Step Free Energy Research Articles

TiO2 phase-controlled synthesis of Li-La-TiO solid electrolytes for advanced all-solid-state batteries

ABSTRACT This study focused on achieving high ionic conductivity in Li-La-TiO (LLTO) solid electrolyte. To enhance ionic conductivity, the synthesis reaction was optimized by controlling the composite crystal structure of TiO2 at the B-site of the perovskite (ABO3) structured LLTO, incorporating rutile, brookite, and anatase phases. The solid-phase LLTO, synthesized utilizing the core – shell structured composite-phase TiO2 developed in this study for the first time, successfully transformed its crystal structure to β-LLTO (tetragonal to cubic). This resulted in a significant improvement in ionic conductivity (i.e. 1.11 × 10−4 Scm−1). The study findings confirmed that the composite crystal structure TiO2 used in the solid-phase synthesis of LLTO induced an increase in oxygen vacancies during the synthesis process, thereby reducing the step-free energy required for the final synthesis.

Leveraging electron spin driven photocatalytic hydrogen evolution ability of BiVO4 via crystal facet engineering and iron ion infiltration strategies

An electron spin regulated hydrogen evolution reaction (HER) for photocatalyst is significant to understand the underlying photocatalytic mechanism. Here, the iron with gradient distribution in BiVO4 can successfully activate HER of Fe-BiVO4. Mechanical performance calculations indicate that doped Fe3+ replacing V site can form stable chemical structure for BiVO4. Theoretical calculations suggest that the photo-generated electrons migrate from bulk to defect sites in surface layers of Fe-BiVO4. The doped Fe ions effectively improves the carrier transport ability and significantly reduces the carrier recombination probability. Electron spin state change of the 1Fe-BiVO4 (Mag) enhances evidently the current density in photocatalysis, and increases markedly the HER performance compared with that of 1Fe-BiVO4. More importantly, the magnetization further prolongs carrier lifetime and optimizes rate determining step free energy of water dissociation for Fe-BiVO4. Our work opens a new way to understand the effect of magnetic field controlling spin states on photocatalytic HER.

Encapsulate lithium sulfide cathodes with carbon-doped MoS2 for fast kinetics in lithium-sulfur batteries, a theoretical study

Li2S-based lithium-sulfur batteries represent a novel potential energy-storage device with high energy-density and superior safety. Metal sulfide surface coating has been regarded as an effective way to improve electrical and dynamic properties of Li2S cathode. We predict that encapsulate Li2S with MoS2 is a potential cathode material that outperforms Li2S@graphene in some aspects. The poor conductivity of MoS2 can be alleviated by doping carbon atoms, which also serve as the catalytic sites to catalyze the activation of Li2S. The doped C atoms in MoS2 surface greatly enhance the Li2S binding strength via the formation of S−C bonds, a pz-pz interaction that is not available in pristine MoS2. Such strong interaction facilitates the decomposition of adsorbed Li2S, thus lowering the activation voltage in the first charge cycle. Although increase the number of C atoms catalyze the decomposition of Li2S, the compact distribution and collective C atoms may hinder the diffusion of Li ion by forming an electrostatic potential well, split lithium polysulfides (LiPSs) by excessively strong S−C interaction, and raise the rate determining step free energy of the S8 to Li2S conversion during discharge process, thus a balance between them is required. Single carbon atom doped MoS2 model balances these factors and shows an excellent electrochemical performance, including improved conductivity, enhanced LiPSs affinity, lowered Li2S decomposition barrier, facilitated Li ion diffusion and fast kinetics of the conversion of LiPSs. This work is instructive in fabricating Li2S cathode with metal sulfides and doping architectures for practical Li-S batteries.

