  We present a calculational method to predict terminations of growing or
as-deposited surfaces as a function of the deposition conditions. Such
characterizations are valuable for understanding catalysis and growth
phenomena. The method combines ab-initio density functional theory (DFT)
calculations and experimental thermodynamical data with a rate-equations
description of partial pressures in the reaction chamber. The use of rate
equations enables a complete description of a complex gas environment in terms
of a few, (experimentally accessible) parameters. The predictions are based on
comparisons between free energies of reaction associated with the formation of
surfaces with different terminations. The method has an intrinsic
non-equilibrium character. In the limit of dynamic equilibrium (with equal
chemical potential in the surface and the gas phase) we find that the
predictions of the method coincide with those of standard ab-initio based
equilibrium thermodynamics. We illustrate the method for chemical vapor
deposition (CVD) of TiC(111) and TiN(111), and find that the emerging
termination can be controlled both by the environment and the growth rate.
