Correction to: Dielectric properties of bismuth layer-structured ferroelectric Bi₃R₂Ti₃FeO₁₅ (R = Bi, Gd, and Nd) at microwave and radiofrequency

Correction to: Journal of Materials Science: Materials in Electronics (2021) https://doi.org/10.1007/s10854-021-06332-4

The original version of this article unfortunately contained a mistake. The Eqs. (11) and (12) in the paper [1] have been published with errors. The correct version of Eqs. 11 and 12 are below

$$ Z^{\prime} = \frac{{R_{g} \left[ {1 + \left( {\tau _{g} \omega } \right)^{{n_{g} }} \cos \left( {\frac{{n_{g} \pi }}{2}} \right)~} \right]}}{{1 + 2\left( {\tau _{g} \omega } \right)^{{n_{g} }} \cos ~\left( {\frac{{n_{g} \pi }}{2}} \right) + \left( {\tau _{g} \omega } \right)^{{2n_{g} }} ~}} + \frac{{R_{{gb}} \left[ {1 + \left( {\tau _{{gb}} \omega } \right)^{{n_{{gb}} }} \cos ~\left( {\frac{{n_{{gb}} \pi }}{2}} \right)~} \right]}}{{1 + 2\left( {\tau _{{gb}} \omega } \right)^{{n_{{gb}} }} \cos ~\left( {\frac{{n_{{gb}} \pi }}{2}} \right) + \left( {\tau _{{gb}} \omega } \right)^{{2n_{{gb}} }} }} $$

(11)

and

$$ - Z^{\prime\prime} = \frac{{R_{g} \left[ {1 + \left( {\tau _{g} \omega } \right)^{{n_{g} }} \sin ~\left( {\frac{{n_{g} \pi }}{2}} \right)~} \right]}}{{1 + 2\left( {\tau _{g} \omega } \right)^{{n_{g} }} \cos ~\left( {\frac{{n_{g} \pi }}{2}} \right) + \left( {\tau _{g} \omega } \right)^{{2n_{g} }} ~}} + \frac{{R_{{gb}} \left[ {1 + \left( {\tau _{{gb}} \omega } \right)^{{n_{{gb}} }} \sin ~\left( {\frac{{n_{{gb}} \pi }}{2}} \right)~} \right]}}{{1 + 2\left( {\tau _{{gb}} \omega } \right)^{{n_{{gb}} }} \cos ~\left( {\frac{{n_{{gb}} \pi }}{2}} \right) + \left( {\tau _{{gb}} \omega } \right)^{{2n_{{gb}} }} ~}}. $$

(12)

Note that the errors were only typographical, calculations and discussions in the article are unaffected, and the conclusions remain unchanged.