Wulff Construction Research Articles

Identifying the effect of tributyl phosphate on the growth of PbTe quantum dots: Linking experimental and theoretical approaches

The effects of tributyl phosphate (TBP), as a process control agent (PCA), on morphology, size and dispersion of PbTe quantum dots (QDs), at 5 h of milling time, are investigated. By using X-ray diffraction, the occurrence of PbTe is detected, while the PbTe formation and morphology, during milling, are studied via transmission electron microscopy (TEM). According to TEM results, the occurrence of nearly spherical and faceted PbTe QDs are ruled by highly structural-defect and oriented attachment mechanisms, respectively. What is more, mechanical kneading is effectively inhibited when 3 wt% TBP is added during milling. Dispersion-corrected density functional theory (DFT) calculations are carried out to understand the factors that affect growth and morphology of PbTe QDs. DFT results demonstrated that both the intrinsic characteristics of PbTe and the adsorption of certain reaction species are responsible for the shape control of PbTe QDs, which is useful to propose adsorption modes of TBF on PbTe surface and to rationalize the facets exposed by PbTe after the surface treatment. In agreement with experimental results, Wulff constructions proposed are cube-like quantum dots with sharp edges, but rounded edges are possible as well.

Surface energy calculation of brookite TiO2 using Inverse Wulff Construction

The Wulff construction methodology proves to be a highly useful approach in predicting the morphologies of nanoparticles. However, this approach requires the precise determination of surface energies for all orientations, which can be a challenging task due to the inherent complexity of measuring surface-free energies. In this work, the inverse Wulff construction is employed to effectively predicted surface energies from brookite TiO2 particle morphologies. This method can provide guidance for researchers to understand how to control the brookite TiO2 crystal morphology according to the synthetic method used.

Origin for the chloride and citrate ions tuned morphology of Pd particles

Capping agents such as halide and citrate (CA) are crucial in the colloidal synthesis of noble metal nanoparticles (NPs) with desirable shape for specific catalytic reaction. Halide ions have been shown to stabilize the cubic NP while CA ions favor the octahedral NP regardless of the noble metals, but the mechanism remains unclear. We combine DFT calculations and Wulff construction to understand how the morphology of Pd particle changes with Cl and CA chemical potential (μ). Three main factors are identified to affect the morphology of Pd particle: μ of adsorbate, its number per unit area (NAS/S), and rigidity or flexibility. Increasing μ of adsorbate or its NAS/S causes decreased surface free energy and increased exposed surface area. Moreover, rigid adsorbates (PdClx) occupy a larger surface area for surfaces with high atomic density such as Pd(111), leading to cubic Pd particle at high μCl. Conversely, flexible adsorbates (CA) that can adjust their structure based on the surface occupy smaller surface area on Pd(111), favoring octahedral Pd particle. This work reveals the origin for capping agent tuned morphology of Pd NP, and the insights can be used to guide metal NP synthesis with desired morphology for catalytic reactions of technological interest.

The surface and grain boundary properties of uranium boride: A DFT calculation

Uranium borides are currently being investigated as an accident tolerance fuel or advanced technology fuels (ATFs) to replace conventional UO2 fuel due to their high uranium density and high thermal conductivity. The surface properties of diverse facets of a crystal are pivotal for understanding different corrosion behaviors, fission gas bubble behaviors, and equilibrium morphologies. In this study, we employ density functional theory (DFT) calculations to investigate the surface properties of uranium borides. The surface orientations with maximum miller index up to 4, 1, and 2 for UB2, UB4 and UB12 were analyzed, respectively. Based on the calculated surface energies, the other surface properties of uranium borides were obtained through Wulff construction, including equilibrium morphology, dominant surface orientations, area-weighted surface energy and work function. Additionally, grain boundaries (GBs) have a significant impact on material properties, such as mechanical properties, corrosion behavior, and resistance to irradiation. Therefore, we use DFT calculations to determine the GB energies and work of separation for three low-Σ (7) symmetrical tilt GBs (STGB) and two twist GBs (TGB).

