Elastic and anelastic relaxations in the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃: II. Strain–order parameter coupling and dynamic softening mechanisms

Abstract

Elastic and anelastic behaviour of single crystal and ceramic samples of Pb(Mg(1/3)Nb(2/3))O(3) has been investigated at frequencies of ~0.1-1.2 MHz through the temperature interval 10-800 K by resonant ultrasound spectroscopy (RUS). Comparison with data from the literature shows that softening of the shear modulus between the Burns temperature and the freezing interval is independent of frequency. The softening is attributed to coupling between acoustic modes and the relaxation mode(s) responsible for central peaks in Raman and neutron scattering spectra below the Burns temperature, and can be described with Vogel-Fulcher parameters. Shear elastic compliance and dielectric permittivity show similar patterns of temperature dependence through the freezing interval, demonstrating strong coupling between ferroelectric polarization and strain such that the response to applied stress is more or less the same as the response to an applied electric field, with a frequency dependence consistent with Vogel-Fulcher-like freezing in both cases. Differences in detail show, however, that shearing induces flipping between different twin orientations, in comparison with the influence of an electric field, which induces 180° flipping: the activation energy barrier for the former appears to be higher than for the latter. Below the freezing interval, the anelastic loss also has a similar pattern of evolution to the dielectric loss, signifying again that essentially the same mechanism is involved in the freezing process. Overall softening at low temperatures is attributed to the contributions of strain relaxations due to coupling with the local ferroelectric order parameter and of coupling between acoustic modes and continuing relaxational modes of the polar nanostructure. Dissipation is attributed to movement of boundaries between PNRs or between correlated clusters of PNRs. Overall, strain coupling is fundamental to the development of the characteristic strain, dielectric and elastic properties of relaxors.

Anelastic relaxor behavior of Pb(Mg1/3Nb2/3)O3

“…5,17 Comparing now dielectric and anelastic data for a same frequency, Figure 3, several observations can be made. As reported by other authors 11,13 our data show that, compared to the respective background susceptibilities, the dielectric relaxation is much stronger than the elastic: over the covered temperature range the electrical permittivity changes by more than five times while the change in elastic susceptibility is less than 10% (compare Figures 1 and 2 and see summary in Figure 3). Cordero et al report 40% increase in elastic susceptibility of PMN modified with 10% PbTiO 3 11 , while data for PMN obtained at high frequencies all show changes below 20%.…”

“…In fact, the mechanical and dielectric susceptibilities in PMN were reported to exhibit important differences in their temperature behavior. First, the maximum in elastic susceptibility for a given frequency is several times weaker than that in dielectric permittivity, while the peak appears broader for elastic than for dielectric susceptibility 11,13 . Importantly, because most studies of mechanical properties have covered a limited frequency range, the Vogel-Fulcher relationship has not been demonstrated in dielectric relaxors for mechanical properties.…”

“…[10][11][12][13] One would a priori expect that PNR in dielectric relaxors respond to dynamic mechanical fields in a similar fashion to what was observed in so-called "strain glass" of metal alloys; 14 that is, mechanical compliance of PMN should show a similar temperature-frequency behavior as dielectric permittivity but this has not been fully demonstrated so far. In fact, the mechanical and dielectric susceptibilities in PMN were reported to exhibit important differences in their temperature behavior.…”

“…Importantly, because most studies of mechanical properties have covered a limited frequency range, the Vogel-Fulcher relationship has not been demonstrated in dielectric relaxors for mechanical properties. Carpenter et al 13 showed that in their experimental studies of anelastic response of PMN the slope of ln! versus T (where…”

Elastic and anelastic relaxation behaviour of perovskite multiferroics I: PbZr0.53Ti0.47O3 (PZT)–PbFe0.5Nb0.5O3 (PFN)

“…This was found to provide good descriptions of precursor softening of the shear modulus in PbMg 1/3 Nb 2/3 O 3 [141] and PbSc 0.5 Ta 0.5 O 3 [142], and it also describes softening ahead of the cubic-tetragonal transition in BaTiO 3 [143]. These models have been tested for PZTFN6 but neither provides a quantitative fit to the precursor softening.…”