Book contents
- Frontmatter
- Contents
- Preface to second edition
- Preface to first edition
- 1 Basic concepts of thermodynamics
- 2 Manipulation of thermodynamic quantities
- 3 Systems with variable composition
- 4 Practical handling of multicomponent systems
- 5 Thermodynamics of processes
- 6 Stability
- 7 Applications of molar Gibbs energy diagrams
- 8 Phase equilibria and potential phase diagrams
- 9 Molar phase diagrams
- 10 Projected and mixed phase diagrams
- 11 Direction of phase boundaries
- 12 Sharp and gradual phase transformations
- 13 Transformations in closed systems
- 14 Partitionless transformations
- 15 Limit of stability and critical phenomena
- 16 Interfaces
- 17 Kinetics of transport processes
- 18 Methods of modelling
- 19 Modelling of disorder
- 20 Mathematical modelling of solution phases
- 21 Solution phases with sublattices
- 22 Physical solution models
- References
- Index
21 - Solution phases with sublattices
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to second edition
- Preface to first edition
- 1 Basic concepts of thermodynamics
- 2 Manipulation of thermodynamic quantities
- 3 Systems with variable composition
- 4 Practical handling of multicomponent systems
- 5 Thermodynamics of processes
- 6 Stability
- 7 Applications of molar Gibbs energy diagrams
- 8 Phase equilibria and potential phase diagrams
- 9 Molar phase diagrams
- 10 Projected and mixed phase diagrams
- 11 Direction of phase boundaries
- 12 Sharp and gradual phase transformations
- 13 Transformations in closed systems
- 14 Partitionless transformations
- 15 Limit of stability and critical phenomena
- 16 Interfaces
- 17 Kinetics of transport processes
- 18 Methods of modelling
- 19 Modelling of disorder
- 20 Mathematical modelling of solution phases
- 21 Solution phases with sublattices
- 22 Physical solution models
- References
- Index
Summary
Sublattice solution phases
In the substitutional solutions discussed in Section 20.4 all lattice sites were equivalent and a solution was formed from a pure substance by substituting new kinds of atoms for the initial one. However, relatively few crystalline phases belong to this class. The great majority have different kinds of lattice sites and can be described by using two or more sublattices. Examples of such phases will be discussed in this chapter. It will be demonstrated that a great variety of such phases can be modelled in a very direct way using an approach often called the compound energy model or formalism. It is a crude model in the sense that it assumes random mixing within each sublattice. The expression for the entropy of such phases is simple and was presented in Section 19.8, ‘Restricted random mixtures’, but the excess Gibbs energy can easily become very complicated. However, it should be realized that actual calculations of equilibria, and even of whole phase diagrams, can now be carried out with sophisticated computer programs which only require that the expression for the molar Gibbs energy of each phase is defined.
Section 19.8 gave the expression for the entropy assuming random mixing of all the components present in each sublattice. The result was expressed in terms of the site fraction variable, yi, and in Section 19.10 it was then applied to interstitial solutions, which are a special case of solution phases with sublattices.
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- Information
- Phase Equilibria, Phase Diagrams and Phase TransformationsTheir Thermodynamic Basis, pp. 460 - 475Publisher: Cambridge University PressPrint publication year: 2007