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Precipitation of a stable quasicrystalline i-phase has been discovered in a Mg-6Zn-3Al (wt%, ZA63) magnesium alloy, possibly a first involving a stable i-phase. Dissolution of i-phase solidified at grain boundaries leads to precipitation in the Mg-matrix during cooling due to a solvus boundary observed by phase diagram calculation. Phase transformation, nucleation characteristics, morphology and interfaces with the matrix have been studied. Differential scanning calorimetry (DSC) and in-situ X-ray diffraction (XRD) showed dissolution and precipitation of i-phase during heating and cooling cycles, forming a hysteresis between about 250 and 325°C. The quasilattice parameter a R of i-phase was calculated to be 5.1704 A at room temperature, close to the c-parameter 5.1831A of the Mg-matrix. At dissolution/nucleation, the diffraction peaks of i-phase were sharper, (quasi)lattice constants a R and c Mg become equal to each other (5.225A) and the lattice strain in the matrix was minimized. Precipitation occurred with a fivefold plane parallel to a matrix pyramidal {0111} plane, which gave rise to two possible orientation relationships (OR): 5f||[0001] (OR3’) and 2f||[0001] (OR1). Presence of both ORs in the same precipitates generated icosahedral twinning. The precipitates were faceted sharply on fivefold, twofold and threefold planes which were on basal, prismatic and pyramidal planes of the Mg matrix. Results suggest the OR selection to be nucleation temperature dependent. Based on the crystallographic relationships, 3-dimensional tiling model of icosahedral lattice has been used to model lattice match with the matrix.

A thermal fluctuation-based nucleation model for use in a phase-field model is proposed. In the model, a normally distributed random temperature fluctuation is imposed on a calculation system, and if a given grid temperature is lower than the average, the undercooling is converted to an increase in the crystallized/precipitated phase fraction. The conversion coefficient is derived as a function of a phase-field critical value for nucleation. The idea of a threshold of nucleation for the phase field, i.e., a critical value, is introduced first in the present study. The model is applied to homogeneous nucleation during solidification in a supercooled pure metal, and a reasonable nucleation probability curve is successfully obtained from the numerical calculations. An application to the homogeneous nucleation of an Al-Cu alloy is also demonstrated.

We developed a Ginzburg-Landau model of long-period stacking order (LPSO) lamellar structure observed in magnesium alloys. Contrary to other models, we do not treat LPSO as a homogeneous stoichiometric phase but as a chemically modulated heterogeneous structure of parallel plates of two phases with different compositions and degrees of ordering. The Turing instability that is, existence of a finite-wavelength linear-instability mode was identified as the origin of formation of LPSO structure. The process of LPSO formation can be understood as a process of finding local minima and saddle points on the free energy landscape of the system. The model explained transformation between the two most common LPSO structures, 18R and 14H, and their general resistance to coarsening. The model can be used for the design of new LPSO materials.

To evaluate the reliability of metal-carbon eutectic systems as fixed points for the next generation of the international temperature scale, the effect of the eutectic microstructure on the temperature at the solid/liquid (s/l) interface during solidification and melting is preliminarily investigated using a multi-phase-field model. First, the effects of furnace temperature, lamellar spacing, and interface energy on the average temperature of the s/l interface are studied in the solidification process. With increased furnace undercooling, the s/l interface temperature was found to decrease. Calculated eutectic microstructures are then adopted as initial conditions for a melting simulation. The interface undercooling during melting is observed to be smaller than that observed during solidification. This difference in interface undercooling is attributed to the solute/solvent concentration profiles in the liquid phase near the s/l interface being different for melting and solidification.

It is very important to understand the development of the microstructure in the interdiffusion zone between coatings and superalloy substrates for designing bond coat materials. In this study, the reaction-diffusion phenomena in the Ir-coating/Ni – Al binary substrate system are simulated using the phase-field model. The thermodynamic database developed based on the CALPHAD method is directly incorporated in the simulation. The effect of coating thickness on the growth of the secondary precipitated -phase is discussed. In the case of a semi-infinite system, the thickness of the -phase increases proportionally with the square root of time. In the case of a thin (1 thick) coating, inconstant -phase growth is observed. It is suggested that the phase growth is related to the change in the -phase fraction, which is derived from a thermodynamic line calculation from the substrate composition to pure Ir.

