Chapter 5. Homogeneous Second-Phase Precipitation

  1. Prof. Gernot Kostorz
  1. Prof. Richard Wagner1,
  2. Dr. Reinhard Kampmann2 and
  3. Prof. Peter W. Voorhees3

Published Online: 28 JAN 2005

DOI: 10.1002/352760264X.ch5

Phase Transformations in Materials

Phase Transformations in Materials

How to Cite

Wagner, R., Kampmann, R. and Voorhees, P. W. (2001) Homogeneous Second-Phase Precipitation, in Phase Transformations in Materials (ed G. Kostorz), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/352760264X.ch5

Editor Information

  1. ETH Zürich, Institut fü Angewandte Physik, CH-8093 Zürich, Switzerland

Author Information

  1. 1

    Forschungszentrum Jülich, D-52425 Jülich, Germany

  2. 2

    GKSS-Forschungszentrum Geesthacht GmbH, Institut für Werkstoffforschung, Postfach 1160, D-21494 Geesthacht, Germany

  3. 3

    Department of Materials Science and Engineering, Northwestern University, 2225 N. Campus Drive, Evanston, IL 60208-3108, USA

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 10 AUG 2001

ISBN Information

Print ISBN: 9783527302567

Online ISBN: 9783527602643



  • homogeneous second-phase precipitation;
  • isothermal precipitation reaction;
  • metastability;
  • instability;
  • decomposition mechanisms;
  • nucleation;
  • growth;
  • spinodal decomposition;
  • phase separation;
  • quenching rate;
  • precipitate morphologies;
  • spinodal theories;
  • Monte Carlo studies;
  • coarsening of precipitates;
  • LSW theory;
  • Langer–Schwartz model;
  • Kampmann–Wagner model


  • List of Symbols and Abbreviations

  • 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 of ‘Spinodol 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 Schwartz Theory (LS Model) and its Modification by Kampmann and Wagner (MLS Model)

    • The Numerical Modell (N Model) of Kampmann and Wagner (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

  • References