  The adsorption of $CO_2$ on the $Fe_3$$O_4$(001)-($\sqrt{2}$ $\times$
$\sqrt{2}$)R45{\deg} surface was studied experimentally using temperature
programmed desorption (TPD), electron spectroscopies (UPS and XPS), and
scanning tunneling microscopy (STM). $CO_2$ binds most strongly at defects
related to Fe2+ including antiphase domain boundaries in the surface
reconstruction and above incorporated Fe interstitials. On the pristine
surface, $CO_2$ adsorbs molecularly at fivefold-coordinated Fe3+ sites with a
binding energy of 0.4 eV. Above a coverage of 4 molecules per ($\sqrt{2}$
$\times$ $\sqrt{2}$)R45{\deg} unit cell, further adsorption results in a
compression of the first monolayer up to a density approaching that of a $CO_2$
ice layer. Surprisingly, desorption of the second monolayer occurs at a lower
temperature ($\approx$ 84 K) than $CO_2$ multilayers ($\approx$ 88 K),
suggestive of a metastable phase or diffusion-limited island growth. The paper
also discusses design considerations for a vacuum system optimized to study the
surface chemistry of metal oxide single crystals, including the calibration and
characterisation of a molecular beam source for quantitative TPD measurements.