The concentration profiles of thin-film Pt/bulk Ni coatings annealed at 1150, 1250 and 1300?C for different time were measured by means of electron probe microanalysis. The corresponding interdiffusion coefficients were then determined using the thin-film solution. The calculated concentration profiles based on the presently obtained interdiffusion coefficients agree well with the experimental ones, but better at a higher temperature or a longer time. The comparison between the presently measured concentration profiles and the DICTRA simulated ones indicates that it is promising to apply the well-established atomic mobility databases due to bulk diffusion information in coating systems with some simple modifications for diffusivities.

The thermodynamic assessment of the Al–Ir binary system was performed using the CALPHAD technique. The B2-AlIr phase was described, using the two sublattice model with the formula (Al,Ir,V a) 1/2 (Al,Ir,V a) 1/2 , while Al 9 Ir 2 , Al 3 Ir, Al 13 Ir 4 , Al 45 Ir 13 , Al 28 Ir 9 , and Al 2.7 Ir compounds were treated as stoichiometric compounds. The fcc-based phases (L1 0 -AlIr, L1 2 -Al 3 Ir, L1 2 -AlIr 3 and A1) were described using the four sublattice model with the formula, (Al,Ir) 1/4 (Al,Ir) 1/4 (Al,Ir) 1/4 (Al,Ir) 1/4 . From ab initio calculations (VASP) the formation enthalpies of the stable/metastable intermetallic phases involved in the Al–Ir system were estimated. The thermodynamic quantities, such as the phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases, were calculated using the obtained parameter set, and agree well with experimental data.

Al-rich portion of the Ir–Al phase diagram has been investigated with 10 alloys by means of differential thermal analysis, X-ray diffraction, scanning electron microscopy, inductivity coupled plasma spectrometry and electron probe microanalysis. Invariant reactions are observed: L ↔ AlIr + Al 2.7 Ir, L + Al 2.7 Ir ↔ Al 3 Ir, L + Al 3 Ir ↔ Al 13 Ir 4 , L + Al 13 Ir 4 ↔ Al 9 Ir 2 . Although the eutectic reaction, L ↔ AlIr + Al 2.7 Ir, cannot be regarded as definitely established by previous research, it is confirmed in the present research. Liquidus curve has been determined for the first time for Al-rich alloy (Ir ≤ 33.0 at%). The Ir–Al binary phase diagram has been modified based on these experimental observations.

Ternary interdiffusion in L12–Ni3Al with ternary alloying additions of Ir and Ta was investigated at 1473 K using solid-to-solid diffusion couples. Average ternary interdiffusion coefficients were determined from an integration of interdiffusion fluxes calculated directly from experimental concentration profiles. The magnitude of D ˜ ¯ NiNi and D ˜ ¯ AlAl coefficients was determined to be much larger than that of D ˜ ¯ IrIr and D ˜ ¯ TaTa coefficients. Ir substituting in Ni-site influenced the interdiffusion of Ni significantly, and D ˜ ¯ NiIr Al coefficients were determined to be large and positive. On the other hand, Ta substituting for Al influenced the interdiffusion of Al significantly, and D ˜ ¯ AlTa Ni coefficients were determined to be large and positive. An excellent agreement was found with ternary interdiffusion coefficients determined by Boltzmann–Matano analysis. Profiles of concentrations and interdiffusion fluxes were also examined to estimate binary interdiffusion coefficients in Ni3Al, and tracer diffusion coefficients of Ir (14.7 × 10−16 ± 1.4 × 10−16 m2/s) and Ta (2.6 × 10−16 ± 2.4 × 10−16 m2/s) in Ni3Al.

The combustion synthesis of Al50Ir48Ni2 (at.%) was conducted at different heating rates in both a differential scanning calorimetry (DSC) chamber and a vacuum furnace. It was found that a higher heating rate, a sufficient amount of reactant powder, and effective control of the heat loss facilitated the complete reaction and resulted in combusted single IrAl phase products. Otherwise, multiphase products containing IrAl, unreacted Ir, and Al3Ir were synthesized. The reactions involved in different processes were discussed in terms of the thermal competition between heat generation and loss during the reaction. All ignition temperatures were below 773 K, indicating that the combustion reaction occurs at the solid–solid state. With increasing heating rate, the ignition temperature increased while the product density decreased.

