Upon application of a uniform strain, internal sub-lattice shifts within the unit cell of a non-centrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric tensor. Several recent studies suggest that strain-gradient induced polarization may be responsible for a variety of interesting and anomalous electromechanical phenomena in materials including electromechanical coupling effects in nonuniformly strained nanostructures, "dead layer" effects in nanocapacitor systems, and "giant" piezoelectricity in perovskite nanostructures among others. In this work, adopting a lattice dynamics based microscopic approach we provide estimates of the flexoelectric tensor for certain cubic ionic crystals, perovskite dielectrics, III-V and II-VI semiconductors. We compare our estimates with experimental/theoretical values wherever available, address the discrepancy that exists between different experimental estimates and also re-visit the validity of an existing empirical scaling relationship for the magnitude of flexoelectric coefficients in terms of material parameters.

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Thin films of high-permittivity dielectrics are considered ideal candidates for realizing high charge density nanoscale capacitors for use in next generation energy storage and nanoelectronics applications. The experimentally observed capacitance of such film nanocapacitors is, however, an order of magnitude lower than expected. This dramatic drop in capacitance is attributed to the so-called "dead layer" -a low-permittivity layer at the metal-dielectric interface in series with the high-permittivity dielectric. Recent evidence suggests that this effect is intrinsic in the sense that its emergence is evident even in "perfectly" fabricated structures. The exact nature of the intrinsic dead-layer and the reasons for its origin still remain somewhat unclear. Based on insights gained from recently published ab initio work on SrRuO 3 /SrTiO 3 /SrRuO 3 and our first principle simulations on Au/MgO/Au and Pt/MgO/Pt nanocapacitors, we construct an analytical model that isolates the contributions of various physical mechanisms to the intrinsic dead layer. In particular we argue that strain-gradients automatically arise in very thin films even in complete absence of external strain inducers and, due to flexoelectric coupling, are dominant contributors to the dead layer effect. Our theoretical results compare well with existing, as well as our own, ab initio calculations and suggest that inclusion of flexoelectricity is essential for qualitative reconciliation of atomistic results. Our results also hint at some novel remedies for mitigating the dead layer effect.

At what characteristic length scale does classical continuum elasticity cease to accurately describe small deformation mechanical behavior? The two dominant physical mechanisms that lead to size dependency of elastic behavior at the nanoscale are surface energy effects and nonlocal interactions. The latter arises due to the discrete structure of matter and the fluctuations in the interatomic forces that are smeared out within the phenomenological elastic modulus at coarser sizes. While surface energy effects have been well characterized in the literature, little is known about the length scales at which nonlocal effects manifest for different materials. Using a combination of empirical molecular dynamics and lattice dynamics (empirical and ab initio), we provide estimates of nonlocal elasticity length scales for various classes of materials: semiconductors, metals, amorphous solids, and polymers.

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An important aspect of multi-scale modelling of materials is to link continuum concepts, such as fields, to the underlying discrete microscopic behaviour in a seamless manner. With the growing importance of atomistic calculations to understand material behaviour, reconciling continuum and discrete concepts is necessary to interpret molecular and quantum-mechanical simulations. In this work, we provide a quantum-mechanical framework to a distinctly continuum quantity: mechanical stress. While the concept of the global macroscopic stress tensor in quantum mechanics has been well established, there still exist open issues when it comes to a spatially varying local quantum stress tensor. We attempt to shed some light on this topic by establishing a general quantummechanical operator-based approach to continuity equations and from those, introduce a local quantum-mechanical stress tensor. Further, we elucidate the analogies that exist between the (classical) molecular-dynamics-based stress definition and the quantum stress. Our derivations appear to suggest that the local quantum-mechanical stress may not be an observable in quantum mechanics and therefore traces the non-uniqueness of the atomistic stress tensor to the gauge arbitrariness of the quantum-mechanical state function. Lastly, the virial stress theorem (of empirical molecular dynamics) is re-derived in a transparent manner that elucidates the analogy between quantum-mechanical global stresses.