Fcc Metals Research Articles

Statistical modeling of the effect of chemical inhomogeneity on incipient plasticity in complex concentrated alloys

In recent years, complex concentrated alloys (CCAs), also referred to as medium- or high-entropy alloys, have attracted substantial research interest due to their excellent mechanical properties including high strength, ductility, and toughness. It is known that the chemical inhomogeneity of CCAs gives rise to spatial variations in local properties such as the generalized stacking fault energy (GSFE) surface, which in turn affect their mechanical properties, but how such an inhomogeneity affects dislocation nucleation and incipient plasticity remains largely unknown and unexplored. Here, we develop a physics-informed statistical model for incipient plasticity in CCAs by combining elasticity theory for dislocation nucleation and statistical modeling of nanoindentation. Our model connects a material's fundamental properties to the statistics of incipient plasticity and is validated by the excellent agreement with the statistical data from molecular dynamics simulations of nanoindentation of CrCoNi CCA samples. By accounting for the spatial variation in the local generalized stacking fault energy surface in CCAs, our model captures the key difference in the nanoindentation-induced incipient plasticity response of CCAs compared with a conventional metal (fcc Cu) and also reproduces the trends across CCA samples with different degrees of short-range ordering. Our model also reveals a critical length scale for the underlying GSFE fluctuations which controls the overall statistics of incipient plasticity during nanoindentation of CCAs, which reflects the critical loop size of the underlying dislocation nucleation mechanism.

Structure and Migration Mechanisms of Small Vacancy Clusters in Cu: A Combined EAM and DFT Study.

Voids in face-centered cubic (fcc) metals are commonly assumed to form via the aggregation of vacancies; however, the mechanisms of vacancy clustering and diffusion are not fully understood. In this study, we use computational modeling to provide a detailed insight into the structures and formation energies of primary vacancy clusters, mechanisms and barriers for their migration in bulk copper, and how these properties are affected at simple grain boundaries. The calculations were carried out using embedded atom method (EAM) potentials and density functional theory (DFT) and employed the site-occupation disorder code (SOD), the activation relaxation technique nouveau (ARTn) and the knowledge led master code (KLMC). We investigate stable structures and migration paths and barriers for clusters of up to six vacancies. The migration of vacancy clusters occurs via hops of individual constituent vacancies with di-vacancies having a significantly smaller migration barrier than mono-vacancies and other clusters. This barrier is further reduced when di-vacancies interact with grain boundaries. This interaction leads to the formation of self-interstitial atoms and introduces significant changes into the boundary structure. Tetra-, penta-, and hexa-vacancy clusters exhibit increasingly complex migration paths and higher barriers than smaller clusters. Finally, a direct comparison with the DFT results shows that EAM can accurately describe the vacancy-induced relaxation effects in the Cu bulk and in grain boundaries. Significant discrepancies between the two methods were found in structures with a higher number of low-coordinated atoms, such as penta-vacancies and di-vacancy absortion by grain boundary. These results will be useful for modeling the mechanisms of diffusion of complex defect structures and provide further insights into the structural evolution of metal films under thermal and mechanical stress.

Atomic structure evolution and linear regression fitting models for pre-breakdown electric field strength of FCC, BCC and HCP metal nano-emitters under high electric field from PIC-ED–MD simulations

