Interdiffusion in the System SrF2-BaF2

A microprobe study of interdiffusion between 1033° and 1238°C in the system SrF₂-BaF₂ was conducted using single crystals. The interdiffusion coefficient, D , generally decreased with increasing SrF₂ concentration, but the composition dependence of D decreased with decreasing temperature. Extrapolation of D values to infinite dilution allowed the impurity cation self- diffusion coefficients:

The values for D_Sr in BaF₂ are in excellent agreement with tracer results. An analysis of the activation energies for cations diffusing in alkaline-earth fluorides shows a direct correlation between constriction ratio and migration energy for a single ion diffusing in different fluorides. An apparent anomaly arises when attempting to correlate migration energy with structural information for different cations diffusing in the same fluoride.     

Anion Diffusion in α-Cr2O3

Oxygen-18 exchange between gaseous oxygen, held at a pressure of 125 mm Hg in a Pt10Rh chamber, and spheres of α-Cr₂O₃ containing three or less grains was determined from 1100° to 1450°C. Isotope equilibrium on crystal surfaces appears to be quickly established, and the rate-determining factor is self-diffusion conforming to the relation D = 15.9 exp(-101,000/ RT) cm²sec⁻¹. Changing sphere diameters caused no detectable variation in diffusion coefficients. Anions are the much slower diffusing species in this oxide.     

Determination of the Si Diffusing Unit in the System Na2O-CaO-SiO2 Using a Multiatomic Ion Model

The composition of the diffusing unit for silicon was determined for the system Na₂O-CaO-SiO₂ at 1200°C from an analysis of the concentration distributions in interdiffusion using a multiatomic ion model described in terms of self-diffusion coefficients of constituent elements. The results indicated that silicon diffuses in a 7-membered ring form and that the number of Si atoms in the silicate ion is not less than 35.     

Creep Deformation in MgO-Saturated Large-Grain-Size Al2O3

Samples of 65 μm-grain-size AL₂O₃ containing 0.05 wt% Mg and 40 μm-grain-size AL₂O₃ containing 0.13 wt% Mg, both MgO-saturated, undergo compressive deformation in the range 1580° to 1800°C with results interpreted as diffusional creep rate-limited by grain-boundary diffusion with the Coble boundary-diffusion model giving
A lower deformation rate for an unsaturated composition indicates that MgO additions enhance grain-boundary diffusion.     

Oxygen Self-Diffusion in Single-Crystal Y2O3

Self-diffusion coefficients of the oxygen ion in single-crystal Y₂O₃ were determined by the gas-solid isotope exchange technique. The results in the range 1100° to 1500°C are described by D=7.3 X 10^-6 exp [-19l(kJ/mol)/RT] cm²/s. Comparison of the results with those for oxides with the fluorite-type structure indicates that the regularly arranged vacant anion sites in the C-type structure do not contribute eflectively to oxygen ion diffusion .     

Diffusion and Reaction Studies in the System Al2O3-SiO2

High-temperature diffusion kinetics and phase relations between couples of fused SiO₂ or cristobalite and sapphire or mullite were investigated in air and in helium. Subsolidus liquid formation between sapphire and cristobalite indicates the existence of a metastable system without mullite. A liquid phase is considered to be essential for the nucleation of mullite. The growth rate of mullite exceeded its dissolution rate in semi-infinite fused-SiO₂-sapphire couples above 1634°C. The inter-facial liquid compositions provided data for a minor revision of the mullite liquidus curve. Diffusion coefficients calculated from the Al profiles vary greatly with concentration and temperature, resulting in a large range of values for apparent activation energy, which decreases with increasing Al₂O₃ content (∼310 to ∼60 kcal/mol for ∼4 to ∼22 wt% Al₂O₃). The diffusion process in the liquid is considered to be cooperative movement of oxygen-containing Al and Si complexes whose nature changes with composition and temperature; this change in the diffusing species contributes to the range in the values of experimental apparent activation energies.     

