Uniform one-dimensional atomic chains and similar systems are generally unstable against so-called Peierls distortion, the process which can be illustrated by the following diagram:
A uniform 1D chain often can lower its energy by doubling its period. Most often it happens in one of the two ways depicted above. Either the neighboring atoms alternately get slightly closer and further apart or they can get displaced (in a symmetric or asymmetric way) forming a chain of buckled dimers. On a surface buckling can happen both in and out of the plane.
The resulting chain with the doubled period is strictly speaking not anymore one-dimensional, since all atoms are not identical any longer (there are two distinctly different types after dimerization). In practice it often leads to systems undergoing a metal-to-insulator transition, as an odd electron count for a metallic 1D chain changes into an even count for a chain of dimers.