Multi-scale and multi-physics simulations are carried out for nano-emitters consisting of FCC (Al, Cu and Au), BCC (V, Mo and W) and HCP (Ti, Zn and Zr) metals, using hybrid electrodynamics coupled with molecular dynamics-particle in cell simulations (PIC-ED–MD). We show that the tilting of the nano-emitter at low temperature and small electric field (E-field) is mainly caused either by the movement of partial dislocations at the apex of the nanotip or by the elastic local distortions of atomic registries away from their ideal lattice sites (FCC/BCC/HCP). At high E-field, the intense resistive heating due to the strong electron emission leads to the direct melting of the apex of nano-emitters. For nano-emitters consisting of low melting point metals such as Al, Zn and Au, the thermal runaway is driven by the elongation, thinning and necking of the molten region. Meanwhile, the elongation, thinning and sharpening produce the nano-protrusion at the apex of metal nano-emitters, and the detachment of atoms or atomic clusters from the nano-protrusion mainly contributes to the thermal runaway event for refractor metals such as Ti, Zr, Mo and W. The critical E-field strength of metal nano-emitters is found to be strongly correlated with structural parameters (atomic coordination number of liquid and equilibrium lattice constant), thermodynamic quantities (cohesive energy and enthalpy of evaporation) and phase transition temperatures (melting point and boiling point). These correlations enable us to establish either single-variable linear fitting models or multi-variable linear regression models to predict the critical E-field value for metal nano-emitters with good credibility.

Diffusion growth mechanism of penta-twinned Ag nanocrystals from decahedral seeds.

Crystals with penta-twinned structures can be produced from diverse fcc metals, but the mechanisms that control the final product shapes are still not well understood. By using the theory of absorbing Markov chains to account for the growth of penta-twinned decahedral seeds via atom deposition and surface diffusion, we predicted the formation of various types of products: decahedra, nanorods, and nanowires. We showed that the type of product depends on the morphology of the seed and that small differences between various seed morphologies can lead to significantly different products. For the case of uncapped decahedra seeds, we compared predictions from our model to nanowire morphologies obtained in two different experiments and obtained favorable agreement. Possible extensions of our model are indicated.

Atomistic-informed kinetic phase-field modeling of non-equilibrium crystal growth during rapid solidification

A novel method based on molecular dynamics (MD) is developed to make the kinetic phase-field (PF) model quantitative in predicting non-equilibrium crystal growth during rapid solidification. MD-calculated variations of the diffuse solid-liquid (SL) interface width versus interface velocity are used to parameterize the kinetic PF model. Two approaches are adopted to study temperature independent and temperature dependent interfacial properties on the accuracy of predictions. MD simulations of slow and rapid solidification regimes for an fcc metal (Ni) show that the SL interface width decreases by increasing the solidification velocity. Fitting the dynamic response of the interface width to the traveling wave solution of hyperbolic PF equation determines the target SL interfacial properties, namely propagation velocity and diffusion coefficient. Independently, the MD calculations of nonlinearity in velocity versus undercooling is used to validate the atomistic-informed kinetic PF model. Both parabolic and kinetic PF models parameterized by temperature-independent material properties can accurately simulate the linear portion of near-equilibrium crystal growth during solidification. However, they both fail to predict the crystal growth kinetics during rapid solidification. The kinetic PF model parameterized with the temperature-dependent SL interfacial properties can accurately predict both the equilibrium and non-equilibrium crystal growth during slow and rapid solidification. MD simulation results on Ni along with some analytical analysis on the variation of interface width versus interface velocity show that for fcc metals, in general, {110} interface has a smaller propagation velocity in comparison to {100} interface, resulting in a larger non-linear behavior at smaller undercooling.

On wear mechanisms and microstructural changes in nano-scratches of fcc metals

Sliding and scratching are fundamental tribological phenomena which affect the surface and surface-near zones of materials. To clarify ongoing tribological and microstructural mechanisms, a thorough analysis of three fcc materials (aluminium, austenitic steel and copper) was performed via nano-sliding and scratching at different load levels. Nanoindentation was used to evaluate the phases’ mechanical properties, namely hardness H, Young’s modulus E and the ratios H/E (yield strain) and H³/E2 (resistance against plastic indentation), which proved to be good measures to understand the abrasive wear behaviour. Electron backscatter diffraction (EBSD) measurements and focused ion beam (FIB) cross-sections of the scratches provided deeper insight into the degree of deformation and deformation induced phase changes.Results show a distinct influence of the materials’ mechanical parameters and phase changes on the deformation and wear mechanisms, and the thereby entailed apparent coefficient of friction (FT/FN). The mechanical properties were a key factor for a change in wear mechanism from sliding to ploughing to chipping. The thresholds were investigated for the three materials and increase from Aluminium to Copper to Austenite with H³/E2 being a good descriptor of the necessary contact pressures entailing changes of the wear mechanism.

