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.

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）.

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.

A theoretical insight about co-pyrolysis reaction of natural gas and coal

The co-pyrolysis of natural gas and coal is a promising way for the production of acetylene due to its high efficiency for energy and hydrogen utilization.This work investigated the thermodynamics for the copyrolysis reaction of natural gas and coal using density functional theory.The favorable reaction conditions are presented in the form of phase diagrams.The calculation results show that the extra amount of methane may benefit the production of acetylene in the co-pyrolysis reaction,and the C/H ratio of 1:1,temperature around 3000 K and pressure at 0.1 MPa are most favorable.The results would provide basic data for related industrial process for the production of acetylene.

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.

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.

Assesment and Prediction of Thermodynamic Functions of Compounds in Sialon System

According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sialon materials possible.

The thermodynamics analysis and experimental validation for complicated systems in CO_2 hydrogenation process

Catalytic conversion of COinto chemicals and fuels is an alternative to alleviate climate change and ocean acidification.The catalytic reduction of COby Hcan lead to the formation of various products:carbon monoxide,carboxylic acids,aldehydes,alcohols and hydrocarbons.In this paper,a comprehensive thermodynamics analysis of COhydrogenation is conducted using the Gibbs free energy minimization method.The results show that COreduction to CO needs a high temperature and H/COratio to achieve a high COconversion.However,synthesis of methanol from COneeds a relatively high pressure and low temperature to minimize the reverse water-gas shift reaction.Direct COhydrogenation to formic acid or formaldehyde is thermodynamically limited.On the contrary,production of CHfrom COhydrogenation is the thermodynamically easiest reaction with nearly 100%CH4 yield at moderate conditions.In addition,complex reactions with more than one product are also calculated in this work.Among the considered carboxylic acids（HCOOH,CHCOOH and CHCOOH）,propionic acid dominates in the product stream（selectivity above 90%）.The same trend can also be found in the hydrogenation of COto aldehydes and alcohols with the major product of propionaldehyde and butanol,respectively.In the process of COhydrogenation to alkenes,low temperature,high pressure,and high Hpartial pressure favor the COconversion.CHis the most thermodynamically favorable among all considered alkynes under different temperatures and pressures.The thermodynamic calculations are validated with experimental results,suggesting that the Gibbs free energy minimization method is effective for thermodynamically understanding the reaction network involved in the COhydrogenation process,which is helpful for the development of high-performance catalysts.

Numerical Study on the Acetylene Concentration in the Hydrogen-Carbon System in a Hydrogen Plasma Torch

Effects of the hydrogen/carbon mole ratio and pyrolysis gas pressure on the acetylene concentration in the hydrogen-carbon system in a plasma torch were numerically calculated by using the chemical thermodynamic equilibrium method of Gibbs free energy. The calculated results indicate that the hydrogen concentration and the pyrolysis gas pressure play crucial roles in acetylene formation. Appropriately abundant hydrogen, with a mole ratio of hydrogen to carbon about 1 or 2, and a relatively high pyrolysis gas pressure can enhance the acetylene concentration. In the experiment, a compromised project consisting of an appropriate hydrogen flow rate and a feasible high pyrolysis gas pressure needs to be carried out to increase the acetylene concentration from coal pyrolysis in the hydrogen plasma torch.

Electrochemical formation of holmium-cobalt alloys

The electrochemical formation processes of holmium-cobalt alloys on cobaltcathode in molten HoCl_3-KCl were investigated by cyclic voltammetry and open current potential-timecurve alter potentiostatic electrolysis. The structure of Ho-Co alloys' films deposited on cobaltelectrode by potentiostatic electrolysis was characterized by X-ray diffraction. The standard Gibbsfree energies of formation for the intermetallic compounds of Ho and Co were determined. Thediffusion coefficient and diffusion activation energy of Ho atom in the alloy phase were calculatedto be 10^(-10) -10^(-11) cm^2/s and 96.0 kJ/mol, respectively, from the current-time curve atpotential step.

Thermodynamic evaluation and hydrothermal preparation of K_xNa_(1-x)NbO_3

The Gibbs free energies of reaction △rGτ of KNbO3 and NaNbO3 were calculated and then that of KxNa1-xNbO3 was estimated. On the basis of the thermodynamic calculation results, the hydrothermal temperatures were designed at 100, 160, and 230℃ respectively. However, NaNbO3 was prepared when the heating temperature was higher than 160℃, and KNbO3 and KxNa1-xNbO3 were obtained at 230℃, suggesting that only at a higher temperature the kinetic requirement is satisfied. According to the X-ray diffraction results, both the solid solutions, NaNbO3-based solid solution, Na1-xKxNbO3, and KNbO3-based solid solution, K1-xNaxNbO3, were hydrothermally synthesized in 6 mol/L alkali （NaOH and KOH） solution at 230℃.