Average ternary interdiffusion coefficients in Ni3Al with Ir additions have been determined using solid-to-solid diffusion couples annealed at 1200°C for 5 hours. Disc shaped alloy specimens were prepared by the vacuum arc melting at compositions of Ni-24Al, Ni-25Al, Ni-26Al, Ni-23.5Al-1Ir, Ni-24.5Al-1Ir, Ni-23Al-2Ir, Ni-23Al-2Ir, Ni-24Al-2Ir, Ni-23Al-3Ir (at.%). Surfaces of alloys were polished down to 1200 grit and diffusion couples were assembled in Si3N4 jig for initial bonding heat treatment at 1200°C for 0.5 hours. Additional diffusion anneal was carried out at 1200°C for 4.5 hours outside of Si3N4 jig so that diffusion couples can be water quenched. Concentration profiles of individual components were measured by electron probe microanalysis using pure standard of Ni, Al and Ir. Interdiffusion flux of individual component was determined directly from the experimental concentration profiles, and the moments of interdiffusion flux were examined to calculate the average ternary interdiffusion coefficients, D˜ ij k either with Al or Ni as dependent component. Calculated interdiffusion coefficients suggest that Ir-alloyed Al2O3-forming oxidation resistant coatings would be beneficial to reduce the interdiffusion flux of Ni from superalloy substrates to the coating, and reduce the interdiffusion flux of Al from the coating to the superalloy substrate.

Thermodynamic assessments of the Ni–Zr and the Cu–Zr binary systems were carried out using thermodynamic properties obtained in a wide range of temperatures. The associated solution model was applied to describe the short range ordering in the liquid. The critical cooling rates for the glass formation were estimated from the optimized parameter set, and compared with experimental data. In both the Cu–Zr and the Ni–Zr systems, the minimum critical cooling rate was found in alloys with compositions around 35 at.% Zr. Smaller critical cooling rates in the Cu–Zr system than those in the Ni–Zr alloys suggest that Cu–Zr alloys have higher GFA than Ni–Zr alloys.

The thermodynamic assessment of the Al-Ir binary system, one of the key sub-systems of the Ir-based alloys, was performed using the CALPHAD technique. The AlIr(B2) phase was described using the two sublattice model with the formula (Al,Ir)0.5(Ir,Va)0.5, while other intermetallic phases were treated as stoichiometric compounds. The calculated data of the phases in the Al-Ir system can be used to accurately reproduce experimental data, such as phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases.

A combination of macroscale solidification simulation and phase-field calculation is employed to predict the volume fraction of the eutectic phase in Sn-4.0 mass% Ag-XCu solder alloys (X=0.5–1.1 mass%). The solidification simulation incorporates the cooling rate in the phase-field simulation. We assume the residual liquid solidifies as eutectic phase when the driving force for the nucleation of Cu6Sn5 amounts to a critical value, which is determined based on the experimental data. Though the calculation results depend on the experimental data, the obtained fractions are about 40% for 0.5 mass% Cu and more than 90% for 1.1 mass% Cu alloy, which shows good agreement with the experimental data.

Thermodynamic assessment of the Cu–Zr binary system was carried out using thermodynamic data obtained over a wide range of temperatures. The associated solution model was applied to describe the short range ordering in a liquid. The glass transition was treated as a second order transition with Hillert–Jarl functions. The driving force for crystallization and time–temperature–transformation (TTT) curves were estimated from the optimized parameter set, and compared with experimental data and the results of previous thermodynamic assessments. Taking into account thermodynamic data at low temperatures, the calculated driving force was found to be lower than the results of previous assessments. Consequently, the nose of the TTT curve was shifted to a longer time.

