Diffusional Creep and Kinetic Demixing in Yttria-Stabilized Zirconia

The creep behavior of fine-grained yttria-stabilized zirconia with 25 mol% Y₂O₃ has been characterized as part of an investigation of kinetic demixing in solid-solution oxides which are subjected to a nonhydrostatic state of stress. At temperatures between 1400° and 1600°C, the steady-state strain rate of (Zr_0.6Y_0.4)O_1.8 samples with average grain sizes between 2.5 and 14.5 μm can be summarized by the flow law ɛ= 6.5 × 10⁻⁷σ^1.2 exp[−550 (kJ/mol)/ RT ] d ^−2.2 (s⁻¹) for stresses in the range 8 to 60 MPa, where σ is in pascals and d is in meters. This flow law indicates that deformation occurs by a Nabarro-Herring creep mechanism in which the creep rate is limited by cation lattice diffusion. Kinetic demixing was not observed in deformed polycrystalline samples even though diffusional creep was rate limited by cation lattice diffusion. This result can be explained if the cation diffusivities are approximately equal or if extensive grain rotation occurs during diffusional creep.     

Creep Behavior and Grain-Boundary Sliding in Polycrystalline A12O3

The creep properties of polycrystalline A1₂O₃ (grain size 14 to 65 μm) were examined under compressive stresses of between 4,000 and 18,000 psi (27.6 and 124 MPa) in the range 1600° to 1700°C. Two distinct types of behavior were observed. The creep rate of medium-grained specimens (14 to 30 μm) could be described by ασ^1.2 / d² where σ is the applied stress and d is the grain size. These results are consistent with the Nabarro-Herring creep mechanism. For the coarse-grained (65 μm) specimens, the creep rate was related to the stress by ασ^2.6. This behavior was not related to cracking; instead, a dislocation mechanism was thought to be rate-controlling. Considerable evidence for grain-boundary sliding was seen, and measurements showed that grain-boundary sliding contributed between 46 and 77% of the total strain in the 3 medium-grained specimens examined and between 38 and 50% in the 3 coarsegrained specimens examined.     

Compressive Creep of Beryllium Oxide-Uranium Dioxide Mixtures

Beryllium oxide-uranium dioxide mixtures were deformed in compression in the region 1375° to 1540°C. The average apparent activation energy for creep of the oxide mixtures containing up to 10 wt% uranium dioxide is 95.1 kcal/mole. The activation energy is not sensitive to the applied stress and does not vary with urania additions. Creep rate is linearly dependent on the applied stress to 6000 psi. At constant stress and temperature, creep rate dependence on grain size for BeO-10 wt% UO₂ specimens can be described by the relation ɛ∼ 1/2². The creep rate dependence on the applied stress and grain size is consistent with the Nabarro-Herring mechanism. Creep behavior of the oxide mixtures is ascribed to the deformation of the beryllium oxide matrix.     

Effect of Doping Simultaneously with Iron and Titanium on the Diffusional Creep of Polycrystalline A12O3

The effect of doping simultaneously with iron and titanium was studied in dense, polycrystalline alumina over a range of grain sizes (10 to 100 μm) and temperatures (1250° to 1550°C). In the double-doped system, the titanium concentration was varied between 0.05 and 0.15 cation %, whereas the iron-dopant level was varied between 0.05 and 6 cation %. For iron concentrations below about 2 to 3%, the aluminum vacancy concentration was dominated by the presence of quadrivalent titanium in substitutional solid solution and Nabarro-Herring diffusional creep at 1450°C was rate-limited by aluminum lattice diffusion. As the iron-dopant level was increased, the concentration of divalent iron became comparable to that of quadrivalent titanium, leading to a suppression in the cation lattice diffusivity at an iron-to-titanium ratio of ∼60. These results suggested that, at the dopant levels and temperatures studied, more than 98% of the iron was in the trivalent state. The diffusional creep of polycrystalline alumina doped with a single iron impurity (0.2 to 2%) was reinterpreted in terms of simultaneous contributions of aluminum lattice and grain-boundary diffusion, consistent with a grain-size dependence corresponding to a mixture of Nabarro-Herring and Coble creep. Aluminum grain-boundary diffusion was found to be significantly enhanced by the presence of iron in solid solution. Evidence is presented to suggest that the diffusional creep of polycrystalline Al₂O₃ doped with a single titanium dopant is interface-controlled. Interfacial kinetics can be promoted by several factors, including (1) a small grain size, (2) a high cation lattice diffusivity, (3) slow cation grain-boundary diffusion, and (4) the presence of a grain-boundary second phase.     

