Degrees of freedom for a metal crystal

AI Thread Summary
The discussion centers on the degrees of freedom for atoms in a metal crystal, specifically addressing the calculation of theoretical heat capacity. It is clarified that each atom in the crystal has 6 degrees of freedom, which includes 3 translational and 3 vibrational modes. While a rigid body has 6 degrees of freedom, the atoms are primarily free to vibrate around their equilibrium positions. Each vibration mode contributes two degrees of freedom, accounting for both kinetic and potential energy. Ultimately, the total degrees of freedom for the atoms in the crystal is confirmed to be 6.
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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.

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