Artículos de revistas: "Thermodynamic Equilibrium Calculations"

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Zhang, Tao y Shuyu Sun. "Thermodynamics-Informed Neural Network (TINN) for Phase Equilibrium Calculations Considering Capillary Pressure". Energies 14, n.º 22 (18 de noviembre de 2021): 7724. http://dx.doi.org/10.3390/en14227724.

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The thermodynamic properties of fluid mixtures play a crucial role in designing physically meaningful models and robust algorithms for simulating multi-component multi-phase flow in subsurface, which is needed for many subsurface applications. In this context, the equation-of-state-based flash calculation used to predict the equilibrium properties of each phase for a given fluid mixture going through phase splitting is a crucial component, and often a bottleneck, of multi-phase flow simulations. In this paper, a capillarity-wise Thermodynamics-Informed Neural Network is developed for the first time to propose a fast, accurate and robust approach calculating phase equilibrium properties for unconventional reservoirs. The trained model performs well in both phase stability tests and phase splitting calculations in a large range of reservoir conditions, which enables further multi-component multi-phase flow simulations with a strong thermodynamic basis.

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2

Sundman, Bo y John Ågren. "Computer Applications in the Development of Steels". MRS Bulletin 24, n.º 4 (abril de 1999): 32–36. http://dx.doi.org/10.1557/s0883769400052167.

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Despite the fact that thermodynamic calculations, strictly speaking, apply only to equilibrium, they may of ten be used in nonequilibrium situations. If one or several of the stable phases are suppressed in the calculations, we have a metastable equilibrium, which is often of practical interest. For example, one may calculate the driving force available to form the more stable phases and model nucleation.Thermodynamic calculations may be performed stepwise to predict microseg-regation during solidification by a Scheil-type calculation (no diffusion in the solid State, infinite diffusion in the liquid, and equilibrium at the interface). In such a calculation, no information other than the thermodynamic properties of the System is used.A more ambitious approach is to com-bine the thermodynamic calculations with kinetic modeis (e.g., diffusion calculations) and thereby predict the rate of reactions. This approach is extremely powerful and may be used to simulate a wide range of different phenomena, including precipitation, homogenization, and diffusional interactionsbetween Substrate and coating.It is usually assumed that thermodynamic equilibrium holds locally at the migrating phase interface between two phases, and the rate of transformation is calculated at each instant by solving a set of flux-balance equations. The fluxes are obtained from a numerical Solution of the multicomponent diffusion equations (see Reference 3).

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3

Belov, G. V. "Calculation of Equilibrium Composition of Complex Thermodynamic Systems using Julia Language and Ipopt Library". Herald of the Bauman Moscow State Technical University. Series Instrument Engineering, n.º 3 (136) (septiembre de 2021): 24–45. http://dx.doi.org/10.18698/0236-3933-2021-3-24-45.

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The article considers the possibility of using the Ipopt optimization package for the calculating the phase and equilibrium compositions of a multicomponent heterogeneous thermodynamic system. Two functions are presented for calculating the equilibrium composition and properties of complex thermodynamic systems, written in the Julia programming language. These functions are the key ones in the program integrated with the IVTANTERMO database on thermodynamic properties of individual substances and used for conducting test calculations. The test calculations showed that Ipopt package allows determining the phase and chemical compositions of simple and complex thermodynamic systems with a fairly high speed. Using the JuMP modeling language significantly simplifies the preparation of the initial data for the Ipopt package, therefore the functions presented in this article are very compact. It is shown how the Ipopt package can be used when the temperature of the thermodynamic system is unknown. The approach proposed in this work is applicable both for analyzing the equilibrium of individual chemical reactions and for calculating the equilibrium composition of complex chemically reacting systems. The simplicity of the proposed functions allows their easy integrating into application programs, embedding them into more complex applications, using them in combination with more complex models (real gas, nonideal solutions, constrained equilibria), and, if necessary, modifying them. It should be noted that the versatility of the JuMP modeling language makes it possible to replace the Ipopt package with another one without significant modification of the program text

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4

Ewing, Mark E. y Daron A. Isaac. "Thermodynamic Property Calculations for Equilibrium Mixtures". Journal of Thermophysics and Heat Transfer 32, n.º 1 (enero de 2018): 118–28. http://dx.doi.org/10.2514/1.t5144.

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5

Lothenbach, Barbara. "Thermodynamic equilibrium calculations in cementitious systems". Materials and Structures 43, n.º 10 (17 de abril de 2010): 1413–33. http://dx.doi.org/10.1617/s11527-010-9592-x.

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6

Földényi, Rita y Aurél Marton. "Organisation of the Analytical, Stoichiometric, and Thermodynamic Information for water Chemistry Calculations". Hungarian Journal of Industry and Chemistry 43, n.º 1 (1 de junio de 2015): 33–38. http://dx.doi.org/10.1515/hjic-2015-0006.

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Abstract A common feature of the chemical processes of the hydrosphere and water treatment plants is that essentially the same types of chemical equilibrium reactions occur in both fields. These equilibria could be acid/base, complexation, redox, precipitation, and interfacial processes. Since these reactions may also occur in combination, the aqueous environments are unavoidably multispecies systems. Due to multiple equilibria, the state of aggregation, the state of oxidation, as well as the electric charge of the species may change dramatically. Calculation of the equilibrium concentration of the species is facilitated by the availability of analytical, stoichiometric, and thermodynamic information that are consistently organised into an ASTI matrix. The matrix makes it possible to apply a uniform algebraic treatment for all occurring equilibria even, if later on, further reactions have to be included in the chemical model. The use of the ASTI matrix enables us to set up the necessary mass balance equations and equilibrium relationships, which together form a non-linear system of equations (NLSE). The goal of our paper is to show that the use of the ASTI matrix approach in cooperation with the powerful engineering calculation software, MATHCAD14, results in fast and easy handling of the NLSE-s and, consequently, the calculations of speciation in aqueous systems. The paper demonstrates the method of application in three examples: the calculation of the pH dependence of the solubility of calcite in closed and open systems, the calculation of the pH and pε in a system where acid/base reactions, complexation equilibria, and redox equilibria occur, and a study of adsorption of lead ions on aluminium oxide.

