A mathematical model for estimation of sulphide capacities of multi-component slags

The present work presents mathematical model for the estimation of sulphide capacities. The sulphide capacity, C_S is expressed as (1) where ΔG⁰ is the standard Gibbs energy change for the reaction, (2) ξ, being a function of both temperature and composition, is characterized by the system under consideration. By optimizing ξ, the sulphide capacities could be estimated as functions of temperature and composition. The slag composition is described using a modified Temkin approach, where complex polymeric ions are considered as dissociated to simple species. The model has been applied to the binary systems CaO-SiO₂, MnO-SiO₂ as well as the CaO-MnO-SiO₂ ternary system. The results show that reliable predictions of the sulphide capacities can be obtained using the present model.     

Thermodynamic behaviour of zinc in Fe‐C and CaO‐FeO‐CaF2 slag at high temperatures

The distribution ratio of zinc between Ag‐Zn and Fe‐Zn alloys was measured to clarify the thermodynamic behaviour of zinc in Fe‐C melt at high temperatures. Also, the distribution ratio between Ag‐Zn alloy and CaO‐FeO‐CaF₂ slag was measured to understand the dissolution mechanism of zinc in molten slags. The activity coefficient of zinc in Ag‐Zn alloy was preliminarily measured as a fundamental thermodynamic data for the activity of zinc in Fe‐C melt. From the dependence of the activity coefficient of zinc in Fe‐C melts on temperature and carbon content, the following equation could be obtained at 1473 ‐ 1623 K: The distribution ratio of zinc between Ag‐Zn alloy and CaO‐FeO‐CaF₂ slag increased by increasing both the oxygen potential and slag basicity. The stoichiometric coefficients of the dissolution reaction were obtained by considering the relationship between zinc distribution ratio and slag basicity or oxygen partial pressure, when one of these two independent variables was fixed. The dissolution reaction of zinc into the slags could be described as follows:      

On the reaction mechanism of the carburization and decarburization of α-iron in CH4/H2-mixtures

The surface reaction of the carburization and decarburization of α-iron in CH₄/H₂-mixtures has been investigated by a method using the radioactive isotope ¹⁴C. Experimentally two different kinetic equations have been confirmed and discussed in detail: In accordance to ¹) the kinetic equation (1) is explained by a slow reaction: . For the kinetic equation (2) the adsorption, respectively the desorption of CH₄, is considered to be the most slow partial step. The correlation of the carburization with the adsorption is supported by the relations: Thus can be regarded as E_a, the activation energy of the adsorption. Its value was determined at 109 kJ/mol being equivalent to 1.1 eV, which is characteristic for a chemisorption. Further it was established, that the rate of the decarburization according to equation (2) increases with decreasing temperature, i.e. the (apparent) activation energy proved to be negative. This is explained by the fact that before its rate-controlling desorption the CH₄-molecule first of all must be formed step-by-step and by the assumption that for thermodynamical reasons the surface concentration of CH₄ increases very much with decreasing temperature. The range of validity of the kinetic equations (1) and (2) can be limited to each other as follows:

• – The kinetic law (1) is established especially at higher H₂-pressures and at surfaces with low, but effective impurities. The impurities simultaneously result in a high decline of the reaction rate.
• – The kinetic law (2) is valid especially at lower H₂-pressures.

     

Phosphorus equilibrium between BaO-BaF2-MnO fluxes and ferro-manganese melts

The equilibrium distribution ratio of phosphorus between BaO-BaF₂-MnO slags and Mn(62–73%)-Fe-C_sat-P melts has been determined for different slag compositions, oxygen partial pressures and at 1573–1673 K. The results showed that with a certain content of BaO in the slags, the phosphorus distribution ratio increased with increasing oxygen partial pressure up to about 10^?17 atm. A high oxygen partial pressure resulted in a substantial oxidation of manganese from metal to slag. The phosphate capacity of BaO-BaF₂-MnO slags increased with the BaO content and decreased with the MnO content in the investigated slag composition range. A high temperature resulted in a low phosphorus distribution ratio. For a BaO(50%)-BaF₂(47%)-MnO(3%) slag, the effect of temperature on the phosphate capacity in the range of 1573–1673 K could be expressed as: (1) The heat of reaction: (2) was estimated to be ?1107 kJ/mole.     