Similarities and trends in adsorbate induced reconstruction – Structure and stability of FCC iron and cobalt surface carbides

Thin FCC (100) iron and cobalt carbide films were prepared on Cu(100) to study the connection between their structure, electronic properties and stability. We present the first detailed, real space experimental confirmation of the C-induced clock reconstruction on the FCC(100) surfaces of iron and cobalt. Both Fe and Co surface carbides show p4g (2 × 2) surface reconstruction with tetracoordinated square planar carbon and pure FCC (100) metal layers underneath. Combining tip-sample distance dependent STM imaging with theoretical calculations we present different imaging modes of Fe2C. Using a combination of angle-resolved x-ray photoelectron spectroscopy (AR-XPS), Auger electron spectroscopy (AES), low energy electron diffraction (LEED), scanning tunneling microscopy (STM), and theoretical calculations we provide detailed electronic and structural models for Fe2C and Co2C p4g (2 × 2) surface carbides and other 2D Fe2X interstitial compound systems. In various Fe2X (X = B, C, N, O) surface compounds moving to the right in the periodic table with increasing electrons the reconstruction becomes less favorable, while iron carbide shows the highest stability.

Universal preference for low-energy core-shifted grain boundaries at the surfaces of fcc metals

Grain boundaries (GBs) with $[111]$ tilt axes are common in polycrystalline face-centered cubic (fcc) metals. For copper (111) films, emergent GBs close to the surface have tilt axes that are shifted away from $[111]$ that are lower in energy than the corresponding truncated bulk boundaries. Geometrical analysis and atomic calculations were used to study the driving force for this same relaxation phenomenon in representative fcc elemental metals. We show that the reduction in boundary energy scales with the elimination of energetically costly boundary core facets. We find that, for a wide range of misorientation angles, low-energy core-shifted boundaries are also favored in Al, Ni, Au, and Pt and discuss the significance for electromigration and other metal properties.

Short-range ordering plays a determining role in the low-cycle fatigue life improvement of fcc metals: A conclusive study on low solid-solution hardening Ni-Cr alloys

The effect of short-range ordering (SRO) on the low-cycle fatigue (LCF) behavior of low solid-solution hardening Ni-Cr alloys with high stacking fault energies (SFEs) was systematically studied under cycling at constant total strain amplitude (Δεt/2) in the range of 0.1%–0.7%. The results show that an inducement of SRO structures can notably improve the fatigue life of the alloy regardless of Δεt/2, and several unique fatigue characteristics have been detected, including the transition of fatigue cracking mode from intergranular cracking to slip band cracking, the non-negligible evolution from non-Masing behavior in pure Ni to Masing behavior in the Ni-40Cr alloy, and the secondary cyclic hardening behavior in the Ni-10Cr and Ni-20Cr alloys. All these experimental phenomena are tightly associated with the transformation in cyclic deformation mechanisms that is induced by SRO based on the “glide plane softening” effect. Furthermore, a comprehensive fatigue life prediction model based on total hysteresis energy has been reasonably proposed, focusing on the analyses of the macroscopic model parameters (namely the fatigue cracking resistance exponent β and the crack propagation resistance parameter W0) and microscopic damage mechanisms. In brief, on the premise that the effects of SFE and friction stress can be nearly ignored, as in the case of the present low solid-solution hardening Ni-Cr alloys with high SFEs, an enhancement of SRO in face-centered cubic metals has been convincingly confirmed to be an effective strategy to improve their LCF performance.

