Degrees of freedom for a metal crystal

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zezima1
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Recently did an exercise calculating the theoretic heat capacity of a metal. In the solutions manual they put the degrees of freedom f=6. Why is that? I know that a rigid body has 6 degrees of freedom but does that apply to each atom in the crystal?
 
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The atoms of the crystal are free to vibrate around their equilibrium points instead of translation. 3 vibration modes belong to each atom.
A vibration mode has two degrees of freedom, (position and velocity): the atoms have both kinetic and potential energy. So the degrees of freedom is 6 for each atom.

ehild