Revealing the electrocatalytic mechanism of layered crystalline CoMoO4 for water splitting: A theoretical study from facet selecting to active site engineering

Deciphering the atomic-level properties and mechanism of electrocatalysts for water splitting is vital for the development of highly active non-noble-metal catalysts. Herein, we conduct a detailed study of layered crystalline CoMoO4 using density functional theory (DFT) calculations. The layered arrangement of CoMoO4 along the [110] lattice direction is observed, and the two thermodynamically stable and most exposed (110)A and (001)A crystal facets are selected among all low-index facets by surface energy calculations and Wulff construction to study the electrocatalytic activity for alkaline water splitting and corresponding mechanism. CoMoO4 with an exposed (110)A facet (i.e., CMO (110)A) exhibited a high hydrogen evolution reaction (HER) activity, with a ΔGH* of 0.22 eV, which is similar to that of Pt because the adsorbed H is allowed to interact with two oxygen atoms (O3 and Oadj). The (110)A facet also possesses better H2O adsorption and dissociation abilities than the (001)A facet, benefiting the HER performance in alkaline solutions. Moreover, the overpotential of the (110)A facet for the electrocatalytic oxygen evolution reaction (OER) is only 0.74 V according to the Gibbs free-energy calculation, this overpotential is lower than that of the (001)A facet (0.84 V) owing to the stronger binding and more stable adsorption states between Co and O for the intermediate *O. By allowing us to identify highly active facets and sites, this approach guided the selective synthesis of CoMoO4 and its isostructural substances, such as Mn(Ni, Fe)MoO4 nanocatalysts, for alkaline water splitting.

Effect of Surface Energetics on Phase Stability of CaMnO3

CaMnO3 is a promising starting point for the search of perovskites which are suitable as electrode materials for the hydrogen evolution reaction (HER). In a previous theoretical study [Phys. Status Solidi B 2022, 260, 2200427], it was established that the global hybrid functional PW1PW is well suited to obtain structural, energetic, and electronic bulk properties. Herein, the focus is extended to surface properties of CaMnO3. All symmetry‐inequivalent low‐index surfaces of CaMnO3 are investigated with PW1PW. Based on the experience with polar surfaces, it is decided to employ stoichiometric and symmetric models, in some cases with Schottky defects. From the calculated surface energies, the crystal morphologies are predicted based on the Gibbs–Wulff theorem. The (101), (100), (011), (001), and (010) surfaces (space group no. 62) and the (010), (110), (011), and (101) surfaces (space group no. 20) dominate the surfaces of respective single crystals and should be considered in future theoretical calculations of the HER. Furthermore, it is found that the modification with space group no. 20 is significantly more stable than space group no. 62 for nanoparticles with a diameter below 10 nm.

WhereWulff: A Semiautonomous Workflow for Systematic Catalyst Surface Reactivity under Reaction Conditions.

This paper introduces WhereWulff, a semiautonomous workflow for modeling the reactivity of catalyst surfaces. The workflow begins with a bulk optimization task that takes an initial bulk structure and returns the optimized bulk geometry and magnetic state, including stability under reaction conditions. The stable bulk structure is the input to a surface chemistry task that enumerates surfaces up to a user-specified maximum Miller index, computes relaxed surface energies for those surfaces, and then prioritizes those for subsequent adsorption energy calculations based on their contribution to the Wulff construction shape. The workflow handles computational resource constraints such as limited wall-time as well as automated job submission and analysis. We illustrate the workflow for oxygen evolution reaction (OER) intermediates on two double perovskites. WhereWulff nearly halved the number of Density Functional Theory (DFT) calculations from ∼240 to ∼132 by prioritizing terminations, up to a maximum Miller index of 1, based on surface stability. Additionally, it automatically handled the 180 additional resubmission jobs required to successfully converge 120+ atoms systems under a 48-h wall-time cluster constraint. There are four main use cases that we envision for WhereWulff: (1) as a first-principles source of truth to validate and update a closed-loop self-sustaining materials discovery pipeline, (2) as a data generation tool, (3) as an educational tool, allowing users (e.g., experimentalists) unfamiliar with OER modeling to probe materials they might be interested in before doing further in-domain analyses, (4) and finally, as a starting point for users to extend with reactions other than the OER, as part of a collaborative software community.

Back to the Basics: Probing the Role of Surfaces in the Experimentally Observed Morphological Evolution of ZnO.