Modeling laser interactions with aluminum and tantalum targets using a hybrid atomistic-continuum model

A hybrid atomistic-continuum method can model the microstructure evolution of metals subjected to laser irradiation. This method combines classical molecular dynamics (MD) simulations with the two-temperature model (TTM) to account for the laser energy absorption and heat diffusion behavior. Accurate prediction of the temperature evolution in the combined MD-TTM method requires reliable accuracy in electron heat capacity, electron thermal conductivity, and electron–phonon coupling factor across the temperatures generated. This study uses the electronic density of states (DOS) obtained from first-principle calculations. The calculated electron temperature-dependent parameters are used in MD-TTM simulations to study the laser metal interactions in FCC and BCC metals and the phenomenon of laser shock loading and melting. This study uses FCC Al and BCC Ta as model systems to demonstrate this capability. When subjected to short pulsed laser shocks, the dynamic failure behavior predicted using temperature-dependent parameters is compared with the experimentally reported single-crystal and nanocrystalline Al and Ta systems. The MD-TTM simulations also investigate laser ablation and melting behavior of Ta to compare with the ablation threshold reported experimentally. This manuscript demonstrates that integrating the temperature-dependent parameters into MD-TTM simulations leads to the accurate modeling of the laser–metal interaction and allows the prediction of the kinetics of the solid–liquid interface.

A New Anti-Alias Model of Ab Initio Calculations of the Generalized Stacking Fault Energy in Face-Centered Cubic Crystals

The anti-alias model is an effective method to calculate the generalized stacking fault energy of the hexagonal close-packed crystals, but it has not been applied to the face-centered cubic crystals due to two different stacking faults occurring in the supercell during the sliding process. Based on the symmetry of these two stacking faults and the existing single analytic formula of the generalized stacking fault energy, we successfully extend the anti-alias model to compute the generalized stacking fault energy of face-centered cubic crystals, and the common fcc metals Al, Ni, Ag and Cu are taken as specific examples to illustrate the computational details. Finally, the validity of the proposed model is verified by data comparison and analysis. It is suggested that the anti-alias model is a good choice for the researchers to obtain more accurate generalized stacking fault energy of face-centered cubic metals.

Assimilated model of work-hardening in FCC metals and its application to devolution of stored work

Assimilated model of work-hardening in FCC metals and its application to devolution of stored work

Formation mechanism of hierarchical twins in the CoCrNi medium entropy alloy

• The competitive mechanisms between primary/conjugate slips and twins are clarified. • The particularity of mechanism of hierarchical twins in CoCrNi MEA is unraveled. • The hierarchical twinning behavior depending on strain rate and deformation temperature is revealed. • The twinning map help predict the formation of hierarchical twins as a reference for experiments. The three-dimensional hierarchical twin network has been proved to be the source of the excellent strength-ductility combination in the CoCrNi medium entropy alloy. Revealing the formation mechanism of hierarchical twins, however, remains a challenge using either the post-mortem or the in-situ microstructural characterization. In this study, the atomistic formation mechanism of hierarchical twins was investigated using molecular dynamics simulations, with special focus on the effects of strain rate and deformation temperature. Compared to the primary twin boundaries kink-driven hierarchical twinning tendency in pure FCC metals, the chemical inhomogeneity in CoCrNi can reduce the necessary kink height to trigger conjugate twins (CTWs), fascinating the formation of twin networks. At room temperature, the plastic deformation is dominated by primary twins (PTWs) and conjugate slips at a relatively lower strain rate (e.g., 5×10 7 s −1 ). The hierarchical twins can be activated in cases of deforming at a higher strain rate (e.g., 2×10 8 s −1 ). Further increasing the strain rate (e.g., 1×10 10 s −1 ) leads to the phase-transformation induced plasticity. At cryogenic temperatures, the hierarchical twins are promoted within a large range of strain rates (e.g., 5×10 7 -1×10 10 s −1 ). A higher temperature leads to the synergy of CTWs and primary slips at a lower strain rate, but hierarchical twins at a higher strain rate. On this basis, a qualitative comparison and scalable trends between experiments and simulations were revealed. The present study would not only provide the basic understanding for the twinning behavior found experimentally, but also contribute to the design of medium/high entropy alloys with excellent mechanical performances by tuning microstructures.