Concurrent Measurement of Volume, Grain-Boundary, and Surface Diffusion Coefficients in the System NiO-Al2O3

Surface, grain-boundary, and volume inter diffusion coefficients for the NiO-Al₂O₃ system were measured concurrently by using a diffusion couple consisting of an A1₂O₃ bicrystal and an NiO single crystal. The A1₂O₃ bicrystals having various tilt angles were fabricated by firing 2 single crystals to be joined in an H₂ atmosphere at 1800°C for 30 h. Diffusion profiles over the surface, along the grain boundary, and in the bulk of the bicrystal were determined with an electron probe microanalyzer. Mathematical analysis of the diffusion profiles gives D _s = 7.41×10^-2 exp (-35,200/ RT ), D _gb = 2.14×10^-1 exp (-63,100/ RT ) (tilt angle =30°), and D _v = 1.26×10⁴ exp (-104,000/ RT ). The grain-boundary diffusion coefficient increases with the mismatch at the boundary.     

Interdiffusion Coefficients in SiO2-K2O Melts

Chemical diffusion coefficients for Si were measured in potassium silicate compositions containing from 64 to 85 wt% SiO₂; unidirectional diffusion couples were heated for 0.1 to 720 h at 600° to 1400°C. The diffusion coefficients, which were calculated by the Boltzmann-Matano method, are described for a silicate containing 70 wt% SiO₂ by:
The diffusion coefficients decreased with increasing O₂ pressure. Below 800°C, the coefficients decreased with increasing SiO₂ concentration; above 800°C, their dependence on SiO₂ concentration was too weak to detect by the methods used. On the basis of a simple structural model for the glass, it was possible, from a phenomenological analysis of the diffusion, to establish a relation between the oxygen self-diffusion coefficient and the chemical diffusion coefficient for a given composition.     

Activity–Composition Relations in NiAl2O4─MnAl2O4 Solid Solutions and Stabilities of NiAl2O4 and MnAl2O4 at 1300° and 1400°C

Activities of NiO were measured in the oxide and spinel solutions of the system MnO–NiO–Al₂O₃ at 1300° and 1400° C with the aim of deriving information on the thermodynamic properties of the spinel phases. Synthetic samples in selected phase assemblages of the system were equilibrated with metallic nickel and a gas phase of known oxygen partial pressures at a total pressure of 1 atm. The data on NiO activities and directions of conjugation lines between coexisting oxide and spinel phases were used to establish the activity–composition relations in spinel solid solutions at 1300° and 1400°C. The MnAl₂O₄–NiAl₂O₄ solid solutions exhibit considerable negative deviations from ideality at these temperatures. The free energy of formation of MnAl₂O₄ from its oxide components (MnO + Al₂O₃) at 1300° and 1400°C is calculated to be −24.97 and −26.56 kJ. mol⁻¹, respectively. The activities determined in the stoichiometric spinel solid solutions are more negative as compared with those predicted from cation distribution models.     

Phase Diagrams for the Systems MgCl2-MgF2, CaCl2-MgF2, and NaCl-MgF2

Equilibrium phase diagrams for the systems MgCl₂-MgF₂, CaCl₂-MgF₂ and NaCl-MgF₂ were determined by differential thermal analysis, thermal analysis, and temperature-composition equilibrium techniques. Simple eutectics were observed at 78.0±0.5 mol% MgCl₂ and 628°±2°C in the MgCl₂-MgF₂ system, at 87.5±0.5 mol% CaCl₂ and 694°±2°C in the CaCl₂-MgF₂ system, and at 95.5±0.5 mol% NaCl and 786°±3°C in the NaCl-MgF₂ system. The phase diagrams determined for these systems were compared with phase diagrams that were computed using Temkin's model. The phase diagrams of the CaCl₂-MgF₂ and NaCl-MgF₂ systems were also compared with diagrams that were computed using the expression suggested by Flood et al. for reciprocal systems. The experimentally determined and computed phase diagrams agreed for the MgCl₂-MgF₂ system but not for the CaCl₂-MgF₂ and NaCl-MgF₂ systems.     