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7

Ramette, Richard W. "REACT: Exploring Practical Thermodynamic and Equilibrium Calculations". Journal of Chemical Education 72, n.º 3 (marzo de 1995): 240. http://dx.doi.org/10.1021/ed072p240.

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8

Novák, Josef P., Vlastimil Růžička, Jaroslav Matouš y Jiří Pick. "Liquid-liquid equilibrium. Computation of liquid-liquid equilibrium in terms of an equation of state". Collection of Czechoslovak Chemical Communications 51, n.º 7 (1986): 1382–92. http://dx.doi.org/10.1135/cccc19861382.

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An algorithm for calculating the boiling point pressure at a chosen temperature and composition was used for computing liquid-liquid equilibrium. A lot of attention is paid to the determination of the first approximation which is specified in terms of the conditions of thermodynamic stability. The conditions of thermodynamic stability make as well possible to localize the lower and upper critical end points (LCEP and UCEP. The Redlich-Kwong-Soave equation of state was applied in calculations, and it was found out that this equation with zero interaction parameters predicts well the lower and upper critical end temperatures in the systems methane-n-hexane, ethane-n-eicosane and ethane-n-docosane.

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9

Pelton, A. D. "Thermodynamic databases and equilibrium calculations in metallurgical processes". Pure and Applied Chemistry 69, n.º 5 (1 de enero de 1997): 969–78. http://dx.doi.org/10.1351/pac199769050969.

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10

Ze-Qing, Wu, Han Guo-Xing y Pang Jin-Qiao. "Opacity Calculations for Non-Local Thermodynamic Equilibrium Mixtures". Chinese Physics Letters 19, n.º 4 (26 de marzo de 2002): 518–20. http://dx.doi.org/10.1088/0256-307x/19/4/321.

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11

Rodríguez, R., R. Florido, J. M. Gil, J. G. Rubiano, P. Martel y E. Mínguez. "RAPCAL code: A flexible package to compute radiative properties for optically thin and thick low and high-Z plasmas in a wide range of density and temperature". Laser and Particle Beams 26, n.º 3 (22 de julio de 2008): 433–48. http://dx.doi.org/10.1017/s026303460800044x.

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AbstractRadiative properties are fundamental for plasma diagnostics and hydro-simulations. For this reason, there is a high interest in their determination and they are a current topic of investigation both in astrophysics and inertial fusion confinement research. In this work a flexible computation package for calculating radiative properties for low and high Z optically thin and thick plasmas, both under local thermodynamic equilibrium and non-local thermodynamic equilibrium conditions, named RAPCAL is presented. This code has been developed with the aim of providing accurate radiative properties for low and medium Z plasmas within the context of detailed level accounting approach and for heavy elements under the detailed configuration accounting approach. In order to show the capabilities of the code, there are presented calculations of some radiative properties for carbon, aluminum, krypton and xenon plasmas under local thermodynamic and non-local thermodynamic equilibrium conditions.

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12

Fateen, Seif-Eddeen K. y Adrian Bonilla-Petriciolet. "On the Effectiveness of Nature-Inspired Metaheuristic Algorithms for Performing Phase Equilibrium Thermodynamic Calculations". Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/374510.

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The search for reliable and efficient global optimization algorithms for solving phase stability and phase equilibrium problems in applied thermodynamics is an ongoing area of research. In this study, we evaluated and compared the reliability and efficiency of eight selected nature-inspired metaheuristic algorithms for solving difficult phase stability and phase equilibrium problems. These algorithms are the cuckoo search (CS), intelligent firefly (IFA), bat (BA), artificial bee colony (ABC), MAKHA, a hybrid between monkey algorithm and krill herd algorithm, covariance matrix adaptation evolution strategy (CMAES), magnetic charged system search (MCSS), and bare bones particle swarm optimization (BBPSO). The results clearly showed that CS is the most reliable of all methods as it successfully solved all thermodynamic problems tested in this study. CS proved to be a promising nature-inspired optimization method to perform applied thermodynamic calculations for process design.

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13

Moussa, Maria, Stéphane Gorsse, Jacques Huot y Jean Louis Bobet. "Effect of the Synthesis Route on the Microstructure of HfxTi(1−x)NbVZr Refractory High-Entropy Alloys". Metals 13, n.º 2 (8 de febrero de 2023): 343. http://dx.doi.org/10.3390/met13020343.

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In the present work, the effects of (i) Ti replacement by Hf and (ii) the synthesis method on microstructure and crystal structure evolution in the high-entropy alloy HfxTi(1−x)NbVZr are reported. The results of scanning electron microscopy and X-ray diffraction analysis of alloys prepared by both arc-melting and induction-melting are compared with theoretical thermodynamic calculations using the CALPHAD approach. The non-equilibrium thermodynamic calculations agree well with the experimental observations for the arc-melted alloys: a mixture of body-centered cubic (BCC) and cubic C15 Laves phases occurs for low-Ti-concentration alloys and a single BCC phase is obtained for high-Ti alloys. The agreement is not as good when using the induction-melting method: equilibrium solidification calculations predict that the most stable state is a phase mixture of BCC, hexagonal close-packed, and a cubic C15 Laves phase, while experimentally only one BCC and one hexagonal C14 Laves phase were found. The estimation of the exact cooling rate and the lack of a thermodynamic database can explain the difference. In addition, for both methods, the thermodynamic calculation confirms that for a high Ti concentration, the BCC phase is stable, whereas phase separation is enhanced with a higher Hf concentration.

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14

Paolini, Christopher P. y Subrata Bhattacharjee. "IGE Model: An Extension of the Ideal Gas Model to Include Chemical Composition as Part of the Equilibrium State". Journal of Thermodynamics 2012 (5 de marzo de 2012): 1–18. http://dx.doi.org/10.1155/2012/870631.

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The ideal gas (IG) model is probably the most well-known gas models in engineering thermodynamics. In this paper, we extend the IG model into an ideal gas equilibrium (IGE model) mixture model by incorporating chemical equilibrium calculations as part of the state evaluation. Through a simple graphical interface, users can set the atomic composition of a gas mixture. We have integrated this model into a thermodynamic web portal TEST (http://thermofluids.sdsu.edu/) that contains Java applets for various models for properties of pure substances. In the state panel of the IGE model, the known thermodynamic properties are entered. For a given pressure and temperature, the mixture's Gibbs function is minimized subject to atomic constraints and the equilibrium composition along with thermodynamic properties of the mixture are calculated and displayed. What is unique about this approach is that equilibrium computations are performed in the background, without requiring any major change in the familiar user interface used in other state daemons. Properties calculated by this equilibrium state daemon are compared with results from other established applications such as NASA CEA and STANJAN. Also, two different algorithms, an iterative approach and a direct approach based on minimizing different thermodynamic functions in different situation, are compared.

