Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of Au_3Cu-type sublattice system

Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of AuCu_3-type sublattice system

Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.

Thermodynamic analysis of combined reforming process using Gibbs energy minimization method: In view of solid carbon formation

Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon formation. The equilibrium calculations employing the Gibbs energy minimization were performed upon wide ranges of pressure （1-25 atm）, temperature （600-1300 K）, carbon dioxide to methane ratio （0-2） and oxygen to methane ratio （0-1）. The thermodynamic results were compared with the results obtained over a Ru supported catalyst. The results revealed that by increasing the reaction pressure methane conversion decreased. Also it was found that the atmospheric pressure is the preferable pressure for both dry reforming and partial oxidation of methane and increasing the temperature caused increases in both activity of carbon and conversion of methane. The results clearly showed that the addition of O2 to the feed mixture could lead to a reduction of carbon deposition.

Molar Surface Gibbs Energy of the Aqueous Solution of Ionic Liquid [C4mim][OAc]

The values of density and surface tension for aqueous solution of ionic liquid（IL） 1-butyl-3-methylimi- dazolium acetate（[C4nim][OAc]） with various molalities were measured in the range of 288.15--318.15 K at intervals of 5 K. On the basis of thermodynamics, a semi-empirical model-molar surface Gibbs energy model of the ionic liquid solution that could be used to predict the surface tension or molar volume of solutions was put forward. The predicted values of the surface tension for aqueous [C4mim][OAc] and the corresponding experimental ones were highly correlated and extremely similar. In terms of the concept of the molar Gibbs energy, a new Eotvos equation was obtained and each parameter of the new equation has a clear physical meaning.

Predicting the Transition between Upper and Lower Bainite via a Gibbs Energy Balance Approach

The transition temperature between upper bainite and lower bainite is calculated with an extended Gibbs energy balance model, which is able to quantitatively describe the evolution of carbon supersaturation within bainitic ferrite sheaves during the entire thickening process. The nucleation rate of intra-lath cementite precipitation on a dislocation is calculated based on of the degree of carbon supersaturation.Upper bainite and lower bainite are thus distinguished by the effective nucleation density and therefore a numerical criterion can be set to define the transition. The model is applied to Fe-xC-1Mn/2Mn/1 Mo ternary alloys. Results show that the transition temperature increases with bulk carbon content at lower carbon concentration but decreases in the higher carbon region. This prediction agrees very well with the experimental observations in Mn and Mo alloyed systems. Moreover, the highest transition temperature and the carbon content at which it occurs in the Fe-xC-2Mn system are in good agreement with reported experimental data. The inverse ＂V＂ shaped character of the carbon concentration-transition temperature curve indicates two opposite physical mechanisms operating at the same time. An analysis is carried out to provide an explanation.

Atomic energies and Gibbs energy functions of Ag-Cu alloys

The rationality of characteristic crystals model has been expounded. Nine new Gibbs energy functions of CC theory have been established. The regular solution model corresponds to the simplest situation of CC model. Any G-functions of CC theory can be used to represent liquid and fcc phases of Ag-Cu system. The lattice stability parameters of characteristic crystals for Ag-Cu alloys can be described with the form accepted by the SGTE group. Only when we have made studies on the law of change of energy, volume and electronic structure of the Ag-Cu system, can we choose the G-function correctly and then establish an integral knowledge system and the database, so as to lay a good foundation for the scientific design of new alloys.

Theoretical Prediction of Gibbs Free Energies of Formation for Crystallineα-MOOH andα-M_2O_3 Based on a Linear Free-Energy Relationship

In the present study,the modified Sverjensky-Molling equation,derived from a linear-free energy relationship,is used to predict the Gibbs free energies of formation of crystalline phases ofα-MOOH （with a goethite structure）andα-M_2O_3（with a hematite structure）from the known thermodynamic properties of the corresponding aqueous trivalent cations（M^（3＋））.The modified equation is expressed asΔG_（f,M_VX）~0=a_（M_VX）ΔG_（0,M^（3＋））^（0）＋b_（M_VX）＋β_（M_VXγM^（3＋））,where the coefficients a_（M_VX）,b_（M_VX）,andβ_（M_VX） characterize a particular structural family of M_VX（M is a trivalent cation[M^（3＋）]and X represents the remainder of the composition of solid）;γ^（3＋）is the ionic radius of trivalent cations（M^（3＋））;ΔG_（f,M_VX）~0 is the standard Gibbs free energy of formation of M_vX;andΔG_（n,M^（3＋））~0 is the non-solvation energy of trivalent cations（M^（3＋））.By fitting the equation to the known experimental thermodynamic data,the coefficients for the goethite family（α-MOOH）are a_（M_VX）=0.8838,b_（M_VX）=-424.4431（kcal/mol）,andβ_（M_VX）=115（kcal/ mol.（？））,while the coefficients for the hematite family（α-M_2O_3）are a_（M_VX）=1.7468,b_（M_VX）=-814.9573（kcal/ mol）,andβ_（M_VX）=278（kcal/mol.（？））.The constrained relationship can be used to predict the standard Gibbs free energies of formation of crystalline phases and fictive phases（i.e.phases that are thermodynamically unstable and do not occur at standard conditions）within the isostructural families of goethite（α-MOOH）and hematite（α-M_2O_3）if the standard Gibbs free energies of formation of the trivalent cations are known.