Strong electronic coupling between single Ru atoms and cobalt-vanadium layered double hydroxide harness efficient water splitting

Atomic coordination modulation and electronic structure engineering are appealing routes to develop versatile electrocatalysts targeting high-performance water electrolysis. Herein, atomically dispersed Ru sites are successfully anchored on the surface of CoV layered double hydroxide (LDH), affording a vertically aligned and interconnected nanosheet array architecture. Benefitting from the strong electronic coupling, fast charge transfer capability and well-defined morphology of as-prepared catalyst, ultralow overpotentials for hydrogen evolution reaction (HER, η10 = 28 mV) and oxygen evolution reaction (OER, η25 = 263 mV) are required. The two-electrode configuration cell only requires a cell voltage of 1.52 V to reach 10 mA cm−2, which is lower than that of commercialized Pt/C||RuO2 couple. Synchrotron X-ray absorption spectroscopy studies in combination with density functional theory calculations reveal that the strong electronic coupling between monatomic Ru with CoV LDH induces spatial charge redistribution and a distorted coordination environment around V atoms, thereby accelerating the hydrogen release for HER and reducing the rate-determining step (O* → OOH*) free energy for OER.

Theoretical and Practical Studies on Effects of External Electrostatic Electric Field on Nucleation and Growth Kinetics of Protein Crystals

The crystallization technique where an electric field is applied is an extremely powerful tool to control the crystallization processes of various materials. In particular, the method with application of an external electrostatic electric field can have a significant effect on the phase equilibrium of the liquid and solid phases. This review demonstrates that the crystallization processes of proteins are significantly impacted by the application of an external electrostatic electric field: (1) Control of both the increase and decrease in the nucleation rate can be achieved by changing the applied frequency of the external electrostatic electric field. (2) The effect of the external electrostatic electric field on the nucleation rate can be controlled by regulating the thickness of the electric double layer (EDL) formed at the interface. (3) The quality of the grown crystals can be improved by an increase in the step free energy under application of an external electrostatic electric field at 1 MHz. The effect of the external electrostatic electric field on nucleation and growth kinetics during crystal growth of proteins is also discussed based on a thermodynamic perspective.

Interface structure dependent step free energy and grain growth behavior of core/shell grains in (Y, Mg)-doped BaTiO3 containing a liquid phase

The grain growth behavior of 92BaTiO3-3Y2O3-3MgO-2SiO2 (mol.%) containing a liquid phase has been systematically investigated with respect to oxygen partial pressure (PO2). Bi-layer samples, where a pre-sintered polycrystalline sample is coupled with a single crystal of pure BaTiO3, were heat-treated under an atmosphere ranging from wet H2 (PO2~ 10−13-10−14 atm) to air (PO2~ 0.2 atm) simulating industrial conditions. The single crystal provided a significantly larger driving force for grain growth than matrix grains, permitting an elaborate analysis. Considering the bi-layer sample as a single system, a clear shift of grain growth behavior was observed: (pseudo) normal grain growth (NGG), delayed abnormal grain growth (AGG), and stagnant grain growth (SGG), as the atmosphere became more oxidizing. The shift was accompanied by structural change of solid/liquid interfaces and grain boundaries and successfully explained by the step free energy effect, emphasizing the validity of interface control in BaTiO3 with a solid/liquid interface.

A general mechanism of grain growth-Ⅱ: Experimental

The formed microstructure inside polycrystalline materials strongly influences their practical performances, which process is mostly dominated by grain growth behaviors. However, the general evolution of grain growth behaviors, especial for the occurrence of abnormal grain growth and stagnant growth, remains ambiguous despite decades of efforts. Here, we investigate systematically the general evolution of grain growth behaviors by combining a new grain growth theory with grain growth experiments in SrTiO3 polycrystalline materials. The results demonstrate that the observed evolution of grain growth behaviors is in accord with the theoretical predictions, which reveals that the abnormal and stagnant behaviors of grain growth may intrinsically occur in polycrystalline systems due to the existence of non-zero step free energy for grain growth. Furthermore, the general growth theory reveals that normal grain growth results from the roughening transition of grain boundaries which corresponding to step free energy equal to zero. Besides the lower GB energy as commonly believed, the narrower grain size distribution is revealed to play an important role on the thermal stability of grains, which may lead to the counter-intuitive phenomenon of smaller nano-sized grains with higher thermal stability as recently reported in the literature. The general, quantitative growth theory may offer an accurate guidance for the microstructural design with optimal physical properties in polycrystalline materials.

