Effects of solute Mg on grain boundary and dislocation dynamics during nanoindentation of Al–Mg thin films

Using in situ nanoindentation in a transmission electron microscope (TEM) the indentation-induced plasticity in ultrafine-grained Al and Al–Mg thin films has been studied, together with conventional quantitative ex situ nanoindentations. Extensive grain boundary motion has been observed in pure Al, whereas Mg solutes effectively pin high-angle grain boundaries in the Al–Mg alloy films. The proposed mechanism for this pinning is a change in the atomic structure of the boundaries, possibly aided by solute drag on extrinsic grain boundary dislocations. The mobility of low-angle boundaries is not affected by the presence of Mg. Based on the direct observations of incipient plasticity in Al and Al–Mg, it was concluded that solute drag accounts for the absence of discrete strain bursts in indentation of Al–Mg.     

Solute segregation transition and drag force on grain boundaries

We investigate solute segregation and transition at grain boundaries and the corresponding drag effect on grain boundary migration. A continuum model of grain boundary segregation based on gradient thermodynamics and its discrete counterpart (discrete lattice model) are formulated. The model differs from much previous work because it takes into account several physically distinctive terms, including concentration gradient, spatial variation of gradient-energy coefficient and concentration dependence of solute–grain boundary interactions. Their effects on the equilibrium and steady-state solute concentration profiles across the grain boundary, the segregation transition temperature and the corresponding drag forces are characterized for a prototype planar grain boundary in a regular solution. It is found that omission of these terms could result in a significant overestimate or underestimate (depending on the boundary velocity) of the enhancement of solute segregation and drag force for systems of a positive mixing energy. Without considering these terms, much higher transition temperatures are predicted and the critical point is displaced towards much higher bulk solute concentration and temperature. The model predicts a sharp transition of grain boundary mobility as a function of temperature, which is related to the sharp transition of solute concentration of grain boundary as a function of temperature. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in both the concentration–temperature plot and the mobility–temperature plot. These predictions agree well with experimental observations.     

Competing deformation mechanisms in nanocrystalline metals and alloys: Coupled motion versus grain boundary sliding

Plastic deformation of nanocrystalline Pd and Cu as well as the demixing systems Cu–Nb and Cu–Fe is studied by means of atomic-scale computer simulations. The microstructures are specifically chosen to facilitate mesoscopic grain boundary sliding. The influence of segregating solutes on the deformation mechanisms is studied and different cases of solute distributions are compared. We find that the competition between mesoscopic grain boundary sliding and coupled grain boundary motion is controlled by the concentration and distribution of segregating solutes. By analyzing the microstructural evolution and dislocation activity we make a connection between the atomistic solute distribution and the mechanisms of deformation, explaining the observed stress–strain behavior. The detailed analysis of the normal grain boundary motion reveals a stick–slip behavior and a coupling factor which is consistent with results from bicrystal simulations.     

Grain boundary segregation,solute drag and abnormal grain growth

By employing a phase-field model, we simulated the grain boundary (GB) kinetics in terms of GB segregation of solute atoms for an isolated grain embedded in a matrix and demonstrated that the phase-field simulation could describe the GB movement under conditions of GB segregation in a quantitatively correct way. We then modeled grain growth in association with GB segregation in two-dimensional polycrystalline systems, and clarified that similarity between the Cottrell effect and the solute drag effect holds even on the macroscopic scale, that is, abnormal grain growth (AGG) can be induced by the solute drag effect. This AGG can take place spontaneously in homogeneous systems without any texture, anisotropy of GB mobility and/or energy, pinning particles and grain size advantage. The basic characteristics of this AGG and the effects of the solute diffusivity and the average grain size were investigated in detail.     

Atomistic Modeling of Solidification Phenomena Using the Phase-Field-Crystal Model

In recent years, a fundamental understanding of solidification and its behavior has been gained through molecular dynamics simulations and the phase-field method, the first of which is limited to short time scales and the latter of which does not represent interface and elastoplastic properties accurately. Recently, the phase-field-crystal (PFC) method, a continuum method operating on atomistic length scales and diffusive time scales, has helped bridge the multiple scale gap between molecular dynamics and phase field. This review surveys the advances of PFC models in the context of various solidification phenomena.     

Investigation of the effects of solutes on the grain boundary stress relaxation phenomenon

An experimental investigation of grain boundary stress relaxation in copper binary alloys with nickel, silicon, aluminum, and silver comprising the range 0.03 to 1 atomic pct solute has been carried out. Two stress relaxation peaks of grain boundary origin have been ascertained and studied. The energy of activation and peak temperature for both peaks have been determined as functions of solute content and type of solute. It is suggested that this technique can be used as a measure of adsorbability of solute at grain boundaries as a consequence of the saturation effects observed in the measured properties in the vicinity of 0.1 atomic pct solute.     