Creep Mechanism of Polycrystalline Yttrium Aluminum Garnet

The high-temperature deformation behavior of a fine-grained polycrystalline yttrium aluminum garnet (YAG) was studied in the temperature range of 1400° to 1610°C using constant strain rate compression tests under strain rates ranging from 10⁻⁵/s to 10⁻³/s. The stress exponent of the creep rate, the activation energy in comparison with that for single-crystal YAG, and the grain size dependence suggest that Nabarro–Herring creep rate limited by the bulk diffusion of one of the cations (Y or Al) is the operative mechanism.     

Creep of Mixed-Oxide Fuel Pellets at High Stress

The rate of steady-state compressive creep in (U,Pu)O_2-ε was investigated in the power-law creep region (at a constant stress of 69 MN/m² between 1600° and 1500°C) as a function of the oxygen-to-metal (O/M) ratio (1.88 to 1.995). The creep rate over this range is independent of the starting material and decreases with increasing O/M ratio. The apparent activation energy for creep and the preexponential structure factor are sensitive functions of the O/M ratio, with approximately the same dependence on this ratio as these parameters measured at low stresses. These results imply that diffusion of the same defect species controls creep deformation in both the stress-assisted diffusion region (ε∞σ) and the dislocation-motion region (ε∞σ^4.4).     

Creep Deformation in an Alumina–Silicon Carbide Composite Produced via a Directed Metal Oxidation Process

Flexural creep studies were conducted in a commercially available alumina matrix composite reinforced with SiC particulates (SiC_p) and aluminum metal at temperatures from 1200° to 1300°C under selected stress levels in air. The alumina composite (5 to 10 μm alumina grain size) containing 48 vol% SiC particulates and 13 vol% aluminum alloy was fabricated via a directed metal oxidation process (DIMOX(tm))† and had an external 15 μm oxide coating. Creep results indicated that the DIMOX Al₂O₃–SiC_p composite exhibited creep rates that were comparable to alumina composites reinforced with 10 vol% (8 (μm grain size) and 50 vol% (1.5 μm grain size) SiC whiskers under the employed test conditions. The DIMOX Al₂O₃–SiC_p composite exhibited a stress exponent of 2 at 1200°C and a higher exponent value (2.6) at ≥ 1260°C, which is associated with the enhanced creep cavitation. The creep mechanism in the DIMOX alumina composite was attributed to grain boundary sliding accommodated by diffusional processes. Creep damage observed in the DIMOX Al₂O₃-SiC_p composite resulted from the cavitation at alumina two-grain facets and multiple-grain junctions where aluminum alloy was present.     

Compressive Deformation of Polycrystalline UO2

The deformation of polycrystalline stoichiometric UO₂ in compression exhibits a low-temperature (<1200°C) behavior that is distinct from its high-temperature behavior. The data for both temperature regions fit either an Arrhenius equation, =ν exp [-Δ H _(τ)/ RT ], or the relation = A τⁿ/ T exp [−Δ H ₀/ RT ]. At low temperatures, the activation energy and volume, the shape of the yield-stress-temperature curve, and the grain size-strength relation suggest a Peierls mechanism as rate-controlling in the deformation process. At high temperatures (≳ 1300°C), a different dislocation mechanism becomes rate-controlling for coarse-grained material, whereas very fine-grained (1 μm) material exhibits Nabarro-Herring deformation.     

Deformation Mechanism of Fine-Grained Magnesium Aluminate Spinel Prepared Using an Alkoxide Precursor

Polycrystalline MgAl₂O₄ spinel with high purity and stoichiometric composition was prepared using alkoxide precursors. The average grain size of the polycrystal was fine (1.7 μm). The deformation mechanism of the polycrystal was investigated in air at temperatures of 1300°–1400°C. At 1300°C, oxygen lattice diffusion controlled the deformation, despite the fine grain size; however, increases in the temperature and applied stress caused cavities to nucleate and grow. Spinel possessed better creep resistance than alumina of comparative grain size. The effective diffusion coefficient was determined as follows: [formula omitted]     

