Kinetic Study and Mathematical Model of Hemimorphite Dissolution in Low Sulfuric Acid Solution at High Temperature

The dissolution kinetics of hemimorphite with low sulfuric acid solution was investigated at high temperature. The dissolution rate of zinc was obtained as a function of dissolution time under the experimental conditions where the effects of sulfuric acid concentration, temperature, and particle size were studied. The results showed that zinc extraction increased with an increase in temperature and sulfuric acid concentration and with a decrease in particle size. A mathematical model able to describe the process kinetics was developed from the shrinking core model, considering the change of the sulfuric acid concentration during dissolution. It was found that the dissolution process followed a shrinking core model with “ash” layer diffusion as the main rate-controlling step. This finding was supported with a linear relationship between the apparent rate constant and the reciprocal of squared particle radius. The reaction order with respect to sulfuric acid concentration was determined to be 0.7993. The apparent activation energy for the dissolution process was determined to be 44.9 kJ/mol in the temperature range of 373 K to 413 K (100 °C to 140 °C). Based on the shrinking core model, the following equation was established: $$ 1.21\ln \left( {1 - 0.83x} \right) - \left[ {1.02\ln \frac{{0.35 + \left( {1 - x} \right)^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3}}} - 0.59\left( {1 - x} \right)^{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}} }}{{0.35 + \left( {1 - x} \right)^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3}}} + 1.18\left( {1 - x} \right)^{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}} }} + 3.52\arctan \left( {1.96\left( {1 - x} \right)^{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}} - 0.58} \right)} \right] + 2.06 = 42,192.59{\text{e}}^{{ - \frac{44,900}{{{\text{R}}T}}}} t. $$      

The Solubility and Diffusivity of Fluorine in Solid Copper from Electrochemical Measurements

The solubility and diffusivity of fluorine in solid copper were determined electrochemically using the double solid-state cell $$Ni + NiF_2 \left| {CaF_2 } \right|Cu\left| {CaF_2 } \right|Ni + NiF_2 .$$ In the temperature range 757 to 920°C, the diffusivity of fluorine in solid copper was found to be $$D_F \left( {{{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } s}} \right. \kern-\nulldelimiterspace} s}} \right) = 9.32 \times 10^{ - 2} \exp \left( {\frac{{ - 98,910 {J \mathord{\left/ {\vphantom {J {mole}}} \right. \kern-\nulldelimiterspace} {mole}}}} {{RT}}} \right).$$ . The results obtained for the dissolution of fluorine as atoms in solid copper showed large scatter. However, the equilibrium dissolution of fluorine follows Sieverts’ law. Above the melting point (770°C) of CuF₂, the mean solubility of fluorine in solid copper, for the equilibrium Cu(s)+ CuF ₂(l), follows the relationship $$N_F^s (atom fraction) = 0.98 \exp \left( {\frac{{ - 79,500 {J \mathord{\left/ {\vphantom {J {mole}}} \right. \kern-\nulldelimiterspace} {mole}}}} {{RT}}} \right).$$      

Silicon-Oxygen equilibrium and nitrogen distribution between CaO-SiO2 slags and liquid iron

Silicon-oxygen equilibria in an Fe-0.003 ~ 27 mass pct Si alloy in equilibrium with the CaO-SiO₂ slags were studied in the temperature range of 1823 to 1923 K using a lime crucible. At the same time, nitrogen distribution ratios, L_N, between slag and metal were measured, and from these results and the reported values for activities of SiO₂, nitride capacities, , defined by (mass pct N). were evaluated. It was found that the values for L_N decreased, whereas those for increased with an increase in temperature. Activities of SiO₂ were determined using the values for L_N and obtained in previous gas-slag experiments. These values were compared with the previous results.     

