Triboelectricity, when rubbing or contacting materials causes electric charge transfer, is ubiquitous across many fields, and has been studied in detail for centuries. Despite this, a complete description of triboelectricity remains elusive. Here, we analyze the contact between a metal asperity and a semiconductor, including contributions from the depletion zone of the semiconductor and from flexoelectric polarization that arises due to the strain gradients at asperity contacts. The free charges involved in charge transfer are then discussed and calculated. As a result, we develop a quantitative model for triboelectric charge transfer that details how charge transfer scales with contact parameters, the relative influence of depletion and flexoelectricity, and which agrees with various trends in multiple classes of triboelectric experiments.

In this report, we look at the fundamental physics of triboelectricity, charge transfer due to contact and sliding. While much of the report focuses upon recent advances such as the incorporation of flexoelectric contributions, we also include older work, some from centuries ago, which can only now be fully understood. Basic concepts and theories ranging from elements of tribology and contact mechanics through semiconductor built-in potentials, electromechanical terms, mechanochemistry and trap states are briefly described, linking to established surface science and interface physics. We then overview the main models that have been proposed, showing that they all fall within conventional electrostatics combined with other established science. We conclude with some suggestions for the future. Based upon this overview, our conclusion is that triboelectricity is a slightly complex combination of classic tribology and standard electrostatic phenomena that can be understood using the generalized Ampère's law connecting the electric displacement field with both Coulomb and polarization contributions, and the free carrier density, that is∇⋅D=ρf. Triboelectricity may be confusing, it is not really confused if care is taken, but it is complex.

Triboelectricity has been a topic of some confusion for many years, probably because it is very diverse and some of the fundamental science has not been clear. This is now starting to change. A few years ago, the importance of flexoelectricity at asperities is pointed out. That paper exploited the established physics of compensation of bound surface or interfacial charges without going into detail. The purpose of this paper is to expand further on this, mapping from the established physics of electrostatics with contact potentials and Maxwell's displacement field to the underlying fundamentals of charge transfer in triboelectricity. Examples from the published literature are used to illustrate this. In the discussion, some of the open questions and challenges to the community are mentioned.

An enduring question in science has been why sliding plays a major role in the triboelectric generation of static electricity-the "tribo" in triboelectricity. We provide here a general explanation which is rooted in established science. When sliding is taking place, there is symmetry breaking due to elastic shear, so the front of the sliding body experiences different elastic strains from the back. Consequently the polarization and associated charges at the front and back are not the same, and the difference between the two leads to current flow similar to the difference in air pressure above and below a plane's wing leading to lift. Specific calculations are provided which show good agreement with prior experimental measurements of size and shape dependencies, and reasonable quantitative agreement with experimental current measurements.

Additive manufacturing (AM) is a valuable tool for the fabrication and repair of refractory parts such as molybdenum alloys. Cracking is a common defect encountered during AM processing of refractory parts, that is generally associated with the segregation of light elements to grain boundaries which affect grain boundary cohesion and, ultimately, affect the final performance of the part. Similarly, because of the high melting points of refractory metals, lack-of-fusion defects are also common. The effect of build substrate and small alloying additions on suppression of defects during multilayer builds was investigated using directed energy deposition (DED) printing. Identical sample matrices were printed on three different build substrates: molybdenum (Mo), commercially pure titanium (Cp-Ti), and 316 stainless steel (316). Twenty-six usable samples were produced. Samples were cross sectioned, polished, and were characterized for total cross-section defect area. Additionally, samples from each substrate material were analyzed for grain boundary oxygen content. The strongest defect suppression, producing crack free material, was observed in samples printed on a Cp-Ti build substrate with a ten atomic percent addition of titanium in the molybdenum powder feed. The part quality was enhanced due to three factors: 1) the moderation of thermal diffusivity through a change in build plate material, 2) the suppression of light element segregation via increased solubility through titanium addition, and 3) a lack of brittle phase formation due to metallurgical compatibility of the build material with the build substrate. Analysis of defect area versus dimensionless number, pi 1, shows that increasing pi 1 reduced defects throughout the part.

Triboelectric and flexoelectric phenomena have seen significant recent interest for energy harvesting. However, the underlying science responsible for triboelectricity has yet to be completely understood, both the fundamentals and an understanding of how the energy output depends upon the shape of the interacting surface. Here, we investigate the role of the contacting shapes (asperities) in triboelectricity. We demonstrate that their shape and size is very important, obtaining qualitative agreement with experimental results. Further, we discuss how the impact of the shape depends on material, geometric, gradient elasticity and electronic transport details. We provide scaling rules which can be exploited to better design energy harvesting devices based upon either triboelectricity or flexoelectricity.