Material removal behaviors of FCC metals in nanoscale and microscale scratching: Theoretical model and experiments

Material removal behaviors of FCC metals in nanoscale and microscale scratching: Theoretical model and experiments

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.

Universality of grain boundary phases in fcc metals: Case study on high-angle [111] symmetric tilt grain boundaries

Grain boundaries often exhibit ordered atomic structures. Increasing amounts of evidence have been provided by transmission electron microscopy and atomistic computer simulations that different stable and metastable grain boundary structures can occur. Meanwhile, theories to treat them thermodynamically as grain boundary phases have been developed. Whereas atomic structures were identified at particular grain boundaries for particular materials, it remains an open question if these structures and their thermodynamic excess properties are material specific or generalizable to, e.g., all fcc metals. In order to elucidate that question, we use atomistic simulations with classical interatomic potentials to investigate a range of high-angle [111] symmetric tilt grain boundaries in Ni, Cu, Pd, Ag, Au, Al, and Pb. We could indeed find two families of grain boundary phases in all of the investigated grain boundaries, which cover most of the standard fcc materials. Where possible, we compared the atomic structures to atomic-resolution electron microscopy images and found that the structures match. This poses the question if the grain boundary phases are simply the result of sphere-packing geometry or if material-specific bonding physics play a role. We tested this using simple model pair potentials and found that medium-ranged interactions are required to reproduce the atomic structures, while the more realistic material models mostly affect the grain boundary (free) energy. In addition to the structural investigation, we also report the thermodynamic excess properties of the grain boundaries, explore how they influence the thermodynamic stability of the grain boundary phases, and detail the commonalities and differences between the materials.

Effects of twin orientation and twin boundary spacing on the plastic deformation behaviors in Ni nanowires

• Effects of twin orientation (θ) on the Ni nanowire (NW) ductility are investigated • NW ductility with θ ∼55° increases with decreasing twin boundary (TB) spacing • In-situ TEM reveals distinct deformation behaviors in NWs with different θ • Atomistic observation reveals different roles of TB can play during deformation • The different ductility can be related with microscopic deformation mechanisms Spreading twins throughout nano metals has been proved to effectively mediate the mechanical behaviors in face-centered-cubic (fcc) metals. However, the experimental investigation concerning the roles of twin boundary (TB) during deformation is rarely reported. Here, with the joint efforts of in-situ nanomechanical testing and theoretical studies, we provide a systematic investigation regarding the effects of TB orientation ( θ , the angle between tensile loading direction and the normal of TB) and spacing on deformation mechanisms in Ni nanowires (NWs). As compared with single-crystalline counterparts, it is found that nano-twinned (nt) NWs with θ ∼0° exhibit limited ductility, whereas TB can serve as an effective blockage to the dislocation propagation. In contrast, in nt NWs with θ ∼20° and 55°, TB migration/detwinning induced by TB-dislocation reaction or partial dislocation movement dominates the plasticity, which contributes to enhanced NW ductility. Regarding nt NWs with θ ∼90°, dislocations are found to be able to transmit through the TBs, suggesting the limited effect of TB on the NW stretchability. Furthermore, decreasing TB spacing ( λ ) can facilitate the detwinning process and thus greatly enhance the ductility of NW with θ ∼55°. This study uncovers the distinct roles that TB can play during mechanical deformations in fcc NWs and provides an atomistic view into the direct linkage between macroscopic mechanical properties and microscopic deformation modes.

