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 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.

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.

CORRELATION BETWEEN CONSTITUENT AND SPUTTERING RATE OF BINARY ALLOYS IN GLOW DISCHARGE LAMP

Investigation was made of the sputtering rate in glow discharge lamp with relaion to constituent of 25 different specimens of 6 binary systems.namely,Cr-Fe,Bi-Sb,Cu-Zn, Ag-Cu,Al-Zn and Cd-Sn.by measuring mass loss sfter each sputtering under constant Ar pressure and voltage applicd.The correlation.in general,between sputtering rate and concentration of constituent of these non-intermetallic binary alloys obeys the hyperbolic law under steady state,that may be approximately regarded as linear correlation only on certain special condition if the two components of the alloys with similar sputte ringrates.

Relationship between the types of binary alloy phase diagrams of Ⅷ and IB group elements and the Mendeleev numbers

The relationship between the types of binary alloy phase diagramsof VIII and Ib group elements and the Men- deleev numbers wasdiscussed for the first time using the VIII and IB group elements assolvent metals (A) and the other elements as solute metals (B),basesd on their alloy phase diagram types. The Mendeleev numbers ofthe solvent metals and the solute metals were expressed as M_A andM_B, respectively. A two-dimension map of M_A/M_B was drawn. It isindi- cated that there is an oblique line in the map, which dividesthe binary alloy phase diagram types of solvent metals into twosymmetry parts, the phase diagram types of the other elements withsolvent metals located at the above or down of the line respectively,while on the line, △M = 0.

Description and Prediction of the Solid Solubilities of Binary Alloys Based on the Actinide Metals

The solid solubilities of 207 binary alloys based on the three actinide metals (Th, U and Pu) at room tem- perature are studied with the two theoretical schemes suggested by one of the present authors (ZBW).The re- sults show that the soluble elements can be distinguished from the insoluble ones by a parabola y_1=a--bx^2 or an ellipse (x_2,-m)~2/c^2+(y_2-n)~2/d^2=l with the total reliabilities of 87.9% and 92.3% respectively for the 207 binary alloys. The contants a and b in the parabola equation, and c, d, m and n in the ellipse equation can be related to some appropriate parameters for each host metal respectively. The reasons are discussed. From the theories the soluble elements in these actinide host metals that have not been measured yet can be predicted in the accuracies of the schemes.

Enthalpies of Formation of Noble Metal Binary Alloys Bearing Rh or Ir

The modified embedded atom method proposed by authors has been applied to calculating the enthalpies of formation of random alloys and the ordered intermetallic compounds for noble metal binary systems bearing Rh or Ir. The present results are in good agreement with those of Miedema theory, available experiments and the first-principles quantum mechanics calculations. The present results indicate that Cu-Rh, Cu-lr, Ag-Rh, Ag-lr, Au-Rh, Au-lr, Pd-Rh and Pd-lr systems are repulsive, however, IMi-Rh, Ni-lr, Pt-lr, Pt-Rh and Rh-lr systems form solid solutions and Ni-Rh, Ni-lr and Pt-Rh show ordering tendency.

Superconducting state parameters of AgxZn1-x and AgxAl1-x binary alloys superconductors

A well-known pseudopotential is used to investigate the superconducting state parameters （SSP）, viz., electronphonon coupling strength, Coulomb pseudopotential, transition temperature, isotope effect exponent and effective interaction strength for AgxZn1-x and AgxAl1-x binary alloys theoretically for the first time. We have incorporated here five different types of the local field correction functions to show the effect of exchange and correlation on the aforesaid properties. Very strong influence of various exchange and correlation functions is concluded from the present study. Comparison with others such experimental values is encouraging, which confirms applicability of the model potential in explaining the superconducting state parameters of binary mixture.

