To further our understanding of how complex anisotropic structure–property relationships may be rationalized by their local atomic arrangements in ferroelectric materials, using the newly found metastable monoclinic Pm phase of potassium niobate (KNbO₃) as an example, we perform first-principles density-functional (perturbation) theory calculations to understand how applied epitaxial strain may influence their structural, thermodynamic, electronic, and (anisotropic) polarization properties in polar KNbO₃ polymorphs – a potential contender for Pb-free piezoelectric applications. Here, we find that the displacement of the center metal cation (niobium, Nb) relies on more complex anisotropic properties than the commonly used isotropic scalar quadratic elongation, 〈λ〉 for the monoclinic Pm phase, showing an anisotropic nonlinear relationship between ε_gap and 〈λ〉. We also show how anisotropic ferroelectric distortion under strain may strongly influence the direction-dependent chemical bonding character in monoclinic KNbO₃. Lastly, building on the isotropic 〈λ〉 index, we propound a revised definition of this key structural descriptor – the modified bond elongation index (_i), which contains vectorial structural information. Using _i, we successfully rationalize and demonstrate the linear dependency of direction-dependent P_s on _i for strained KNbO₃ polymorphic phases.

中文翻译：

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用于无铅机电应用的外延应变单斜铌酸钾的增强极化

为了进一步了解复杂的各向异性结构 - 性能关系如何通过它们在铁电材料中的局部原子排列合理化，以新发现的铌酸钾 (KNbO ₃ )亚稳单斜Pm相为例，我们执行第一性原理密度-功能（微扰）理论计算，以了解施加的外延应变如何影响其在极性 KNbO _{3 中}的结构、热力学、电子和（各向异性）极化特性多晶型——无铅压电应用的潜在竞争者。在这里，我们发现中心金属阳离子（铌，Nb）的位移依赖于比单斜Pm相常用的各向同性标量二次伸长率 < λ >更复杂的各向异性特性，显示出ε _gap和〈λ〉。我们还展示了应变下的各向异性铁电变形如何强烈影响单斜晶 KNbO _{3 中}的方向相关化学键合特性。最后，在各向同性〈λ〉指数的基础上，我们提出了这个关键结构描述符的修订定义——修正的键伸长指数（_i )，其中包含向量结构信息。使用_i，我们成功地合理化并证明了应变 KNbO ₃多晶相的方向相关P _s对_i的线性依赖性。