Homogeneous Second‐Phase Precipitation

Abstract

The sections in this article are Introduction General Considerations General Course of an Isothermal Precipitation Reaction Thermodynamic Considerations–Metastability and Instability Decomposition Mechanisms: Nucleation and Growth versus Spinodal Decomposition Thermodynamic Driving Forces for Phase Separation Experimental Techniques for Studying Decomposition Kinetics Microanalytical Tools Direct Imaging Techniques Scattering Techniques Experimental Problems Influence of Quenching Rate on Kinetics Distinction of the Mode of Decomposition Precipitate Morphologies Experimental Results Factors Controlling the Shapes and Morphologies of Precipitates Early Stage Decomposition Kinetics Cluster‐Kinetics Approach Classical Nucleation–Sharp Interface Model Time‐Dependent Nucleation Rate Experimental Assessment of Classical Nucleation Theory Non‐Classical Nucleation–Diffuse Interface Model Distinction Between Classical and Non‐Classical Nucleation Diffusion‐Controlled Growth of Nuclei from the Supersaturated Matrix The Cluster‐Dynamics Approach to Generalized Nucleation Theory Spinodal Theories The Philosophy of Defining a ‘Spinodal Alloy' —Morphologies of ‘Spinodal Alloys' Monte Carlo Studies Coarsening of Precipitates General Remarks The LSW Theory of Coarsening Extensions of the Coarsening Theory to Finite Precipitate Volume Fractions Other Approaches Towards Coarsening Influence of Coherency Strains on the Mechanism and Kinetics of Coarsening–Particle Splitting Numerical Approaches Treating Nucleation, Growth and Coarsening as Concomitant Processes General Remarks on the Interpretation of Experimental Kinetic Data of Early Decomposition Stages The Langer and S chwartz Theory ( LS Model) and its Modification by K ampmann and W agner ( MLS Model) The Numerical Model ( N Model) of K ampmann and W agner ( KW ) Decomposition of a Homogeneous Solid Solution General Course of Decomposition Comparison Between the MLS Model and the N Model The Appearance and Experimental Identification of the Growth and Coarsening Stages Extraction of the Interfacial Energy and the Diffusion Constant from Experimental Data Decomposition Kinetics in Alloys Pre‐Decomposed During Quenching Influence of the Loss of Particle Coherency on the Precipitation Kinetics Combined Cluster‐Dynamic and Deterministic Description of Decomposition Kinetics Self‐Similarity, Dynamical Scaling and Power‐Law Approximations Dynamical Scaling Power‐Law Approximations Non‐Isothermal Precipitation Reactions Acknowledgements

Modeling over-ageing in Al-Mg-Si alloys by a multi-phase CALPHAD-coupled Kampmann-Wagner Numerical model

“…The methodology of the KWN approach, initially proposed by Kampmann and Wagner in [19] for modeling precipitation kinetics, is also found in the seminal work of Maxwell and Hellawell published earlier, i.e. in 1975 on as-cast grain size prediction [26].…”

“…In contrast with the accurate but computationally expensive phase field approach [13], the KWN approach has been gaining popularity [14][15][16][17][18][19][20][21][22][23][24][25][26] recently. This is due to its mathematical simplicity and convenient coupling with the CALPHAD database, enabling an efficient treatment of multi-scale, multi-component industrially significant problems [14][15][16][17][18][19][20][21][22][23][24][25]. It should be noted that the coupling of the KWN model with the thermodynamic databases developed in the CALPHAD research community is a scale-bridging feature as the databases could be established on the base of first principle calculations [27,28].…”

Precipitation of Non-Spherical Particles in Aluminum Alloys Part I: Generalization of the Kampmann–Wagner Numerical Model

“…The reported approaches for this purpose fall into two categories: direct detailed approaches [6,7] and physically based internal state variable approaches [8,9]. The former is represented by the phase field method or Finite Difference Method and excels in providing detailed descriptions of nucleation, growth and coarsening.…”

“…The former is represented by the phase field method or Finite Difference Method and excels in providing detailed descriptions of nucleation, growth and coarsening. The latter, represented by KampmannWagner Numerical (KWN) model [9], prevails in handling precipitation involving multiscale transportation phenomena (e.g., concurrent nucleation, growth and coarsening of an ensemble of precipitates, precipitation in matrix with an uneven compositional profile etc. ).…”

The Supersaturation and Transient Volume Measurement for Nucleation, Growth, Coarsening in a Concentrated Ni-Based Superalloy

“…However, the second phase is nucleated, grow, and coarsened by diffusion of solute from the matrix towards the precipitates in an elevated temperature for sufficient atomic mobility. Nucleation is the first-order phase transition by which a metastable phase transforms into a more stable one [2]. Two important aspects for the initial phase transition in a concentrated Al-Ni system are reviewed by atom probe tomography experiments.…”