Nonlinear Theory on Dynamic Controlling Interface Patterns DuringSolidification of a Dilute Binary Alloy

In non-equilibrium nonlinear region, the nonlinear equations of time dependence of perturbation amplitude at the solid/liquidinterface during solidification of a dilute binary alloy are established on the base of assuming that there is local equilibrium at the solid/liquid interface and considering that curvature, temperature and composition at the solid/liquid interface which are related to the perturbation amplitude are nonlinear. As a result, patterns at the solid/liquid interface during solidification process, which is from nonsteadystate to steady state can be controlled by these nonlinear equations.

Microstructure,Mechanical Properties and Fracture Behavior of As-Extruded Zn-Mg Binary Alloys

In the present work, Zn-（0-1）Mg（wt%） alloys were prepared by casting and indirect extrusion at 200 and300 ℃, respectively. With Mg addition, both the size and amount of second phase Mg2Zn（11） increased, and the equiaxed grains were significantly refined. The extrusion temperature had little influence on Mg2Zn（11）, but the grains were refined at low extrusion temperature. For the alloys extruded at 200 ℃, as Mg content increased, the tensile yield strength（TYS）increased from 64 MPa for pure Zn to 262 MPa for Zn-1Mg; the elongation increased from 14.3% for pure Zn to 25% for Zn-0.02Mg and then decreased to 5% for Zn-1Mg. For the alloys extruded at 300 ℃, as Mg content increased, the TYS increased from 67 MPa for pure Zn to 252 MPa for Zn-1Mg, while the elongation decreased from 11.7% to 2%. The alloy extruded at 200 ℃ exhibited higher TYS and elongation than the corresponding alloy extruded at 300 ℃. The combination of grain refinement and second phase Mg2Zn（11） contributed to the improvement in the TYS, and the grain refinement played a major role in strengthening alloy. Zn-0.02Mg and Zn-0.05Mg alloys extruded at 200 ℃ show a mixture of cleavage and ductile fracture corresponding to higher elongation, while the other alloys show cleavage fracture.

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 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.

Characterization ofα_(2)Precipitates in Ti–6Al and Ti–8Al Binary Alloys:A Comparative Investigation

Transmission electron microscopy(TEM)and atom probe tomography(APT)techniques were used to investigate the nanoscale orderedα_(2)(Ti_(3)Al)precipitates in Ti–Al binary alloys.Ti–6Al and Ti–8Al binary alloys were solution treated and aged to obtain Widmanstatten microstructure and promoteα_(2)precipitates.The TEM results displayed strong short-range ordering ofα_(2)precipitates in Ti–8Al alloy,while no evidence of the superlattice reflections ofα_(2)in Ti–6Al alloy.The results acquired from APT showed theα_(2)clusters and atoms distribution at the interface between the matrix andα_(2)precipitates.The size and morphology ofα_(2)particles in Ti–8Al alloy,respectively,obtained by TEM and APT are closely consistent.Meanwhile,the APT results displayed tiny size clusters in Ti–6Al alloy,which supposed to give evidence of the initial ordering process ofα_(2)precipitates in the absence of correlative results from TEM.

Phase-Field Modeling of Free Dendritic Growth in Binary Alloy under Forced Flow

A phase-field model(PFM)coupling with phase field,flow field and diffuse equation is presented for simulating isothermal dendrite growth of a nickel-copper alloy under a forced flow.Based on the finite difference method with uniform grid,the C programming code is implemented to complete the phase-field simulations.The simulation results indicate that the interfacial morphology,the symmetry of dendrite formation,the tip growth velocity and the concentration distribution are strongly influenced by the fluid flow.

