Gibbs Free Energy Diagram Research Articles

Computational electrochemistry of doped graphene as electrocatalytic material in fuel cells

AbstractIn this work, we present an overview on how density functional theory calculations can be used to design novel electrocatalytic materials for fuel cells. In particular, we focus the attention on non‐metal doped graphene systems, which were reported to present excellent performances as electrocatalysts for the oxygen reduction reaction (ORR) at the cathodic electrode of fuel cells and are, thus, considered promising substitutes of platinum or platinum alloys electrodes. The methodology, originally proposed by Nørskov et al. (J. Phys. Chem. B 2004, 108, 17886) for electrochemical processes at metal electrodes, is revisited and applied specifically to doped graphene. Finite molecular models of graphene are found to perform as well as periodic models for localized properties or reactions. Therefore, the sophisticated molecular quantum mechanics methodologies can be safely used to compute reliable Gibbs free energies of reaction in an aqueous environment for the various steps of reduction (at the cathode) or of oxidation (at the anode). Details of the reaction mechanisms and accurate cell onset‐ or over‐potentials can be derived from the Gibbs free energy diagrams. The latter are computational quantities which can be directly compared to experimentally obtained cell overpotentials. Modeling electrocatalysis at fuel cells is, thus, an extremely powerful and convenient tool to improve our understanding of how fuel cells work and to design novel potentially active electrocatalytic materials. In this work, we present two specific applications of B‐doped graphene, as electrocatalysts for the ORR at a half‐cell cathode and for the methanol oxidation reaction (MOR) at a half‐cell anode.

Water interaction with perfect and fluorine-doped Co3O4 (100) surface

We report the results of theoretical investigations of water adsorption on undoped and fluorine-doped Co3O4 (100) surface by means of the plane-wave periodic density functional theory (DFT) calculations combined with the Hubbard-U approach and statistical thermodynamics. We discuss the effect of fluorine-doping of the Co3O4 (100) surface and calculated oxygen evolution reaction overpotential based on the Gibbs free-energy diagram of undoped and F-doped surfaces.

Size-dependent electrocatalytic reduction of CO2 over Pd nanoparticles.

Size effect has been regularly utilized to tune the catalytic activity and selectivity of metal nanoparticles (NPs). Yet, there is a lack of understanding of the size effect in the electrocatalytic reduction of CO2, an important reaction that couples with intermittent renewable energy storage and carbon cycle utilization. We report here a prominent size-dependent activity/selectivity in the electrocatalytic reduction of CO2 over differently sized Pd NPs, ranging from 2.4 to 10.3 nm. The Faradaic efficiency for CO production varies from 5.8% at -0.89 V (vs reversible hydrogen electrode) over 10.3 nm NPs to 91.2% over 3.7 nm NPs, along with an 18.4-fold increase in current density. Based on the Gibbs free energy diagrams from density functional theory calculations, the adsorption of CO2 and the formation of key reaction intermediate COOH* are much easier on edge and corner sites than on terrace sites of Pd NPs. In contrast, the formation of H* for competitive hydrogen evolution reaction is similar on all three sites. A volcano-like curve of the turnover frequency for CO production within the size range suggests that CO2 adsorption, COOH* formation, and CO* removal during CO2 reduction can be tuned by varying the size of Pd NPs due to the changing ratio of corner, edge, and terrace sites.

Interplay between Reaction Mechanism and Hydroxyl Species for Water Formation on Pt(111)

