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Free, publicly-accessible full text available August 1, 2025
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A new H(divdiv)-conforming finite element is presented, which avoids the need for supersmoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for the biharmonic equation. Moreover, new finite element divdiv complexes are established. Finally, new weak Galerkin and C0 discontinuous Galerkin methods for the biharmonic equation are derived.more » « lessFree, publicly-accessible full text available March 20, 2025
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Spontaneous polarization as large as ∼28 μC/cm2 was recently observed around the dislocation cores in non-polar SrTiO3 bulk crystals, and its origin was attributed to the flexoelectric effect, i.e., polarization induced by strain gradients. However, the roles of flexoelectricity, relative to other electromechanical contributions, and the nature of dislocations, i.e., edge vs screw dislocations in the induced polarization, are not well understood. In this work, we study the role of flexoelectricity in inducing polarization around three types of dislocation cores in SrTiO3: b=a(100) edge dislocation, b=a(110) edge dislocation, and b=a(010) screw dislocation, where b is the Burgers vector. For the edge dislocations, polarization can be induced by electrostriction alone, while flexoelectricity is essential for stabilizing the symmetric polarization pattern. The shear component of the flexoelectric tensor has a dominant effect on the magnitude and spatial distribution of the flexoelectric polarization. In contrast, no polarization is induced around the b=a(010) screw dislocation through either electrostriction or flexoelectricity. Our findings provide an in-depth understanding of the role of flexoelectricity in inducing polarization around dislocation cores and offer insights into the defect engineering of dielectric/ferroelectric materials.
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A Landau–Devonshire thermodynamic energy density function for ferroelectric wurtzite aluminum scandium nitride (Al1−xScxN) solid solution is developed. It is parametrized using available experimental and theoretical data, enabling the accurate reproduction of composition-dependent ferroelectric properties, such as spontaneous polarization, dielectric permittivity, and piezoelectric constants, for both bulk and thin films. The maximum concentration of Sc for the wurtzite structure to remain ferroelectric is found to be 61 at. %. A detailed analysis of Al1−xScxN thin films reveals that the ferroelectric phase transition and properties are insensitive to substrate strain. This study lays the foundation for quantitative modeling of novel ferroelectric wurtzite solid solutions.
Free, publicly-accessible full text available March 7, 2025