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
10 - Projected and mixed phase diagrams
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
Schreinemakers' projection of potential phase diagrams
Another method of reducing the number of axes is based on projection. By projecting all the features onto one side of the phase diagram, one will retain all the features, but the features of the highest dimensionality will no longer be visible because the dimensionality of a geometrical element will decrease by one unit by projection and they may thus overlap each other and also overlap features of the next-higher dimensionality. As an example, Fig. 10.1(b) shows a P, T diagram obtained by projection of Fig. 8.11 (shown again as Fig. 10.1(a)) in the μB direction. Such a P, T diagram is called Schreinemakers' projection [16]. In a system with c components it is obtained by projecting in the directions of c − 1 μi axes. It will show invariant equilibria with c + 2 phases as points, univariant equilibria with c + 1 phases as lines and in the angles between them there will be surfaces representing divariant equilibria with c phases. Using a short-hand notation developed by Schreinemakers, the coexistence lines for c − 1 phases are here identified also by giving in parentheses the phases from the invariant equilibrium which do not take part. For example, the (α) curve represents the α-absent equilibrium, i.e. β + γ + δ. By comparison with Fig. 10.1(a) it can be seen that the angle between (α) and (β) is covered by the γ + δ surface but also by the α + δ surface which extends to the (γ) line and by the β + γ surface which extends to the (δ) line.
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- Information
- Phase Equilibria, Phase Diagrams and Phase TransformationsTheir Thermodynamic Basis, pp. 205 - 232Publisher: Cambridge University PressPrint publication year: 2007