A D V A N C E D M A T E R I A L S & P R O C E S S E S | A P R I L 2 0 2 1 5 9 shape memory effect is the nature of the phase boundary. In the shape memory field, researchers are accustomed to a linear phase boundary given by the Clausius-Clapeyron equation. For example, in classical (thermomechanical) shape memory, temperature and stress trade off linearly for one another, as shown for zirconia on the right-hand side of Fig. 3. In the case of a susceptibility mismatch, however, the second-order nature of the property plays out literally as a higher order correction to the Clausius-Clapeyron equation: It provides a parabolic dependence. The left-hand side of Fig. 3 illustrates the effect in the case of shape memory zirconia, where there is no linear term (no spontaneous polarization), and only the parabolic term (from susceptibility mismatch) separates the two phases. From the equilibrium transformation temperature, the phase boundary increases with a square-root dependence on field. There are many practical implications of this second- order thermodynamic effect for actuation. For example, as Fig. 3 shows for zirconia, electric field can be viewed as a third axis for control, with an opposite dependence from stress and a negative Clausius-Clapeyron slope; stresses promote martensite, but fields promote austenite. What is more, the slowly changing temperature dependence of the parabolic phase boundary suggests that there may be large design windows where the transformation field is less affected by changes in temperature, compared with a typically tight temperature window for stress-based activation. And whereas the mechanical yield or fracture stress provides an upper bound on the stresses achieved in shape memory alloys, the dielectric breakdown provides an analog for the upper limits on field, as shown in Fig. 3. Fig. 3 — A schematic phase diagram for both thermally and electrically triggered martensitic transformation in zirconia. Under zero stress and field, transformation occurs at T0, the equilibrium temperature. As stress is applied (right side), the phase boundary rises linearly following the Clausius-Clapeyron equation, and the transformation can be triggered by stress in the maroon-shaded region, up until the yield or fracture occur instead. However, when an electric field is applied (left side), the phase boundary is not linear but parabolic, creating a curved region where a field-driven transformation can occur, provided the field is below the point of dielectric breakdown. CONCLUSION In paraelectroactive shape memory ceramics, the intersection and collaboration among stresses, field, and temperature require more detailed elaboration both theoretically and practically. At the same time, development of new materials in this category is likely to unveil new complexities and competitions. But the opportunity to directly trigger shape memory strains with applied electric fields remains a tantalizing prospect for faster, more addressable, and distributable actuation. The extension of field-activated shape memory to paraelectric ceramics may provide new paths toward that goal.~SMST Acknowledgment The authors acknowledge the support of the Institute for Soldier Nanotechnologies funded by the U.S. Army Research Office under Collaborative Agreement Number W911NF-18-2-0048. For more information: Christopher A. Schuh, Department of Materials Science and Engineering, MIT, 77 Massachusetts Ave., Room 8-201, Cambridge, MA 02139, 617.452.2659, schuh@mit.edu. References 1. A. Lai, et al., Shape Memory and Superelastic Ceramics at Small Scales, Science, Vol 341, p 1505-1508, 2013. 2. I. Crystal, A. Lai, and C. Schuh, Cyclic Martensitic Transformations and Damage Evolution in Shape Memory Zirconia: Single Crystals vs. Polycrystals, J. Am. Ceram. Soc., Vol 103, p 4678-4690, 2020. 3. P. Reyes-Morel, J.-S. Cherng, and I.-W. Chen, Transformation Plasticity of CeO2‐Stabilized Tetragonal Zirconia Polycrystals: II, Pseudoelasticity and Shape Memory Effect, J. Am. Ceram. Soc., Vol 71, p 648-657, 1988. 4. A. Lai and C. Schuh, Direct Electric-Field Induced Phase Transformation in Paraelectric Zirconia via Electrical Susceptibility Mismatch, Phys. Rev. Lett., Vol 126, Issue 1, 2021. 5. K. Otsuka and C.M. Wayman, Shape Memory Materials, Cambridge University Press, 1998. 6. D. Damjanovic, Ferroelectric, Dielectric and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics, Reports Prog. Phys., Vol 61, p 1267, 1998. 7. R. Hannink, P. Kelly, andB. Muddle, Transformation Toughening in Zirconia‐Containing Ceramics, J. Am. Ceram. Soc., Vol 83, p 461-487, 2000. FEATURE 1 1
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