Solubility of calcium in Fe-Ca-Xi melts

The equilibrium experiments on liquid Fe-Ca-X_i were carried out in a high pressure induction furnace in dense CaO crucibles. The solubility of calcium, saturated with CaO, in iron was determined as a function of temperature under 10 bar argon pressure. In pure iron the maximum solubility of calcium at 1 600°C is 0.03 wt.%. The alloying elements silicon, aluminium and nickel remarkably increase the calcium solubility in iron, whereas manganese causes an almost negligible increase. Chromium significantly reduces calcium solubility. The opposite influence of chromium and nickel on calcium solubility is balanced in an 18/8 steel. The interaction parameters of the alloying elements in the solvent iron with respect to Raoultian standard state are as follows:      

Equilibrium between ammonia-hydrogen mixtures and the ε phase of iron

Foils made from pure iron with a porous structure were nitrided in mixtures of pure and entirely decomposed ammonia until constant weight was reached. The relationship between nitriding potential, temperature and concentration was measured in the ε region between 350 and 725°C and at concentrations between and . This relationship can be mathematically represented, if the ε phase is considered to be a subregular solution of nitrogen in hexagonal iron. From the Gibbs free energy of the nitrogen in the gas phase, the numerical relation and the parameters L′ = ? 600 000 + 775.6 T J/mole L″ = 1270000 ? 1423 T J/mole are deduced. The results of a calculation of the (γ + ε)/ε phase boundary using this equations are in accordance with an experimental measurement.     

Conventional chemical potentials of elements in dilute ferrous solution

Conventional thermochemical standard data are defined for dissolved elements i in iron. The standard partial enthalpy and entropy and in ideal dilute solution are described as simple temperature functions a_i and b_i are constants and denotes the partial molar heat capacity, which may be considered constant within a certain temperature range. From and further functions are derived, e.g. the conventional standard chemical potential and the modified Planck function β_i. The constants a_i, b_i, are evaluated and compiled for α-, γ, δ-iron as well as for liquid iron, as far as experimental data are available. In addition to the standard data the first order interaction coefficients for elements dissolved in liquid iron at 1873 K have been revised and tabulated.     

Equilibria of Ce-Al-O and Nd-Al-O in molten iron

Equilibrium of Ce-Al-O or Nd-Al-O system in molten iron was studied by separately melting radioactive isotope ¹⁴¹Ce or ¹⁴⁷Nd in an Al₂O₃ crucible filled with pure iron to form ¹⁴¹CeAlO₃ or ¹⁴⁷NdAlO₃ around its inner wall. The content of dissolved Ce or Nd in iron was determined by means of electrolysis in anhydrous electrolyte and radioassay. The concentration of dissolved Al in iron was obtained by photometry and followed by calculation. Activity of oxygen in liquid iron was directly measured by solid electrolyte sensors made of ZrO₂(MgO) tube. By extrapolation of data obtained, the temperature dependence of the equilibrium constant of RE-Al-O in molten iron, , or of interaction coefficient, may be described as:      

Solubility of nitrogen in austenitic FeCrMn alloys

The equilibrium solubility of nitrogen in austenitic iron-chromium, iron-manganese, and iron-chromium-manganese alloys with mass up to 20 % Cr and 18 % Mn was measured in the temperature range 1273 to 1473 K. The following interaction parameters were obtained: (1) Describing the effect of chromium and/or manganese on the nitrogen solubility by the excess term , the present measurements correspond satisfactorily to those of Hertzmann and Jarl and of Zheng in the system Fe-Cr-N, but they differ somewhat from values calculated by means of parameters published by Frisk. For the system Fe-Mn-N the present measurements correspond to measurements by Grabke et al. and to values calculated with parameters published by Qiu. Using parameters deduced from the present measurements in the austenitic Fe-Cr-Mn-N system similar nitrogen solubilities were calculated as Zheng had measured, but small deviations were found between the analysis by Qiu and this investigation.     

Connection between diffusivity and activity coefficient

On the basis of linear nonequilibrium thermodynamics, the connection between diffusivity and activity interaction coefficients in melts was delineated and this relation can be expressed as the following mathematic formula: (1)     

Some aspects on MgO solubility in complex slags

A magnesia capacity is defined, C_Mg²⁺ = (%Mg²⁺)/a_MgO and its relation to optical basicity is examined and discussed. The solubility of MgO in complex slags, in equilibrium with magnesiowustite, is derived from the activity of MgO in the magnesiowustite and from the magnesia capacity as given by the slag's optical basicity. It is found that the activity of MgO in the magnesiowustite can be derived from [%O] assuming ideality in the FeO–MgO system at 1600°C. It is also found that the MgO saturation contents in complex slags are accurately derived from the equation: In addition, the relation between the magnesia capacity and the capacities of vanadium and phosphorus is examined and the relative basicity of the oxides is discussed.     

