Phase——field model of isothermal solidification withmultiple grains growth

This paper develops a new phase--field model for equiaxed dendrite growth of multiple grains in multicomponent alloys based on the Ginzberg--Landau theory and phase--field model of a single grain. Taking Al--Cu and Al--Cu--Mg alloys for example, it couples the concentration field and simulates the dendrite growth process of multiple grains during isothermal solidification. The result of the simulation shows dendrite competitive growth of multiple grains, and is reapplied to the process of dendrite growth in practical solidification.     

Numerical simulation of dendrite growth and microsegregation formation of binary alloys during solidification process

The dendrite growth and solute microsegregation of Fe-C binary alloy are simulated during solidification process by using cellular automaton method. In the model the solid fraction is deduced from the relationship among the temperature, solute concentration and curvature of the solid/liquid interface unit, which can be expressed as a quadric equation, instead of assuming the interface position and calculating the solid fraction from the interface velocity. Then by using this model a dendrite with 0 and 45 degree of preferential growth direction are simulated respectively. Furthermore, a solidification microstructure and solute microsegregation are simulated by this method. Finally, different Gibbs-Thomson coefficient and liquid solute diffusing coefficient are adopted to investigate their influences on the morphology of dendrite.     

Effect of Low Diffusion Coefficient on Eutectic Instability of Al-25wt%Sm Alloy

Diffusion coefficient decides the solute diffusion length and is a critical parameter in the selection of microstructare scales and in governing microstructure transitions. Al-25 wt%Sm alloy is selected to reveal the impact of low diffusion coefficient on the eutectic instability, and the results are compared with those of Al-Cu alloys. Laser remelting experiments are performed and the transition growth velocity from euteetic to α-Al dendrite is examined. Compared with Al-Cu alloys, the eutectic instability takes place at a velocity more than one order of magnitude smaller. The theoretical calculation by the Trivedi-Magnin-Kurz （TMK） model also predicts that the eutectic will become instable at smaller growth velocity for Al-Sm alloy than Al-Cu alloy, which is ascribed to the low diffusion coefficient.     

Phase-field simulation of dendritic growth in a binary alloy with thermodynamics data

This paper simulates the dendrite growth process during non-isothermal solidification in the Al-Cu binary alloy by using the phase-field model. The heat transfer equation is solved simultaneously. The thermodynamic and kinetic parameters are directly obtained from existing database by using the Calculation of Phase Diagram （CALPHAD） method. The effects of the latent heat and undercooling on the dendrite growth, solute and temperature profile during the solidification of binary alloy are investigated. The results indicate that the dendrite growing morphologies could be simulated realistically by linking the phase-field method to CALPHAD. The secondary arms of solidification dendritic are better developed with the increase of undercooling. Correspondingly, the tip speed and the solute segregation in solid-liquid interface increase, but the tip radius decreases.     

Rapid solidification and dendrite growth of ternary Fe-Sn-Ge and Cu-Pb-Ge monotectic alloys

The phase separation and dendrite growth characteristics of ternary Fe-43.9%Sn- 10%Ge and Cu-35.5%Pb-5%Ge monotectic alloys were studied systematically by the glass fluxing method under substantial undercooling conditions. The maximum undercoolings obtained in this work are 245 and 257 K, respectively, for these two alloys. All of the solidified samples exhibit serious macrosegregation, indicating that the homogenous alloy melt is separated into two liquid phases prior to rapid solidification. The solidification structures consist of four phases including α-Fe, (Sn), FeSn and FeSn2 in Fe-43.9%Sn-10%Ge ternary alloy, whereas only (Cu) and (Pb) solid solution phases in Cu-35.5%Pb-5%Ge alloy under different undercoolings. In the process of rapid monotectic solidification, α-Fe and (Cu) phases grow in a dendritic mode, and the transition "dendrite→monotectic cell" happens when alloy undercoolings become sufficiently large. The dendrite growth velocities of α-Fe and (Cu) phases are found to increase with undercooling according to an exponential relation.     

Effect of Ni and vacancy concentration on initial formation of Cu precipitate in Fe–Cu–Ni ternary alloys by molecular dynamics simulation

In the present work, the effects of Ni atoms and vacancy concentrations(0.1%, 0.5%, 1.0%) on the formation process of Cu solute clusters are investigated for Fe–1.24%Cu–0.62%Ni alloys by molecular dynamics(MD) simulations. The presence of Ni is beneficial to the nucleation of Cu precipitates and has little effect on coarsening rate in the later stage of aging. This result is caused by reducing the diffusion coefficient of Cu clusters and the dynamic migration of Ni atoms. Additionally, there are little effects of Ni on Cu precipitates as the vacancy concentration reaches up to 1.0%,thereby explaining the embrittlement for reactor pressure vessel(RPV) steel. As a result, the findings can hopefully provide the important information about the essential mechanism of Cu cluster formation and a better understanding of ageing phenomenon of RPV steel. Furthermore, these original results are analyzed with a simple model of Cu diffusion, which suggests that the same behavior could be observed in Cu-containing alloys.     