Gibbs Free Energy and Activation Energy of ZrTiAlNiCuSn Bulk Glass Forming Alloys

The Gibbs free energy differences between the supercooled liquid and the crystalline mixture for the (Zr_(52.5)Ti_5Al_(10)-Ni_(14.6)Cu_(17.9))_((100-x)/100)Sn_x (x=0, 1, 2, 3, 4 and 5) glass forming alloys are estimated by introducing the equationproposed by Thompson, Spaepen and Turnbull. It can be seen that the Gibbs free energy differences decrease firstas the increases of Sn addition smaller than 3, then followed by a decrease due to the successive addition of Snlarger than 3, indicating that the thermal stabilities of these glass forming alloys increase first and then followed by adecrease owing to the excessive addition of Sn. Furthermore, the activation energy of Zr_(52.5)Ti_5Al_(10)Ni_(14.6)Cu_(17.9) and(Zr_(52.5)Ti_5Al_(10)Ni_(14.6)Cu_(17.9))_(0.97)Sn_3 was evaluated by Kissinger equation. It is noted that the Sn addition increases theactivation energies for glass transition and crystallization, implying that the higher thermal stability can be obtainedby appropriate addition of Sn.

Gibbs Free Energy of Formation of 3Y_2O_3·5Al_2O_3

Thermodynamic properties of 3Y_2O_3·5Al_2O_3 double compound have been determined with CaF_2 single crystal electrolyte galvanic cell at 1049 K to 1230 K.The galvanic cell used can be expressed as: Pt,O_2(g)丨Y_2O_3(s),YOF_((s))丨CaF_2丨YOF_((s)), 3Y_2O_3·5Al_2O_(3(s))丨Al_2O_(3(s))丨O_2(g),Pt, of which the cell reaction is; 3Y_2O_(3(s))+SAl_2O_(3(s))=3Y_2O_3·SAl_2O_(3(s)) The following result is obtained: A_fG°(3Y_2O_3·5Al_2O_3)=-939500+765.90T±710J/mol where,△fG°(3Y_2O_3·5Al_2O_3)is the free energy of formation of 3Y_2O_3·5Al_2O_3 from Y_2O_3 and Al_2O_3.

Estimation of Gibbs free energy difference in Pd-based bulk metallic glasses

A new thermodynamic expression for Gibbs free energy difference AG between the under-cooled liquid and the corresponding crystals of bulk metallic glasses was derived. The newly proposed expression always gives results in fairly good agreement with experimental values over entire temperature range between the fusion temperature Tm and the glass transition temperature Tg of Pd40Ni40P20, Pd40Cu30Ni10P20 and Pd43Cu27Ni10P20, which possess different heat capacities. However, the TS and KN expressions cannot always provide results in good agreement with the experimental values. In addition, the deviations between the experimental values and the AG calculated by the proposed expression at Tg are smaller than those given by other expressions for all the bulk metallic glasses studied.

Electrochemical determination of Gibbs free energy of formation of magnesium ferrite

The standard Gibbs free energy of formation of magnesium ferrite was determined by means of two types of solid state electrochemical cells： one using MgZr4（PO4）6 （MZP） as the solid electrolyte and the other using CaF2 as the solid electrolyte. The first cell was operated in the range of 950 to 1100 K. The second cell was operated in the range of 1125 to 1200 K. The reversibility of the cell EMFs was confirmed by microcoulometric titration. The Gibbs energy changes of magnesium ferrite relative to component oxides were calculated based on EMF measurements and are given by following expressions, respectively： AG1 = -3579-15 T （J/mol） and AGⅡ =6258-24.3 T （J/mol）. The results obtained from two different cells are consistent with each other. The results also are in agreement with Rao＇ s and Tretjakov＇s data in the measured temperature range. When the Gibbs free energies of formation of MgO and Fe203 were substituted in the reaction, the Gibbs free energies of formation of MgFe204 was obtained in two temperature ranges and the for mations are shown as follows： AG 1Formation =-1427394＋360.5 T （J/mol） and AGⅡ Formition =-1417557＋351.2 T （J/mol）.

