Thermodynamic Treatment Research Articles

Thermodynamic Calculations and Heat Treatments on Phase Transformation Characteristics of 9Cr1Mo Steel

Abstract 9Cr1Mo steels are widely used for high-temperature applications in thermal power plants, owing to their relatively high strengths and low costs. In the present study, thermodynamic calculations of equilibrium and nonequilibrium transformations are carried out by JMatPro software. In the equilibrium condition, the austenite transforms to ferrite with saturated amount of M23C6 carbides ((Cr,Fe)23C6) at a temperature lower than 600°C. By contrast, austenite-martensite transformation accompanied by precipitation of a lesser amount of M23C6 carbides occurs lower than 340°C under a certain cooling rate during the nonequilibrium process. Meanwhile, an experimental investigation on the effect of various cooling rates after austenization on the microstructure and hardness of austenitized and tempered steel has been presented. The experimental results are close to the calculated ones. As the cooling rate after austenization increases, the ferrite transformation turns into martensite transformation, which could be verified by the variations of hardness, phase compositions, precipitation behaviors and grain boundary characteristics.

Partition Constant of Binary Mixtures for the Equilibrium between a Bulk and a Confined Phase.

It is well-known that the thermodynamic, kinetic and structural properties of fluids, and in particular of water and its solutions, can be drastically affected in nanospaces. A possible consequence of nanoscale confinement of a solution is the partial segregation of its components. Thereby, confinement in nanoporous materials (NPM) has been proposed as a means for the separation of mixtures. In fact, separation science can take great advantage of NPM due to the tunability of their properties as a function of nanostructure, morphology, pore size, and surface chemistry. Alcohol-water mixtures are in this context among the most relevant systems. However, a quantitative thermodynamic description allowing for the prediction of the segregation capabilities as a function of the material-solution characteristics is missing. In the present study we attempt to fill this vacancy, by contributing a thermodynamic treatment for the calculation of the partition coefficient in confinement. Combining the multilayer adsorption model for binary mixtures with the Young equation, we conclude that the liquid-vapor surface tension and the contact angle of the pure substances can be used to predict the separation ability of a particular material for a given mixture to a semiquantitative extent. Moreover, we develop a Kelvin-type equation that relates the partition coefficient to the radius of the pore, the contact angle, and the liquid-vapor surface tensions of the constituents. To assess the validity of our thermodynamic formulation, coarse grained molecular dynamics simulations were performed on models of alcohol-water mixtures confined in cylindrical pores. To this end, a coarse-grained amphiphilic molecule was parametrized to be used in conjunction with the mW potential for water. This amphiphilic model reproduces some of the properties of methanol such as enthalpy of vaporization and liquid-vapor surface tension, and the minimum of the excess enthalpy for the aqueous solution. The partition coefficient turns out to be highly dependent on the molar fraction, on the interaction between the components and the confining matrix, and on the radius of the pore. A remarkable agreement between the theory and the simulations is found for pores of radius larger than 15 Å.

Compositional Glass: A State with Inherent Chemical Disorder, Exemplified by Ti-rich Ni3(Al,Ti)1 D024 Phase