Phase field modeling of grain boundary migration with solute drag

The grain boundary (GB) motion in the presence of GB segregation is investigated by means of phase field simulations. It is found that the solute concentration at the moving GB may increase with increasing velocity and becomes larger than the equilibrium value, which is unexpected according to the solute drag theory proposed by Cahn, but has been observed in some experiments. A non-linear relation between the driving force (curvature) and the GB velocity is found in two cases: (1) the GB motion undergoes a transition from the low-velocity extreme to the high-velocity extreme; (2) the GB migrates slowly in a strongly segregating system. The first case is consistent with the solute drag theory of Cahn. As for the second case, which is unexpected according to solute drag theory, the non-linear relation between the GB velocity and curvature comes from two sources: the non-linear relation of the solute drag force with GB velocity, and the variation in GB energy with curvature. It is also found that, when the diffusivity is spatially inhomogeneous, the kinetics of GB motion is different from that with a constant diffusivity.     

Modelling the influence of grain-size-dependent solute drag on the kinetics of grain growth in nanocrystalline materials

The large relative change in total grain-boundary area that accompanies grain growth in a nanocrystalline material has a potentially strong influence on the kinetics of grain growth whenever grain-boundary migration is controlled by solute (impurity) drag. As the grain-boundary area decreases, the concentration of solute or impurity atoms segregated to the boundaries is expected to increase rapidly, introducing a grain-size dependence to the retarding force on boundary migration. We have modified the Burke equation—which assumes the drag force to be independent of the average grain size—to take into account a linear dependence of grain-boundary pinning on grain size. The form of the resulting grain-growth curve is surprisingly similar to Burke's solution; in fact, a constant rescaling of the boundary mobility parameter is sufficient to map one solution approximately onto the other. The activation energies for grain-boundary motion calculated from the temperature dependence of the mobility parameter are therefore identical for both models. This fact provides an explanation for the success of Burke's solution in fitting grain-growth data obtained in systems, such as nanocrystalline materials, for which the assumption of grain-size-independent solute drag is incorrect.     

Computation of Five-Dimensional Grain Boundary Energy

A broken-bond type computational method has been developed for the calculation of the five-dimensional grain boundary energy. The model allows quick quantification of the unrelaxed five-dimensionally specified grain boundary energy in arbitrary orientations. It has been validated on some face-centred cubic metals. The stereo projections of grain boundary energy of ∑3,∑5,∑7,∑9,∑11,∑17 b and ∑31a have been studied. The results of Ni closely resemble experimentally determined grain boundary energy distribution figures, suggesting that the overall anisotropy of grain boundary energy can be reasonably approximated by the present simple model. Owing to the overlooking of relaxation matter, the absolute values of energy calculated in present model are found to be higher than molecular dynamic-based results by a consistent magnitude, which is 1 J/m2 for Ni. The coverage of present method forms a bridge between atomistic and meso-scale simulations regarding polycrystalline microstructure.     

Phase-Field Crystal Model for Fe Connected to MEAM Molecular Dynamics Simulations

A recently developed phase-field crystal (PFC) model incorporates elasticity and plasticity in the microstructural evolution of materials naturally by representing the density field for the crystalline state by periodic functions and by using a constant density for liquid state. PFC is of great interest in nano- and micro-structural modeling of materials because it is a model with atomistic scale details but is applicable to diffusive time scales. However, determining model parameters for specific materials is one of the less developed aspects of PFC modeling. In this article, molecular dynamics (MD) simulations of solid–liquid structures for Fe were performed using the modified embedded-atom method to determine the melting point, latent heat, expansion in melting, density profile, and liquid structure factor. The influence of simulation cell size on the results of MD simulations was also investigated. The melting temperature, density profile, and liquid structure factor were used as inputs to find model parameters required by the PFC model for Fe. The spatial derivative order of the PFC time-evolution equation was reduced from four to two, and the resultant system of partial differential equations was solved numerically using the finite element method. The required simulation domain and element size for the convergence of the PFC simulations were determined, and the expansion in melting, latent heat and solid–liquid surface free energy were calculated. The PFC results were compared with the results of other computational and experimental works in the literature.     

Grain coarsening inhibited by solute segregation

It will be shown that grain boundaries are in a metastable thermodynamic equilibrium in the presence of solute atoms and, therefore, grain coarsening is stopped as there is no driving force. This is in contradiction to a generally accepted interpretation, where solute drag, i.e. zero mobility of the boundaries, stops grain coarsening. Based on the empirical relation between terminal solubility of a solute and its grain boundary segregation it can be shown that a two-phase mixture with solute atoms agglomerating in a precipitated phase will be the stable thermodynamic equilibrium state. However, if precipitation is kinetically hindered, the metastable equilibrium with a certain grain boundary area and a zero grain boundary energy is attained. Changes in this grain boundary area or grain size respectively are calculated as a function of temperature and compared with experimental findings.     