A Generalized Gibbs Potential Model for Materials Degradation

It is well known that work done on a material by conservative forces (electrical, mechanical, chemical) will increase the Gibbs Potential of the material. The increase in Gibbs Potential can be stored in the material and is free/available to do work at some later time. However, it will be shown in this paper that while in this state of higher Gibbs potential, the material is metastable and the material will degrade spontaneously/naturally with time in an effort to reach a lower Gibbs Potential. A generalized Gibbs Potential Model is developed herein to better understand its impact on a materials degradation rate. Special attention will be given to dielectrics degradation.

Standard Gibbs Energies of Transfer for KBPh_4 from Water to Water+PrOH and Water+TBA Mixtures and the Primary Medium Effects

The standard Gibbs energies of transfer (Δ tr G 0) for potassium tetraphenylborate (KBPh 4) have been studied in the systems of water and water +1 propanol (PrOH) as well as water and water + t butyl alcohol (TBA) at 298.15?K. The results show that -Δ tr G 0 exhibits a complicated changing pattern with the mole fraction of TBA( x (TBA)) or PrOH ( x (PrOH)), and Δ tr G 0 has the a maximum value at x (TBA) = 0.2 or x (PrOH)=0.2. Especially, -Δ tr G 0 of KBPh 4 changes unusually with increasing x (TBA) when x (TBA) < 0.05. The reasons for these changes were analyzed and discussed.

Correlation between hydration properties and electrochemical performances on Ln cation size effect in layered perovskite for protonic ceramic fuel cells

PrBa_(0.5)Sr_(0.5)Co_(1.5)Fe_(0.5)O_(5+δ)(PrBSCF) has attracted much research interest as a potential triple ionic and electronic conductor(TIEC) electrode for protonic ceramic fuel cells(PCFCs). The chemical formula for Pr BSCF is AA'B_(2)O_(5+δ), with Pr(A-site) and Ba/Sr(A'-site) alternately stacked along the c-axis. Due to these structural features, the bulk oxygen ion diffusivity is significantly enhanced through the disorder-free channels in the PrO layer;thus, the A site cations(lanthanide ions) play a pivotal role in determining the overall electrochemical properties of layered perovskites. Consequently, previous research has predominantly focused on the electrical properties and oxygen bulk/surface kinetics of Ln cation effects,whereas the hydration properties for PCFC systems remain unidentified. Here, we thoroughly examined the proton uptake behavior and thermodynamic parameters for the hydration reaction to conclusively determine the changes in the electrochemical performances depending on LnBa_(0.5)Sr_(0.5)Co_(1.5)Fe_(0.5)O_(5+δ)(LnBSCF,Ln=Pr, Nd, and Gd) cathodes. At 500 ℃, the quantitative proton concentration of PrBSCF was 2.04 mol% and progressively decreased as the Ln cation size decreased. Similarly, the Gibbs free energy indicated that less energy was required for the formation of protonic defects in the order of Pr BSCF < Nd BSCF < Gd BSCF. To elucidate the close relationship between hydration properties and electrochemical performances in LnBSCF cathodes, PCFC single cell measurements and analysis of the distribution of relaxation time were further investigated.

Thermodynamic description of the ternary compounds in the Cu-In-Se system

A set of thermodynamic descriptions of the temary compounds （mainly α-CulnSe2, δ-CulnSe2, Culn3Se5 and CulnsSe8） in the Cu-In-Se system was established by adopting sub-lattice model. The model parameters are carefully evaluated by integrating the experimental data of thermodynamic properties, phase equilibrium and theoretical calculation of formation energies of different point defects. The evaluated Gibbs energies of the compounds reasonably agree with that estimated from EMF experiment and ab initio calculation. The calculated phase relationships in the Cu-In-Se system are in accord with the experimental phase diagrams. The obtained standard enthalpy of formation of CulnSe2 is close to that reported in the literatures.

A novel interfacial thermodynamic model for predicting solubility of nanoparticles coated by stabilizers

To improve the stability of nanoparticles in aqueous solution,polymer or surfactant,etc.are often added in solutions during the preparation process of nanoparticles,which can induce new interfaces that influence the solubility of nanoparticles.In this work,a novel interfacial thermodynamic model for describing the Gibbs energy of the nanoparticles coated by stabilizers was proposed to predict the solubility of nanoparticles.Within the developed model,the activity coefficient of nano metal system was determined by Davies model and that of nano drug system by Perturbed-Chain Statistical Associating Fluid Theory(PC-SAFT).The Gibbs energy of the interface was established as a function of molecular parameters via the application for nano metal system.Furthermore,the model was further used to predict the solubility of nano drugs itraconazole,fenofibrate,and griseofulvin.It was found that the Gibbs energy of the interface plays an important role especially when the radius of nano metal is less than 40 nm,and the developed model can predict the solubility of nano drug with high accuracy in comparison with the experimental data as well as predict the changing trend of solubility of nano drugs that increases as the particle size decreases.Meanwhile,the stabilization mechanism of stabilizers on nano drugs was studied which provided theoretical guidance for the selection of polymer or surfactant stabilizer.These findings showed that the developed model can provide a reliable prediction of the solubility of nanoparticles and help to comprehend the stabilization mechanism of the stabilizers on nano drugs with different particle sizes,which is expected to provide important information for the design of nano drugs formulations.

