Orientation-Dependent Mechanical Behaviors of BCC-Fe in Light of the Thermo-Kinetic Synergy of Plastic Deformation.

The orientation-dependent mechanical behaviors of metallic alloys are governed by deformation mechanisms, but the underlying physics remain to be explored. In this work, the mechanical responses along different orientations and behind the mechanisms of BCC-Fe are investigated by performing molecular dynamic simulations. It is found that the mechanical properties of BCC-Fe exhibit apparent anisotropic characteristics. The <100>-oriented BCC-Fe presents a Young's modulus of E = 147.56 GPa, a strength of σy = 10.15 GPa, and a plastic strain of εy = 0.084 at the yield point, whereas the <111> orientation presents E = 244.84 GPa, σy = 27.57 GPa, and εy = 0.21. Based on classical dislocation theory, the reasons for such orientation-dependent mechanical behaviors are analyzed from the perspective of thermo-kinetic synergy upon deformation. It turns out that the anisotropic mechanical responses of BCC-Fe are associated with the magnitude of the thermodynamic driving force (ΔG) and kinetic energy barrier (Q) for dislocation motion, which dominate the corresponding deformation mechanism. Compared with the low ΔG (6.395 GPa) and high Q (11.95 KJ/mol) of the <100>-oriented BCC-Fe dominated by deformation twinning, the <111> orientation governed by dislocation slip presents a high ΔG (17.37 GPa) and low Q (6.45 KJ/mol). Accordingly, the orientation-dependent deformation behaviors of BCC-Fe are derived from the thermo-kinetic synergy for dislocation motion.

Effect of Forced Convection on Magnesium Dendrite: Comparison between Constant and Altering Flow Fields.

Convection has a nonnegligible effect on the growth of the magnesium dendrite with six-primary-branch pattern. Most work, however, investigates the effect of the convection by simplifying the melt flow as a constant horizontal flow. In this work, four convection behaviors, including equally distributed convection, linearly distributed convection, sinusoidal-wave convection, and square-wave convection, are imposed and simulated through the phase-field lattice-Boltzmann schemes. The effects of constant (the former two) and altering (the latter two) flow fields are quantified by the length ratio of the upstream primary arm to the downstream one. The results show that the dendrite asymmetry increases under the constant forced convections but presents nonmonotonic change under the altering convections. A simple mathematical relation is fitted to summarize the dependence of the dendrite asymmetry on the input velocity, the undercooling, and the flow frequency. Deep understanding of the convection effects can guide the prediction and control of the magnesium dendrite under more complex situations.

General hierarchical structure to solve transport phenomena with dissimilar time scales: Application in large-scale three-dimensional thermosolutal phase-field problems.

A general hierarchical structure is developed for phase-field lattice-Boltzmann simulations with dissimilar time scales. The number of the grid levels can be artificially selected in a reasonable range, which can enhance the time marching step by two to three orders of magnitude in comparison with explicit methods. Constructed on a massively parallel platform, the mesh distribution is dynamically adjusted according to a gradient criterion. The developed high performance computing scheme is applied to simulate the coupled thermosolutal dendrite evolution. Numerical tests indicate that the computing efficiency can be further improved by two to three orders of magnitude, which makes numerical simulation of fully coupled thermosolutal dendrite growth viable for alloys with Lewis number ∼10^{4}. The domain size which equivalently consists of billions of uniform meshes is handled to simulate multidendrite evolution. Results show that the domain temperature becomes extremely uneven due to the release of latent heat, which causes a significant difference from isothermal solidification. A simple analytical model is proposed to predict the relation between growth velocity and Lewis number, and the growth morphologies of both equiaxed and directional multiple dendrites are discussed. The combination of the hierarchical mesh structure and the phase-field lattice-Boltzmann method provides an efficiency-driven approach to solve the coupled thermosolutal microstructure evolution.

Regulating lamellar eutectic trajectory through external perturbations.

The present understanding of asymmetric lamellar eutectics focuses on pure diffusive transport, and how the external perturbations cause asymmetric pattern transitions remains unclear. In this work, the effect of external perturbations is discussed in terms of both thermal and convective effects via phase-field modeling. The presence of thermal perturbation distorts eutectic lamellae, while the convective perturbation causes a tilt band. Both can adjust the eutectic trajectory to accommodate newly established thermodynamics by reconstructing the transport equilibrium. Furthermore, how to regulate the eutectic growth (eutectic colony, zigzag, and snakelike patterns) by altering external perturbations is investigated, which provides information on how to control eutectic evolution.

Conservative phase-field method with a parallel and adaptive-mesh-refinement technique for interface tracking.

