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Phys. Status Solidi A 209, No. 11, 2108–2113 (2012) / DOI 10.1002/pssa.201228314
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applications and materials science
Phase switching at low field and large sustainable strain output in domain engineered ferroic crystals
Advanced Materials Physics
Peter Finkel*,1, Ahmed Amin1, Sam Lofland2, Jaojin Yao3, and Dwight Viehland3 1
Naval Undersea Warfare Center (NUWC), Newport, Rhode Island 02841, USA Department of Physics and Astronomy, Rowan University, Glassboro, New Jersey 08028, USA 3 Department of Materials Science, Virginia Tech, Blacksburg, Virginia 24061, USA 2
Received 28 April 2012, revised 8 July 2012, accepted 10 July 2012 Published online 8 August 2012 Keywords domains, ferroelectrics, piezoelectricity * Corresponding
author: e-mail
[email protected], Phone: þ1-401-8323914, Fax: þ1-401-8328634
Fundamental shortcomings of ferroelectrics (FEs) are low induced strain and high electric field often required for practical application in actuation, sensors, and acoustics. Although domain engineered FE single crystals deliver an order of magnitude improvement, fatigue remains another drawback in achieving reliable multiple domain switching crucial for memory storage. We demonstrate that under specially compressive stresses FE relaxors exhibit low field induced reversible and sustainable strain associated with FE–FE phase
switching and unusual and unexpected lack of fatigue after several millions cycles is believed due to strain accommodation occurring in ferroics. Polarized light microscopy and X-ray diffraction are in a very good agreement with macroscopic observation and phenomenological model confirming proposed transformational path. The phenomena presented in this work are envisioned to be universal in domain engineered ferroics enabling mechanical stress to be used for strain and polarization control of electromechanical energy conversion.
ß 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction The term ferroic [1, 2] is used to describe the many types of mimetically twinned crystals in which the orientation of one or more twin components (domains) may be affected by a suitably chosen driving force. Ferroelectrics (FEs), ferromagnetics, and ferroelastics are examples of primary ferroic crystals in which the active domain walls, that are crystallographic boundaries can be moved by the application of electric, magnetic, and elastic fields, respectively: leading to enhanced piezoelectricity and large induced strain such as demanded by transduction and actuation systems and sensors. Higher order ferroic phenomena in which the domain states may differ in one or more property tensor components are possible [3]. The equilibrium domain structure of ferroic crystals is obtained when the conditions of Landau–Ginzburg–Devonshire free energy minima are satisfied [4]. Ferroic crystals can be classified into symmetry species according to their high- and low-temperature symmetries. The symmetry species symbol consists of the hightemperature point group followed by that of the low temperature. Barium titanate (BaTiO3), for example,
belongs to the ferroic species m3mF4mm. Here the two groups are separated by the letter F indicating ferroic behavior in the low-temperature phase. The number of FE domains is given by the index of the FE species point group in the high-temperature paraelectric point group. There are six domain states in tetragonal BaTiO3, with both FE 1808 and FE–ferroelastic 908 domains being equally probable. Remarkable progress has been made in the synthesis, and application of relaxor-FE single crystals with high electromechanical coupling. In the early 1980’s Kuwate et al. [5] discovered the extraordinary high electromechanical properties in relaxor-FE lead zinc niobate (PZN)–lead titanate (PT) single crystals, for compositions on the rhombohedral side of the morphotropic phase boundary (MPB), with piezoelectric coefficients of d33 >1500 pm V1, and electromechanical coupling of k33 ¼ 0.92. This discovery was revived by a significant research effort in the mid 1990’s in relaxor-FE single crystals [6], particularly in binary systems with the general formula (1 x)Pb(BI1/3Nb2/3)O3–(x)PbTiO3, where BI can either be Zn or Mg, and more recently, work was focused on ternary lead indium niobate (PIN)–lead magnesß 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Advanced Materials Physics Phys. Status Solidi A 209, No. 11 (2012)
