Embedded Atom Method Potential Research Articles

Formation and growth of transition metal carbides in ferrite

Carbide nano-precipitates are commonly used to improve mechanical properties of steel. It has been experimentally observed that TiC, NbC, and VC carbide precipitates initially form as ‘plate-like’ particles oriented in the {100} planes of the ferrite lattice. These platelets share similarities with Guinier-Preston zones in Al-Cu alloys.The clustering of group IV and V transition metal atoms (M = Ti, Zr, Hf, V, Nb, Ta) in ferrite is studied using density functional theory. It is deduced that the transition metal carbides all form in a similar way. Furthermore, the transition from an initial M–C cluster to a NaCl-structured platelet to a NaCl-structured precipitate is examined through atomistic simulations using Modified Embedded Atom Method potentials. A route is established along which transition metal carbides form and transform into precipitates that possess the Baker-Nutting orientation relation with the ferrite matrix.

Towards atomistic modelling of solid Pb-O formation and dissolution in liquid lead coolant: Interatomic potential development

Microscopic description of solid Pb-O formation and dissolution in liquid lead coolant is important for the modelling of fast neutron reactors. For this purpose, in this work we develop interatomic potential models for lead melt with dissolved oxygen. Potentials fitting is based on ab initio density functional theory (DFT) calculations and quantum molecular dynamics. Two different potential models are trained on the DFT data using the force-matching method: a computationally cheap embedded atom method (EAM) potential and a computationally expensive machine-learned moment tensor potential (MTP) that allows reproducing DFT data very accurately. The potentials are further validated to reproduce the properties of lead melt and the coordination of oxygen atoms in molten lead. The diffusion coefficient for oxygen in molten lead is calculated and compared with the available experimental data. We analyse how these interatomic potential models describe the crystal structure of the solid lead oxide to consider PbO nucleation and dissolution in molten lead. We extensively discuss the arising problems with the description of long-range electrostatic interactions. The possibility of matching the experimental data on the oxygen solubility limit by tuning the EAM potential is shown.

Moment tensor potential for static and dynamic investigations of screw dislocations in bcc Nb

A new machine-learning interatomic potential, specifically a moment tensor potential (MTP), is developed for the study of screw-dislocation properties in body-centered-cubic (bcc) Nb in the thermally- and stress-assisted temperature regime. Importantly, configurations with straight screw dislocations and with kink pairs are included in the training set. The resulting MTP reproduces with near density-functional theory (DFT) accuracy a broad range of physical properties of bcc Nb, in particular, the Peierls barrier and the compact screw-dislocation core structure. Moreover, it accurately reproduces the energy of the easy core and the twinning-anti-twinning asymmetry of the critical resolved shear stress (CRSS). Thereby, the developed MTP enables large-scale molecular dynamics simulations with near DFT accuracy of properties such as for example the Peierls stress, the critical waiting time for the onset of screw dislocation movement, atomic trajectories of screw dislocation migration, as well as the temperature dependence of the CRSS. A critical assessment of previous results obtained with classical embedded atom method potentials thus becomes possible.

Extracting free energies from local composition fluctuations in solids: A frequency distribution analysis of simulated atom probe data obtained by TAPSim

The present work proposes a novel methodology to extract direct thermodynamic information, i.e. Gibbs free energies, from local composition fluctuations found in atom probe data based on statistical mechanics. The proof-of-concept is demonstrated with an exemplary simulated Cu–Ni alloy, which has first been equilibrated using Monte Carlo techniques with an embedded-atom method potential and subsequently field evaporated by TAPSim. It is shown that the variance of the frequency distribution of the local composition on the reconstructed data reveals a systematic dependence on the size of the chosen spherical (sub-) volume used for the evaluation, but nevertheless the extrapolation to an infinitely large volume unveils a unique link to the curvature of the Gibbs free energy. Given the composition range is explored at several points, the Gibbs excess free energy of mixing could be recovered in a CALPHAD-style parametrization. This methodology promises to improve the accuracy of thermodynamic information (e.g. miscibility gap, mixing/demixing tendencies, critical solution temperature) from direct atom probe measurements.

