Elsevier

Acta Materialia

Volume 191, 1 June 2020, Pages 13-23
Acta Materialia

Full length article
Effect of electric field orientation on ferroelectric phase transition and electrocaloric effect

https://doi.org/10.1016/j.actamat.2020.03.020Get rights and content

Abstract

The influence of electric field orientation on phase transitions and electrocaloric effects (ECEs) in BaTiO3 single crystals is studied by performing molecular dynamics simulation of first-principles-based effective Hamiltonian. The ECE is directly characterized via the adiabatic temperature change (ΔT) under the microcanonical ensemble. The simulation results demonstrate that different orientation relationship between the electric field and the polarization direction of ferroelectric phase leads to abundant phase structures and ECE behaviors. The electric-field-induced phase transitions produce remarkable ECE peaks/valleys, whereas the polarization rotation and/or extension without phase transition induced by the electric field produces small positive ECEs, which are insensitive to temperature and electric field direction. For the tetragonal-cubic phase transition, ECEs are always positive regardless of the applied electric field direction, and the value and width of ECE peak both increase with the reduction of the angle between electric field and crystallographic orientation. For the orthorhombic-tetragonal and rhombohedral-orthorhombic phase transitions, the sign of ECE gradually changes from negative to positive during the field direction rotates in planes between crystallographic orientations, and the coexistence of positive and negative appears when the field along non-crystallographic directions. Our simulated results shed light on a comprehensive physical understanding of the electric-field-orientation dependent ECE and offer instruction for the design of the refrigeration cycle by combining positive and negative ECEs.

Introduction

The modern industries desire novel solid-state refrigeration technologies with excellent performance, small size, and high reliability. Under such circumstances, solid-state refrigeration based on caloric effects becomes a popular and compelling research field [1]. Caloric effects, including electrocaloric, elastocaloric and magnetocaloric effects, perform cooling under adiabatic conditions by the electric field, stress, and magnetic field, respectively. Among them, the electrocaloric effect (ECE) refers to an adiabatic temperature change (ΔT) or isothermal entropy change (ΔS) when the electric field is applied on or removed from a dielectric material. For a long time, the objects of ECE researches were limited to bulk materials with low electric breakdown strength, so the refrigeration capacity was too weak to be used in practical applications [2]. Until 2006, Mischenko et al. [3] produced a giant ECEs with ΔT = 12 K in PbZr0.95Ti0.05O3 thin film under ultrahigh electric fields, which stimulated enormous ECE research interests. In the following years, giant ECEs with ΔT > 10 K have been reported in various materials [4], [5], [6], [7], which accelerates the development of ferroelectric refrigeration technology towards easy miniaturization, high energy efficiency, and low cost.

The ECE is determined by the polarization state under various electric field conditions. The phase structure and spontaneous polarization would change with temperature, and the application or removal of an electric field can induce the rearrangement of electric dipoles, lattice distortion, and even phase transitions [8, 9]. For the ferroelectric phase transition under changing electric field, the entropy changes greatly and the ECE would increase strongly in the vicinity of the phase transition [1]. It was reported that the ECEs reach the largest value near the Curie temperature (Tc), where the polarization varies rapidly with temperature [10]. Based on all-atom molecular dynamics simulations, Qi et al. [11] predicted that an ultrafast electric field pulse caused an ultrafast and large ΔT max = 32 K under 600 kV/cm in PbTiO3 near Tc. Peng et al. [12] experimentally obtained the ECE of ΔTmax = 45 K in the Pb0.8Ba0.2ZrO3 relaxor ferroelectric thin film under 598 kV/cm at 290 K. Many theoretical studies have made efforts on ECEs in various aspects, including different material systems [13], [14], [15], [16], defects controlling [17], [18], [19] and stress loading [20], [21], [22]. Most of them involved the effect of electric fields on ECEs. Electric fields affect not only the magnitude but also the positions of ECE peaks [23, 24]. For ferroelectric-to-paraelectric phase transition near Tc, under the electric field below a critical value, the first-order phase transition occurs and the peak of ΔT is sharp and narrow. However, under a large electric field, the phase transition is diffusive, leading to a broad ΔT peak, and the ΔTmax moves along a Widom line and shifts to higher temperatures with increasing fields [25], [26], [27]. Unfortunately, these studies mainly focus on the intensity of the electric field and make less concern on the orientation relationship between the external field orientation and the crystalline direction.