Activity–Composition Relations in MnCr2O4–CoCr2O4 Solid Solutions and Stabilities of MnCr2O4 and CoCr2O4 at 1300°C

Phase equilibria in the system MnO–CoO–Cr₂O₃ were investigated at 1300°C under controlled oxygen partial pressures by using the gas equilibration technique. The CoO activities in various phase assemblages of the system were measured by determining the partial pressures of oxygen in the gas phase for coexistence with metallic cobalt. The activity data revealed that at 1300°C, MnO–CoO and MnCr₂O₄–CoCr₂O₄ solid solutions exhibit mild positive departures from ideal behavior. The activities in the stoichiometric spinel solutions were found to be in good agreement with those predicted from a model based on cation distribution equilibria. The standard free energy of formation of the compound CoCr₂O₄ from its oxide components at 1300°C was determined as −37 636 J/mol, while that for MnCr₂O₄ was found as −44 316 J/mol.     

Equilibrium Cation Distribution in NiAl2O4, CuAl2O4, and ZnAl2O4 Spinels

Stoichiometric NiAl₂O₄, CuAl₂O₄, and ZnAl₂O₄ spinels were prepared and equilibrated at temperatures from 600° to 1400°C. The parameters u and x , denoting the oxygen position and fraction of divalent cations on tetrahedral sites, respectively, were determined from a detailed X-ray diffraction analysis. In NiAl₂O₄, x increased from 0.07 at 595° to 0.26 at 1391°C; in CuAl₂O₄, x decreased from 0.68 at 613° to 0.64 at 1195°C; and in ZnAl₂O₄, x decreased from 0.96 at 905° to 0.94 at 1197°C. The form of the temperature dependence of x could not be described using theoretically based equations advanced in the literature. A more general equation which allows for a non-distributional contribution to the configurational entropy was derived and observed to properly describe the temperature dependence; the results indicate that short-range order is of definite significance in these intermediate aluminate spinels.     

Sintering and Grain-Growth Kinetics of MgAl2O4

The sintering and grain-growth kinetics of finely divided MgAl₂O₄ were determined from 1300° to 1600°C for densities up to 96% of theoretical. These results show that sintering is governed by volume diffusion and that the temperature dependence of the diffusivities is 157 exp [(-118 kcal/mol)/ RT ] cm²/s. Grain growth follows the expression ( G ²- G ₀²)= Kt , where K =51.3 exp [(-110 kcal/mol)/ RT ] cm²/s.     

Measurement of Oxygen Diffusion in Dy2O3 and Gd2O3 by Studying High-Temperature Oxidation of the Metals

Studies of the oxidation of Gd and Dy at P _O2's from 10^−0.3 to 10^−14.5 atm and temperatures from 727° to 1327°C indicate both semiconducting and ionic-conducting domains in the sesquioxides formed. At higher temperatures, where dense coarsegrained oxide layers developed, the rate of oxidation in the high- P ₀₂ semiconducting domain yielded oxygen diffusion coefficients in Dy₂O₃ in excellent agreement with literature values derived from oxidation of partially reduced oxide single crystals. Under the same conditions, the oxidation of Gd yielded oxygen diffusion coefficients in cubic Gd₂O₃ which are considerably below literature values for monoclinic single-crystal Gd₂O₃. At lower temperatures, porous scales were formed, and apparent diffusion coefficients derived from oxidation rates show a smaller temperature dependence than the high-temperature data. At low P _O2, the oxides behave as ionic conductors, and metal oxidation rates result in estimates of the electronic contribution to the electrical conductivity of the order of 10⁻⁶ to 10⁻⁷Ω⁻¹ cm⁻¹.     

Subsolidus Equilibria in the TiO2-SnO2 System

The subsolidus miscibility gap for the TiO₂-SnO₂ system was redetermined. The critical temperature, 1430°C, is intermediate between that determined by Padurow, 1330°C, and that determined by Garcia and Speidel, 1475°C. Although the phase boundary is slightly asymmetric (the critical composition occurs at 47 mol% TiO₂), it fits the regular-solution model down to 1200°C. Calculations of the coherent spinodal using the regular-solution model indicated depression of the spinodal below T_c , by 105°, 310°, and 387° for composition fluctuations along the [001], <101>, and <100> directions, respectively. These depressions of the spinodal are much greater than those calculated by Stubican and Schultz; this discrepancy is believed to result from an error in the latter workers' calculations. During the present work, positive deviations from Vegard's law were found in this system. Both the magnitude and the sign of the deviation can be predicted using a theory based on nonlinear second-order elasticity.     

