Abstract
In Sect. 4.2 we saw how the 3rN equations of motion of a periodic solid can be largely decoupled by means of the plane-wave ansatz and the assumption of harmonic forces. With (4.7) we arrived at a system of equations that, for a given wave vector q, couples the wave amplitudes of the atoms within a unit cell. It can be shown mathematically that within the harmonic approximation the equations of motion, even for a nonperiodic solid, can be completely decoupled by means of a linear coordinate transformation to so-called normal coordinates. We thereby obtain a total of 3rN independent forms of motion of the crystal, each with a harmonic time dependence and a specific frequency which, in the case of a periodic solid, is given by the dispersiOn relation ?(q). Any one of these “normal modes” can gain or lose energy independently of the others.
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© 2009 Springer-Verlag Berlin Heidelberg
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Ibach, H., Lüth, H. (2009). Thermal Properties. In: Solid-State Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93804-0_5
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DOI: https://doi.org/10.1007/978-3-540-93804-0_5
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