Predicting the reaction mechanism of water and hydrogen peroxide formation on a platinum catalyst is a crucial step toward the understanding of the corresponding selectivity in polymer electrolyte membrane fuel cells. In this perspective, the environment of the catalytic active site should play an important role; however, its explicit description at the atomic scale is an ongoing challenge for theoretical approaches. In this study, we propose to model three effects of the environment: surface hydroxyl coverage, temperature, and reactant pressure. A detailed investigation of the reaction mechanism of water and hydrogen peroxide formation on a platinum surface is reported on the basis of density functional theory (DFT) calculations and Gibbs free energy diagrams. In standard conditions of reaction (1 atm and 353 K), the selectivity toward water and hydrogen peroxide depends on the competition between two reaction paths (molecular oxygen direct dissociation and hydrogenation), which can be tuned by the partial coverage of OH intermediate. At a low coverage of 1/12 ML, the catalyst activity is expected to be low due to a preferential but activated direct oxygen dissociation. When the OH partial coverage increases, the hydroperoxyl route becomes favorable, hence leading to hydroxyl and water by the nonactivated OOH dismutation. The direct oxygen dissociation and the whole reaction mechanism are sensitive to the hydroxyl partial coverage. Our gas/metal model opens the way to new elementary mechanisms in the presence of aqueous electrolyte and electric field that would explain how water can be produced at the beginning of the reaction (at low coverage).

Effect of joining parameters on microstructure of dissimilar metal joints between aluminum and galvanized steel

Abstract The interfacial microstructures of aluminum and galvanized steel dissimilar joint formed by pulsed double electrode gas metal arc (Pulsed DE-GMA) welding–brazing were characterized. Electron probe microanalyzer (EPMA) analysis revealed that the intermetallic compound layer of the welding–brazing joint consisted of Fe2Al5 and FeAl3. Comprehensive analysis of the effect of the heat input parameters showed that, at a constant total welding current (Itotal), the thickness of intermetallic compound at the interface of aluminum and steel decreased with the increase of bypass current. Thermodynamic calculations were carried out to derive the Gibbs free energy diagram for Fe2Al5 and FeAl3. These calculations presented that Fe2Al5 firstly formed, subsequently FeAl3 precipitated during welding process. Further model of the Fe2Al5 and FeAl3 intermetallic compounds formation process was proposed.

Ta–Rh binary alloys as a potential diffusion barrier between Cu and Si: Stability and failure mechanism of the Ta–Rh amorphous structures

Thermodynamic calculations were carried out to derive the Gibbs free energy diagram for the amorphous and crystalline phases in the Ta–Rh system. These calculations predicted that the compositional range for the amorphous Ta–Rh phase was within 37–66at.% Ta, which was validated by X-ray diffraction (XRD) analysis, high-resolution transmission electron microscopy (HRTEM) observations and resistivity measurements of as-deposited films. The thermodynamic modeling provided a valuable guide for selecting an amorphous composition suitable for diffusion barrier applications. The stability and metallurgical failure mechanism for TaRhx diffusion barriers in contact with Cu and/or Si were investigated by resistivity measurements, XRD analysis and detailed electron microscopy on samples annealed in 5% H2/95% N2 gas for 30min at various temperatures. Amorphous TaRhx in contact with the Si substrate was stable up to 700°C, whereupon TaRhx decomposed and reacted to form TaSi2 and RhSi. Si/amorphousTaRhx (13nm)/Cu stacks, on the other hand, were stable only up to 550°C. Failure occurred by reaction of Rh with the Si substrate to form RhSi at the interface. The large density of defects formed in the barrier layer as a result of outward diffusion of Rh facilitated diffusion of Cu to the Si/TaRhx interface to form Cu3Si particles. The formation of Cu3Si was observed to trigger further silicidation of the barrier to form a discontinuous TaSi2 layer.

Density Functional Theoretical Study on the Oxidative Additions of Silyl Halides to the Rh Pincer Complex

