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 st...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.展开更多
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 estimat...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.展开更多
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_2...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.展开更多
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...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）.展开更多
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 result...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.展开更多
The theoretical model and the numerical analyses on the Gibbs-free-energy of the association states of amphiphilic molecules in nanoconfined aqueous solutions are presented in detail. We exhibit the continuous change ...The theoretical model and the numerical analyses on the Gibbs-free-energy of the association states of amphiphilic molecules in nanoconfined aqueous solutions are presented in detail. We exhibit the continuous change of the Gibbs-free-energy trend, which plays a critical role in the association states of the system transforming from the dispersion state, through the "reversible state", and finally to the aggregation state in amphiphilic molecule solutions. Furthermore, for the "reversible state", we present the difference in the free-energy barrier heights of the dispersion state and aggregation state, resulting from the competition between the entropy,which makes the solute molecules evenly disperse in the solution and the energy contribution driving the amphiphilic molecules to aggregate into a larger cluster. These findings provide a comprehensive understanding of confinement effects on the solute association processes in aqueous solutions and may further improve the techniques of material fabrication.展开更多
This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimat...This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.展开更多
A new method for the calculation of Gibbs free energy of formation of zeolites is introduced, which is based on the assumption that the Gibbs free energy of formation of zeolites is equal to the sum of the Gibbs free ...A new method for the calculation of Gibbs free energy of formation of zeolites is introduced, which is based on the assumption that the Gibbs free energy of formation of zeolites is equal to the sum of the Gibbs free energy of all oxide components and the Gibbs free energy of reaction between the exchange ion oxide and alumina.The Gibbs free energy values of many zeolites were calculated.The results showed that the deviation between the experimental value of ΔG<sup><sup>0<sub>f of zeolite formation and those calculated by this method was less than 1%, and the molar Gibbs free energy of formation of hypothetical [SiO2] unit in each zeolite was below that of silica of all phase states.The presence of crystal water in zeolite was in favor of increasing the thermodynamic stability of zeolite.展开更多
基金supported by the NSFC(no 40473024 and 40343019)Project of the 11th and 10th Five-Year Research and Development of International Seabed(noDYXM-115-02-1-11,PY105-01-04-13 and DY 105-01-02-1)+2 种基金Project of Key Laboratory of Marginal Sea Geology,Guangzhou Institute of Geochemistry and South China Sea Institute of Oceanology,CAS(no MSGL08-01,MSGLCAS03-4)Specialized Research Fund for the Doctoral Program of Higher Education(no 20040558049)the Fundamental Research Funds for the Central Universities
文摘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.
文摘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.
文摘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.
基金the National Natural Science Foundation of China (No.50572024) the Education Ministry Foundation for Returning Overseas Scholar of China.
文摘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）.
基金Acknowledgement The project was supported by Scientific Research Fund of Hunan Provincial Education Department （06B038） and Postdoctoral Science Foundation of Central South University.
文摘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.
基金Supported by National Science Fund for Outstanding Young Scholars(No.11422542)Key Research Program of the Chinese Academy of Sciences(No.KJZD-EW-M03)+2 种基金Knowledge Innovation Program of Chinese Academy Sciencesthe High Performance Computing Center of Shanghai University(No.ZQ4000)Shanghai Supercomputer Center of China
文摘The theoretical model and the numerical analyses on the Gibbs-free-energy of the association states of amphiphilic molecules in nanoconfined aqueous solutions are presented in detail. We exhibit the continuous change of the Gibbs-free-energy trend, which plays a critical role in the association states of the system transforming from the dispersion state, through the "reversible state", and finally to the aggregation state in amphiphilic molecule solutions. Furthermore, for the "reversible state", we present the difference in the free-energy barrier heights of the dispersion state and aggregation state, resulting from the competition between the entropy,which makes the solute molecules evenly disperse in the solution and the energy contribution driving the amphiphilic molecules to aggregate into a larger cluster. These findings provide a comprehensive understanding of confinement effects on the solute association processes in aqueous solutions and may further improve the techniques of material fabrication.
文摘This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.
基金Project(SKL-SPM-202003) supported by the State Key Laboratory of Advanced Technologies for Comprehensive Utilization of Platinum Metals,ChinaProject(1920001004360) supported by the Foshan Science and Technology Innovation Program,China。
文摘A new method for the calculation of Gibbs free energy of formation of zeolites is introduced, which is based on the assumption that the Gibbs free energy of formation of zeolites is equal to the sum of the Gibbs free energy of all oxide components and the Gibbs free energy of reaction between the exchange ion oxide and alumina.The Gibbs free energy values of many zeolites were calculated.The results showed that the deviation between the experimental value of ΔG<sup><sup>0<sub>f of zeolite formation and those calculated by this method was less than 1%, and the molar Gibbs free energy of formation of hypothetical [SiO2] unit in each zeolite was below that of silica of all phase states.The presence of crystal water in zeolite was in favor of increasing the thermodynamic stability of zeolite.
