The possibility of directly growing carbon nanofibers (CNFs) and carbon nanotubes (CNTs) on half-Heusler alloys by Chemical Vapour Deposition (CVD) is investigated for the first time, without using additional catalysts, since the half-Heusler alloys per se may function as catalytic substrates, according to the findings of the current study. As a carbon source, acetylene is used in the temperature range of 700–750 °C. The n-type half-Heusler compound ${\left({\mathrm{Z}\mathrm{r}}_{0.4}{\mathrm{T}\mathrm{i}}_{0.6}\right)}_{0.33}{\mathrm{N}\mathrm{i}}_{0.33}{\left({\mathrm{S}\mathrm{n}}_{0.98}{\mathrm{S}\mathrm{b}}_{0.02}\right)}_{0.33}$ is utilized as the catalytic substrate. At first, a computational model is developed for the CVD reactor, aiming to optimize the experimental process design and setup. The experimental process conditions are simulated to investigate the reactive species concentrations within the reactor chamber and the activation of certain reactions. SEM analysis confirms the growth of CNFs with diameters ranging from 450 nm to 1 μm. Raman spectroscopy implies that the formed carbon structures resemble CNFs rather than CNTs, and that amorphous carbon also co-exists in the deposited samples. From the characterization results, it may be concluded that a short reaction time and a low acetylene flow rate lead to the formation of a uniform CNF coating on the surface of half-Heusler alloys. The purpose of depositing carbon nanostructures onto half-Heusler alloys is to improve the current transfer, generated from these thermoelectric compounds, by forming a conductive coating on their surface.