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.     

Effect of Oxygen Partial Pressure on the Creep of Polycrystalline Al2O3 Doped with Cr, Fe, or Ti

Steady-state creep was studied in hot-forged polycrystalline Al₂O₃ (3 to 42 μm) of nearly theoretical density doped with≤1 cation % of Fe, Ti, or Cr. Tests were conducted at stresses between 10 and 550 kg/cm² at 1375° to 1525°C under O₂ partial pressures of 0.88 to 10⁻¹⁰ atm. Except in the 10-μm Fe-doped material tested at very small stresses, slightly nonviscous creep behavior was generally observed. The effects of P _o2 on the creep rate indicated that increased concentration of a divalent (Fe²⁺) or quadrivalent (Ti⁴⁺) impurity in solid solution enhances the creep rate of polycrystalline Al₂O₃. The activation energies for the creep of Fe- and Ti-doped Al₂O₃ samples (148 and 145 kcal/mol, respectively) were significantly higher than that for Cr-doped material (114 kcal/mol). Taking into account the effects of P_o2, temperature, and grain size, it was concluded that the steady-state creep of transition-metal-doped Al₂O₃ is controlled by cation lattice diffusion.     

Electrical Conductivity of Y2O3 as a Function of Oxygen Partial Pressure in Wet and Dry Atmospheres

The electrical conductivity of polycrystalline Y₂O₃ has been studied as a function of the partial pressure of oxygen (10^–14 to 10⁵ Pa) at 900° to 1500°C in atmospheres saturated with water vapor at 12°C or dried with P₂O₅. Yttria is a p -conductor at high oxygen activities. The p -conductivity increases with increasing P _O2 and decreases with increasing P_H2O. At low oxygen activities the oxide is a mixed ionic/electronic conductor. The ionic conductivity is approximately independent of P _O2 and increases with increasing P _H2O. In the Y₂O₃ samples, excesses of lower-valent cation impurities (in the 10 to 100 mol-ppm range) are the dominating negatively charged defects, and in the presence of water vapor they are compensated by interstitial protons. At high P _H2O levels additional protons are probably compensated by interstitial oxygen ions. At high temperatures (±1100°C) and for high P _O2 and low P _H2O, the protons are no longer dominant, and the lower-valent cations are mainly compensated by electron holes. The electrical conductivity exhibits hysteresis-like effects which are interpreted in terms of segregation/desegregation of impurities at grain boundaries. The mobility of electron holes in yttria at 1500°C is estimated to be of the order of magnitude of 0.05 cm². s^–1. V^–1     

High-Temperature Creep of Y2O3-Stabilized ZrO2

The compression creep behavior of Y₂O₃-stabilized ZrO₂ (YSZ) was studied at temperatures to 2000 ° C. The function of Y₂O₃ content and grain size was tested in specimens with various impurity concentrations and porosity distributions. For relatively fine-grained specimens, creep rates increased with the 1.5 power of the applied stress at low stresses and with the third power at high stresses. The results for coarse-grained specimens can, in general, be fit by the cube dependence. The 1.5 power can be reduced to a linear dependence by correcting for an apparent threshold stress, which decreases with increasing temperature. Creep activation energies for YSZ are 128 ± 10 kcal/mol, independent of Y₂O₃ content, impurity level, grain size, and porosity distribution. In addition, over a broad range of temperatures and stresses the absolute values of the steady-state creep rates are influenced only by grain size and O₂ partial pressure.     

Interdiffusion and Association Phenomena in the System NiO-Al2O3

The rate of formation of NiAl₂O₄ by reaction between single crystals of NiO and Al₂O₃ can be described by k = 1.1 × 10⁴ exp (−108,000 ± 5,000/ RT ) cm²/s. In NiO the behavior of D as a function of concentration supports the Lidiard theory of diffusion by impurity-vacancy pairs. A good fit of the theory to the experimental results was obtained by assuming that Al³⁺ ions diffuse as [Al_Ni· V_Ni]'pairs. The diffusion coefficient of pairs, D_p , obeys the equation 6.6 × 10⁻² exp (−54,000 ± 3,000/ RT ) cm²/s. The free energy of association for pairs was calculated to range from 6.5 kcal/mol at 1789°C to 9.0 kcal/mol at 1540°C. The interdiffusion coefficients in the spinel showed a constant small increase with increasing concentration of Al³⁺ dissolved in the spinel.     