The oxidative addition reactions of C–X bonds in alkyl halides or aryl halides to transition-metal complexes are one of the fundamental reactions in organometallic chemistry. However, the reaction involving silicon receives less attention. Recently oxidative addition reactions involving silicon-halide bonds to a rhodium complex were reported. (PNP)Rh fragment 1 (where PNP is the bis(o-diisopropylphosphinophenyl)amide “pincer” ligand), generated from (PNP)Rh(SPr2), reacts with silyl halides compounds to undergo a silicon-halogen oxidative addition reaction. The fragment 1 has been considered to be convenient for the comparative studies because it is compatible with many reactions which provide several kinetic and thermodynamic parameters of the reactions. In this study the density functional theoretical (DFT) studies were conducted in order to determine the Gibbs free energy of reaction for the Si–X oxidative addition to 1 and hence to compare the relative stability between the initial adduct and the oxidative addition product. These kinetic and thermodynamic quantities are the key parameters for elucidating the reactivity and the preference toward the chemical species. B3LYP/LACVP** level calculations were chosen because the level of theory was successfully applied to the oxidative addition/reductive elimination reactions involving organometallic pincer complexes. First we examined the dependence of the reactivity and the thermodynamics of the reaction on the halide species. Figure 1 shows the Gibbs free energy diagrams for the reaction between 1 and SiMe3X, where X = Cl, Br, or I. The Gibbs activation energy, ΔG, were 10.8 kcal/mol for Cl, 8.7 kcal/ mol for Br, and 7.8 kcal/mol for I in the gas phase at 298 K. In addition the Gibbs free energy of reaction, ΔGreaction, were –9.1 kcal/mol for Cl, –17.6 kcal/mol for Br, and –20.9 kcal/ mol for I, indicating higher stability of the oxidative addition reaction products over the reactants. The reactivities of silyl halides toward (PNP)Rh fragments are potentially related to the bond dissociation enthalpies of the Si–X bond in the SiMe3X molecule. For instance weaker bonds in heavier silyl halides are less inert to the Rh fragment. Furthermore the thermodynamics of the reaction is

Water splitting on TiO 2 nanotube arrays

TiO 2 nanotube arrays can be synthesized by several experimental procedures. Here we construct the first theoretical model of the array. Based on the density functional theory calculations, the formation energy of the TiO 2 nanotube array is nearly the same as that of rutile TiO 2 (1 1 0) surface. Moreover the electronic properties of TiO 2 nanotube arrays have been analyzed. The thermodynamic properties of H 2O splitting on the TiO 2 nanotube and nanotube arrays have been discussed using the density functional theory calculations and Gibbs free energy diagrams. The overpotential of H 2O splitting is 0.51 and 1.0 eV on the outside and inside of nanotube and 1.13 eV on the inside TiO 2 nanotube of an array.

Use of Enthalpy and Gibbs Free Energy to Evaluate the Risk of Amorphous Formation

The control of crystalline and amorphous phases is important during the development of a new drug candidate. Our approach begins with an understanding of the thermodynamics of these two phases. We have developed a quantitative yet practical work flow consisting of three steps towards the analysis of the risk of amorphous material formation. First, we derive the thermodynamic equations to calculate the enthalpy, Gibbs free energy, and the solubility of each phase and their differences as a function of temperature. The enthalpy for each crystalline drug substance at its melting point is selected as the reference state to enable a consistent approach for all analysis. Second, we use data from DSC measurements and the derived thermodynamic equations to construct the enthalpy, Gibbs free energy and solubility diagrams so as to compare the characteristics of these two phases. Finally, we use the results of these calculations to evaluate the potential risk of crystalline-to-amorphous phase conversion during processing of either the drug substance or the drug product. In addition, the impact of amorphous formation on solubility is evaluated. Two drug candidates are used to illustrate this workflow for risk analysis.

Interphase energies of hcp precipitates in fcc metals: A density-functional theory study in Al-Ag

Density-functional theory (DFT) calculations of interphase boundary energies relevant to hexagonal-close-packed (hcp) $\ensuremath{\gamma}$-precipitate formation were performed within approximate unit cells that mirror the experimental conditions in face-centered-cubic (fcc) Al-Ag solid solutions. In Al-rich, fcc Al-Ag, $\ensuremath{\gamma}$ precipitates are observed to form rapidly with large $(300+)$ aspect ratios even though the Al stacking-fault energy is high (approximately $130\text{ }\text{mJ}/{\text{m}}^{2}$), which should suppress hcp ribbon formation according to standard arguments. Our DFT results show why high-aspect ratio plates occur and why previous estimates based on Wulff construction were orders of magnitude less than observed values. Using DFT, we obtain a Gibbs free-energy diagram that gives the relevant hcp equilibrium precipitate structure occurring at $50\text{ }\text{at}\text{.}\text{ }\mathrm{%}$ Ag. We derive the critical nucleation parameters for $\ensuremath{\gamma}$-precipitate formation, which require our calculated bulk-driving force for nucleation and interphase boundary energies. From our DFT-based nonequilibrium estimate for precipitation that accounts for growth via coarsening by ledge and edge migrations, we obtain time-dependent aspect ratio that agrees well with experiment. The same energetics and growth model are relevant to other phenomena, such as lath morphology in martensites or island coarsening.