The choice of temperature and gas conditions used in a water pressure-controlled reactor is guided by density functional theory (DFT) to synthesize nearly phase-pure lanthanide scandate nanoparticles (LnScO3, Ln = La, Nd, Sm, Gd). In this synthetic method, low water-vapor partial pressures, well below water's gas liquidus, inhibit particle growth, while an excess of water vapor results in undesired rare-earth hydroxide and oxyhydroxide secondary phases. The optimal humidity for high-purity LnScO3 particle synthesis is shown to vary with the lanthanide; DFT is used to calculate the thermodynamics of secondary phase formation for each lanthanide tested such that the role of water vapor may be quantified and used to maintain phase purity (greater than 96 mol %) across the series. The combination of thermodynamic calculation and experimental confirmation with this pressure-controlled reactor provides an opportunity to explore analogous syntheses of other inorganic perovskite nanoparticles.

To address the challenges of processing ultrahigh-temperature refractory metal alloys, a novel reactive synthesis-based additive manufacturing technique has been developed to fabricate chemically uniform and dense alloys. The present study demonstrates the reactive additive manufacturing of Mo-4Si-6B (at.%), a high-temperature refractory alloy, using directed energy deposition. For the alloy in the Mo-Si-B system, a premixed blend of molybdenum, silicon nitride, and boron nitride powder was used to make an alloy with the desired composition. A dimensionless number was used to design the process parameters and build efficiency. High-throughput synthesis using build height measurements of individual samples validated the predicted process parameters. Microstructural characterization investigations and indentation hardness testing indicated chemically uniform samples with refined microsegregation in samples with high hardness and no cracking, even with a 10-kg force load. The results demonstrate an effective strategy for additively manufacturing refractory alloys.

It is easy to miss the scientific implications of our recent work on Triboelectricity. Everyone knows that rubbing and contact can produce static electricity; less appreciated is that the thermodynamic driver has been an open question since static electricity was first observed by Thales of Miletus around 585 BC. People think they understanding it, for instance one common explanation that can still be found in the current literature is that differences in the work function drives charge transfer, often called the Volta-Helmholtz hypothesis. As summarized in 1967 by Harper, this fails to explain many experimental observations, for instance that charging can occur when two pieces of the same material are rubbed against each other. We are the first to place triboelectricity on a solid foundation rooted in quantum mechanics – the flexoelectric effect. We were able to explain a significant number of previously unexplained phenomena: Bipolar tribocurrents associated with stick-slip, due to the change in sign of the strain gradients. A one-third power scaling of tribocurrents with indentation force. Tribocharging when two identical materials are used, these being due to local variations in the asperities so there are usually local potential differences. Inhomogeneous charging of insulators, related to the statistical nature of asperities. An experimentally observed reversal in the sign of charge transfer for negative and positive curvature, which is related to a change in the sign of the strain gradient. Exploiting our DOE prior funded work on flexoelectricity, we obtained semi-quantitative matching to existing experimental measurements of the surface charge in triboelectric experiments. The work has been well received in the literature. The work has been the focus of a number of popular science press articles, and also formed the basis for a Podcast for children 6-10 “The Rise and Fall of Static Man” posted in December 2019 by NPR as part of their “Wow in the World” series. I was also briefly interviewed by the Chicago PBS station in January 2020. This work are significant for a wide range of energy applications; to quote from an independent source: Triboelectric power has plenty of potential, says Wenzhuo Wu, an assistant professor of engineering at Purdue. If the basics of static electricity are better understood, we could maximize the efficiency of wind or wave power generators, Wu says. The body's own movement could be used to power internal medical devices. Imagine being able to create a roof shaped to harness the power of a raindrop — the friction of the rain passing over the surface — to generate triboelectricity, powering the building below it. This is the start of new science, some of which we already partially understand such as the role of band bending in charge transfer. We need to understand charge transfer combining elasticity, quantum mechanics, band bending and defect states. These directly involve several of the DOE Grand Challenges How do we control material processes at the level of electrons? How do remarkable properties of matter emerge from complex correlations of the atomic or electronic constituents and how can we control these properties? How do we characterize and control matter away—especially very far away— from equilibrium? I will argue that this work truly falls into the class of disruptive science; it is not just a simple extension, linear science. Not everyone will accept the approach. Since we explain far more about triboelectricity than anyone before, the preponderance of evidence supports the model. The feedback I have received is that many agree with the work, to quote: The model makes sense, says Michael McAlpine, a professor of engineering at the University of Minnesota. "It's such a simple explanation, I was surprised I didn't put my finger on that," McAlpine says. The proposal received strong reviews. It was also publicized on the Department of Energy Web Site.

