Comparative analysis of isothermal and non-isothermal solidification of binary alloys using phase-field model

Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit(ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni-Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.

Phase-field simulation of secondary dendrite growth in directional solidification of binary alloys

Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ_(11) < 45o and θ_A < 45o, as θ_(11) was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary(GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θ_A, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection,and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites.When θ_A = 45o and θ_(11) = 45o, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain's orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.

Two-dimensional cellular automaton model for simulating structural evolution of binary alloys during solidification

Two-dimensional cellular automaton(CA)simulations of phase transformations of binary alloys during solidification were reported.The modelling incorporates local concentration and heat changes into a nucleation or growth function,which is utilized by the automaton in a probabilistic fashion.These simulations may provide an efficient method of discovering how the physical processes involved in solidification processes dynamically progress and how they interact with each other during solidification.The simulated results show that the final morphology during solidification is related with the cooling conditions.The established model can be used to evaluate the phase transformation of binary alloys during solidification.

Phase-field simulation of competitive growth of grains in a binary alloy during directional solidification

Taking Al-2%mole-Cu binary alloy as an example, the influence of grain orientation on competitive growth of dendrites under different competitive modes was investigated by using the three-dimensional(3-D) phasefield method. The result of phase-field simulation was verified by applying cold spray and directional remelting. In the simulation process, two competitive modes were designed: in Scheme 1, the monolayer columnar grains in multilayer columnar crystals had different orientations; while in Scheme 2, they had the same orientation. The simulation result showed that in Scheme 1, the growth of the dendrites, whose orientation had a certain included angle with the direction of temperature gradient, was restrained by the growth of other dendrites whose direction was parallel to the direction of temperature gradient. Moreover, the larger the included angle between the grain orientation and temperature gradient, the earlier the cessation of dendrite growth. The secondary dendrites of dendrites whose grain orientation was parallel to the temperature gradient flourished with increasing included angles between the grain orientation and temperature gradient. In Scheme 2, the greater the included angle between grain orientation and temperature gradient, the easier the dendrites whose orientation showed a certain included angle with temperature gradient inserted between those grew parallel to the temperature gradient, and the better the growth condition thereafter. Some growing dendrites after intercalation were deflected to the temperature gradient, and the greater the included angle, the lower the deflection. The morphologies of the competitive growth dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the two modes of competitive growth of dendrites characterized in the simulation do exist and frequently appear in practical solidification processes.

FORMATION ENTHALPIES FOR FCC METAL BASED BINARY ALLOYS BY EMBEDDED ATOM METHOD

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Microstructure and properties of Mg-Al binary alloys

The effects of different amounts of added Al, ranging from 1 % to 9 %, on the microstructure and properties of Mg-Al binary alloys were investigated. The results showed that when the amount of added Al is less than 5%, the grain size of the Mg-Al binary alloys decreases dramatically from 3 097 μm to 151 μm with increasing addition of Al. Further addition of Al up to 9% makes the grain size decrease slowly to 111 μm. The α-Mg dendrite arms are also refined. Increasing the amount of added Al decreases the hot cracking susceptibility of the Mg-Al binary alloys remarkably, and enhances the micro-hardness of the α-Mg matrix.

Calculation of Activity Coefficient from Immiscible Binary Alloy Phase Diagram by Means of Modified Sub-regular Solution Model

The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.

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.

Phase field modeling of multiple dendrite growth of Al-Si binary alloy under isothermal solidification

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.

A New Thermodynamic Calculation Method for Binary Alloys: Part I: Statistical Calculation of Excess Functions

The improved form of calculation formula for the activities of the components in binary liquids and solid alloys has been derived based on the free volume theory considering excess entropy and Miedema's model for calculating the formation heat of binary alloys. A calculation method of excess thermodynamic functions for binary alloys, the formulas of integral molar excess properties and partial molar excess properties for solid ordered or disordered binary alloys have been developed. The calculated results are in good agreement with the experimental values.

