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Effect of applied potential on metal surfaces: Surface energy, Wulff shape and charge distribution
Here we use grand canonical density functional theory to predict the surface energies, Wulff shapes, charge distributions and catalytically active sites of different metal surfaces under electrochemical conditions. We propose a method for computing surface energies from grand canonical density functional theory (GC-DFT) calculations of periodic slab models and use it to compute the surface energies of the facets of Pt, Cu, and Ag crystals to predict their Wulff shapes under electrochemical conditions. GC-DFT predicts that, for the pure metals studied, solvation only slightly affects the Wulff shape while applied potentials considerably affect the surface energies and corresponding Wulff shapes. We used Bader charge analysis of GC-DFT computed electron densities to investigate the effect of applied potential on the distribution of electron density over the atoms of the surfaces of Pt, Cu, Ag, and the 75–25 Ag-Pt and Au-Ni alloys. This analysis shows that, under an applied potential, the electron density is unevenly distributed over the surface atoms and that the charges of atoms more exposed to solvent are more sensitive to bias. Our results show that the most sensitive atom to bias can be used to identify the most favorable adsorption site and thus, the active sites of electrochemical reactions, which is computationally less demanding than calculating the adsorption energies on all possible adsorption sites.
DNA origami single crystals with Wulff shapes
DNA origami technology has proven to be an excellent tool for precisely manipulating molecules and colloidal elements in a three-dimensional manner. However, fabrication of single crystals with well-defined facets from highly programmable, complex DNA origami units is a great challenge. Here, we report the successful fabrication of DNA origami single crystals with Wulff shapes and high yield. By regulating the symmetries and binding modes of the DNA origami building blocks, the crystalline shapes can be designed and well-controlled. The single crystals are then used to induce precise growth of an ultrathin layer of silica on the edges, resulting in mechanically reinforced silica-DNA hybrid structures that preserve the details of the single crystals without distortion. The silica-infused microcrystals can be directly observed in the dry state, which allows meticulous analysis of the crystal facets and tomographic 3D reconstruction of the single crystals by high-resolution electron microscopy.
Versatile stochastic model for predictive KMC simulation of fcc metal nanostructure evolution with realistic kinetics
Stochastic lattice-gas models provide the natural framework for analysis of the surface diffusion-mediated evolution of crystalline metal nanostructures on the appropriate time scale (often 10 1 –10 4 s) and length scale. Model behavior can be precisely assessed by kinetic Monte Carlo simulation, typically incorporating a rejection-free algorithm to efficiently handle the broad range of Arrhenius rates for hopping of surface atoms. The model should realistically prescribe these rates, or the associated barriers, for a diversity of local surface environments. However, commonly used generic choices for barriers fail, even qualitatively, to simultaneously describe diffusion for different low-index facets, for terrace vs step edge diffusion, etc. We introduce an alternative Unconventional Interaction–Conventional Interaction formalism to prescribe these barriers, which, even with few parameters, can realistically capture most aspects of behavior. Here, the model is illustrated for single-component fcc metal systems, mainly for the case of Ag. It is quite versatile and can be applied to describe both the post-deposition evolution of 2D nanostructures in homoepitaxial thin films (e.g., reshaping and coalescence of 2D islands) and the post-synthesis evolution of 3D nanocrystals (e.g., reshaping of nanocrystals synthesized with various faceted non-equilibrium shapes back to 3D equilibrium Wulff shapes).
Thermal Shape Stability of fcc Metal Nanocrystals Synthesized with Faceted Nonequilibrium Shapes
Highly refined capabilities of the shape-controlled solution-phase synthesis of metal nanocrystals (NCs) allow the generation of NCs with faceted nonequilibrium shapes, which optimize properties for target applications such as catalysis and plasmonics. Often, for such applications and also for TEM analysis, the NCs are removed from the solution-phase environment. We explore the postsynthesis evolution of these metastable NCs in a high-vacuum TEM environment. Specifically, here we analyze their reshaping toward the equilibrium Wulff shapes mediated by surface diffusion, where such reshaping degrades the above-mentioned optimized properties. Typical sizes for these NCs range from 5 to 30 nm or 10 3 –10 6 atoms, and reshaping often occurs on the time scale of minutes for temperatures around, say, 400 °C. We discuss the development of predictive stochastic atomistic-level models for NC evolution with a realistic description of surface diffusion. These models, in contrast to Molecular Dynamics, can naturally address the relevant time and length scales for these systems. KMC simulation results for the stochastic models are described, focusing on the reshaping of slightly elongated nanorods and of mildly truncated octahedra and nanocubes. In addition, we review appropriate theoretical formulations for reshaping, which involves the nucleation and growth on 2D islands or layers on outer facets of the NC. We note the limitations of classical nucleation theory in some scenarios and demonstrate the successes of a more fundamental and general master equation-based analysis.