To protect various gas turbine components against high temperature in the hot sections of power generation plants and aircraft engines, thermal barrier coatings (TBCs) have been developed and widely used. Conventional TBCs consist of a MCrAlY bond coating for oxidation resistance and a ceramic top coating for thermal insulation. High quality coatings of MCrAlYs have been produced mostly by low pressure plasma spraying but other more economical processes are also used depending on the operating conditions of the component to be coated. In this study, CoNiCrAlY powders were deposited on Inconel 718 substrate with 3 types spraying system, i.e., low pressure plasma spraying, high velocity oxy-fuel spraying, and atmosphere plasma spraying. The specimens without top ceramic coating were isothermally tested for up to 100 hrs in air at 1373 K and mass gain of the coatings was measured. Microstructure of the coating cross sections and the surface oxides were observed with SEM. Moreover, phase changes during the oxidation test were investigated with calculated phase diagrams for the CoNiCrAlY alloy. [doi:10.2320/matertrans.47.1638]

An IrAl intermetallic compound was fabricated by a self-propagating high-temperature synthesis (SHS) process. Single phase IrAl pellets were produced; however, the IrAl coatings produced, with the aid of numerical simulations, contained unreacted Ir and was found to have poor adhesion. Nevertheless, this study confirmed that IrAl coatings can be obtained using the SHS process.

Using thermodynamic data obtained over a wide range of temperatures, a thermodynamic assessment of the Ni–Zr system was carried out. The associated solution model was applied to describe the short range ordering in the liquid, and the glass transition was treated as a second order transition, using the Hillert–Jarl functions. The driving force of crystallization, and the time–temperature–transformation (TTT) curves were estimated from the optimized parameter set, and compared with experimental data and the results of previous thermodynamic assessments. Taking into account the low temperature thermodynamic data, the calculated driving force was found to have decreased compared to the previous assessments. Consequently, the nose of the TTT curve was shifted to higher times.

We present a eutectic phase-field model, developed by extending the interface field method (Steinbach and Pezzolla, Physica D 134 (1999) 385) under a condition that coexisting phases at a given point have an equal chemical potential difference between solute atom and solvent atom. Also an anisotropic eutectic phase-field equation is derived explicitly. The equilibrium interface geometries, calculated using the isotropic and anisotropic models, at a triple junction under a thermal gradient are in good agreement with the exact solutions, indicating the maintenance of mechanical equilibrium at the junction. The model successfully reproduces a variety of eutectic lamellar patterns observed in experiments on directional solidification of thin film CBr4–C2Cl6 organic alloys, under the real experimental conditions without any fitting parameters. Most of the characteristics of the pattern change with lamellar spacing in both eutectic and hypereutectic alloys are in good agreement with experimental observations.

A combination of macroscale solidification simulation and phase-field calculation is employed to predict solute segregation behavior during soldering using a Sn-Bi alloy. The solidification simulation predicts that the final solidified point appears at the edge of the fillet adjacent to the substrate side. The calculation incorporates the cooling rate in the phase-field simulation. The phase-field calculation suggests that microsegregation will not always lead to a thin liquid film at the solder/Cu-land interface and thus mechanical weakness.

Recent progress on the thermodynamic databases of calculated phase diagrams in microsolders and Cu-based alloys is presented. A thermodynamic tool, Alloy Database for Microsolders (ADAMIS), is based on comprehensive experimental and thermodynamic data accumulated with the calculation of phase diagrams (CALPHAD) method and contains eight elements, namely, Ag, Bi, Cu, In, Sb, Sn, Zn, and Pb. It can handle all combinations of these elements and all composition ranges. The elements of Al and Au have also been added to ADAMIS within a limited range of compositions. Furthermore, a database of Cu-based alloys, including binary (Cu-X), ternary (Cu-Fe-X, Cu-Ni-X, and Cu-Cr-X), and multicomponent (Cu-Ni-Cr-Sn-Zn-Fe-Si) systems, has also been developed. Typical examples of the calculation and application of these data-bases are presented. These databases are expected to be a powerful tool for the development of Pb-free solders and Cu substrate materials as well as for promoting the understanding of the interfacial phenomena between them in electronic packaging technology.

A phase-field model coupled to real thermodynamic data in which the vanishing kinetic coefficient condition is proposed. The validity of the model is examined by comparing the calculated result of the equilibrium state with theoretical predictions for both one and two-dimensional simulations. Numerical simulations of micro-segregation and isothermal dendrite growth is presented to demonstrate the effectiveness of the model.

Microstructure evolution during the rapid solidification of Fe-C alloys is simulated using the phase-field model for binary alloys with thin interface limit parameters. The heat transfer equation i...

