Energy Minimization Theory Research Articles

High-speed videomicroscopy of sheared carbonyl iron suspensions

The postyield rheological regime is investigated in sheared magnetic field-responsive composites (i.e. carbonyl iron based magnetorheological fluids). When subjected to uniaxial DC fields, high-speed videomicroscopy techniques and dedicated image analysis tools demonstrate that dispersed magnetic microparticles self-assemble to form concentric layered patterns above a particular shear rate (). This critical shear rate for layer formation is dictated by a critical Mason number 1 that is associated to the destruction of the last doublet in the chain-like aggregates. The number of layers, mean width, percentage of occupation and mean period are found to be very weakly dependent on the shear rate in start-up shearing flow tests. Experimental data for the mean period are in good agreement with an energy minimization theory.

On the impact of lattice parameter accuracy of atomistic simulations on the microstructure of Ni–Ti shape memory alloys

Ni–Ti is a key shape-memory alloy (SMA) system for applications, being cheap and having good mechanical properties. Recently, atomistic simulations of Ni–Ti SMAs have been used with the purpose of revealing the nano-scale mechanisms that control superelasticity and the shape-memory effect (SME), which is crucial to guide alloying or processing strategies to improve materials performance. These atomistic simulations are based on molecular dynamics (MD) modelling that relies on (empirical) interatomic potentials (IAPs). These simulations must reproduce accurately the mechanism of martensitic transformation and the microstructure that it originates, since this controls both superelasticity and the SME. As demonstrated by the energy minimization theory of martensitic transformations (Ball and James (1987 Arch. Ration. Mech. Anal. 100 13–52)), the microstructure of martensite depends on the lattice parameters of the austenite and the martensite phases. Here, we compute the bounds of possible microstructural variations based on the experimental variations/uncertainties in the lattice parameter measurements. We show that both density functional theory and MD lattice parameters are typically outside the experimental range, and that seemingly small deviations from this range induce large deviations from the experimental bounds of the microstructural predictions, with notable cases where unphysical microstructures are predicted to form. Therefore, our work points to a strategy for benchmarking and selecting IAPs for atomistic modelling of SMAs, which is crucial to modelling the development of martensitic microstructures and their impact on the SME.

Statistical energy minimization theory for systems of drop-carrier particles.

Drop-carrier particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution without using costly microfluidic equipment and techniques. DCPs are useful for automated and high-throughput biological assays and reactions, as well as single-cell analyses. Surface energy minimization provides a theoretical prediction for the volume distribution in pairwise droplet splitting, showing good agreement with macroscale experiments. We develop a probabilistic pairwise interaction model for a system of such DCPs exchanging fluid volume to minimize surface energy. This leads to a theory for the number of pairwise interactions of DCPs needed to reach a uniform volume distribution. Heterogeneous mixtures of DCPs with different sized particles require fewer interactions to reach a minimum energy distribution for the system. We optimize the DCP geometry for minimal required target solution and uniformity in droplet volume.

A Low-Cost Ni-Mn-Ti-B High-Temperature Shape Memory Alloy with Extraordinary Functional Properties.

The rapid development of aerospace, automotive, and energy exploration industries urgently requires high-temperature shape memory alloys (HTSMAs) which are utilized as compact solid-state actuators, sensors, and energy conversion devices at elevated temperatures. However, the currently prevailing Ni-Ti-X (X = Pd, Pt, and Hf) HTSMAs are very expensive owing to the high cost of Pd, Pt, and Hf elements, which greatly limits their widespread applications. Here, we have developed an inexpensive (Ni50Mn35.5Ti14.5)99.8B0.2 bulk polycrystalline HTSMA with extraordinary high-temperature superelasticity and a giant two-way shape memory effect (TWSME). This alloy exhibits perfect superelasticity with a fully recoverable strain of as high as 7.1% over a wide temperature range from 150 to 280 °C. Furthermore, it shows a giant TWSME with a remarkably high recoverable strain of 6.0%. Both the recoverable strain of superelasticity and the two-way shape memory strain of the present alloy are the highest among the bulk polycrystalline HTSMAs. The theoretical maximum transformation strain was calculated with energy-minimization theory using the crystal structure information of martensite and austenite obtained from in situ synchrotron high-energy X-ray diffraction experiments to help understand the superelastic behavior of the present alloy. Combining the advantages of low cost and easy fabrication, the present bulk polycrystalline (Ni50Mn35.5Ti14.5)99.8B0.2 alloy shows great potential for high-temperature shape memory applications. This work is instructive for developing cost-effective high-performance HTSMAs.