A compositional glass is a state with an unavoidable disorder in chemical compositions on each site, characterized by frustration and freezing of the compositional degrees of freedom at low temperature. From this state a full atomic long-range order is unachievable by a reasonable thermodynamic treatment. There is a similarity between a spin glass (a magnetic state with disorder in spin orientations) and a compositional glass (with disorder in site occupations by chemical elements): both have frustrated ground states and a frozen disorder at low temperatures T < Tf (here Tf is called the freezing temperature). While it is possible to perform a ground-state search in a compositional glass, the resulting set of the fully ordered structures does not adequately represent the real solid with an inherent atomic disorder. Compositional glasses constitute a class of materials, which is insufficiently understood, but is of high industrial importance. Some of the phases in the precipitated alloys (including steels, high-entropy alloys, and superalloys) might be compositional glasses, and their better understanding would facilitate materials design. Due to their strength at high operating temperatures, superalloys are used in combustion engines and particularly in jet turbine engines. Precipitation strengthening of nickel superalloys is an area of active research. Local phase transformations inside Ni3Al-based precipitates are of particular interest due to their impact on creep strength. In the Ni3(Al1−xTix)1 ternary system, the competing phases are Ni3Al-type L12 (γʹ) and Ni3Ti-type D024 (η), while D019 (χ) is higher in energy. These three phases differ by the stacking of atomic layers: locally, the last two look like the internal and external stacking faults in L12. We compute enthalpies of disordered and ordered Ni3(Al1−xTix)1 ternary structures, examine phase stability, investigate the ground states and competing structures, and predict that the Ti-rich Ni3(Al1−xTix)1 D024 phase is a compositional glass with the atomic disorder on the Al/Ti sublattice. To resolve apparent contradictions among the previous experiments and to confirm our prediction, we perform X-ray diffraction and scanning electron microscopy analysis of the cast Ni3(Ti0.917Al0.083)1 sample. Our measurements appear to confirm the ab initio computed results. Our results elucidate properties of compositional glasses and provide a better understanding of precipitation strengthening mechanisms in Ni superalloys.

Thermodynamic investigations of the LiF-CsF and NaF-CsF pseudo-binary systems

The present study describes the thermodynamic assessment of two pseudo-binary systems of relevance to CsF solubility in molten fluoride salts: LiF-CsF and NaF-CsF. Prior to this work, there was limited experimental data published in the open literature on these systems, some of which were inconsistent and had some knowledge gaps. New equilibrium data have been obtained using Differential Scanning Calorimetry on both systems. The motivation for this experimental campaign was threefold: 1) to corroborate previously reported data, 2) to elucidate prior irregularities, and 3) fill some knowledge gaps. These measurements also revealed evidence of another stoichiometric phase, LiCsF2−β, which was not captured in previous assessments. In addition to new experimental measurements, thermodynamic treatments of the two binary systems have been revised using the CALPHAD method with the thermodynamic software FactSage and Optima. This combined experimental and computational campaign provides greater confidence in CsF thermochemical behaviour in Molten Salt Reactor systems.

Lorentzian Taub-NUT spacetimes: Misner string charges and the first law

Motivated by recent activities in Lorentzian Taub-NUT space thermodynamics, we calculate conserved charges of these spacetimes. We find additional mass, nut, angular momentum, electric and magnetic charge densities distributed along Misner string. These additional charges are needed to account for the difference between the values of the above charges at horizon and at infinity. We propose an unconstrained thermodynamical treatment for Taub-NUT spaces, where we introduce the nut charge $n$ as a relevant thermodynamic quantity with its chemical potential \phi_n. The internal energy in this treatment is M-n\phi_n rather than the mass M. This approach leads to an entropy which is a quarter of the area of the horizon and all thermodynamic quantities satisfy the first law, Gibbs-Duhem relation as well as Smarr's relation. We found a general form of the first law where the quantities depend on an arbitrary parameter. Demanding that the first law is independent of this arbitrary parameter or invariant under electric-magnetic duality leads to a unique form which depends on Misner string electric and magnetic charges. Misner string charges play an essential role in the first law, without them the first law is not satisfied.

Quick and enhanced separation of Eosin Yellow dye from aqueous solution by FeCl3 interaction: thermodynamic study and treatment cost analysis

ABSTRACT Dyes and their metabolites have noxious and carcinogenicity potential and are known to be hazardous for human beings and other living organisms. The discharge of untreated wastewater comprising wide varieties of synthetic dyes into the water resources is one of the vital environmental problems. Therefore, in this study, the efficacy of the chemical coagulation method was explored using ferric chloride as a coagulant to remove the toxic dye Eosin Yellow (EY) from aqueous solution. The interaction between FeCl3 and EY dye was quick and profound at a solution pH of 2.2, yielding the brownish precipitate with a dye removal efficiency of more than 98%. An extremely high dye removal capacity of 1263 mg/g is reported for 100 mg/L of EY dye concentration at optimum experimental conditions. The possible chemical interaction between FeCl3 and EY dye can be attributed to the formation of polymeric complex, as oxygen atoms of carbonyl, phenolate and carboxylate groups of EY dye molecule interact strongly with Fe3+ ions. The presence of various coexisting anions could reduce the EY dye removal efficiency by 2%–5%; however, the required FeCl3 dose has increased from 64 to 170 mg/L. Thermodynamic studies showed that the interaction of EY dye with FeCl3 was exothermic and spontaneous in nature. The investigation of real industrial wastewater samples has exhibited a 90%–215% increase in the required FeCl3 dose as compared to the control experiment for the initial EY dye concentration from 100 to 750 mg/L. Sludge volume index analysis indicates that FeCl3 generated highly dense sludge with good settling characteristics. X-ray diffraction and field emissionscanning electron microscopy characterisation of the generated sludge indicate the polycrystalline nature with a combination of spherical and irregular shape grains of the sludge. Treatment cost analysis revealed that the cost involved in dye removal is in the range of 0.99–3.60 USD ($)/kg of dye removed.