Particle Size Dependence of the Electrical Conductivity of NaCl

The ac and dc conductivities of single-crystal and polycrystalline NaCl were measured as a function of both temperature and particle size. The ac conductivity results for single-crystal NaCl agreed well with the literature: intrinsic activation energy = 1.86 ev; extrinsic, impurity-controlled range = 0.74 ev; extrinsic, association range = 1.16 ev; and the intrinsic-extrinsic knee in the curve was at 10³/ T ∼ 1.4°K⁻¹ and σ₀∼ 6 × 10⁻⁸ ohm⁻¹ cm⁻¹. In the intrinsic range, however, the total conductivity (σ₀) was the sum of two ionic contributions: a steady state, nonblocked contribution (σ_θ and a blocked contribution (σ₀—σ_θ). The activation energy for the dc steady state conductivity was 1.6 ev. When the extrinsic, impurity-controlled contribution to the total conductivity was made insignificant by anion doping, the same 1.6 ev was the activation energy for the intrinsic ac conductivity at low temperatures. The data for the polycrystalline samples showed that ac conductivity increased inversely with particle size and dc steady state conductivity increased only slightly, if any, with decreasing particle size. It is postulated that the steady state conductivity is the result of the nonblocked ionic transport of sodium ions and that the ac portion of the total conductivity is due to the movement of chlorine ions which are blocked, giving rise to the polarization phenomenon. The increase in the ac conductivity with decreasing particle size is correlated with the enhanced movement of Cl⁻ in the subgrain boundary region, as has been previously shown by diffusion measurements.     

High-Temperature Creep and Kinetic Demixing in (Co,Mg)O

The creep behavior of fine-grained (Co_0.5Mg_0.5)O and (Co_0.25Mg_0.75)O has been characterized as part of an investigation of kinetic demixing in solid-solution oxides due to a nonhydrostatic stress. (i) For low stresses and small grain sizes, the dominant deformation mechanism for both compositions is diffusional creep limited by the transport of oxygen along grain boundaries. The oxygen grain-boundary diffusivity, D _o ^b is independent of oxygen partial pressure. The values of ω D _o ^b , where ω is the grain-boundary width, that have been determined from the steady-state diffusional creep rates are given by ω D _o ^b =4.7×10⁻⁸ exp[-230 (kJ/mol)/ RT ] (cm³/s) for (Co_0.5Mg_0.5)O in the range 950° to 1200°C and ω D _o ^b =7.4 × 10⁻⁸ exp[-263 (kJ/mol)/ RT ] (cm³/s) for (Co_0.25Mg_0.75)O in the range 1100° to 1250°C. Since oxygen diffusion controls the rate of diffusional creep, kinetic demixing is not observed in deformed samples of either composition. (ii) For high stresses and large grain sizes, the dominant deformation mechanism in both cases is dislocation-climb-controlled creep, where the rate of dislocation climb is controlled by oxygen lattice diffusion. Based on the positive dependence of creep rate on oxygen partial pressure, it is concluded that oxygen diffuses through the lattice by an interstitial mechanism.     

Deformation of UO2 at High Temperatures

The effects of temperature, strain rate, and grain size on the mechanical properties of UO₂ were investigated using the four-point bending technique. Strain rates were varied by two orders of magnitude, and test temperatures up to 1800°C were used. Data are presented on the ultimate tensile stress, yield stress, and plastic strain-to-fracture. Below the brittle-to-ductile transition temperature, T_c , the material fractured in a brittle manner, with no macroscopic plastic deformation. Between T_c and a second transition at a higher temperature, T_t , a small amount of plastic deformation was measured before fracture. Beyond T_t , the strength of UO₂ decreased continuously, and extensive plasticity was observed. This high-temperature plasticity was characterized by a thermally activated rate-controlling process; this behavior is consistent with observations of creep behavior under high stresses. The following phenomenological equations for the strain rate fit the data for the material with 8-μm grain size above T_t :
and
where σ_p and σ_88f are the proportional limit and steady-state flow stress, respectively, and temperature T is in °K.     

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.     