Although the physics and chemistry of materials are driven by exposed surfaces in the morphology, they are fleeting, making them inherently challenging to study experimentally. The rational design of their morphology and delivery in a synthesis process remains complex because of the numerous kinetic parameters that involve the effective shocks of atoms or clusters, which end up leading to the formation of different morphologies. Herein, we combined functional density theory calculations of the surface energies of ZnO and the Wulff construction to develop a simple computational model capable of predicting its available morphologies in an attempt to guide the search for images obtained by field-emission scanning electron microscopy (FE-SEM). The figures in this morphology map agree with the experimental FE-SEM images. The mechanism of this computational model is as follows: when the model is used, a reaction pathway is designed to find a given morphology and the ideal step height in the whole morphology map in the practical experiment. This concept article provides a practical tool to understand, at the atomic level, the routes for the morphological evolution observed in experiments as well as their correlation with changes in the properties of materials based solely on theoretical calculations. The findings presented herein not only explain the occurrence of changes during the synthesis (with targeted reaction characteristics that underpin an essential structure-function relationship) but also offer deep insights into how to enhance the efficiency of other metal-oxide-based materials via matching.

The Relationship between Photoluminescence Emissions and Photocatalytic Activity of CeO2 Nanocrystals.

In this work, we focus on understanding the morphology and photocatalytic properties of CeO2 nanocrystals (NCs) synthesized via a microwave-assisted solvothermal method using acetone and ethanol as solvents. Wulff constructions reveal a complete map of available morphologies and a theoretical-experimental match with octahedral nanoparticles obtained through synthesis using ethanol as solvent. NCs synthesized in acetone show a greater contribution of emission peaks in the blue region (∼450 nm), which may be associated with higher Ce3+ concentration, originating shallow-level defects within the CeO2 lattice while for the samples synthesized in ethanol a strong orange-red emission (∼595 nm) suggests that oxygen vacancies may originate from deep-level defects within the optical bandgap region. The superior photocatalytic response of CeO2 synthesized in acetone compared to that of CeO2 synthesized in ethanol may be associated with an increase in long-/short-range disorder within the CeO2 structure, causing the Egap value to decrease, facilitating light absorption. Furthermore, surface (100) stabilization in samples synthesized in ethanol may be related to low photocatalytic activity. Photocatalytic degradation was facilitated by the generation of ·OH and ·O2- radicals as corroborated by the trapping experiment. The mechanism of enhanced photocatalytic activity has been proposed suggesting that samples synthesized in acetone tend to have lower e'─h· pair recombination, which is reflected in their higher photocatalytic response.

Effect of particle anisotropy on the thermodynamics and kinetics of ordering transitions in hard faceted particles.

Monte Carlo simulations were used to study the influence of particle aspect ratio on the kinetics and phase behavior of hard gyrobifastigia (GBF). First, the formation of a highly anisotropic nucleus shape in the isotropic-to-crystal transition in regular GBF is explained by the differences in interfacial free energies of various crystal planes and the nucleus geometry predicted by the Wulff construction. GBF-related shapes with various aspect ratios were then studied, mapping their equations of state, determining phase coexistence conditions via interfacial pinning, and computing nucleation free-energy barriers via umbrella sampling using suitable order parameters. Our simulations reveal a reduction of the kinetic barrier for isotropic-crystal transition upon an increase in aspect ratio, and that for highly oblate and prolate aspect ratios, an intermediate nematic phase is stabilized. Our results and observations also support two conjectures for the formation of the crystalline state from the isotropic phase: that low phase free energies at the ordering phase transition correlate with low transition barriers and that the emergence of a mesophase provides a steppingstone that expedites crystallization.

Gibbs–Wulff optical vortex array

Optical vortex array (OVA) containing multiple optical vortices is an optimal candidate for applications of optical communications, complex manipulation of multi-particle systems, and mass-synchronous fabrication. However, the existing OVAs have not been constructed to respond to the application requirements, particularly for micro-/nanomaterial fabrication where the boundary, size, and stability need to be carefully considered. To address this issue, we propose a Gibbs–Wulff OVA (GWOVA) by analogizing the Gibbs–Wulff theorem in solid-state physics. Herein, the Gibbs–Wulff theorem is first generalized to OVA's generation as the condition to confine its growth boundary. The GWOVA, which possesses versatile structures and arrangement modes (simple- and close-packed modes), is successfully generated and grown. It exhibits high stability and perfect symmetry during growth and rotation, which satisfies the symmetric group of D2s. Owing to its stable structure and growth boundary conditions, the GWOVA has great potential for a wide range of applications, particularly in micro-/nanomaterial fabrication.