Thermodynamics of PNJL model at zero temperature in a strong magnetic field

In this paper, the deconfinement and chiral restoration transitions in a strong magnetic field are realized at zero temperature in the Polyakov Nambu-Jona-Lasinio model. We provide the thermodynamic treatment to mimic the deconfinement phase transition at zero temperature together with the entangled scalar and vector interactions coupled with the Polyakov loop. The magnetic catalysis is found by a rising behavior of the critical chemical potential for the first-order deconfinement phase transition. While the magnetic catalysis on the chiral restoration could convert to inverse magnetic catalysis under the running coupling interaction ansatz. Furthermore, the stronger magnetic field makes the possible quarkyonic phase window to be enlarged under the running coupling interaction.

Measures of fluctuations for a liquid near critical drying.

We investigate density fluctuations in a liquid close to a solvophobic substrate at which a surface critical drying transition occurs. Using classical density functional theory, we determine three measures of the spatial extent and strength of the fluctuations, i.e., the local compressibility χ_{μ}(z), the local thermal susceptibility χ_{T}(z), and the reduced density χ_{*}(z); z is the distance from the substrate. While the first measure is frequently used, the second and third were introduced very recently by Eckert etal., [T. Eckert et al., Phys. Rev. Lett. 125, 268004 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.268004]. For state points in the critical drying regime, all three measures, each scaled by its bulk value, exhibit very similar forms and the ratio of χ_{T}(z) to χ_{μ}(z), for fixed z in the vapor-liquid transition region, is constant. Using a scaling treatment of surface thermodynamics, we show that such behavior is to be expected on general grounds.

Strange quark matter and proto-strange stars in a baryon density-dependent quark mass model * *Supported by the National Natural Science Foundation of China (11875052, 11575190, 11135011)

The properties of strange quark matter and the structures of (proto-)strange stars are studied within the framework of a baryon density-dependent quark mass model, where a novel quark mass scaling and self-consistent thermodynamic treatment are adopted. Our results indicate that the perturbative interaction has a significant impact on the properties of strange quark matter. It is determined that the energy per baryon increases with temperature, while the free energy decreases and eventually becomes negative. At fixed temperatures, the pressure at the minimum free energy per baryon is zero, suggesting that the thermodynamic self-consistency is preserved. Furthermore, the sound velocity v in quark matter approaches the extreme relativistic limit ( ) as the density increases. By increasing the strengths of the confinement parameter D and perturbation parameter C, the tendency for v to approach the extreme relativistic limit at high density is slightly weakened. For (proto-)strange stars, the novel quark mass scaling can accommodate massive proto-strange stars with their maximum mass surpassing twice the solar mass by considering the isentropic stages along the star evolution line, where the entropy per baryon of the star matter is set to be 0.5 and 1 with the lepton fraction = 0.4.