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15

Sechenov, P. A. y I. A. Rybenko. "Numerical method and mathematical model for finding the equilibrium composition of the thermodynamic system of the T-Energy software package". Herald of Dagestan State Technical University. Technical Sciences 49, n.º 4 (9 de febrero de 2023): 104–12. http://dx.doi.org/10.21822/2073-6185-2022-49-4-104-112.

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Objective. The aim of the study is to develop a mathematical model and numerical methods for finding the equilibrium composition of a thermodynamic system.Method. To find the equilibrium composition of the thermodynamic system, a combination of numerical methods was used: Lagrange, Newton–Raphson and Gauss.Result. The analysis of existing software systems and numerical methods used in them for the calculation of thermodynamic systems is carried out. Based on the analysis, practical implementation attempts, it was possible to develop a mathematical model consisting of numerical Lagrange methods (allows you to move from a conditional problem to an unconditional one); Newton–Raphson (an approximate method for solving a nonlinear system of equations); Gauss (solving a linear system of equations). For the convergence of the Newton–Raphson method, the required quantities were replaced by their squares, and ranges of variation were set for each quantity. The results of comparing the calculations of the equilibrium composition with the Terra program show satisfactory results.Conclusion. The T-Energy software package allows you to calculate the equilibrium composition for a thermodynamic system.

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16

Proidak, A., M. Hasyk, Yu Proidak y O. Bezshkurenko. "Modeling of temperature-concentration ranges of phase stability and liquidus surface in the ternary Fe–P–C system and phase composition experimental study". Voprosy Khimii i Khimicheskoi Tekhnologii, n.º 6 (diciembre de 2023): 167–76. http://dx.doi.org/10.32434/0321-4095-2023-151-6-167-176.

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This paper reports thermodynamic properties and phase equilibria in the iron-phosphorus-carbon system for developing a technology for smelting ferrophosphorus as well as for utilizing them in the processes of phosphorus-alloying of metals. According to the results of thermodynamic calculations, we plotted a ternary Fe–P–C phase equilibrium diagram (liquidus surface) in the form of graphical dependences, which indicate the concentration fields of phase coexistence. The results of simulation allowed finding out five nonvariant points, three of which are new: E1 eutectic (teutectic=12170С), U1 peritectic (tperitectic=10950С), and Е3 eutectic (teutectic=3380С). The experimental studies of the phase composition of ferrophosphorus showed that the phosphorus microstructure is represented by Fe3P phosphide, Fe3C carbide, and carbophosphide eutectic. We carried out the thermodynamic calculation of the temperature-concentration ranges of phase stability in the Fe–P–C system that are at equilibrium with the smelts of both the carbon solid solutions and phosphorus ones in - and -iron, FeP, Fe2P, Fe3P phosphides, and graphite. In this study, three previously unknown nonvariant equilibria have been determined: a eutectic equilibrium at 1216.580C; a peritectic one with a transformation point at 1095.190C; and a eutectic one at a temperature of 337.510C. In experiments, we obtained an equilibrium concentration of carbon which decreases in the Fe–P–C system when the content of phosphorus increases. The research findings largely reveal special features of preparation of ferrophosphorus by carbon reduction of phosphorites.

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17

Bobyr, S. V. "Non-equilibrium thermodynamics model for calculating diffusion fluxes under phase transformations in alloy steels". Proceedings of the National Academy of Sciences of Belarus, Physical-Technical Series 66, n.º 1 (2 de abril de 2021): 28–36. http://dx.doi.org/10.29235/1561-8358-2021-66-1-28-36.

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The phase transformations in alloyed iron-carbon alloys is largely related to diffusion of components, foremost to the carbon. For the analysis of diffusive processes in alloy steels, it is possible to use the mathematical methods of non-equilibrium thermodynamics. The equation for the diffusive fluxes of the system contains unknown in general case of coefficients activity of elements and vacancies, and their derivatives for to the concentrations, that extraordinarily makes it difficult being of values of cross coefficients. In the article a non-equilibrium thermodynamics methodology of calculation of diffusive fluxes at presence of two phases in alloy steels is described. It allows one to calculate both direct- and cross coefficients in the Onsager equations. Formulas for calculation of thermodynamics forces in the alloy steel – for iron, alloying element of substitution – chrome, of element of introduction – carbon and vacancies, are presented. Common expressions are suggested for calculation of cross-factors, motive forces and fluxes in the Onsager’s equations for a multicomponent thermodynamic system. The example of using the developed model to find changes in concentrations and diffusion fluxes over time is given. For the model system used, it was established that at the stage of predominant diffusion of carbon in the alloy steel, cementite inclusions with a size of about 18 nm are formed rather quickly (within ~ 200 s). The technique developed in the article allows one to perform diffusion kinetics calculations in multicomponent thermodynamic systems, which are also iron-carbon alloys and to control the size of the phases formed, for example, of carbide nanoparticles.

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А. A. Myrzagaliyev, S. O. Baisanov, N. Z. Nurgali, Ye. U. Zhumagaliyev y N. A. Ulmaganbetov. "DETERMINATION OF THE THERMODYNAMIC PARAMETERS OF α-IRON IN BINARY SYSTEMS Fe-Cr AND Fe-Ti". Science and Technology of Kazakhstan, n.º 4,2023 (29 de diciembre de 2023): 162–71. http://dx.doi.org/10.48081/bqpi6828.

