## Phase Transformations in MaterialsFor all kinds of materials, phase transformations show common phenomena and mechanisms, and often turn a material, for example metals, multiphase alloys, ceramics or composites, into its technological useful form. The physics and thermodynamics of a transformation from the solid to liquid state or from one crystal form to another are therefore essential for creating high-performance materials. This handbook covers phase transformations, a general phenomenon central to understanding the behavior of materials and for creating high-performance materials. It will be an essential reference for all materials scientists, physicists and engineers involved in the research and development of new high performance materials. It is the revised and enhanced edition of the renowned book edited by the late P. Haasen in 1990 (Vol. 5, Materials Science and Technology). |

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appropriate ordering field. In fact, this is also true for Eq. (4-4), but then the

physical significance of Xt changes. For a two-sub- lattice antiferromagnet, the

ordering field is a "staggered field", which changes sign between the two

sublattices, and hence is thermodynamically conjugate to the

the antiferromagnet. Although such a field normally cannot be applied in the

laboratory, the second derivative, Xt (m tn's case it is called "staggered

susceptibility") is experimentally ...

appropriate ordering field. In fact, this is also true for Eq. (4-4), but then the

physical significance of Xt changes. For a two-sub- lattice antiferromagnet, the

ordering field is a "staggered field", which changes sign between the two

sublattices, and hence is thermodynamically conjugate to the

**order parameter**ofthe antiferromagnet. Although such a field normally cannot be applied in the

laboratory, the second derivative, Xt (m tn's case it is called "staggered

susceptibility") is experimentally ...

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Since for MnO the

independent components, and hence the total number of

components is m = 8 (Mu- kamel and Krinsky, 1976). An even larger number of

components is needed to describe the ordering of solid 3He. In view of this, it is

clear that even m -*<*>, which is also called the spherical model (Berlin and Kac,

1952; Joyce, 1972) is a useful limit to consider from the theoretical point of view.

Apart from ...

Since for MnO the

**order parameter**can take any orientation is a plane, it has twoindependent components, and hence the total number of

**order parameter**components is m = 8 (Mu- kamel and Krinsky, 1976). An even larger number of

components is needed to describe the ordering of solid 3He. In view of this, it is

clear that even m -*<*>, which is also called the spherical model (Berlin and Kac,

1952; Joyce, 1972) is a useful limit to consider from the theoretical point of view.

Apart from ...

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tion of the dumbbell-shaped CN~-ions: at the same time, it can be considered as

an example for an elastic transition, where the

tensor (^(jr))! Such an ambiguity is typical of many first-order transitions, because

various dynamical variables (such as a local dielectric polarization P(x), a local

quadruple moment /MV(x) and the strain ^v(jc) may occur simultaneously in a

crystal and are coupled together. In a Landau expansion, such couplings are

typically of the ...

tion of the dumbbell-shaped CN~-ions: at the same time, it can be considered as

an example for an elastic transition, where the

**order parameter**is the straintensor (^(jr))! Such an ambiguity is typical of many first-order transitions, because

various dynamical variables (such as a local dielectric polarization P(x), a local

quadruple moment /MV(x) and the strain ^v(jc) may occur simultaneously in a

crystal and are coupled together. In a Landau expansion, such couplings are

typically of the ...

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### Contents

List of Symbols and Abbreviations | 3 |

Contents | 4 |

Prof Yves J M Brechet Dr Reinhard Kampmann | 5 |

Copyright | |

12 other sections not shown

### Common terms and phrases

Acta Metall alloys anisotropy approximation atoms behavior binary Binder Cahn calculated Chem chemical chemical potential cluster coarsening composition concentration constant correlation factor critical crystal defect dendritic diffusion coefficient dynamics effects elastic equation equilibrium eutectic example experimental field Figure fluctuations Fratzl function Gibbs energy gradient grain boundary growth rate Helmholtz energy impurity interaction interface interstitial Ising model jump frequency kinetics Kurz Landau Langer lattice Lebowitz length Lett linear liquid magnetic materials mechanism metastable microstructure mixtures Monte Carlo Murch nucleation order parameter particles phase diagram phase separation phase transitions Phvs Phys polymer precipitate quench radius random regime region scaling shown in Fig simulations solid solution solidification spacing spinodal curve spinodal decomposition stability structure sublattices supersaturation surface temperature ternary theory thermal thermodynamic tion tracer diffusion transformation tricritical point ture two-phase undercooling vacancy velocity volume fraction Wagner wavelength