Structural phase transitions and out-of-plane dust lattice instabilities   in vertically confined plasma crystals
  The formation of plasma crystals confined in an external one-dimensional parabolic potential well is simulated for a normal experimental environment employing a computer code called BOXITREE. Under appropriate conditions, crystals were found to form layered systems. The system's structural phase transitions, including transitions between crystals with differing numbers of layers and the same number of layers but different intralayer structures, were investigated and found to agree with previous theoretical and experimental research results. One- to two-layer transitions were examined in detail and shown to start at the point where the out-of-plane lattice instability appears. The resulting three layer system caused by this instability was observed at the center of the system. Finally, growth rates for this out-of-plane lattice instability were obtained using the BOXITREE simulation with these results shown to agree with those obtained from analytical theory. 
K. Qiao and T. W. Hyde