Thermodynamic modeling of the La-Mg-Y system and Mg-based alloys database

As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed） were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg2Y, Mg24Y5, Mg12La, Mg17La2, Mg41Las, Mg3La and Mg2La in the La-Mg-Y system were treated as the formulae （Mg,Y）2（La,Mg,Y）, Mg24（La,Mg,Y）4Y, Mg12（La, Y）, Mg17（La,Y）2, Mg41（La,Y）5, Mg3（La,Mg,Y） and Mg2（La, Y）, respectively. A model （La, Mg,Y）0.5（La,Mg,Y）0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution （A2） and MgM with CsCl-type structure （B2） in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.

Thermodynamic modeling and elemental migration for the early stage of rodingitization:An example from the Xialu massif of the Xigaze ophiolite,southern Tibet

The analysis of early stage rodingite from the ultramafic rocks of the Xialu Massif in the Xigaze Ophiolite,Tibet,in China shows that the rodingitization involved continuous changes in fluid composition during different stages of subduction.The early stage prehnite-bearing rodingite was produced at low pressures and temperatures along extensional fractures.Samples of rodingite were collected along a profile from the center to the margin of a rodingitized intrusive igneous rock(^10 m×30 m),and they record wide variations in bulk composition,mineralogy,and texture.The mineral assemblages,from center to margin,vary from(1)relics of primary clinopyroxene(Cpx_(r))and primary amphibole(Amp_(r))+newly formed late amphibole(Act)+primary plagioclase(Pl_(r))+clinozoisite+prehnite+albite+chlorite+titanite+ilmenite(R1 rodingite),through(2)relics of primary clinopyroxene(Cpx_(r))+newly formed late clinopyroxene(Cpx_(n))+primary and late amphiboles(Amp_(r)+Act)+clinozoisite+prehnite+albite+chlorite+titanite(R2 rodingite),to(3)newly formed late clinopyroxene(Cpx_(n))and amphibole(Act)+clinozoisite+prehnite+albite+chlorite+titanite(R3 rodingite).As a result of the metasomatic process of rodingitization,the content of CaO in the whole rock chemical composition from R1 to R3 increases,SiO_(2) decreases,and Na_(2)O+K_(2)O is almost completely removed.Massbalance diagrams show enrichments in large ion lithophile elements such as Rb,Cs,Ba,and Pb as well as Ni during rodingitization.The central part of the rodingitized intrusion(R1 rodingite)was only slightly affected by metasomatism.On the other hand,the contents of the rare earth elements(REEs),high field strength elements(HFSEs;e.g.Zr,Nb,Ta,Hf,and Y),and some highly compatible elements such as Cr and Sc decreased slightly during rodingitization.Thermodynamic modeling based on equilibrium mineral assemblages indicates that the rodingite of the Xialu Massif formed in an H_(2)O-saturated,CO_(2)-rich environment.The estimated conditions of metamorphism were-281-323℃and 0.4-3.9 kbar,representing the subgreenschist facies.In this environment,REEs and HFSEs were soluble in the fluids and partly removed.Moreover,these prehnite rodingites formed in a progressively reducing and less alkaline environment,as indicated by decreases in f(O_(2))and bulk-rock Fe^(3+)/Fe^(2+) ratios,and the records of fluidΔpH from the center to the margin of the studied rodingitized intrusion.

Thermodynamic modeling of gas solubility in aqueous sodium chloride solution

An electrolyte Equation of State is presented by combining the Cubic Plus Association Equation of State,Mean Spherical Approximation and the Born equation.This new model uses experimental relative static permittivity,intend to predict well the activity coefficients of individual ions(ACI)and liquid densities of aqueous solutions.This new model is applied to model water+Na Cl binary system and water+gas+Na Cl ternary systems.The cation/anion-water interaction parameters of are obtained by fitting the experimental data of ACI,mean ionic activity coefficients(MIAC)and liquid densities of water+Na Cl binary system.The cation/anion-gas interaction parameters are obtained by fitting the experimental data of gas solubilities in aqueous Na Cl solutions.The modeling results show that this new model can correlate well with the phase equilibrium and volumetric properties.Without gas,predictions for ACI,MIAC,and liquid densities present relative average deviations of 1.3%,3.6%and 1.4%compared to experimental reference values.For most gas-containing systems,predictions for gas solubilities present relative average deviations lower than 7.0%.Further,the contributions of ACI,and salting effects of Na Cl on gases are analyzed and discussed.