Untersuchung der ausscheidungsinduzierten magnetischen Nachwirkung in Fe-N-Legierungen mit verschiedenen Ausscheidungsstrukturen

Es wurde eine Fe-80 Gew.ppm-N-Legierung nach verschiedenen Anlaßbehandlungen mit Hilfe der magnetischen Nachwirkung untersucht, um den Effekt der Ausscheidungsstruktur auf die schon früher gefundenen Relaxationsprozesse⁶) ^{bis 8}) zu bestimmen. Es wurden zwei Prozesse gefunden: I. Diffusion im Spannungsfeld der Ausscheidung mit den mittleren Aktivierungsparametern Die Atome im Spannungsfeld erreichen ihre Gleichgewichtslage durch weitreichende Diffusion. Da dieser Effekt – ähnlich der hydrostatischen Relaxation bei Koiwa²⁶) – nur bei bestimmten geometrischen Konfigurationen der Blochwände und der spontanen Magnetisierung stattfindet und außerdem die Diffusion durch Versetzungen behindert werden kann, verschwindet diese Relaxation bei zunehmender Ausscheidungsgröße. Sie geht dann über in einen zweiten Reorientierungsprozeß, der im Spannungsfeld abläuft. Dieser hat wegen der Wechselwirkung mit den Versetzungen eine im Vergleich zur Richter-Nachwirkung erhöhte Aktivierungsenergie (1,10 eV). Für die Bindungsenergie der Stickstoffatome an die Oberfläche der Ausscheidungen findet man Werte im Bereich 0,3 … 0,5 eV, wobei die Stärke der Bindung mit wachsender Ausscheidungsgröße zunimmt. Dies weist darauf hin, daß die Versetzungen die Ausscheidungsoberfläche stabilisieren. II. Reorientierung der Stickstoffatome in der Randzone der Ausscheidung mit den mittleren Aktivierungsparametern Die Aktivierungsparameter werden von der Ausscheidungsstruktur kaum beeinflußt, ihre Verteilungen werden jedoch bei stabilisierten Ausscheidungen schärfer.     

The oxygen pressure of dilute FexO‐CaO‐Al2O3 slag in equilibrium with liquid iron

The relationship between slag composition and oxygen partial pressure of dilute Fe_xO‐CaO‐Al₂O₃ slag in equilibrium with iron the activity of which is below 1 was extrapolated to give the oxygen partial pressure of a slag equilibrated with iron of the activity 1. In the process of extrapolation, the oxygen partial pressure and the activity of iron were unified to give a single thermodynamic quantity which is defined as: , where K(x) is the equilibrium constant for the formation reaction of Fe_xO and is considered to be a function of x. The dependence of on the slag composition was obtained experimentally. On the other hand, it was found that the plot of against log a_Fe has the slope ?1 as expected from the theoretical consideration. The relation has been employed to estimate the composition of slag in equilibrium with liquid iron. Thus, the obtained composition is used to calculate the values of and of the slag in equilibrium with liquid iron.     

Korrekturverfahren für die Röntgenfluoreszenzanalyse hochlegierter Stähle

Untersuchung des Ansatzes auf seine Wirksamkeit zur Korrektur der Meßergebnisse. Erprobung an zahlreichen Werkzeugstählen und hochlegierten Stählen mit max. etwa 2% C, 1,4% Si, 1,7% Mn, 25% Cr, 25% Ni, 8% Mo, 3,5% V, 18% W, 5% Co, 0,3% Al, 0,5% Ti und 0,6% Cu. Fehlerabschätzung und Einsatz von Kleinrechnern zur schnellen Ermittlung des korrigierten Wertes.     