Kinetic and thermodynamic examinations for the unsteady couette flow problem of a plasma using the BGK cylindrical model

We aim to investigate the kinetic and irreversible thermodynamic treatment of the Couette flow of gaseous plasma (GP) confined between two coaxial rotating circular rigid cylinders. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann kinetic equation (BKE) is solved by applying the perturbation method coupled with the moments' approach with a two-stream Maxwellian distribution function (MDF). Nonlinear partial differential equations are precisely solved. As an actual application, we are considering the laboratory Argon GP. An interesting comparison between the non-equilibrium electron velocity distribution function (EVDF) and the equilibrium EVDF is made carefully with 3-Dimensional graphics in various time values. We found that the system goes to an equilibrium state (ES) with time compatible with Le Chatelier's principles. Moreover, we determined with very high precision the value of the system equilibrium time, which is tequ.≅2.4. That great advantage cannot be reached by solving other macroscopic magnetohydrodynamic models. The relations between the various macroscopic variables of the GP are studied. The irreversible non-equilibrium thermodynamics (NT) properties of the system are presented. We present the extended Gibbs equation (EGE) for the internal energy variation (IEV) in cylindrical geometry for GP for the first time, to the best of our knowledge. We have shown that our model is compatible with the H-theorem of Boltzmann and the Onsager-Casimir relations. The various participations in IEV are introduced. The significance of this search is due to its vast implementations in various fields, such as in GP physics, electrical engineering, medicine, biological systems, and numerous commercial and industrial deployments.

A solar thermal sorption-enhanced steam methane reforming (SE-SMR) approach and its performance assessment

This paper proposes an integration of concentrating solar power (CSP) with a sorption-enhanced steam methane reforming (SE-SMR) process and assesses its overall solar-to-fuel conversion performance. A thermodynamic treatment of the SE-SMR process for H2 production is presented and evaluated in an innovative two reactors system configuration using CSP as a heat input. Four metal carbonate/metal oxide pairs are considered, and the equilibrium thermodynamics reveals that CaCO3/CaO pair is the most suitable candidate for this process. Additionally, a reactor-scale thermodynamic model is developed to determine the optimum operating conditions for the process. For the carbonation step, temperatures between 700 and 900 K and steam-to-methane ratio ≥4 are found to be the most favorable. Furthermore, an advanced process model, which utilizes operating conditions determined from the reactor-scale model, is developed to evaluate the process efficiency. The model predicts that the proposed process can achieve a solar-to-fuel efficiency ∼41% for calcination temperature of 1500 K and carbonation temperature of 800 K, without considering any solid heat recovery. An additional 2.5% increase in the process efficiency is feasible with the consideration of the solid heat recovery. This study shows the thermodynamic feasibility of integrating the SE-SMR process with CSP technologies.

On Kinetic and Irreversible Thermodynamic Treatments of a Rarefied Gaseous Plasma Bounded by a Moving Plate.

On Kinetic and Irreversible Thermodynamic Treatments of a Rarefied Gaseous Plasma Bounded by a Moving Plate.

Strangelets at finite temperature in a baryon density-dependent quark mass model

The properties of strangelets at finite temperature are studied within the framework of a baryon densitydependent quark mass model, where a new quark mass scaling and self-consistent thermodynamic treatment are adopted. The effects of finite volume and Coulomb energy are taken into account. Our results show that the temperature $T$, baryon number $A$, and perturbation interactions have strong influences on the properties of strangelets. It is found that the energy per baryon $M/A$ and charge-to-mass ratio ${f}_{z}$ decrease with baryon number $A$, while the mechanically stable radius $R$ and strangeness per baryon ${f}_{S}$ are increasing. For a strangelet with a fixed baryon number, we note that as temperature $T$ increases the quantities $M/A$, $R$, and ${f}_{S}$ are increasing while ${f}_{z}$ is decreasing. The effects of confinement and perturbative interactions are investigated as well by readjusting the corresponding parameters.

Energy-Optimal Structures of HVAC System for Cleanrooms as a Function of Key Constant Parameters and External Climate

