Diffusion Foundations Vol. 15

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Authors: Ying Tang, Qing Chen, Anders Engström
Abstract: In this chapter, we present computational kinetics of diffusion-controlled phase transformations in Cu-based alloys, which becomes possible only most recently due to the establishment of the first atomic mobility database (MOBCU) for copper alloys. This database consists of 29 elements including most common ones for industrial copper alloys. It contains descriptions for both the liquid and Fcc_A1 phases. The database was developed through a hybrid CALPHAD approach based on experiments, first-principles calculations, and empirical rules. We demonstrate that by coupling the created mobility database with the existing compatible thermodynamic database (TCCU), all kinds of diffusivities in both solid and liquid solution phases in Cu-based alloys can be readily calculated. Furthermore, we have applied the combination of MOBCU and TCCU to simulate diffusion-controlled phenomena, such as solidification, nucleation, growth, and coarsening of precipitates by using the kinetic modules (DICTRA and TC-PRISMA) in the Thermo-Calc software package. Many examples of simulations for different alloys are shown and compared with experimental observations. The remarkable agreements between calculation and experimental results suggest that the atomic mobilities for Cu-based alloys have been satisfactorily described. This newly developed mobility database is expected to be continuously improved and extended in future and will provide fundamental kinetic data for computer-aided design of copper base alloys.
Authors: Wei Min Chen, Xiong Yang, Li Jun Zhang
Abstract: Multicomponent diffusion in metallic melts is a very important phenomenon during the solidification/casting process of the metallic alloys. However, there exist extremely limited reports on the diffusivity information in multicomponent metallic liquids. In this chapter, a universal and effective phenomenological approach to predict the composition– and temperature–dependent diffusivities in liquid multicomponent systems is systematically proposed. The presently proposed phenomenological method is then adopted to construct the diffusivity/mobility databases of liquid solders, cemented carbides, Co–Cr–Fe–Mn–Ni high entropy alloys and Al–Ce–Ni alloys. Then, the accurate diffusivity/mobility data are further utilized to perform the simulations of the dissolutions of the substrate into the solders, the gradient layer formation of the cemented carbides, the diffusion behavior of liquid Co–Cr–Fe–Mn–Ni high entropy alloys and the rapid solidification of Al–Ce–Ni system. The simulated results indicate that the presently proposed phenomenological method is applicable to investigate the diffusion kinetics in multicomponent metallic melts.
Authors: Yu Lu Zhou, Xiao Ma Tao, Qing Hou, Yi Fang Ouyang
Abstract: Molecular dynamics (MD) simulations, which treat atoms as point particles and trace their individual trajectories, are always employed to investigate the transport properties of a many-body system. The diffusion coefficients of atoms in solid can be obtained by the Einstein relation and the Green-Kubo relation. An overview of the MD simulations of atoms diffusion in the bulk, surface and grain boundary is provided. We also give an example of the diffusion of helium in tungsten to illustrate the procedure, as well as the importance of the choice of interatomic potentials. MD simulations can provide intuitive insights into the atomic mechanisms of diffusion.
Authors: Kai Ming Cheng, Ji Xue Zhou, Hui Xia Xu, Li Jun Zhang, Yong Du
Abstract: Graded sintering is the fundamental process of fabricating functionally gradient cemented carbide (FGCC). The diffusion-induced mass transport in cemented carbide can result in the formation of gradient microstructure and thusly lead to gradual changes in micro property. So far, several types of FGCC have been developed, and the factors that can influence the gradient formation are complex. Section 2 introduces the process of forming diffusion-controlled near-surface layer in WC-Ti (C,N)-Co hardmetal as well as the kinetic modeling work that reveals the key factors for the layer formation. Section 3 reviews the dual properties carbide produced under carburization atmosphere, for which the carbon content is a main factor of the gradient thickness. There are two models describing this process, representing different mass-transport mechanism of the so-called liquid phase migration (LPM) process. In section 4, previous and new results of modeling LPM in different dimensions and scales are presented, and the diffusion-controlled nature of LPM are discussed.
Authors: Yun Chen, Na Min Xiao, Dian Zhong Li, Tong Zhao Gong, Henri Nguyen-Thi
Abstract: Directional solidification is a paradigm process to gain the desired microstructure via certain applied solidification parameters. A thorough understanding of the diffusion-limited solid-liquid interface morphology evolution from initial transient to steady state is of uppermost importance to optimize the solidification processes. The rapid development of quantitative phase-field model provides a feasible computational tool to explore the underlying physics of the morphological transition at different stages. On basis of the diffusion-limited quantitative phase-field simulations using adaptive finite element method, the directional solidification of Al-4wt.%Cu alloy is characterized and both the solid interface propagation speed and solute profile are analyzed. The simulations are then compared with the in situ and real-time observation by means of synchrotron radiation x-ray radiography image. Good agreements are obtained between simulations and experimental data. Detailed mechanism that controls the morphological instability and transition are then addressed.
Authors: Hui Xing, Xiang Lei Dong, Jian Yuan Wang, Ke Xin Jin
Abstract: In this paper, we review our results from phase field simulations of tilted dendritic growth dynamics and dendrite to seaweed transition in directional solidification of a dilute alloy. We focus on growth direction selection, stability range and primary spacing selection, and degenerate seaweed-to-tilted dendrite transition in directional solidification of non-axially orientated crystals. For growth direction selection, the DGP law (Phys. Rev. E, 78 (2008) 011605) was modified through take the anisotropic strength and pulling velocity into account. We confirm that the DGP law is only validated in lower pulling velocity. For the stability range and primary spacing selection, we found that the lower limit of primary spacing is irrelative to the misorientation angle but the upper limit is nonlinear with respect to the misorientation angle. Moreover, predicted results confirm that the power law relationship with the orientation correction by Gandin et al. (Metall. Mater. Trans. A. 27A (1996) 2727-2739) should be a universal scaling law for primary spacing selection. For the seaweed-to-dendrite transition, we found that the tip-splitting instability in degenerate seaweed growth dynamics is related to the M-S instability dynamics, and this transition originates from the compromise in competition between two dominant mechanisms, i.e., the macroscopic thermal field and the microscopic interfacial energy anisotropy.
Authors: Guang Long Xu, Yu Wen Cui
Abstract: The Ginzburg-Landau (G-L) model possesses the thermodynamic foundation of energy minimization and is available for many dynamic formalisms, thus holds great potential for investigating the complex materials behaviors. The common ingredient in energy spawns the real-time control of diffusion potential and chemical mobility by integrating G-L model with CALPHAD technique. The coupling between martensitic transformation and dislocation evolution is achieved by mean of continuous mechanism. The updated G-L model is then validated against the martensitic transformation coupled with composition redistribution in Fe-C binary system. The modeling allows some deeper insights into the mechanisms of coupling effects behind the observed phenomena. It has been proven that the partitioning of carbon in steels is an ordinary diffusion governed by instantaneous diffusion potential and chemical mobility. The rough twin boundaries and retained austenite within the martensite should be attributed to the effect of dislocations. Although the developed model in this chapter has deficiencies, it sheds some lights on the integration of multi-physics models for a complex phase transformation.

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