Atomic-scale origin of ultrahigh piezoelectricity in samarium-doped PMN-PT ceramics

Designing high-performance piezoelectric materials based on atomic-scale calculations is highly desired in recent years, following the understanding of the structure-property relationship of state-of-the-art piezoelectric materials. Previous mesoscale simulations showed that local structural heterogeneity plays an important role in the piezoelectric property of ferroelectrics; that is, larger structural heterogeneity leads to higher piezoelectricity. In this Rapid Communication, by combining first-principles calculations and experimental characterizations, we explored the atomic-scale origin of the high piezoelectricity for samarium-doped $\mathrm{Pb}\left(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}\right){\mathrm{O}}_3\text{−}\mathrm{PbTi}{\mathrm{O}}_3$ (PMN-PT) ceramics, which possesses the highest piezoelectric $d_{33}$ of $\sim 1500\mathrm{pC}{\mathrm{N}}^{-1}$ among all known piezoelectric ceramics. The impacts of various dopants on local structure and piezoelectric properties of PMN-PT ceramics were investigated in terms of the effective ionic radius and cation valence. Our results show that A-site dopants with a valence of 3+ are more effective to produce local structural heterogeneity in PMN-PT when compared with the A-site dopants with a valence of 2+, and a smaller dopant size leads to a larger variation of local structure. According to this study, the outstanding piezoelectricity in Sm-doped PMN-PT ceramics is attributed to the fact that $\mathrm{S}{\mathrm{m}}^{3+}$ is the smallest ions that can entirely go to the A site of PMN-PT rather than the B site. The present work may benefit the design of high-performance piezoelectric materials based on the concept of local structural engineering.

Figure 1

Room-temperature piezoelectric coefficients and dielectric permittivities for 2.5 mol % R-doped (a) PMN-29PT and (b) PMN-31PT; electrical-field-induced strain curves for 2.5 mol % R-doped (c) PMN-29PT and (d) PMN-31PT.

Figure 2

(a) XRD patterns of 2.5 mol % R-PMN-31PT, and enlarged peak around $2\theta =29.6^{\circ }$ for clarifying the diffraction peak of pyrochlore phase; (b) variation in cell volume as a function of composition; (c), (d) Room-temperature XRD profiles for La- and Dy-doped PMN-31PT with respect to doping levels; (e) variation in the unit cell volume of PMN-31PT with various dopants ($\mathrm{L}{\mathrm{a}}^{3+}$, $\mathrm{S}{\mathrm{m}}^{3+}$, $\mathrm{D}{\mathrm{y}}^{3+}$, and ${\mathrm{Y}}^{3+}$) as a function of doping content.

Figure 3

Temperature dependence of the dielectric constant and loss tangent at three fixed frequencies (100 Hz, 1 kHz, and 10 kHz) for PMN-31PT with 2.5 mol % dopants: (a) La, (b) Nd, (c) Sm, (d) Gd, (e) Dy, and (f) Y. $T_C$ values shown in the inset were recorded at 1 kHz.

Figure 4

Structure models, DFT calculated lattice constants, and polarizations for undoped and doped PMN-25PT. (a) A $2\times 2\times 2$ supercell with 40 atoms for PMN-25PT; (b) the supercell with A-site dopant for one Pb atom; (c) the supercell with B-site dopant for one Mg, Nb1, Nb2, or Ti atom. The large gray spheres represent Pb atoms; the small red spheres denote O atoms; and the orange, blue, and green spheres are for Mg, Nb, and Ti atoms, respectively. (c) The lattice parameters ($a$, $b$, $c$), and (d) the polarization components $\left(P_x,P_y,P_z\right)$ of the PMN-25PT and those with dopants. The ionic radius values are from Ref. [34] for $\mathrm{P}{\mathrm{b}}^{2+}$, $\mathrm{B}{\mathrm{a}}^{2+}$, $\mathrm{L}{\mathrm{a}}^{3+}$, $\mathrm{N}{\mathrm{d}}^{3+}$, and $\mathrm{S}{\mathrm{m}}^{3+}$ with coordination number 12 and for $\mathrm{G}{\mathrm{d}}^{3+}$, $\mathrm{D}{\mathrm{y}}^{3+}$, ${\mathrm{Y}}^{3+}$, and $\mathrm{L}{\mathrm{u}}^{3+}$ with coordination number 6.