Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Notation
- Part I Basic thermodynamics and kinetics of phase transformations
- Part II The atomic origins of thermodynamics and kinetics
- Part III Types of phase transformations
- 10 Melting
- 11 Transformations involving precipitates and interfaces
- 12 Spinodal decomposition
- 13 Phase field theory
- 14 Method of concentration waves and chemical ordering
- 15 Diffusionless transformations
- 16 Thermodynamics of nanomaterials
- 17 Magnetic and electronic phase transitions
- 18 Phase transitions in quantum materials
- Part IV Advanced topics
- Further reading
- References
- Index
14 - Method of concentration waves and chemical ordering
from Part III - Types of phase transformations
Published online by Cambridge University Press: 05 September 2014
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Notation
- Part I Basic thermodynamics and kinetics of phase transformations
- Part II The atomic origins of thermodynamics and kinetics
- Part III Types of phase transformations
- 10 Melting
- 11 Transformations involving precipitates and interfaces
- 12 Spinodal decomposition
- 13 Phase field theory
- 14 Method of concentration waves and chemical ordering
- 15 Diffusionless transformations
- 16 Thermodynamics of nanomaterials
- 17 Magnetic and electronic phase transitions
- 18 Phase transitions in quantum materials
- Part IV Advanced topics
- Further reading
- References
- Index
Summary
This chapter analyzes the thermodynamic stability of “static concentration waves.” The idea is that an ordered structure can be described as a variation of chemical composition from site to site on a crystal lattice, and this variation can be written as a wave, with crests denoting B-atoms and troughs the A-atoms, for example. The wave does not propagate, so it is called a “static” concentration wave. Another important difference from conventional waves is that the atom sites are exactly on the tops of crests or at the bottoms of troughs, so we do not consider the intermediate phases of the concentration wave, at least not in our main examples. A convenient feature of this approach is that an ordered structure can be described by a single wavevector, or a small set of wavevectors. The disordered solid solution has no such periodicity, so the amplitude of the concentration wave, η, serves as a long-range order parameter.
This chapter begins with a review of how periodic structures in real space are described by wavevectors in k-space, and then explains the “star” of the wavevector of an ordered structure. A key step for phase transitions is writing the free energy in terms of the amplitudes of static concentration waves.
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- Phase Transitions in Materials , pp. 332 - 354Publisher: Cambridge University PressPrint publication year: 2014