ium niobate (PMN)–PT [7–11]. As a result, sound projectors fabricated from PMN–PT single crystals offer nearly triple the bandwidth, and an order of magnitude higher acoustic power than that of standard PZT projectors because of their significantly higher coupling factor and piezoelectric coefficient [9]. Medical ultrasound imagining systems have also benefited from the broadband capabilities of single crystals with vast improvements in axial resolution and contrast. Large induced strains in FEs can be broadly classified into two types: (i) non1808 domain switching, and (ii) phase transformation [12]. A combined mechanical stress and electric field are used to induce 908 domain switching in FE tetragonal single crystal BaTiO3 [14]. A complete switching of polarization direction by 908, i.e., from a- to c-domains will result in a large lattice strain of approximately 1% (c/a 1.01) at 3 MV m1. The lattice strain associated with 908 domain switching in PT is even higher at 6%. A number of issues were recognized by researchers, amongst which are a quick degradation of the strain due to electrode choice and friction. There are other possible mechanisms of large field induced strain by reversible 908 domain switching in aged FE single crystal BaTiO3 due to a symmetry conforming property of point defects [15]. The transduction mechanism strongly depends on the sample prehistory, and the stability of particular stoichiometry and defect configuration. Park and Shrout [6] have demonstrated an ultrahigh strain of 1.2% in domain engineered PZN–PT single crystals driven by very high fields of about 4 MV m1. This huge strain was attributable to a FE rhombohedral FR to FE tetragonal FT phase transformation and is commensurate with model calculations [7]. In spite of extremely attractive electromechanical response of the MPB FEs the transducers fabricated from relaxor-FE single crystals as well as PZT piezoceramics are designed to operate well below any phase transition temperature in order to avoid large swings in load impedance, high electric field drive, and hysteresis losses. Ideally, the material exhibiting anhysteretic response and nearly instant phase transformation induced strain change would be able to overcome these caveats. Therefore, by making the field induced phase transition to occur at significantly lower electric fields and at much faster rates would make it possible to create a material with high effective piezoelectric properties. Recently, it was shown that domain-engineered relaxor-FE crystals with 4 mm and 2 mm macrosymmetries exhibited a large and reversible phase transformation strain under mechanical compression that is tunable by an electric field [7–9, 13]. A very sharp hysteretic quasistatic strain curve and polarization jumps accompanied by a dramatic change in stiffness (by a factor of 6–8) at stress less than 15 MPa have been reported first in the PZN–PT crystals [7]. However in PMN–PT crystals, the effect was more diffuse and continuous [13]. Later this elastic nonlinearity was also reported in different crystals and was shown to be a strong function of temperature and geometry of the crystals [16–18]. Recently, we demonstrated a large and reversible strain up to 0.5% at field of www.pss-a.com
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0.1 MV m1 in domain-engineered relaxor-FE PIN– PMN–PT single crystals [16]. In all cases this nonlinearity was explained as the stress-induced FE rhombohedral FR–FE orthorhombic FO phase transformations. It is the reorientation of the polarization vector Ps aligned along the h111i direction (see Fig. 1a) under the combined effect of external stress and electric field bias is accountable for this phase transformation switching in the domain engineered systems [10, 16]. Surprisingly, the crystal was successfully switched for more than 106 cycles without any signs of fatigue, cracks, or failure. Even though the phenomenology of the field and stress induced phase transition is salient, very limited information is available about general universal descriptive rules governing the dynamics of this large polarization and strain generated at phase transition in nearly MPB relaxor FE single crystals. If properly understood, one can discover new systems exhibiting extremely high and sharp reversible fieldor stress-induced sustainable strain at phase transitions for transduction. In this work we investigated field induced reversible FR ! FO phase transitions in near-MPB [011] poled (32)-mode PIN–PMN–0.3PT FE single crystals as a function of applied stress and electrical bias. To gain further insights on domain states and dynamics, we have performed polarized light microscopy (PLM) experiments under applied electric field.
