A set of embedded atom model (EAM) interatomic potentials was developed to represent highly idealized face-centered cubic (FCC) mixtures of Fe–Ni–Cr–Co–Al at near-equiatomic compositions. Potential functions for the transition metals and their crossed interactions are taken from our previous work for Fe–Ni–Cr–Co–Cu [D. Farkas and A. Caro: J. Mater. Res. 33 (19), 3218–3225, 2018], while cross-pair interactions involving Al were developed using a mix of the component pair functions fitted to known intermetallic properties. The resulting heats of mixing of all binary equiatomic random FCC mixtures not containing Al is low, but significant short-range ordering appears in those containing Al, driven by a large atomic size difference. The potentials are utilized to predict the relative stability of FCC quinary mixtures, as well as ordered L12 and B2 phases as a function of Al content. These predictions are in qualitative agreement with experiments. This interatomic potential set is developed to resemble but not model precisely the properties of this complex system, aiming at providing a tool to explore the consequences of the addition of a large size-misfit component into a high entropy mixture that develops multiphase microstructures.

A set of embedded atom method model interatomic potentials is presented to represent a high-entropy alloy with five components. The set is developed to resemble but not model precisely face-centered cubic (fcc) near-equiatomic mixtures of Fe–Ni–Cr–Co–Cu. The individual components have atomic sizes deviating up to 3%. With the heats of mixing of all binary equiatomic random fcc mixtures being less than 0.7 kJ/mol and the corresponding value for the quinary being −0.0002 kJ/mol, the potentials predict the random equiatomic fcc quinary mixture to be stable with respect to phase separation or ordering and with respect to bcc and hcp random mixtures. The details of lattice distortion, strain, and stress states in this phase are reported. The standard deviation in the individual nearest neighbor bond lengths was found to be in the range of 2%. Most importantly, individual atoms in the alloy were found to be under atomic strains up to 0.5%, corresponding to individual atomic stresses up to several GPa.

We present classical potential molecular dynamics simulations of nanoporous gold (np-Au) impacted by a spherical indenter. The atomic structure was generated using a phase field model as a template. In agreement with previous experiments, we observe densification in the region under the indenter. The hardness values obtained from our simulations exhibit a transition from an initially perfect-plastic plateau to hardening behavior in the later stages of indentation. This transition occurs when the relative density beneath the indenter exceeds ∼0.9. Hardness values obtained from the nanoindentation simulations reach 0.6 GPa, due to the densification of the material under the indenter. Elevated dislocation densities are observed in the densified region. The mechanism of pore collapse in the densified layer under the indenter is seen to switch from uniaxial to triaxial, consistent with a change in deformation mechanism from one based on shearing of individual ligaments in np-Au to one involving dislocation-mediated plasticity around voids in a Au single crystal undergoing uniaxial compression.

Nanoporous metals made by dealloying are macroscopic network architectures that can contain ∼1015 nanoscale struts or ligaments per sample. Their mechanical performance is critical to their applications as functional or lightweight high-strength materials. Testing nanoporous metals at the macroscopic scale offers opportunities for unraveling the properties of nanoscale solids in general. The central questions in this area include whether the macroscopic strength and elastic modulus of nanoporous metals can be correlated with the properties of nanoscale ligaments by the classical Gibson–Ashby equations, whether the dealloying-made network structure differs from the conventional foam metals, how network connectivity influences mechanical response, and how ligament size and surface properties affect the elastic and plastic response of nanoscale solids and that of nanoporous metals, particularly the tension–compression asymmetry in strength. This article reviews the fundamental observations of the mechanical response of nanoporous metals with a focus on gold and the emerging understanding of the aforementioned issues.