Phase equilibria in the titanium-oxygen system

Data in the literature on the Magneli oxides of titanium have been critically evaluated and equations have been developed from these data for the standard-state Gibbs energy of formation of the following oxides: Ti₄O₇, Ti₅O₉, Ti₆O₁₁, Ti₈O₁₅, and Ti₉O₁₇. Examination of those data yielded the following:

Kinetics of hydrochloric acid leaching of smithsonite

The dissolution kinetics of smithsonite ore in hydrochloric acid solution has been investigated. As such, the effects of particle size (−180 + 150, −250 + 180, −320 + 250, −450 + 320 μm), reaction temperature (25, 30, 35, 40, and 45°C), solid to liquid ratio (25, 50, 100, and 150 g/L) and hydrochloric acid concentration (0.25, 0.5, 1, and 1.5 M) on the dissolution rate of zinc were determined. The experimental data conformed well to the shrinking core model, and the dissolution rate was found to be controlled by surface chemical reaction. From the leaching kinetics analysis it can be demonstrated that hydrochloric acid can easily and readily dissolve zinc present in the smithsonite ore, without any filtration problems. The activation energy of the process was calculated as 59.58 kJ/mol. The order of the reaction with respect to HCl concentration, solid to liquid ratio, and particle size were found to be 0.70, −0.76 and −0.95, respectively. The optimum leaching conditions determined for the smithsonite concentrate in this work were found to be 1.5 M HCl, 45°C, −180 + 150 μm, and 25 g/L solid to liquid (S/L) ratio at 500 rpm, which correspond to more than 95% zinc extraction. The rate of the reaction based on shrinking core model can be expressed by a semi-empirical equation as:

Prediction of dendrite arm spacings in unsteady-and steady-state heat flow of unidirectionally solidified binary alloys

Various theoretical dendrite and cell spacing formulas have been tested against experimental data obtained in unsteady- and steady-state heat flow conditions. An iterative assessment strategy satisfactorily overcomes the circumstances that certain constitutive parameters are inadequately established and/or highly variable and that many of the data sets, in terms of gradients, velocities, and/or cooling rates, are unreliable. The accessed unsteady- and steady-state observations on near-terminal binary alloys for primary and secondary spacings were first examined within conventional power law representations, the deduced exponents and confidence limits for each alloy being tabularly recorded. Through this analysis, it became clear that to achieve predictive generality the many constitutive parameters must be included in a rational way, this being achievable only through extant or new theoretical formulations. However, in the case of primary spacings, all formulas, including our own, failed within the unsteady heat flow algorithm while performing adequately within their steady-state context. An earlier untested, heuristically derived steady-state formula after modification,

Determination of standard gibbs energies of formation of Cr2N and CrN

The standard Gibbs energies of formation of Cr₂N and CrN have been measured by an equilibration technique and by using thermogravimetry and differential thermal analysis (TG-DTA) at temperatures ranging from 1232 to 1523 K. The results are expressed as follows:

Embrittlement Analysis of $$\sum {{{{5}\left[ {{21}0} \right]} \mathord{\left/ {\vphantom {{{5}\left[ {{21}0} \right]} {\left( {\overline{1}\overline{2}0} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {-{1}-{2}0} \right)}}}$$ FeAl Grain Boundary in Presence of Defects: An Ab Initio Study

Iron aluminide (FeAl) inter-metallic compounds are potential candidates for structural applications at high temperatures owing to their superior corrosion resistance, high temperature oxidation, low density and inexpensive material cost. However, the presence of defects can lead to reduction in the strength and ductility of FeAl-based materials. Here we present a density functional theory (DFT) study of the effect of the presence of defects including Fe and Al vacancies as well as H dopants at the substitutional and interstitial sites at a \(\sum {{{{5}\left[ {{21}0} \right]} \mathord{\left/ {\vphantom {{{5}\left[ {{21}0} \right]} {\left( {\overline{1}\overline{2}0} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\overline{1}\overline{2}0} \right)}}}\) FeAl grain boundary focusing on the energetics. The plane wave pseudopotential code Vienna Ab initio Simulation Package (VASP) in the generalized gradient approximation (GGA) is used to carry out the computations. The formation energy calculations showed that intrinsic defects such as Fe and Al vacancies probably form at the GB, indicated by their negative formation energies. These vacancies can further form defect complexes with H impurities, indicated by lowered formation energies, compact bonds and charge gain of H atoms. Electronic structure analysis showed stronger hybridization of 1s orbitals of H with Fe and Al atoms, which leads to the stabilization of these defects resulting in degradation of material strength.

