Dielectric properties of the nanoporous MCM-41 matrix filled with the (NH$_4$)$_2$SO$_4$ ferroelectric

Variations with temperature of the linear dielectric permittivity and amplitude of the third harmonic were studied for nanoporous MCM-41 matrices with 4.0-nm channel pores filled with the (NH$_4$)$_2$SO$_4$ ferroelectric, in comparison with bulk ammonium sulfate. The measurements were performed upon heating and cooling in the temperature range from 100 K to room temperature. A noticeable shift to low temperatures (by approximately 25 K) for the ferroelectric phase transition in the MCM-41/(NH$_4$)$_2$SO$_4$ nanocomposite as compared to bulk (NH$_4$)$_2$SO$_4$ was revealed. The temperature hysteresis observed at the phase transition in the nanocomposite was approximately 2 K which is close to that in bulk ammonium sulfate. The significant decrease of the transition temperature in nanostructured ammonium sulfate agrees with the theoretical predictions based on the Landau and Ising models of the size effect on the ferroelectric phase transition in isolated small particles.