pydiffusion: A Python Library for Diffusion Simulation and Data Analysis

Chen, Zhangqi; Zhang, Qiaofu; Zhao, Ji‐Cheng

doi:10.5334/jors.255

Cited by 18 publications

(9 citation statements)

References 19 publications

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“…The ratios of the intrinsic diffusion coefficients of Fe and Al in the bcc_B2 and bcc_A2 phases, α and β, respectively, are introduced in this study, because the interdiffusion coefficient can be calculated from the concentration distribution. The Sauer-Freise method 15) was used to calculate the interdiffusion coefficient from the concentration distribution; specifically, pydiffusuion, 16) a diffusion library in Python, was used.…”

Section: Numerical Calculation Of Kirkendall Poresmentioning

confidence: 99%

Formation of Kirkendall Pores in Aluminized Steel Sheets and Effect of Si in Aluminizing Bath

Maki

2022

ISIJ Int.

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Aluminized steel sheets are highly resistant to elevated temperature. When they are heated for several hours above 800°C, part of the coating layer may delaminate owing to the presence of continuous Kirkendall pores, which are formed between the bcc_A2 and bcc_B2 phases because of the differences in the diffusion coefficients of Al and Fe in each phase. In this study, a numerical simulation was performed to predict the occurrence of Kirkendall pores, and the simulation results were compared with experimental results. The Si in the aluminizing bath significantly increased the number of Kirkendall pores owing to its effect on the ratio of the intrinsic diffusion coefficients (D Fe /D Al ) in the bcc_B2 phase.

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Section: Numerical Calculation Of Kirkendall Poresmentioning

confidence: 99%

Formation of Kirkendall Pores in Aluminized Steel Sheets and Effect of Si in Aluminizing Bath

Maki

2022

ISIJ Int.

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Section: Computational Modeling Of Interdiffusionmentioning

confidence: 99%

“…Pydiffusion is an open-source python library designed to efficiently simulate various types of 1D binary or ternary diffusion problems [38]. A method within Pydiffusion has been developed to construct concentration profiles of binary multi-phase systems governed by temperature dependent interdiffusion data and time [38]. Based on pre-constructed 1D grids, the simulation applies the finite difference method (FDM) to numerically solve the diffusion problems using Fick's two laws of solid-state diffusion (Eq.…”

Section: Computational Modeling Of Interdiffusionmentioning

confidence: 99%

“…where, 𝐷 ̃ is the interdiffusion coefficient, 𝜕𝑐 𝜕𝑥 is the concentration gradient, J is the diffusion flux, and 𝜕𝐶 𝜕𝑡 is derivative of diffusion flux. This is applied to within a given phase [38]. To account for a system containing multiple phases, the position of the interface between two adjacent phases is calculated by Eq.…”

Section: 𝐽 = −𝐷 ̃𝜕𝑐mentioning

confidence: 99%

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Microstructure and Fracture Toughness of an Aluminum-Steel Impact Weld and Effect of Thermal Exposure

Kohlhorst

Kapil

Chen

et al. 2021

Metall Mater Trans A

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Welding of aluminum alloys to steel is increasingly important in manufacturing, however the use of fusion welding is difficult because of disparate melting points and the possibility of intermetallic compound (IMC) formation. Here, an impact welding technique, vaporizing foil actuator welding, was utilized to produce solid-state joints between AA1100-O and 1018 mild steel. The relationship between weld processing conditions, microstructure, and mechanical properties were investigated. For this purpose, the welds were annealed between 300°C and 600°C and a combination of optical and scanning electron microscopy, along with image analysis was performed to characterize the weld microstructure and monitor IMC growth. Wedge testing was applied to understand the effect of annealing on the weld fracture toughness. A numerical model incorporating the Fick's laws of diffusion, grain boundary diffusion, and grain growth kinetics was also developed to simulate the IMC growth. The heterogeneity in the original microstructure caused persistent differences in IMC growth, as initial IMC seemed to increase nucleation and growth. Simulation results indicated short circuit diffusion to be the major contributor to IMC growth since it is consistently faster then experimental IMC growths compared with the computational results that used lattice diffusion only. Wedge testing reveals increased weld toughness for modest anneals of 300°C, possibly due to homogeneity at the weld interface while avoiding IMC growth.

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“…FSA has been successfully applied to a wide range of systems to obtain both interdiffusion and impurity diffusion coefficients. [18,[22][23][24][25][26][27][28][29] The original diffusion composition profiles of all four temperatures (250, 300, 350, and 380°C) were kindly provided to us by Hoxha et al FSA was applied to these profiles to obtain both impurity and interdiffusion coefficients of the solid solution and intermetallic phases without assuming constant diffusion coefficients for the intermetallic phases. In this study, the molar volume variation in each phase in the Cu-Zn system is not considered and it is assumed constant.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Coefficients and Phase Equilibria of the Cu-Zn Binary System Studied Using Diffusion Couples

Eastman

Zhang

Zhao

2020

J. Phase Equilib. Diffus.

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The diffusion behavior and phase equilibria in the Cu-Zn binary system were investigated using solidsolid and solid-liquid diffusion couples. Heat treatments at temperatures ranging from 100 to 750°C were performed and the samples were examined using optical microscopy, energy dispersive x-ray spectroscopy, and electron probe microanalysis to identify the phases and to obtain composition profiles. Solubility limits of both solid solution and intermetallic phases were then evaluated, and a forwardsimulation analysis (FSA) was applied to extract interdiffusion coefficients. The composition profiles from Hoxha et al. were also re-analyzed using FSA to obtain more reliable diffusion coefficient data without the assumption of constant diffusion coefficients for the intermetallic phases. A comprehensive assessment of the interdiffusion coefficients in three intermetallic phases of the Cu-Zn system was performed based on the results from the current study as well as those in the literature. Activation energies and Arrhenius pre-factors were evaluated for each phase as a function of composition. The fitted equations based on the comprehensive assessment have the capabilities of computing the interdiffusion coefficients of each of the phases at a given composition and temperature. Suggested modifications to the Cu-Zn binary phase diagram were presented based on the new experimental information gathered from the present study. A clear explanation is provided for the puzzling low Zn concentrations often observed in the Cu-rich fcc phase of Cu-Zn diffusion couples in comparison with the expected high solubility values based on the equilibrium Cu-Zn phase diagram.

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pydiffusion: A Python Library for Diffusion Simulation and Data Analysis

Cited by 18 publications

References 19 publications

Formation of Kirkendall Pores in Aluminized Steel Sheets and Effect of Si in Aluminizing Bath

Formation of Kirkendall Pores in Aluminized Steel Sheets and Effect of Si in Aluminizing Bath

Microstructure and Fracture Toughness of an Aluminum-Steel Impact Weld and Effect of Thermal Exposure

Diffusion Coefficients and Phase Equilibria of the Cu-Zn Binary System Studied Using Diffusion Couples

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