This chapter describes a type of oscillatory particle motion that is related to wave motion-namely, simple harmonic motion. MARION, in Physics in the Modern World (Second Edition), 1981 Publisher Summary The sum of the simple harmonic oscillation of each nucleus, as a function of nucleus position in the lattice and time, produces an overall displacement wave in the crystal lattice, which can be expressed as a sum of normal vibration modes. The displacement of the nuclei from their equilibrium positions, is caused by heating of the crystal lattice or another means of energy exchange, such as neutron collisions.
The nucleus displacement vector u 0 d ( 0 ) at time t = 0 and u 0 d ( t ) for the same nucleus at later time t, as well as displacement vector u l d ′ ( t ) for another nucleus at later time t, can be expressed as the sum of displacements, which arise from a set of normal vibration modes.
The interatomic forces between the crystal atoms (ions) are assumed to undergo simple harmonic motion, where the force acting on a displaced nucleus, is proportional to the displacement distance of the nucleus from its equilibrium lattice position.
Jay Theodore Cremer Jr., in Advances in Imaging and Electron Physics, 2012 2 The Nucleus Displacement Vector in a Non-Bravais Crystal with Nuclei Vibrations
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