Nano Mechanical Characterization and Physical Modeling of Plastic Deformation Chapter 2: Strengthening Mechanisms by Various Lattice Defects

Mechanical behaviors of metallic materials in a small scale are characterized and physically modeled based on experimental measurements and computational simulation. An effect of in-solution carbon or silicon in Fe on a plasticity initiation was characterizes by nanoindentation pop-in phenomenon. A coherency at a ferrite-cementite interface significantly affects to a plasticity initiation leading to a different macroscopic yielding behavior. A stability of an austenite phase in TRIP steel was evaluated though the analysis of indentation-induced deformation behavior, demonstrating a significant constraint effect on stabilization by an adjacent harder phase. Heterogeneous microstructures with a bimodal grain size in fcc metals show an inhomogeneous mechanical behavior depending on a location of the fine microstructure. An intermittent plasticity in pure iron was analyzed through a statistical model showing a Gaussian function by thermally activated process in the early stage and a power-law one by an avalanche type phenomenon in the subsequent stage. An elementally step in a plastic deformation in a metallic glass was characterized through Molecular Dynamics simulation indicating that the plasticity inhomogeneity depends remarkably on the initially inhomogeneous atomistic structure.

Predicting adsorption energies and the physical properties of H, N, and O adsorbed on transition metal surfaces: A machine learning study

We present a machine learning study utilizing the Hierarchically Interacting Particle Neural Network to predict the adsorption properties of atomic H, N, and O on various single metal and bimetallic single crystal FCC surfaces. Our trained HIP-NN models directly predict, from atomic species and coordinates of the clean surface, and initial adsorption site, adsorption energies with a MAE of 0.08 eV to 0.16 eV, adsorption heights with a MAE of 0.08 Å to 0.09 Å, and a buckling of the first layer of the substrate with a MAE of 0.07 Å to 0.12 Å, illustrating that a neural network can calculate the physical properties of a surface/adsorbate system along with adsorption energy. Our MAEs for adsorption energy also compare favorably with MAEs presented by other works predicting the adsorption energies of H, N, and O. We also demonstrate that while HIP-NN can predict on these systems without explicit periodic boundary conditions, the inclusion of explicit periodic boundary conditions drastically improves the results. Our results also reveal that the buckling of the first layer of the substrate can be utilized to prune datasets, removing unstable surfaces.

Unified crystal plasticity model for fcc metals: From quasistatic to shock loading

Mechanical response of metals is strongly dependent on the strain rate and exhibits drastic change as the strain rate varies across >10 orders of magnitude from quasistatic to shock loading. In this paper, we developed a unified crystal plasticity model for face-centered cubic (fcc) metals to describe the mechanical response in a wide range of strain rate from ${10}^{\ensuremath{-}5}$ to ${10}^{7}/\mathrm{s}$. The plasticity framework adopts the dislocation-based Orowan equation. Specifically, the mobility law for dislocation velocity incorporates both the thermal activation mechanism dominating at low strain rates and drag mechanism dominating at high strain rates, through a repeating waiting-running model. The rate dependence of total dislocation density (${\ensuremath{\rho}}_{t}$) evolution in the Orowan equation (implicitly) is captured by coupling the rate-dependent annihilation and the stress-dependent nucleation. More importantly, to capture the huge variation in mobile/total dislocation ratio ($f={\ensuremath{\rho}}_{m}/{\ensuremath{\rho}}_{t}$) at different strain rates, we propose a physics-based law for mobile dislocation fraction $f$ based on the exponential distribution of dislocation link lengths through a critical link length determined by the local stress. In addition, a thermohyperelastic model is supplemented to account for the nonlinear elastic behavior and thermoelastic coupling at shock loading. This unified model is validated against the mechanical response of single-crystal aluminum from quasistatic $(10{}^{\ensuremath{-}}5/\mathrm{s})$ to shock loading (${10}^{7}/\mathrm{s}$), where the features of thermal softening in static loading, thermal hardening in shock loading, and the strain-rate hardening in the medium strain-rate range are all quantitatively evaluated by a single set of parameters with a high average ${R}^{2}$ value of 0.93.