| Summary: | K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> is considered as one of the most promising lead-free piezoelectric ceramics in the field of wearable electronics because of its excellent piezoelectric properties and environmental friendliness. In this work, the temperature-dependent longitudinal piezoelectric coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>d</mi><mrow><mn>33</mn></mrow><mo>*</mo></msubsup></mrow></semantics></math></inline-formula> was investigated in K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> single crystals via the Landau–Ginzburg–Devonshire theory. Results show that the piezoelectric anisotropy varies with the temperature and the maximum of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>d</mi><mrow><mrow><mn>33</mn><mi>m</mi><mi>a</mi><mi>x</mi></mrow></mrow><mo>*</mo></msubsup></mrow></semantics></math></inline-formula> deviates from the polar direction of the ferroelectric phase. In the tetragonal phase, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>d</mi><mrow><mrow><mn>33</mn><mi>m</mi><mi>a</mi><mi>x</mi></mrow></mrow><mrow><msup><mi>t</mi><mo>*</mo></msup></mrow></msubsup></mrow></semantics></math></inline-formula> parallels with cubic polarization direction near the tetragonal-cubic transition region, and then gradually switches toward the nonpolar direction with decreasing temperatures. The maximum of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>d</mi><mrow><mn>33</mn></mrow><mrow><msup><mi>o</mi><mo>*</mo></msup></mrow></msubsup></mrow></semantics></math></inline-formula> in the orthorhombic phase reveals a distinct varying trend in different crystal planes. As for the rhombohedral phase, slight fluctuation of the maximum of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>d</mi><mrow><mn>33</mn></mrow><mrow><msup><mi>r</mi><mo>*</mo></msup></mrow></msubsup></mrow></semantics></math></inline-formula> was observed and delivered a more stable temperature-dependent maximum <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>d</mi><mrow><mrow><mn>33</mn><mi>m</mi><mi>a</mi><mi>x</mi></mrow></mrow><mrow><msup><mi>r</mi><mo>*</mo></msup></mrow></msubsup></mrow></semantics></math></inline-formula> and its corresponding angle <i>θ<sub>max</sub></i> in comparison with tetragonal and orthorhombic phases. This work not only sheds some light on the temperature-dependent phase transitions, but also paves the way for the optimization of piezoelectric properties in piezoelectric materials and devices.
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