at short distances above the small hexagonal loops differed significantly from linear isotropic inelasticity theory predictions. The stacking fault tetrahedra were found to be more stable than the hexagonal loops, although both were locally stable, which is in accord with experimental observations of both defects in copper.

Yttria stabilized zirconia (YSZ) is an important engineering ceramic oxide used for various applications, including solid electrolytes in solid oxide fuel cells due to its high ionic conductivity. Accurate and computationally inexpensive interatomic potentials for cubic ZrO2 and YSZ are required to accommodate the large number of defect configurations originating from high concentrations of Y and oxygen vacancies and to statistically understand their properties in realistic time. In this study, a genetic algorithm has been used to optimize empirical interatomic potential parameters for cubic ZrO2 and 10Y2O3 mol% YSZ using energies, forces acting on atoms, and stresses generated by ab initio calculations as training data. The optimized potentials reproduce the structural, mechanical, and thermal properties as well as the ionic conduction properties more accurately than previously reported empirical interatomic potentials. The developed potentials will be useful for a statistical characterization of YSZ properties, combined with more accurate ab initio calculations.

Advances in nanotechnology lead to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators with ultra-high resonant frequencies. The ultra-high-frequency resonators have recently received significant attention for wide-ranging applications such as molecular separation, molecular transportation, ultra-high sensitive sensing, high-frequency signal processing, and biological imaging. It is well known that for micrometer length scale, first-principles technique, the most accurate approach, poses serious limitations for comparisons with experimental studies. For such larger size, classical molecular dynamics (MD) simulations are desirable, which require interatomic potentials. Additionally, a mesoscale method such as the coarse-grained (CG) method is another useful method to support simulations for even larger system sizes. Furthermore, quasi-two-dimensional (Q2D) materials have attracted intensive research interest due to their many novel properties over the past decades. However, the energy dissipation mechanisms of nanomechanical resonators based on several Q2D materials are still unknown. In this work, the addressed main issues include the development of the CG models for molybdenum disulphide (MoS2), investigation of the mechanism effects on black phosphorus (BP) nanoresonators and the application of graphene nanoresonators. The primary coverage and results of the dissertation are as follows: Method development. Firstly, a two-dimensional (2D) CG model for single layer MoS2 (SLMoS2) is analytically developed. The Stillinger-Weber (SW) potential for this 2D CG model is further parametrized, in which all SW geometrical parameters are determined analytically according to the equilibrium condition for each individual potential term, while the SW energy parameters are derived analytically based on the valence force field model. Next, the 2D CG model is further simplified to one-dimensional (1D) CG model, which describes the 2D SLMoS2 structure using a 1D chain model. This 1D CG model is applied to investigate the relaxed configuration and the resonant oscillation of the folded SLMoS2. Owning to the simplicity nature of the 1D CG model, the relaxed configuration of the folded SLMoS2 is determined analytically, and the resonant oscillation frequency is derived analytically. Considering the increasing interest in studying the properties of other 2D layered materials, and in particular those in the semiconducting transition metal dichalcogenide class like MoS2, the CG models proposed in current work provide valuable simulation approaches. Mechanism understanding. Two energy dissipation mechanisms of BP nanoresonators are focused exclusively, i.e. mechanical strain effects and defect effects (including vacancy and oxidation). Vacancy defect is intrinsic damping factor for the quality (Q)-factor, while mechanical strain and oxidation are extrinsic damping factors. Intrinsic dissipation (induced by thermal vibrations) in BP resonators (BPRs) is firstly investigated. Specifically, classical MD simulations are performed to examine the temperature dependence for the Q-factor of the single layer BPR (SLBPR) along the armchair and zigzag directions, where two-step fitting procedure is used to extract the frequency and Q-factor from the kinetic energy time history. The Q-factors of BPRs are evaluated through comparison with those of graphene and MoS2 nanoresonators. Next, effects of mechanical strain, vacancy and oxidation on BP nanoresonators are investigated in turn. Considering the increasing interest in studying the properties of BP, and in particular the lack of theoretical study for the BPRs, the results in current work provide a useful reference. Application. A novel application for graphene nanoresonators, using them to self-assemble small nanostructures such as water chains, is proposed. All of the underlying physics enabling this phenomenon is elucidated. In particular, by drawing inspiration from macroscale self-assembly using the higher order resonant modes of Chladni plates, classical MD simulations are used to investigate the self-assembly of water molecules using graphene nanoresonators. An analytic formula for the critical resonant frequency based on the interaction between water molecules and graphene is provided. Furthermore, the properties of the water chains assembled by the graphene nanoresonators are studied.