If the electric field is applied on a ferroelectric single crystal in different directions, it tends to rearrange the electric dipoles along the external field direction. If the electric field intensity is large enough, it can distort the lattice to induce the low symmetry phases, shift the phase transition temperatures and lead to phase transitions between different ferroelectric phases [28], [29], [30]. The ECE always reaches the maximum near the phase transition temperature due to the significant change of polarization value, and the peak position is strongly dependent on the electric field direction [31, 32]. The field-induced phase transition also determines the magnitude and even the sign of positive or negative of ECE [31, 33]. It was reported that the ferroelectric single crystals exhibited negative ECEs under the electric field along with some certain directions. Some experimental and theoretical researches were conducted to investigate the ECEs of single crystals under different electric field orientations [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]. Negative ECEs were observed experimentally in [001] oriented PMN-PT single crystal because of the noncollinear relation between the electric field and the spontaneous polarization direction [30, 33, 35]. Such negative ECEs were also reported theoretically in materials of PMN-PT [34], BaTiO3 [29, 32] and Ba0.5Sr0.5TiO3 [28]. Ponomareva and Lisenkov [28] predicted the negative ECE in Ba0.5Sr0.5TiO3 due to the transition from orthorhombic to tetragonal phase under the electric field along [001] direction. Marathe et al. [32] simulated the ECEs of BaTiO3 under the electric field along [001], [011] and [111] directions, and found that the orthorhombic-tetragonal phase transition induced both positive and negative ECEs under different electric field directions, indicating that the noncollinear electric field direction is not a sufficient condition for the negative ECE. Wu et al. [39] reported that the compression-stress-induced two types of pseudo-first-order phase transitions below Tc contributed to the coexistence of negative and positive ECEs in ferroelectric nanoparticles. The multi-field coupling of temperature, electric field, and stress field is an effective way to achieve large and tunable ECEs [39], [40], [41].

Previous ECE researches are limited to the electric field directions along the high-symmetry crystallographic orientations of ferroelectric phases, such as [001], [011] and [111], but the electric field along arbitrary directions has not been reported, which is very important to understand the physical mechanism of ECE. In literature, the indirect thermodynamic calculation based on the Maxwell relation is widely used to characterize ECEs in both experiments and theoretical simulations [5, 31, 33, 34]. Although the indirect calculation is workable in most ECE researches [42], it usually produces artifactual results in some cases, such as relaxor ferroelectrics with polar nano-regions [43], [44], [45], [46]. Furthermore, the accuracy of the indirect method is suspected in some aspects [47, 48], such as the leakage current [5], the unsaturated polarization at low temperature or at high frequency [49, 50], the discontinuous change of polarization and heat capacity at the phase transition point, the insufficient sampling of temperature and electric field, the accuracy of numerical processing of the Maxwell differential equation, etc.

In this work, we study the phase transitions and the associated ECEs in BaTiO3 (BTO) single crystals under the electric field along arbitrary directions by performing molecular dynamics (MD) simulation of first-principles-based effective Hamiltonian, where the ECE is directly characterized by the temperature change of the system in a reversible adiabatic process.

Section snippets

Calculation method

We use the first-principles-based effective Hamiltonian as the potential function to model the phase transition and the ECE of BTO. The effective Hamiltonian can be expressed as:Heff=Mdipole*2R,αuα2(R)+Macoustic*2R,αwα2(R)+Vself({u})+Vdpl({u})+Vshort({u})+Velas,homo(η1,,η6)+Velas,inho({w})+Vcoup,homo({u},η1,,η6)+Vcoup,inho({u},{w})Z*Rɛ·u(R),where w(R) is the local acoustic displacement vector, u(R) is the local soft mode vector and ηi (i = 1,…, 6; Voigt notation) are strain components. Mdi

Phase structure under different electric field directions

Electric fields affect the polarization state of BTO and change the phase structure. Under a zero electric field, the phase transition process during cooling is T phase → O phase → R phase, and the temperature dependence of the polarization components Px, y, z and the lattice constants a, b, c are shown in Fig. 2(a) & (b). Under the applied electric field in different directions, the polarization vectors of three ferroelectric phases deviate from the original polar direction and the lattice

Effect of electric field directions on the electrocaloric effect

The above discussions show that the electric field direction has a great influence on the phase structure, polarization state, and phase transition temperature. Next, we focus on the ECEs during electric field changing. Under the application or removal of a noncollinear electric field, the polarization is induced to rotate and extend along the field direction, and the change of the degree of order determines the ECE under an adiabatic condition. In order to study such influence, the ECE ΔT in

Conclusion

In summary, we studied the phase structure and the associated ECE of BTO single crystal under the electric field along arbitrary directions by performing molecular dynamics simulations. The results show that the electric field orientation has a great impact on the phase structure, polarization path, phase transition temperature, and ECE. Under an electric field collinear with the spontaneous polarization direction, the phase structure remains unchanged; whereas under the noncollinear electric

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by grants from the Beijing Natural Science Foundation (2192032), the National Key Research and Development Program of China (2018YFB0704301), and Fundamental Research Funds for the Central Universities (FRF-AT-19-012). H. H. Wu acknowledges the financial support from the Natural Science Foundations of China (51901013).

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