Crystal structure and dielectric properties of aurivillius phases $A_{0.5}$Bi$_{4.5}$B$_{0.5}$Ti$_{3.5}$O$_{15}$ ($A$ = Na, Ca, Sr, Pb; $B$ = Cr, Co, Ni, Fe, Mn, Ga)

New polycrystalline Bi-containing layered perovskite-like oxides having the Aurivillius phase (AP) structure with the general formula $A_{0.5}$Bi$_{4.5}$B$_{0.5}$Ti$_{3.5}$O$_{15}$ ($A$ = Na, Ca, Sr, Pb; $B$ = Cr, Co, Ni, Fe, Mn, Ga) have been synthesized. The unit cell parameters of the synthesized compounds have been determined by X-ray powder diffraction. All studied APs crystallize in the orthorhombic system (space group $A2_1am$ (36)). The degree of distortion of AP unit cells has been analyzed based on the obtained structural parameters. The temperature dependences of the permittivity have been measured and the Curie temperatures have been determined for all the samples. The significant difference in the values of the permittivity maxima for APs Sr$_{0.5}$Bi$_{4.5}$Co$_{0.5}$Ti$_{3.5}$O$_{15}$ and Sr$_{0.5}$Bi$_{4.5}$Ni$_{0.5}$Ti$_{3.5}$O$_{15}$ has been interpreted based on the electron microscopy data and explained by substantial changes in the porosity and crystal grain sizes of these ceramic samples.