Interface kinetics modeling of binary alloy solidification by considering correlation between thermodynamics and kinetics

By considering collision-limited growth mode and short-range diffusion-limited growth mode simultaneously,an extended kinetic model for solid−liquid interface with varied kinetic prefactor was developed for binary alloys.Four potential correlations arising from effective kinetics coupling the two growth modes were proposed and studied by application to planar interface migration and dendritic solidification,where the linear correlation between the effective thermodynamic driving force and the effective kinetic energy barrier seems physically realistic.A better agreement between the results of free dendritic growth model and the available experiment data for Ni−0.7at.%B alloy was obtained based on correlation between the thermodynamics and kinetics.As compared to previous models assuming constant kinetic prefactor,a common phenomenon occurring at relatively low undercoolings,i.e.the interface migration slowdown,can be ascribed to both the thermodynamic and the kinetic factors.By considering universality of the correlation between the thermodynamics and kinetics,it is concluded that the correlation should be considered to model the interface kinetics in alloy solidification.

Phase Stability, Kinetic Diagrams and Diffusion Path in High Temperature Oxidation of Binary Solid-Solution Alloys

The phase diagrams of ternary systems involving two metal components and one oxidant are considered first, the limitations to their use is discussed in relation to the high temperature oxidation of binary alloys. Kinetic diagrams, which are useful to predict the conditions for the stability of the two mutually insoluble oxides as the external scale, are then calculated on the basis of thermodynamic and kinetic data concerning both the alloys and the oxides, assuming the validity of the parabolic rate law. A combination of the two types of diagrams provides a more detail information about the oxidation behavior of binary alloys. The calculation of the diffusion paths, which relate the oxidant pressure to the composition of the system in terms of the alloy components both in the alloy and in the scale during an initial stage of the reaction in the presence of the parabolic rate law, is finally developed.

A New Thermodynamic Calculation Method for Binary Alloys Part II:Exploring the Correction Factor Function

A new method of revising activity values has been derived based on the so called correction factor function for binary alloys with a large difference between two components. The correction factor is a function of physical properties formed by the difference of two components. Its absolute value increases with the enhancement of the difference in the character of components. It can be either positive or negative and the rules for selecting the sign of correction factor have been analyzed. Results are in good agreement with the experimental values.

Effect of Zr on microstructure and mechanical properties of binary TiAl alloys

Ti43Al and Ti47Al alloys with different contents of zirconium were prepared by non-consumable vacuum arc melting furnace.The microstructure and mechanical properties were investigated.The results showed that Zr had no obvious effect on microstructure morphology of Ti43Al,while that of Ti47Al was modified from dendrites into equiaxed grains.The addition of Zr could refine the grains.Zr promoted the formation ofγphase significantly and the solubility values of Zr inγphase were 12.0%and 5.0%(molar fraction)in Ti43Al and Ti47Al,respectively.Zr-richγphase mainly formed throughβ→γin Ti43Al-xZr(molar fraction,%)andβ→α→γin Ti47Al-xZr(molar fraction,%).Fine-grain strengthening and solution strengthening were beneficial to improving the compressive strength while severe micro-segregation was detrimental to compressive properties.Large solubility of Zr was bad for ductility of alloys as well.The maximum compressive strengths of Ti43Al-xZr and Ti47Al-xZr were 1684.82 MPa(x=5.0%)and 2158.03 MPa(x=0.5%),respectively.The compressive strain fluctuated slightly in Ti43Al-xZr and reached the maximum value of 35.24%(x=0.5%)in Ti47Al-xZr.Both alloys showed brittle fracture.

Phase-field numerical simulation of three-dimensional competitive growth of dendrites in a binary alloy