Surface phase transitions and crystal habits of ice in the atmosphere.

With climate modeling predicting a raise of at least 2°C by year 2100, the fate of ice has become a serious concern, but we still do not understand how ice grows (or melts). In the atmosphere, crystal growth rates of basal and prism facets exhibit an enigmatic temperature dependence and crossover up to three times in a range between 0° and -40°. Here, we use large-scale computer simulations to characterize the ice surface and identify a sequence of previously unidentified phase transitions on the main facets of ice crystallites. Unexpectedly, we find that as temperature is increased, the crystal surface transforms from a disordered phase with proliferation of steps to a smooth phase with small step density. This causes the anomalous increase of step free energies and provides the long sought explanation for the enigmatic crossover of snow crystal growth rates found in the atmosphere.

Controlled-Atmosphere Sintering of KNbO3

The effect of sintering atmosphere (O2, air, N2, N2-5% H2, and H2) on the densification, grain growth, and structure of KNbO3 was studied. KNbO3 powder was prepared by solid state reaction, and samples were sintered at 1040 °C for 1–10 h. The sample microstructure was studied using Scanning Electron Microscopy (SEM). The sample structure was studied using X-Ray Diffraction (XRD). H2-sintered samples showed reduced density, whereas other sintering atmospheres did not affect density much. Samples sintered in N2-5% H2 showed abnormal grain growth, whereas sintering in other atmospheres caused stagnant (O2, air, N2) or pseudo-normal (H2) grain growth behavior. Samples sintered in reducing atmospheres showed decreased orthorhombic unit cell distortion. The grain growth behavior was explained by the mixed control theory. An increase in vacancy concentration caused by sintering in reducing atmospheres led to a decrease in the step free energy and the critical driving force for appreciable grain growth. This caused grain growth behavior to change from stagnant to abnormal and eventually pseudo-normal.

Structure and fluctuations of the premelted liquid film of ice at the triple point

ABSTRACTIn this paper, we study the structure of the ice/vapour interface in the neighbourhood of the triple point for the TIP4P/2005 model. We probe the fluctuations of the ice/film and film/vapour surfaces that separate the liquid film from the coexisting bulk phases at basal, primary prismatic and secondary prismatic planes. The results are interpreted using a coupled sine Gordon plus Interface Hamiltonian model. At large length scales, the two bounding surfaces are correlated and behave as a single complex ice/vapour interface. For small length, on the contrary, the ice/film and film/vapour surfaces behave very much like independent ice/water and water/vapour interfaces. The study suggests that the basal facet of the TIP4P/2005 model is smooth, the prismatic facet is close to a roughening transition, and the secondary prismatic facet is rough. For the faceted basal face, our fluctuation analysis allows us to estimate the step free energy in good agreement with experiment. Our results allow for a quantitative characterisation of the extent to which the adsorbed quasi-liquid layer behaves as water and explains experimental observations which reveal similar activation energies for crystals grown in bulk vapour or bulk water.

Role of Oxygen Vacancies on Oxygen Evolution Reaction Activity: β-Ga2O3as a Case Study

Neutral oxygen vacancies (Ovʼs) in semiconductor oxides give rise to excess electrons that have the potential to affect the binding of adsorbates to the surface through surface-to-adsorbate charge transfer, and, as a result, to alter the overpotential (OP) of reactions on oxygen-deficient materials compared to stoichiometric materials. We report a systematic computational investigation of the effects of Ovʼs on the oxygen evolution reaction (OER) overpotential for β-Ga2O3, a d10 semiconductor that has been shown to exhibit high activity for water splitting. We investigated 18 β-Ga2O3 surfaces/slabs, with and without Ovʼs and observed a clear dependence of OER activity on Ovʼs. A general finding emerged that the excess electrons associated with Ovʼs are found to participate in charge transfer to OER intermediates, making their bonds to the surface more ionic and stronger, depending on the amount of charge transfer. The OER reaction step free energies are significantly affected and the ensuing overpotential...