Comparative CFD modeling of a bubbling bed using a Eulerian–Eulerian two-fluid model (TFM) and a Eulerian-Lagrangian dense discrete phase model (DDPM)

Eulerian–Eulerian and Eulerian-Lagrangian numerical approaches are both widely used to investigate hydrodynamic behavior in dense gas-solid fluidized bed reactors, yet there has been a lack of comparative investigations involving the two. Therefore, the present work compares the numerical performance of a two-fluid model (TFM) and a dense discrete phase model (DDPM) in describing the hydrodynamic behavior of a pilot-scale bubbling bed reactor. The effects of several different parameters – drag force, grid size, fluid time-step, time-averaging interval, particle-wall specularity coefficient, particle-particle restitution coefficient, particle-wall reflection coefficient, and numbers of parcels (the latter two parameters only for the DDPM) – are investigated and compared for the two approaches using two-dimensional (2D) simulations. The numerical results for both models indicate that sub-grid drag correction based on the energy minimization and multiscale (EMMS) theory is the most essential modeling parameter to account for the multiscale structures (i.e., bubbles and void spaces) and to resolve the axial and radial solid distributions. Both the TFM and DDPM, coupled with the EMMS/bubbling drag, predict similar hydrodynamics behavior; however, the better accuracy in terms of axial and radial solids concentration profiles is achieved from the TFM approach. Further, our grid size analysis results indicate that the DDPM generates a better grid-independent solution than the TFM. This important advantage of the DDPM over TFM makes it a suitable candidate for large-scale industrial applications by employing it on much coarser grids. Meanwhile, the results from the time-step, time-averaging interval, specularity coefficient, restitution coefficient, reflection coefficient, and numbers of parcels represent a minor effect on the overall hydrodynamics behavior of the pilot-scale bubbling bed reactor.

Microstructural Characterization, Functional Behavior and Deformation Mechanism of Ni>sub>54Mn <sub>25</sub>Ga <sub>21-x</sub>Dy <sub>x</sub> High Temperature Shape Memory Alloys with Low Thermal Hysteresis

Potential applications at elevated temperatures require shape memory alloys (SMAs) to possess high transformation temperature, excellent shape recovery ability and thermal/functional stability. The present study investigated the influences of Dy addition on the microstructural characterization, functional behavior and possible deformation mechanisms in high temperature Ni54Mn25Ga21 SMAs. The results indicated that adequate Dy addition contributed to a desirable tradeoff among compressive strength, ductility and functional performance. Ni54Mn25Ga20.9Dy0.1 alloy showed the highest shape memory recoverable strain due to the improvement of mechanical properties and formation of small Dy-rich precipitates. Simultaneously, an obvious pseudoelasticity was observed over a wide temperature range with a maximum recoverable strain of 3.74% at 320°C in this alloy. All the Dy-containing alloys exhibited high thermal cyclic stability and quite low thermal hysteresis. However, it was revealed that a complicated and abnormal relationship between thermal hysteresis and the middle eigenvalue λ2 existed for the investigated alloys with a lattice transition from cubic to tetragonal. Calculated results based on energy minimization theory revealed that both the transformation strain and critical stress for inducing martensitic transformation varied with crystallographic orientations. The detwinning of pre-existing (112) compound twins and formation of (112) deformation twins were the dominant deformation mechanisms of martensite, which were highly compatible with the macroscopical recoverable strain. The present study provided valuable insights for developing high-performance multifunctional shape memory alloys for high temperature applications.

Passive mixing rate of trapped squeezed nanodroplets—A time scale analysis

The elegance of digital microfluidics is in incorporating high quantities of manipulated micro and nanodroplets on-chip, each of which can be considered a small-volume carrier of various chemical and biological reagents. Therefore, the analysis of on-demand manipulation of these micro and nanocarriers is extremely important in developing an optimized lab on a chip. In this work, passive coalescence and mixing between two trapped, squeezed nanodroplets inside a closed microfluidic device was investigated. The droplets are composed of glycerol dyed in blue and red, dispersed inside oleic acid as the carrier oil. A microwell with a circular cross section was fabricated on the top wall of the microchannels to trap the first droplet for increasing the mixing precision and minimizing the viscous shear stress imposed on the droplets from the channel walls. The energy minimization theory was used to develop a parametric study for this trapping technique and to choose the optimum design parameters for droplet trapping in terms of efficiency. Image processing was performed on the snapshots of the trapped glycerol nanodroplets during mixing. Growth in passive mixing percentage was demonstrated to be asymptotical and was formulated with an empirical equation of exponential form as a function of the passive mixing relaxation time. The required time for the passive mixing of a glycerol droplet pair was measured considering various thresholds for the final standard deviation of the gray intensity indices. This finding was of the order of magnitude of the diffusive mixing time scale and physically consistent with the Stokes flow regime.