The deposition properties of tetrahedral amorphous carbon coatings deposited on piston ring: Molecular dynamics simulation

The tetrahedral amorphous carbon (ta-C) coatings are deposited on piston rings to improve the tribological property of the piston ring-cylinder liner system of the internal combustion engines. The deposition parameters are optimized by molecular dynamics simulation to reduce the cost of coatings’ fabrication. The ta-C coatings with higher sp3 fraction, lower friction coefficient, and superior anti-wear properties are achieved by optimizing the incident energy and substrate temperature of carbon atoms. The second nearest-neighbor modified embedded-atom method potential and Tersoff potential are used to describe the interatomic interactions. The effects of the incident energy of the carbon atoms and substrate temperature on the deposition properties of the ta-C coatings are discussed. The numerical results show that the ta-C coatings with high sp3 fraction, high density, and good interface mixing are obtained, and the deposition properties of the ta-C coatings are improved.

Studying the influence of surface roughness with different shapes and quantities on convective heat transfer of fluid within nanochannels using molecular dynamics simulations.

In the past decade, rapid advancements in microtechnology and nanotechnology have propelled modern science and technology into the nanoscale domain, where miniaturization and high integration have found extensive applications across various fields, including industry, biotechnology, and information technology. Mechanisms of nanofluid flow and heat transfer properties have received increasing attention. In the flow and convective heat transfer of fluids at the nanoscale, the shape and dimensions of the surfaces play a crucial role. So, the main purpose of our paper is to investigate the influence of surface roughness with different shapes and quantities on fluid flow and convective heat transfer. In this study, we have chosen argon atoms as the fluid and used copper atoms to simulate the nanochannel walls. In order to investigate the influence of the shape and quantity of roughness on the convective heat transfer of fluids within nanochannels, we computed and analyzed the velocity, temperature, and density distributions of fluids inside channels with triangular, hemispherical, and rectangular roughness. Through simulation results, we found that triangular, hemispherical, and rectangular surface roughness at the same height can result in differences in temperature and velocity of the fluid within nanochannels. With a nanochannel roughness number of 5, the temperature and velocity of the fluid at the middle position of the nano-channel for the triangular roughness increased by 6% and 25% compared to the rectangular roughness, and by 4% and 10% compared to the hemispherical roughness. The fluid temperature and velocity are highest in channels with triangular surface roughness and lowest in those with rectangular roughness. Furthermore, increasing the quantity of surface roughness decreases the temperature and velocity of the fluid within nanochannels. When the quantity of rectangular surface roughness is 5, the fluid temperature within the nanochannel decreases by 12%, and the velocity decreases by 38% compared to a roughness quantity of 1. We also found, through velocity contours, that the presence of roughness increases the local fluid velocity in the rough regions of nanochannels. Roughness also reduces the density fluctuations of the fluid near the walls within the nanochannel. Roughness significantly affects the heat transfer performance of the fluid during its flow, and this influence should not be overlooked. In this study, molecular dynamics theory was employed, and simulations were conducted using the open-source software LAMMPS to investigate the influence of different shapes and quantities of surface roughness on fluid flow within nanochannels. The model in this paper was constructed using the LAMMPS software, and the surface roughness shapes on the walls were implemented as rectangular, hemispherical, and triangular. The wall surfaces were composed of copper atoms, while the fluid consisted of argon atoms. The copper atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 3.615 Å. Similarly, the argon atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 5.62 Å. The interactions between copper atoms were modeled using the EAM (Embedded Atom Method) potential, while the interactions between argon atoms were described using the LJ (Lennard-Jones) potential. The LJ potential was also employed to represent interactions between argon and copper atoms.

Development of U-Zr-Xe ternary interatomic potentials appropriate for simulation of defect and Xe behaviors in U-Zr system

U-10Zr metallic fuel (alloys of U with 10 wt% Zr) is considered as a potential candidate for fast reactors due to its excellent performance. However, the fission gas swelling has a significant impact on its properties and prevents it from reaching higher burnup. To gain a deeper understanding of the fission gas swelling mechanism, molecular dynamics simulations based on interatomic potentials are underway to fill the key knowledge gaps. In this work, two modified embedded-atom method (MEAM) potentials are developed for the U-Zr system with Xe, one for α-U-Zr and δ-UZr2, and the other for γ-U-Zr. The parameters of the potentials are determined by fitting the material properties from experiments or density functional theory (DFT) calculations. It is verified that the potentials can reproduce well the lattice constants, elastic constants, point defects, surface energy, and the melting point of U. In addition, the lattice constants, elastic constants, cohesive energy, and point defect formation energy of Zr are in good agreement with the experimental and DFT results. For the alloy system, the typical defect properties of Zr and Xe in U, as well as the formation energy and elastic constant of δ-UZr2 are close to the DFT. The lattice constant, linear thermal expansion, and mixing enthalpy of γ-U-Zr alloy are following the experimental values. The results show that the obtained potentials are suitable for simulating the defect evolution and Xe behaviors in the U-Zr system.

