Effect of Al2O3 and Cr2O3 on loquidus temperatures in the cristobalite and tridymite primary phase fields of the MgO-"FeO"-SiO2 ststem in equilibrium with metallic iron

The effects of alumina and chromite impurities on the liquidus temperatures in the cristobalite/tridymite (SiO2) primary phase fields in the MgO-FeO-SiO, system in equilibrium with metallic iron have been investigated experimentally. Using high temperature equilibration and quenching followed by electron probe X-ray microanalysis (EPMA), liquiclus isotherms have been determined in the temperatures range 1 673 to 1 898 K. The results are presented in the form of pseudo-ternary sections of the MgO-FeO-SiO, system at 2, 3 and 5 wt% Al2O3, 2 wt% Cr2O3, and 2 wt% Cr2O3+2 wt% Al2O3. The study enables the liquidus to be described for a range of SiO2/MgO and MgO/FeO ratios. It was found that liquiclus temperatures in the cristobalite and tridymite primary phase fields, decrease significantly with the addition of Al2O3 and Cr2O3.

Experimental study of phase equilibria in the system PbO-ZnO-SiO2

An experimental study on the ternary system PbO-ZnO-SiO2, in air by high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis was carried out as part of the wider research program on the six-component system PbO-ZnO-SiO2-CaO-FeO-Fe2O3, which combines experimental and thermodynamic computer modeling techniques to characterize zinc and lead industrial slags. Liquidus and solidus data were reported for all primary phase fields in the system PbO-ZnO-SiO2 in the temperature range 640 degrees C to 1400 degrees C (913 to 1673 K).

Experimental study of phase equilibria in the PbO-MgO-SiO2 system

Equilibrium phase relations in the PbO-Al2O3-SiO2 system have been investigated experimentally by means of high-temperature equilibration, quenching, and electron probe X-ray microanalysis (EPMA). The system has 21 primary phase fields including three monoxides (PbO, Al2O3, and SiO2), seven binary compounds (Al6Si2O13, PbAl2O4, PbAl12O19, Pb2Al2O5, PbSiO3, Pb2SiO4, and Pb4SiO6), and eleven ternary compounds (PbAl2Si2O8, Pb3Al10SiO20, Pb4Al2Si2O11, Pb4Al4SiO12, Pb4Al4Si3O16, Pb4Al4Si5O20, Pb5Al2Si10O28, Pb6Al2Si6O21, Pb8Al2Si4O19, Pb12Al2Si17O49, and Pb12Al2Si20O55). Three new ternary compounds, Pb4Al4SiO12, Pb4Al4Si5O20, and Pb12Al2Si17O49, were observed and characterized by EPMA. No extensive solid solution in any of the compounds was found in the present study. The liquidus isotherms were experimentally determined in most of the primary phase fields in the temperature range from 923 to 1873 K, and the ternary phase diagram of the PbO-Al2O3-SiO2 System has been constructed.

Experimental study of phase equilibria in the "FeO"-ZnO-(CaO+SiO2) system with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron

The pseudoternary sections FeO-ZnO-(CaO + SiO2) with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron have been experimentally investigated in the temperature range from 1000 degreesC to 1300 degreesC (1273 to 1573 K). The liquidus surfaces in these pseudoternary sections have been experimentally determined in the composition range from 0 to 33 wt pct ZnO and 30 to 70 wt pct (CaO + SiO2). The sections contain primary-phase fields of wustite (FexZn1-xO1+y), zincite (ZnzFe1-zO), fayalite (Fu(w)Zn(2-w)SiO(4)), melilite (Ca2ZnuFe1-uSi2O7), willemite (ZnvFe2-vSiO4), dicalcium silicate (Ca2SiO4), pseudowollastonite and wollastonite (CaSiO3), and tridymite (SiO2). The phase equilibria involving the liquid phase and the solid solutions-have also been measured.