Circular bead-like shapes of cell adhesion structures in 2D case

ABSTRACT Due to the strong deformation ability of cells, the cell adhesive stacking systems are more intricate than atom stacking systems. A general method to reveal their configurations still remains challenging. In this work a theoretic model is proposed to study the circular bead-like adhesion structures composed by equal cells in the two-dimensional (2D) case. Based on the free energy minimization theory, the equilibrium shape equations are obtained and analytical solutions are investigated for high symmetrical structures without volume constraints. All results are confirmed by the finite element method. These shapes are close to some bio-structures, such as the cross section of raspberry and orange. The symmetrical breaking is studied for high symmetrical structures with volume constraints and it reveals that there are abundant degenerated states in a cell adhesion system. These results are helpful for understanding the formation mechanism of the self-organizing cell adhesion structures.

Static recrystallization study on pure aluminium using crystal plasticity finite element and phase-field modelling

In-depth understanding of the recrystallization process in alloys is critical for generating desirable small grains and weak textured microstructure, which provides high strength and toughness for metal formed parts. The manufacturing industry has a high demand for a valid computational model to accurately predict the level of recrystallization and recrystallized grain size under different strain paths and temperatures. However, current understanding and numerical calculation have not been linked properly for a reliable, physically based model to simulate the deformation and annealing process. Our phase-field model coupled with crystal plasticity simulations, which is based on the theory of stored energy minimization, enables a reliable prediction on the microstructure evolution under different processing routes. We hope that this modelling work provides a solution for the prediction of some long standing microstructure formation problems.

Multiphase equilibrium modeling of oxygen bottom-blown copper smelting process

Abstract A computational thermodynamics model for the oxygen bottom-blown copper smelting process (Shuikoushan, SKS process) was established, based on the SKS smelting characteristics and theory of Gibbs free energy minimization. The calculated results of the model show that, under the given stable production condition, the contents of Cu, Fe and S in matte are 71.08%, 7.15% and 17.51%, and the contents of Fe, SiO2 and Cu in slag are 42.17%, 25.05% and 3.16%. The calculated fractional distributions of minor elements among gas, slag and matte phases are As 82.69%,11.22%, 6.09%, Sb 16.57%, 70.63%, 12.80%, Bi 68.93%, 11.30%, 19.77%, Pb 19.70%, 24.75%, 55.55% and Zn 17.94%, 64.28%, 17.79%, respectively. The calculated results of the multiphase equilibrium model agree well with the actual industrial production data, indicating that the credibility of the model is validated. Therefore, the model could be used to monitor and optimize the industrial operations of SKS process.

A New Reactive-Transport Modeling Framework for Simulating Pore Solution Chemistry at Localized Imperfections Along Steel-Concrete Interface

The variability and uncertainty associated with chloride thresholds for corrosion initiation in reinforced concrete structures can be partly explained by the presence of localized defects and imperfections along steel-concrete interface such as elongated cracks, pores, gaps, crevices, and mill scale. It has been demonstrated in prior research that pore solution in these imperfections might be different from that of the bulk pore solution, and this difference may create the necessary conditions for the breakdown of the passive film. These studies showed that the chemistry of the pore solution, in particular pH and Cl-/OH-, within localized defects provide more favorable conditions for depassivation than the bulk concrete pore solution. Local acidification and increase in Cl-/OH- within these defects were observed, albeit to different degrees. Defect geometry has been found to be a critical parameter affecting local acidification and the increase in Cl-/OH-. However, chemical composition of the pore solution, reactions between corrosion products and the ionic species in the pore solution and changes in transport properties within the defect due to accumulation of solid corrosion product have also been shown to affect the process. Due to these complications, it is challenging to study these effects experimentally, hence numerical investigation techniques are required. In order to better understand the processes that take place within local defects along the steel-concrete interface a reactive-transport modeling framework is developed. The model incorporates finite element analysis (FEM) with thermodynamic/kinetic modeling of cementitious systems. The FEM module is responsible for modeling multiphysics phenomena such as corrosion, mass transport, heat transfer, phase flow and kinetics, while thermodynamic module is used to model chemically complex reaction computations based on Gibbs Energy Minimization (GEM) theory. A non-iterative operator splitting technique in a time marching scheme is used for uncoupling the multiphysics phenomena from reaction equations. The framework is able to analyze complex chemical systems including processes that take place in cementitious materials and as a result of corrosion reactions. The presentation will highlight the main components of developed framework and demonstrate its functionality though case studies and hypothetical simulations.