The predicted shapes of voids and Xe bubbles in UO 2
Morphology is a fundamental attribute when investigating voids and bubbles in UO 2 . Here we use molecular dynamics and Monte Carlo simulations to predict the lowest energy shapes for voids and bubbles in UO 2 . The energies of the {100}, {110} and {111} surfaces have been calculated and used to predict the equilibrium void shape from Wulff construction. This equilibrium shape is compared to low energy faceted voids exhibiting different relative proportions of each family of terminating surfaces. It is found that the equilibrium Wulff shape does not represent the lowest energy morphology for nm void sizes at temperatures between 300 K and 1200 K. Furthermore, the lowest energy faceted voids are slightly more energetically favourable than spherical voids, and as Xe is added, and bubble pressure increases, the faceted morphology becomes even more favourable than the spherical shape.
Complex Fluorine Chemical Potential Effects on the Shape and Compositional Heterogeneity of KTa 1– x Nb x O 3 Nanoparticles
When kinetic conditions dominate and dictate the growth in a nanoparticle synthesis, properties of the synthesis environment can have considerable effects on the properties of the products. Such effects were studied here, where the solution environment was changed via the addition of KF to the hydrothermal syntheses of KTa 1– x Nb x O 3 and KTaO 3 . One result demonstrated the straightforward cause-and-effect relationship between the solution and reaction kinetics: KF directly increased the solution stability of the Ta species and therefore decreased its reaction rate, resulting in a change in composition heterogeneity of Ta and Nb in the KTa 1– x Nb x O 3 particles. However, not all effects are so simple; changing the chemical potential of the solution with KF can also promote the formation of particles with anisotropic defect enhanced kinetic Wulff shapes instead of cuboidal shapes. The increased F chemical potential in the solution enabled the formation of planar defects in the bulk, which accelerated growth in-plane to form particles characterized by flat rectangular flake geometries. In this work, thermodynamic modeling with density functional theory calculations confirmed that sufficient KF concentrations can drive the formation of a defect phase K n +1 Ta n O 3 n F.
Size dependent lattice pseudosymmetry for frustrated decahedral nanoparticles
Geometric frustration—where geometry prevents simultaneous satisfaction of local interactions—generates pseudosymmetry and emergent behaviors across physical and biological systems. At the nanoscale, pseudosymmetric features in crystalline materials manifest as local strain and distortion, but how they depend on particle size and control structural stability remains unclear. Here, we report the first study of a size-dependent crossover in pseudosymmetry in multi-twinned gold nanoparticles (NPs), combining four-dimensional scanning transmission electron microscopy with nanoscale strain mapping grounded in continuum solid mechanics. Analysis of more than 20 decahedral NPs (20–55 nm) reveals pronounced heterogeneity in multiple modes of in-plane strain and displacement field in small NPs as five tetrahedral grains close the geometric gap, without extended defects. With increasing particle size, strain fields homogenize across grains and local phases shift from predominantly low-symmetry body-centered tetragonal motifs at small sizes to face-centered cubic character approaching the bulk limit. We identify a crossover particle size of ~35 nm, well below bulk, correlating with a transition from modified-Wulff shapes to pentagonal bipyramids, consistent with finite element predictions. This quantitative framework for mapping size-dependent strain and pseudosymmetry enables precise design and control of functional crystalline solids and phase transformation for catalysis, photonics, electronics, and energy storage.
A physics informed model for the prediction of surface energies and the shape of metal particles
Surface energies of metal-based systems are important for determining the Wulff-constructed shapes of metal nanoparticles and understanding the stability. We have developed a physics informed method to predict the total energy of metal-based systems across a wide range of configurations. Our method has been tested against density functional theory (DFT) calculations for late transition metals. This method enables on-the-fly surface energy predictions based on the fundamental of materials property and allows for the Wulff construction of metal particles for a random number of elemental atoms and without the need for DFT calculations. By making a division between atoms in the different layers of the model system, we can improve the accuracy of the model, suggesting a dissimilarity between the electronic structure due to an alternating compression and expansion of atomic layers. We find that our model accurately and effectively provides valuable insights into the distribution and stability of nanoparticles.