Ion-Probe Measurement of Oxygen Self-Diffusion in Single-Crystal Al2O3

Anion self-diffusion coefficients normal to (1102) were obtained for single-crystal Al₂O₃ in a 1.3 × 10 ³ N/m² (10⁻⁵ torr) vacuum at 1585° to 1840°C. Tracer was supplied from an initial 650 to 1300 A Al₂¹⁸O₃ layer produced by the oxidation of vapor-deposited Al metal films in an ¹⁸O₂ atmosphere at 520°C. Concentration gradients extended over depths of 3000 to 5000 A and were measured by mass spectrometry of material sputtered from the samples with a beam of Ar⁺ ions. Crystals which had not been preannealed to remove surface damage displayed enhanced diffusion. Diffusion coefficients from preannealed crystals may be described by D₀ =6.4×10⁵cm²/s, with an activation energy of 188 ± 7 kcal/mol. The diffusion is interpreted as an extrinsic vacancy mechanism.     

Formation of ZnAl2O4 in the Presence of Cl2

The formation of ZnAl₂O₄ spinel in diffusion couples of Al₂O₃ and ZnO was investigated between 1000° and 1390°C in air and in air containing 4.8 vol% Cl₂ by X-ray diffraction, electron probe microanalysis, and scanning electron microscopy. The rate of formation of a spinel layer obeyed a parabolic rate law and was accelerated remarkably by the presence of Cl₂. The interdiffusion coefficient, , and the activation energy, E, were calculated to be 10⁻⁸ to 10⁻⁹ cm²/s and 123 kcal/mol (514 kJ/mol) in air and 10⁻⁷ cm²/s and 31 kcal/mol (130 kJ/mol) in air containing 4.8 vol% Cl₂, respectively.     

Creep of CaO-Stabilized ZrO2

The compressive creep of 18 mol% CaO-stabilized ZrO₂ was studied at 1200° to 1400°C and 500 to 4000 psi. The specimens were polycrystalline with grain diameters from 7 to 29 μm. The activation energy for creep is 94 kcal/mol, and the creep rates are linearly proportional to the stress and to the inverse of the grain size. These results lead to the conclusion that creep in 18 mol% CaO-stabilized ZrO₂ may be controlled by cation diffusion associated with grain-boundary sliding.     

Self-Diffusion of Er in Pure and HfO2-Doped Polycrystalline Er2O3

Using a tracer sectioning technique, the self-diffusion of Er in pure and HfO₂-doped polycrystalline Er₂O₃ was measured at 1614° to 1900°C. Up to ≊ 10 mol% HfO₂ dopant level, the Er self-diffusion coefficients followed a relation based on cation vacancies as the principal mobile defects present and available for cation diffusion. Above 10 mol% HfO₂, deviation from this relation occurred, apparently due to clustering of cation vacancies and oxygen interstitials around the dopant hafnium ions. The activation energy for the self-diffusion of Er in pure Er₂O₃ was 82.2 kcal/mol and increased with the HfO₂ dopant level present.     

Influence of Dopant Concentration on Creep Properties of Nd2O3-Doped Alumina

The microstructural features and tensile creep behavior of Al₂O₃ doped with Nd₂O₃ at levels ranging from 100 to 1000 ppm (Nd:Al atomic ratio) were systematically investigated. Compositional mapping, using both high-resolution scanning transmission electron microscopy and secondary ion mass spectroscopy revealed that, for all of the compositions studied, the Nd³⁺ ions were strongly segregated to the Al₂O₃ grain boundaries. Microstructural observations revealed that the solubility of Nd₂O₃ was between 100 and 350 ppm. Tensile creep tests were conducted over a range of temperatures (1200°–1350°C) and stresses (20–75 MPa). Both the stress and grain-size exponents were analyzed. In selected experiments, controlled grain-growth anneals were used to enable creep testing of samples of the same average grain size but different neodymium concentrations. Independent of dopant level, the neodymium additions decreased the creep rate by 2–3 orders of magnitude, compared with that of undoped Al₂O₃. The value of the apparent creep activation energy increased with increased dopant concentration and then saturated at dopant levels exceeding the solubility limit. Overall, the results of the present study were consistent with a creep-inhibition mechanism whereby oversized segregant ions reduce grain-boundary diffusivity by a site-blocking mechanism.     

Interdiffusion in the System MgO-MgAl2O4

Interdiffusion coefficients in single-crystal MgO were determined using an MgO-MgAl₂O₄ diffusion couple. For a concentration of 1 mol% Al₂O₃ in MgO, the interdiffusion coefficient can be expressed as D =2.0±0.2 exp (−76,000±3,000/ RT ) for the MgO-MgAl₂O₄ couple. This relation compares well with previous measurements in the MgO-Al₂O₃ system. The interdiffusion coefficients, which increased with the mol fraction of cation vacancies, were in the range of 10⁻⁸ to 10⁻¹⁰ cm²s⁻¹ for the concentrations and temperatures studied. Diffusion was enhanced below 1640°C if powdered MgAl₂O₄ was used. Self-diffusion coefficients for Al³⁺ ions in MgO were calculated; Al³⁺ diffuses faster than Cr³⁺ in MgO.     

