Atomic-level Stresses Research Articles

Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses

It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearrangements and the local atomic environment as measured by the atomic-level stresses, kinetic and potential energies, and the per-atom Voronoi volume. In addition, there is only a weak correlation between atomic rearrangements and the largest and smallest eigenvalues of the dynamical matrix. Our results confirm the transient nature of dynamical heterogeneities and suggest that the notion of defects may be less relevant than that of a propensity for rearrangement.

First-principles atomic level stresses: application to a metallic glass under shear

Unlike crystalline alloys, metallic glasses (MGs) do not possess distinctive defects but exhibit a highly heterogeneous response to shear deformation. The difficulties in describing such non-uniform behaviour hamper the prediction of the mechanical properties of MGs. Using the first-principles athermal quasi-static shear simulation on a CuZr glass, we investigate the mechanical responses of various atomic-level parameters, such as the first-principles atomic stresses and electronic properties (an atomic charge, chemical bonds, etc), and their correlations. We find that the atomic von Mises stress is correlated with a parameter, which is commonly employed and also serves as a unique measure of the degree of non-uniform responses. We also show little correlation between the mechanical and electronic properties during the relaxation process, while we perceive a high correlation between the change in chemical and topological bonds. We discuss the physical insights behind these correlations.

Transient nature of fast relaxation in metallic glass

Metallic glasses exhibit fast mechanical relaxations at temperatures well below the glass transition, one of which shows little variation with temperature known as nearly constant loss (NCL). Despite the important implications of this phenomenon to deformation, the origin of the relaxation is unclear. Through molecular dynamics simulations of a model metallic glass, Cu64.5Zr35.5, we implement molecular dynamics dynamical mechanical spectroscopy (MD-DMS) with system stress decomposed into atomic-level stresses to identify the group of atoms responsible for NCL. This work demonstrates that NCL relaxation is due to transient groups of atoms that revert to the typical atomic-level viscoelastic behavior over picosecond timescales. They are homogenously distributed throughout the glass and have no outstanding features, rather than having defect-like local structure as previously reported.

Atomic simulations of melting behaviours for TiAl alloy nanoparticles during heating

Titanium alloys not only have a high strength to weight ratio and good corrosion resistance but also have a higher cost on traditionally metallurgy. In additive manufacturing (AM) process, the thermal stability of alloy particles during heating has an important influence on fabricating parts. This article presents atomic simulations to study changes of packing structures and atomic level stresses by using a molecular dynamics (MD) approach within the framework of embedded atom method (EAM). This research provides different evolution patterns of TiAl nanoparticles with different sizes owing to the following facts that the atoms undergo different strain states. In these particles, a large proportion of Al atoms are subjected to tensile or compressive strain, whereas a considerable number of Ti atoms are stretched or compressed only at high temperatures. Back propagation neural network is used to calculate data of specific heat, and the machine learning provides the possibility to determine critical size suitable for the classical Dulong–Petit law under certain thermal conditions.

Inherent relation between atomic-level stresses and nanoscale heterogeneity in Zr-based bulk metallic glass under a rejuvenation process

This study addresses the role of rejuvenation process on the fluctuation of atomic-level stresses and nanoscale topological heterogeneity in ZrCuNiAl bulk metallic glass (BMG). Based on atomic force microscopy (AFM) results, the rejuvenation process leads to an increase in nanoscale spatial heterogeneity manifested by the intensification of the local viscoelastic response of the BMG nanostructure. It means that the rejuvenation process induces more loose-packing structures which behave towards an external load in a viscoelastic way. Hence, it is suggested that the alteration of such heterogeneity may be attributed to the variation of positional atomic rearrangement during the evolution of structural rejuvenation. On the other side, the synchrotron X-ray diffraction (XRD) results indicate that the rejuvenation intensifies variation of internal stresses at the atomic level. This conclusion unfolds that the increase of atomic-level stresses during rejuvenation induces structural disordering and nanoscale heterogeneity in the amorphous material.

