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Published in Chad A. Mirkin, Spherical Nucleic Acids, 2020
Subas Dhakal, Kevin L. Kohlstedt, George C. Schatz, Chad A. Mirkin, Monica Olvera de la Cruz
In addition to the diffusion parameters required to determine the nucleation and growth process of spherical nuclei, the growth models of anisotropic nuclei require the growth velocities of the different crystal planes [47, 48]. The shapes of the bcc superlattice grains are not isotropic since the unit cells are not isotropic. In equilibrium, the crystal shapes are generally determined by the Wulff construction method [49], which leads to regular polyhedral crystal shapes. In our MD simulations, we observe faceted shapes, which are kinetic shapes and are studied by crystal growth using anisotropic growth models [47, 48]. Our aim is not to classify the kinetic shapes. Instead, our goal is to relate the SNA colloid model parameters to the SNA crystallite kinetics to determine the model range of validity by comparing our results to experiments.
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Published in Chad A. Mirkin, Spherical Nucleic Acids, 2020
Matthew N. O’Brien, Hai-Xin Lin, Martin Girard, Monica Olvera de la Cruz, Chad A. Mirkin
The equilibrium shape of a crystal can be predicted with a Wulff construction, which plots the surface energy (γ) along each direction of a crystalline lattice in order to identify local minima in γ [1–3]. The crystalline planes corresponding to these minima possess the most stable interactions, and thus one would expect crystals bound by these facets. However, experimental realization of equilibrium structures represents a significant challenge in many atomic, molecular, and nanoscale systems due to energetic fluctuations in the system greater than the differences in γ. In the context of DNA-mediated nanoparticle crystallization, the most stable interactions often contain the greatest number of hybridization events, or “bonding” interactions, between the DNA ligands on neighboring particles [4-11]. Control of crystal habit therefore relates to the relative number of hybridization events along different crystalline planes [12], which can be tuned based on nanoparticle size and shape, DNA length and density, and lattice symmetry [13–18]. Despite their widespread use, high symmetry spherical nanoparticles are particularly challenging building blocks to use in this endeavor. This challenge originates from the weak interaction strength between spheres along their curved surfaces, as evidenced by relatively low DNA dehybridization temperatures (Tm) [19, 20] and small fractions of hybridized DNA, and the rotational freedom of spheres within a lattice [12, 21]. In contrast, the reduced symmetry of polyhedral nanoparticles yields structures that can template an oriented array of densely packed DNA on each facet, which facilitates stronger, directional interactions. Recent work has introduced the concept of a “zone of anisotropy” for polyhedral nanoparticles, or the phase space where directional interactions templated by the anisotropy of the particle core persist and result in correlated particle orientations [11, 13, 15, 16, 19, 20]. Importantly, the face-to-face interactions that occur within this zone of anisotropy possess greater fractions of hybridized DNA and greater rotational restrictions than spherical nanoparticles, which in principle, should enable experimental realization of equilibrium habits (Fig. 29.1).
Local surface crystal structure fluctuation on Li, Na and Mg metal anodes
Published in Molecular Physics, 2022
Ingeborg Treu Røe, Sondre Kvalvåg Schnell
The equilibrium shape, or Wulff construction [28], minimises the surface energy of the deposit by organising the facets belonging to its bulk crystal structure such that the facets with the lowest surface energies dominate. In other words, the bulk crystal structure provides the boundaries of the Wulff construction, resulting in differences between the shapes of Li and Na in their bcc bulk crystal structure on one hand, and Mg in its hcp structure on the other. The surface energies of these allowed facets are determined by the properties of the elements, as well as the electrochemical environment. For Li, Na and Mg, the Wulff constructions have been successfully used to predict the morphology of the dendrites as the applied potential varies [29]. However, the prediction does not account for local fluctuations in the surface crystal structure of the anode. The substrate surface structure can affect the bulk crystal structure of the deposits through epitaxial growth, which may impact the morphology of the dendrites.
First-principles study of the morphology and surface structure of LaCoO3 and La0.5Sr0.5Fe0.5Co0.5O3 perovskites as air electrodes for solid oxide fuel cells
Published in Science and Technology of Advanced Materials: Methods, 2021
Masanobu Nakayama, Katsuya Nishii, Kentaro Watanabe, Naoto Tanibata, Hayami Takeda, Takanori Itoh, Toru Asaka
where , R, T, and ai correspond to the chemical potential of species i under standard conditions, gas constant, temperature, and activity of species i, respectively. As we consider O to be nonstoichiometric, activity ai can refer to the O partial pressure, p(O2). Further details are described in [44]. In this study, the other temperature-dependent contributions, such as the vibrational enthalpy and entropy or configurational entropy, were ignored. The thermodynamic equilibrium morphology of a crystal was determined using the Wulff construction procedure [45].
Understanding the fundamentals of TiO2 surfaces
Published in Surface Engineering, 2022
The process of minimizing the total surface energy of crystals during growth leads to the dominance of thermodynamically stable facets with low surface energy, such as anatase (101) and rutile (110) surfaces in the equilibrium shape [38–40]. The equilibrium shape of a macroscopic crystal, with minimum surface energy, can be obtained using a Wulff construction [5,41]. This is based on calculated surface energies of all facets, assuming perfectly clean, stoichiometric and defect-free bulk-terminated surfaces. The computed Wulff shape for anatase and rutile is shown in Figure 1a [38–40,42] and 2a [39], respectively.