Secondary Grain Growth of Li2O-A12O3-SiO2-TiO2 Glass-Ceramics

The kinetics of secondary grain growth in a Ti0₂-nucleated β-spodumene solid-solution glass-ceramic was studied. The thermal stability of the grains was excellent. Grain growth followed the cube-root-of-time law. The activation energy of the grain boundary migration was 55 ± 10 kcal/mol. Grain growth inhibition due to Ti0₂ precipitates and the residual glassy phase was closely examined. The excellent thermal stability of the grains is due to grain growth inhibition by the residual glassy phase, not by rutile precipitates. It is suggested that the diffusion of A²⁺, and probably the simultaneous diffusion of Li⁺, through the residual glass is the rate-limiting process for the grain boundary migration.     

Strength of Hot Isostatically Pressed Si3N4 After Heat Treatment in Ar-O2 and H2-H2O

The effects of heat treatment in Ar-O₂ and H₂-H₂O atmospheres on the flexural strength of hot isostatically pressed Si₃N₄ were investigated. Increases in room-temperature strength, to values significantly above that of the aspolished material, were observed when the Si₃N₄ was exposed at 1400°C to (1) H₂ with water vapor pressure ( P _H2O) greater than 1 × 10⁻⁴ MPa or (2) Ar with oxygen partial pressure ( P _O2) of between 7 × 10⁻⁶ and 1.5 × 10⁻⁵ MPa. However, the strength of the material was degraded when the P _H2O in H₂ was lower than 1 × 10⁻⁴ MPa, and essentially unaffected when the P _O2 in Ar was higher than 1.5 × 10⁻⁵ MPa. We suggest that the observed strength increases are the result of strength-limiting surface flaws being healed by a Y₂Si₂O₇ layer formed during exposure.     

The Effect of Atmosphere on the Sintering of Fe3O4 and Fe2O3 Powders at Low Temperatures

The sintering kinetics of submicrometer Fe₃O₄ and Fe₂O₃ powders were investigated at 300° to 500°C. Using measurements of the rate of reduction of surface area, the coefficients of surface diffusion on the oxides are estimated for a range of oxygen partial pressures. The surface-diffusion coefficients appear to be independent of P _O2 for magnetite and only slightly dependent on P _O2 for hematite.     

High-Temperature Creep Behavior of Mixed Conducting La0.5Sr0.5Fe1−xCoxO3-δ (0.5≤x≤1) Materials

Steady-state compressive creep rate of La_0.5Sr_0.5Fe_0.5Co_0.5O_3−δ (LSFC) and La_0.5Sr_0.5CoO_3−δ (LSC) is reported in the temperature region 900°–1050°C and stress range 5–28 MPa. The stress exponents for the two materials were 1.71±0.18 and 1.24±0.15, respectively. The activation energy for creep was considerably higher for LSC (619±56 kJ/mol) than for LSFC (392±28 kJ/mol). The grain size exponent for LSC was 1.28±0.14. Considerably higher creep rates were observed for both materials in N₂ compared with air. Relaxation by creep of chemical-induced stresses in oxygen-permeable membranes is addressed, especially at low partial pressure of oxygen.     

Superplastic Deformation in Fine-Grained YBa2Cu3O7−x

The superplastic behavior of YBa₂Cu₃O_{7− x} ceramic superconductors was studied. Large compressive deformation over 100% strain was measured in the temperature range of 775°–875°C, with a strain rate of 1 × 10⁻⁵ to 1 × 10⁻³/s, and a grain size of 0.5–1.4 μm. The nature of the deformation was investigated in terms of three deformation parameters: the stress exponent ( n ), the grain size exponent ( p ), and the activation energy ( Q ). The measured values of these parameters were n = 2 ± 0.3, p = 2.7 ± 0.7, and Q = 745 ± 100 kJ/mol. With the aid of the deformation map, the deformation mechanism was identified as grain boundary sliding accommodated by grain boundary diffusion. The conclusion is consistent with the microstructural observations made by SEM and TEM: the invariance of equiaxed grain shape, the absence of significant dislocation activity, no grain boundary second phases, and no significant texture development.     