Predicting Morphological Evolution during Coprecipitation of MnCO 3 Battery Cathode Precursors Using Multiscale Simulations Aided by Targeted Synthesis
The performance of lithium-ion batteries is intimately linked to both the structure and the morphology of the cathode material, which in turn is critically linked to the synthesis conditions. However, few studies focus on understanding synthesis, especially during the coprecipitation of metal oxide precursors, a process that largely determines the final morphology of the material. In this paper, we go beyond the typical equilibrium particle shape analysis conducted in the literature and incorporate kinetic aspects of morphology evolution. We perform these studies using controlled synthesis on a well-defined metal salt system (MnCO 3 ) combined with multiscale simulations and high-resolution microscopy. Results show that with increasing metal concentration, the particles transition from rhombohedral to cubic to spherical shapes. Computational analysis using density functional theory (DFT) reveals that rhombohedral shaped particles evolve under equilibrium conditions. Phase field techniques indicate that at higher metal concentrations, fast growth kinetics of the precipitates result in the transition to cubic and, subsequently, spherical shapes, accompanied by a decrease in particle size. This study, while limited to the one metal salt system, provides an approach to shed light on the synthesis process of mixed transition metal salts, gradient materials, and other cathode materials of interest to the battery community.
A semi-empirical model for the complete orientation dependence of the growth rate for vapor phase epitaxy - Chloride VPE of GaAs
A semi-empirical model has been developed to determine the complete crystallographic orientation dependence of the growth rate for vapor phase epitaxy (VPE). Previous researchers have been able to determine this dependence for a limited range of orientations; however, our model yields relative growth rate information for any orientation. This model for diamond and zincblende structure materials is based on experimental growth rate data, gas phase diffusion, and surface reactions. Data for GaAs chloride VPE is used to illustrate the model. The resulting growth rate polar diagrams are used in conjunction with Wulff constructions to simulate epitaxial layer shapes as grown on patterned substrates. In general, this model can be applied to a variety of materials and vapor phase epitaxy systems.
Orientation and Morphology Effects in Rapid Silicon Sheet Solidification
Radial growth anisotropies and equilibrium forms of point nucleated, dislocation free silicon sheets spreading horizontally on the free surface of a silicon melt were measured for (100), (110), (111), and (112) sheet planes. The growth process was recorded. Qualitative Wulff surface free energy polar plots were deduced from the equilibrium shapes for each sheet plane. Predicted geometries for the tip shape of unidirectional, dislocation free, horizontally grown sheets growing in various directions within the planes were analyzed. Polycrystalline sheets and dendrite propagation were analyzed. For dendrites, growth rates on the order of 2.5 m/min and growth rate anisotropies of 25 are measured.
Determining the Role of Synthesis and Reaction Conditions on the Exposed Surface and Shape of ..beta..-Mo2C Catalysts
The production of drop-in quality biofuels typically can be achieved through catalytic fast pyrolysis (CFP) of biomass, followed by hydrodeoxygenation (HDO) of the vapor-phase product to reduce the oxygen content and stabilize the bio-oil product. To favor selectivity toward desired deoxygenation products, bifunctional catalysts with both acidic and hydrogenation sites are often employed. Due to both its oxophilicity and its ability to promote hydrogenation reactions, molybdenum carbide catalysts have shown promise for promoting the HDO of CFP vapors. However, the surface structure and composition of carbide catalyst particles are not well understood, precluding the establishment of fundamental structure-function relationships needed for the rational development of molybdedum carbide for HDO, as well as other reactions. For orthorhombic ..beta..-Mo2C, the (100) facet is largely studied for computational surface-reaction analyses, possibly due to its similarities with the close-packed (111) facet of noble-metal catalysts. However, it has previously been postulated through ab initio thermodynamic studies that the (111), (110), and (011) facets are most stable, though there is no consensus. Furthermore, while a majority of previous surface stability analyses of ..beta..-Mo2C focus on bulk terminations, the highly carburizing synthesis conditions and the use of ..beta..-Mo2C in carbon-containing reaction applications could introduce non-stoichiometric coverages of surface carbon. As such, this study uses ab initio thermodynamics calculations to assess the relative surface stability of the low-index facets of ..beta..-Mo2C, including consideration of varying the coverage of surface carbon. From this information, Wulff constructions are utilized to predict the synthesis and reaction condition-dependent shape and surface carbon composition of ..beta..-Mo2C catalyst particles.