Thermodynamic modeling and phase diagram prediction of salt lake brine systems.Ⅰ. Aqueous Mg^2+–Ca^2+–Cl^- binary and ternary systems

Salt lake brine is a complex salt-water system under natural environment.Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution,the multi-temperature characteristics and predictability are still the goals of model development.In this study,a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements:(1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range;(2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients,the liquid parameters,which associated with Gibbs energy,enthalpy,and heat capacity contribution;and(3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range.Together the activity coefficient model,property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl2-CaCl2-H2 O binary and ternary systems,and it shows excellent agreement with the literature data for the ternary and binary systems.The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-idealitv system,and the ability to extrapolate the temperature.

Thermodynamic modeling and phase diagram prediction of salt lake brine systemsⅡ.Aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems

It is still a challenging task to accurately and temperature-continuously express the thermodynamic properties and phase equilibrium behaviors of the salt-lake brine with multi-component,multitemperature and high concentration.The essential subsystem of sulfate type brine,aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems across a temperature range from 250 K to 643 K are investigated with the improved comprehensive thermodynamic model.Liquid parameters(Δg_(IJ),Δh_(IJ),and ΔC_(p,IJ))associated with the contributions of Gibbs energy,enthalpy,and heat capacity to the binary interaction parameters,i.e.the temperature coefficients of eNRTL parameters formulated with a Gibbs Helmholtz expression,are determined via multi-objective optimization method.The solid constantsΔ_(f)G_(k)°^((298.15))andΔ_(f)H_(k)°^((298.15))of11 solid species occurred in the quaternary system are rebuilt from multi-temperature solubilities.The modeling results show the accurate representation of(1)solution properties and binary phase diagram at temperature ranges from eutectic points to 643 K;(2)isothermal phase diagrams for Li_(2)SO_(4)-Na_(2)SO_(4)-H_(2)O,Li_(2)SO_(4)-K_(2)SO_(4)-H_(2)O and Na_(2)SO_(4)-K_(2)SO_(4)-H_(2)O ternary systems.The predicted results of complete structure and polythermal phase diagram of ternary systems and the isothermal phase diagrams of quaternary system excellently match with the experimental data.

Fluid-rock interactions leading to the formation of the epithermal Ag-Pb-Zn veins:A perspective of thermodynamic modeling

Although vein-type silver-lead-zinc ore deposits have been extensively studied,the factors controlling their formation are still poorly understood and their genesis is a matter of ongoing debate.In this contribution,I present new mineralogical data and the results of thermodynamic modeling that constrain the conditions of metal transport and deposition for the Aerhada epithermal Pb-Zn-Ag deposit(reserves of>1,000 t Ag@58 g/t and 1.0 Mt Pb+Zn@5.2%)in NE China.Three primary paragenetic stages have been identified,the second of which(Stage II)is the main base metal and silver mineralization.Freibergite,argentite,pyrargyrite,and canfieldite are the main Ag-bearing minerals and are spatially associated with an alteration assemblage of quartz-muscovite±chlorite±epidote.Dissolution textures and evidence of compositional heterogeneity for freibergite suggest that its decomposition may have redistributed the Ag and contributed in part to the high Ag grade ores in the deposit.Thermodynamic calculations indicate that there was extensive silver ore deposition from a strongly reducing(e.g.,∆log fO_(2)(HM)of<-8.6 to-2.4)and nearly neutral to weakly alkaline(e.g.,pH of 5.5 to 6.8)aqueous fluid at temperatures between 220℃ and 170℃.These calculations reveal that a reduction in fO_(2)and decreasing temperature,both as a result of fluid-rock interactions,were the key factors leading to silver and base metal mineral deposition.Further path modeling showed that the sole evolution of a magmatic-derived fluid is capable of forming the large Ag-Pb-Zn veins via fluid-rock interactions,which is contrary to the conclusions of some other studies that the mixture of an externally derived fluid is required to explain their formation.The genetic model for Ag-Pb-Zn ore formation developed in this study is applicable to other polymetallic vein-type deposits in comparable geological settings elsewhere.

FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

Thermodynamic Modeling of Deoxidation Products and Inclusion Chemistry in Mn/Si Killed Tire-Cord Steel

The present work deals with thermodynamic modeling of oxide systems, in the context of slags and inclusions in steelmaking. The work has emphasis on oxides encountered during the production of tire – cord steel. Control of inclusion chemistry and variation in eutectic temperature and eutectic composition of MnO-Al2O3-SiO2 slag system have been studied, using Thermo-CalcR software. Relatively low liquidus temperatures are obtained for ratio of MnO / SiO2 = 0.5 - 1.5 and Al2O3 content from 10 - 20 mass%. It has been observed that the addition of Alumina leads to further increase in the liquidus temperature. The stability of inclusions is analyzed in terms of free energy values of related slag systems; and an appropriate minimum of Gibbs free energy value of slag phase observed at around 50 ppm of Oxygen. The observations could not be verified using thermodynamic experiments, but have been compared with findings in the open literature.