Atomistic simulations of nanoindentation of a 20-nm-thick Ni thin film oriented in the [111] direction were carried out to study the effects of indenter velocity and radii, interatomic potentials, and the boundary conditions used to represent the substrate. The simulation results were compared directly with experimental results of Ni thin film of the same thickness and orientation. It was found that the high indenter velocity does not affect the hardness value significantly. Different radii used for indentation also have negligible effects on the hardness value. Two different interatomic potentials were tested, giving significantly different hardness values but both within 20% of the experimental result. Different boundary conditions used to represent the substrate have a significant effect for relatively deep indentation simulations.

Atomic scale computer simulations were used to investigate the surface stress induced deformation in nanoporous metals. A phase field model was used to generate digital nanoporous structures that are quantitatively similar to those created experimentally via dealloying. We analyze the important effects of surface relaxations on the macroscopic deformation in these samples as well as in small spherical clusters.

Molecular dynamics simulations of nanoindentation were performed using embedded atom potentials. The indentation was simulated on a Ni substrate using a diamond-like spherical indenter. In this study, we focused on the interaction of a σ=5 (210) grain boundary with the dislocations that were nucleated and expanded as loops under the indenter during nano- indentation. The results showed that dislocation loops were nucleated beneath the surface and propagated on multiple {111} slip planes. These dislocations impinged into the grain boundary in the course of nanoindentation. The lattice dislocations changed the atom configuration at the boundary region as they merged into the grain boundary and at later stages they transmitted across the grain boundary. The results also showed that the presence of a grain boundary affected the indenting speed and dislocation motion during nanoindentation, with the grain boundary retarding the indentation process.

One of the most interesting unsolved problems in fracture mechanics is the precise understanding of the energy-dissipation mechanisms that occur as a crack advances. In most cases, this energy-release rate is many times the surface energy created. One of the main reasons for this difference is the fact that plastic deformation can occur in the crack-tip region as dislocations nucleate and are emitted from the crack tip. Experimental studies provide little insight into the precise mechanisms for this process because they cannot reach the atomistic scale. For example, a crack that may seem experimentally sharp, and therefore indicative of brittle fracture, may not be sharp at the atomic level. Continuum mechanics has a similar limitation, since the assumptions of elasticity theory usually break down in the crack-tip region. Atomistic simulation studies provide researchers an opportunity to obtain precise atomic configurations in the crack-tip region under various loading conditions and to observe the basic energy-dissipation mechanisms.

We present a study of the atomistic mechanisms of crack propagation along grain boundaries in metals and alloys. The failure behavior showing cleavage crack growth and/or crack-tip dislocation emission is demonstrated using atomistic simulations for an embedded-atom model. The simulations follow the quasi-equilibrium growth of a crack as the stress intensity applied increases. Dislocations emitted from crack tips normally blunt the crack and inhibit cleavage, inducing ductile behavior. When the emitted dislocations stay near the crack tip (sessile dislocations), they do blunt the crack but brittle cleavage can occur after the emission of a sufficient number of dislocations. The fracture process occurs as a combination of dislocation emission/micro-cleavage portions that are controlled by the local atomistic structure of the grain boundary. The grain boundary is shown to be a region where dislocation emission is easier, a mechanism that competes with the lower cohesive strength of the boundary region.

Using embedded atom potentials and molecular statics we calculate the structure and energy of [001] tilt grain boundaries in NiAl for 25 orientations with Σ values from 5 to 185. For three structures (stoichiometric, Ni-rich and Al-rich) of the Σ = 5 (210) boundary we simulate tracer self-diffusion by the vacancy mechanism both parallel and perpendicular to the tilt axis using the Monte Carlo technique. The effective activation energy calculated in a wide temperature range is compared with the spectrum of individual jump energies in the boundary core. The results are interpreted in terms of the grain boundary structure-diffusion relationship and the role of the jump correlation effect in grain boundary diffusion.

We present atomistic simulations of the crack tip configuration near a high angle Σ= 5 [001](210) symmetrical tilt grain boundary in NiAl. The simulations were carried out using molecular statics and embedded atom (EAM) potentials. The cracks are stabilized near a Griffith condition involving the cohesive energy of the grain boundary. The atomistic configurations of the tip region are different in the presence of the high angle grain boundary than in the bulk. Three different configurations of the grain boundary were studied corresponding to different local compositions. It was found that in ordered NiAl, cracks along symmetrical tilt boundaries show a more brittle behavior for Al rich boundaries than for Ni-rich boundaries. Lattice trapping effects in grain boundary fracture were found to be more significant than in the bulk.

