Advertisement

Order Variables and the Adiabatic Potential

  • Minoru Fujimoto
Chapter

Abstract

Crystals constitute a representative group of condensed matter, composed of a large number of identical ions and molecules. Because of imprecise theories of cohesive forces available today, we considered their geometrical structure as granted [1]. Nevertheless, their correlation energy is essential for structural stability, for which we may consider permutable constituents quantum-mechanically. On the other hand, if symmetry in a chemically pure crystal pertains to the thermodynamic environment, the stability can be attributed to the invariance under symmetry operations like rotation, reflection, translation, etc.; the structural invariance determines the correlation energy in a stable crystal. However, the local symmetry can be disrupted below the critical temperature, if a displacement occurs in the constituent. Exhibiting local fluctuations, the strained lattice suffers instability, which is however relaxed thermally to a strain-free structure with decreasing temperature, as postulated by Born and Huang. Meanwhile, symmetry in stable crystals is well documented by X-ray crystallography, as classified by the group theory. In this chapter, leaving details of the symmetry group to references, we discuss the origin of internal variables at the critical temperature, which are known as order variables and responsible for structural transitions.

Keywords

Brillouin Zone Order Variable Reciprocal Lattice Acoustic Mode Phonon Scattering 
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. 1.
    H.D. Megaw, Crystal Structures: A Working Approach (Saunders, Philadelphia, 1973)Google Scholar
  2. 2.
    T. Asida, S. Bando, M. Kakudo, Acta Cryst. B28, 1131 (1972)Google Scholar
  3. 3.
    J.M. Ziman, Models of Disorder (Cambridge Univ. Press, London, 1958)Google Scholar
  4. 4.
    M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford Univ. Press, 1968)Google Scholar
  5. 5.
    C. Kittel, Introduction to Solid State Physics, 6th edn. (Wiley, New York, 1986)Google Scholar
  6. 6.
    C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963)Google Scholar
  7. 7.
    M. Tinkham, Group Theory of Quantum Mechanics (McGraw-Hill, New York, 1964)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Minoru Fujimoto
    • 1
  1. 1.Department of PhysicsUniversity of GuelphGuelphCanada

Personalised recommendations