This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano-and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.

We use a symmetry-based structural analysis combined with an electronic descriptor for bond covalency to explain the origin of the second-order nonlinear optical response (second harmonic generation, SHG) in noncentrosymmetric nonpolar ATeMoO6 compounds (where A = Mg, Zn, or Cd). We show that the SHG response has a complex dependence on the asymmetric geometry of the AO6 and AO4 functional units and the orbital character at the valence band edge, which we are able to distinguish using an A–O bond covalency descriptor. The degree of covalency between the divalent A-site cation and the oxygen ligands dominates over the geometric contributions to the SHG arising from the acentric polyhedra, and this can be understood from considerations of the local static charge density distribution. The use of a local dipole model for the polyhedral moieties (AO4/AO6, MoO4, and TeO4) can account for a nonzero SHG response, even though the materials exhibit nonpolar structures; however, it is insufficient to explain the change in the magnitude of the SHG response upon A-cation substitution. The atomic scale and electronic structure understanding of the macroscopic SHG behavior is then used to identify hypothetical HgTeMoO6 as a candidate telluromolybdate with an enhanced nonlinear optical response.

Lattice dynamics of MX2 transition metal dichalcogenides (M = Mo, W; X = S, Se, Te) have been studied with density functional theory techniques to control the macroscopic tribological behavior. Long-range van der Waals forces have been modeled with Grimme correction to capture the interlayer interactions. A new lattice dynamic metric, named cophonicity, is proposed and used in combination with electronic and geometric descriptors to relate the stability of the lattice distortions with the electro-structural features of the system. The cophonicity analysis shows that the distortion modes relevant to the microscopic friction can be controlled by tuning the relative M/X atomic contributions to the phonon density of states. Guidelines on how to engineer macroscopic friction at nanoscale are formulated, and finally applied to design a new Ti-doped MoS2 phase with enhanced tribologic properties.

The compositional dependence of metal-oxygen BO6 octahedral distortions, including bond elongations and rotations, is frequently discussed in the ABO3 perovskite literature; structural distortions alleviate internal stresses driven by under- or over-coordinated bond environments. Here we identify the dependence of octahedral rotations from changes in metal-oxygen bond covalency in orthorhombic perovskites. Using density functional theory we formulate a covalency metric, which captures both the real and k-space interactions between the magnitude and sense, i.e., in-phase or out-of-phase, octahedral rotations, to explore the link between the ionic-covalent Fe-O bond and the interoctahedral Fe-O-Fe bond angles in Pbnm ferrates. Our survey finds that the covalency of the metal-oxygen bond is correlated with the rotation amplitude: We find the more covalent the Fe-O bond, the less distorted is the structure and the more important the long-range inter-octahedral (Fe-O-Fe bond angle) interactions. Finally, we show how to indirectly tune the B-O bond covalency by A-cation induced BO6 rotations independent of ionic size, facilitating design of targeted bonding interactions in complex perovskites.

We investigated the metal-insulator transition for epitaxial thin films of the perovskite CaFeO3, a material with a significant oxygen ligand hole contribution to its electronic structure. We find that biaxial tensile and compressive strain suppress the metal-insulator transition temperature. By combining hard X-ray photoelectron spectroscopy, soft X-ray absorption spectroscopy, and density functional calculations, we resolve the element-specific changes to the electronic structure across the metal-insulator transition. We demonstrate that the Fe electron valence undergoes no observable spectroscopic change between the metallic and insulating states, whereas the O electronic configuration undergoes significant changes. This strongly supports the bond-disproportionation model of the metal-insulator transition for CaFeO3 and highlights the importance of ligand holes in its electronic structure. By sensitively measuring the ligand hole density, however, we find that it increases by ∼5-10% in the insulating state, which we ascribe to a further localization of electron charge on the Fe sites. These results provide detailed insight into the metal-insulator transition of negative charge transfer compounds and should prove instructive for understanding metal-insulator transitions in other late transition metal compounds such as the nickelates.

Geometry calculations were performed on pure BaCeO(3) fragments and on Y- and In-doped derivatives. HF and DFT approaches were used to investigate monoclinic and orthorhombic structures. The computational methods, structural models, and electronic structure investigation protocols were tuned taking into consideration and balancing the consistency of the results against the computational cost. The calculated structures and energetics parameter, as well as the detailed orbital analysis performed on the corresponding BaCeO(3) derivatives allowed us to explain experimental findings and to develop a procedure to study the cationic octahedral environment of doped X:BaCeO(3) (X = Y, In) and undoped BaCeO(3) protonic conductors useful to interpret experimental results and hopefully to design new experimental approaches. In detail, distances and angles of the studied materials are easily captured in the frame of the HF paradigm even by using low-level ECP basis sets. While, pure electronic-based approaches, involving the investigation of the Partial Density of States resulting from the C-Squared Population Analysis, show that the dopant species must leave unchanged, or even decrease, the local basicity of the oxygen octahedral environment in order to increase the conductivity of the BaCeO(3) derivatives. Whereas local structural changes that are not related to the basicity above affect to a less, if not null, extent the conductivity of the same derivatives.

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Group theory and ab initio electronic structure calculations are combined to formulate a general protocol called "SAFOR" to understand and predict how to improve the second harmonic generation (SHG) response in acentric nonlinear optical crystals. Using the prototypical SHG borate β-BaB 2 O 4 , we show how the SHG d-tensor can be formulated from mode effective d ij coefficients obtained as a linear combination of symmetry-adapted displacement patterns that transform as irreducible representations of a centrosymmetric parent structure. Since this protocol does not require any constraints on the crystal topology or anionic moieties in the structure, we suggest it constitutes a powerful tool to understand and design new SHG compounds through atomic-structure governing principles.