Effects of Microalloying on Glass Forming Ability and Thermodynamic Fragility of Cu-Pr-Based Amorphous Alloys

The effects of microalloying of Ti and B on the glass formation of Cu60Pr30Ni10Al10-2xTixBx（x = 0, 0.05% （atom fraction）） amorphous alloys was investigated using differential scanning calorimetry （DSC） and X-ray diffraction （XRD）. XRD analysis showed that mieroalloying with 0.05% Ti and 0.05% B improved the glass forming ability （GFA）. The smaller difference in the Gibbs free energy between the liquid and crystalline states at the glass transition temperature （△G1-X（Tg）） and the smaller thermodynamic fragility index （△Sf/Tm, where ASf is the entropy of fusion, and Tm is the melting temperature） after mieroalloying correlated with the higher GFA.

Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate

The transition among multiple charging states of a semiconductor＇s localized intrinsic/impurity defects is considered as phase transitions, and the concept of transition Gibbs free energy level （TGFEL） is proposed. Dependence of the cross section of TGFEL on its charge state is discussed. Introduction of TGFEL to replace acti- vation energy has fundamentally important consequences for semiconductor physics and devices. TGFEL involves entropy. What is to be included and not included in the entropy term consistently for all defect levels is an unre- solved open question, related to correct interpretation of various experimental data associated with various defect levels. This work is a first step towards resolving this question.

Equilibrium Composition of a Plasma in the Low Voltage Air Circuit Breaker Contaminated by the Vapor of AgSnO2 Alloy Electrical Contacts

When the circuit breaker cuts the electric current, an electric arc is created between its electrodes. The success or failure of breaking the electric current by the circuit breaker depends strongly on the physico-chemical properties of the electric arc created, such as the composition of which depends on the material of the electrical contacts. In this work, we determine the equilibrium composition of the electric arc in the low voltage air circuit breaker with silver tin dioxide alloy contacts, in a temperature range from 500 K to 15,000 K and at atmospheric pressure. We use the Gibbs free energy minimization method and develop a computer code to determine the equilibrium composition of the created plasma. The analysis of the results obtained shows that O2 particles with a dissociation energy of 5.114 eV, NO with a dissociation energy of 6.503 eV, and N2 dissociation 9.756 eV dissociate around 3500 K, 5000 K, and 7500 K, respectively. We note that the electro-neutrality is established between the electrons and the cations: Ag+ and NO+, for temperatures lower than 6500 K. For temperatures higher than 6500 K, the electro-neutrality is established between the electrons and the cations: N+, O+, and Ag+. The numerical density of the electrons increases when the proportion of the vapor of the electrical contacts increases in the mixture, in particular for temperatures lower than 11,000 K.

Thermodynamic properties of LaCrO_3

The nano powders of LaCrO3 were prepared by a sol-gel route. The heat capacity of LaCrO3 nano powders from 350 to 550 K was measured by DSC method and expressed as： Cpa2CrO3） （±0.112） = 166.844 - 8.500 ×10^-3T- 1.022×10^6T^-2 （J/（mol.K）） （350-550 K）. An EMF measurement assembly was developed with CaF2 as an electrolyte for the galvanic cell. From measured EMF data of the reversible cell, （-） PL La2O3, LaF3, O2 （1 atm）lCaF2O2（1 atm）, LaF3, LaCrO3, Cr2O3, Pt（＋）, and the relevant value of Gibbs free energy, the Gibbs free energy of formation of LaCrO3 was calculated from 700 to 885 K： △G ФaLaCrO3 = -1555.364 ＋ 0.354T （kJ/mol） （700-885 K）. And the Gibbs free energy change of reaction from simple oxides La2O3 and Cr2O3 was calculated to be： AG f Oox（LaCrO3） = -94.758 ＋ 8.530×10^-2T（kJ/mol） （700-885 K）.

Co-Generation of C_2 Hydrocarbons and Synthesis Gases from Methane and Carbon Dioxide: a Thermodynamic Analysis

This paper deals with thermodynamic chemical equilibrium analysis using the method of direct minimization of Gibbs free energy for all possible CH4 and CO2 reactions. The effects of CO2/CH4 feed ratio, reaction temperature, and system pressure on equilibrium composition, conversion, selectivity and yield were studied. In addition, carbon and no carbon formation regions were also considered at various reaction temperatures and CO2/CH4 feed ratios in the reaction system at equilibrium. It was found that the reaction temperature above 1100 K and CO2/CH4 ratio=1 were favourable for synthesis gas production with H2/CO ratio unity, while carbon dioxide oxidative coupling of methane （CO2 OCM） reaction to produce ethane and ethylene is less favourable thermodynamically. Numerical results indicated that the no carbon formation region was at temperatures above 1000 K and CO2/CH4 ratio larger than 1.

Thermodynamic Evaluation of Gadolinium

Based on the analysis and evaluation of the thermodynamic information (including heat capacity, enthalpy, entropy, relative magnetic parameter, solid transition temperature, melting point, solid transition enthalpy and melting enthalpy, etc.) on all the condensed phases (hcp-, bcc-Gd and the liquid Gd), a description of the Gibbs energy of various condensed phases of gadolinium at 101325 Pa was obtained for the whole temperature range from 200 to 3600 K. The magnetic contribution to the Gibbs energy of hcp-Gd was described by using the Inden-Hillert-Jarl phenomenological model. The data of different measurable thermodynamic properties of hcp-, bcc-Gd and the liquid Gd were calculated by using the above description of the Gibbs energy, which reproduces very well with the experimental data from different sources.