COVID-19 Update: We are currently shipping orders daily. However, due to transit disruptions in some geographies, deliveries may be delayed. To provide all customers with timely access to content, we are offering 50% off Science and Technology Print & eBook bundle options. Terms & conditions.
Handbook of Solid State Diffusion: Volume 1 - 1st Edition - ISBN: 9780128042878, 9780128043608

Handbook of Solid State Diffusion: Volume 1

1st Edition

Diffusion Fundamentals and Techniques

Editors: Aloke Paul Sergiy Divinski
Hardcover ISBN: 9780128042878
eBook ISBN: 9780128043608
Imprint: Elsevier
Published Date: 10th April 2017
Page Count: 548
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


Handbook of Solid State Diffusion, Volume 1: Diffusion Fundamentals and Techniques covers the basic fundamentals, techniques, applications, and latest developments in the area of solid-state diffusion, offering a pedagogical understanding for students, academicians, and development engineers. Both experimental techniques and computational methods find equal importance in the first of this two-volume set.

Volume 1 covers the fundamentals and techniques of solid-state diffusion, beginning with a comprehensive discussion of defects, then different analyzing methods, and finally concluding with an exploration of the different types of modeling techniques.

Key Features

  • Presents a handbook with a short mathematical background and detailed examples of concrete applications of the sophisticated methods of analysis
  • Enables readers to learn the basic concepts of experimental approaches and the computational methods involved in solid-state diffusion
  • Covers bulk, thin film, and nanomaterials
  • Introduces the problems and analysis in important materials systems in various applications
  • Collates contributions from academic and industrial problems from leading scientists involved in developing key concepts across the globe


Students, academicians, researchers dealing with solid-state diffusion. Scientists and professionals involved in materials for various applications and for the development of new materials

Table of Contents

Chapter 1: Defects, Driving Forces and Definitions of Diffusion Coefficients in Solids

  • Abstract
  • 1.1. Defects in Crystalline Solid
  • 1.2. Driving Forces for Diffusion
  • 1.3. Definitions of Different Types of Diffusions
  • References

Chapter 2: Tracer Diffusion and Understanding the Atomic Mechanisms of Diffusion

  • Abstract
  • 2.1. Introduction
  • 2.2. (Radio-)Tracer Method
  • 2.3. Solute (Impurity) Diffusion
  • 2.4. Experimental Determination of the Diffusion Mechanism
  • References

Chapter 3: Estimation of Diffusion Coefficients in Binary and Pseudo-Binary Bulk Diffusion Couples

  • Abstract
  • 3.1. Fick's Laws of Diffusion
  • 3.2. Solutions of Fick's Second Law Considering Constant Diffusion Coefficients
  • 3.3. Matano–Boltzmann Analysis for the Estimation the Variable Interdiffusion Coefficients
  • 3.4. Den Broeder Approach to Determine the Interdiffusion Coefficient
  • 3.5. Wagner's Approach for the Calculation of the Interdiffusion Coefficient [11]
  • 3.6. Deviation From Ideal Molar Volume and Error in Locating the Initial Contact Plane (or Matano Plane)
  • 3.7. Comparison of the Interdiffusion Coefficients Estimated by Different Methods
  • 3.8. The Concept of the Integrated Interdiffusion Coefficient for the Phases With Narrow Homogeneity Range
  • 3.9. Parabolic Growth Constant
  • 3.10. Estimation of the Intrinsic Diffusion Coefficients of Components
  • 3.11. Identifying the Location of Kirkendall Marker Plane
  • 3.12. Multifoil Technique to Estimate the Intrinsic Diffusion Coefficients for Many Compositions From a Single Diffusion Couple
  • 3.13. Estimation of the Tracer Diffusion Coefficients Indirectly From Diffusion Couple Experiments
  • 3.14. Intrinsic and Tracer Diffusion Coefficients in a Phase With Narrow Homogeneity Range
  • 3.15. Estimation of the Impurity Diffusion Coefficients
  • 3.16. A Pseudo-Binary Approach in Multicomponent Diffusion
  • 3.17. Important Steps for Estimation of the Diffusion Parameters
  • 3.18. Analysis of Diffusion Data for Understanding the Role of Thermodynamic Driving Force and Defects
  • 3.19. Predicting the Defects Present Based on the Estimated Diffusion Coefficients in Intermetallic Compounds
  • 3.20. Physical Significance of the Estimated Diffusion Coefficients
  • References

Chapter 4: Diffusion in Multicomponent Alloys

  • Abstract
  • 4.1. Intrinsic Diffusion in Multicomponent Alloys
  • 4.2. Atomic Mobility and Vacancy Wind Effect in Multicomponent Alloys
  • 4.3. Interdiffusion in Multicomponent Alloys
  • 4.4. Zero Flux Plane (ZFP)
  • 4.5. Average Effective and Integrated Diffusion Coefficients in Multicomponent Systems
  • 4.6. Average Ternary Interdiffusion Coefficients
  • 4.7. A Transfer Matrix Analysis of Multicomponent Diffusion
  • 4.8. Estimation of Tracer Diffusion Coefficients in a Ternary System
  • 4.9. Determination of Equilibrium Phase Diagram
  • 4.10. Examples of Multicomponent Diffusion
  • References

