Multi-phase-field simulation of austenite peritectic solidification based on a ferrite grain

A multi-phase-field model is implemented to investigate the peritectic solidification of Fe-C alloy. The nucleation mode of austenite is based on the local driving force, and two different thicknesses of the primary austenite on the surface of the ferrite equiaxed crystal grain are used as the initial conditions. The simulation shows the multiple interactions of ferrite, austenite, and liquid phases, and the effects of carbon diffusion, which presents the non-equilibrium dynamic process during Fe-C peritectic solidification at the mesoscopic scale. This work not only reveals the influence of the austenite nucleation position, but also clarifies the formation mechanism of liquid phase channels and molten pools. Therefore, the present study contributes to the understanding of the micro-morphology and micro-segregation evolution mechanisms of Fe-C alloy during peritectic solidification.     

Directional solidification of Al–Cu–Ag alloy

Al–Cu–Ag alloy was prepared in a graphite crucible under a vacuum atmosphere. The samples were directionally solidified upwards under an argon atmosphere with different temperature gradients (G=3.99–8.79 K/mm), at a constant growth rate (V=8.30 μm/s), and with different growth rates (V=1.83–498.25 μm/s), at a constant gradient (G=8.79 K/mm) by using the Bridgman type directional solidification apparatus. The microstructure of Al-12.80-at.%–Cu-18.10-at.%–Ag alloy seems to be two fibrous and one lamellar structure. The interlamellar spacings (λ) were measured from transverse sections of the samples. The dependence of interlamellar spacings (λ) on the temperature gradient (G) and the growth rate (V) were determined by using linear regression analysis. According to these results it has been found that the value of λ decreases with the increase of values of G and V. The values of λ ² V were also determined by using the measured values of λ and V. The experimental results were compared with two-phase growth from binary and ternary eutectic liquid.     

Directional solidification of Ti–49 at.%Al alloy

Ti–49Al (at.%) alloy was directionally solidified in Bridgman-type directional solidification furnace. The specimens were directionally solidified under an argon atmosphere with the different growth rate (V=5–30 μm/s) at a constant temperature gradient (G=12.1 K/mm), and with the different temperature gradient (G=2.8–12.1 K/mm) at a constant growth rate (V=10 μm/s). The dendritic spacings (λ ₁) were measured from both transverse and longitudinal sections of the specimens. The dependence of λ ₁ on the growth rate (V) and temperature gradient (G) were determined by using linear regression analysis. According to the experimental results, the value of λ ₁ decreases with the increase of values of V and G. The experimental results were compared with the current theoretical and numerical models, and similar previous experimental results.     

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.     

Monte Carlo simulation of the dynamic evolution ofbinary lamellar eutectic in directional solidification

The dynamic evolution of the lamellar eutectic of binary alloys in directional solidification is studied in detail using the Monte Carlo technique. The simulated results can be summarized into two aspects: ({1}) the lamellar spacing λ is found to be inversely proportional to the chemical potential difference Δμ, predicting a linear relationship between the kinetic supercooling ΔT_k and total supercooling at the solid/liquid (S/L) interface; (2) as the solidifying velocity R is low, the dynamic product λ^{2}R shows a considerable dependence on temperature gradient G_T in the liquid in front of the S/L interface, although this dependence becomes much weaker at a high R.     

Formation and evolution mechanisms of large-clusters during rapid solidification process of liquid metal Al

A molecular dynamics simulation study has been performed for the formation and evolution characteristics of nano-clusters in a large-scale system consisting of 400000 atoms of liquid metal Al. The center-atom method combined with pair-bond analysis technique and cluster-type index method (CTIM) has been applied here to describe the structural configurations of various basic clusters. It is demonstrated that both the 1551 bond-type and the icosahedral cluster (12 0 12 0) constructed by 1551 bond-types are dominant among all the bond-types and cluster-types, respectively, in the system and play a critical role in the microstructure transitions of liquid metal Al. The nano-clusters (containing up to 150 atoms) are formed by the combination of some middle and small clusters with distinctly different sizes, through mutual competition by unceasing annex and evolution in a seesaw manner (in turn of obtaining and losing), which do not occur as the multi-shell structures accumulated with an atom as the center and     

Influence of initial solid–liquid interface morphology on further microstructure evolution during directional solidification