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This article presents the results of calculations of the thermodynamic parameters of binary Fe-Cr and Fe-Ti systems based on their state diagrams using the Bjerrum-Guggenheim osmotic coefficient, for the region of iron crystallization from the iron activity of an ideal α-γ solution for the above systems. When calculating the lines of phase equilibrium in the Fe-Cr and Fe-Ti systems, it was established that the Bjerrum-Guggenheim coefficient can serve as an assessment parameter characterizing the role of exchange forces between atoms, and by its dimension (Фi><1) one can qualitatively judge the nature of the intermolecular interactions in the system. The results of this work made it possible to correctly solve the direct Gibbs problem, namely, to obtain an analytical dependence of phase compositions on temperature at phase equilibria based on the laws of phase formation. It is shown that with the help of the Bjerrumm-Guggenheim osmotic coefficient (Fi), the real equilibrium in the system under study can be determined in detail and their correct analytical expression can be obtained. When calculating phase equilibrium lines in systems with different types of interaction between components, it was established that the Bjerrum-Guggenheim coefficient can serve as an assessment parameter characterizing the role of exchange forces between atoms. Keywords: thermodynamics; Bjerrum-Guggenheim coefficient; state diagram; osmotic coefficient; binary systems.

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19

Abdellah, Z. Nait, Redoune Chegroune, Mourad Keddam, B. Bouarour, L. Haddour y A. Elias. "The Phase Stability in the Fe-B Binary System: Comparison between the Interstitial and Substitutional Models". Defect and Diffusion Forum 322 (marzo de 2012): 1–9. http://dx.doi.org/10.4028/www.scientific.net/ddf.322.1.

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In the present work, a thermodynamic study was carried out in order to analyze the thermodynamic stability of the and phases in equilibrium with the phase using the calculation of phase diagrams (Calphad) formalism. The two phases and are modelled as substitutional and interstitial solid solutions of boron. The expressions of the chemical potentials ofBandFeare derived in both phases to perform the thermodynamic calculations. A comparison is made between the results provided by the substitutional and interstitial models and good agreement is observed between these two models.

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20

Luo, Taiming y A. Yu Chirkov. "Calculation of thermodynamic properties of mixtures in two-phase equilibrium". Journal of Physics: Conference Series 2039, n.º 1 (1 de octubre de 2021): 012016. http://dx.doi.org/10.1088/1742-6596/2039/1/012016.

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Abstract Thermodynamic properties of mixtures in vapor-liquid equilibrium (VLE) were studied. Thermodynamic properties of the methane-ethane mixtures in VLE were calculated with highly accurate Helmholtz free energy equation of state GERG-2008, simplified GERG-2008 and common cubic PR equation of state (EOS). Results show that GERG-2008 has high accuracy in VLE calculations. However, simplified GERG-2008 and PR-EOS both work unsatisfactorily in VLE calculations.

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21

Budzhak, Ya S. y T. Wacławski. "On the Question of the Problems of Statistical Calculations of the Conducting Crystals Thermodynamic and Kinetic Properties". Фізика і хімія твердого тіла 20, n.º 4 (15 de diciembre de 2019): 345–53. http://dx.doi.org/10.15330/pcss.20.4.345-353.

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This paper presents an elementary model of a crystal and its thermodynamic equilibrium state. It was shown that the thermodynamic characteristics of the crystal at this state are described by the Gibbs grand thermodynamic potential. If the crystal is removed away from the equilibrium state, then in this state it will be described by the set of kinetic properties, and these properties are statistically calculated with the use of the non-equilibrium Gibbs grand thermodynamic potential. Crystals’ thermodynamic and kinetic properties have analytical dependence on the current carriers dispersion law and chemical potential of these carriers. In this work, it was shown that the determination of the dispersion law and chemical potential – these are complicated problems of statistical and kinetic theories of crystals’ properties.

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BUCHOWIECKI, MARCIN. "TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION". Journal of Theoretical and Computational Chemistry 12, n.º 04 (junio de 2013): 1350026. http://dx.doi.org/10.1142/s0219633613500260.

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The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

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XU, W. W., X. Y. SONG y Z. X. ZHANG. "MULTIPHASE EQUILIBRIUM, PHASE STABILITY AND PHASE TRANSFORMATION IN NANOCRYSTALLINE ALLOY SYSTEMS". Nano 07, n.º 02 (abril de 2012): 1250012. http://dx.doi.org/10.1142/s1793292012500129.

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A nanoscale thermodynamic approach is developed to quantify the multiphase equilibrium in nanocrystalline alloy systems. The nanoscale multiphase equilibrium calculations indicate that the activities and mole numbers of phases in alloy systems change diversely as a function of the nanograin size at constant temperature, which results in distinctly different characteristics of phase stability and phase transformation behavior in nanocrystalline alloys with respect to coarse-grained polycrystalline counterparts. Take the nanocrystalline Sm–Co alloy system as an example, the diverse phase stabilities and phase transformations are demonstrated. To verify the thermodynamic predictions, a series of experiments on preparation and characterization of nanocrystalline SmCo3, Sm2Co7 and SmCo2 alloys have been performed. The experimental results are in agreement with the model calculations, which validate the present thermodynamic approach for nanoscale multiphase equilibrium.

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Pelton, A. D. "Thermodynamic modeling and phase equilibrium calculations in nuclear materials". Pure and Applied Chemistry 69, n.º 11 (1 de enero de 1997): 2245–52. http://dx.doi.org/10.1351/pac199769112245.

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25

Hosseini, Mostafa y Amir H. Mohammadi. "A Gibbs free energy minimization based model for liquid–liquid equilibrium calculation of a system containing oil, brine, and surfactant". Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 75 (2020): 17. http://dx.doi.org/10.2516/ogst/2020012.

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Accurate and reliable phase equilibrium calculations of microemulsion systems are of great importance. This study deals with the thermodynamic modeling of Liquid–Liquid Equilibrium (LLE) of a system including oil (n-decane), brine (containing CaCl2 salt), and ionic surfactant (sodium dodecyl sulfonate). Two models of UNIQUAC and UNIQUAC + Debye–Hückel were used for thermodynamic calculations. The LLE experimental data were utilized to estimate the binary interaction parameters of UNIQUAC model and the adjustable parameter, b, of the Debye–Hückel model. The thermodynamic model calculates the microemulsion phase’s compositions by minimizing the Gibbs free energy of the LLE system using a combination of genetic algorithm and fmincon function in order to prevent local minima. The thermodynamic modeling results show an appropriate agreement with the experimental data. Accordingly, the presented model of this study can be used as a suitable method to investigate the liquid–liquid equilibrium of systems containing oil, water, and surfactant.