Two-Dimensional Palladium Diselenide with Strong In-Plane Optical Anisotropy and High Mobility Grown by Chemical Vapor Deposition
Two-dimensional (2D) palladium diselenide (PdSe 2 ) has strong interlayer coupling and a puckered pentagonal structure, leading to remarkable layer-dependent electronic structures and highly anisotropic in-plane optical and electronic properties. However, the lack of high-quality, 2D PdSe 2 crystals grown by bottom-up approaches limits the study of their exotic properties and practical applications. In this work, chemical vapor deposition growth of highly crystalline few-layer (≥2 layers) PdSe 2 crystals on various substrates is reported. The high quality of the PdSe 2 crystals is confirmed by low-frequency Raman spectroscopy, scanning transmission electron microscopy, and electrical characterization. In addition, strong in-plane optical anisotropy is demonstrated via polarized Raman spectroscopy and second-harmonic generation maps of the PdSe 2 flakes. A theoretical model based on kinetic Wulff construction theory and density functional theory calculations is developed and described the observed evolution of “square=like” shaped PdSe 2 crystals into rhombus due to the higher nucleation barriers for stable attachment on the (1,1) and (1,-1) edges, which results in their slower growth rates. Finally, few-layer PdSe 2 field-effect transistors reveal tunable ambipolar charge carrier conduction with an electron mobility up to ≈294 cm 2 V -1 s -1 , which is comparable to that of exfoliated PdSe 2 , indicating the promise of this anisotropic 2D material for electronics.
Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals
In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and electronic gap of rutile titania nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Angstrom (24 atoms) to 10.3 Angstrom (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Angstrom. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS is highly dependent on the shape and size of these particles. Furthermore, the DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigen value distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.
Fragmentation of faceted crystalline wires
The reduction of surface energy is a well-known driving force for the fragmentation of nanowires. Fragmentation can limit the service life of those small low-dimensional building blocks or can be controlled to induce beneficial shape changes. For isotropic surface energy, fragmentation is analogous to the classic Rayleigh-Plateau instability of liquid jets. However, commonly synthesized crystalline nanowires have strongly anisotropic surface energies and exhibit facets coinciding with cusps in the Wulff plot. Depending on growth orientation, different fragmentation behaviors have been seen in nanowires. Using phase-field simulations, we show that fragmentation of faceted nanowires with cubic crystal symmetry may occur by a finite-amplitude nonlinear instability, as opposed to a Rayleigh-Plateau-like linear instability, depending on nanowire growth orientation. Here, we carry out a weakly nonlinear analysis based on sharp interface theory to characterize the faceted nanowire shape corresponding to a surface-energy saddle point. The analysis predicts that the minimum amplitude of a periodic shape perturbation to trigger fragmentation increases with cusp strength but decreases inversely proportionally to the perturbation wavelength for long wavelengths, in good quantitative agreement with phase-field predictions. The results provide the theoretical foundation to predict nanowire stability as a function of length and surface energy in diverse applications.
Modified Winterbottom Construction Including Boundaries
There has been extensive work on the equilibrium shape of isolated nanoparticles with internal boundaries, and also single crystals on substrates. Surprisingly, almost shockingly, there has been very little work on the equilibrium shape of particles with internal boundaries on substrates. Here in this paper, the general solution is given for the configuration of particles which contain twin and other grain boundaries on a flat substrate, which can be applied to any polycrystalline or multiphase nanoparticle configuration. The solution is based upon combining the established modified-Wulff construction that has been extensively validated for twinned particles with the Winterbottom construction for single particles on a substrate. The solution is illustrated for the specific case of five-fold multiply twinned particles. Good agreement is observed between both existing experimental data in the literature as well as some experimental data included within this work.
Imaging how thermal capillary waves and anisotropic interfacial stiffness shape nanoparticle supracrystals
Abstract Development of the surface morphology and shape of crystalline nanostructures governs the functionality of various materials, ranging from phonon transport to biocompatibility. However, the kinetic pathways, following which such development occurs, have been largely unexplored due to the lack of real-space imaging at single particle resolution. Here, we use colloidal nanoparticles assembling into supracrystals as a model system, and pinpoint the key role of surface fluctuation in shaping supracrystals. Utilizing liquid-phase transmission electron microscopy, we map the spatiotemporal surface profiles of supracrystals, which follow a capillary wave theory. Based on this theory, we measure otherwise elusive interfacial properties such as interfacial stiffness and mobility, the former of which demonstrates a remarkable dependence on the exposed facet of the supracrystal. The facet of lower surface energy is favored, consistent with the Wulff construction rule. Our imaging–analysis framework can be applicable to other phenomena, such as electrodeposition, nucleation, and membrane deformation.