Dielectric nonlinearity and spontaneous polarization of ${\mathrm{KTa}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Nb}}_{\mathit{x}}$${\mathrm{O}}_3$ in the diffuse transition range

${\mathrm{KTa}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Nb}}_{\mathit{x}}$ ${\mathrm{O}}_3$ (KTN) in an intermediate-concentration range (x=15.7%) has been studied using dielectric-constant and spontaneous-polarization measurements. A large peak in the dielectric constant (${\mathrm{\epsilon }}_{\max }$≃70 000) is observed at the temperature ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$. From room temperature down to ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$+20 K, ε obeys a Curie-Weiss law with ${\mathit{T}}_0$∼142.3 K. Below, ε deviates from this law and P-E hysteresis loops are observed. These results indicate that the phase transition exhibits a diffuse character which is related to the appearance of microscopic polarized regions or cells. The ε peak at ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$ exhibits a cusp shape and becomes flattened upon application of low dc-bias fields. A corresponding dielectric loss peak is also observed, the position of which reveals the relaxational character of the transition. Through measurements of ε(E,T) for different dc-bias fields, we have characterized the dielectric nonlinearities in the transition range; the first nonlinear coefficient, ${\mathrm{\epsilon }}^{\mathrm{}\left(2\right)\mathrm{}}$, diverges in two distinct ranges, as (T-${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$ ${)}^{\mathrm{-}\mathit{n}}$, with n∼9 initially and with n≃2 closer to ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$. These results suggest that diffuse phase transitions in mixed ferroelectrics are due to the ordering of polar cells modified by mutual strain interactions.