Nanopore-induced dielectric and piezoelectric enhancement in PbTiO3 nanowires

doi:10.1016/j.actamat.2020.01.023

Acta Materialia

Volume 187, 1 April 2020, Pages 146-152

https://doi.org/10.1016/j.actamat.2020.01.023 Get rights and content

Abstract

Porous tetragonal PbTiO₃ nanowires, synthesized through an intermediate pre-perovskite structure, exhibit distinct behaviors from those of the corresponding bulk PbTiO₃. Here we investigate the role of nanopores in the ferroelectric, dielectric, and piezoelectric properties of ferroelectric PbTiO₃ nanowires employing phase-field simulations. It is found that the presence of pores gives rise to large enhancements in both dielectric constant and piezoelectric coefficient by ~50% and 30%, respectively, compared with those of the bulk PbTiO₃. It is shown that the smaller the pore size is, the higher the dielectric and piezoelectric responses of the nanowire are. A charge compensation mechanism is proposed to explain the experimentally measured change of oxygen ions concentration at the pore surfaces. The findings provide in-depth insights into modulation of material properties through nanopores.

Graphical abstract

Introduction

Ferroelectric materials find a variety of applications such as ferroelectric random access memories (FRAMs), sensors, actuators, and microelectromechanical systems (MEMS) [1], [2], [3], [4], [5]. The demand for device minimization has led to extensive experimental and theoretical efforts on the low-dimension ferroelectrics, such as thin films [5], [6], [7], [8], [9], nanowires [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], nanotubes [3,21,22], etc., have been carried out recently.

Lead titanate (PbTiO₃), a prototypical ferroelectric material of the ABO₃ perovskites [23], [24], [25], [26], [27], [28], is a model system for understanding the ferroelectric properties and related phenomena at the nanoscale [29,30]. There are two known structures for PbTiO₃ (PTO), its room-temperature tetragonal phase (TP) and high-temperature cubic phase (CP) [31]. Recently, a new phase, named as pre-perovskite phase (PP) with a significantly larger molar volume than either TP and CP phases, was discovered in PTO nanowires fabricated through a hydrothermal method [11,[13], [14], [15], [16], [17], [18], [19], [20],[32], [33], [34]]. Annealed at temperatures higher than 350°C, the PP phase was found to transform into the TP phase, resulting in the appearance of nanopores in the nanowires due to the higher density of TP phase than the PP phase [13,18]. A number of interesting behaviors were observed for the TP phase, including near-zero thermal expansion [13], enhanced piezoelectric properties [18], and inhomogeneous distribution of oxygen ions [13]. However, the underlying mechanisms for these phenomena are not well understood [13].

In this work, we employed the phase-field model of ferroelectrics [3,24] to study the effects of nanopores on phase transition and ferroelectric properties in PTO nanowires taking into account of charge compensation and surface stress. In particular, we study the influence of nanopores on the dielectric constant ε_r₃₃ and piezoelectric coefficient d₃₃ in the PTO nanowire and compare them with those in bulk PTO. We also determine the temperature dependence of lattice parameters and inhomogeneous distributions of polarization and depolarization field and discuss their effect on oxygen vacancy distribution.

Section snippets

Phase-field model

In the phase-field model of ferroelectrics, the temporal evolution of the polarization P can be obtained by solving the time-dependent Ginzburg–Landau equation [3,19]: $\frac{\partial P}{\partial t} = - L \frac{δ F}{δ P},$ with L relating to the domain wall mobility. Eq. (1) is numerically solved with the boundary condition of ∂P/∂n = 0 (n being the surface normal) [35,36] on all outside surfaces of a nanowire.

The total free energy F in Eq. (1) includes bulk energy, gradient energy, elastic energy, and electrostatic energy [24]: $F = \int_{V} f d x^{3} = \int$

Results and discussions

We first model a TP-PTO nanowire containing 3 identical spherical pores with a radius of R = 6.8 nm, as illustrated in Fig. 1 (a). The radius and length of the nanowire are taken as 10 nm and 100 nm, respectively, which are smaller than experimental values due to computation load concerns. The total volume of the pores takes up 13% that of the nanowire, which is established under an assumption of a constant volume of the PTO nanowire during the PP-PTO → TP-PTO phase transition and the fact that

Summary

A systematic investigation on the structure and properties of porous PTO ferroelectric nanowires is carried out using phase-field simulations. It is shown that the introduction of nanopores within the PTO nanowires significantly alters the ferroelectric, dielectric and piezoelectric properties. First, a notable enhancement of both dielectric and piezoelectric performances of porous PTO nanowires is observed due to significantly enhanced polarization responses near the pore surfaces. For

Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Alexander K. Tagantsev, Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland.

Acknowledgments

The work at Tsinghua (M.-J. Z. and C.-W. N.) was supported by the NSF of China (Grant no. 51788104) and China Scholarship Council (no 201706210108). T. Y. and L.-Q. C. acknowledge the support from the National Science Foundation under grant number DMR-1744213. J.-J. W. and L.-Q. C. acknowledge the support from the Army Research Office under grant number W911NF-17-1-0462. The authors acknowledge support for computational resources from the Institute for CyberScience Advanced CyberInfrastructure

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Full length articleNanopore-induced dielectric and piezoelectric enhancement in PbTiO3 nanowires

Abstract

Graphical abstract

Introduction

Section snippets

Phase-field model

Results and discussions

Summary

Declaration of Competing Interest

Acknowledgments

Prog. Mater. Sci.

Acta Mater.

Acta Mater.

Acta Mater.

Acta Mater.

Acta Mater

Decoding the fingerprint of ferroelectric loops: comprehension of the material properties and structures

J. Am. Ceram. Soc.

Understanding, predicting, and designing ferroelectric domain structures and switching guided by the phase-field method

Annu. Rev. Mater. Res.

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Science

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J. Appl. Phys.

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Ann. Phys.

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Full length article
Nanopore-induced dielectric and piezoelectric enhancement in PbTiO₃ nanowires

Strain, temperature, and electric-field effects on the phase transition and piezoelectric responses of K0.5Na0.5NbO₃ thin films

Phase transition and piezoelectricity of BaZrO₃ -modified (K,Na)NbO₃ lead-free piezoelectric thin films

Ferroelectric domain structures and temperature-misfit strain phase diagrams of K1-xNaxNbO₃ thin films: a phase-field study

Three-dimensional oriented attachment growth of single-crystal pre-perovskite PbTiO₃ hollowed fibers

Length-controlled synthesis and the photoluminescence of pre-perovskite PbTiO₃ nanofibers

Size-controlled single-crystal perovskite PbTiO₃ nanofibers from edge-shared TiO₆ octahedron columns

Doping and phase transformation of single-crystal pre-perovskite PbTiO₃ fibers with TiO₆ edge-shared octahedra