This article presents approximating relations defining energy-optimal structures of the HVAC (Heating, Ventilation, Air Conditioning) system for cleanrooms as a function of key constant parameters and energy-optimal control algorithms for various options of heat recovery and external climates. The annual unit primary energy demand of the HVAC system for thermodynamic air treatment was adopted as the objective function. Research was performed for wide representative variability ranges of key constant parameters: cleanliness class—Cs (ISO5÷ISO8), unit cooling loads—q˙j (100 ÷ 500) W/m2 and percentage of outdoor air—αo (5 ÷ 100)%. HVAC systems are described with vectors x¯ with coordinates defined by constant parameters and decision variables, and the results are presented in the form of approximating functions illustrating zones of energy-optimal structures of the HVAC system x¯* = f (Cs, q˙j, αo). In the optimization procedure, the type of heat recovery as an element of optimal structures of the HVAC system and algorithms of energy-optimal control were defined based on an objective function and simulation models. It was proven that using heat recovery is profitable only for HVAC systems without recirculation and with internal recirculation (savings of 5 ÷ 66%, depending on the type of heat recovery and the climate), while it is not profitable (or generates losses) for HVAC systems with external recirculation or external and internal recirculation at the same time.

Flux-limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability. II. Quadrupled Spatial Resolution

Abstract While collisional accumulation is nearly universally accepted as the formation mechanism of rock and ice worlds, the situation regarding gas giant planet formation is more nuanced. Gas accretion by solid cores formed by collisional accumulation is the generally favored mechanism, but observations increasingly suggest that gas disk gravitational instability might explain the formation of at least the massive or wide-orbit gas giant exoplanets. This paper continues a series aimed at refining three-dimensional (3D) hydrodynamical models of disk instabilities, where the handling of the gas thermodynamics is a crucial factor. Boss (2017, 2021) used the β cooling approximation to calculate 3D models of disks with initial masses of 0.091 M ⊙ extending from 4 to 20 au around 1 M ⊙ protostars. Here we employ 3D flux-limited diffusion (FLD) approximation models of the same disks, in order to provide a superior treatment of disk gas thermodynamics. The new models have quadrupled spatial resolution compared to previous 3D FLD models, in both the radial and azimuthal spherical coordinates, resulting in the highest spatial resolution 3D FLD models to date. The new models continue to support the hypothesis that such disks can form self-gravitating, dense clumps capable of contracting to form gas giant protoplanets, and suggest that the FLD models yield similar numbers of clumps as β cooling models with β ∼ 1 to ∼10, including the critical value of β = 3 for fragmentation proposed by Gammie.

Properties of the ionisation glitch

Context. Determining the properties of solar-like oscillating stars can be subject to many biases. A particularly important example is the helium-mass degeneracy, where the uncertainties regarding the internal physics can cause a poor determination of both the mass and surface helium content. Accordingly, an independent helium estimate is needed to overcome this degeneracy. A promising way to obtain such an estimate is to exploit the so-called ionisation glitch, that is, the deviation from the asymptotic oscillation frequency pattern caused by the rapid structural variation in the He ionisation zones. Aims. Although it is progressively becoming more sophisticated, the glitch-based approach faces problems inherent to its current modelling such as the need for calibration using realistic stellar models. This requires a physical model of the ionisation region that explicitly involves the parameters of interest, such as the surface helium abundance, Ys. Methods. Through a thermodynamic treatment of the ionisation region, an analytical approximation for the first adiabatic exponent Γ1 is presented. Results. The induced stellar structure is found to depend on only three parameters, including the surface helium abundance Ys and the electron degeneracy ψCZ in the convective region. The model thus defined allows a wide variety of structures to be described, and it is in particular able to approximate a realistic model in the ionisation region. The modelling work we conducted enables us to study the structural perturbations causing the glitch. More elaborate forms of perturbations than those that are usually assumed are found. It is also suggested that there might be a stronger dependence of the structure on the electron degeneracy in the convection zone and on the position of the ionisation region rather than on the amount of helium itself. Conclusions. When analysing the ionisation glitch signature, we emphasise the importance of having a relation that can take these additional dependences into account.

