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Order Variables and Adiabatic Potentials

  • Minoru Fujimoto
Chapter

Abstract

Thermal properties of a crystal are primarily due to the vibrating lattice, while dielectric, magnetic, and mechanical properties can be determined from measured response functions of a crystal to an applied field or force. Such an external action X on internal variables σ is primarily an adiabatic variable independent of temperature. As in a compressed gas, the external work on a crystal is expressed by \( - \sigma X\), and hence the Gibbs potential can be defined by \(G = U - {\it{TS}} + \sigma X\). On the other hand, internal variables σ at lattice sites can be independent of each other in some cases, but correlated in other conditions. In the latter, the effect of X is expressed effectively as \( - \sigma (X + {X_{{\mathop{\rm int}} }})\), where \({X_{{\mathop{\rm int}} }}\) is an internal field that was originally proposed by P. Weiss for a ferromagnet. In this chapter, these internal variables σ and \({X_{{\mathop{\rm int}} }}\) are discussed in terms of correlations in a crystal, leading to Weiss’ concept to be included in the Gibbs function.

Keywords

Lattice Site Brillouin Zone Internal Variable Electric Dipole Moment Order Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 2.
    M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, 1968)Google Scholar
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    T. Ashida, S. Bando and M. Kakudo, Acta Crystallogr. B 28, 1131 (1972)Google Scholar
  3. 5.
    M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of GuelphGuelphCanada

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