Understanding Homogeneous Nucleation in Solidification of Aluminum by Molecular Dynamics Simulations

Homogeneous nucleation from aluminum (Al) melt was investigated by million-atom molecular dynamics (MD) simulations utilizing the second nearest neighbor modified embedded atom method (MEAM) potentials. The natural spontaneous homogenous nucleation from the Al melt was produced without any influence of pressure, free surface effects and impurities. Initially isothermal crystal nucleation from undercooled melt was studied at different constant temperatures, and later superheated Al melt was quenched with different cooling rates. The crystal structure of nuclei, critical nucleus size, critical temperature for homogenous nucleation, induction time, and nucleation rate were determined. The quenching simulations clearly revealed three temperature regimes: sub-critical nucleation, super-critical nucleation, and solid-state grain growth regimes. The main crystalline phase was identified as face-centered cubic (fcc), but a hexagonal close-packed (hcp) and an amorphous solid phase were also detected. The hcp phase was created due to the formation of stacking faults during solidification of Al melt. By slowing down the cooling rate, the volume fraction of hcp and amorphous phases decreased. After the box was completely solid, grain growth was simulated and the grain growth exponent was determined for different annealing temperatures.Comment: 41 page

Nanoscale solidification of metals by atomistic simulations: From nucleation to nanostructural evolution

Homogeneous nucleation during solidification in Al (fcc), Fe (bcc) and Mg (hcp) is studied by million-atom molecular dynamics (MD) utilizing the second nearest neighbor modified embedded atom method (2NN-MEAM) potentials. Spontaneous homogenous nucleation from the melt was produced without any influence of pressure, free surface effects and impurities. We also study the effect on the simulation size on homogenous nucleation and the heterogeneity in homogenous nucleation. The heterogeneity in homogenous nucleation originates from the twins, grain boundaries and short range order in the liquid during the initial stages of solidification. To study the solid-liquid coexistence in binary Al alloys, interatomic potentials for binary Al-Cu, Al-Fe, Al-Ni, Al-Mg, Al-Si and Al-Ge alloys were developed based on 2NN-MEAM formalism. Using these interatomic potentials, we compare formation energies, elastic constants, lattice parameters, enthalpy of solid and liquid mixing with experimental or first principle data of the binary Al alloys. In addition, we also compare the liquidus temperature of the Al-alloys from the phase diagram to the MD simulation. Finally, directional solidification of Al-11 at. % Cu is shown utilizing the 2NN-MEAM interatomic potential. The condition for directional solidification is produced by imposing dissimilar temperatures at the model boundaries along the [100] solidification direction to create a temperature gradient. Both the microstructural properties of solidified alloys and the mechanical properties under uniaxial tension is investigated”--Abstract, page iv

Probing the chirality-dependent elastic properties and crack propagation behavior of single and bilayer stanene

Stanene, a quasi-two-dimensional honeycomb-like structure of tin belonging to the family of 2D-Xenes (X = Si, Ge, Sn) has recently been reported to show promising electronic, optical and mechanical properties. This paper investigates the elastic moduli and crack propagation behaviour of single layer and bilayer stanene based on molecular dynamics simulations, which have been performed using the Tersoff bond order potential (BOP). We have parameterized the interlayer van der Waals interactions for the bilayer Lennard-Jones potential in the case of bilayer stanene. Density functional calculations are performed to fit the Lennard-Jones parameters for the properties which are not available from the scientific literature. The effect of temperature and strain rate on the mechanical properties of stanene is investigated for both single layer and bilayer stanene in the armchair and zigzag directions. The results reveal that both the fracture strength and strain of stanene decrease with increasing temperature, while at higher loading rate, the material is found to exhibit higher fracture strength and strain. The effect of chirality on the elastic moduli of stanene is explained on the basis of a physics-based analytical approach, wherein the fundamental interaction between the shear modulus and Young's modulus is elucidated. To provide a realistic perspective, we have investigated the compound effect of uncertainty on the elastic moduli of stanene based on an efficient analytical approach. Large-scale Monte Carlo simulations are carried out considering different degrees of stochasticity. The in-depth results on mechanical properties presented in this article will further aid the adoption of stanene as a potential nano-electro-optical substitute with exciting features such as 2D topological insulating properties with a large bandgap, the capability to support enhanced thermoelectric performance, topological superconductivity and a quantum anomalous Hall effect at near-room-temperature

Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk

In this paper, we examine an optimal dynamic decision-making problem for a retailer’s inventory system of deteriorating items under two-level trade credit financing where the supplier, as well as the retailer, offers trade credit to the subsequent downstream member, the demand rate of which varies simultaneously with time and the length of credit period that is offered to the customers. The deterioration rate is non-decreasing over time. In addition, the risk of default increases with the credit period length. A generalized model is presented to determine the optimal trade credit and replenishment strategies that maximize the retailer’s annual total profit. We then demonstrate that the retailer’s optimal credit period and replenishment cycle time not only exist but also are unique. Thus, the search of the global optimal solution reduces to finding a local solution. Finally, we run several numerical examples to illustrate the problem and gain managerial insights

Probing the chirality-dependent elastic properties and crack propagation behavior of single and bilayer stanene