Experimental study of phase equilibria in the "FeO"-ZNO-(CaO+SiO2) system with the CaO/SiO2 weight ratio of 0.71 at metallic iron saturation

The pseudoternary section FeO-ZnO-(CaO + SiO2) with a CaO/SiO2 weight ratio of 0.71 in equilibrium with metallic iron has been experimentally investigated in the temperature range from 1000 degreesC to 1300 degreesC (1273 to 1573 K). The liquidus surface in this pseudoternary. section has been determined in the composition range of 0 to 33 wt pct ZnO and 30 to 70 wt pct (CaO + SiO2)The system contains primary-phase fields of wustite (FexZn1-xO1+y), zincite (ZnzFe1-zO), fayalite (FewZn2-wSiO4), melilite (Ca2ZnuFe1-uSi2O7), and pseudowollastonite (CaSiO3). The phase equilibria involving the liquid phase and the solid solutions have also been measured.

Phase equilibrium studies in the "MnO"-Al2O3-SiO2 system

Phase relations and the liquidus surface in the system "MnO"-Al2O3-SiO2 at manganese-rich alloy saturation have been investigated in the temperature range from 1373 to 1773 K. This system contains the primary-phase fields of tridymite and cristobalite (SiO2); mullite (3Al(2)O(3).2SiO(2)); corundum (Al2O3); galaxite (MnO.Al2O3); manganosite (MnO); tephroite (2MnO.SiO2); rhodonite (MnO.SiO2); spessartine (3MnO.Al2O3.SiO2); and the compound MnO.Al2O3.2SiO(2).

Phase-equilibrium data and liquidus for the system "MnO"-CaO-Al2O3-SiO2 at Al2O3/SiO2 of 0.55 and 0.65

Phase-equilibrium data and liquidus isotherms for the system MnO-CaO-(Al2O3 + SiO2) at silicomanganese alloy saturation have been determined in the temperature range of 1373 to 1723 K. The results are presented in the form of the pseudoternary sections MnO-CaO-(Al2O3 + SiO2) with Al2O3/SiO2 weight ratios of 0.55 and 0.65. The primary-phase fields have been identified in this range of conditions.

Experimental study of phase equilibria in the Al-Fe-Zn-O system in air

The phase equilibria in the Al-Fe-Zn-O system in the range 1250 °C to 1695 °C in air have been experimentally studied using equilibration and quenching techniques followed by electron probe X-ray microanalysis. The phase diagram of the binary Al2O3-ZnO system and isothermal sections of the Al2O3-“Fe2O3”-ZnO system at 1250 °C, 1400 °C, and 1550 °C have been constructed and reported for the first time. The extents of solid solutions in the corundum (Al,Fe)2O3, hematite (Fe,Al)2O3, Al2O3*Fe2O3 phase (Al,Fe)2O3, spinel (Al,Fe,Zn)O4, and zincite (Al,Zn,Fe)O primary phase fields have been measured. Corundum, hematite, and Al2O3*Fe2O3 phases dissolve less than 1 mol pct zinc oxide. The limiting compositions of Al2O3*Fe2O3 phase measured in this study at 1400 °C are slightly nonstoichiometric, containing more Al2O3 then previously reported. Spinel forms an extensive solid solution in the Al2O3-“Fe2O3”-ZnO system in air with increasing temperature. Zincite was found to dissolve up to 7 mole pct of aluminum in the presence of iron at 1550 °C in air. A meta-stable Al2O3-rich phase of the approximate composition Al8FeZnO14+x was observed at all of the conditions investigated. Aluminum dissolved in the zincite in the presence of iron appears to suppress the transformation from a round to platelike morphology.

