  An equally spaced linear chain of ions provides a test-bed for studying the
defect formation in a finite size 1D system. In particular, defect formation
related to topological phase transition from a linear configuration to a
zig-zag one is of interest here. A semi-empirical expression provides an
excellent agreement to the numerical results. The non-adiabatic transition
between the chain and zig-zag topologies for a finite size system of 30 ions
shows clear distinction from non-uniformly distributed ion chain. Thus the
underlying Homogeneous Kibble-Zurek model can be tested in presently accessible
ion trap experiments. Furthermore, our study indicates collective defect
behaviour appearing through the correlation length measurements.