High Temperature Tensile Creep of Magnesium Oxide Single Crystals

The creep behavior and the dislocation substructure developed during creep were investigated for 〈011〉 oriented MgO single crystals creep tested in tension. Creep deformation was studied over stress and temperature ranges of 29.0 to 86.2 MN/m² and 1200 to 1500°C, and the minimum creep rate, ε, was found to obey the relation:

where σ = applied tensile stress, k = the Boltzmann constant, T = absolute temperature, n = 3.8 to 4.5, and A = ll × 10⁻² (MN/m²)^-4 s^-1. Dislocation substructures developed during creep were studied by transmission electron microscopy and etch pitting techniques. At 1400°C, the dislocation density, ρ , at 0.10 tensile creep strain depended on applied stress as ρασ ^2.1. Numerous dislocation loops and long straight dislocations were present, but subboundaries were seldom observed. The results are discussed in terms of two possible operative creep mechanisms: (1) a recovery process based on annealing out of dislocation dipoles and loops, and (2) dislocation glide limited by atmospheres of charged defects surrounding dislocations.     

High-Temperature Thermophysical Properties of Uranium Monocarbide

Thermal conductivity ( k ), electrical resistivity ( p ), total hemispherical emittance (ε_t), and normal spectral emittance (ε_0.65μ) of dense, arc-cast uranium monocarbide (5.3 wt % total carbon) were measured in the temperature range 1150° to 2050°K. The results were as follows: k , 0.057 cal/sec-cm-deg, 1200° < T < 2050°K, probable error ± 0.002; p, 20.4 × 10⁻⁶+ 114.8 T × 10⁻⁹ ohm-cm, 1175° < T < 2050°K, probable error ± 1.7 × 10⁻⁶; ε_t0.42, 1250° < T < 1980°K, probable error ± 0.02; ε_0.65 0.539 – 0.02 T × 10⁻³ 1150° < T < 1890°K, probable error ± 0.02. Experimental methods are discussed and error sources are analyzed. Uranium monocarbide exhibited typical metallic behavior in its thermophysical properties.     

High-Temperature Creep Behavior of Polycrystalline SrZrO3

The high-temperature creep behavior of sintered polycrystalline SrZrO₃ containing 1.35 wt% Fe₂O₃ was investigated as a function of temperature, stress, grain size, and strain level over the ranges 1160° to 1275°C, 780 to 3110 psi, 0.45 to 2.04 μm, and 0.0014 to 0.014, respectively. A constant-load 4-point (pure bending) method was used to load the specimens. The creep rate is time-dependent, decreasing exponentially with strain, i.e.     , where the decay constant (β=118, measured at the 1560 psi stress level over the strain range 0.0014 to 0.014) is independent of temperature and grain size. No significant grain growth occurred during creep. The activation energy of 169±10 kcal/mol obtained for creep is relatively independent of temperature, stress, grain size, and strain level over the ranges investigated. The creep rate is directly proportional to the cube of the stress and the reciprocal of the grain size; this result is consistent with nonviscous creep theories based on dislocation generation and climb as the rate-controlling deformation mechanism.     

High-Temperature Deformation of Polycrystalline Fe2O3

The effects of stress, temperature, grain size, porosity, and O₂ partial pressure on the creep of polycrystalline Fe₂O₃ were studied in the range 770° to 1105°C by tests in 4-point bending and compression. Deformation rates are controlled by the stress-directed diffusion of either oxygen or iron. Diffusion coefficients computed from the Nabarro-Herring formula modified by including an empirical porosity-correction term are also consistent with the values reported for oxygen and iron.     

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.     

Creep of Dense, Polycrystalline Magnesium Oxide

Creep of polycrystalline MgO was studied using four-point transverse bending at 1380° to 1800°K and stresses from 1000 to 5000 psi. The effects of temperature, stress, and grain size on the creep rate were determined for grain sizes from 2 to 20μ. Activation energies for creep decreased sharply with increasing grain size from 96,000 cal/mole at 2μ to 54,100 cal/mole at 5.5μ and then remained constant over the grain-size range 5.5 to 20μ. Creep was attributed in part to a stress-directed diffusional mechanism controlled by extrinsic oxygen ion diffusion in the 5.5 to 20μ grain sizes, although the calculated ionic self-diffusion rates were higher than those predicted by the Nabarro-Herring theory. It is suggested that the discrepancy may be due to a vacancy formation mechanism, which is consistent with the observed formation of dislocation substructure and preferentially distributed porosity during creep, as well as with the observed decrease in creep rate with increasing creep strain.     

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.