def _get_facet_chempots(self, facet):
        """
        Calculates the chemical potentials for each element within a facet.

        Args:
            facet: Facet of the phase diagram.

        Returns:
            { element: chempot } for all elements in the phase diagram.
        """
        complist = [self.qhull_entries[i].composition for i in facet]
        energylist = [self.qhull_entries[i].energy_per_atom for i in facet]
        m = [[c.get_atomic_fraction(e) for e in self.elements] for c in
             complist]
        chempots = np.linalg.solve(m, energylist)
        return dict(zip(self.elements, chempots))