Oxidative reforming of methane for hydrogen and synthesis gas production:Thermodynamic equilibrium analysis

A thermodynamic analysis of methane oxidative reforming was carried out by Gibbs energy minimization （at constant pressure and temperature） and entropy maximization （at constant pressure and enthalpy） methods,to determine the equilibrium compositions and equilibrium temperatures,respectively.Both cases were treated as optimization problems （non-linear programming formulation）.The GAMS 23.1 software and the CONOPT2 solver were used in the resolution of the proposed problems.The hydrogen and syngas production were favored at high temperatures and low pressures,and thus the oxygen to methane molar ratio （O 2 /CH 4） was the dominant factor to control the composition of the product formed.For O 2 /CH 4 molar ratios higher than 0.5,the oxidative reforming of methane presented autothermal behavior in the case of either utilizing O 2 or air as oxidant agent,but oxidation reaction with air possessed the advantage of avoiding peak temperatures in the system,due to change in the heat capacity of the system caused by the addition of nitrogen.The calculated results were compared with previously published experimental and simulated data with a good agreement between them.

A theoretical study of electrocatalytic ammonia synthesis on single metal atom/MXene

Electrocatalytic ammonia synthesis under mild conditions is an attractive and challenging process in the earth’s nitrogen cycle,which requires efficient and stable catalysts to reduce the overpotential.The N2 activation and reduction overpotential of different Ti3C2O2-supported transition metal(TM)(Sc,Ti,V,Cr,Mn,Fe,Co,Ni,Cu,Zn,Mo,Ru,Rh,Pd,Ag,Cd,and Au)single-atom catalysts have been analyzed in terms of the Gibbs free energies calculated using the density functional theory(DFT).The end-on N2 adsorption was more energetically favorable,and the negative free energies represented good N2 activation performance,especially in the presence Fe/Ti3C2O2(﹣0.75 eV).The overpotentials of Fe/Ti3C2O2,Co/Ti3C2O2,Ru/Ti3C2O2,and Rh/Ti3C2O2 were 0.92,0.89,1.16,and 0.84 eV,respectively.The potential required for ammonia synthesis was different for different TMs and ranged from 0.68 to 2.33 eV.Two possible potential-limiting steps may be involved in the process:(i)hydrogenation of N2 to*NNH and(ii)hydrogenation of*NH2 to ammonia.These catalysts can change the reaction pathway and avoid the traditional N–N bond-breaking barrier.It also simplifies the understanding of the relationship between the Gibbs free energy and overpotential,which is a significant factor in the rational designing and large-scale screening of catalysts for the electrocatalytic ammonia synthesis.

Thermodynamically Revealing the Essence of Order and Disorder Structures in Layered Cathode Materials

Layered transition metal(TM) oxides are one of the most widely used cathode materials in lithium-ion batteries. The atomic configuration in TM layer of these materials is often known to be random when multiple TM elements co-exist in the layer(e.g. Ni, Co and Mn). By contrast, the configuration tends to be ordered if the elements are Li and Mn. Here, by using special quasi-random structures(SQS) algorithm, the essential reasons of the ordering in a promising Li-rich Mn-based cathode material Li2MnO3 are investigated. The difference of internal energy and entropy between ordered and disordered materials is calculated. As a result, based on the Gibbs free energy, it is found that Li2MnO3 should have an ordered structure in TM layer. In comparison, structures with Ni-Mn ratio of 2:1 are predicted to have a disordered TM layer, because the entropy terms have larger impact on the structural ordering than internal energy terms.

Thermodynamic Study of Water-Steam Plasma Pyrolysis of Medical Waste for Recovery of CO and H_2

This paper describes the equilibrium compositions of the typical medical waste under high temperature pyrolysis by a steam plasma torch using the NASA CEA2 program. Various components from selected typical medical waste were input to the program along with the treatment temperature from 1000 K -4100 K. The program then performed the Gibbs free energy calculations and searched for the equilibrium composition with minimizing the total system Gibbs free energy. The calculation results indicate that, the equilibrium composition of a system C-H-O at C/O = 1 in the temperature range of 1400 K - 2000 K has demonstrated that gas composition are CO and H2 mainly, the other components （CO2, C2H4, C2H2, CH4 etc.） is less than 1% by volume and the degree of raw material transformation is about 100%. Comparison with air plasma, the steam plasma treatment will not produce nitrogen oxides, if the materials are free of nitrogen element.