By Rudolf P. Huebener
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Extra resources for Conductors, Semiconductors, Superconductors: An Introduction to Solid State Physics
Chapter 3 Permanent Movement in the Crystal Lattice Abstract The quantized energy of the vibrations of the atoms in the crystal lattice contributes to the speciﬁc heat and the thermal conductivity. As noted ﬁrst by Albert Einstein, the energy spectrum of the phonons is given by Planck’s radiation law, resulting in a distinct deviation from the classic law of Dulong and Petit. Subsequently, the Einstein model, based on a single phonon frequency, was extended by Peter Debye by including the complete phonon spectrum.
2) and are deﬁned as follows: A ¼ 2p bÂc ; ab Â c B ¼ 2p cÂa ; ab Â c C ¼ 2p aÂb ab Â c ð2:6Þ We see that the vectors A, B, C of the reciprocal lattice are oriented perpendicularly to two fundamental axes of the crystal lattice, respectively. The convenience of the introduction of the reciprocal lattice becomes obvious, if one wants to express mathematically a function having exactly the periodicity of the crystal lattice (for example, the scattering potential of the electrons). Such a function is obtained in the form X UðrÞ ¼ uG eiGr ð2:7Þ G where the summation extends over all vectors G of the reciprocal lattice.
Student of Sommerfeld, that crystals are Fig. 3 Wilhelm Conrad Röntgen (Photo Deutsches Museum) 2 Well Ordered Lattice Structures in Crystals 19 Fig. 4 Left Max von Laue. Right Set-up of the Laue experiment. On the left we note the X-ray tube and on the right the stage for mounting the crystal (Photos Deutsches Museum) likely to consist of a regular lattice arrangement of atoms. Von Laue noted immediately that crystals would be well suited for the diffraction of X-rays, as long as the distance between the atoms in the crystal and the wavelength of the X-rays had a similar magnitude.