Lattice Vibrations and Heat Capacity

  • Shigeji Fujita
  • Kei Ito


Einstein’s and Debye’s theories of the heat capacity of a solid are presented. The quantum particles (phonons) for the lattice vibrations are introduced.

Let us consider a crystal lattice at low temperatures. We may expect each atom forming the lattice to execute small oscillations around the equilibrium position. For illustration let us consider the one-dimensional lattice shown in Figure 2.1.


Heat Capacity Normal Mode Debye Temperature Lattice Vibration Lagrangian Density 
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  1. 1.
    A. Einstein, Ann. Physik 22, 186 (1907).ADSGoogle Scholar
  2. 2.
    P. Debye, Ann. Physik 39, 789 (1912).CrossRefADSGoogle Scholar
  3. 3.
    F.W. Sears and G.L. Salinger, Thermodynamics, Kinetic Theory, and Statistical Mechanics, 3rd ed. (Addison-Wesley, Reading, MA, 1975).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsUniversity at Buffalo, The State University of New YorkBuffaloUSA
  2. 2.Research DivisionThe National Center for University Entrance ExaminationsTokyoJapan

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