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The two experimental studies reported in this thesis contribute important new knowledge about phase transitions in two-dimensional complex plasmas: in one case a determination of the coupling parameter (ratio of mean potential to mean kinetic energy of the particles in an ensemble), and in the other a detailed characterization of the non-equilibrium recrystallization of a two-dimensional system. The latter results are used to establish the connection between structural order parameters and the kinetic energy, which in turn gives novel insights into the underlying physical processes determining the two-dimensional phase transition.