Chapter 5: Point Defects and Diffusion in Semiconductors

  • Abstract
  • 5.1. Introduction
  • 5.2. Point Defect Fundamentals in Semiconductors
  • 5.3. Diffusion Mechanism Basics in Semiconductors
  • 5.4. Diffusion in Silicon
  • 5.5. Diffusion in Germanium
  • 5.6. Diffusion in Gallium Arsenide
  • 5.7. Diffusion–Segregation: A Special Subject
  • 5.8. Concluding Remarks
  • References

Chapter 6: CALPHAD-Type Modeling of Diffusion Kinetics in Multicomponent Alloys

  • Abstract
  • 6.1. Multicomponent Diffusion Theory
  • 6.2. Atomic Mobility and Its Relation With Diffusion Coefficients
  • 6.3. Models for Atomic Mobility in Different Phases
  • 6.4. A Simulation Tool for Diffusion-Controlled Transformation – DICTRA
  • 6.5. General Strategy for Establishment of Atomic Mobility Database in Multicomponent Alloys
  • 6.6. Applications of DICTRA in Different Multicomponent Alloys
  • 6.7. Further Extension to Complex Precipitation and Microstructure Simulation
  • References

Chapter 7: Phase-Field Modeling as a Method Relevant for Modeling Phase Transformation During Interdiffusion

  • Abstract
  • 7.1. Introduction
  • 7.2. Phase-Field Models
  • 7.3. Phase-Field Model: Relevant to Modeling Phase Transformations in Diffusion Couples
  • 7.4. Modeling Kirkendall Effect in a Binary Alloy
  • 7.5. Multicomponent Couples (no Vacancies)
  • 7.6. Incorporating Databases
  • 7.7. Conclusions
  • References

Chapter 8: Thermodynamic Treatment of Diffusive Phase Transformation (Reactive Diffusion)

  • Abstract
  • Acknowledgements
  • 8.1. Introduction
  • 8.2. Formulation of TEP in Discrete Characteristic Parameters
  • 8.3. Treatment of Reactive Diffusion in Binary Systems With Multiple Stoichiometric Phases by Adapted Diffusion Equations
  • 8.4. Treatment of Reactive Diffusion in Binary Systems With Multiple Stoichiometric Phases by Application of TEP
  • 8.5. Formation of Multiple Stoichiometric Phases in Binary Systems by Combined Bulk and Grain Boundary Diffusion – Experiments and Modeling by the TEP
  • References

Chapter 9: Monte Carlo Methods in Solid State Diffusion

  • Abstract
  • Acknowledgements
  • 9.1. Introduction
  • 9.2. Solid State Diffusion and Kinetic Monte Carlo
  • 9.3. Solid State Diffusion and Lattice Monte Carlo
  • References

Chapter 10: Defects and Diffusion in Ordered Compounds

  • Abstract
  • 10.1. Introduction
  • 10.2. Point Defects in Intermetallic Compounds
  • 10.3. Diffusion Mechanisms in Ordered Intermetallics
  • 10.4. Measurements of Al Diffusion in Aluminides
  • 10.5. Diffusion in Ordered Binary Aluminides
  • 10.6. Diffusion in the Ternary System Ni–Fe–Al
  • 10.7. General Conclusions
  • References


No. of pages:
© Elsevier 2017
10th April 2017
Hardcover ISBN:
eBook ISBN:

About the Editors

Aloke Paul

Aloke Paul

Professor Aloke Paul heads a research group working on various aspects of diffusion in solids in the Department of Materials Engineering, Indian Institute of Science, Bengaluru, India. Major research areas include developing new phenomenological models, materials in electronic packaging, bond coat in jet engine applications, the growth of A15 intermetallic superconductors etc. He teaches a postgraduate level course on Diffusion in solids. He has guided several Ph.D. and M.E. students and co-authored around 100 articles in various international journals. During his Ph.D. at the Eindhoven University of Technology, he was part of one of the most important discoveries of recent times on previously unknown phenomena related to the Kirkendall effect. After joining the Indian Institute of Science, his group developed new methods for estimation of the diffusion coefficients such as a physicochemical approach that relates microstructural evolution with the rate of diffusing components and a pseudo-binary method in multicomponent diffusion. These are included in course curriculum in many universities and also included in the books written on this topic. He has co-authored a textbook titled Thermodynamics, Diffusion and the Kirkendall effect in Solids.

Affiliations and Expertise

Department of Materials Engineering, Indian Institute of Science

Sergiy Divinski

Sergiy Divinski

Professor Dr. Sergiy Divinski leads the radiotracer laboratory at the Institute of Materials Physics, University of Münster, Germany. The research activities are concentrated on kinetic and thermodynamic properties of interfaces in solids, including intergranular and interphase boundaries. Other major interests include diffusion phenomena in intermetallic compounds, effects of ordering on diffusion kinetic and diffusion mechanisms, interfaces in severely deformed materials. He teaches graduate and postgraduate courses on Diffusion in Solids, Numerical methods in Material Science and different aspects of Materials Science. He has co-authored more than 150 articles in various international journals, several book chapters in the field of Diffusion in Solids and a textbook titled Thermodynamics, Diffusion and the Kirkendall effect in Solids.

Affiliations and Expertise

Institute of Materials Physics, University of Münster, Germany

Ratings and Reviews