Fig. 7: Comparison of ferroelectric instabilities in displacive and order-disorder incipient ferroelectrics.
From: Incipient ferroelectricity in methylammonium lead halide perovskites
a Quantum paraelectric oxide perovskites (incipient ferroelectrics of displacive type). b Hybrid MAPbX3 halide perovskites (incipient ferroelectrics of order-disorder type). In the paraelectric phase of quantum paraelectrics the phonon soft mode frequency, ω, obeys the Cochran law, ω2 ∝ (T − TC) and the static electric susceptibility, \({\chi }_{{FE}}=\varepsilon -{\varepsilon }_{\infty }\), obeys the CW law, Eq. (2). In the paraelectric phase of MAPbX3 the susceptibility \({\chi }_{{FE}}\) also obeys the CW law, while the relaxation frequency, ω = 1/τ, follows Eq. (3). The paraelectric behavior is violated at low temperatures, and the crystal remains in a non-ferroelectric state because of (a) the quantum fluctuations or (b) the appearance at the temperature Tm = Ttilt of the phase in which halide octahedra are tilted around all three pseudocubic axes.