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Turkevych, V. Z., Yu Yu Rumiantseva, I. О. Hnatenko, I. O. Hladkyi y Yu I. Sadova. "Thermodynamic Calculation of Fe–N and Fe–Ga Melting Diagrams at Pressures from 0.1 MPa to 7 GPa". Uspehi Fiziki Metallov 22, n.º 4 (diciembre de 2021): 531–38. http://dx.doi.org/10.15407/ufm.22.04.531.

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This paper presents results of melting-diagrams’ calculations for the Fe–N and Fe–Ga systems at atmospheric pressure (0.1 MPa) and at high pressures (3, 5, and 7 GPa). Thermodynamic calculations are performed within the models of phenomenological thermodynamics. As shown, the increase of pressure results in destabilization of high-temperature b.c.c.-Fe modification in Fe–N system and stabilization of Fe4N equilibrium with the liquid phase. In Fe–Ga system, the intermetallic compounds Fe3Ga, Fe6Ga5, Fe3Ga4, and FeGa3 retain their stability up to pressure of 7 GPa. The stabilization of Fe4N equilibrium with the liquid phase at high pressures indicates that the Fe4N can be a competing phase in the gallium-nitride crystallization from the Fe–Ga–N system melt.

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27

Hussain, B. y M. Ahsan. "A Numerical Comparison of Soave Redlich Kwong and Peng-Robinson Equations of State for Predicting Hydrocarbons’ Thermodynamic Properties". Engineering, Technology & Applied Science Research 8, n.º 1 (20 de febrero de 2018): 2422–26. http://dx.doi.org/10.48084/etasr.1644.

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Mixture phase equilibrium and thermodynamic properties have a significant role in industry. Numerical analysis of flash calculation generates an appropriate solution for the problem. In this research, a comparison of Soave Redlich Kwong (SRK) and Peng-Robinson (PR) equations of state predicting the thermodynamic properties of a mixture of hydrocarbon and related compounds in a critical region at phase equilibrium is performed. By applying mathematical modeling of both equations of states, the behavior of binary gases mixtures is monitored. The numerical analysis of isothermal flash calculations is applied to study the pressure behavior with volume and mole fraction. The approach used in this research shows considerable convergence with experimental results available in the literature.

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28

Belov, G. V. "Development of Tools for Thermodynamic Calculation of Rocket Engine Characteristics using the Julia Programming Language". Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, n.º 4 (139) (diciembre de 2021): 80–93. http://dx.doi.org/10.18698/0236-3941-2021-4-80-93.

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The experience in developing an algorithm and a program for the thermal-chemical calculation of the characteristics of a rocket engine is presented. The program is written in Julia. To calculate the equilibrium composition of combustion products the freely distributed library Ipopt is used. The program is interfaced to the database on thermodynamic properties of individual substances IVTANTERMO. For the convenience of processing, the information on thermodynamic properties is stored in two text files of a special form. The program has been developed using the simplest working process model according to which the flow is one-dimensional, the product flow is adiabatic, there are no friction losses, the product flow is equilibrium, and the speed of condensed particles is equal to the gas flow speed. Ratios for calculating the derivatives of composition, as well as equilibrium values of heat capacity and sound velocity are given. The text of the program can be used in the study process and can easily be adapted to more complex models of the rocket engine workflow. The calculation results obtained using the developed program are in good agreement with the results of TERRA calculations. The execution time of one calculation for a four-element fuel, which includes the determination of the combustion products characteristics in the chamber, the critical cross section and at the nozzle cross section, varies in the range of 3--5 s

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Mikhailenko, V. I. y A. Yu Popovskii. "Thermodynamic properties of epitropic liquid crystals". Physics of Aerodisperse Systems, n.º 54 (14 de diciembre de 2017): 51–57. http://dx.doi.org/10.18524/0367-1631.2017.54.132727.

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In this paper we used developed theoretical model earlier (called “two-component”) for numerical calculation of temperature dependencies of equilibrium ELC layer thickness hs(T), its specific heat Cp(T) and latent molar heat of phase transition ELC-bulk liquid q(T) with further comparison with experiment. This model postulates the existence of both monomers and dimers in the wall-adjacent layer, and the appearance of ELC layer is caused by the orientational interaction between these liquid particles and the solid substrate. The calculations were compared with results of experimental investigation of thin nitrobenzene interlayer symmetrically bounded by quartz substrates.

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KHOKHA, Yurii, Myroslava YAKOVENKO, Oleksandr LYUBCHAK y Dmytro BRYK. "Equilibrium temperatures of hydrocarbon gas formation in sedimentary strata of the Western oil and gas region of Ukraine (according to thermodynamic modelling)". Geology and Geochemistry of Combustible Minerals 4, n.º 181 (27 de diciembre de 2019): 66–77. http://dx.doi.org/10.15407/ggcm2019.04.066.

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The article reviews the question of interpretation of natural gases component composition from the aspect of their evolution. The parameters available for study, which show a strong correlation with the conditions of formation, migration and accumulation of natural hydrocarbon gases, are selected. Among these parameters, the ratio of the butanes isomeric form (i-C4/n-C4) was selected for thermodynamic analysis as a dependable indicator of the kerogen degradations temperature regime. It is shown that the dependence of the i-C4/n-C4 ratio on the normalized methane content shows the trend of increasing kerogen maturity, and deviations from this trend indicate a distant migration of hydrocarbon fluid from the formation zone to the current deposit. Analysis of the residence and thermodynamic conditions of hydrocarbons in the deposits of the Western oil and gas region showed that kerogen/gas systems are in a state close to equilibrium, in terms of thermodynamics. The composition of the gas/kerogen equilibrium system in the conditions of sedimentary thickness for two heat fluxes – 75 and 100 mW/m2 was calculated by the method based on Jaynes’s formalism. Among hydrocarbons in gases, the content of isomeric forms of butane and pentane, as well as methane, ethane and propane was calculated. The results of the calculations revealed a monotonic dependence of the equilibrium temperature and depth of formation on the ratio of isobutane to n-butane. It was found that the results of thermodynamic calculations coincide with experiments on kerosene pyrolysis and correlate with studies of the composition and residence of natural gases. Equilibrium formation temperatures were determined for 59 gas, oil and gas condensate fields of the Western oil and gas region, the information on which contained data on the i-C4/n-C4 ratio. Based on the results of calculations, maps of these temperatures distribution within the region were constructed. The analysis of the maps showed the presence of two distinct temperature maxima, which are concentrated in the Boryslav-Pokuttya oil and gas region and are located at the intersection of regional faults. It has been suggested that the hydrocarbon source is significantly distant from modern deposits for the study region. The results of the calculation are compared with the data obtained using the model of fossil hydrocarbons inorganic origin.