Kink Distance and Binding Energy of Colloidal Crystals

Particle interaction is a critical parameter for growth kinetics of colloidal crystals. The equilibrium concentration and step free energy are strongly dependent on the particle interaction. The growth mechanism of the attractive system of colloidal crystals is similar to that of vapor or solution growth, where crystals grow by incorporating diffusing ad-particles on the terrace into kinks of steps (Terrace-Step-Kink model). Here, we have applied the theory of crystal growth to experimentally determine the binding energy that originates from the particle interaction. We focus on the relationship between kink distance and bond energy, which is described by BCF (Burton-Cabrera-Frank) theory. The value of the step free energy determined by the kink distance measurement agrees well with the values obtained from other measurements, including nucleation rate and critical radius. The obtained value also accounts well for the change in step velocity of two-dimensional islands, which is due to the Gibbs–Thomson ef...

Capillary fluctuations of surface steps: An atomistic simulation study for the model Cu(111) system.

Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number (k) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for 〈110〉 and 〈112〉 steps on the {111} surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of (37±1)meV/A[over ˚] for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a k dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017)2469-995010.1103/PhysRevB.95.155444]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.

In-plane characterization of structural and thermodynamic properties for steps at faceted chemically heterogeneous solid/liquid interfaces

We present a methodology for studying steps at faceted chemically heterogeneous solid/liquid interfaces, based on equilibrium molecular-dynamics simulations. The methodology is applied to a faceted Al(111)/Pb(liquid) interface (750 K, ambient pressure), yielding a direct calculation of step free energy and extensive atomic-scale characterization for the interfacial layer containing the step. We demonstrate the power spectrum of the equilibrium step fluctuations obeys the capillary wave theory, and the calculated step free energy is consistent with experimental measurement [Acta Mater 2001; 49:4259]. The step fluctuations are identified to be governed by the attachment/detachment limited kinetics. Furthermore, we characterize the step by calculating the in-plane profiles of density, concentration, potential energy, pressure components and stresses. The fundamental properties of interface solid and interface liquid extracted from the in-plane profiles show orders of magnitudes difference in comparing with those predicted from the bulk Al-Pb alloy phase diagram. Several excess step properties are also determined along with defining a generalized Gibbs dividing surface.

Heterogeneous Nucleation of Colloidal Crystals on a Glass Substrate with Depletion Attraction.

The heterogeneous nucleation of colloidal crystals with attractive interactions has been investigated via in situ observations. We have found two types of nucleation processes: a cluster that overcomes the critical size for nucleation with a monolayer, and a method that occurs with two layers. The Gibbs free energy changes (ΔG) for these two types of nucleation processes are evaluated by taking into account the effect of various interfacial energies. In contrast to homogeneous nucleation, the change in interfacial free energy, Δσ, is generated for colloidal nucleation on a foreign substrate such as a cover glass in the present study. The Δσ and step free energy of the first layer, γ1, are obtained experimentally based on the equation deduced from classical nucleation theory (CNT). It is concluded that the ΔG of q-2D nuclei is smaller than of monolayer nuclei, provided that the same number of particles are used, which explains the experimental result that the critical size in q-2D nuclei is smaller than that in monolayer nuclei.