Thermodynamic Modeling as a Strategy for Casting High Alloy Steels

Strategies based on thermodynamic calculations can be used to overcome the problems associated with oxides encountered in steel plant operations, which can lead to certain difficulties in the process such as clogging of submerged entry nozzle during continuous casting. Approaches to producing high alloy steels by continuous casting have been taken. One of the strategies to avoid the oxidation of chromium is to add a small amount of other elements （subject to other constraints）, which do not cause subsequent problems. The problem has been studied using the Thermo-CalcR software, with related databases; and the results obtained for different process conditions or generic compositions have been presented.

Inter-comparisons of thermodynamic sea-ice modeling results using various parameterizations of radiative flux

Radiative fluxes are of primary importance in the energy and mass balance of the sea-ice cover. Various parameterizations of the radiative fluxes are studied in a thermodynamic sea-ice model. Model outputs of the surface radiative and heat fluxes and mass balance are compared with observations. The contribution of short-wave radiation is limited to a long part of winter. Therefore, simple schemes are often sufficient. Errors in estimations of the short-wave radiation are due mainly to cloud effects and occasionally to multi-reflection between surface and ice crystals in the air. The long-wave radiation plays an important role in the ice surface heat and mass balance during most part of a winter. The effect of clouds on the accuracy of the simple radiative schemes is critical, which needs further attention. In general, the accuracy of an ice model depends on that of the radiative fluxes.

Thermodynamic modeling of Cr-Al-C and Ni-Al-C systems for low-density steels

The so-called low-density steels have generated a lot of interests with their high specific strength and ductility due to the addi-tion of the light element Al.ln order to accelerate the low-density steel design,a thermodynamic database has been developedwithin the present author group.Two Al-containing systems,i.e.,Cr-Al-Cand Ni-Al-C,were modeled and optimirzed with CALPHAD approach based on the reliable binary descriptions.For Cr-Al-C,system,the Gibbs energy of Cr2AlC phasewas described by a temperature-dependent polynomial with the aid of the experimental data on the heat capacity,instead of estimating heat capacity from Ncumann-Kopp rule.The incongruent melting temperature of Cr2AlC is 1762 K with theinvariant reaction of liquid+Cr3C2+Al4C3→Cr2AlC.The phase equilibria between Cr2AlC and binary phases were wellreproduced by using the present model parameters.For Ni-Al-C system,the liquid,fec and bec phases have been optimizedto fit the carbon solubility in these three phases.A good agreement between the calculated and experimental data has beenobtained using the present description of Ni-Al-C system.The reliable descriptions of the two ternary systems developedin the present work can be implemented into the thermodynamic database for low-density steels.

Experimental Investigation and Thermodynamic Modeling of the NaCI-NaNO3-Na2SO4 Ternary System

Molten salts as heat transfer and storage materials have been used to nuclear energy and concentrated solar power（CSP） applications. In this work, the system of molten salt mixture based on thermodynamic principles was designed as thermal energy storage（TES） materials. The substitutional solution model can be employed to describe the Gibbs energies of all liquid phase. Thermodynamic model parameters for the NaCl-NaNO3-Na2SO4 subsystems were conducted by thermodynamic evaluation and optimization based on experimental phase-equilibria data. Thus, a set of self-consistent thermodynamic database was eventually obtained to reliably calculate the whole phase diagram and thermodynamic properties for the NaCl-NaNO3-Na2SO4 ternary system. The results manifest that the eutectic point of theternary system located at T=280 ℃ and XNaCl=8.4%, XNaNO3=86.3% and xNa2SO4=5.3%. Moreover, the results predicted were verified experimentally using differential scanning calorimetry（DSC） and the agreement between the measured value[T=（287±2） ℃] and predicted value（T=280 ℃） was satisfactory. Thus, the thermodynamic calculation method will be used to design and develop novel molten salt mixture as thermal energy storage materials.

