We present an extensive characterization of a quantum wire (QWR) structure using transmission electron microscopy (TEM). The structure consisted of a single GaAs layer in between AlGaAs barriers, grown on a GaAs substrate patterned with a submicrometre grating of V-grooves. For reference we also studied other QWR, as well as, quantum well (QW) samples, fabricated under similar conditions. We used bright field and dark field imaging to study the overall structure, high-resolution TEM to study the layer thickness and the interface quality, and chemical lattice imaging to study the compositional variations across the interfaces. In the QWR sample, there were mainly two distinctly different areas of the QW: on the (100) planes between the V-grooves, the QW was flat, whereas the QW on the near {111}A side walls of the V-grooves had a flat lower interface and a saw-tooth shaped upper interface. The QWRs at the bottom of the V-grooves were crescent shaped. We also observed a fundamental difference in growth of the GaAs and the AlGaAs on the side wall, where the AlGaAs formed straight interfaces, determined by high-index planes, whereas the GaAs tended to form alternating low-index planes giving a saw-tooth appearance of the GaAs QW.