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31

Klancnik, G., Steiner Petrovic y J. Medved. "Thermodynamic calculation of phase equilibria in stainless steels". Journal of Mining and Metallurgy, Section B: Metallurgy 48, n.º 3 (2012): 383–90. http://dx.doi.org/10.2298/jmmb121119048k.

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In this paper two examples of thermodynamic investigation of stainless steels using both, experimental and modeling approach are described. The ferritic-austenitic duplex stainless steel and austenitic stainless steel were investigated using thermal analysis. The complex melting behavior was evident for both alloy systems. Experimentally obtained data were compared with the results of the thermodynamic calculations using the CALPHAD method. The equilibrium thermal events were also described by the calculated heat capacity. In spite of the complexity of both selected real alloy systems a relative good agreement was obtained between the thermodynamic calculations and experimental results.

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32

Liu, Jing-yong, Limao Huang, Shuiyu Sun y Wuming Xie. "Thermodynamic Equilibrium Calculations on Cd Transformation during Sewage Sludge Incineration". Water Environment Research 88, n.º 6 (1 de junio de 2016): 548–56. http://dx.doi.org/10.2175/106143016x14504669768895.

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33

Espósito, Rogério O., Marcelo Castier y Frederico W. Tavares. "Calculations of thermodynamic equilibrium in systems subject to gravitational fields". Chemical Engineering Science 55, n.º 17 (septiembre de 2000): 3495–504. http://dx.doi.org/10.1016/s0009-2509(00)00010-5.

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34

Joubert, Jean-Marc, Wisline St-Fleur, Julia Sarthou, Antonin Steckmeyer y Benjamin Fournier. "Equilibrium characterization and thermodynamic calculations on highly alloyed refractory steels". Calphad 46 (septiembre de 2014): 55–61. http://dx.doi.org/10.1016/j.calphad.2014.02.002.

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35

Jin-Qiao, Pang, Wu Ze-Qing, Yan Jun y Han Guo-Xing. "Theoretical Calculations of Opacity for Non-Local-Thermodynamic-Equilibrium Plasmas". Chinese Physics Letters 21, n.º 10 (octubre de 2004): 2005–7. http://dx.doi.org/10.1088/0256-307x/21/10/039.

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36

Yang, W., Feng Liu y Gen Cang Yang. "Description of Recalescence in Bulk Undercooled Alloys". Advanced Materials Research 97-101 (marzo de 2010): 995–98. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.995.

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Assuming phenomenological thermal flow balance and solute conservation, a numerical model was proposed for recalescence in bulk undercooled alloy. During the calculation, the evolution of residual melt temperature and concentration is solved as function of the transformed solid fraction. After quantitative thermodynamic calculations, a transition from non-equilibrium to equilibrium process can be described by the change of liquid/solid Gibbs energy difference. The proposed model has been applied to Cu-Ni solid solution and Fe-B hypereutectic alloy. The predicted post-recalescence temperature TR agrees well with the experimental results.

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37

Zhang, Yeqin, Wenwen Wang, Hongyu Zhang, Libin Liu y Lijun Huang. "Thermodynamic databases of Ti-Al-Fe-V quaternary alloy systems and its application". Journal of Physics: Conference Series 2686, n.º 1 (1 de enero de 2024): 012014. http://dx.doi.org/10.1088/1742-6596/2686/1/012014.

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Abstract Pandat software based on Calculations of phase diagram (CALPHAD) was used in this study. Six binary systems and four ternary systems in the Ti-Al-Fe-V system were evaluated, compared, and optimized. A thermodynamic database of Ti-Al-Fe-V titanium alloys was established by selecting the most recent, accurate, and self-consistent thermodynamic parameters. The database was used to simulate the organization of equilibrium solidification and non-equilibrium solidification alloys of Ti-10V-2Fe-3Al, Ti-10V-3Al-1Fe and Ti-10V-3Al. The precipitated phase fractions of Ti-10V-2Fe-3Al at different temperatures were calculated using the database. The effect of different Fe contents and aging temperatures on the phase composition of the Ti-10V-2Fe-3Al alloy is given in conjunction with the calculated results. There is good agreement with the experimental results for the heat treatment regimens given by the calculations. The above results show that thermodynamic calculations based on phase diagrams can guide the formulation of process parameters for alloy casting and heat treatment. The established thermodynamic database for Ti-Al-Fe-V titanium alloys is accurate and reliable.

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38

Voigt, W., V. Brendler, K. Marsh, R. Rarey, H. Wanner, M. Gaune-Escard, P. Cloke, Th Vercouter, E. Bastrakov y S. Hagemann. "Quality assurance in thermodynamic databases for performance assessment studies in waste disposal". Pure and Applied Chemistry 79, n.º 5 (1 de enero de 2007): 883–94. http://dx.doi.org/10.1351/pac200779050883.

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Performance assessment studies in underground disposal of radioactive or toxic waste need to consider all reactive interactions between waste and its surroundings. Thermodynamic equilibrium and reaction path calculations represent an important tool for this purpose. The reliability of the results depends first of all on the quality of the thermodynamic database used for the calculations. Several quality criteria of thermodynamic databases are discussed in connection with the characteristics of current database projects [Nuclear Energy Agency Thermochemical Database (NEA-TDB), Yucca Mountain database, Dortmund Databank (DDB), Common Thermodynamic Database (CTD), FreeGS, and Thermodynamic Reference Database (THEREDA)] including the situation for molten salts. The future role of the IUPAC standard for thermophysical and thermochemical data storage is emphasized.

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39

Belyanchikov, L. N. "Thermodynamic calculations for solid alloys produced under equilibrium, quasi-equilibrium, and nonequilibrium solidification conditions". Russian Metallurgy (Metally) 2007, n.º 8 (diciembre de 2007): 682–87. http://dx.doi.org/10.1134/s0036029507080095.

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40

Gapsys, Vytautas, Laura Pérez-Benito, Matteo Aldeghi, Daniel Seeliger, Herman van Vlijmen, Gary Tresadern y Bert L. de Groot. "Large scale relative protein ligand binding affinities using non-equilibrium alchemy". Chemical Science 11, n.º 4 (2020): 1140–52. http://dx.doi.org/10.1039/c9sc03754c.