Equilibria of SiF4 with SiO2, Be2SiO4, and BeO in Molten Li2BeF4

Equilibrium partial pressures of SiF₄ were measured for the reactions 2SiO₂( c )+2BeF₂( d )⇋SiF₄( g )+Be₂SiO₄( c ) (log P _siF4(mm) = [8.790 - 7620/ T ] ±0.06(500°–640°C)) and Be₂SiO₄( c ) +2BeF₂( d )⇋SiF₄( g ) +4BeO( c )(log P _siF4(mm) = [9.530–9400/T] ±0.04 (700°–780°C)), wherein BeF₂ was present in solution with LiF as molten Li₂BeF₄. The solubility of SiF₄ was low (∼0.04 mol kg^-1 atm^-1) in the melt. The results for the first equilibrium were combined with available thermochemical data to calculate improved Δ H_f and Δ G_f values for phenacite (–497.57 ±2.2 and –470.22±2.2 kcal, respectively, at 298°K). The few measurements above 700°C for the second equilibrium are consistent with the temperature of the subsolidus decomposition of phenacite to BeO and SiO₂ and with the heat of this decomposition as determined by Holm and Kleppa. Below 700°C, the pressures of SiF₄ generated showed an increasing positive deviation from the expression given for the equilibrium involving Be₂SiO₄ and BeO. This deviation might have been caused by the formation of an unidentified phase below 700°C which replaced the BeO; it more likely resulted from a metastable equilibrium involving BeO and SiO₂.     

Oxidation Kinetics of Single-Crystal SrTiO3

The oxidation kinetics were determined for single-crystal SrTiO₃ by measuring the time and temperature dependence of the weight gain of reduced crystals. The oxidation can be described as a diffusion-controlled process. The calculated diffusion coefficients between 850° and 1460°C are represented by D = 0.33 exp (-22.5 ± 5.0 kcal/ RT ) cm²/sec. Directly measured oxygen ion diffusion coefficients in the same temperature interval reported earlier are interpreted as being extrinsic and can be represented by D = 5.2 × 10⁻⁶ exp (-26.1 ± 5.0 kcal/ RT ) cm²/sec, where the activation energy is for mobility only. Assuming that the calculated diffusion coefficients are for vacancy diffusion and the two activation energies are equivalent within experimental error, a vacancy concentration (fraction of vacant lattice sites), [O□], fixed by impurities in the fully oxidized crystal is calculated to be 1.6 × 10⁻⁵ by virtue of the relation between the oxygen self-diffusion coefficient, D_02-, and the oxygen vacancy diffusion coefficient, D_o□ ; D _o2-= [O□] D _o□ where the oxygen ion concentration [O^2-] is taken as unity.     

Kinetics of Solid-State Reaction of Bi2O3 and Fe2O3

Solid-state reactions of equimolar mixtures of Bi₂O₃ and Fe₂O₃ from 625° to 830°C and their kinetics were investigated. The reaction rates were determined from the integrated X-ray diffraction intensities of the strongest peaks of the reactants and products. The activation energy for the formation of BiFeO₃ was 96.6±9.0 kcal/mol; that for a second-phase compound, Bi₂Fe₄O₉, which formed above 675°C, was 99.4±9.0 kcal/mol. Specific rate constants for these simultaneous reactions were obtained. The preparation of single-phase BiFeO₃ from the stoichiometric mixture of Bi₂O₃ and Fe₂O₃ is discussed.     

Vapor Pressure, Enthalpy, Evaporation Coefficient, and Enthalpy of Activation of the Beryllium Nitride (Be3N2) Decomposition Reaction

Beryllium nitride (Be₃N₂) vaporizes congruently in the range 1640° to 1960°K by the reaction Be, N₂( c ) = 3Be( g ) + N₂( g ). The equilibrium nitrogen partial pressure, in atmospheres, at the composition for congruent sublimation is given by the expression log P _N2= [(–1.952 ± 0.038) × 10⁴] T ⁻¹+ (6.509 ± 0.207). The measured enthalpy of decomposition (370 ± 5 kcal at 298° K) yields an enthalpy of formation for Be₃N₂( c ) of –136 ± 6 kcal/mole. The upper limit to the evaporation coefficient at 1600° to 2000°K can be set as 10^–4 by comparison of equilibrium data to Langmuir data obtained with a sample of 18% porosity. The apparent enthalpy of activation for the reaction is 409 ± 7 kcal/mole at 1800°K for the porous Langmuir specimen. An expression is developed to predict the temperature dependence of the reduced apparent pressures in Knudsen studies of substances with low evaporation coefficients in terms of the enthalpy of activation. The variation in temperature dependence of the Langmuir measurements and Knudsen measurements with three different-sized orifices is consistent with predictions from this expression.