On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions

A fully implicit numerical method,based upon a combination of adaptively refined hierarchical meshes and geometric multigrid,is presented for the simulation of binary alloy solidification in three space dimensions.The computational techniques are presented for a particular mathematical model,based upon the phase-field approach,however their applicability is of greater generality than for the specific phase-field model used here.In particular,an implicit second order time discretization is combined with the use of second order spatial differences to yield a large nonlinear system of algebraic equations as each time step.It is demonstrated that these equations may be solved reliably and efficiently through the use of a nonlinear multigrid scheme for locally refined grids.In effect this paper presents an extension of earlier research in two space dimensions(J.Comput.Phys.,225(2007),pp.1271–1287)to fully three-dimensional problems.This extension is validated against earlier two-dimensional results and against some of the limited results available in three dimensions,obtained using an explicit scheme.The efficiency of the implicit approach and the multigrid solver are then demonstrated and some sample computational results for the simulation of the growth of dendrite structures are presented.

Corrosion characteristics of single-phase Mg-3Zn alloy thin film for biodegradable electronics

Biodegradable metals as electrodes, interconnectors, and device conductors are essential components in the emergence of transient electronics, either for passive implants or active electronic devices, especially in the fields of biomedical electronics. Magnesium and its alloys are strong candidates for biodegradable and implantable conducting materials because of their high conductivity and biocompatibility, in addition to their well-understood dissolution behavior. One critical drawback of Mg and its alloys is their considerably high dissolution rates originating from their low anodic potential, which disturbs the compatibility to biomedical applications. Herein, we introduce a single-phase thin film of a Mg-Zn binary alloy formed by sputtering, which enhances the corrosion resistance of the device electrode, and verify its applicability in biodegradable electronics. The formation of a homogeneous solid solution of single-phase Mg-3Zn was confirmed through X-ray diffraction and transmission electron microscopy. In addition, the dissolution behavior and chemistry was also investigated in various biological fluids by considering the effect of different ion species. Micro-tensile tests showed that the Mg-3Zn alloy electrode exhibited an enhanced yield strain and elongation in relation to a pure Mg electrode. Cell viability test revealed the high biocompatibility rate of the Mg-3Zn binary alloy thin film. Finally, the fabrication of a wireless heater demonstrated the integrability of biodegradable electrodes and highlighted the ability to prolong the lifecycle of thermotherapy-relevant electronics by enhancing the dissolution resistance of the Mg alloy.

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.

Stability of supersaturated solid solution of quenched Al–X(X 5 Zn, Mg, Cu) binary alloys

In this study, the changing trend of crystal-lattice constant and the influential factors of the stability of supersaturated solid solutions with various alloying additions in the Al–X（Zn, Mg, Cu） binary alloys were investigated. The samples were analyzed using X-ray diffraction（XRD）,X-ray absorption fine structure（XAFS）, and scanning electron microscope（SEM）. It is found that the addition of Cu causes the largest change of crystal-lattice constant of the Al–xCu supersaturated solid solution binary alloy. The most dramatic change occurs in the initial stage of Cu addition.The change is stabilized thereafter. Also, at the same alloying element addition to the Al–X（X = Zn, Mg, Cu）binary alloys, the Al–xCu is the most unstable system.Influential factors of the stability include the lattice constant change and the type of alloying element. The larger the lattice constant changes, the more unstable the supersaturated solid solution is. The alloying element, easy to aggregate, often leads to the solid solution less stable.

PRECIPITATION IN BINARY Al-Li ALLOYS

Studies were carried out on the precipitation in two sets of binary Al-Li alloys by means of hardness tests,DSC analyses and TEM observations.When the alloys were aged for constant time,a peak appeared on the plot of temperature dependence upon their hardness in the range of low temperatures,and the endothermic dissolution peak was quite distinct on the DSC curve also at low temperatures.These are believed that an Li-rich GP zone formed in the al- loys aged at low temperatures,but no more GP zone if aging at elevated temperatures.The hardness of the alloys raises rapidly with coarsening of δ′-phase grains.The two endothermic peaks of δ′ dissolution on the DSC curve relate to the structural adjustment at twice of the δ′ precipitation.The equilibrium δ-phase,being of higher thermal stability,nucleates and grows directly from the supersaturated solid solution with the aid of the gram boundary.