Interfacial morphology and grain orientation during bumpless direct Cu bonding

Twelve inch wafer-to-wafer bumpless direct Cu bonding was achieved at room temperature for 60h, and followed by annealing at 300°C for 30min. Interconnections with different pad pitches from 6μm to 25μm were obtained. Low electrical resistances of 27.73mΩ indicated the bonding was completed. High shear strength of 35.9MPa suggested the potential application of this process in wafer thinning. Observations of interface morphology presented continuous and tight bonding interface. Grain orientation inspections indicated that two kinds of preferred orientations were found at the bonding interface, one of which was near (100) and the other was near (110). This difference for preferred orientations may be related with yielding process. Furthermore, grain boundaries were found to be respectively zigzag and straight at the bonding interface. Based on these observations, bonding mechanism is proposed by the driven force of energy minimization theory. In bonded Cu pads, strain-favorable grain (with lower free energy) growth happened at the expense of other less strain-favorable grains (with higher free energy). Besides initial grain nucleation was formed by small grain connection with the same orientation at the bonding interface and grain growth happened after further annealing.

Sodium Ion Diffusion and Voltage Trends in Phosphates Na4M3(PO4)2P2O7 (M = Fe, Mn, Co, Ni) for Possible High-Rate Cathodes

Polyanionic phosphates have the potential to act as low-cost cathodes and stable framework materials for Na ion batteries. The mixed phosphates Na4M3(PO4)2P2O7 (M = Fe, Mn, Co, Ni) are a fascinating new class of materials recently reported to be attractive Na ion cathodes which display low-volume changes upon cycling, indicative of long-lifetime operation. Key issues surrounding intrinsic defects, Na ion migration mechanisms, and voltage trends have been investigated through a combination of atomistic energy minimization, molecular dynamics (MD), and density functional theory simulations. For all compositions, the most energetically favorable defect is calculated to be the Na/M antisite pair. MD simulations suggest Na+ diffusion extends across a 3D network of migration pathways with an activation barrier of 0.20–0.24 eV, and diffusion coefficients (DNa) of 10–10–10–11 cm2 s–1 at 325 K, suggesting good rate capability. The voltage trends indicate that doping the Fe-based cathode with Ni can significantly i...

Subcritical damping of S step energy on Si(001) vicinals by lowering terrace stress

Abstract Si(001) vicinals with monoatomic steps present an alternation of (1 × 2) and (2 × 1) terraces and SA and SB steps. Our calculations, by using MEAM potential, show a surface stress difference between neighbouring terraces. By both energy minimization and lowering terrace stress, we observe a deformation transfer between neighbouring terraces. The deformation lowers the stress of the higher stress terrace. But the deformation logarithmically varies with step–step distance L. In theory of energy minimization, the great difficulty is to accept, or not, the logarithmic divergence for large L. We show that the logarithmic variation with L is accompanied by the vanishing of the SA step energy. The terrace–terrace deformation transfer disappears when the SA step energy is reduced to zero. This explains the large roughness of the step SB in experiment, because it is perpendicular to SA. This paper clearly confirms that surface stress and surface energy are different quantities to be considered in equilibrium of surfaces. The minimization of the surface energy is accompanied by the lowering of the surface stress for the higher stress terrace. Consequently, this terrace is contracted, while the other terrace is expanded in order to render the sum of equilibrium deformations over the period including the two terraces nul.

A kinetically driven growth mechanism: AlF3 over Cu(0 0 1)

A new diffusion model based on kinematic properties and supported by Metropolis Monte Carlo free energy minimization and density functional theory calculations is proposed in this work. This new mechanism breaks the isotropic features of random adatom diffusion over a single crystal surface, not only about the main directions but also about the sense of movement. The present model allows us to understand all the anomalous growing features characterizing the behaviour of an insulator film, such as aluminum fluoride, over a metallic Cu(1 0 0) single crystal surface. The growth process of this system is characterized by several non-fully understood features, including a large diffusion coefficient, sticking at both sides of steps, and island atomistic arrangement along special directions. Although we focus our analysis on the AlF3/Cu(1 0 0) system, our conclusions may be extended to the diffusion of other complex molecules over different surfaces.

