Properties D and aD are different

Under $({\mathrm{♢}}^{\ast })$ we construct a locally countable, locally compact, 0-dimensional $T_2$ space $X$ of size $\text{omg}$ which is aD however not even linearly D. This consistently answers a question of Arhangel’skii, whether aD implies D. Furthermore we answer two problems concerning characterization of linearly D-spaces, raised by Guo and Junnila.