The Wulff construction goes low-symmetry.

The Wulff construction goes low-symmetry.

Liquid-Metal-Assisted Synthesis of Single-Crystalline TiC Nanocubes with Exposed {100} Facets for Enhanced Electrocatalytic Activity in the Hydrogen Evolution Reaction.

Although TiC nanostructures show promise as non-noble-metal-based electrocatalysts, improved synthesis methods are required. Herein, single-crystalline TiC nanocubes with exposed {100} facets are grown by combusting TiO2 + kMg + C reactive mixtures (k= 4-6.5mol) in argon. During the synthesis, the temperature increases to 1200-1550°C and excess Mg (2-4.5mol) forms a liquid pool. The obtained TiC nanocubes have edge lengths of 50-300nm and surface areas of 12.2-30.05 m2 g-1 . Insights into the TiC nanocube formation mechanism are obtained using density functional theory modeling of the surface energies of TiC nanocrystals and shape visualization using the Wulff construction method. During TiC nucleation and growth within the Mg melt, liquid Mg likely acts as a capping agent for {111} facets, thus promoting the formation of {100} facets. The TiC nanocubes show high electrocatalytic activity for the hydrogen evolution reaction, with a lower overpotential (0.298V at 10mA cm-2 ) than other TiC nanostructures (0.400-0.815V).

Defining shapes of two-dimensional crystals with undefinable edge energies

The equilibrium shape of crystals is a fundamental property of both aesthetic appeal and practical importance: the shape and its facets control the catalytic, light-emitting, sensing, magnetic and plasmonic behaviors. It is also a visible macro-manifestation of the underlying atomic-scale forces and chemical makeup, most conspicuous in two-dimensional (2D) materials of keen current interest. If the crystal surface/edge energy is known for different directions, its shape can be obtained by the geometric Wulff construction, a tenet of crystal physics; however, if symmetry is lacking, the crystal edge energy cannot be defined or calculated and thus its shape becomes elusive, presenting an insurmountable problem for theory. Here we show how one can proceed with auxiliary edge energies towards a constructive prediction, through well-planned computations, of a unique crystal shape. We demonstrate it for challenging materials such as SnSe, which is of C2v symmetry, and even AgNO2 of C1, which has no symmetry at all.

Surface-dependent properties and morphological transformations of rutile GeO2 nanoparticles

Recently, the knowledge of surface-dependent properties has attracted a lot of attention since it is crucial for materials functionalization based on the morphological control of nanoparticles (NPs). This study describes the surface-dependent properties and morphological transformation routes of rutile germanium dioxide (r-GeO2) using the density functional theory (DFT) and the Wulff construction procedure. The calculations revealed the following order of relative surface stability: (110) > (100) > (321) > (311) > (201) > (211) > (101) > (103) > (001) > (111), with the Ge-O bonds being attributed to Ge4p-O2p and Ge4s-O2p interactions. The results demonstrate that the different coordination breakages on the outermost polyhedra are related to atomic charges, band gap, relative stability, and Fermi energy. Additionally, a map of the morphological transformation routes and the band alignment were elaborated, showing that cubic, octahedral, or hexadecahedral morphologies can have photocatalytic activity for H2 production via water splitting. The methodology and results reported herein can help target the synthesis and functionalization of rutile-type materials.

Edge-controlled growth of single-crystal hexagonal boron nitride domains by chemical vapor deposition

Understanding the role of the edge during the growth of hexagonal boron nitride (hBN) by chemical vapor deposition (CVD) is essential for its controllable synthesis and applications. We demonstrated two kinds of hydrogen-induced edge evolution of single-crystal hBN domains over time on liquid Cu via CVD. The morphology and edge evolution of the hBN domains in growth were well explained by the kinetic Wulff construction theory. This work provides a detailed understanding of the role of the edge during the growth progress of hBN, which will be helpful for the production of wafer-scale single-crystalline hBN.

A Comparative DFT Study on Process Control Agents in the Mechanochemical Synthesis of PbTe.

