Differential cross sections for the elastic scattering of 14.6 MeV neutrons from $^{9}\mathrm{Be}$, C, $^{27}\mathrm{Al}$, Fe, $^{59}\mathrm{Co}$, $^{89}\mathrm{Y}$, $^{93}\mathrm{Nb}$, In, $^{140}\mathrm{Ce}$, $^{181}\mathrm{Ta}$, $^{197}\mathrm{Au}$, $^{208}\mathrm{Pb}$, and $^{209}\mathrm{Bi}$ have been measured using a time-of-flight facility. The measured cross sections cover the angular range from 9.2\ifmmode^\circ\else\textdegree\fi{} to 159\ifmmode^\circ\else\textdegree\fi{}. Calculations have been carried out using two local microscopic optical potentials, based on the work of Jeukenne, Lejeune, and Mahaux, and of Brieva and Rook. Reasonably good agreement with the measurements is found over the whole mass range, with the Jeukenne-Lejeune-Mahaux potential giving systematically better agreement with the data. The quality of the results with the Jeukenne-Lejeune-Mahaux potential compares well with that obtained from phenomenological optical model calculations using global parameters.