Preparation of the initial solid–liquid interface on which growth is started is a very critical step in directional solidification experiments. Dedicated experiments concerning preparation of the initial solid–liquid interface morphology and its influence on further directionally solidified microstructure were performed on Cu-20 wt% Sn peritectic alloy in a Bridgman-type furnace. To verify the morphology of the initial solid–liquid interface, steady-state directional dendritic growth was interrupted by thermal stabilization ranging from 0 to 1 h prior to quenching. With thermal stabilization duration increase, the solid–liquid interface morphology degenerated from dendritic to cellular and finally to planar. To verify the influence of the initial state on further solidification microstructure, directional solidification experiments were performed at a low pulling rate of 1 μm/s with different initial solid–liquid interface morphologies. The initial state affects solute redistribution and formation of peritectic coupled growth structure in the subsequent directional solidification process.     

Disorder trapping and grain refinement during solidification of undercooled Fe–18 at% Ge melts

The electromagnetic levitation technique has been used to systematically study microstructure evolution and growth rate as a function of undercooling in concentrated Fe–18 at% Ge alloy. The samples are undercooled to a maximum of 240?K. Growth-rate analysis and transmission electron microscopy reveal that, beyond an undercooling of 120?K, the primary phase to solidify is disordered. Microstructural investigations show a decrease in grain size with increasing undercooling. Orientation-imaging microscopy using electron back-scattered diffraction (EBSD) and microhardness measurements have been used to show that recovery and recrystallization play a significant role in the evolution of final microstructure. Microstructural evolution has also been discussed in light of current models of dendrite growth and grain refinement.     

Growth of tertiary dendritic arms during the transient directional solidification of hypoeutectic Pb–Sb alloys

Despite the importance of a complete characterization of dendritic patterns in castings, the availability of studies on the development of tertiary dendrite arms is scarce in the literature. In the present study, the tip cooling rate, local solidification time, primary and tertiary dendrite arm spacings have been determined in Pb–Sb alloys castings directionally solidified under unsteady-state heat flow conditions. The alloys compositions experimentally examined are widely used in the as-cast condition for the manufacture of positive and negative grids of lead-acid batteries. The initial growth of tertiary dendritic arms from the secondary branches was found to occur only for a Pb–3.5 wt% Sb alloy at cooling rates in the range 0.4–0.2?K/s, with no evidence of this spacing pattern for Pb–Sb alloys having lower solute content. Tertiary dendritic branches have been observed along the entire casting lengths for alloys of the Pb–Sb hypoeutectic range having compositions higher than 4.0 wt% Sb. It is shown that a power function experimental law with a characteristic ?0.55 exponent is able to characterize the tertiary spacing evolution with the solidification cooling rate for alloys compositions ≥4.0 wt% Sb. The only exception was the Pb–3.5 wt% Sb alloy for which λ ₃ exhibited significant lower values when compared with the experimental values obtained for the other Pb–Sb alloys for a same solidification cooling rate.     

What happens to the initial planar instability when the thermal gradient is increased during directional solidification？

The positive thermal gradient is one of the most important parameters during directional solidification. The increase of the thermal gradient usually stabilizes the planar interface in the steady state analysis. However, in the initial transient range of planar instability, the thermal gradient presents complicated effects. Time-dependent analysis shows that the increase of the thermal gradient can enhance both the stabilizing effects and the destabilizing effects on a planar interface. The incubation time first decreases and then increases with the increase of the thermal gradient. Moreover, the initial average wavelength always increases with the thermal gradient increasing, contrary to the effect of the thermal gradient on the steady cellular/dendritic spacing. This reveals the types of spacing adjustment after planar instability.     

Superconducting property of Zr–Co and Zr–Co–Al alloys fabricated by rapid solidification

The superconducting property of Zr_(1−x)Co_x (x = 10–50 at.%) alloys and a Zr₅₅Co₃₀Al₁₅ bulk metallic glass fabricated using techniques of rapid solidification was investigated. The Zr₅₅Co₃₀Al₁₅ alloy crystallized by heat treatment in a vacuum atmosphere exhibited superconductivity of T_c,on = 2.4 K. This was attributable to the superconducting property of a crystalline Zr–Co alloy precipitated in the Zr₅₅Co₃₀Al₁₅ alloy. The T_c,on of the crystalline Zr_(1−x)Co_x alloy was sensitive to the Co content. The increase of Co content for the Zr_(1−x)Co_x alloy led to the decrease of T_c,on. The Zr_(1−x)Co_x alloy exhibited superconductivity of a maximum T_c,on = 3.9 K for the Zr₈₀Co₂₀ alloy with superconducting nanocrystal particles embedded in the amorphous matrix.     