Thermochemische Kennwerte für die Reaktion,Mo + O2 ⇌ MoO2 sowie in Eisenschmelzen

Zusammenstellung von Schrifttumsangaben für die Änderung der freien Standardenthalpien der Reaktionen , Mo + O₂ ? MoO₂ und in Eisenschmelzen. Neubestimmung der Temperaturabhängigkeiten der Größen ΔG^oCr₂O₃, ΔG^oMoO₂ und ΔG^o_O im Eisen bei Temperaturen zwischen 1460 bzw. 1530 und 1725 °C. Nachweis der Anwendbarkeit der neu ermittelten thermodynamischen Funktionen durch EMK-Parallelmessungen an ThO₂ (Y₂O₃)- und ZrO₂ (MgO)-Festelektrolytzellen mit Cr-Cr₂O₃- und Mo-MoO₂-Referenzelektroden in Reineisenschmelzen bei 1600 °C. Ermittlung des Parameters p_e′ der Elektronenteilleitfähigkeit für einen teilstabilisierten ZrO₂-Festelektrolyten mit einem Stoffmengengehalt von 5% MgO.     

Thermodynamics of iron oxide in FexO‐dilute CaO + Al2O3 + SiO2 + FexO slags at 1873 K

The ferrous and ferric ion capacities, and , for the slag of CaO + Al₂O₃ + SiO₂ are determined at 1873 K by means of the distribution equilibrium of iron between Fe_xO dilute slags of the system and Pt + Fe alloys under a controlled atmosphere. Compared with the values of for CaO + Al₂O₃ binary slag at a constant ratio of Al₂O₃ to decreases with an increase in SiO₂ content. Nearly linear relationships are observed between the logarithm of the ferrous and ferric ion capacities and the optical basicity. Applying these capacities, the relationship between (%Fe^T) and PO₂ under iron saturation, as well as the iron redox equilibrium in slag in relation to the optical basicity were discussed.     

Control of the aluminium-oxygen reaction in pure iron melts

Modified electrochemical oxygen sensors based on CaO-doped ZrO₂ and Y₂O₃-doped ThO₂ were developed and applied to study the aluminium-oxygen reaction in pure liquid iron with special regard to the provision of reliable experimental conditions and the attainment of true chemical equilibrium. The sensors represent valuable tools particularly for EMF long-term measurements over several hours. At 1600 °C, values of the constant and of the interaction parameters and were determined. When Fe-O-Al melts are covered with a slag phase at an activity a(Al₂O₃) < 1, e.g., CaO-saturated CaO-Al₂O₃ slag, the Al-O relationship in the iron may nevertheless be controlled by an equilibrium oxide phase at an activity a(Al₂O₃) = 1, presumably represented by inclusion particles consisting of pure Al₂O₃.     

Reduction of Fe1-xO in liquid state by H2+Ar mixtures

The investigations of reducing Fe_1-xO in liquid state with H₂+Ar mixtures, in top blowing stream of gas reactor, by using thermobalance method have been carried out. To make the system more homogeneous pure iron crucibles were used in the experiment. The experiments were carried out in the range of gas flow rate V = (5+80) · 10^?6 m³/s and in 1723 K. Reduction rate depends on hydrogen partial pressure and flow rate of gas mixture. The logarithm of apparent reduction rate constant is a linear function of logarithm of gas flow rate. In experimental conditions of this work, the initial rate of reduction satisfies the relation . Thus it has been shown that the reduction process is controlled by the mass transfer in the gaseous phase. Sherwood numbers obtained from observed values of reduction rates and empirical equation of the gas-phase mass transfer rate are correlated by equation . The values of mass transfer coefficient in gas phase calculated from Sherwood numbers are consistent with the values of apparent reduction rate constant and with estimated rate constant of chemical reaction of liquid F_e1-xO reduction.     

Nitride capacities in CaO–SiO2 and CaO–SiO2–Al2O3 melts

Nitride capacities, , defined by (mass-% N) · in the CaO–SiO₂ and CaO–SiO₂–AI₂O₃ melts were measured in the temperature range of 1 723 to 1 923 K by a gas-slag equilibration technique using CaO, Al₂O₃, and Mo crucibles. Nitrogen content in slag, (mass-% N), was proportional to oxygen partial pressure, , to the power of ?3/4 at constant nitrogen partial pressure, . The values for increased linearly with increasing temperature and increased with the content of nitride formers, SiO₂ and Al₂O₃, but the effect of SiO₂ on value was found to be greater than that of Al₂O₃. The activity coefficients of Si_3/4N in the CaO–SiO₂ melts tended to increase with increasing the content of SiO₂.