Molecular Dynamics Simulation of Xe Behavior in U-Mo Alloys Fuel

Classical molecular dynamics simulations are used to investigate the fission gas Xe behavior in a U-Mo alloy fuel matrix. The embedded atom method potential proposed by Smirnova et al. is used to describe the U-Mo-Xe system. The results show that the initial configuration of interstitial Xe atoms in U-Mo alloys is very instable and has a strong tendency to get together and to form a Xe bubble by ejecting the adjacent U atoms and Mo atoms from their former normal lattice sites. The pressure in Xe bubbles is initially quite high and then drops with increasing Xe concentration obviously. The matrix swelling of U-Mo alloys associated with the Xe bubble growth follows approximately a linear relationship with the ratio of Xe to U at low Xe concentration while the rate of swelling increases rapidly at high Xe concentration. The simulation results are in good agreement with the experimental data. The recovery of the damaged structure in the U-Mo alloys matrix is also investigated. It is shown that a damaged structure cannot be recovered completely after a system is relaxed for a long time while still having lots of defects.     

Solute distribution in KNbO3 melt-solution and its effect on dendrite growth during rapid solidification

This paper reports that the rapid solidification of mixed Li 2 B 4 O 7 and KNbO 3 melted in a Pt loop heater has been performed experimentally by the method of quenching, and various morphologies of KNbO 3 crystals have been observed in different regions of the quenched melt-solution. Dendrites were formed in the central region where mass transfer is performed by diffusion, whereas polygonal crystals with smooth surface grew in the marginal region where convection dominates mass transport. Based on measurement of KNbO 3 concentration along crystal interface by electronic probe analysis, it finds the variety of crystal morphologies, which is the result of different solute distributions: in the central region the inhomogeneity of solute concentration is much sharper and morphological instability is easier to take place; nevertheless in the marginal region the concentration homogeneity has been greatly enhanced by convection which prevents the occurrence of morphological instability. Additional solute distribution in the melt along the primary dendrite trunk axis as well as that in mushy zones has also been determined. Results show that the solute concentration in the liquid increases linearly with distance from the trunk tip and more solutes were found to be concentrated in mushy zones. The closer the mushy zone is to trunk tip, the lower the solute concentration will be there.     

Preparation of High-Density Nanocrystalline Bulk Selenium by Rapid Compressing of Melt

The melt＇s solidification behavior of elemental selenium is investigated by a series of experiments including rapid compressing to 2.8 and 3.5 GPa within 20ms respectively, slow compressing to 2.8 GPa for 20 min and natural cooling at ambient pressure. Based on the x-ray diffraction, scanning electron microscope and transmission electron microscope results of the recovered samples, it is clearly shown that homogenous nanostructures are formed only by the rapid compression processes, and that the average crystal sizes are about 18.7 and 19.0 nm in the samples recovered from 2.8 and 3.5 GPa, respectively. The relative density of the nanocrystalline bulk reaches 98.17% of the theoretical value. It is suggested that rapid compression could induce pervasive nucleation and restrain grain growth during the solidification, which is related to fast supercooling, higher viscosity of the melt and lower diffusivity of atoms under high pressure.     

Growth of NaBi（WO4）2 Dendrite and Mechanism

The solid-liquid interface motion of NaBi（WO4）2 （NBWO） melt crystal growth is observed in an in situ system, in which the whole processes of interface transition from fiat interface and cellular to dendrite are visualized. The spacing of the dendrite under smaller temperature gradient turns out to be larger than that under larger temperature gradient, which is found to be sensitive to the temperature distribution. The mechanism of dendrite growth of NBWO is studied based on the model of the growth units of anion coordination polyhedra. The { 001} face has two apex links, so it shows higher stability and has high growth rate and forms the arm of dendrite, whereas the {010} face has only one apex link, and thus shows relative slower growth rate and firstly forms the branches.     

Anisotropic growth of multigrain in equiaxial solidification simulated with the phase field method

The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidification is developed, which takes into account the random crystallographic orientations of crystallites and preserves the rotational invariance of the free energy. The morphological evolution of equiaxial multigrain solidification is predicted and the effect of composition on transformation kinetics is studied. The numerical results indicate that due to the soft impingement of grains the Avrami exponent varies with the initial melt composition and the solidification fraction.     

Dendritic and eutectic growth in Sb<Subscript>60</Subscript>Ag<Subscript>20</Subscript>Cu<Subscript>20</Subscript> ternary alloy

The rapid solidification of Sb60Ag20Cu20 ternary alloy was realized by high undercooling method, and the maximum undercooling is up to 142 K (0.18TL). Within the wide undercooling range of 40-142 K, the solidified microstructures are composed of (Sb), θand ε phases. High undercooling enlarges the solute solubility of (Sb) phase, which causes its crystal lattice to expand and its crystal lattice constants to increase. Primary (Sb) phase grows in two modes at small undercoolings non-faceted dendrite growth is the main growth form; whereas at large undercoolings faceted dendrite growth takes the dominant place. The remarkable difference of crystal structures between (Sb) and θphases leads to (θ Sb) pseudobinary eutectic hard to form, whereas strips of θform when the alloy melt reaches the (θ Sb) pseudobinary eutectic line. The cooperative growth of θand ε phases contributes to the formation of (ε θ) pseudobinary eutectic easily. In addition, the crystallization route has been determined via microstructural characteristic analysis and DSC experiment.     

