  Carbon dioxide is abundant in ice mantles of dust grains; some is found in
the pure crystalline form as inferred from the double peak splitting of the
bending profile at about 650 cm$^{-1}$. To study how CO$_2$ segregates into the
pure form from water-rich mixtures of ice mantles and how it then crystallizes,
we used Reflection Absorption InfraRed Spectroscopy (RAIRS) to study the
structural change of pure CO$_2$ ice as a function of both ice thickness and
temperature. We found that the $\nu_1+\nu_3$ combination mode absorption
profile at 3708~cm$^{-1}$ provides an excellent probe to quantify the degree of
crystallinity in CO$_2$ ice. We also found that between 20 and 30~K, there is
an 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 limiting
process is the diffusion/segregation of CO$_2$ molecules in the ice instead of
the phase transition from amorphous to crystalline after clusters/islands of
CO$_2$ are formed.