Phase equilibria in high MgO ferro-manganese and silico-manganese smelting slags

Liquidus isotherms and phase equilibria have been determined experimentally for a pseudo-ternary section of the form MnO-(CaO+MgO)-(SiO2+Al2O3) with a fixed Al-2,O-3,/SiO2, weight ratio of 0.17 and MgO/CaO weight ratio of 0.17 for temperatures in the range 1473-1673 K. The primary phase fields present for the section investigated include manganosite (Mn,Mg,Ca)O; dicalcium silicate alpha-2(Ca,Mg,Mn)O (.) SiO2; merwinite 3CaO(.) ((Mg,Mn)O.2SiO(2); wollastonite [(Ca,Mg,Mn)(OSiO2)-Si-.]; ;tephroite [2(Mn,Mg)O.SiO2]; rhodonite [(Mn,Mg)O. diopside [(CaO,MgO,MnO,Al2O3)(SiO2)-Si-.]; tridymite (SiO2), SiO2] and melilite [2CaO (.) (MgO,MnO,Al2O3).2(SiO2,Al2O3)]. The liquidus temperatures relevant to ferro-manganese and silico-manganese smelting slags have been determined. The liquiclus temperature is shown to be principally dependent on the modified basicity weight ratio (CaO+Mgo)/(SiO2+Al2O3) at low MnO concentrations, and dependent on the mole ratio (CaO+ MgO+MnO)/(SiO2+Al2O3) at higher MnO concentrations.

Phase equilibria in high MgO ferro- and silico-manganese smelting slags

Phase equilibria have been determined experimentally for pseudo-ternary sections of the form “MnO”- (CaO+MgO)-(SiO2+Al2O3) with a fixed Al2O3/SiO2 weight ratio of 0.17 and MgO/CaO weight ratios of 0.25 and 0.17 respectively for temperatures in the range 1473-1673 K. The primary phase fields present for the MgO/CaO weight ratio of 0.17 include manganosite (Mn,Mg,Ca)O; dicalcium silicate α-2(Ca,Mg,Mn)O·SiO2; merwinite 3CaO⋅(Mg,Mn)O⋅2SiO2; wollastonite [(Ca,Mg,Mn)O·SiO2]; diopside [(CaO,MgO,MnO,Al2O3)·SiO2]; tridymite (SiO2); tephroite [2(Mn,Mg)O·SiO2]; rhodonite [(Mn,Mg)O·SiO2] and melilite [2CaO·(MgO,MnO,Al2O3)·2(SiO2,Al2O3)]. For the section with MgO/CaO weight ratio of 0.25 the anorthite phase (CaO⋅Al2O3⋅2SiO2) is also present. The liquidus temperatures of ferro- and silico-manganese smelting slags have been determined. The liquidus temperatures at low MnO concentrations are shown to be principally dependent on the modified basicity weight ratio (CaO+MgO)/(SiO2+Al2O3).

Phase-field analysis of finite-strain plates and shells including element subdivision

With the theme of fracture of finite-strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase- field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.

Coupled experimental and thermodynamic study of the Zn-Fe-Si-O system

Experimental and thermodynamic modeling studies have been carried out on the Zn-Fe-Si-O system. This research is part of a wider program to characterize zinc/lead industrial slags and sinters in the PbO-ZnO-SiO2-CaO-FeO-Fe2O3 system. Experimental investigations involve high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis (EPMA). Liquidus temperatures and solid solubilities of the crystalline phases were measured in the temperature range from 1200 °C to 1450 °C (1473 to 1723 K) in the zinc ferrite, zincite, willemite, and tridymite primary-phase fields in the Zn-Fe-Si-O system in air. These equilibrium data for the Zn-Fe-Si-O system in air, combined with previously reported data for this system, were used to obtain an optimized self-consistent set of parameters of thermodynamic models for all phases.

Liquidus temperatures in calcium ferrite slags in equilibrium with molten copper

Experimental laboratory methods have been developed that enable phase-equilibria studies to be carried out on slags in the system Ca-Cu-Fe-O in equilibrium with metallic copper. These techniques involve equilibration at temperature, rapid quenching, and chemical analysis of the phases using electron-probe X-ray microanalysis (EPNIA). Equilibration experiments have been carried out in the temperature range of 1150 degreesC to 1250 degreesC (1423 to 1523 K) and in the composition range of 4 to 80 wt pct "Cu2O," 0 to 25 wt pct CaO, and 20 to 75 wt pct "Fe2O3" in equilibrium with metallic copper. Liquidus and solidus data are reported for the primary-phase fields of spinel (magnetite) and dicalcium ferrite. The resulting data have been used to construct liquidus isotherms of the CaO-"Cu2O"-"Fe2O3" system at metallic copper saturation.

