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lattice first contracts, producing the comes from two characteristic electromechanical hyster- closely related esis shown in Figure 3(b). The results effects. The first in Figure 3 correspond to a structural is the piezoelec- observation of the hysteresis of fer- tric expansion of roelectric capacitors, an effect that is the lattice. A sec- useful for decoupling the fundamental ond, more subtle origin of hysteresis from artifacts associ- effect, is the rota- ated with electrical measurements. tion of the {103} In Figures 2 and 3, the direction rotates the peak (Credit: R. Sichel, U. Wisconsin-Madison.)cplanes as the Piezoelectricity in thin films with lattice constant complex microstructures increases, which along which the X-ray experiments position around probed the piezoelectric strain was the origin in parallel to the direction of the applied reciprocal space. electric field. Thus, the piezoelectric The values of d Figure 4. Field-dependent projections of the three-dimensional dif- coefficients measured in this case cor- and d for each fraction pattern of a BiFeO3 thin film onto the qx–qz plane. The BiFeO333 respond to the d component of the distinct structural layer exhibits four {103} diffraction peaks, resulting from structural31 piezoelectric tensor. In the thin-film volume, shown spot. Arrows indicate the directions of the shifts of these reflectionsvariants with various crystallographic orientation within the X-ray33 case, only E3 is nonzero, and the piezo- next to the reflec- in electric fields from 0 to 250 kV/cm. The SrRuO3 reflection is not electric coefficients that determine the tions in Figure 4, displaced by the applied field because there is no piezoelectric strain tensile or compressive strain are d31, d32, do not account in the bottom electrode.14 and d . Shear strains are determined for rotations of by coefficients, d , d , and d . Time- the atomic planes and represent only be in the more relaxed regions than in33 resolved microdiffractometry probes the the apparent change in lattice con- regions with no in-plane piezoelectric363534 out-of-plane and the in-plane piezoelec- stant. Nevertheless, it is clear that the response. These effects are even more tric response, measuring the strains ε1, piezoelectric response varies for each pronounced in ceramics, where in situ ε , and ε from changes to the in-plane domain. The apparent value of d diffractometry studies have shown that lattice constants and the out-of-plane domains at this location on the sample the fraction of the overall piezoelectric3132 c-axis lattice constants, respectively. ranges from –37 picometers per volt to distortion that directly results from the The full piezoelectric tensor is par- +0.69 picometers per volt. The nonzero expansion of the lattice is small com- ticularly important for BiFeO3 because values of d31 occur because the in-plane pared with the motion of domain walls the bulk rhombohedral unit cell is dis- lattice constant within the domains and other long-range elastic effects.7 torted during epitaxial growth, leading is not completely clamped by the sub- to a complex thin-film microstructure.13 strate, and each domain is in a different High fields, ultrafast dynamics, Instead of a single intense peak, the stress states because of the incomplete and complex domains {103} reflections of BiFeO3 are split relaxation of the film. A domain near The precision and high resolution of because the film has regions with the the edge of a mosaic block or any other in situ diffractometry probes provide a four possible orientations of its rhom- type of defect, for example, is under way to study electromechanical materi- bohedral distortion relative to the cubic mechanical constraints very different als in new regimes, such as ultrashort substrate, as well as varying degrees of from one in a perfectly epitaxial region plastic relaxation and tilt. Applying a of the film. of the BiFeO3 pseudocubic {103} reflec- Wafer flexure studies have shown that Reprinted with permission.)(Credit: Chen, et al.; American Institute of Physics.- of zero. lies313dThe in-plane piezoelectric responsebetween the polycrystalline and epitaxial regimes. A completely clampedfilm would have an effectiveof the partially relaxed BiFeO-tions for several electric fields.14 The polycrystalline Pb(Zr,Ti)O3 thin films voltage in this case results in a piezo electric response that depends on the local structure of the thin film. Figure 4 shows the piezoelectric response by plotting positions in reciprocal space arrows in Figure 4 indicate the change grown by the sol–gel method have val- in reflection positions as E increases ues of d31 that increase with increasing piezoelectric strain in BiFeO thin filmsFigure 5. Electric-field dependence of the from 0 to 250 kilovolts per centimeter. film thickness, probably because the at very high electric fields. The low-field3 There is no distortion of the electrode substrate clamps the film less effec- piezoelectric coefficient of 55 pm/V does material, SrRuO3. tively as the film gets thicker.4 BiFeO3 not provide a good fit to strains observed The distortion evident in Figure 4 domains with nonzero d31 are likely to at fields above ~150 MV/m.11 American Ceramic Society Bulletin, Vol. 92, No. 1 | www.ceramics.org 21


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