Glass forming ability of the binary Cu–Hf system studied by thermodynamic calculation and ion beam mixing

Based on Miedema's semi-empirical model, a Gibbs free energy diagram is constructed for the Cu–Hf system and shows that the amorphous phase is favored to be formed over 8–94 at.% Hf, which is much broader than the experimentally determined 30–70 at.% Hf. Three Cu–Hf multilayered films were therefore designed with the overall compositions of Cu 93Hf 7, Cu 81Hf 19 and Cu 23Hf 77, respectively, and then an ion beam mixing experiment was conducted using 200 keV xenon ions to see whether the metallic glass forming range of the Cu–Hf system could be extended beyond the previously reported range. Interestingly, ion beam mixing results show that a uniform amorphous phase can be obtained in the Cu 23Hf 77 sample and the amorphous phase is also observed to coexist with crystalline Cu in the Cu 81Hf 19 sample. These results suggest that the metallic glass forming range of the Cu–Hf system could, at least, be extended to 77 at.% Hf, which falls in the range predicted by the Gibbs free energy diagram.

Non-equilibrium alloy formation in the Ag–Zr system by ion beam mixing

Based on Miedema's model, a Gibbs free energy diagram was first constructed for the Ag–Zr system and showed that the free energy of the Ag–Zr multilayered films could be higher than that of the corresponding supersaturated solid solutions and amorphous phase. Ion beam mixing with Ag 90Zr 10, Ag 48Zr 52 and Ag 12Zr 88 multilayered films was then conducted by 200 keV xenon ions. It was found that an fcc supersaturated solid solution, a mixture of fcc and hcp metastable crystalline structures and an hcp supersaturated solid solution were formed and that amorphous phases were also observed to coexist with the metastable crystalline structures. The experimental observations concerning the non-equilibrium alloy formation matched well with the calculated Gibbs free energy diagram.

Oxidization Characteristics of Some Standard Platinum Resistance Thermometers

The oxidization characteristics of some standard platinum resistance thermometers are discussed on the basis of the Gibbs free energy diagram of the platinum-oxygen ensemble. The oxidization characteristics are estimated from the measurement of the resistance changes at the triple point of water. The resistance changes of thermometers are caused by pure chemical reactions of Pt to PtO2, PtO2 to PtO, and the deoxidization. The oxidized platinum of PtO on the platinum sensing wire does not grow directly from Pt but through PtO2. This hysteresis in the formation of PtO makes the resistance characteristics of the thermometers complicated, particularly in the range above 300 °C.

Phase stabilities and thermal decomposition in the Zr 1− xAl xN system studied by ab initio calculation and thermodynamic modeling

The ab initio density functional theory is used to calculate the lattice constants, total energy and bulk modulus of binary hexagonal close packed (hcp) and face-centered cubic (fcc) ZrN, AlN and ternary Zr 1− x Al x N phases. The calculated results are supported by previously reported experimental and theoretical data. The lattice stabilities of binary phases and demixing energies of ternary phases calculated by the ab initio method are then used in thermodynamic modeling to construct the Gibbs free energy diagram of the immiscible quasi-binary ZrN–AlN system at different temperatures. The results show that, for the composition x ⩽ 0.472, Zr 1− x Al x N solid solutions are more stable in fcc than in hcp structure, which is in a good agreement with the experimentally reported value of x < 0.43. The constructed chemically binodal and spinodal decomposition curves show that fcc Zr 1− x Al x N solution coatings should undergo phase decomposition into fcc ZrN and fcc AlN. However, considering the relatively large lattice mismatch between the fcc ZrN and the fcc AlN, the coherent spinodal decomposition may probably be hindered due to rapid phase transformation from fcc AlN to the stable hcp AlN. This is supported experimentally in that no intermediate fcc AlN has so far been observed in the Zr–Al–N system.

