This work describes a process-oriented, microphysical-chemical model to simulate the formation and evolution of aerosols and ice crystals under the conditions prevailing in the upper troposphere and lower stratosphere. The model can be run as a box model or along atmospheric trajectories, and considers mixing, gas phase chemistry of aerosol precursors, binary homogeneous aerosol nucleation, homogeneous and heterogeneous ice nucleation, coagulation, condensation and dissolution, gas retention during particle freezing, gas trapping in growing ice crystals, and reverse processes. Chemical equations are solved iteratively using a second order implicit integration method. Gas-particle interactions and coagulation are treated over various size structures, with fully mass conserving and non-iterative numerical solution schemes. Particle types include quinternary aqueous solutions composed of H₂SO₄, HNO₃, HCl, and HBr with and without insoluble components, insoluble aerosol particles, and spherical or columnar ice crystals deriving from each aerosol type separately. Three case studies are discussed in detail to demonstrate the potential of the model to simulate real atmospheric processes and to highlight current research topics concerning aerosol and cirrus formation near the tropopause. Emphasis is placed on how the formation of cirrus clouds and the scavenging of nitric acid in cirrus depends on small-scale temperature fluctuations and the presence of efficient ice nuclei in the tropopause region, corroborating and partly extending the findings of previous studies.