Morphing Mncore@Ptshell nanoparticles: Effects of core structure on the ORR performance of Pt shell

Currently, the catalysts performance for the oxygen reduction reaction (ORR) is limited by two major factors, their price and the scaling relationship, i.e. constant offset, between the binding energy of reactants and reaction intermediates. Here we show that both limitations may be eased by using nanoparticle catalysts composed of a core of earth-abundant Mn and Pt shell of two atomic layers. The unusual atomic-structure of Mn core renders the distribution of coordination numbers and related atomic-level stresses on the Pt shell very broad in comparison to pure Pt particles. This increases the chances of nearby sites on the shell to affect each other’s activity such that the dissociative absorption of molecular oxygen is facilitated without correspondingly increasing the binding strength of reaction intermediates, thereby promoting the ORR kinetics. Our findings introduce the concept of structural flexibility of the 3d-metal core and 5d-Pt shell as a strategy for catalysis performance.

Electronic structure and atomic level complexity in Al0.5TiZrPdCuNi high-entropy alloy in glass phase

High entropy alloys (HEAs), or concentrated solid solution alloys, are chemically complex metallic solid solutions in which five or more elements occupy the same crystallographic lattice sites with nearly equal compositions. The high degree of chemical disorder gives rise to considerable local lattice distortions, atomic-level stresses, and complex electronic structure, resulting in interesting properties. We calculated the electronic structure and the atomic-level stresses of AlxTiyZryPdyCuyNiy, x = 0.5, y = 1 (Al0.5TiZrPdCuNi) HEA in the glassy phase using the density functional theory (DFT) approach. We also briefly discuss the electronic structure in its crystalline phase. Whereas it has been reported recently that the crystalline phase of this HEA is obtained as a metastable phase during the crystallization of a glassy phase, the crystalline phase was found to be unstable at T = 0 in the DFT calculation. For this reason, we focus mainly on the glassy phase in this work. The importance of charge transfer among elements on the atomic-level pressure and the role for atomic-level stresses to characterize the electronic and structural heterogeneity are discussed.

Pressure effects on local atomic structure of Ni15Co15Al70 metallic glasses

Molecular dynamics simulations are used to study the pressure effects on the local atomic structure of Ni15Co15Al70 metallic glasses. Interatomic interactions are modeled by the semi-empirical embedded atom method. The effects of pressure were systematically investigated through a variety of local structural analysis methods, such as bond angle distribution, structure factor, Voronoi tessellation and total and partial coordination numbers. Via the Went-Abraham parameter, our numerical results show an increase of the glass transition temperature Tg with increasing pressure. In the same context, Voronoi tessellation and coordination number analyses indicate that the local structure of glassy Ni15Co15Al70 is obviously influenced by the applied pressure, and the degree of local fivefold symmetry in the quenched systems decreases when the pressure increases. Lastly, we also investigated other parameters of structural disorder in amorphous alloys Ni15Co15Al70, including the concept of free volume and the atomic-level stresses. Implications of these findings are discussed.

First principle study of magnetism and vacancy energetics in a near equimolar NiFeMnCr high entropy alloy

We report the results of ab initio calculations of a novel NiFeMnCr high entropy alloy (HEA) with potential applications as a high performance structural material. The bulk and defect property variations due to chemical disordering and magnetic frustration have been studied using both supercell and coherent potential approximation-based techniques. While magnetic frustration due to the presence of multiple 3d transition metals can severely affect the accuracy of vacancy formation energy in first-principles calculations, this effect should be suppressed at intermediate and high temperatures. An efficient approach to evaluate the chemical potential in HEA is constructed and implemented. Vacancy formation energies are computed based on the chemical potential. The statistical distribution of formation energies is weakly dependent upon the chemical identity of the vacancy. On the other hand, the calculated vacancy migration energies show that Fe is more likely to have a large migration barrier than Cr, Mn, or Ni. Finally, atomic-level stresses are computed. A qualitative model to explain the elemental segregation trend in HEA is built upon the atomic-level stress calculation results and provides a reasonable qualitative agreement with ion irradiation experimental data of a NiFeMnCr HEA.

