Phase-field modeling of isothermal dendritic coarsening in ternary alloys

The process of isothermal dendritic coarsening in a Ni–Al–Nb ternary system is simulated by using the phase-field method. The coarsening behaviors and coarsening mechanisms with different solid fractions f_S are investigated in detail. Simulated results show that, as f_S increases from 64% to 88%, the coarsened morphology of the liquid phase varies from connected plate to rod-like shape, which is similar to the lamellar to rod transition in eutectics due to the interface energy. Simulated results also indicate that the dendritic isothermal coarsening mechanisms are dominated by remelting of the third arms, coalescence and smoothing in the case of low solid fraction, while in the case of high solid fraction, coalescence, smoothing, Rayleigh instability, rounding and shrinking away of small liquid droplets are the main mechanisms of dendritic coarsening. The increase of liquid diffusion coefficient D^L will also trigger the Rayleigh instability to accelerate the morphology transition from plate to cylindrical for the liquid phase.     

Phase-field modeling of coring structure evolution in Pu–Ga alloys

During casting of Pu–Ga alloys, the huge difference in Ga diffusivity in ε (body centered cubic) and δ (face centered cubic) phases results in the formation of coring structures which consist of Ga-rich cores with Ga-poor edges. The elastic interaction among different oriented δ grains, matrix ε and diffusive Ga atoms may lead to a directional diffusion and δ grain growth. A phase-field model for modeling the coring structure evolution and Ga homogenization kinetics in three dimensions is developed. The effects of diffusivity inhomogeneity, internal stresses and cooling rate on the coring structure evolution are studied.     

晶体相场法模拟晶界预熔区液相熔池的演化

预熔是指晶体在低于熔点温度时,晶界处预先出现类似液体而块体仍为晶体状的现象。采用晶体相场法研究原子密度对晶界预熔的影响。结果表明:晶界处液相熔池的早期演化主要涉及4个形态特征:固-固状态→小液滴状态→较大的液相熔池→均质熔融层。通过对比不同平均原子密度下的微观结构和能量变化,表明平均原子密度对液相池的形态特征敏感。二维与三维模拟结果表明,平均原子密度的降低能抑制刃型位错聚集区域中原子的结晶相特征,这有助于液相熔池的形成。从热力学的角度验证平均原子密度与液相熔池宽度之间的关系,在一定程度上为后续施加高温应变提供前提条件。     

Phase-field modeling of dendritic growth of magnesium alloys with a parallel-adaptive mesh refinement algorithm

A two-dimensional phase field (PF) model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement (Para-AMR) algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.     

Thermodynamics of phosphorus grain boundary segregation in 17Cr12Ni austenitic steel

The paper presents results of thermodynamic analysis of phosphorus grain boundary segregation in 17Cr12Ni austenitic steel annealed for 1000 h at 923, 973 and 1073 K. With respect to values of compensation temperature τ_P=930 K and segregation enthalpy ΔH_P⁰=−14.1 kJ/mol the analyzed interfaces were considered to be special grain boundaries.     

Thermodynamics and kinetics of grain boundary triple junctions in metals: Recent developments

This paper assesses the contribution of grain boundary triple junctions to the driving force for grain growth and the “energetic” effect of boundary junctions on grain growth in nanocrystalline materials. The first measurement of grain boundary line tension allows the quantitative estimation of the fraction of the driving force due to boundary triple junctions. For polycrystals with a grain size in the range ～50 nm, it is comparable with the driving force from grain boundaries.     

Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

The energies of a set of 388 distinct grain boundaries have been calculated based on embedded-atom method interatomic potentials for Ni and Al. The boundaries considered are a complete catalog of the coincident site lattice boundaries constructible in a computational cell of a prescribed size. Correlations of the boundary energy with other boundary properties (disorientation angle, Σ value, excess boundary volume and proximity of boundary normals to 〈1 1 1〉) are examined. None of the usual geometric properties associated with grain boundary energy are useful predictors for this data set. The data set is incorporated as supplementary material to facilitate the search for more complex correlations. The energies of corresponding boundaries in Ni and Al are found to differ by approximately a scaling factor related to the Voigt average shear modulus or C₄₄. Crystallographically close boundaries have similar energies; hence a table of grain boundary energies could be used for interpolation.     