Numerical methods for solar tomography in the STEREO era

In this thesis, we propose several advances in the numerical and computational algorithms that are used to determine tomographic estimates of physical parameters in the solar corona. We focus on methods for both global dynamic estimation of the coronal electron density and estimation of local transient phenomena, such as coronal mass ejections, from empirical observations acquired by instruments onboard the STEREO spacecraft. We present a first look at tomographic reconstructions of the solar corona from multiple points-of-view, which motivates the developments in this thesis. In particular, we propose a method for linear equality constrained state estimation that leads toward more physical global dynamic solar tomography estimates. We also present a formulation of the local static estimation problem, i.e., the tomographic estimation of local events and structures like coronal mass ejections, that couples the tomographic imaging problem to a phase field based level set method. This formulation will render feasible the 3D tomography of coronal mass ejections from limited observations. Finally, we develop a scalable algorithm for ray tracing dense meshes, which allows efficient computation of many of the tomographic projection matrices needed for the applications in this thesis.

Electron microprobe investigations of metamorphic reactions and mineral growth histories, Kwoiek area, British Columbia

The Kwoiek Area of British Columbia contains a pendant or screen of metamorphosed sedimentary and volcanic rocks almost entirely surrounded by a portion of the Coast Range Batholith, and intruded by several dozen stocks. The major metamorphic effects were produced by the quartz diorite batholithic rocks, with minor and later effects by the quartz diorite stocks. The sequence of important metamorphic reactions in the metasedimentary and metavolcanic rocks, ranging in grade from chlorite to sillimanite, is:

1. chlorite + carbonate + muscovite → epidote + biotite

2. chlorite + carbonate → actinolite + epidote

3. chlorite + muscovite → garnet + biotite

4. chlorite + epidote → garnet + hornblende

5. chlorite + muscovite → garnet + staurolite + biotite

6. chlorite + muscovite → aluminum silicate + biotite

7. muscovite + staurolite → garnet + aluminum silicate + biotite

8. staurolite → garnet + aluminum silicate

Continuous reactions, occurring between reactions 5 and 7, are:

A. chlorite + (high Ti) biotite + Al₂O₃ (from plagioclase?)→ garnet + staurolite + (low Ti) biotite + O₂

B. muscovite (phengitic) → garnet + staurolite +muscovite (less phengitic) + O₂ (?)

Detailed electron microprobe work on garnet, staurolite, biotite, and chlorite shows that:

(1) The garnet porphyroblasts are zoned according to a depletion model, called the Rayleigh depletion model, which assumes equilibrium between the edge of a growing garnet and the minerals which are unzoned, notably biotite, chlorite, and muscovite, but which assumes disequilibrium within the garnet.

(2) The staurolite porphyroblasts are also zoned, and from their zoning patterns reactions A, B, and 5 are documented. Progressive reduction of iron with increasing grade of metamorphism is also inferred from the staurolite zoning patterns.

(3) During a late period of falling temperature garnet continued to grow and the biotite and chlorite reequilibrated. The biotite, chlorite, and garnet edge compositions can vary from point to point in a given thin section, indicating that the volume of equilibrium at the final stage of metamorphism was only a few cubic microns.

(4) The horizon within the garnet that grew at maximum temperature can be identified. The Mg/Fe ratio of this horizon, if the garnet composition is a limiting composition in the Al₂O₃ - K₂O - FeO - MgO tetrahedron, increases systematically with increasing metamorphic grade. Biotite and chlorite compositions also show a general increase in Mg/Fe ratio with increasing metamorphic grade, but staurolite appears to show the reverse effect.

(5) The Mg/Fe ratio at the maximum temperature horizon of the garnet porphyroblasts is a function of its Mn content as evidenced from the study of five garnet-bearing rocks, collected from one outcrop area, with the same assemblage but with differing proportions of minerals.

An important implication of zoned minerals is that the effective composition of a system in a phase lies on the join between the homogeneous minerals (if there are two) and not within three-or- four-phase fields when a zoned mineral, such as garnet or staurolite, is present in the assemblage.

Study of the three aluminum silicates found in the Kwoiek Area showed that a constant pressure change in polymorphs from andalusite to kyanite to sillimanite took place with increasing temperature. This transition series is best explained by the metastable formation of andalusite.

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