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability(RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.     

Non-monotonic dependence of current upon i-width in silicon p–i–n diodes

Silicon p–i–n diodes with different i-region widths are fabricated and tested. It is found that the current shows the non-monotonic behavior as a function of i-region width at a bias voltage of 1.0 V. In this paper, an analytical model is presented to explain the non-monotonic behavior, which mainly takes into account the diffusion current and recombination current contributing to the total current. The calculation results indicate that the concentration ratio of p-region to n-region plays a crucial role in the non-monotonic behavior, and the carrier lifetime also has a great influence on this abnormal phenomenon.     

Melting kinetics of bulk SiC using molecular dynamics simulation

The melting kinetics of bulk SiC is studied by using classical molecular dynamics simulation.The mean square displacement,diffusion coefficient,Lindemann index and non-Gaussian parameter are used to analyze the melt nucleation and macrokinetics in the melting process.Melting occurs when the superheated crystal spontaneously generates many Lindemann particles in which they coalesce together to form melt nucleation inside the crystal.The melting process is similar to the solidification process,but also experiences three processes such as nucleation,growth and relaxation.The melting process can be divided into premelting,accelerated melting and relaxation stages.Using the sectional method can properly reflect the kinetic characteristics of the melting process.     

In Situ Observation of Cell-to-Dendrite Transition

The cell-to-dendrite transition of succinonitrile melt suspended on a loop-shaped Pt heater is observed in real time by a differential interference microscope coupled with Schlieren technique. The transition is divided into two parts： a dendrite coalition process and a subsequent dendrite elimination process. Firstly the dendrites from the same cell are united into a single dendrite. Secondly the competitive growth of dendrites from different cells leads to the elimination of dendrites. The two processes can be understood when involving crystallographic orientation. In addition, the tip velocity and primary spacing of a cell/dendrite are also measured. It turns out that the primary spacing has a significant jump, whereas the growth velocity has no abrupt change during the cell-to-dendrite transition.     

Effects of Nb and Mo additions on thermal behavior,microstructure and magnetic property of FeCoZrBGe alloy

Both Nb and Mo additions play a vital role in FeCo-based alloys and it is crucial to understand their roles and contents on thermal behavior,microstructural feature and magnetic property of alloys.Nanocrystalline alloy ribbons Fe40Co40Zr9?yMyB10Ge1(y=0–4;M=Nb,Mo)were prepared by crystallizing the as-quenched amorphous alloys.The effects of Nb and Mo additions on structures and properties of the Fe40Co40Zr9B10Ge1 alloy are investigated systemically and compared.With increasing Nb or Mo content,the primary crystallization temperature,grain size ofα-Fe(Co)phase and coercivity Hc all decrease.Moreover,the effect of Mo addition on thermal behavior,microstructure and magnetic properties of the FeCoZrBGe alloy is greater compared to Nb addition.The gap between primary and secondary crystallization peaks of Mo-containing alloys is wider than that of Nb-containing alloys.Both grain size and Hc of Mo-containing alloys are smaller than those of Nb-containing alloys.For Fe40Co40Zr9B10Ge1 alloy,high Mo addition proportion is better compared to high Nb addition proportion.     

Diffusion behavior of hydrogen isotopes in tungsten revisited by molecular dynamics simulations

Molecular dynamics simulations were performed to study the diffusion behavior of hydrogen isotopes in single-crystal tungsten in the temperature range of 300–2000 K. The simulations show that the diffusion coefficient of H isotopes exhibits non-Arrhenius behavior, though this deviation from Arrhenius behavior is slight. Many-body and anharmonic effects of the potential surface may induce slight isotope-dependence by the activation energy; however, the dependence of the pre-factor of the diffusion coefficient on the isotope mass is diminished. The simulation results for H-atom migration near W surfaces suggest that no trap mutations occur for H atoms diffusing near either W{100} or W{111} surfaces, in contrast to the findings for He diffusion near W surfaces. Based on the H behavior obtained by our MD simulations, the time evolution of the concentration distribution of interstitial H atoms in a semi-infinite W single crystal irradiated by energetic H projectiles was calculated. The effect of H concentration on H diffusion is discussed, and the applicability of the diffusion coefficients obtained for dilute H in W is assessed.     

Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.     

A steady solution of the gasar eutectic growth in directional solidification

This paper presents the general mathematical model on gasar eutectic growth in directional solidification. Using multiple scale expansion and matching method, we obtain the global steady solution of gasar eutectic growth as the Peclet number ε≤1, where ε is defined as the ratio of half an inter-pore spacing and solutal diffusion length. We also give the interfacial shape and predict the porosity of gasar eutectic growth. Results show that porosity is mainly dependent on gas pressure above the metal melt, but independent of pulling velocity. Our predicted results are in agreement with experimental data.