Development of an interatomic potential for the W–Ta system

A physics-inspired, data-driven interatomic potential framework for multi-element system is presented. This potential is based on the generalization of the embedded atom method potential and systematically incorporates two-, three- and many-body effects. Different atomic environments are described by atom-centered Gaussian basis sets which provides sufficient flexibility to capture diverse atomic environments and allows for easy optimization of the free parameters. An interatomic potential model for the tungsten–tantalum (W–Ta) system is developed using this framework by training on data from ab initio density functional theory (DFT) calculations. The potential is thoroughly tested at various compositions by comparing bulk and defect properties from experimental and DFT data. It is shown that the potential predicts the elastic constants, defect properties, such as vacancy and interstitial formation energies, core structures of dislocations, and melting points for both pure and tantalum and tungsten with an accuracy comparable to other single element machine learning based potentials. The potential model is used to investigate the formation energies of ordered alloys and vacancy formation energies for chemically random W–Ta alloys.

Parametrization of embedded-atom method potential for liquid lithium and lead-lithium eutectic alloy

Liquid lead-lithium eutectic remains as a promising candidate for various breeding-blanket designs in future nuclear-fusion technologies. The lack of a generalized theory of interatomic forces in the liquid state is reflected on the wide variety of proposed functional forms to describe interatomic interactions even in simple liquids. Computer simulations facilitate the study of liquid metal properties, due to mathematical and experimental challenges. A classical-MD EAM potential is parametrized using mechanical and non-mechanical (melting-point) properties to minimize the arbitrariness of functional forms, where the employed pair potential stems from the liquid-state theory to avoid the issue of the uniqueness of the potential. Enhanced performance is obtained for liquid density, energy, structure, diffusivity and shear viscosity of Li, and their temperature-dependencies. In a similar manner, reference experimental and ab initio MD data are used to parametrize a functional to describe Pb-Li pairwise interactions in liquid Pb-Li alloy, which is used with the derived EAM of liquid Li and a reference EAM of liquid Pb to investigate properties of liquid Pb-Li alloy. Enhanced transferability characteristics are obtained for low-in-lithium liquid Pb-Li melts, where Coulombic interactions are negligible. In specific, the exhibited behaviour of Li in liquid lead-lithium eutectic is consistent with findings from ab initio MD methods, and drastically different from predictions of previous C-MD studies which suggested a substantial segregation of Li atoms instead of dispersion. It is concluded that the functional form of the pair potential and its uniqueness influence both the pure liquid-metal properties and the validity of the potential transferability in multi-component systems, where a theoretical functional results in enhanced performance in pure and alloyed liquid systems.

Atomistic simulation of the effect of porosity on shock response of nanoporous gold.

Nanoporous metals (NPMs) have a three-dimensional bicontinuous porous network structure that consists of interconnected nanoligaments. NPMs have the potential to effectively attenuate and dissipate the effects of impacts and blasts. Previous studies do not provide data on the possible effects of porosity at the nanoscale. Molecular dynamics simulations based on the embedded-atom method potential were performed using the open-source code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Nanoporous gold (NPG) absorbs shock energy first through the elastic-plastic deformation of ligaments and then through the collapse of ligaments. After the shock loading is relaxed, NPG with lower porosity has a higher amount of springback, and new voids tend to nucleate and grow at collapsed ligaments where the packing is looser. NPG with higher porosity has a better ability to resist the propagation of a shock wave and is subjected to a smaller stress effect.