The development of differentiable invariant descriptors for accurate representations of atomic environments plays a central role in the success of interatomic potentials for chemistry and materials science. We introduce a method to generate fast proper orthogonal descriptors for the construction of many-body interatomic potentials and discuss its relation to exising empirical and machine learning interatomic potentials. A traditional way of implementing the proper orthogonal descriptors has a computational complexity that scales exponentially with the body order in terms of the number of neighbors. We present an algorithm to compute the proper orthogonal descriptors with a computational complexity that scales linearly with the number of neighbors irrespective of the body order. We show that our method can enable a more efficient implementation for a number of existing potentials and provide a scalable systematic framework to construct new many-body potentials. The new potentials are demonstrated on a data set of density functional theory calculations for Tantalum and compared with other interatomic potentials.

The atomic kinetic Monte Carlo method plays an important role in multi-scale physical simulations because it bridges the micro and macro worlds. However, its accuracy is limited by empirical potentials. We therefore propose herein a triple-encoding algorithm and vacancy-cache mechanism to efficiently integrate ab initio neural network potentials (NNPs) with AKMC and implement them in our TensorKMC codes. We port our program to SW26010-pro and innovate a fast feature operator and a big fusion operator for the NNPs for fully utilizing the powerful heterogeneous computing units of the new-generation Sunway supercomputer. We further optimize memory usage. With these improvements, TensorKMC can simulate up to 54 trillions of atoms and achieve excellent strong and weak scaling performance up to 27,456,000 cores.

The need for sources of efficient and renewable energy has become an issue of great importance in recent years. Fossil fuels are diminishing in supply, and they not only pollute the environment, but have also proven to be inefficient in many cases, losing a large portion of the total energy generated to waste heat, instead of usable energy. The first work this thesis addresses is the development of a Genetic Algorithm (GA) optimization method for the search and discovery of semiconductor materials for use in thermoelectric devices. The specific material in question is the Silicon Germanium superlattice. This structure made of alternating layers of Si and Ge is known to be one of the better materials for thermoelectric energy generation at elevated temperature, along with Bismuth-Telluride that targets room temperature. Previously, it has been shown that random multilayer (RML) structures can lower thermal conductivity as compared to periodic superlattices due to phonon localization. However, it was unknown which specific RML would yield the lowest thermal conductivity, due to the large design space from which these RML’s can be generated. Considering this, a global and non-smooth optimization method was employed to search for the best possible structure. Results not only showed that the thermal conductivity could be lowered even further, but that there was an optimal average period for the RML’s that produced the best results.The second work discussed in this thesis concerns itself with the development of a Neural Network Potential (NNP) for use in Molecular Dynamics (MD) simulations. There are multiple methods for running MD including ab-initiomethods such as Density Functional Theory (DFT) calculations and classical MD with the use of empirical potentials. Unfortunately, DFT is too time consuming for systems larger than a few hundred atoms, and empirical potentials can be inaccurate. Therefore, a NNP for bulk Silicon trained on DFT was developed, and it was shown that the phonon dispersion for Si could be accurately reproduced.

Sintering of alumina nanoparticles is of interest both from the view of fundamental research as well as for industrial applications. Atomistic simulations are tailor-made for understanding and predicting the time- and temperature-dependent sintering behaviour. However, the quality and predictability of such analysis is strongly dependent on the performance of the underlying interatomic potentials. In this work, we investigate and benchmark four empirical interatomic potentials and discuss the resulting properties and drawbacks based on experimental and density functional theory data from the literature. The potentials, which have different origins and formulations, are then used in molecular dynamics simulations to perform a systematic study of the sintering process. To analyse the results, we develop a number of tailored data analysis approaches that are able to characterise and quantify the sintering process. Subsequently, the disparities in the sintering behaviour predicted by the potentials are critically discussed. Finally, we conclude by providing explanations for the differences in performance of the potentials, together with recommendations for molecular dynamics sintering simulations of alumina.

Confinement and alloy disorder effects on the lattice dynamics and Raman scattering in Si1−xGex nanocrystals (NCs) are investigated numerically employing two different empirical inter-atomic potentials. Relaxed NCs of different compositions (x) were built using the Molecular Dynamics method and applying rigid boundary conditions mimicking the effect of surrounding matrix. The resulting variation of bond lengths with x was checked against Vegard's law and the NC phonon modes were calculated using the same inter-atomic potential. The localization of the principal Raman-active (Si-Si, Si-Ge, and Ge-Ge) modes is investigated by analysing representative eigenvectors and their inverse participation ratio. The dependence of the position and intensity of these modes upon x and NC size is presented and compared to previous calculated results and available experimental data. In particular, it is argued that the composition dependence of the intensity of the Si-Ge and Ge-Ge modes does not follow the fraction of the corresponding nearest-neighbour bonds as it was suggested by some authors. Possible effects of alloy segregation are considered by comparing the calculated properties of random and clustered SixGe1−x NCs. It is found that the Si-Si mode and Ge-Ge mode are enhanced and blue-shifted (by several cm−1for the Si-Si mode), while the intensity of the Si-Ge Raman mode is strongly suppressed by clustering.