A general thermodynamic model for the long-period stacking ordered phases in magnesium alloys

A thermodynamic model Mg x(Xs,Mg)6(Xl,Mg)8(Xs and Xl are elements smaller and larger than Mg)for long-period stacking ordered phases(LPSOs)was proposed based on two key factors:the Xs 6 Xl 8-type L12 clusters and the variation of chemical compositions.In general,all available LPSOs can be described with this model.As a representative system,Mg-Y-Zn with three LPSOs was investigated using the CALPHAD(calculation of phase diagram)approach aided with first-principles calculations.Two new three-phase equilibria were predicted and were validated by key experiments.The model-based descriptions will be the basis for the research and development of magnesium alloys.

Thermodynamic Research on Precipitates in Low Carbon Nb-Microalloyed Steels Produced by Compact Strip Production

Microalloying element Nb in low carbon steels produced by compact strip production （CSP） process plays an important role in inhibiting recrystallization, decreasing the transformation temperature and grain refinement.With decreasing the rolling temperature, dislocations can be pinned by carbonitrides and the strength is increased. Based on the two sublattice model, with metal atom sublattice and interstitial atom sublattice,a thermodynamic model for carbonitride was established to calculate the equilibrium between matrix and carbonitride. In the steel produced by CSP, the calculation results showed that the starting temperature of precipitation of Ti and Nb are 1340℃ and 1040℃, respectively. In the range of 890-950℃, Nb rapidly precipitated. And the maximum of the atomic fraction of Nb in carbonitride was about 0.68. The morphologies and energy spectrum of the precipitates showed that （NbTi） （CN） precipitated near the dislocations. The experiment results show that Nb rapidly precipitated when the temperature was lower than 970℃, and the atomic fraction of Nb in carbonitride was about 60%-80%. The calculation results are in agreement with the experiment data. Therefore the thermodynamic model can be a useful assistant tool in the research on the precipitates in the low carbon steels produced by CSP.

Design and Numerical Simulation of an Arctic Ocean Circulation and Thermodynamic Sea－Ice Model

In this paper, the first version of a new Arctic Ocean circulation and thermodynamic sea-ice model is presentedby the authors based on the framework of a twenty-layer World Oceanic general circulation model developed byZhang et al. in 1994. The model's domain covers the Arctic Ocean and Greenland-Norwegian Seas with the horizontal resolution of 200 km×200 km on a stereographic projection plane. In vertical, the model uses the Eta-coordinate(Sigma modified to have quasi-horizontal coordinate surfaces) and has ten unevenly-spaced layers to cover the deepest water column of 3000 m. Two 150-year integrations of coupling the ocean circulation model with the sea-icemodel have been performed with seasonally cyclic surface boundary conditions. The only difference between the tWoexperiments is in the model's geography. Some preliminary analyses of the experimental results have been done focused on the following aspects: (1) surface layer temperature, salinity and current; (2) the' Atlantic Layer'; (3)sea-ice cover and its seasonal variation. In comparison with the available observational data, these results are acceptable with reasonable accuracy.

A novel hybrid thermodynamic model for pore size distribution characterisation for shale

Scholars often see the gas adsorption technique as a straight-to-interpret technique and adopt the pore size distribution(PSD)given by the gas adsorption technique directly to interpret pore-structure-related issues.The oversimplification of interpreting shale PSD based on monogeometric thermodynamic models leads to apparent bias to the realistic pore network.This work aims at establishing a novel thermodynamic model for shale PSD interpretation.We simplified the pore space into two geometric types—cylinder-shaped and slit-shaped.Firstly,Low-temperature Nitrogen Adsorption data were analyzed utilizing two monogeometric models(cylindrical and slit)to generate PSD_(cyl).and PSD_(slit);Secondly,pore geometric segmentation was carried out using Watershed by flooding on typical SEM images to obtain the ratio of slit-shaped(∅_(s))and cylinder-shaped pores(∅_(c)).Combining the results of the two,we proposed a novel hybrid model.We performed pyrolysis,XRD,FE-SEM observation,quantitative comparison with the results obtained by the DFT model,and fractal analysis to discuss the validity of the obtained PSD_(Hybrid).The results showed that:the hybrid model proposed in this work could better reflect the real geometry of pore space and provide a more realistic PSD;compared with thermodynamic monogeometric models,PSD obtained from the hybrid model are closer to that from the DFT model,with an improvement in the deviation from the DFT model from 5.06%to 68.88%.The proposed hybrid model has essential application prospects for better interpretation of shale pore space.It is also worth noting that we suggest applying the proposed hybrid model for PSD analysis in the range of 5-100 nm.