The phase-field models for binary and ternary alloys are introduced, and the governing equations and phase-field parameters for dilute alloys are derived at a thin interface limit. The phase-field simulations on isothermal dendrite growth for Fe-C, Fe-P and Fe-C–P alloys are carried out and the effect of the ternary alloying element on dendrite growth is examined. The secondary arm spacing for Fe-C, Fe-P and Al–Cu alloys is numerically predicted using the phase-field model and compared to the experimental data. The change in the arm spacing, and the exponent of local solidification time depending on alloy is systematically examined by imposing artificial set of physical properties. The phase-field simulation for the microstructure evolution during rapid solidification is also successfully carried out. Through the numerical examples, the wide potentiality of the phase-field model to the applications on solidification has been demonstrated.

Microstructure evolution during the rapid solidification of Fe-C and Fe-C-P alloys is simulated using the phase-field model for alloys with thin interface limit parameters. Heat transfer equation is solved simultaneously to study the heat flow and the effect of latent heat generation on the microstructure. The calculations have been carried out using a double grid method and parallel computing technique. The competitive growth of growing cells is reproduced, and the cellular/dendritic transition is also observed. Since there is a negative thermal gradient in front of a leading tip, the growth can be regarded as unidirectional free dendrite growth. The microstructure changes depending on the preferred growth orientation and impurity are also studied. The secondary arms grow preferably towards inside of the melt and develop well with increase of the tilted angle. The secondary and primary arm spacing decrease by the small amount of phosphorus addition. The time change of averaged surface temperature depending on the initial undercooling shows that the surface undercooling is always observed even when the initial value is zero.

The recent development of the phase-field models for solidification and their application examples are briefly reviewed. The phase-field model is firstly proposed for pure material systems and then extended to binary alloy, multi-phase and multi-component systems theoretically. Though the calculation conditions are limited due to the sharp interface limit parameters in the early stage, it is widened in the thin interface limit model. The development of the phase-field model is summarized from a viewpoint of the formulation of phase-field equation and parameters. The important studies and the latest results such as application examples of free dendrite growth, directional solidification, Ostwald ripening, interface-particle interaction and multi-phase simulation are mentioned. Finally future works of the phase-field model are prospected.

The Ostwald ripening phenomena is studied using a phase-field model. The phase-field parameters are obtained at a thin interface limit proposed by Kim et al. It is shown that small solid particles preferably melt out, and large particles grow and agglomerate due to the curvature undercooling. Calculation results are consistent with the LSW rule. The rate constant of average particle radius is estimated as 0.57 at 0.2 solid fraction. The change in shape of the invariant particle size distribution due to finite volume fraction agrees with experiment and a statistical model. The difference of the calculation results by Diepers et al. and by the present work is discussed. The change in the shape of the invariant size distribution depending on solid fraction is also shown. The shape becomes more wide and symmetry with increase of the solid fraction.

The secondary arm spacing in Fe-C, Fe-P, Fe-C-P and Al-Cu alloys are numerically predicted using a phase-field model. The calculated arm spacing and the exponent of the local solidification time are compared with the experimental data. Each calculated exponent differs depending on Fe-base or Al-base alloys. The change in the arm spacing and the exponent depending on alloy is systematically examined by the imposing artificial sets of physical properties. Interface energy and solute diffusivity in liquid change the arm spacing but not the exponent. On the other hand, liquidus slope and partition coefficient change both the arm spacing and the exponent. The change of the exponent is discussed by examining the process of deriving the value of 1/3 in the analytical model by Kattamis et al. and the expression for the estimation of the exponent is proposed.

The particle/interface problem is numerically analyzed using a phase-field model in thin interface limit. A new double-well potential function in free energy density of the alloy is defined using a dilute solution approximation. With the function, a negative value of double-well potential height is usable and the mesh size restriction is largely relaxed. A pushing force for alloy systems is also introduced so as to relate to the interface energy change caused by the deformation of interface shape. With the pushing and drag forces calculated from the interface shape, the acceleration and velocity of the particle are estimated and the particle movement relative to the interface is analyzed. Using the model, the particle pushing and engulfment behaviors are successfully reproduced for the system of Fe-C alloys and an alumina particle. The critical velocities for the pushing/engulfment transition are determined for the particles with different diameters. The effect of initial carbon content on critical velocity is also examined and discussed in terms of the pushing force.