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41

Najafloo, Azam y Hossein Sakhaeinia. "Modeling the solubility of carbon dioxide in the MDEA + AEEA aqueous solution using the SAFT-HR equation of state and extended UNIQUAC model". Main Group Chemistry 21, n.º 1 (8 de abril de 2022): 1–17. http://dx.doi.org/10.3233/mgc-210061.

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In this study, a thermodynamic model has been used to determine the solubility of carbon dioxide in an aqueous solution which is the combination of methyldiethanolamine (MDEA) and aminoethylethanolamine (AEEA). The physical equilibriums have been considered between the liquid and vapor phases and chemical equilibrium in the liquid phase. The SAFT-HR equation of state has been used to specify the fugacity coefficients of the components in the vapor phase. The liquid phase is considered as an electrolyte solution besides; the extended UNIQUAC has been applied to figure out the activity coefficients. The bubble point calculation has been used in this research. This method includes two main loops. Calculations related to chemical equilibrium are performed in the interior loop and the ones associated with phase equilibrium are done in the exterior loop. The solubility of carbon dioxide has been predicted by the optimized parameters of the model in the temperature range of 308.2–368.2 K. It has been calculated that the absolute average relative deviations of the model are 16.65, 19.33, 28.91 and 19.99 in the calculation of partial pressure of carbon dioxide in various loadings at the temperatures of 308.2, 328.2, 343.2 and 368.2 K.

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42

Salgansky, E. A., D. N. Podlesniy, M. V. Tsvetkov y A. Yu Zaichenko. "Thermodynamically Equilibrium Compositions of the Products Formed During the Filtration Combustion of the Metal-Containing Mixtures". Eurasian Chemico-Technological Journal 22, n.º 4 (30 de diciembre de 2020): 263. http://dx.doi.org/10.18321/ectj998.

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Thermodynamic calculations for describing the compositions of the products formed in conditions of the filtration combustion of the metal-containing mixtures were carried out. The analysis of the equilibrium compositions of the products was carried out using the TERRA high-temperature thermochemical equilibrium calculation program. According to the results of calculations, the metals were divided into two groups. First one forms both the condensed and gaseous phases and in the second one ‒ metals that are only in the condensed phase. In case of the presence of metal compounds in the gas phase, as a rule, these are the following compounds: metals, oxides, hydroxides, hydrides, sulfides and metal sulfates. Metals of the second group cannot be subjected to mass transfer under conditions of the filtration combustion wave and will remain in solid combustion products (in ash).

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43

Onderka, B., A. Dębski y W. Gąsior. "Thermodynamic Assessment Of The Bi-In-Zn System". Archives of Metallurgy and Materials 60, n.º 2 (1 de junio de 2015): 567–75. http://dx.doi.org/10.1515/amm-2015-0175.

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Abstract A thermodynamic description of the entire ternary Bi-In-Zn system was obtained by the CALPHAD modelling of the Gibbs energy of the liquid phase. The experimental data on the phase equilibria and the thermodynamic properties published and complemented by the authors’ own experiments were taken into account. In order to verify the phase equilibria in the Bi-In-Zn system, 15 different samples were studied in the temperature range of 300-900 K by the DTA technique during heating and cooling cycles. Coexisting phases and their composition were analyzed by the SEM and EDX techniques for 9 distinct samples after their thermal equilibration at 373 K and 473 K. Assessment and selected phase equilibrium calculations were performed with ThermoCalc and Pandat softwares, and compared with experimental data. The obtained results reproduce well the experimental data on both the phase equilibria and the thermodynamic properties in the optimized system.

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44

LABIDI, M., H. MERADJI, S. GHEMID, S. LABIDI y F. EL HAJ HASSAN. "STRUCTURAL, ELECTRONIC, OPTICAL AND THERMODYNAMIC PROPERTIES OF PbS, PbSe AND THEIR TERNARY ALLOY PbS1-xSex". Modern Physics Letters B 25, n.º 07 (20 de marzo de 2011): 473–86. http://dx.doi.org/10.1142/s0217984911025729.

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On the basis of ab initio calculations employing density functional theory (DFT), we investigate the structural, electronic, optical and thermodynamic properties of two binaries: PbS and PbSe in rock-salt structures. In addition, several compositions with various ordered structures of PbS 1-x Se x alloys were studied. The calculations were performed using the full potential linearized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA). Various quantities, such as equilibrium lattice constants, bulk modulus, band structures and refractive index for all Se -concentrations are presented. The microscopic origins of the gap bowing were explained by using the approach of Zunger and coworkers. On the other hand, the thermodynamic stability of these alloys was investigated by calculating the excess enthalpy of mixing ΔHm as well as the phase diagram.

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45

Hack, Klaus. "Computational thermodynamics: A mature scientific tool for industry and academia". Pure and Applied Chemistry 83, n.º 5 (4 de abril de 2011): 1031–44. http://dx.doi.org/10.1351/pac-con-10-12-06.

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The paper gives an overview of the general theoretical background of computational thermochemistry as well as recent developments in the field, showing special application cases for real world problems. The established way of applying computational thermodynamics is the use of so-called integrated thermodynamic databank systems (ITDS). A short overview of the capabilities of such an ITDS is given using FactSage as an example. However, there are many more applications that go beyond the closed approach of an ITDS. With advanced algorithms it is possible to include explicit reaction kinetics as an additional constraint into the method of complex equilibrium calculations. Furthermore, a method of interlinking a small number of local equilibria with a system of materials and energy streams has been developed which permits a thermodynamically based approach to process modeling which has proven superior to detailed high-resolution computational fluid dynamic models in several cases. Examples for such highly developed applications of computational thermodynamics will be given. The production of metallurgical grade silicon from silica and carbon will be used to demonstrate the application of several calculation methods up to a full process model.

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46

Tertyshna, Olena, Konstantin Zamikula, Oleg Tertyshny, Olena Zinchenko y Petro Topilnytskyi. "Phase Equilibrium of Petroleum Dispersion Systems in Terms of Thermodynamics and Kinetics". Chemistry & Chemical Technology 15, n.º 1 (15 de febrero de 2021): 132–41. http://dx.doi.org/10.23939/chcht15.01.132.