Triboelectricity was recognized millennia ago, but the fundamental mechanism of charge transfer is still not understood. We have recently proposed a model where flexoelectric band bending due to local asperity contacts drives triboelectric charge transfer in non-metals. While this ab initio model is consistent with a wide range of observed phenomena, to date there have been no quantitative analyses of the proposed band bending. In this work we use a Pt0.8Ir0.2 conductive atomic force microscope probe to simultaneously deform a Nb-doped SrTiO3 sample and collect current-bias data. The current that one expects based upon an analysis including the relevant flexoelectric band bending for a deformed semiconductor quantitively agrees with the experiments. The analysis indicates a general ratcheting mechanism for triboelectric transfer and strong experimental evidence that flexoelectric band bending is of fundamental importance for triboelectric contacts.

We report experimental values for the flexoelectric responses of SrTiO3, KTaO3, TiO2, and YAlO3 single crystals using a three-point bending approach. We find all samples possess a linear flexoelectric response with effective short-circuit flexoelectric coefficients similar to vertical bar 1-10 vertical bar nC/m. Flexocoupling voltages computed from these measured effective flexoelectric coefficients are found to significantly vary across the investigated materials and refute the previous suggestions that they should be similar to vertical bar 1-10 vertical bar V. Importantly, we find that low dielectric constant materials can have large flexocoupling voltages exceeding nominal expectations.

Triboelectricity has been known since antiquity, but the fundamental science underlying this phenomenon lacks consensus. We present a flexoelectric model for triboelectricity where contact deformation induced band bending at the nanoscale is the driving force for charge transfer. This framework is combined with first-principles and finite element calculations to explore charge transfer implications for different contact geometry and materials combinations. We demonstrate that our ab initio based formulation is compatible with existing empirical models and experimental observations including charge transfer between similar materials and size/pressure dependencies associated with triboelectricity.

Ni-Cr-based alloys are considered amongst the most corrosion-resistant when utilized in aqueous marine applications. The superior corrosion resistance of these alloys is known to depend on the presence of a homogeneous solid solution and the desirable attributes of their oxide films. However, the scientific basis for excellent passivation and protection against localized corrosion initiation remains uncertain and insights are often based on short term laboratory testing under limited conditions even though exposures are long-term. The engineering basis for alloy choice often relies on lab testing, field exposures or empirical metrics such as the PREN that do not even consider exposure time. Both highly engineered legacy and emerging alloys lack information on the precise attributes of protective passive films after long-time exposures. However, relevant field exposure periods are nearly infinite in time. The focus of the current work was on solid solution Ni-22Cr, Ni-22Cr-6Mo, and Ni-22Cr-6Mo-3W alloys. Potential step passivation studies in 0.1 NaCl pH 4 solutions in the passive range were investigated over 10s to 10 days at select potentials. To characterize the formation and exposure aging of oxide films, electrochemical methods were used as well as XPS and three-dimensional APT. Improvements in passive films protectiveness was correlated Cr 3+ enrichment and aliovalent cation accumulation (Figure 1), and minimal morphological roughening. There is possibility of either oxide doping and/or phase separation promoted by aliovalent cations associated with alloying with Mo and W. Ni 2+ rich oxides and hydroxides were preferentially dissolved with time. The most corrosion resistant alloys possess passivating films that are efficacious not only just after formation, but that self-healing capabilities and improve over long exposure times as evident from impedance spectroscopy and metastable pit studies. Such alloys were observed to be the most resistant when interrogated for local corrosion after various periods of exposure compared to other alloys whose impedance response degraded over exposure time. The latter alloys eventually arrived at conditions favoring breakdown. This work contributes to the scientific understanding of the long-term passivation process in Ni-based alloys in acidic chloride-containing environments. The presence of Mo and W as minor alloying elements on aqueous passivation and localized corrosion resistance initiation and stabilization correlated with certain features of electrochemically grown oxide films. Oxide exposure aging time, potential, and oxide “transformation” diagrams are introduced and shown to provide valuable insights on alloy. Passivated films may form as solute captured solid solutions after short term passivation or when grown quickly but are gradually enriched in Cr, Mo and W over long time. Can such Cr enrichment continue during exposure without limits? Factors affecting and limiting Cr enrichment are discussed as time allows. This work was supported by the Office of Naval Research under MURI “Understanding Atomic Scale Structure in Four Dimensions to Design and Control Corrosion Resistant Alloys” through Northwestern University #SP0028970-PROJ0007990-MURI ONR N00014-16-1-2280. Figure 1