Improvement in the ductility of molybdenum alloys due to grain boundary segregation

An improvement in the tensile ductility from the traditional 3–20% in 6.35-mm-thick molybdenum weldments has been achieved through the addition of Zr, Al, C and B at the ppm level. Atom probe tomography has revealed segregation of Zr, B and C to and depletion of O at the grain boundaries in the base metal and the heat affected zone.     

Phase field modeling of grain boundary migration with solute drag

The grain boundary (GB) motion in the presence of GB segregation is investigated by means of phase field simulations. It is found that the solute concentration at the moving GB may increase with increasing velocity and becomes larger than the equilibrium value, which is unexpected according to the solute drag theory proposed by Cahn, but has been observed in some experiments. A non-linear relation between the driving force (curvature) and the GB velocity is found in two cases: (1) the GB motion undergoes a transition from the low-velocity extreme to the high-velocity extreme; (2) the GB migrates slowly in a strongly segregating system. The first case is consistent with the solute drag theory of Cahn. As for the second case, which is unexpected according to solute drag theory, the non-linear relation between the GB velocity and curvature comes from two sources: the non-linear relation of the solute drag force with GB velocity, and the variation in GB energy with curvature. It is also found that, when the diffusivity is spatially inhomogeneous, the kinetics of GB motion is different from that with a constant diffusivity.     

Phase-field simulations of solidification of AI-Cu binary alloys

The dendrite growth process during the solidification of the Al-4.5 %Cu binary alloy was simulated using the phase-field model, proposed by Kim et al. Solute diffusion equation and heat transfer equation were solved simultaneously. The effects of the noise on the dendrite growth, solute and temperature profile in the undercooled alloy melt were investigated. The results indicate that the noise can trigger the growth of the secondary arms, and increase the highest temperature and solute concentration, but not influence the tip operating state. The solute and temperature gradients in the tip are the highest.     

Phase-field simulations of solidification of Al-Cu binary alloys

The dendrite growth process during the solidification of the Al-4.5%Cu binary alloy was simulated using the phase-field model, proposed by Kim et al. Solute diffusion equation and heat transfer equation were solved simultaneously. The effects of the noise on the dendrite growth, solute and temperature profile in the undercooled alloy melt were investigated. The results indicate that the noise can trigger the growth of the secondary arms, and increase the highest temperature and solute concentration, but not influence the tip operating state. The solute and temperature gradients in the tip are the highest.     

Thermodynamic aspects of the grain boundary segregation in Cu(Bi) alloys

The grain boundary segregation of Bi in dilute polycrystalline Cu–Bi alloys was systematically studied as a function of temperature and composition. The temperature dependencies of the Gibbsian excess of Bi at the grain boundaries exhibited discontinuous changes at the temperatures close to, but different from the bulk solidus temperatures. The observed segregational phase transition was interpreted in terms of prewetting model.     

Analysis of grain growth process in melt spun Fe-B alloys under the initial saturated grain boundary segregation condition

A grain growth process in the melt spun low-solid-solubility Fe-B alloys was analyzed under the initial saturated grain boundary (GB) segregation condition. Applying melt spinning technique, single-phase supersaturated nanograins were prepared. Grain growth behavior of the single-phase supersaturated nanograins was investigated by performing isothermal annealing at 700 °C. Combined with the effect of GB segregation on the initial GB excess amount, the thermo-kinetic model [Chen et al., Acta Mater. 57 (2009) 1466] was extended to describe the initial GB segregation condition of nanoscale Fe-B alloys. In comparison of pure kinetic model, pure thermodynamic model and the extended thermo-kinetic model, an initial saturated GB segregation condition was determined. The controlled-mechanism of grain growth under initial saturated GB segregation condition was proposed using two characteristic annealing times (t₁ and t₂), which included a mainly kinetic-controlled process (t ≤ t₁), a transition from kinetic-mechanism to thermodynamic-mechanism (t₁ < t < t₂) and pure thermodynamic-controlled process (t ≥ t₂).