Step free energies at faceted solid surfaces: Theory and atomistic calculations for steps on the Cu(111) surface

A theory for the thermodynamic properties of steps on faceted crystalline surfaces is presented. The formalism leads to the definition of step excess quantities, including an excess step stress that is the step analogy of surface stress. The approach is used to develop a relationship between the temperature dependence of the step free energy ($\gamma^\mathrm{st}$) and step excess quantities for energy and stress that can be readily calculated by atomistic simulations. We demonstrate the application of this formalism in thermodynamic-integration (TI) calculations of the step free energy, based on molecular-dynamics simulations, considering $\left< 110 \right>$ steps on the $\{111\}$ surface of a classical potential model for elemental Cu. In this application we employ the Frenkel-Ladd approach to compute the reference value of $\gamma^\mathrm{st}$ for the TI calculations. Calculated results for excess energy and stress show relatively weak temperature dependencies up to a homologous temperature of approximately 0.6, above which these quantities increase strongly and the step stress becomes more isotropic. From the calculated excess quantities we compute $\gamma^\mathrm{st}$ over the temperature range from zero up to the melting point ($T_\mathrm{m}$). We find that $\gamma^\mathrm{st}$ remains finite up to $T_\mathrm{m}$, indicating the absence of a roughening temperature for this $\{111\}$ surface facet, but decreases by roughly fifty percent from the zero-temperature value. The strongest temperature dependence occurs above homologous temperatures of approximately 0.6, where the step becomes configurationally disordered due to the formation of point defects and appreciable capillary fluctuations.

Free energy of steps at faceted (1 1 1) solid-liquid interfaces in the Si-Al system calculated using capillary fluctuation method

Molecular-dynamics simulations using interatomic potentials of the angular embedded atom method form have been performed on the Al-Si system to compute the excess free energy of steps on the (111) solid-liquid interface. The solid-liquid step free energy was obtained by monitoring equilibrium fluctuations in the step position for Si solids in contact with Al-Si liquids of compositions Al-87.4at.%Si and Al-59.4at.%Si at two step orientations, [112¯] and [1¯10]. No anisotropy in the step free energy was observed for these two alloying systems, and also, the step free energy for the high concentration and high temperature 87%Si alloy was found to be greater than that of the Al-59.4% alloy. For the low temperature case of Al-30at.%Si the capillary fluctuation method can no longer be applied to extract the step free energy due to smoothness of the steps.

Two-Dimensional Nucleation on the Terrace of Colloidal Crystals with Added Polymers.

Understanding nucleation dynamics is important both fundamentally and technologically in materials science and other scientific fields. Two-dimensional (2D) nucleation is the predominant growth mechanism in colloidal crystallization, in which the particle interaction is attractive, and has recently been regarded as a promising method to fabricate varieties of complex nanostructures possessing innovative functionality. Here, polymers are added to a colloidal suspension to generate a depletion attractive force, and the detailed 2D nucleation process on the terrace of the colloidal crystals is investigated. In the system, we first measured the nucleation rate at various area fractions of particles on the terrace, ϕarea. In situ observations at single-particle resolution revealed that nucleation behavior follows the framework of classical nucleation theory (CNT), such as single-step nucleation pathway and existence of critical size. Characteristic nucleation behavior is observed in that the nucleation and growth stage are clearly differentiated. When many nuclei form in a small area of the terrace, a high density of kink sites of once formed islands makes growth more likely to occur than further nucleation because nucleation has a higher energy barrier than growth. The steady-state homogeneous 2D nucleation rate, J, and the critical size of nuclei, r*, are measured by in situ observations based on the CNT, which enable us to obtain the step free energy, γ, which is an important parameter for characterizing the nucleation process. The γ value is found to change according to the strength of attraction, which is tuned by the concentration of the polymer as a depletant.

A Monte Carlo Resampling Approach for the Calculation of Hybrid Classical and Quantum Free Energies.

Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are postprocessed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation, however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semiempirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.

On the probability of staying above a wall for the $$(2+1)$$-dimensional SOS model at low temperature

We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\Lambda$, this probability turns out to behave like $\exp(-\tau_\beta(0) L \log L )$, with $\tau_\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.