Figure 1 (online color at: www.pss-a.com) Stress and field induced phase transformations in relaxor domain-engineered ferroelectrics. (a) Polarization orientations and external stress and electric field geometry for h011i PIN–PMN–PT single crystal with (32) mode geometry. Combining effect of stress and electric field bias is leading to the spontaneous polarization reorientation inducing FR–FO phase transition; (b) elastic response as a function of electric bias (top) and temperature (bottom) with very sharp nonlinearity at critical stress sc. Note that both electric field bias and higher temperature shifts this transition to lower critical stresses; (c) Gibbs’s free energy is affected by applied electrical bias and stress. ß 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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P. Finkel et al.: Phase switching and strain output in domain engineered ferroic crystals
2 Experiment, results and discussion The elastic temperature dependent quasistatic response was measured under various mechanical and electrical boundary conditions using method described in details elsewhere (see Supporting Information, online at: www.pss-a.com) and Ref. [10]. Figure 1b displays the extremely abrupt strain change with prominent relaxation phenomena at the entrance and exit of phase change at the critical stress sc corresponding to the FR ! FO transition tunable both by field and temperature (Fig. 1b). This destabilizing bias field effect is in accord to a scenario depicted in Fig. 1a. At zero stress and field conditions there are only two domains states with R3m symmetry corresponding to FR sates with spontaneous polarization Ps along h111i (Fig. 1a) with the spontaneous polarization reorientation from h111i to h011i under cumulative effect of h100i compressive stress (s22) and h011i electric field E (Fig. 1b). It has to be noted that in contrast to the [100] poled (33-mode), the elastic responses of the [011] poled (32-mode) crystals exhibit much sharper nonlinearity and strain change associated with the FR ! FO stress-induced phase transition with sc in the range of 12–14 MPa for near-MPB composition. As expected, sc is a function of electric field applied along [011]. In distinction with 33-mode geometry, electrical bias in [011] poled crystals actually destabilizes the FR phase along with the temperature (Fig. 1c) [15]. It is important to note the FR ! FO phase switching and transition are fully controlled by electric field, either enhanced or completely suppressed by rather low electrical bias [16]. In order to explain the driving force governing this transition, we invoke a standard description of the minimization of the Gibbs’s free energy as a function of polarization and strain. From first principles, a stability of phases and energy required to stimulate phase transition is determined by minimization of free energy occurred in near critical state (Fig. 1a). The presence of several unresolved minima is strongly affected by applied stress or electric field. For the system with nearly MBP composition with relatively flat energy landscape phases can be readily switched by applying rather small external stress or electric field. As discussed above, here we are interested to predict and tailor special electro-mechanical–thermal boundary conditions satisfying the physical requirements for the system to be within the marginal states that are equally energetically favorable. Meeting these conditions allows for the FR and FO phases to simultaneously coexist. This can be envisioned on the boundary between FR and FO phases at the stability diagram proposed earlier in Refs. [18]. Stress– temperature–field stability diagram can be established based on the quasistatic measurements (Fig. 2). The stability diagram clearly defines the plane separating two stable FR and FO states for the h011i poled (32-mode) crystal as a function of external parameters such as stress, field and temperature. For states poised at a FR–FO phase boundary a small perturbation, for example, in h011i electrical bias, temperature or h100i stress would be able to trigger polarization reorientation generating large reversible bulk h100i strain. Consider a crystal that is at room temperature in ß 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 2 (online color at: www.pss-a.com) Stress–fieldtemperature stability surface for 32-mode geometry for [011] poled PIN–PMN–PT samples. The value of critical compressive stress deduced from the quasistatic elastic isothermal response is plotted as function of applied bias field. States on this surface are poised at FR–FO–FR boundary. ‘‘FO’’ stable states for any stress, field, and temperature are above surface, while ‘‘FR’’ stable states for any stress, field, and temperature below surface.
equilibrium in (FR) macrodomain state now is preloaded to a stress s sc near the FR–FO transition. In accord to the diagram (Fig. 1a), a sufficient magnitude of the ac electric field drive E3 will induces a strain in the h001i direction corresponding to the difference between FR and FO equilibrium states. The magnitude of the [001] strain difference was estimated in terms of polarization (P) and electrostriction (Q) assuming polarization continuity in the different phases (R, O, and T). The following analytic expressions can be explicitly written (in reduced tensor notation) for the strain difference DS3(R O) and DS3(R T) associated with the FR–FO and FR–FT transitions, respectively [7], DS3 ðR OÞ ¼ S3 ðRÞ S3 ðOÞ ¼ ðQ11 Q12 ÞP23 ;
(1)
DS3 ðR TÞ ¼ S3 ðRÞ S3 ðTÞ ¼ ðQ11 Q12 ÞP23 ðRÞ:
(2)
For electrostriction coefficients Q11 ¼ 0.0535 m4/C2, Q12 ¼ 0.0267 m4/C2, and polarization P3(R) ¼ 0.25 C m2 (see Ref. [7]) the calculated DS3(R O) from Eq. (1) is 0.51%, which is in excellent agreement with experimental results [18]. It is interesting to note that according to Eq. (2), the FR–FT transition strain is DS3(R T) 1% close to that observed in Ref. [6]. In this case for FR–FO phase transformation maximum theoretical strain of 0.5% that, as shown in our previous work, can be achieved at a significantly lower (