Formation mechanism of banded structure during directional solidification of Sn–Cd peritectic alloy under convection condition

Directional solidification experiments of Sn-0.75 wt%Cd and Sn-1.6 wt%Cd peritectic alloys have been conducted under convection condition to investigate the formation mechanism of banded structure. Many types of banded structure were obtained, which cannot be interpreted by the Karma’s model. The reason for this conflict is that there are many banded structure formation mechanisms such as abundant nucleation, regrowth, fast radial cellular growth and radial competitive growth under convection condition, but the Karma’s model only considers the abundant nucleation and ignores other mechanisms. The analyses showed that these formation mechanisms changed along with an increase in alloy composition. Based on these analyses, a simple modified banding window, which considered these different formation mechanisms, has been presented. Compared with the banding window defined by the Karma’s model, this modified banding window contained it and could predict different banded structure formations under convection condition appropriately.     

A lattice Boltzmann–cellular automaton study on dendrite growth with melt convection in solidification of ternary alloys

A lattice Boltzmann(LB)–cellular automaton(CA) model is employed to study the dendrite growth of Al-4.0 wt%Cu–1.0 wt%Mg alloy. The effects of melt convection, solute diffusion, interface curvature, and preferred growth orientation are incorporated into the coupled model by coupling the LB–CA model and the CALPHAD-based phase equilibrium solver,Pan Engine. The dendrite growth with single and multiple initial seeds was numerically studied under the conditions of pure diffusion and melt convection. Effects of initial seed number and melt convection strength were characterized by newdefined solidification and concentration entropies. The numerical result shows that the growth behavior of dendrites, the final microstructure, and the micro-segregation are significantly influenced by melt convection during solidification of the ternary alloys. The proposed solidification and concentration entropies are useful characteristics bridging the solidification behavior and the microstructure evolution of alloys.     

a绝对=a相对＋a牵连在动力学中的运用

凡惯性定律成立的参照系，叫做惯性系；惯性定律不成立的参照系，叫做非惯性系．牛顿第一定律和第二定律在非惯性系中是不适用的．因此，在研究动力学问题时通常应选择惯性系做为参照系．为了在非惯性系中仍能应用牛顿运动定律，往往需引入惯性力的概念．但如果不是使用惯性力的概念，而是同时考虑非惯性系的变速运动以及质点相对非惯性系的相对运动，则在惯性系中使用牛顿运动定律依然方便．     

Influences of travelling magnetic field on the dendritic structures of Sn–1.8Cd peritectic alloy during directional solidification

The effects of melt flow driven by a travelling magnetic field (TMF) on solidification structures of Sn–1.8 wt.% Cd peritectic alloy have been investigated numerically and experimentally. Numerical results indicate that the flow velocity at the solid–liquid interface under a downward TMF is smaller than that under an upward TMF. The experimental results show that the growth directions of dendrites are chaotic, and several crotches among the dendrites are observed at the solid–liquid interface in the case of no field. It is concluded from TMF results that the ordered growth of dendrites at two different directions occurs, and only one crotch among the dendrites appears at the solid–liquid interface. The location of the crotch gradually approaches the interface center with increasing magnetic field intensity (B≤10.3 mT). Moreover, the growth of high-order branches occurs at the crotch under a downward TMF. A simple model is established for explanation and it well corresponds to the experimental results.     

A simulation study of rapid solidification and crystal configuration of Cu_(70)Ni_(30) alloy

1 Introduction It is well known that the performances of metal materials are mainly determined by their special microcosmic configuration formed in the concreting processes. For under- standing the relationship between the configuration and performance, it is very impor- tant both in theory and practice to find out the form and transition feature of microcos- mic configuration by tracking the concreting processes of liquid metals. Cu-Ni alloy is a completely solid solution or a single-phase al…     

Radiation Rate of a Two-Level Atom in a Spacetime with a Reflecting Boundary

We study a two-level atom in interaction with a real massless scalar quantum field in a spacetime with a reflecting boundary. We calculate the rate of change of the atomic energy for the atom. The presence of the boundary modifies the quantum fluctuations of the scalar field, which in turn modifies the rate of change of the atomic energy. It is found that the modifications induced by the presence of a boundary make the spontaneous radiation rate of an excited atom to oscillate near the boundary and this oscillatory behaviour may offer a possible opportunity for experimental tests for geometrical （boundary） effects in flat spacetime.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.