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Carbon dioxide is abundant in ice mantles of dust grains; some is found inthe pure crystalline form as inferred from the double peak splitting of thebending profile at about 650 cm$^{-1}$. To study how CO$_2$ segregates into thepure form from water-rich mixtures of ice mantles and how it then crystallizes,we used Reflection Absorption InfraRed Spectroscopy (RAIRS) to study thestructural change of pure CO$_2$ ice as a function of both ice thickness andtemperature. We found that the $\nu_1+\nu_3$ combination mode absorptionprofile at 3708~cm$^{-1}$ provides an excellent probe to quantify the degree ofcrystallinity in CO$_2$ ice. We also found that between 20 and 30~K, there isan ordering transition that we attribute to reorientation of CO$_2$ molecules,while the diffusion of CO$_2$ becomes significant at much higher temperatures.In the formation of pure crystalline CO$_2$ in ISM ices, the rate limitingprocess is the diffusion/segregation of CO$_2$ molecules in the ice instead ofthe phase transition from amorphous to crystalline after clusters/islands ofCO$_2$ are formed.

Characterization of thin film CO$_2$ ice through the infrared $\nu_1+\nu_3$ combination mode