Problem:Classical vibrations with a two-atom unit cell: Difference between revisions
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Latest revision as of 15:49, 20 September 2020
We here consider the one-dimensional chain with two atoms per unit cell, of masses \(m\) and \(M\), with one spring constant, \(K\), and with distances between atoms of \(d/2\). This system is illustrated in the two-atom spring figure on the Scattering from lattice vibrations page, and the basic definition are given in this equation on the Scattering from lattice vibrations page.
Question 1
Write down the equations of motion for each of the two atoms.
Question 2
Write down the trial solutions for the two atoms of the plane wave form type introduced on the Scattering from lattice vibrations page. Remember that there may be a phase shift, \(\phi(q)\) between the two types of atoms.
Question 3
Show that there are only two allowed values of \(\phi(q)\), which differ by \(\pi\).
Question 4
Show that the vibration frequencies can be written by this equation from the Scattering from lattice vibrations page.