Tetrahedral amorphous carbon (ta-C) is a dense form of amorphous carbon with a structure consisting of a highly tetrahedral bonding network. Approximately 20% of the atoms in ta-C are ${\mathit{sp}}^{2}$ hybridized and the presence of these sites plays an important role in the electrical and optical properties of the material. In the present investigation, we use 50 keV ${\mathrm{C}}^{+}$ and 200 keV ${\mathrm{Xe}}^{+}$ ion implantation to damage the structure in a controlled manner. The structure of the ta-C following ion irradiation is monitored using the dose dependence of the electrical conductivity, Raman spectroscopy, electron diffraction, and electron energy-loss spectroscopy. It is shown that the damage is predominantly reflected in an increased concentration of ${\mathit{sp}}^{2}$-bonded sites. With increasing dose, the structure is observed to change from an essentially tetrahedral network containing ${\mathit{sp}}^{2}$ sites as ``defects'' to an essentially ${\mathit{sp}}^{2}$-bonded structure in which there is a high degree of in-plane disorder combined with a regular stacking of the planes.