Case Study Oxygen Ordering in High Tc Superconductors

5 Case Study Oxygen Ordering in High Tc Superconductors 

There is much to be admired in the analyses presented here. In my opinion, this serves as a shining example of many different elements in the quest to build effective theories of material response. First, it is to be noted again that the key structural features of these complex materials have been mapped onto a corresponding two-dimensional model, itself already an intriguing and useful idea. In addition, the construction of the cluster expansion illustrates the way in which first-principles calculations for a relatively complex material can be used to inform a more tractable (and enlightening) model. Finally, the tools of statistical mechanics can be used to explore the phase diagrams of these systems which helps explain observed features of these problems but also suggests further complexity as can be seen in fig. 3 of de Fontaine et al. (1990). 

This chapter has shown how the zero-temperature analyses presented earlier in the book may be extended to incorporate finite-temperature effects. By advancing the harmonic approximation we have been able to construct classical and quantum mechanical models of thermal vibrations that are tractable. These models have been used in the present chapter to examine simple models of both the specific heat and thermal expansion. In later chapters we will see how these same concepts emerge in the setting of diffusion in solids and the description of the vibrational entropies that lead to an important class of structural phase transformations. 

Thermodynamics of Crystals by D. C. Wallace, Dover Publications, Inc., Mineola New York, 1998. This book has already appeared in the further reading list for chap. 5, but it is pertinent to the subject of the present chapter as well, especially his chap. 4. 

Thermophysical Properties of Materials by G. Grimvall, North-Holland Publishing Company, Amsterdam The Netherlands, 1986. GrimvalTs book is full of insights into the vibrational and electronic contributions to the entropy, in addition to much else. 

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