Local structures and undercooling ability of Zr–Ti melts

We developed an accurate model of Zr–Ti melts for classical molecular-dynamics simulations via regauging the existing embedded-atom method (EAM) potential, using particularly the diffusion coefficient data obtained from quasielastic neutron scattering. This EAM potential well reproduces the properties of the melts observed in experiments, including mass density, transport coefficients, melting temperatures, and static structure factors. The latter are also obtained from ab initio simulations. Using the developed EAM potentials, we analyzed the short-range order of the liquids and found a chemically preferred formation of Zr–Zr and Zr–Ti nearest neighbor pairs. When decreasing the temperature the number of icosahedral-like aggregates increases on the expense of more crystal-like structures. This is most pronounced at intermediate alloy compositions. At intermediate compositions also the lowest thermodynamic driving force for crystallization is found, resulting in the largest undercooling ability of the alloys.

Molecular dynamics simulation for radiation response of Nb bicrystal having Σ 13, Σ 29, and Σ 85 grain boundary

Nb is considered a promising candidate as a refractory element due to its high-temperature endurance, excellent thermal conductivity, and compatibility with liquid-metallic coolants in nuclear reactors. In the present study, radiation-based molecular dynamics numerical simulations were conducted in Σ 13, Σ 29, and Σ 85 symmetric tilt grain boundary models for pure Nb specimens. The stochastic high-energy collisions were modeled via large-scale atomic/molecular parallel simulator code to accurately investigate the radiation-induced defects generated in the order of picoseconds at the atomic level. The long-range embedded atom method potential and coulombic repulsive Ziegler–Biersack–Littmark potentials were smoothly overlaid for precise force-field interactions among Nb atoms. To investigate the ability to arrest the radiation-induced damage, the bi-crystal Nb specimens were irradiated at varying magnitudes of primary-knock-on atom (PKA) energies EPKA = 10 20, and 30 keV at temperature regimes 300, 600, and 900 K, respectively. The Frenkel pairs, complex linear defects, distribution of point defects as clusters, rate of defect annihilation, and temperature fluctuations within the displacement cascades of irradiated Nb specimens were comprehensively studied and reported. Here, the Nb-Σ 29 GB model survived with the lowest number of residual defects. Also, the recombination rate of the irradiated Nb specimens increases with the increase in temperature and PKA energy magnitude due to enhanced atomic mobility of the dislodged atoms. Hence, the bi-crystal Nb specimen can be favored for a radiation-tolerant material as structural components in next-generation reactors.

A Modified Embedded-Atom Method Potential for a Quaternary Fe-Cr-Si-Mo Solid Solution Alloy

Ferritic-martensitic steels, such as T91, are candidate materials for high-temperature applications, including superheaters, heat exchangers, and advanced nuclear reactors. Considering these alloys' wide applications, an atomistic understanding of the underlying mechanisms responsible for their excellent mechano-chemical properties is crucial. Here, we developed a modified embedded-atom method (MEAM) potential for the Fe-Cr-Si-Mo quaternary alloy system-i.e., four major elements of T91-using a multi-objective optimization approach to fit thermomechanical properties reported using density functional theory (DFT) calculations and experimental measurements. Elastic constants calculated using the proposed potential for binary interactions agreed well with ab initio calculations. Furthermore, the computed thermal expansion and self-diffusion coefficients employing this potential are in good agreement with other studies. This potential will offer insightful atomistic knowledge to design alloys for use in harsh environments.

Transferability of Zr-Zr interatomic potentials

Tens of Zr inter-atomic potentials (force fields) have been developed to enable atomic-scale simulations of Zr alloys. These can provide critical insight in the in-reactor behaviour of nuclear fuel cladding and structural components exposed, but the results are strongly sensitive to the choice of potential. We provide a comprehensive comparison of 13 popular Zr potentials, and assess their ability to reproduce key physical, mechanical, structural and thermodynamic properties of Zr. We assess the lattice parameters, thermal expansion, melting point, volume-energy response, allotropic phase stability, elastic properties, and point defect energies, and compare them to experimental and ab-initio values. No potential was found to outperform all others on all aspects, but for every metric considered here, at least one potential was found to provide reliable results. Older embedded-atom method (EAM) potentials tend to excel in 2-3 metrics each, but at the cost of poorer transferability. The two highest-performing potentials overall, with complementary strengths and weaknesses, were the 2021 angular-dependent potential of Smirnova and Starikov (Comp. Mater. Sci. 197, 110581) and the 2019 embedded-atom method potential of Wimmer et al (J. Nucl. Mater. 532, 152055). All potentials trained through machine learning algorithms proved to have lower overall accuracy, and less transferability, than simpler and computationally faster potentials available. Point defect structures and energies is where the greatest divergence and least accuracy is observed. We created maps that will help modellers select the most suitable potential for a specific application, and which may help identify areas of improvement in future potentials.