     

Microstructure and Mechanical Properties of CP-Titanium Processed by ECAP Followed by Warm Caliber Rolling

In this study, microstructural evolution and mechanical properties of commercial purity titanium after a combined equal channel angular pressing (ECAP) and warm caliber rolling (WCR) was investigated. The ECAP process was applied to enhance the hardness and strength of the specimen by decreasing the grain size and producing UFG microstructure. WCR was applied to reduce cross-section and increase the ductility of the ECAPed specimens. Results show that WCR reduces the work-hardening rate by increasing grain size and also increases elongation and workability while it reduces the yield and ultimate tensile strength. It has been shown that the strength ratio (\({{\sigma_{UTS} } \mathord{\left/ {\vphantom {{\sigma_{UTS} } {\sigma_{y} }}} \right. \kern-0pt} {\sigma_{y} }}\)) and strain ratio (\({{\varepsilon_{UTS} } \mathord{\left/ {\vphantom {{\varepsilon_{UTS} } {\varepsilon_{t} }}} \right. \kern-0pt} {\varepsilon_{t} }}\)) of the processed samples are comparatively larger than all previously post processed ECAPed materials at lower temperatures.     

Thermodynamic properties and phase equilibria for Pt-Rh alloys

The activity of rhodium in solid Pt-Rh alloys is measured in the temperature range from 900 to 1300 K using the solid-state cell

Effect of Slag Composition on the Concentration of Al2O3 in the Inclusions in Si-Mn-killed Steel

The thermodynamic equilibria between CaO-Al₂O₃-SiO₂-CaF₂-MgO(-MnO) slag and Fe-1.5 mass pct Mn-0.5 mass pct Si-0.5 mass pct Cr melt was investigated at 1873 K (1600 °C) in order to understand the effect of slag composition on the concentration of Al₂O₃ in the inclusions in Si-Mn-killed steels. The composition of the inclusions were mainly equal to (mol pct MnO)/(mol pct SiO₂) = 0.8(±0.06) with Al₂O₃ content that was increased from about 10 to 40 mol pct by increasing the basicity of slag (CaO/SiO₂ ratio) from about 0.7 to 2.1. The concentration ratio of the inclusion components, \( {{X_{{{\text{Al}}_{2} {\text{O}}_{3} }} \cdot X_{\text{MnO}} } \mathord{\left/ {\vphantom {{X_{{{\text{Al}}_{2} {\text{O}}_{3} }} \cdot X_{\text{MnO}} } {X_{{{\text{SiO}}_{2} }} }}} \right. \kern-0pt} {X_{{{\text{SiO}}_{2} }} }} \) , and the activity ratio of the steel components, \( {{a_{\text{Al}}^{2} \cdot a_{\text{Mn}} \cdot a_{\text{O}}^{2} } \mathord{\left/ {\vphantom {{a_{\text{Al}}^{2} \cdot a_{\text{Mn}} \cdot a_{\text{O}}^{2} } {a_{\text{Si}} }}} \right. \kern-0pt} {a_{\text{Si}} }} \) , showed a good linear relationship on a logarithmic scale, indicating that the activity coefficient ratio of the inclusion components, \( {{\gamma_{{{\text{SiO}}_{2} }}^{i} } \mathord{\left/ {\vphantom {{\gamma_{{{\text{SiO}}_{2} }}^{i} } {\left( {\gamma_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{i} \cdot \gamma_{\text{MnO}}^{i} } \right)}}} \right. \kern-0pt} {\left( {\gamma_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{i} \cdot \gamma_{\text{MnO}}^{i} } \right)}} \) , was not significantly changed. From the slag-steel-inclusion multiphase equilibria, the concentration of Al₂O₃ in the inclusions was expressed as a linear function of the activity ratio of the slag components, \( {{a_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{s} \cdot a_{\text{MnO}}^{s} } \mathord{\left/ {\vphantom {{a_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{s} \cdot a_{\text{MnO}}^{s} } {a_{{{\text{SiO}}_{2} }}^{s} }}} \right. \kern-0pt} {a_{{{\text{SiO}}_{2} }}^{s} }} \) on a logarithmic scale. Consequently, a compositional window of the slag for obtaining inclusions with a low liquidus temperature in the Si-Mn-killed steel treated in an alumina ladle is recommended.     