Orientation Relationships of Reactively Grown Ba6Ti17O40 and Ba2TiSi2O8 on BaTiO3 (001) Determined by X-ray Diffractometry

Fresnoite grows at 700° and 800°C, and Ba₆Ti₇O₄₀ grows at 1200°C with definite orientations, which are determined by X-ray diffraction pole figure analysis. Partially textured fresnoite is formed at higher temperatures. The SiO₂ films react with the BaTiO₃ crystals, forming the phases Ba₂TiSi₂O₈ (fresnoite) and Ba₆Ti₁₇O₄₀. At 700° and 800°C, both phases grow with definite orientations, which are determined by X-ray diffraction pole figure analysis. Partially textured polycrystalline phases are formed at higher temperatures.     

Effect of Homovalent Framework Cation Substitutions on the Sodium Ion Conductivity in Na3Zr2Si2PO12

The reported activation volume for sodium ion transport in the fast-ion conductor Na₃Zr₂Si₂PO₁₂ is surprisingly large. Therefore, attempts were made to alter the size of the diffusion channels through partial substitution of As, Ge, Ti, Th, and Hffor the framework cations to decrease geometric structural hinderance of the diffusion process. Sodium ion conductivity is improved at temperatures below 200°C far the Hf substitutions. The existence and electrical properties of the apparently isostructural Na₃Hf₂Si₂PO₁₂, which has a room-temperature conductivity of 1.0Ω10⁻³Ω cm⁻¹, are reported.     

Zirconium–Hafnium Interdiffusion in Polycrystalline Fluorite-Cubic CeO2─ZrO2─HfO2 Solid Solution

Zr–Hf interdiffusion was studied in the temperature range of 1650° to 1850°C in air for polycrystalline fluorite-cubic systems of 90CeO₂·10(Zr_{1- x} Hf _x )O₂ and 60CeO₂·40(Zr_{1- x} Hf _x )O₂. Lattice and grain-boundary diffusion parameters were calculated from the Zr–Hf concentration distributions by using the grain-boundary diffusion equation of Oishi and Ichimura. The cation iattice diffusivity was close to that in the fluorite-cubic Y₂O₂-ZrO₂ solid solution.     

Phase Equilibria in the System HfO2–Y2O3–CaO

Phase equilibria in the system HfO₂–Y₂O₃–CaO were studied in the temperature range 1250° to 2850°C by both experimental methods (X-ray phase analysis at 20° to 2000°C, petrography, annealing and quenching, differential thermal analysis in He at temperatures to 2500°C, thermal analysis in air using a solar furnace at temperatures to 3000°C, and electron microprobe X-ray analysis) and theoretical means (development of a mathematical model for the liquidus surface by means of the reduced polynomial method). Phase equilibria were determined by the structure of the restricting binary systems. No ternary compounds were found. The liquidus was characterized by the presence of six four-phase, invariant equilibria. Solid solutions were based on monoclinic (M), tetragonal (T), and cubic (F) modifications of HfO₂; C and H forms of Y₂O₃; CaO; and CaHfO₃ that crystallized in two polymorphous modifications, namely, the cubic and rhombic perovskite-type structure.     

Coherent Precipitation in the System MgO-Al2O3-Cr2O3

An isothermal section of the ternary system MgO–Al₂O₃-Cr₂O₃ was determined at 1700°± 15°C to delineate the stability field for spinel crystalline solutions (cs). Crystalline solutions were found between the pseudobinary joins MgAl₂O₄–Cr₂O₃ and MgCr₂O₄-Al₂O₃, and the binary join MgAl₂O₄-MgO. The first two crystalline solutions exhibit cation vacancy models while the latter can probably be designated as a cation interstitial model. Precipitation from spinel cs may proceed directly to an equilibrium phase, (Al_1-xCr_x)₂O₃, with the corundum structure or through a metastable phase of the probable composition Mg(Al_1-xC_r)₂₆O₄₀. The composition and temperature limits were defined where the precipitation occurs via metastable monoclinic phases. The coherency of the metastable monoclinic phase with the spinel cs matrix can be understood by considering volume changes with equivalent numbers of oxygens and known crystallographic orientation relations. Electron probe and metallographic microscope investigations showed no preferential grain boundary precipitation.