Technical note: Adsorption and desorption equilibria from statistical thermodynamics and rates from transition state theory

Abstract. Adsorption and desorption represent the initial processes of the interaction of gas species with the condensed phase. They have important implications for evaluating heterogeneous (gas-to-solid) and multiphase chemical kinetics involved in catalysis; environmental interfaces; and, in particular, aerosol particles. When describing gas uptake, gas-to-particle partitioning, and the chemical transformation of aerosol particles, parameters describing adsorption and desorption rates are crucial to assessing the underlying chemical kinetics such as surface reaction and surface-to-bulk transfer. For instance, the desorption lifetime, in turn, depends on the desorption free energy which is affected by the chosen adsorbate model. To assess the impact of those conditions on desorption energy and, thus, desorption lifetime, we provide a complete classical and statistical thermodynamic treatment of the adsorption and desorption process considering transition state theory for two typically applied adsorbate models, the 2D ideal gas and the 2D ideal lattice gas, the latter being equivalent to Langmuir adsorption. Both models apply to solid and liquid substrate surfaces. We derive the thermodynamic and microscopic relationships for adsorption and desorption equilibrium constants, adsorption and desorption rates, first-order adsorption and desorption rate coefficients, and the corresponding pre-exponential factors. Although some of these derivations can be found in the literature, this study aims to bring all derivations into one place to facilitate the interpretation and analysis of the variables driving adsorption and desorption for their application in multiphase chemical kinetics. This exercise allows for a microscopic interpretation of the underlying processes including the surface accommodation coefficient and highlights the importance of the choice of adsorbate model and standard states when analyzing and interpreting adsorption and desorption processes. We demonstrate how the choice of adsorbate model affects equilibrium surface concentrations and coverages, desorption rates, and decay of the adsorbate species with time. In addition, we show how those results differ when applying a concentration- or activity-based description. Our treatment demonstrates that the pre-exponential factor can differ by orders of magnitude depending on the choice of adsorbate model with similar effects on the desorption lifetime, yielding significant uncertainties in the desorption energy derived from experimentally derived desorption rates. Furthermore, uncertainties in surface coverage and assumptions about standard surface coverage can lead to significant changes in desorption energies derived from measured desorption rates. Providing a comprehensive thermodynamic and microscopic representation aims to guide theoretical and experimental assessments of desorption energies and estimate potential uncertainties in applied desorption energies and corresponding desorption lifetimes important for improving our understanding of multiphase chemical kinetics.

Elastic dipole tensor of a defect at a finite temperature: Definition and properties

The concept of the elastic dipole tensor of a defect is generalized to enable the treatment of lattice distortions produced by defects at elevated temperatures. Thermodynamic and statistical mechanics treatments show the feasibility of applying the formalism to the evaluation of formation free energies and finite-temperature elastic dipole tensors of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ prismatic self-interstitial atom dislocation loops. The method exhibits good numerical stability even in the high-temperature limit, and relates discrete atomic and continuum representations of displacement and stress and strain fields of defects.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes.

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy. As a result, such solvent's unusual thermodynamics is found to be relevant to the temperature and pressure dependence of the isochoric solvation energy and entropy as well as to the isothermal density derivative of the solvation free energy. This sharply contrasts with the findings of the first part of this series indicating that the solvation free energy of small hard spheres responds to temperature and pressure changes as solvent's density does, with such a contrasting picture embodying a "pressure-density dichotomy." As for the length-scale dependence, we find the zero nominal pressure and the solvent's temperature of the maximum density as singular conditions for cavity surface-area size scaling of large solutes to occur for all solvation quantities. We finally argue that the overall study undertaken in this series suggests that water's unusual thermodynamics may be relevant to the thermodynamic stability of clusters of solvophobic units in the temperature-pressure plane. Some comments on the role of solute-solvent attractive interactions are also depicted.

(Invited) Applications of the Hakoniwa Method to Impurity Atoms Wandering Inside Si Wafers

In this presentation, we review applications for Si-related materials by utilizing the Hakoniwa method, an approach that predicts material properties on the basis of statistical thermodynamics and ab initio calculations. This method describes the behavior of Cu/Fe atoms in B-doped Si crystals. The target material (inside Si wafers) is not uniform and therefore needed to be described in a local circumstance around wandering impurity atoms inside the wafers in order to estimate compatible values with the experiments. Further descriptions are also discussed to estimate Cu/O solubility. These all approaches are spatial-averaged from the viewpoint of statistical thermodynamic treatments. Expanding the Hakoniwa method to a time-averaged approach for the SiO2/Si interface can provide a novel description of oxidizing reactions in the SiO2/Si interface and enable estimation of the interface state density.