Kinetic modeling of titania reduction by a methane-hydrogen-argon gas mixture

This article describes kinetic modeling of titania reduction and carburization by methane-containing gas, based on experimental data reported previously by Zhang and Ostrovski. A sequence of titania reduction to titanium oxycarbide,

Removal of B from Si by solidification refining with Si-Al melts

To discuss the removal of B by solidification refining of Si with a Si-Al melt, the segregation of B between solid Si and the Si-Al melt was investigated by use of the temperature-gradient-zone melting (TGZM) method. The segregation ratio of B at its infinite dilution was determined to be 0.49 (1473 K), 0.32 (1373 K), and 0.22 (1273 K), respectively. With the obtained segregation ratio, the activity coefficient of B in solid Si at its infinite dilution relative to pure solid B was determined by the following equation:

Sulfation Kinetics of Low-Grade Nickel–Copper Sulfide Ore in the Sulfuric Acid Roasting Process

The enormous demand for and consumption of nickel in industrial applications has induced the depletion of high-grade nickel sulfide ore, which has inevitably led to the utilization of the substantial deposits of depreciated low-grade nickel-copper sulfide ore. In this work, the mineral phase transformation and sulfation kinetics of nickel, copper, iron, and magnesium in the roasting process were studied. The kinetic parameters of the metals were calculated by using the sulfation rates under different roasting temperatures, ratios of acid to ore and particle size of ore. The results showed that the sulfation process of metals is fit well by the kinetic function $$1 - {{\text{2}} \mathord{\left/ {\vphantom {{\text{2}} 3}} \right. \kern-0em} 3}x - {{(1 - x)}^{{{{\text{2}} \mathord{\left/ {\vphantom {{\text{2}} 3}} \right. \kern-0em} 3}}}} = kt$$ (G–B equation) over 0–20 min and 30–150 min for nickel, copper, and iron, as well as over 5–30 min in the case of magnesium. Furthermore, internal diffusion (three-dimensional diffusion, D4) was the restricting factor in the sulfation processes of the metals, as suggested by experimental data regarding the ratio of acid to ore and the particle size of ore.     

Effects of Zr Additions on the Microstructure and Impression Creep Behavior of AZ91 Magnesium Alloy

The effects of 0.2, 0.6, and 1.0 wt pct Zr additions on the microstructure and creep behavior of AZ91 Mg alloy were investigated by impression tests carried out under constant punching stress (σ _imp) in the range 100 to 650 MPa, corresponding to the modulus-compensated stress levels of 0.007 ￡ s_\textimp \mathord

Phase equilibrium and minor element distribution between FeO x -SiO2-MgO-based slag and Cu2S-FeS matte at 1573 K under high partial pressures of SO2

As part of a fundamental study of copper smelting processes using oxygen or oxygen-enriched air as a blowing gas, phase equilibrium and distribution of minor elements between copper matte and SiO₂-saturated FeO _x -SiO₂-MgO-based slag containing 5 to 10 wt pct MgO have been investigated at 1573 K under the SO₂ partial pressures of 10.1, 50.7, and 101.3 kPa. The copper and sulfur solubilities in the slag were found to be independent of when the matte grade was specified, and this behavior was ascribed to the constancy of against at a given matte grade. When the distribution ratio of a minor element (X) between the slag and matte phases was defined as L _x ^s/m =(wt pct X in slag)/{wt pct X in matter}, L _x ^s/m for arsenic, antimony, and bismuth at a given matte grade increased with increasing . On the other hand, the distribution ratio of silver at a given matte grade was almost constant against .