Solute drag effects during the dynamic recrystallization of nickel

Solute drag effects during dynamic recrystallization were studied using five different nickel–sulfur alloys. The steady state stress for dynamic recrystallization, measured using hot compression tests, depends on the sulfur concentration. The experimental results are analyzed using a model that relates the steady state stress to the grain boundary mobility. At the lower temperatures, the mobilities are strongly reduced by a solute drag effect; above a transition temperature, the drag effect becomes negligible. The extent of sulfur segregation at grain boundaries during recrystallization was assessed using cryogenic tensile tests of microsamples removed from the hot compressed specimens. The fracture surfaces exhibit the characteristics of intergranular brittleness when hot compression is carried out within the “grain boundary segregation” temperature range; above the transition temperature, the fracture surfaces are purely ductile.     

Grain boundary grooving with simultaneous grain boundary sliding in Ni-rich NiAl

Thermal grooving at grain boundaries in Ni-rich NiAl was studied by atomic force microscopy technique. The determined average ratio of grain boundary to surface energy for large-angle grain boundaries at 1400°C is 0.45, which is in a good agreement with the results of computer simulations. It has been found that in most cases thermal grooving at the grain boundaries is accompanied by relative shift of the adjacent grains. This shift is associated with the grain boundary sliding caused by the relaxation of internal substructure of the specimen. A model of grain boundary grooving with the simultaneous sliding is developed. The calculated grain boundary groove profiles are in a good agreement with the experimentally measured ones.     

Modeling of solute drag in the massive phase transformation

The role of solute drag in the massive phase transformation is evaluated through the dissipation of Gibbs energy by diffusion. As an introduction, the solute drag in grain boundary migration is first examined using the wedge-shaped energy function considered by Cahn and by Lücke and Stüwe. The effect of a diffusivity varying from a low value in the bulk to a high value in the center of the boundary is examined. It decreases the solute drag drastically. For the massive phase transformation it is demonstrated how the solute drag increases by the tendency for segregation and by a high diffusivity in the interface but it decreases if the diffusivity is lower than in the parent phase. The most important contribution to solute drag comes from the spike of solute atoms in the parent phase being pushed forward by the advancing interface. The spike is thus an obstacle for growth that must be broken through in order for diffusion-controlled growth to turn partitionless. The possibility of dynamic nucleation is also discussed.     

Atomistic mechanism for nanocrystallization of metallic glasses

Although considerable effort has been devoted to understanding the nanocrystallization of bulk metallic glasses in deep undercooling conditions, the atomistic mechanisms underlying the detailed growth of atomic clusters existing in amorphous states into three-dimensional (3-D) nanocrystals remains unclear. We resolve this problem here via a combination of careful statistical analyses of high-resolution transmission electron microscope images of pulse-annealed bulk amorphous samples and detailed molecular dynamic simulations of crystallization in deep undercooling conditions. Our results reveal that the atomistic growth mechanism involves three distinguishable steps in succession: formation of quasi-ordered structures with 1-D periodicity, 2-D periodicity on a length scale of 2–4 nm and the formation of 3-D nanocrystals with clear interfaces. These steps take place successively but in a non-uniform manner over the entire sample, and the adjustment of relative atomic position is realized without any long-range diffusion.     

Modelling precipitation in binary alloys by cluster dynamics

Cluster dynamics is an original way to bridge the gap between atomistic simulations and macroscopic approaches of precipitation, but its application to alloys of high solubility limit and solute concentration raise a number of difficulties. The underlying thermodynamic model has been recently extended to treat this type of situation. New tools are presented to explore some of the consequences of this extension, validated by comparing with kinetic Monte-Carlo simulations.     

Length scale and time scale effects on the plastic flow of fcc metals

We examine size scale and strain rate effects on single-crystal face-centered cubic (fcc) metals. To study yield and work hardening, we perform simple shear molecular dynamics simulations using the embedded atom method (EAM) on single-crystal nickel ranging from 100 atoms to 100 million atoms and at strain rates ranging from 10⁷ to 10¹² s⁻¹. We compare our atomistic simulation results with experimental data obtained from interfacial force microscopy (IFM), nano-indentation, micro-indentation and small-scale torsion. The data are found to scale with a geometric length scale parameter defined by the ratio of volume to surface area of the samples. The atomistic simulations reveal that dislocations nucleating at free surfaces are critical to causing micro-yield and macro-yield in pristine material. The increase of flow stress at increasing strain rates results from phonon drag, and a simple model is developed to demonstrate this effect. Another important aspect of this study reveals that plasticity as reflected by the global averaged stress–strain behavior is characterized by four different length scales: (1) below 10⁴ atoms, (2) between 10⁴ and 10⁶ atoms (2 μm), (3) between 2 μm and 300 μm, and (4) above 300 μm.