Thermodynamic Behavior Research Analysis of Twin-roll Casting Lead Alloy Strip Process

The thermodynamic behavior of twin-roll casting （TRC） lead alloy strip process directly affects the forming of the lead strip, the quality of the lead strip and the production efficiency. However, there is little research on the thermodynamics of lead alloy strip at home and abroad. The TRC lead process is studied in four parameters： the pouring temperature of molten lead, the depth of molten pool, the roll casting speed, and the rolling thickness of continuous casting. Firstly, the thermodynamic model for TRC lead process is built. Secondly, the thermodynamic behavior of the TRC process is simulated with the use of Fluent. Through the thermodynamics research and analysis, the process parameters of cast rolling lead strip can be obtained： the pouring temperature of molten lead： 360-400 ℃, the depth of molten pool： 250-300 mm, the roll casting speed： 2.5-3 m/min, the rolling thickness： 8-9 mm. Based on the above process parameters, the optimal parameters（the pouring temperature of molten lead： 375-390 ℃, the depth of molten pool： 285-300 mm, the roll casting speed： 2.75-3 m/min, the rolling thickness： 8.5-9 mm） can be gained with the use of the orthogonal experiment. Finally, the engineering test of TRC lead alloy strip is carried out and the test proves the thermodynamic model is scientific, necessary and correct. In this paper, a detailed study on the thermodynamic behavior of lead alloy strip is carried out and the process parameters of lead strip forming are obtained through the research, which provide an effective theoretical guide for TRC lead alloy strip process.

Multi-stage rodingitization of ophiolitic bodies from Northern Apennines(Italy): Constraints from petrography, geochemistry and thermodynamic modelling

The investigated mantle bodies from the External Ligurians(Groppo di Gorro and Mt.Rocchetta)show evidences of a complex evolution determined by an early high temperature metasomatism,due to percolating melts of asthenospheric origin,and a later metasomatism at relatively high temperature by hydrothermal fluids,with formation of rodingites.At Groppo di Gorro,the serpentinization and chloritization processes obliterated totally the pyroxenite protolith,whereas at Mt.Rocchetta relics of peridotite and pyroxenite protoliths were preserved from serpentinization.The rodingite parageneses consist of diopside+vesuvianite+garnet+calcite+chlorite at Groppo di Gorro and garnet+diopside+serpentine±vesuvianite±prehnite±chlorite±pumpellyite at Mt.Rocchetta.Fluid inclusion measurements show that rodingitization occurred at relatively high temperatures(264-334℃ at 500 bar and 300-380℃ at 1 kbar).Garnet,the first phase of rodingite to form,consists of abundant hydrogarnet component at Groppo di Gorro,whereas it is mainly composed of grossular and andradite at Mt.Rocchetta.The last stage of rodingitization is characterized by the vesuvianite formation.Hydrogarnet nucleation requires high Ca and low silica fluids,whereas the formation of vesuvianite does not need CO2-poor fluids.The formation of calcite at Groppo di Gorro points to mildly oxidizing conditions compatible with hydrothermal fluids;the presence of andradite associated with serpentine and magnetite at Mt.Rocchetta suggests Fe^3+-bearing fluids with fO2 slightly higher than iron-magnetite buffer.We propose that the formation of the studied rodingite could be related to different pulses of hydrothermal fluids mainly occurring in an oceancontinent transitional setting and,locally,in an accretionary prism associated with intra-oceanic subduction.

A thermodynamic model of calculating mass action concentrations for structural units or ion couples in NaClO_4-H_2O and NaF-H_2O binary solutions and NaClO_4-NaF-H_2O ternary solution

A thermodynamic model of calculating mass action concentrations for structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions and NaClO4-NaF-H2O ternary strong electrolyte aqueous solutions was developed based on the ion and molecule coexistence theory （IMCT）. A transformation coefficient was needed to compare the calculated mass action concentration and the reported activity, because they were usually obtained at different standard states and concentration units. The results show that transformation coefficients between the calculated mass action concentrations and the reported activities of the same components change in a very narrow range. The transformed mass action concentrations of structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions agree well with the reported activities. The transformed mass action concentrations of structural units or ion couples in NaClO4-NaF-H2O ternary solution are also in good agreement with the reported activities in a total ionic strength range from 0.1 to 0.9 mol/kg H2O by the 0.1 mol/kg step with different ionic strength fractions of 0, 0.2, 0.4, 0.5, 0.6, 0.8, and 1, respectively. The results indicate that the developed thermodynamic model can reveal the structural characteristics of binary and ternary strong electrolyte aqueous solutions, and the calculated mass action concentrations of structural units or ion couples also strictly follow the mass action law.