The phase-field model for binary alloys by Kim et al. is briefly introduced and the main difference in the definition of free energy density in interface region between the models by Kim et al. and by Wheeler et al. is discussed. The governing equations for a dilute binary alloy are derived and the phase-field parameters are obtained at a thin interface limit. The examples of the phase-field simulation on Ostwald ripening, isothermal dendrite growth and particle/interface interaction for Fe–C alloys are demonstrated. In Ostwald ripening, it is shown that small solid particles preferably melt out and then large particles agglomerate. In isothermal dendrite growth, the kinetic coefficient dependence on growth rate is examined for both the phase-field model and the dendrite growth model by Lipton et al. The growth rate by the dendrite model shows strong kinetic coefficient dependence, though that by the phase-field model is not sensitive to it. The particle pushing and engulfment by interface are successfully reproduced and the critical velocity for the pushing/engulfment transition is estimated. Through the simulation, it is shown that the phase-field model correctly reproduces the local equilibrium condition and has the wide potentiality to the applications on solidification.

In this study we presented a double-grid method for efficient computation of complex dendritic pattern evolving in a large scale solidifying system of pure undercooled melt. The method, which is based on the large difference in phase-field diffusivity and thermal diffusivity in pure material, enables us to use a large time step. The phase field was calculated adaptively only on the grids within the interfacial region and also the thermal field was calculated only within the thermal boundary layer. The computation showed that the complex dendritic patterns with well-developed tertiary arms can be obtained even in a personal computer with a moderate memory space. The computational efficiency of this method, the competitive growth and coarsening of the secondary arms and the tertiary branching from secondary arms were discussed.

The first trial for numerical simulations of solid/liquid interface shape change around an insoluble particle for Fe-C alloys has been carried out. Real-time interface shape evolution during unidirectional solidification has been calculated using the phase-field model with parameters determined by thin interface limit condition. The interface becomes concave near the particle because of solute enrichment in the liquid between interface and a particle. Liquid trench ahead of the particle and thin liquid film along its surface remain until the late stage of solidification. The results are qualitatively in good agreement with the reported experimental observations. The effects of interface velocity and initial carbon content on the interface shape are also examined. Using the obtained interface shapes, the forces to the particle are estimated and the particle engulfment behavior by interface is discussed.

To evaluate the reliability of metal-carbon eutectic systems as fixed points for the next generation of high-temperature standards the effect of thermodynamic properties related to the shape of eutectic phase diagram on the freezing temperature is investigated within the context of the numerical multi-phase-field model. The partition coefficient and liquidus slopes of the two solids involved in the eutectic reaction are varied deliberately and independently. The difference between the eutectic temperature and the freezing temperature is determined in dependence of the solid/liquid (s/l) interface shape and concentration. Where appropriate reference is made to the Jackson-Hunt analytical theory. It is shown that there are mainly two typical conditions to decrease the undercooling: 1) a small liquidus slope and 2) the associated difference between the eutectic composition and the liquid composition during solidification.

Ternary interdiffusion in L12-Ni3Al with ternary alloying addition of Re was investigated at 1473 K using solid-to-solid diffusion couples. Interdiffusion flux of Ni, Al, and Re were directly calculated from experimental concentration profiles and integrated for the determination of average ternary interdiffusion coefficients. The magnitude of main interdiffusion coefficients \( \bar{\tilde{D}}_{\text{NiNi}}^{\text{Al}} \) and \( \bar{\tilde{D}}_{\text{AlAl}}^{\text{Ni}} \) was determined to be much larger than that of the main interdiffusion coefficient \( \bar{\tilde{D}}_{\text{ReRe}}^{\text{Al (or Ni)}}. \) A moderate tendency for Re to substitute for Al sites was reflected by its influence on interdiffusion of Al, quantified by large and positive \( \bar{\tilde{D}}_{\text{AlRe}}^{\text{Ni}} \) coefficients. Similar trends were observed from ternary interdiffusion coefficients determined by Boltzmann-Matano analysis. Profiles of concentrations and interdiffusion fluxes were also examined to estimate binary interdiffusion coefficients in Ni3Al, and tracer diffusion coefficients of Re (5.4 × 10−16 ± 2.3 × 10−16 m2/s) in Ni3Al.