Effect of Grain-Size in Nanocrystalline Tungsten on Hardness and Dislocation Density: A Molecular Dynamics Study

We have simulated a series of nanoindentation experiments on nanocrystalline tungsten specimens using a combination of molecular dynamics simulations and the embedded atom method potential. The research aimed to investigate the impact of grain size on the mechanical properties of tungsten. Nanoindentation is a technique used to measure the mechanical properties of materials at a small scale. In this study, the researchers varied the grain size of the tungsten specimens, ranging from 7.9 to 10.5 nanometers. They also applied a loading rate of 3 angstroms per picosecond at a temperature of 300 Kelvin. The study found that as the grain size increased, the hardness increased, and the elastic modulus decreased. Hardness is a measure of a material’s resistance to deformation, and the elastic modulus is a measure of a material’s stiffness. The findings suggest that as the grain size of tungsten increases, the material becomes harder but less stiff. Additionally, the study explored the ways in which nanocrystalline tungsten deformed during nanoindentation. The researchers found that the deformation of the material was primarily due to dislocation activity, which is consistent with previous research on the topic. Overall, the findings of this research provide valuable insights into the mechanical properties of nanocrystalline tungsten and the ways in which the material deforms under stress. These findings could have practical applications in the development of materials for use in various industries.

Simple Parameterization of Embedded Atom Method Potentials for FCC Alloys

We extend our simple parametric form for Embedded Atom Method interatomic potentials for FCC metals [Daw & Chandross, “Simple Parameterization of Embedded Atom Method Potentials FCC Metals”] to treat alloys. Using this model, which we refer to as “EAM-X”, we study the generic dependence of alloy properties on the model parameters. We introduce the idea of spread alloys, where the constituent elements are defined as parametric perturbations from a central, “average” FCC metal, and where different alloys are quantified by a measure of the magnitude of the perturbation. As an example, we consider a spread binary where the only differences between the constituent elements are lattice mismatch and the cross-interaction parameters and show that the model robustly describes the clustering and ordering tendencies of metal alloys. We use the model to prove a general theorem of “parametric simplicity” in random equimolar alloys: alloy properties differ from a simple rule of mixtures in a way that depends only on the standard deviation among the constituent parameters but are otherwise not dependent on the number of constituents, consistent with previous theoretical results.

A comparative study on surface tension, diffusion coefficient and shear viscosity coefficient of liquid transition metals

Surface tensions of liquid transition metals of the 3d, 4d and 5d series have been calculated using modified Mayer’s formula involving hard sphere (HS) interaction of liquids derived from first and second order approximations of Percus–Yevick (PY) solutions of isothermal compressibility. Effective HS diameter and packing fraction are key ingredients of this study. To determine them, we have used effective pair potential derived from both Bretonnet–Silbert (BS) pseudopotential model and many body potential obtained from embedded atom method (EAM) in conjunction with variational modified hypernetted chain (VMHNC) integral equation theory of liquid structure. Calculated values of surface tension are used to evaluate transport coefficients such as diffusion and shear viscosity coefficients. Comparing with experimental and simulated data, calculated results suggest that expression derived from second order approximation of PY solution with the combination of EAM potential and VMHNC theory works better than any other combinations for the concerned systems.

Comparative studies of interatomic potentials for modeling point defects in wurtzite GaN