Ultrathin Gold Nanowires with the Polytetrahedral Structure of Bulk Manganese.

Despite the intensive interest in thin gold nanowires for a variety of technologically important applications, key details of the mechanism of their formation and atomic-scale structure remain unknown. Here we synthesize highly uniform, very long, and ultrathin gold nanowires in a liquid-phase environment and study their nucleation and growth using in situ high-energy synchrotron X-ray diffraction. By controlling the type of solvents, reducing agents, and gold precursor concentration, it is shown that the nucleation and growth of gold nanowires involve the emergence and self-assembly of transient linear gold complexes, respectively. In sharp contrast with the face-centered-cubic bulk gold, the evolved nanowires are found to possess a tetrahedrally close packed structure incorporating distorted icosahedra and larger size coordination polyhedra of the type observed with the room-temperature phase of bulk manganese. We relate the complexes to synergistic effects between the selected precursor and reducing agents that become appreciable over a narrow range of their molar ratios. We attribute the unusual structural state of gold nanowires to geometrical frustration effects arising from the conflicting tendencies of assemblies of metal atoms to evolve toward attaining high atomic packing density while keeping the atomic-level stresses low, ultimately favoring the growth of cylindrical nanowires with a well-defined diameter and atomically smooth surface. Our work provides a roadmap for comprehensive characterization and, hence, better understanding of 1D metallic nanostructures with an unusual atomic arrangement and may have important implications for their synthesis and performance in practical applications.

Contribution to viscosity from the structural relaxation via the atomic scale Green-Kubo stress correlation function.

We studied the connection between the structural relaxation and viscosity for a binary model of repulsive particles in the supercooled liquid regime. The used approach is based on the decomposition of the macroscopic Green-Kubo stress correlation function into the correlation functions between the atomic level stresses. Previously we used the approach to study an iron-like single component system of particles. The role of vibrational motion has been addressed through the demonstration of the relationship between viscosity and the shear waves propagating over large distances. In our previous considerations, however, we did not discuss the role of the structural relaxation. Here we suggest that the contribution to viscosity from the structural relaxation can be taken into account through the consideration of the contribution from the atomic stress auto-correlation term only. This conclusion, however, does not mean that only the auto-correlation term represents the contribution to viscosity from the structural relaxation. Previously the role of the structural relaxation for viscosity has been addressed through the considerations of the transitions between inherent structures and within the mode-coupling theory by other authors. In the present work, we study the structural relaxation through the considerations of the parent liquid and the atomic level stress correlations in it. The comparison with the results obtained on the inherent structures also is made. Our current results suggest, as our previous observations, that in the supercooled liquid regime, the vibrational contribution to viscosity extends over the times that are much larger than the Einstein's vibrational period and much larger than the times that it takes for the shear waves to propagate over the model systems. Besides addressing the atomic level shear stress correlations, we also studied correlations between the atomic level pressure elements.

Molecular Simulations of Free and Graphite Capped Polyethylene Films: Estimation of the Interfacial Free Energies

We present a reliable simulation strategy for estimating the surface tension, the work of adhesion, and all related macroscopic work functions of fluid/vacuum and fluid/solid interfaces, directly from the atomic-level stresses in the system. Our methodology employs efficient algorithms (developed here and from the literature) for fast and reliable simulations of high molar mass polymer melts and is applied to the well-tested molten polyethylene/graphite interface, as well to the free surface of molten polyethylene, using a united atom model for the polymer. The surface thermodynamic properties are obtained for a broad range of molar masses and temperatures and are compared to experimental data, theoretical models, and earlier simulation studies. The individual components of the stress tensor are isolated, and their profiles along the aperiodic dimension are correlated to the orientational and structural features of the polymer chains near the interfaces. The distributions of end segments in free and cappe...