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The process of paraffin formation has been considered, including the peculiarities of the paraffin structure as a result of phase transitions with a decreasing temperature. Mathematical models for thermodynamic and kinetic calculations of the "solid-liquid" system phase equilibrium have been developed. To shift the "fuel oil-paraffin" balance towards the liquid, it is necessary to reduce the activity ratio of solid and liquid phases by introducing into the system a substance with a lower solubility parameter. To increase the stability, as well as structural and mechanical characteristics of fuel oil, the additive of plant origin was synthesized. The phase transitions in fuel oil depending on the temperature when adding different amounts of additives have been studied.

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47

Fountoukis, C., A. Nenes, A. Sullivan, R. Weber, T. VanReken, M. Fischer, E. Matías, M. Moya, D. Farmer y R. C. Cohen. "Thermodynamic characterization of Mexico City aerosol during MILAGRO 2006". Atmospheric Chemistry and Physics Discussions 7, n.º 3 (28 de junio de 2007): 9203–33. http://dx.doi.org/10.5194/acpd-7-9203-2007.

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Abstract. Fast measurements of aerosol and gas-phase constituents coupled with the ISORROPIA-II thermodynamic equilibrium model are used to study the partitioning of semivolatile inorganic species and phase state of Mexico City aerosol sampled at the T1 site during the MILAGRO 2006 campaign. Overall, predicted semivolatile partitioning agrees well with measurements. PM2.5 is insensitive to changes in ammonia but is to acidic semivolatile species. Semi-volatile partitioning equilibrates on a timescale between 6 and 20 min. When the aerosol sulfate-to-nitrate molar ratio is less than 1, predictions improve substantially if the aerosol is assumed to follow the deliquescent phase diagram. Treating crustal species as "equivalent sodium" (rather than explicitly) in the thermodynamic equilibrium calculations introduces important biases in predicted aerosol water uptake, nitrate and ammonium; neglecting crustals further increases errors dramatically. This suggests that explicitly considering crustals in the thermodynamic calculations are required to accurately predict the partitioning and phase state of aerosols.

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48

Dahl, Amy L., John Sanseverino y Jean-François Gaillard. "Bacterial bioreporter detects mercury in the presence of excess EDTA". Environmental Chemistry 8, n.º 6 (2011): 552. http://dx.doi.org/10.1071/en11043.

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Environmental contextUnderstanding the uptake of mercury by bacteria is essential for predicting the amount of toxic methyl mercury formed in the environment. This study shows that the uptake of mercury by a whole-cell bacterial biosensor as a function of a strong ligand was greater than predicted by chemical speciation measurements or equilibrium calculations. These results call into question the use of chemical measurements and equilibrium modelling for predicting the toxicity of metals to living organisms in the environment and suggest that direct biological methods yield more accurate results. AbstractA whole-cell bacterial reporter was used to probe the bioavailability of mercury in the presence of a strong metal chelator, ethylenediaminetetraacetic acid (EDTA). Strain ARL1 was constructed by inserting a merR::luxCDABE fusion into the chromosome of Escherichia coli. The response of the bioreporter to HgII was monitored as a function of added EDTA. In parallel, square-wave voltammetry (SWV) measurements and thermodynamic calculations using MINEQL were performed to study the chemical speciation of mercury. The amount of electro-labile HgII measured by SWV was similar to the amount of non-complexed HgII predicted from equilibrium calculations. In contrast, the bioavailable fraction measured by the bioreporter was greater than the fraction predicted by either equilibrium calculation or electrochemical analysis. These results suggest that conventional chemical measurements and equilibrium calculations are not necessarily good proxies for predicting the bioavailable metal fraction. Additional factors such as kinetic effects or biological ligand competition must be considered.

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49

Mikhailov, S., R. Brovko, S. Mushinskii y M. Sulman. "N-Methyl-D-Glucoseimine Synthesis Reaction Thermodynamic Properties Calculation". Bulletin of Science and Practice 6, n.º 11 (15 de noviembre de 2020): 40–46. http://dx.doi.org/10.33619/2414-2948/60/04.

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The presented article is devoted to thermodynamic calculations of the N-methyl-D-glucosimine reversible formation reaction, an intermediate product for N-methyl-D-glucosamine synthesis, which is widely used in pharmaceutical practice as a ballast or counterion that improves the bioavailability of the main active substance. N-methyl-D-glucosimine is synthesized as a result of the interaction of D-glucose with methylamine in organic solvents, the reaction is reversible, and the yield of the target product depends entirely on the reaction conditions. The use of thermodynamic calculations makes it possible to evaluate the influence of the chemical process conditions on the yield of target products, which in turn contributes to a deeper understanding of the chemical reactions mechanisms. In chemical equilibrium, direct and reverse reactions proceed at equal rates, while the concentrations of products and reagents remain constant. When the reaction proceeds in a closed system, after a certain time, a state of equilibrium occurs, while the reaction does not proceed with a complete transformation of the reagents. This article presents the results of thermodynamic calculations of the reaction for the synthesis of N-methyl-D-glucosimine by the Van Kravlen – Cheremnov method. The Gibbs energy, equilibrium constants, and D-glucose conversion were calculated as activity function of reacting substances. It was shown that an increase in the temperature of the reaction mixture from 20 to 160 °C promotes an increase in the conversion of D-glucose from 3 to 32%, and therefore it is possible to recommend carrying out this reaction at elevated temperatures.

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50

Markström, Andreas, Susanne Norgren, Karin Frisk, Bo Jansson y Thérèse Sterneland. "Experimental and thermodynamic evaluation of the Co–Cr–C system". International Journal of Materials Research 97, n.º 9 (1 de septiembre de 2006): 1243–50. http://dx.doi.org/10.1515/ijmr-2006-0197.

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Abstract New experimental results on the liquid + graphite + M7C3 equilibrium are presented. The solubility of Co in the M7C3 carbide has been measured at 1523 and 1723 K. These measurements together with recently published measurements on the fcc + graphite + M7C3 equilibrium show that the solubility of Co in the M7C3 is much higher than predicted from thermodynamic calculations. A new thermodynamic description of the Co–Cr –C system is presented which accurately describes the solubility of Co in the M7C3 carbide in the temperature range 1373 – 1723 K.

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