CO adsorption and dissociation on "perfect" and "defect-rich" Ir(111) surfaces were studied by a combination of surface-analytical techniques, including polarization-dependent (PPP and SSP) sum frequency generation (SFG) vibrational spectroscopy, low-energy electron diffraction (LEED), Auger electron spectroscopy, X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations. CO was found to be ordered and tilted from the surface normal at high coverage on the "perfect" surface (e.g., θ = 30° at 0.70 ML), whereas it was less ordered and preferentially upright (θ = 4-10°) on the "defect-rich" surface for coverages of 0.55-0.70 ML. SFG, LEED, and XPS revealed that CO adsorption at low pressure/high temperature and high pressure/low temperature was reversible. In contrast, upon heating to ∼600 K in near mbar CO pressure, "perfect" and even more "defect-rich" Ir(111) surfaces were irreversibly modified by carbon deposits, which, according to DFT, result from CO disproportionation.

The underlying mechanisms responsible for triboelectricity have yet to be completely understood. We have previously proposed a model which explains charge transfer in non-metals via band bending due to electromechanical, especially flexoelectric, effects at deformed asperities coupled with work function differences. Here, we investigate whether the shape of asperities is important for triboelectricity. The results indicate that the shape is important in general, since how the electromechanical response scales with force and asperity size depends on the shape. This is qualitatively in agreement with experimental results. Further, we discuss how the impact of the shape depends on material, geometric, and electronic transport details. Additionally, gradient elasticity is incorporated into the model. As asperity contact is a nanoscale phenomenon, size-dependent mechanics can become significant and give more physically reasonable results. In some cases, the impact of gradient elasticity terms on the electromechanical potentials is very large, indicating that standard elasticity theory is not enough to cover some relevant cases in modelling triboelectricity.

Flexoelectricity has garnered much attention owing to its ability to bring electromechanical functionality to nonpiezoelectric materials and its nanoscale significance. In order to move towards a more complete understanding of this phenomenon and improve the efficacy of flexoelectric-based devices, it is necessary to quantify microstructural contributions to flexoelectricity. Here we directly measure the flexoelectric response of bulk centrosymmetric LaAlO3 crystals with different twin-boundary microstructures. We show that twin-boundary flexoelectric contributions are comparable to intrinsic contributions at room temperature and enhance the flexoelectric response by ∼4× at elevated temperatures. Additionally, we observe time-dependent and nonlinear flexoelectric responses associated with strain-gradient-induced twin-boundary polarization. These results are explained by considering the interplay between twin-boundary orientation, beam-bending strain fields, and pinning site interactions, and directly demonstrate that macroscopic flexoelectric responses are very sensitive to structural defects.

Some catalytic oxide supports are more equal than others, with numerous variable properties ranging from crystal symmetry to surface chemistry and electronic structure. As a consequence, it is often very difficult to determine which of these act as the driver of performance changes observed in catalysis. In this work, we hold many of these variable properties constant with structurally similar LnScO3 (Ln = La, Sm, and Nd) nanoparticle supports with cuboidal shapes and a common Sc-rich surface termination. Using CO oxidation over supported Au nanoparticles as a probe reaction, we observe higher activation energy and a slower rate using NdScO3 as the support material. This change is found to correlate to the strength of CO2 binding to the support surface, identified by temperature-programmed desorption measurements. The change is due to differences in the 4f electrons of the lanthanide cations, the cations' Lewis acidity, and the inductive effect they impose.

Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, the internal workings of the code, and the number of iterations to convergence, with the latter being controlled by what is called "mixing". This paper describes a new approach to handling trust regions within these and other fixed-point problems. Rather than adjusting the trust region based upon improvement, the prior steps are used to estimate what the parameters and trust regions should be, effectively estimating the optimal Polyak step from the prior history. Detailed results are shown for eight structures using both the "good" and "bad" multisecant versions as well as the Anderson method and a hybrid approach, all with the same predictive method. Additional comparisons are made for 36 cases with a fixed algorithm greed. The predictive method works well independent of which method is used for the candidate step, and it is capable of adapting to different problem types particularly when coupled with the hybrid approach.