Molecular Dynamics Study of Polyethylene under Extreme Confinement

We present results concerning the dynamics and the structure of adsorbed layers of molten polyethylene (PE) between two graphite surfaces. The molecular weight of the monodisperse PE chains reaches the entanglement regime. We study three cases of interwall distances, equal to two, three and four times the unperturbed radius of gyration (Rg) of PE chains. The confined system is equilibrated by use of efficient Monte Carlo (MC) algorithms. Conducting molecular dynamics (MD) simulations, we reveal the distribution of relaxation times as a function of distance from the graphite walls at the temperature of 450 K. From the atomic-level stresses we calculate a realistic estimate of the adhesion tension, which is not affected significantly by the width of the pore. Although the distance between the two walls is comparable to the width of the adsorbed layer, we do not record the formation of ‘glassy bridges’ under the studied conditions. The diffusion of polymer chains in the middle layer is not inhibited by the existence of the two adsorbed layers. Extreme confinement conditions imposed by the long range wall potentials bring about an increase in both the adsorption and desorption rates of chains. The presented results seem to cohere with a reduction in the calorimetric (heat capacity step) glass transition temperature (Tg).

Analysis of spatial correlations in a model two-dimensional liquid through eigenvalues and eigenvectors of atomic-level stress matrices

Considerations of local atomic-level stresses associated with each atom represent a particular approach to address structures of disordered materials at the atomic level. We studied structural correlations in a two-dimensional model liquid using molecular dynamics simulations in the following way. We diagonalized the atomic-level stress tensor of every atom and investigated correlations between the eigenvalues and orientations of the eigenvectors of different atoms as a function of distance between them. It is demonstrated that the suggested approach can be used to characterize structural correlations in disordered materials. In particular, we found that changes in the stress correlation functions on decrease of temperature are the most pronounced for the pairs of atoms with separation distance that corresponds to the first minimum in the pair density function. We also show that the angular dependencies of the stress correlation functions previously reported by Wu etal. [Phys. Rev. E 91, 032301 (2015)10.1103/PhysRevE.91.032301] do not represent the anisotropic Eshelby's stress fields, as it is suggested, but originate in the rotational properties of the stress tensors.

Local Electronic Effects and Irradiation Resistance in High-Entropy Alloys

High-entropy alloys are multicomponent solid solutions in which various elements with different chemistries and sizes occupy the same crystallographic lattice sites. Thus, none of the atoms perfectly fit the lattice site, giving rise to considerable local lattice distortions and atomic-level stresses. These characteristics can be beneficial for performance under radiation and in a high-temperature environment, making them attractive candidates as nuclear materials. We discuss electronic origin of the atomic-level stresses based upon first-principles calculations using a density functional theory approach.

Anisotropic stress correlations in two-dimensional liquids.

In this paper we demonstrate the presence of anisotropic stress correlations in the simulated two-dimensional liquids. Whereas the temporal correlation of macroscopic shear stress is known to contribute to viscosity via the Green-Kubo formula, the general question regarding angular dependence of the spatial correlation among atomic-level stresses in liquids without external shear has not been explored. We observed the apparent anisotropicity with well-defined symmetry which can be explained in terms of the elastic continuum theory by Eshelby. In addition, we found that the shear stress correlation is screened compared to the prediction by the elastic continuum theory, and the screening length depends on temperature and follows the power law, suggesting divergence around the glass transition temperature. The success of the Eshelby theory to explain the anisotropy of the stress correlations justifies the idea that the mismatch between the atom and its nearest neighbor cage produces the atomic-level stress as well as the long-range stress fields.