The normal vector of migration direction in the solid-liquid interface of dendrites was used to describe the phase-field governing equation. By using the three angles formed by the normal vector for the migration direction of the dendritic growth interface and the coordinate axes of the simulation region, the authors expressed the interfacial anisotropy equation, and built a phase-field model for the competitive growth of multiple grains. Taking a Al-2%mole-Cu binary alloy as an example, the competitive growth of multiple grains during isothermal solidification was simulated by applying parallel computing techniques. In addition, the phase field simulation results were verified by the experimental method. The simulation results show that the competitive growth of equiaxed dendrite is divided into two types: the first occurs during the process of competitive growth, the tips of primary dendrite on different grains taking part in the competition stop growing in their optimal growth direction; the second also occurs during competitive growth, the tips of primary dendrite which participate in the competition on different grains never stop growing in their optimal growth direction. The dendritic morphologies of the first competition growth type are divided into two types. Primary dendrites of grains taking part in the competition stop growing in their optimal growth direction and the competition plane enlarges when neither one wins the competition. However, when one wins the competition, the primary dendrites of grains with superiority go through the blocking grains and continue to grow in their optimal growth direction. The primary dendrites of inferior grains stop growing in their optimal growth direction and then instead grow in those areas without obstacles. The dendritic morphology of the second competition-growth type is shown to be the deformation of primary dendrites, which are mainly represented as the deflection and bending observed from different views. Compared with the metallographic picture, the simulation results can show the morphology of the competitive growth in all directions, so this simulation method can better characterize the competitive growth process.

Morphological evolution and growth kinetics of Kirkendall voids in binary alloy system during deformation process-Phase field crystal simulation study

The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.

Free dendritic growth model considering both interfacial nonisothermal nature and effect of convection for binary alloy

Considering both the effect of the nonisothermal nature of the interface as well as the effect of forced convection,an extended free dendritic growth model for binary alloys was proposed.Comparative analysis indicates that the effect of convection on solute diffusion is more remarkable compared with the ignorable effect of convection on thermal diffusion at low bath undercooling,due to the fact that solute diffusion coefficient is usually three orders of magnitude less than thermal diffusion coefficient.At high bath undercooling,the effect of convection on the dendritic growth is very slight.Furthermore,a satisfying agreement between the model predictions with the available experiment data for the Cu70Ni30 alloy was obtained,especially at low bath undercoolings,profiting from the higher values of interfacial migration velocity predicted by the present model with nonideal fluid case than that predicted by the one ignoring the effect of convection.

Application of the Embedded-atom Method to Liquid Binary Cu-Ni Alloys

A simple analytic embedded-atom model of monoatoms that includes more than nearest neighbours has been extended to study properties of binary liquid Cu-Ni alloys, here the two-body potential between different species of atoms is taken as a function of the two-body potential for the pure metals with a unique form which yields alloy models with the same invariance to electron density transformations as monoatomic models. Faber-Ziman structure factors have been computed by molecular dynamics simulation on the base of this model. The results are in good agreement with experimental data given by Waseda, thus supporting the overall validity of the approach, especially for cross potential of Cu-Ni pair. Further, a detailed description of structure of binary liquid Cu-Ni alloys with different compositions have been performed using pair analysis and bond orientational order method etc., and then the chemical short range order has also been examined to reveal the structural characterization.

Preparation of ferromagnetic binary alloy fine fibers by organic gel-thermal reduction process

Ferromagnetic metal fibers with a high aspect ratio (length/diameter) are attractive for use as high performance electromagnetic interference shielding materials. Ferromagnetic binary alloy fine fibers of iron-nickel, iron-cobalt and cobalt-nickel were prepared by the organic gel-thermal reduction process from the raw materials of critic acid and metal salts. These alloy fibers synthesized were featured with a diameter of about 1 μm and a length as long as 1 m. The structure, thermal decomposition process and morphologies of the gel precursors and fibers derived from thermal reduction of the gel precursors were characterized by FTIR, XRD, TG/DSC and SEM. The gel spinnability largely depends on the molecular structure of metal- carboxylates formed during the gel formation. The gel consisting of linear-type structural molecules shows good spinnability.

COLOR CHARACTERISTICS OF BINARY COPPER-BASE ALLOYS

The effect of Al, Zn, Sn, Mn, Si and Ni on the color characteristics of binary copper-base alloys has been researched systematically and quantitatively. The results show that all alloying elements decrease the red content of an alloy at different levels but have different effects on the yellow color. Al and Zn enhance the yellow content of an alloy, whereas Sn, Mn, Si and Ni decrease the yellow content. When the alloys with different karat gold colors are imitated, Al and Zn are the most important color mixing elements and Sn, Mn, Si and Ni can be used as auxiliary.