The supercell slab is the structural model used in first-principles simulations to determine thermodynamic, kinetic, and electronic properties of surfaces and interfaces. We present a general ...algorithm to reorient bulk unit cells using basis and covariant transformations — the first step for constructing surface slabs of any Miller index from bulk unit cells of any Bravais lattice. We further review and discuss subtleties of surface slab creation relevant for performing efficient and accurate calculations of surface properties. We also demonstrate that the nonconvergence of surface energy with respect to slab thickness can be mitigated if the bulk reference energy is calculated from a surface-oriented bulk unit cell, which eliminates Brillouin zone integration errors between the slab and the bulk. Using Pt(111) and Si(111) surfaces as examples, this technique converges the surface energy with respect to slab thickness requiring only one bulk and one relatively thin slab calculation, with moderate k-point densities. This process is about an order of magnitude more efficient than popular surface energy convergence techniques involving multiple slab calculations.
•We present an approach for efficient high-throughput DFT surface calculations.•Algorithm to create surface slabs of any orientation from any crystal structure.•DFT parameters important for efficient and accurate surface modeling is discussed.•Bulk energy calculated from surface oriented bulk converges surface energy rapidly.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
As disclosed by various business reports, Farfetch’s strengths in gaining market share and consumer insights have yielded great revenues and Gross Merchandise Volume in the Chinese market. This study ...has discussed the significance of Farfetch’s marketing strategies and business strategies and how those strategies fit into the current Chinese market by analysing a combination of business reports, interview scripts, and news. The study’s significance lies in its ability to provide insight into how premium luxury brands and Western e-commerce platforms may win the Chinese market. With evaluations of the current market environment and Chinese consumers’ needs, this study has examined the reasons behind Farfetch’s success. The study suggests that Farfetch’s consumer-centric strategies could be employed by other brands to build awareness and to build a loyal customer base. Beyond that, the company’s business-to-business strategies and their alliance with Alibaba and Richemont have a significant impact on both Farfetch and luxury brands.
While control over crystal structure is one of the primary objectives in crystal growth, the present lack of predictive understanding of the mechanisms driving structure selection precludes the ...predictive synthesis of polymorphic materials. We address the formation of off-stoichiometric intermediates as one such handle driving polymorph selection in the diverse class of MnO2-framework structures. Specifically, we build on the recent benchmark of the SCAN functional for the ab initio modeling of MnO2 to examine the effect of alkali-insertion, protonation, and hydration to derive the thermodynamic conditions favoring the formation of the most common MnO2 phasesβ, γ, R, α, δ, and λfrom aqueous solution. We explain the phase selection trends through the geometric and chemical compatibility of the alkali cations and the available phases, the interaction of water with the system, and the critical role of protons. Our results offer both a quantitative synthesis roadmap for this important class of functional oxides, and a description of the various structural phase transformations that may occur in this system.
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When a solution is supersaturated with respect to multiple polymorphs, the polymorph with the lowest nucleation barrier will form first. If this is a metastable polymorph, it will persist until the ...induction of nuclei of a lower free-energy phase, marking the onset of a polymorphic transformation. Induction of a more stable polymorph can occur under two conditions: a.) during steady-state nucleation, or b.) after complete crystal growth of the metastable phase. Using the theory of competing stochastic processes, we derive the rare probability of forming a higher-barrier, more-stable polymorph during steady-state nucleation, and use this to explain variations in crystallization products between repeat experiments, which may underlie the phenomenon of "Disappearing Polymorphs". We also derive the induction time of a stable phase from a solution equilibrated with a metastable phase, and show that once the stable phase nucleates, bulk metastable crystals will spontaneously ripen onto nanoscale nuclei or seeds of a more stable phase, thermodynamically driving dissolution-reprecipitation processes. Existing strategies to prolong or shorten the lifetimes of transient metastable phases are reviewed and interpreted within the context of polymorphic induction. The analyses in this work are conducted from classical nucleation and crystal growth theories, suggesting that paradigms shifts to 'non-classical' nucleation theories may not be necessary to rationalize multistage crystallization.
We analyze the processes governing the lifetimes of transient metastable polymorphs, within the context of classical nucleation theory.
Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams. Without a precise understanding ...of which metastable phases form, or their lifetimes, targeted synthesis of specific metal oxides can become a trial-and-error process. Here, we construct a theoretical framework to reveal the nanoscale and metastable energy landscapes of Pourbaix (E-pH) diagrams, providing quantitative insights into the size-dependent thermodynamics of metastable oxide nucleation and growth in water. By combining this framework with classical nucleation theory, we interrogate how solution conditions influence the multistage oxidation pathways of manganese oxides. We calculate that even within the same stability region of a Pourbaix diagram, subtle variations in pH and redox potential can redirect a non-equilibrium crystallization pathway through different metastable intermediates. Our theoretical framework offers a predictive platform to navigate through the thermodynamic and kinetic energy landscape towards the rational synthesis of target materials.
Nucleation of metastable aragonite CaCO₃ in seawater Sun, Wenhao; Jayaraman, Saivenkataraman; Chen, Wei ...
