Synthesis and luminescent properties of bismuth titanates Bi$_{1.6}$Ho$_{x}$Ti$_{2}$O$_{7-\delta}$ and Bi$_{1.6}$Mg$_{0.1}$Ho$_{x}$Ti$_{2}$O$_{7-\delta}$

Pyrochlores Bi$_{1.6}$Ho$_{x}$Ti$_{2}$O$_{7-\delta}$ and Bi$_{1.6}$Mg$_{0.1}$Ho$_{x}$Ti$_{2}$O$_{7-\delta}$, where $x$ = 0, 0.01, 0.05, and 0.1, and Bi$_{1.5}$Ho$_{x}$Ti$_{2}$O$_{7-\delta}$, where $x$ = 0.25 and 0.5, have been synthesized and their structural, optical, and luminescence properties have been studied. As a result of analyzing the data obtained experimentally and the available theoretical data, it is shown that the intrinsic luminescence of the samples is due to the O2$p\leftrightarrow$ Bi6$p$ and Bi6$s\leftrightarrow$ Bi6$p$ electron transitions and the impurity luminescence is due to the $f$–$f$ transitions in Ho$^{3+}$ and the O2$p\to$ Ho$^{3+}$ charge transfer.