content_image/408003.jpg content_image/408004.jpg content_image/408008.jpg content_image/408005.jpg content_image/408007.jpg content_image/408006.jpg content_image/408013.jpg content_image/408009.jpg content_image/408010.jpg content_image/408012.jpg content_image/408014.jpg content_image/408011.jpg
ation 

<img src='content_image/408003.jpg'>

determines the crystal viscosity 

<img src='content_image/408004.jpg'>

For models of magnetic relaxation wherein acoustic heat- ing dominates via magnetostriction 33 and for models of electric relaxation wherein acoustic heating dominates via electrostriction, the relaxation time tensor in Eq.(2) can be related to the viscosity tensor Eq.(6). An inde- pendent microscopic derivation of viscosity induced re- laxation is given in Appendix A. In the concluding Sec.V, the sound wave absorption physics of the viscous damp- ing mechanism will be noted. 

Our purpose is to review the thermodynamic proper- ties of both magnetically ordered crystals and polariza- tion ordered crystals. The former is characterized by a remnant magnetization M for vanishing applied mag- netic intensity H → 0 while the latter is characterized by a remnant polarization P for vanishing applied electric field E → 0. 

Let w be the enthalpy per unit volume. The funda- mental thermodynamic law determining the equations of state for magnetically ordered crystals is given by 

wherein s is the entropy per unit volume, T is the temper- ature, e is the crystal strain and σ is the crystal stress. The magnetic adiabatic susceptibility is defined by 

If 

denotes a unit vector in the direction of the magnetiza- tion, then the tensor Λ$_{ijkl}$ describing adiabatic magne- tostriction coefficients may be defined as 34 

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## II. THERMODYNAMICS 

## A. Magnetically Ordered Crystals 

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<img src='content_image/408007.jpg'>

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When the system is out of thermal equilibrium, the driv- ing magnetic intensity is 

wherein τ are the relaxation time tensor transport co- efficients which determine the relaxation of the ordered magnetic system into a state of thermal equilibrium. 

The fundamental thermodynamic law determining the equations of state for ordered polarized crystals is given by 

wherein w is the enthalpy per unit volume, s is the en- tropy per unit volume, T is the temperature, e is the crystal strain and σ is the crystal stress. The electric adiabatic susceptibility is defined by 

The tensor β$_{ijk}$ describing adiabatic electrostriction co- efficients may be defined as 34 

The piezoelectric tensor is closely related to the elec- trostriction tensor via 

<img src='content_image/408013.jpg'>

When the system is out of thermal equilibrium, the driv- ing electric field is 

wherein τ is the relaxation time tensor transport coef- ficients which determine the relaxation of the ordered polarized system into a state of thermal equilibrium. 

Here we shall show how the magnetic intensity H$_{d}$ drives the magnetic resonance equations of motion in magnetically ordered systems. Similarly, we shall show how the electric field E$_{d}$ drives the polarization resonance equations of motion for polarized ordered systems. 

<img src='content_image/408009.jpg'>

## B. Ordered Polarized Crystals 

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<img src='content_image/408012.jpg'>

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## III. RESONANCE DYNAMICS 

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