Order Variables and Adiabatic Potentials

  • Minoru Fujimoto


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.


Lattice Site Brillouin Zone Internal Variable Electric Dipole Moment Order Variable 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of GuelphGuelphCanada

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