Soft Modes



Soft modes can be considered as direct evidence for structural changes in crystals because of their frequencies diminishing toward the critical temperature, destabilizing lattice structure. In dielectric crystals, soft modes are detected with time-dependent electric fields at low frequencies. In nondielectric crystals, neutron inelastic scatterings are the method for studying soft phonons. Although the spatial detail of condensates is implicit, the soft mode can be analyzed for symmetry changes at phase transitions, that is caused by an adiabatic potential. In this chapter, we discuss the relation between critical anomalies and soft modes observed in dielectric and neutron inelastic scattering experiments.


Transverse Mode Phonon Scattering Soft Mode Neutron Inelastic Scattering Adiabatic Potential 
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  1. 16.
    X. Pan and H.-G. Unruh, J. Phys. Condens. Matter 2, 323 (1990)ADSCrossRefGoogle Scholar
  2. 19.
    J. Petzelt, G. V. Kozlov and V. V. Volkov, Ferroelectrics 73, 101 (1987)CrossRefGoogle Scholar
  3. 20.
    A. Cowley, Prog. Phys. 31, 123 (1968)ADSCrossRefGoogle Scholar
  4. 21.
    R. Currat, K. A. Müller, W. Berlinger and F. Desnoyer, Phys. Rev. B 17, 2937 (1978)ADSCrossRefGoogle Scholar
  5. 22.
    S. M. Shapiro, J. D. Axe, G. Shirane and T. Riste, Phys. Rev. B 6, 4332 (1972)ADSCrossRefGoogle Scholar
  6. 23.
    J. F. Scott, Raman spectroscopy of structural phase transitions in Light Scattering Near Phase Transitions, ed. H. Z. Cummins and A. P. Levanyuk (North-Holland, Amsterdam, 1983)Google Scholar
  7. 24.
    J. Feder and E. Pytte, Phys. Rev. B 1, 4803 (1970)ADSCrossRefGoogle Scholar
  8. 36.
    W. Cochran, The Dynamics of Atoms in Crystals, Chap. 8 (Edward Arnold, London, 1973)Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of GuelphGuelphCanada

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