A process control agent is an organic additive used to regulate the balance between fracturing and mechanical kneading, which control the size of the as-milled particles. Tributyl phosphate (TBP) is evaluated to act as surface modifier of PbTe, and it is compared with the results obtained using formaldehyde (CH2O). In order to elucidate the nature of the interaction between TBP and the PbTe surface, global and local descriptors were calculated via the density functional theory. First, TBP and CH2O molecules are structurally optimized. Then, vertical ionization energies as well as vertical electron affinities are calculated to elucidate how both molecules behave energetically against removal and electron gain, respectively. The results were compared with those obtained from the electrostatic potential mapped on the van der Waals isosurface. It is inferred that the theoretical insights are useful to propose adsorption modes of TBP and CH2O on the PbTe surface, which are usable to rationalize the facets exposed by PbTe after the surface treatment. The optimized structures of the compound systems showed a close correlation between the surface energy shift (Δγ) and the PbTe facets exhibited. Finally, a Wulff construction was built to compare the usage of TBP and CH2O molecules in PbTe morphology.

Deducing surface chemistry and annealing conditions from observed nanoparticle shapes: A study of scandate cathodes

Since the early 1900s it has been understood that knowledge of the surface energies of stable crystal facets under given chemical conditions allows prediction of the equilibrium shape of the crystal via the Wulff construction. Here, we demonstrate a practical application of an inverse Wulff construction: leveraging computed temperature- and chemical-environment-dependent surface energies to determine the chemical conditions under which particles exhibiting an experimentally observed equilibrated shape were formed. We apply this approach to reveal the chemical conditions required to fabricate high-performing scandate thermionic cathodes. Thermionic cathodes are critical components in vacuum electron devices, and scandate cathodes have exhibited dramatically enhanced performance compared to state-of-the-art cathodes. Despite this, manufacturing difficulties limit their integration into devices. In the following we show that fabrication of high-performing scandate cathodes exhibiting a characteristic W particle shape requires processing in narrow windows of temperature and oxygen partial pressure. We further show that small variations from these conditions result in large changes in cathode work function (and therefore thermionic emission) and that the role of Sc in enhancing emission performance may not be to directly modify surface work functions, but rather to control chemical conditions to stabilize (Sc-free) low work function surface configurations.

Design of CuCs-doped Ag-based catalyst for ethylene epoxidation

Our recent theoretical studies have screened out CuCs-doped Ag-based promising catalysts for ethylene epoxidation [ACS Catal. 11, 3371 (2021)]. The theoretical results were based on surface modeling, while in the actual reaction process Ag catalysts are particle shaped. In this work, we combine density functional theory (DFT), Wulff construction theory, and micro kinetic analysis to study the catalytic performance of Ag catalysts at the particle model. It demonstrates that the CuCs-doped Ag catalysts are superior to pure Ag catalysts in terms of selectivity and activity, which is further proved by experimental validation. The characterization analysis finds that both Cu and Cs dopant promote particle growth as well as particle dispersion, resulting in a grain boundary-rich Ag particle. Besides, CuCs also facilitate electrophilic atomic oxygen formation on catalyst surface, which is benefitial for ethylene oxide formation and desorption. Our work provides a case study for catalyst design by combining theory and experiment.

Cell‐friendly regulation of ice crystals by antifreeze organism‐inspired materials

AbstractThere is a dilemma between ice growth inhibition and cell‐threatening sharp‐edged ice formation, dominating an unfavorable efficiency of cell cryoprotection using ice control materials (ICMs). Herein, we design different‐type antifreeze organism‐inspired ICMs and show the cell‐friendly regulation of ice crystals by a synergistic effect for cell cryoprotection. Preferred rapid adsorption of “high‐diffusivity ICM” on the curved ice crystal surface induced by “ice‐binding ICM,” owing to the Gibbs–Curie–Wulff theorem, promotes smooth‐shaped and small ice crystal formation during the freeze–thaw cycle. Meanwhile, their intracellular and extracellular osmotic balance well protects the cryopreserved cells. All‐round protection benefits cell survival to achieve a cryopreservation efficiency of 97%. After cryopreservation, ice‐binding ICM exhibits double thermosensitive behaviors to directly encapsulate post‐thaw cells by gels, to further support cell‐based therapies. This work provides an in‐depth understanding of cell cryoprotection, and paves the road to the development of even better ICMs for biospecimen cryopreservation.