| Summary: | Environmentally friendly lead-free K<sub>1-x</sub>Na<sub>x</sub>NbO<sub>3</sub> (KNN) ceramics possess electromechanical properties comparable to lead-based ferroelectric materials but cannot meet the needs of device miniaturization, and the corresponding thin films lack theoretical and experimental studies. To this end, we developed the nonlinear phenomenological theory for ferroelectric materials to study the effects of non-equiaxed misfit strain on the phase structure, electromechanical properties, and electrical response of K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> epitaxial films. We constructed in-plane misfit strain (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>−</mo><msub><mi>u</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>) phase diagrams. The results show that K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> epitaxial film under non-equiaxed in-plane strain can exhibit abundant phase structures, including orthorhombic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mi>c</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mi>c</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><msub><mi>a</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> phases, tetragonal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>c</mi></semantics></math></inline-formula> phases, and monoclinic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>r</mi><mrow><mn>12</mn></mrow></msub></mrow></semantics></math></inline-formula> phases. Moreover, in the vicinity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mi>c</mi><mo>−</mo><msub><mi>r</mi><mrow><mn>12</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mi>c</mi><mo>−</mo><mi>c</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><msub><mi>a</mi><mn>2</mn></msub><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> phase boundaries, K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> epitaxial films exhibit excellent dielectric constant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula>, while at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mi>c</mi><mo>−</mo><msub><mi>r</mi><mrow><mn>12</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mi>c</mi><mo>−</mo><mi>c</mi></mrow></semantics></math></inline-formula> phase boundaries, a significant piezoelectric coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mrow><mn>15</mn></mrow></msub></mrow></semantics></math></inline-formula> is observed. It was also found that high permittivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mrow><mn>33</mn></mrow></msub></mrow></semantics></math></inline-formula> and piezoelectric coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mrow><mn>33</mn></mrow></msub></mrow></semantics></math></inline-formula> exist near the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mi>c</mi><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><msub><mi>a</mi><mn>2</mn></msub><mo>−</mo><msub><mi>r</mi><mrow><mn>12</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mi>c</mi><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> phase boundaries due to the existence of polymorphic phase boundary (PPB) in the KNN system, which makes it easy to polarize near the phase boundaries, and the polarizability changes suddenly, leading to electromechanical enhancement. In addition, the results show that the K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> thin films possess a large electrocaloric response at the phase boundary at the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><msub><mi>a</mi><mn>2</mn></msub><mo>−</mo><msub><mi>r</mi><mrow><mn>12</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mi>c</mi><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> phase boundaries. The maximum adiabatic temperature change <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Δ</mi><mi>T</mi></mrow></semantics></math></inline-formula> is about 3.62 K when the electric field change is 30 MV/m at room temperature, which is significantly enhanced compared with equiaxed strain. This study provides theoretical guidance for obtaining K<sub>1−x</sub>Na<sub>x</sub>NbO<sub>3</sub> epitaxial thin films with excellent properties.
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