Proceedings of the National Academy of Sciences - PNAS,
03/2015, Volume:
112, Issue:
11
Journal Article
Peer reviewed
Open access
Significance Crystallization from solution is a materials synthesis process common both in nature and in the laboratory. Unlike conventional high-temperature solid-state synthesis, solution-based ...syntheses often yield metastable phases, contrary to expectations from equilibrium thermodynamics. Using a recently developed ab initio scheme to calculate the surface energy of a critical nucleus in equilibrium with the aqueous environment, we present a framework to compare relative nucleation rates between competing polymorphs as a function of solution chemistry. We apply this approach to demonstrate how seawater chemistry can preferentially bias nucleation toward the metastable aragonite phase of calcium carbonate, rather than the stable phase calcite––which is of great relevance to biomineralization, carbon sequestration, paleogeochemistry, and the vulnerability of marine life to ocean acidification.
Predicting the conditions in which a compound adopts a metastable structure when it crystallizes out of solution is an unsolved and fundamental problem in materials synthesis, and one which, if understood and harnessed, could enable the rational design of synthesis pathways toward or away from metastable structures. Crystallization of metastable phases is particularly accessible via low-temperature solution-based routes, such as chimie douce and hydrothermal synthesis, but although the chemistry of the solution plays a crucial role in governing which polymorph forms, how it does so is poorly understood. Here, we demonstrate an ab initio technique to quantify thermodynamic parameters of surfaces and bulks in equilibrium with an aqueous environment, enabling the calculation of nucleation barriers of competing polymorphs as a function of solution chemistry, thereby predicting the solution conditions governing polymorph selection. We apply this approach to resolve the long-standing “calcite–aragonite problem”––the observation that calcium carbonate precipitates as the metastable aragonite polymorph in marine environments, rather than the stable phase calcite––which is of tremendous relevance to biomineralization, carbon sequestration, paleogeochemistry, and the vulnerability of marine life to ocean acidification. We identify a direct relationship between the calcite surface energy and solution Mg–Ca ion concentrations, showing that the calcite nucleation barrier surpasses that of metastable aragonite in solutions with Mg:Ca ratios consistent with modern seawater, allowing aragonite to dominate the kinetics of nucleation. Our ability to quantify how solution parameters distinguish between polymorphs marks an important step toward the ab initio prediction of materials synthesis pathways in solution.
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Compared to oxides, the nitrides are relatively unexplored, making them a promising chemical space for novel materials discovery. Of particular interest are nitrogen-rich nitrides, which often ...possess useful semiconducting properties for electronic and optoelectronic applications. However, such nitrogen-rich compounds are generally metastable, and the lack of a guiding theory for their synthesis has limited their exploration. Here, we review the remarkable metastability of observed nitrides, and examine the thermodynamics of how reactive nitrogen precursors can stabilize metastable nitrogen-rich compositions during materials synthesis. We map these thermodynamic strategies onto a predictive computational search, training a data-mined ionic substitution algorithm specifically for nitride discovery, which we combine with grand-canonical DFT-SCAN phase stability calculations to compute stabilizing nitrogen chemical potentials. We identify several new nitrogen-rich binary nitrides for experimental investigation, notably the transition metal nitrides Mn3N4, Cr3N4, V3N4, and Nb3N5, the main group nitride SbN, and the pernitrides FeN2, CrN2, and Cu2N2. By formulating rational thermodynamic routes to metastable compounds, we expand the search space for functional technological materials beyond equilibrium phases and compositions.
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The surface energy is a fundamental property of the different facets of a crystal that is crucial to the understanding of various phenomena like surface segregation, roughening, catalytic activity, ...and the crystal's equilibrium shape. Such surface phenomena are especially important at the nanoscale, where the large surface area to volume ratios lead to properties that are significantly different from the bulk. In this work, we present the largest database of calculated surface energies for elemental crystals to date. This database contains the surface energies of more than 100 polymorphs of about 70 elements, up to a maximum Miller index of two and three for non-cubic and cubic crystals, respectively. Well-known reconstruction schemes are also accounted for. The database is systematically improvable and has been rigorously validated against previous experimental and computational data where available. We will describe the methodology used in constructing the database, and how it can be accessed for further studies and design of materials.
Exploratory synthesis in new chemical spaces is the essence of solid-state chemistry. However, uncharted chemical spaces can be difficult to navigate, especially when materials synthesis is ...challenging. Nitrides represent one such space, where stringent synthesis constraints have limited the exploration of this important class of functional materials. Here, we employ a suite of computational materials discovery and informatics tools to construct a large stability map of the inorganic ternary metal nitrides. Our map clusters the ternary nitrides into chemical families with distinct stability and metastability, and highlights hundreds of promising new ternary nitride spaces for experimental investigation-from which we experimentally realized seven new Zn- and Mg-based ternary nitrides. By extracting the mixed metallicity, ionicity and covalency of solid-state bonding from the density functional theory (DFT)-computed electron density, we reveal the complex interplay between chemistry, composition and electronic structure in governing large-scale stability trends in ternary nitride materials.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Realizing the growing number of possible or hypothesized metastable crystalline materials is extremely challenging. There is no rigorous metric to identify which compounds can or cannot be ...synthesized. We present a thermodynamic upper limit on the energy scale, above which the laboratory synthesis of a polymorph is highly unlikely. The limit is defined on the basis of the amorphous state, and we validate its utility by effectively classifying more than 700 polymorphs in 41 common inorganic material systems in the Materials Project for synthesizability. The amorphous limit is highly chemistry-dependent and is found to be in complete agreement with our knowledge of existing polymorphs in these 41 systems, whether made by the nature or in a laboratory. Quantifying the limits of metastability for realizable compounds, the approach is expected to find major applications in materials discovery.
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