In this paper, a new version of the Stillinger–Weber (SW) potential for wurtzite GaN is presented, by which we systematically explore the structural and thermodynamical properties of native point defects and their complexes. In parallel, the semi-empirical Modified Embedded-Atom Method (MEAM) potential is selected for comparison. The SW and MEAM potentials are assessed by the reproduction of the fundamental properties of wurtzite GaN and by the ability to describe the inversion domain boundaries and the wurtzite–rocksalt phase transition. Then the structural search of native point defects and their complexes in GaN is implemented using both SW and MEAM potentials with the benchmark of Density Functional Theory (DFT) calculations. Besides vacancies and antisites, four N and five Ga interstitials are confirmed by refining the DFT calculations, among which two N split interstitials N+−N⟨21̄1̄0⟩ and N+−Ga⟨011̄0⟩, and two Ga split interstitials, Ga+−Ga⟨011̄0⟩−g and Ga+−N⟨011̄0⟩, are observed for the first time. The SW potential correctly predicts the octahedral occupation GaOct to be the most stable Ga interstitial, while the MEAM potential predicts the ground state of the N+−N⟨011̄0⟩ split interstitial (N+−N⟨011̄0⟩−g) as the most stable N interstitial. However, neither of the two potentials could simultaneously generate the most stable configurations of N and Ga interstitials. The investigations of point defect complexes reveal that N octahedral Frenkel [FrenkelOct(N)] and paired antisite (NGaGaN) defects are unstable and get converted into VN⊕N+−N⟨011̄0⟩−g configurations with different separations between VN and N+−N⟨011̄0⟩−g point defects based on the DFT calculations. The formation energies calculated by the DFT and SW potential demonstrate that Schottky, Ga octahedral Frenkel [FrenkelOct(Ga)], and VN⊕N+−N⟨011̄0⟩−g point defect complexes are energetically feasible and that they should not dissociate into two isolated point defects. In contrast, the MEAM potential predicts the dissociation to be exothermic for Schottky and VN⊕N+−N⟨011̄0⟩−g. Overall, the structural features concerned with N–N or Ga–Ga bonds relaxed by the SW potential are more consistent with DFT calculations than the MEAM counterpart.

<i>Ab Initio</i> Local-Energy and Local-Stress Calculations for Materials Science and Engineering

Revealing atomic-scale distributions of energy and stress in defective or complex systems, based on the behavior of electrons, should contribute much to materials science and engineering, while only few practical ab initio methods were developed for this purpose. Thus, we developed computational techniques of local-energy and local-stress calculations within the plane-wave PAW (projector augmented wave)-GGA (generalized gradient approximation) framework. This is natural extension of ab initio energy-density and stress-density schemes, while the inherent gauge dependency is removed by integrating these densities in each local region where the contained gauge-dependent terms are integrated to be zero. In this overview, we explain our scheme with some details and discuss the concepts or physical meanings of local energy and local stress via the comparison with related schemes using similar densities, LCAO (linear combination of atomic orbitals) methods, Green’s function formulation implemented by multiple scattering or TB (tight-binding) methods, or EAM (embedded-atom method) potentials. We present recent applications to metallic surfaces, grain boundaries (GBs) with and without solute segregation, tensile tests of metallic GBs, local elastic constants of microstructures in alloys, and machine-learning based GB-energy prediction, where the local-energy and local-stress analyses provide novel aspects of phenomena, deep insights into the mechanism, and effective data for novel machine-learning based modelling. We discuss unsettled issues and future applications, especially for large-scale metallic systems.

Molecular dynamics simulations of glass formation, structural evolution and diffusivity of the Pd-Si alloys during the rapid solidification process

The atomic structure, glass formation process and diffusion mechanism of Pd100-xSix (x = 10, 20, 30, 40 and 50) alloys during rapid solidification have been investigated by molecular dynamics simulations using embedded atom method potentials. The structure factors, total (or Pd90Si10) and partial pair distribution functions calculated for Pd80Si20 bulk metallic glass are in good agreement with the experimental/other data. Bond angle distribution function, Honeycutt-Andersen index and Voronoi tessellation analysis have revealed that the increasing Si amount caused a decrease in the number of icosahedral-like clusters and an increase in the number of crystal-like clusters. The majority of icosahedral-like clusters in the systems are mostly composed of Pd-centered clusters, suggesting that Pd has an effective role in the glass formation process in Pd-Si systems. It has been observed that the mobility of Si atoms decreases in environments with more Pd atoms. The critical temperature and T0 temperature for Pd-Si liquids have been determined from the self-diffusion coefficients using the mode-coupling theory and the Vogel-Fulcher-Tammann law, respectively. The present findings show us that the Pd70Si30 compound has a critical importance in terms of the glass formation process, which is consistent with experimental observations. We hope that the results will contribute to understanding the Si effect on the atomic local structure of Pd-Si systems and will encourage research on many properties of these systems, such as their mechanical properties.