Phase stabilities of self-organized nc-TiN/a-Si 3N 4 nanocomposites and of Ti 1 − xSi xN y solid solutions studied by ab initio calculation and thermodynamic modeling

Bulk properties of stable binary fcc-TiN and hcp(β)-Si 3N 4, hypothetical fcc-SiN and hcp(β)-Ti 3N 4, and ternary Ti 1 − x Si x N y phases are calculated by ab initio method. The values of total energies are then used for thermodynamic calculations of the lattice instabilities of hypothetical binary phases of fcc-SiN and hcp-Ti 3N 4, and of the interaction parameters of ternary Ti 1 − x Si x N y phases. Based on these data, Gibbs free energy diagrams of the quasi-binary TiN y –SiN y system are constructed in order to study the relative phase stability of the metastable ternary fcc- and hcp-Ti 1 − x Si x N y phases over the entire range of compositions. The results are supported by the published data from chemical and physical vapor deposition experiments. The constructed Gibbs free energy diagram and phase selection diagram of quasi-binary TiN y –SiN y system in fcc structure show that metastable fcc-Ti 1 − x Si x N coatings should undergo chemically spinodal decomposition into coherent fcc-TiN and fcc-SiN. Due to a high lattice mismatch between fcc-TiN and hcp-Si 3N 4, and to much higher lattice instability of fcc-SiN with respect to stable hcp-Si 3N 4, only about one monolayer of pseudomorphic SiN y interfacial phase is stable.

Phase stabilities and spinodal decomposition in the Cr 1− xAl xN system studied by ab initio LDA and thermodynamic modeling: Comparison with the Ti 1− xAl xN and TiN/Si 3N 4 systems

The total energies and lattice constants of binary hexagonal close-packed (hcp)- and face-centered cubic (fcc)-CrN, AlN and ternary Cr 0.5Al 0.5N phases are calculated using the Vienna Ab-initio Simulation Program. The calculated total energies of the structures are then used to calculate the lattice stabilities of binary hcp- and fcc-CrN and AlN, and the interaction parameters of the ternary hcp- and fcc-Cr 1− x Al x N solution phases. These results are used in the sublattice thermodynamic model to construct the Gibbs free energy diagram of the immiscible quasi-binary CrN–AlN system at different temperatures. Based on these results, we discuss the relative phase stability of the metastable ternary hcp- and fcc-Cr 1− x Al x N solid solutions over the entire range of compositions. The predictions are compared with and supported by the published results from physical and chemical vapor deposition experiments. The constructed Gibbs free energy diagrams show that metastable fcc-Cr 1− x Al x N coatings may undergo spinodal decomposition into coherent fcc-CrN and fcc-AlN, but there is a relatively large barrier for a direct formation of the stable hcp-AlN. A comparison with the Ti 1− x Al x N and TiN–Si 3N 4 systems shows that the phase segregation will be more difficult and, therefore, the solid solution more stable in the Cr 1− x Al x N case.

Bulk mechanical alloying of Cu–Ag and Cu/Zr two-phase microstructures by accumulative roll-bonding process

Cu–Ag eutectic alloy and multilayered stacked sheets of Cu/Zr were repeatedly cold-rolled by the accumulative roll-bonding (ARB) process as attempts of bulk mechanical alloying. Both ARB-processed two-phase microstructures were deformed into a very fine lamellar structure with a spacing of several nm. The Cu–Ag sheets were deformed by a number of multiple shear bands after two cycles of ARB. Intermixing of Cu and Ag occurred within the fine Cu lamellae and the shear bands. On the other hand, the Cu/Zr sheets were deformed inhomogeneously accompanied by the formation of multiple fracturing and necking of the coarse Zr layers. The Zr layers were fragmented into fine nodules after five or six cycles. The ARB processed specimen with an equivalent strain of 14.1 showed that amorphization starts from the Cu/Zr interfaces. The microstructural changes are discussed from the Gibbs free energy diagrams.

