In this research, formation of finite two-dimensional (2D) plasma crystals was numerically simulated. The structure was investigated for systems with various Debye length and it was found there is a transition from a complete hexagonal structure to a structure with concentric rings on the outer edge and hexagonal lattice in the interior as the Debye length increases. The vertical as well as horizontal oscillation modes thermally excited in the 2D dust coulomb clusters were investigated. The horizontal mode spectra is shown to agree with published results while the vertical mode spectra obtained from numerical simulation and analytical method agree with one another. The frequency of the vertical modes is shown to have a maximum corresponding to the whole system acting as a solid plane. For low frequency modes, the largest amplitude particle motion is concentrated in a few inner rings with the outer rings remaining almost motionless in contrast to the horizontal modes for which the strongest motion of the particles is concentrated in the inner rings at high frequencies.
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