A process for separating acid gases such as CO.sub.2, H.sub.2 S, and SO.sub.2, other sulfur-containing molecules such as COS, and other relatively high boiling point impurities from lower boiling point components of a gas stream comprises: dehydrating the gas stream and contacting it, at an elevated pressure and at substantially the dew point temperature of carbon dioxide therein, with a liquid carbon dioxide refrigerant-absorbent to absorb such impurities other than CO.sub.2, and separating the liquid carbon dioxide and absorbed impurities; condensing CO.sub.2, and separating the liquid carbon dioxide and absorbed impurities; condensing CO.sub.2 from the residual gas stream at such pressure, preferably by indirect heat exchange; contacting the residual gas stream at such pressure with a second refrigerant-absorbent below the triple point temperature of carbon dioxide, and separating additional carbon dioxide therewith. The second refrigerant-absorbent is preferably a liquid-solid slurry comprising an organic liquid vehicle and carbon dioxide in the solid phase to provide in situ refrigeration by melting of the solid phase. The final, residual gas stream is heat exchanged to recover its refrigeration potential. Further, a crystallization process is disclosed for separating a crystallizable material and an excluded material which is at least partially excluded from the solid phase of the crystallizable material obtained upon freezing a liquid mixture of the materials. The solid phase is formed and melted at spaced locations in a liquid mixture of the materials and, within the liquid mixture, internal solid and liquid flows are maintained in opposite directions to effect separation of the materials. The solid phase is formed by evaporative cooling of the liquid mixture and melted by direct contact with a condensing vapor phase of the materials, each of these operations being performed substantially at the prevailing triple point locus conditions in the respective locations in the liquid mixture.