Inhomogeneous thermal expansion of metallic glasses in atomic-scale studied by in-situ synchrotron X-ray diffraction

Numerous investigations have demonstrated that the elastic strain in metallic glasses subjected to mechanical loading could be inhomogeneous in the atomic-scale and it increases with distance from an average atom and eventually reaches the macroscopic strain at larger inter-atomic distances. We have observed a similar behavior for the thermal strain imposed by heating of Co40Fe22Ta8B30 glassy particles below the glass transition temperature by analysis of the scattering data obtained by in-situ high-energy synchrotron X-ray diffraction (XRD). The results imply that the volumetric thermal strains calculated from the shift in position of the principal diffraction maximum and reduced pair correlation function (PDF) peaks are in good agreement for the length scales beyond 0.6 nm, corresponding to the atoms located over the third near-neighbor shell. However, smaller and even negative volumetric thermal strains have been calculated based on the shifts in the positions of the second and first PDF peaks, respectively. The structural changes of Co40Fe22Ta8B30 glassy particles are accompanied by decreasing the average coordination number of the first near-neighbor shell, which manifests the occurrence of local changes in the short-range order upon heating. It is believed that the detected length-scale dependence of the volumetric thermal strain is correlated with the local atomic rearrangements taking place in the topologically unstable regions of the glass governed by variations in the atomic-level stresses.

Effect of atomic-level stresses on local dynamic and mechanical properties in CuxZr100−x metallic glasses: A molecular dynamics study

In this article, molecular dynamics simulations of CuxZr100−x metallic glasses are performed to study the dynamic and mechanical behaviors of structural defects. Based on atomic-level stress theory, atomic strain energy and von Mises shear stress were correlated with the local dynamic/mechanical properties of MGs. Atoms with high atomic strain energy (n-type/p-type defects) are found to exhibit larger mean square displacements than solid-like atoms during structural relaxation process, indicating that these atoms have faster dynamics than solid-like entities. Additionally, simulated shear loading was conducted to investigate the relationship between von Mises shear stress and local shear properties in MGs. By monitoring the von Mises shear strain for each atom, γ-defects (atoms with excessive shear stress) are proven to be fertile regions for shear transformations.

Understanding the atomic-level Green-Kubo stress correlation function for a liquid through phonons in a model crystal

In order to gain insight into the connection between the vibrational dynamics and the atomic-level Green-Kubo stress correlation function in liquids, we consider this connection in a model crystal instead. Of course, vibrational dynamics in liquids and crystals are quite different and it is not expected that the results obtained on a model crystal should be valid for liquids. However, these considerations provide a benchmark to which the results of the previous molecular dynamics simulations can be compared. Thus, assuming that vibrations are plane waves, we derive analytical expressions for the atomic-level stress correlation functions in the classical limit and analyze them. These results provide, in particular, a recipe for analysis of the atomic-level stress correlation functions in Fourier space and extraction of the wave-vector and frequency-dependent information. We also evaluate the energies of the atomic-level stresses. The energies obtained are significantly smaller than the energies previously determined in molecular dynamics simulations of several model liquids. This result suggests that the average energies of the atomic-level stresses in liquids and glasses are largely determined by the structural disorder. We discuss this result in the context of equipartition of the atomic-level stress energies. Analysis of the previously published data suggests that it is possible to speak about configurational and vibrational contributions to the average energies of the atomic-level stresses in a glass state. However, this separation in a liquid state is problematic. We also introduce and briefly consider the atomic-level transverse current correlation function. Finally, we address the broadening of the peaks in the pair distribution function with increase of distance. We find that the peaks' broadening (by $\ensuremath{\approx}40%$) occurs due to the transverse vibrational modes, while contribution from the longitudinal modes does not change with distance.

First-principles local stress in crystalline and amorphous metals

Atomic size is perhaps the most commonly used concept to describe material properties. Advances in the understanding of materials are hindered by the available choices of simplifying concepts that can be used. However, the precise definition of atomic size is not easy, and often controversial. Atomic level stress provides a new interpretive tool that draws on the rich formalism of solid mechanics for use with density functional calculations to advance a deeper understanding of the properties of materials. We discuss atomic level stresses in liquids and glasses and make comparisons with ordered and disordered crystals. Somewhat surprisingly, even ordered compounds that are under no macroscopic stress and whose individual atoms are completely relaxed, i.e., no force acting on them, can have substantial atomic level stresses. On top of concepts such as the ionicity or covalency, the atomic level stresses add to the arsenal of analysis tools that are available to interpret the results of density functional calculations.