Topological zoo of free-standing knots in confined chiral nematic fluids

Knotted fields are an emerging research topic relevant to different areas of physics where topology plays a crucial role. Recent realization of knotted nematic disclinations stabilized by colloidal particles raised a challenge of free-standing knots. Here we demonstrate the creation of free-standing knotted and linked disclination loops in the cholesteric ordering fields, which are confined to spherical droplets with homeotropic surface anchoring. Our approach, using free energy minimization and topological theory, leads to the stabilization of knots via the interplay of the geometric frustration and intrinsic chirality. Selected configurations of the lowest complexity are characterized by knot or link types, disclination lengths and self-linking numbers. When cholesteric pitch becomes short on the confinement scale, the knotted structures change to practically unperturbed cholesteric structures with disclinations expelled close to the surface. The drops with knots could be controlled by optical beams and may be used for photonic elements.

Computer modelling of undoped and Eu3+‐doped LiLa(WO4)2

AbstractIn this work, computer modelling of the undoped and Eu3+‐doped LiLa(WO4)2 structure was successfully achieved by energy minimization and mean field theory. The results were compared with experimental data previously published and are in good agreement with them. A linear regression of the lattice parameters was also proposed as a function of the dopant concentration. The lattice ordering was evaluated to understand the possibility of structural changes in the crystal. Regarding the optical luminescence, the concentration limit of Eu doping was also determined. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Variation of magnetic domain structure during martensite variants rearrangement in ferromagnetic shape memory alloys

Studies of magnetic domain and anisotropy in ferromagnetic shape memory alloys (FSMAs) are crucial for both understanding their ferromagnetism and engineering in applications. The experimental measurements showed that magnetization rotations and domain-wall motions exhibit distinct characteristics in the field-preferred variants and stress-preferred variants of FSMAs [Y. W. Lai, N. Scheerbaum, D. Hinz, O. Gutfleisch, R. Schäfer, L. Schultz, and J. McCord, Appl. Phys. Lett. 90, 192504 (2007)]. Aiming at characterization of formation and variation of the complex magnetic microstructure in FSMAs, we present an analytical approach based on the energy minimization theory and Boltzmann relation on magnetic domains. The magnetic domain behavior during the martensite variants rearrangement is captured to show a good agreement with the experimental observations.

Influence of growth parameters on the microstructures of erbium films deposited on Si(111) substrates

Erbium films were grown on single crystal Si(111) substrates by electron beam vapor deposition. The microstructures of the erbium films were systematically investigated by X-ray diffraction, scanning electron microscopy, and energy dispersive spectroscopy. Results indicate that the surface morphologies and microstructures of the erbium films with Si as substrates are susceptible to the substrate temperatures when the deposition rates are fixed. The pure erbium films with columnar grains were obtained at temperatures below 200 °C, but in the films grown at temperatures higher than 350 °C, some pinholes that are composed of erbium silicides were found. The pinholes have triangular shapes which is in accordance with the geometry of the underlying Si(111) substrate. The films grown at a substrate temperature equal or greater than 450 °C have cracks which would be formed due to the different shrinkage degree of erbium and silicon when the substrate temperature was cooled down to room temperature. The films grown at 200 °C show the (002) preferred orientation, which is consistent to the prediction by the theory of surface energy minimization. The deposition rate and deposition time are considered as factors to affect the reaction of the erbium film and the silicon substrate.

Prediction of crystallographic characteristics of martensitic transformation in a Ni–Mn–Ga based Heusler alloy

The energy minimization theory was applied to analyze the crystallographic features of the martensitic transformation in the alloy Ni52.5Mn23.5Ga24 and the results obtained were compared with those determined by experiments. It is revealed that the index of the boundary between martensite variants belongs to the lattice plan family of {112}M and the orientation relationship between the martensite variant 1 and 2 is characterized by a rotation of 82.1° about [1 0 0]M1/[0 1 0]M2. The orientation relationship between the parent phase and the martensite features a rotation of approximately 4° about the c axis of the parent lattice from the position of the conventional Bain relationship.