Based on Fick's second law and Cahn-Hilliard theory, a conservative phase-field model is developed to track interface. The phase-field variable changes in a hyperbolic tangent behavior across the diffuse interface over which the interface curvature can be easily calculated. Different from the frequently used lattice-Boltzmann-based discrete method, the phase-field equation is discretized using a fourth-order Runge-Kutta method. Accordingly, the present numerical scheme alleviates the programming burden, reduces the memory usage, but maintains a high numerical accuracy. To achieve large-scale interface tracking, a parallel and adaptive-mesh-refinement algorithm is developed to reduce the computing overhead. Various cases of the interface evolutions under steady flow fields indicate that the proposed numerical scheme can capture the interface with high accuracy. Furthermore, the robustness of the numerical scheme is validated by simulating the Rayleigh-Taylor instability, and good agreement with previous work is achieved.

Correlation between crystallographic anisotropy and dendritic orientation selection of binary magnesium alloys.

Both synchrotron X-ray tomography and EBSD characterization revealed that the preferred growth directions of magnesium alloy dendrite change as the type and amount of solute elements. Such growth behavior was further investigated by evaluating the orientation-dependent surface energy and the subsequent crystallographic anisotropy via ab-initio calculations based on density functional theory and hcp lattice structure. It was found that for most binary magnesium alloys, the preferred growth direction of the α-Mg dendrite in the basal plane is always [Formula: see text], and independent on either the type or concentration of the additional elements. In non-basal planes, however, the preferred growth direction is highly dependent on the solute concentration. In particular, for Mg-Al alloys, this direction changes from [Formula: see text] to [Formula: see text] as the Al-concentration increased, and for Mg-Zn alloys, this direction changes from [Formula: see text] to [Formula: see text] or [Formula: see text] as the Zn-content varied. Our results provide a better understanding on the dendritic orientation selection and morphology transition of magnesium alloys at the atomic level.

Atomistic Determination of Anisotropic Surface Energy-Associated Growth Patterns of Magnesium Alloy Dendrites.

Because of the existence of anisotropic surface energy with respect to the hexagonal close-packed (hcp) lattice structure, magnesium alloy dendrite prefers to grow along certain crystallographic directions and exhibits a complex growth pattern. To disclose the underlying mechanism behind the three-dimensional (3-D) growth pattern of magnesium alloy dendrite, an anisotropy function was developed in light of the spherical harmonics and experimental findings. Relevant atomistic simulations based on density functional theory were then performed to determine the anisotropic surface energy along different crystallographic directions, and the corresponding anisotropic strength was quantified via the least-square regression. Results of phase field simulations showed that the proposed anisotropy function could satisfactorily describe the 3-D growth pattern of the α-Mg dendrite observed in the experiments. Our investigations shed great insight into understanding the pattern formation of the hcp magnesium alloy dendrite at an atomic level.

Hidden electronic rule in the "cluster-plus-glue-atom" model.

Electrons and their interactions are intrinsic factors to affect the structure and properties of materials. Based on the "cluster-cluster-plus-glue-atom" model, an electron counting rule for complex metallic alloys (CMAs) has been revealed in this work (i. e. the CPGAMEC rule). Our results on the cluster structure and electron concentration of CMAs with apparent cluster features, indicate that the valence electrons' number per unit cluster formula for these CMAs are specific constants of eight-multiples and twelve-multiples. It is thus termed as specific electrons cluster formula. This CPGAMEC rule has been demonstrated as a useful guidance to direct the design of CMAs with desired properties, while its practical applications and underlying mechanism have been illustrated on the basis of CMAs' cluster structural features. Our investigation provides an aggregate picture with intriguing electronic rule and atomic structural features of CMAs.

Electrochemical Potential Derived from Atomic Cluster Structures.

Based on the atomic cluster structures and free electron approximation model, it is revealed that the electrochemical potential (ECP) for the system of interest is proportional to the reciprocal of atomic cluster radius squared, i.e., φ = k·(1/r(2)). Applied to elemental crystals, the correlation between atomic cluster radii and the ECP that we have predicted agrees well with the previously reported results. In addition, some other physicochemical properties associated with the ECP have also been found relevant to the atomic cluster radii of materials. Thus, the atomic cluster radii can be perceived as an effective characteristic parameter to measure the ECP and related properties of materials. Our results provide a better understanding of ECP directly from the atomic structures perspective.

Phase stability limit of c-BN under hydrostatic and non-hydrostatic pressure conditions.

Phase stability limit of cubic boron nitride (c-BN) has been investigated by the crystal structure search technique. It indicated that this limit is ∼1000 GPa at hydrostatic pressure condition. Above this pressure, c-BN turns into a metastable phase with respect to rocksalt type boron nitride (rs-BN). However, rs-BN cannot be retained at 0 GPa owing to its instability at pressure below 250 GPa. For non-hydrostatic pressure conditions, the phase stability limit of c-BN is substantially lower than that under hydrostatic pressure conditions and it is also dramatically different for other pressure mode.