Metastable phases and spinodal decomposition in Ti 1− xAl xN system studied by ab initio and thermodynamic modeling, a comparison with the TiN–Si 3N 4 system

The total energies and lattice constants of binary hcp- and fcc-TiN, AlN and ternary Ti 0.5Al 0.5N phases are calculated by ab initio method using the Vienna ab initio simulation package (VASP). The values of total energies are then used to calculate the lattice stabilities of binary hcp- and fcc-TiN, AlN and the interaction parameter of ternary Ti 1− x Al x N phases on the basis of the semiempirical, thermodynamic sub-lattice model. Based on these data, the Gibbs free energy diagram of the immiscible quasi-binary TiN–AlN system are constructed in order to discuss the relative phase stability of the metastable ternary hcp- and fcc-Ti 1− x Al x N phases over the entire range of compositions. The prediction is compared with the published results from PVD and CVD experiments. The calculated lattice energy and the constructed Gibbs free energy diagram show, in agreement with the experiments, that metastable fcc-Ti 1− x Al x N coatings can easily undergo spinodal decomposition into coherent fcc-TiN and fcc-AlN, but there is a relatively large barrier for the formation of the stable hcp-AlN. A comparison with the TiN–Si 3N 4 system shows that, due to the much higher de-mixing energy of this system as compared to the TiN–AlN one, spinodal decomposition may occur in that system also for semicoherent TiN and Si 3N 4 phases.

Formation and structural transformation of the nonequilibrium phases in the Ru–Tasystem induced by ion beam mixing

A Gibbs free energy diagram of the Ru–Ta system is derived from Miedema’stheory, which predicts that the metallic glass forming range of the systemis within 25–55 at.% of Ta. The unique amorphous alloys are produced for theRu75Ta25,Ru65Ta35,Ru57Ta43 and Ru50Ta50 multilayers upon ion irradiation, matching well with the predicted glass forming range. However, forthe Ru43Ta57 multilayer, a mixing microstructure consisting of the amorphous and crystallinephases is obtained. Besides, an interesting phenomenon is observed for theRu25Ta75 multilayer, i.e. the transient fcc-Ru and fcc-Ta are first formed respectivelyfrom the original hcp-Ru and bcc-Ta upon irradiation and then a uniquefcc-Ru25Ta75 phase is eventually formed from the transient fcc-Ru and fcc-Ta upon further irradiation. Abrief discussion of the experimental results is presented based on the ab initiocalculations.

Nonequilibrium solid phases studied by thermodynamic calculation, molecular dynamics simulation, ab initio calculation and ion-beam manipulation in an immiscible Au–Co system at equilibrium

For an immiscible Au–Co system at equilibrium, a calculated Gibbs free energy diagram suggests that the composition range favoring metallic glass formation is approximately 22–83 at.% Co and that the nonequilibrium crystalline phases at both Co 75Au 25 and Co 25Au 75 prefer to be in a face-centred cubic (fcc) structure. Based on a proven realistic n-body Au–Co potential, molecular dynamics simulations predict that the metallic glass-forming range of the Au–Co system is 18–88 at.% Co. Employing the Vienna ab initio simulation package, the first principles calculations indicate that the L1 2 (fcc) and D0 19 (hexagonal close packed (hcp)) structures could relatively be stable for both nonequilibrium crystalline AuCo 3 and Au 3Co phases, whereas the B h (hcp) structure could be stable for the AuCo phase. Interestingly, ion beam manipulation confirms that a uniform Au 42Co 58 amorphous phase is indeed obtained and that some nonequilibrium fcc-type and hcp-type Au–Co phases can also be formed, the lattice constants of which are in agreement with those derived from the ab initio calculations.