Interatomic potentials of the embedded atom (EAM) type were used to study the atomistic structure of high index surfaces in metals and ordered alloys. The results show that a structural unit model can be developed to model the structure of the high index surfaces on the basis of the structure of a few low energy surfaces. The model can predict the structural features and give an estimate of the energies of the higher index surfaces. We present examples of Fe, B2 FeAl and NiAl.

We present atomistic simulations of the crack tip configuration in multilayered Cu-Ni materials. The simulations were carried out using molecular statics and EAM potentials. The atomistic structure of the interface was studied first for a totally coherent structure. Cracks were simulated near a Griffith condition in different possible configurations of the crack plane and front with respect to the axis of the layers. Results show that interface effects predominately control the mechanical behavior of the system studied.

The elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in a-Fe, loaded in mode I. In these examples, the interatomic interaction in α-Fe is described by an empirical embedded atom (EAM) potential.

The elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in α-Fe, loaded in mode I. In these examples, the interatomic interaction in α-Fe is described by an empirical embedded atom (EAM) potential.

The behavior of mode I cracks in α-Fe is investigated using molecular statics methods with EAM potentials. A double ended crack of finite size embedded in a cylindrical simulation cell and fixed boundary conditions are prescribed along the periphery of the cell, whereas periodic boundary conditions are imposed parallel to the crack front. The displacement field of the finite crack is represented by that of an equivalent pileup of opening dislocations distributed in a manner consistent with the anisotropy of the crystal and traction free conditions of the crack faces. The crack lies on the {110} plane and the crack front is located either along á100ñ, á110ñ or á111ñ directions. The crack tip response is rationalized in terms of the surface energy (γs) of the cleavage plane and the unstable stacking energies (γus) of the slip planes emanating from the crack front.

Atomistic computer simulation with embedded atom method potentials has been performed to study the energetics and structures of point defects in L12Ni3A1 and B2 NiAl. The large size of Al atoms plays a dominant role in the relaxed atomic configurations of vacancies and antisite defects in the system. In both Ni3Al and NiAl, it was found that excess Ni can be accommodated by Ni in Al sites. Accommodation of excess Al by locating Al in Ni sites is not energetically favorable in NiAl. The most stable di-vacancy configuration is two vacancies as first nearest neighbors in Ni sublattices for Ni3Al and as second nearest neighbors in Al sublattices for NiAl. General attraction of two vacancies in Ni3Al was found. On the contrary, vacancies in NiAl show repulsive interaction in several cases. This accounts for the existence of structural vacancies in B2 NiAl. The effects of different degrees of random disorder on the lattice parameters were evaluated, and it was found that these effects can be correlated with the local distortion around antisite defects using a simple model.

Interatomic potentials of the Embedded Atom and Embedded Defect types were used to study the effect of the angular dependent term in the Embedded Defect potential on the properties of defects in TiAl. The defect properties were computed with interatomic potentials developed with and without angular dependent terms. It was found that the inclusion of the angular dependent terms tends to increase the energies of the APB’s and lower the energies of stacking faults. The effects of the angular term on the relaxation around vacancies and antisites in TiAl was also studied, as well as the core structure of several dislocations in this compound.

Two different interatomic potentials of the embedded atom type were used to study the relationships between dislocation core structure and mobility. Core structures were computed for a variety of dislocations in B2 NiAl. Several non-planar cores were studied as they reacted to applied stress and moved. The results show that in some cases, the dislocation core transforms to a planar structure before the dislocation glides, whereas in some other cases the core retains the non-planar structure at stresses sufficient to sustain glide. The effects of stoichiometry deviations on the core structure and motion were also studied.