Lattice Dynamics and Density Functional Perturbation Theory

  • Jonathan BreezeEmail author
Part of the Springer Theses book series (Springer Theses)


The focus of this thesis now shifts towards the physics that describes the properties of microwave dielectrics and the means of computationally predicting them. Lattice dynamics describes the vibrational collective excitations in solids known as phonons and is a cornerstone of solid-state physics. Infrared, Raman and neutron-diffraction spectra, specific heat capacity, thermal expansion, heat conduction and electron–phonon interaction-related phenomena such as resistivity of metals and superconductivity are a few examples of where lattice dynamics has been applied with great success.


Atomic Displacement Dynamical Matrix Electron Charge Density Longitudinal Optic Phonon Dispersion Relation 
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  1. 1.
    M. Born, K. Huang, Dynamical Theory of Crystal Lattices, 1st ed. (Oxford University Press, Oxford, 1954)Google Scholar
  2. 2.
    P.D. De Cicco, F.A. Johnson, The quantum theory of lattice dynamics IV. Proc. R. Soc. Lond. A. 310, 111 (1969)Google Scholar
  3. 3.
    R. Pick, M.H. Cohen, R.M. Martin, Microscopic theory of force constants in the adiabatic approximation. Phys. Rev. B 1, 910 (1970)CrossRefGoogle Scholar
  4. 4.
    P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964)CrossRefGoogle Scholar
  5. 5.
    W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965)CrossRefGoogle Scholar
  6. 6.
    S. Baroni, R. Resta, Ab initio calculation of the macroscopic dielectric constant in silicon. Phys. Rev. B 33, 7017 (1986)CrossRefGoogle Scholar
  7. 7.
    M. Born, J.R. Oppenheimer, Zur Quantentheorie der Molekeln. Annelen der Physik 389, 457 (1927)CrossRefGoogle Scholar
  8. 8.
    D.M. Ceperley, B.J. Alder, Exchange-correlation potential and energy for density-functional calculation. Phys. Rev. Lett. 45, 567 (1980)CrossRefGoogle Scholar
  9. 9.
    J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048 (1981)CrossRefGoogle Scholar
  10. 10.
    S. Baroni, P. Giannozzi, A. Testa, Green’s-function approach to linear response in solids. Phys. Rev. Lett. 58, 1861 (1987)CrossRefGoogle Scholar
  11. 11.
    X. Gonze, Adiabatic density-functional perturbation theory. Phys. Rev. A 52, 1096 (1995)CrossRefGoogle Scholar
  12. 12.
    X. Gonze, Perturbation expansion of variational principles at arbitrary order. Phys. Rev. A 52, 1086 (1995)CrossRefGoogle Scholar
  13. 13.
    D. Bohm, Quantum Theory (Prentice Hall, New Jersey, 1951)Google Scholar
  14. 14.
    D. Vanderbilt, R.D. King-Smith, Electric polarization as a bulk quantity and its relation to surface charge. Phys. Rev. B 48, 4442 (1993)CrossRefGoogle Scholar
  15. 15.
    R. Resta, Macroscopic polarization in crystalline dielectrics: the geometrical phase approach. Rev. Mod. Phys. 66, 899 (1994)CrossRefGoogle Scholar
  16. 16.
    S. Baroni et al., Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515 (2001)CrossRefGoogle Scholar
  17. 17.
    W.E. Pickett, Pseudopotential methods in condensed matter applications. Comput. Phys. Rep. 9, 115 (1989)CrossRefGoogle Scholar
  18. 18.
    P. Pulay, Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules: I. Theory. Mol. Phys. 17, 197 (1969)CrossRefGoogle Scholar
  19. 19.
    D. Hamann, M. Schlüter, C. Chiang, Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494 (1979)CrossRefGoogle Scholar
  20. 20.
    S.G. Louie, S. Froyen, M.L. Cohen, Nonlinear ionic pseudopotentials in spin-density-functional calculations. Phys. Rev. B 26, 1738 (1982)CrossRefGoogle Scholar
  21. 21.
    L. Kleinman, D.M. Bylander, Efficacious form for model pseudopotentials. Phys. Rev. Lett. 48, 1425 (1982)CrossRefGoogle Scholar
  22. 22.
    M.C. Payne et al., Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045 (1992)CrossRefGoogle Scholar
  23. 23.
    P. Giannozzi, in Computational Approaches to Novel Condensed Matter Systems: Applications to Classical and Quantum Systems, ed. by D. Neilson, M. Das (Plenum, 1995), p. 67Google Scholar
  24. 24.
    R.H. Lyddane, R.G. Sachs, E. Teller, On the polar vibrations of alkali halides. Phys. Rev. 59, 673 (1941)CrossRefGoogle Scholar
  25. 25.
    H. Böttger, Principles of the Theory of Lattice Dynamics (Physik-Verlag, 1983)Google Scholar

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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Imperial College LondonLondonUK

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