Stanene, a quasi-two-dimensional honeycomb-like structure of tin belonging to the family of 2D-Xenes (X = Si, Ge, Sn) has recently been reported to show promising electronic, optical and mechanical properties. This paper investigates the elastic moduli and crack propagation behaviour of single layer and bilayer stanene based on molecular dynamics simulations, which have been performed using the Tersoff bond order potential (BOP). We have parameterized the interlayer van der Waals interactions for the bilayer Lennard-Jones potential in the case of bilayer stanene. Density functional calculations are performed to fit the Lennard-Jones parameters for the properties which are not available from the scientific literature. The effect of temperature and strain rate on the mechanical properties of stanene is investigated for both single layer and bilayer stanene in the armchair and zigzag directions. The results reveal that both the fracture strength and strain of stanene decrease with increasing temperature, while at higher loading rate, the material is found to exhibit higher fracture strength and strain. The effect of chirality on the elastic moduli of stanene is explained on the basis of a physics-based analytical approach, wherein the fundamental interaction between the shear modulus and Young's modulus is elucidated. To provide a realistic perspective, we have investigated the compound effect of uncertainty on the elastic moduli of stanene based on an efficient analytical approach. Large-scale Monte Carlo simulations are carried out considering different degrees of stochasticity. The in-depth results on mechanical properties presented in this article will further aid the adoption of stanene as a potential nano-electro-optical substitute with exciting features such as 2D topological insulating properties with a large bandgap, the capability to support enhanced thermoelectric performance, topological superconductivity and a quantum anomalous Hall effect at near-room-temperature.</p

A polynomial chaos expansion based molecular dynamics study for probabilistic strength analysis of nano-twinned copper

Nano-twinned structures are mechanically stronger, ductile and stable than its non-twinned form. We have investigated the effect of varying twin spacing and twin boundary width (TBW) on the yield strength of the nano-twinned copper in a probabilistic framework. An efficient surrogate modelling approach based on polynomial chaos expansion has been proposed for the analysis. Effectively utilising 15 sets of expensive molecular dynamics simulations, thousands of outputs have been obtained corresponding to different sets of twin spacing and twin width using virtual experiments based on the surrogates. One of the major outcomes of this work is that there exists an optimal combination of twin boundary spacing and twin width until which the strength can be increased and after that critical point the nanowires weaken. This study also reveals that the yield strength of nano-twinned copper is more sensitive to TBW than twin spacing. Such robust inferences have been possible to be drawn only because of applying the surrogate modelling approach, which makes it feasible to obtain results corresponding to 40 000 combinations of different twin boundary spacing and twin width in a computationally efficient framework

Manipulation of mechanical properties of monolayer molybdenum disulfide: Kirigami and hetero-structure based approach

The two-dimensional monolayer structure of molybdenum disulfide (MoS2) is widely used in the advanced flexible electronic devices due to their unique mechanical, physical, and electronic properties. The main disadvantage of MoS2 is the limited mechanical strain, which restricts its application in flexible and stretchable devices. Therefore, it is required to develop various methods to modify the mechanical behavior of MoS2 monolayer depending on the environmental situation and the complexity of real applications. In this investigation, we have incorporated Kirigami and hetero-structure approaches for the manipulation of the mechanical behavior of MoS2. Kirigami is an ancient Japanese art of paper cutting. Monolayer MoS2 with circular/square/rectangular Kirigami pattern have simulated under uniaxial tensile load using molecular dynamics simulation. We observe that the stretch-ability (mechanical strain) significantly enhanced by the shape/size and location of Kirigami pattern during uniaxial tensile deformation. However, strength (mechanical stress and Young's modulus) of MoS2 can be enhancing by creating a hetero-structure with graphene. A large number of simulations have been performed to explore stress/energy distribution, Young's modulus, the effect of temperature, and strain rate during load applications. We believe that our results will provide extensive information related to enhancement in the mechanical strain and strain toward the application in flexible devices

Modified embedded-atom method interatomic potentials for Al-Cu, Al-Fe and Al-Ni binary alloys: from room temperature to melting point

Second nearest neighbor modified embedded-atom method (2NN-MEAM) interatomic potentials are developed for binary aluminum (Al) alloys applicable from room temperature to the melting point. The binary alloys studied in this work are Al-Cu, Al-Fe and Al-Ni. Sensitivity and uncertainty analyses are performed on potential parameters based on the perturbation approach. The outcome of the sensitivity analysis shows that some of the MEAM parameters interdependently influence all MEAM model outputs, allowing for the definition of an ordered calibration procedure to target specific MEAM outputs. Using these 2NN-MEAM interatomic potentials, molecular dynamics (MD) simulations are performed to calculate low and high-temperature properties, such as the formation energies of stable phases and unstable intermetallics, lattice parameters, elastic constants, thermal expansion coefficients, enthalpy of formation of solids, liquid mixing enthalpy, and liquidus temperatures at a wide range of compositions. The computed data are compared with the available first principle calculations and experimental data, showing high accuracy of the 2NN-MEAM interatomic potentials. In addition, the liquidus temperature of the Al binary alloys is compared to the phase diagrams determined by the CALPHAD method.</p

Liquid ordering induced heterogeneities in homogeneous nucleation during solidification of pure metals

Homogeneous crystal nucleation is prone to formation of defects and often experiences heterogeneities, the inferences of which are crucial in processing crystalline materials and controlling their physical properties. It has been debated in literature whether the associated heterogeneities are an integral part of the homogenous nucleation. In this study by integrating a probabilistic approach with large-scale molecular dynamics simulations based on the most advanced high-temperature interatomic potentials, we attempt to address the ambiguity over the sources and mechanisms of heterogeneities in homogenous nucleation during solidification of pure melts. Different classes of structured metals are investigated for this purpose, including face-centered cubic aluminum, body-centered cubic iron, and hexagonal close-packed magnesium. The results reveal, regardless of the element type or the solidified crystal structure, that the densification process of liquid metals is accompanied by short-range orderings of atoms prior to the formation of crystals, controlling the heterogeneities during homogenous nucleation.</p