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High-temperature (1160 to 1450‡ C) deformation of dense polycrystalline (10 to 90 Μm) Al2O3 and MgO doped with Fe (up to 2.65 cation %) was studied by stress relaxation, dead-load creep and creep recovery. In some cases, all three deformation tests were conducted on a single specimen. A comparison of strain rate-stress data calculated from both stress relaxation and dead-load creep experiments revealed discrepancies in both the magnitude of the strain rates and the dependence between the strain rate and stress. These differences were attributed to the existence of anelastic deformation effects. The correction of stress relaxation data in the low stress regime for linear anelasticity led to strain rate-stress data in reasonably close agreement with results obtained from dead-load creep tests conducted in the viscous creep regime. Creep recovery experiments indicated that anelastic deformation in these ceramic materials was relatively insensitive to changes in temperature and grain size over the range of variables studied.

An analysis of mass transport in the diffusional creep of iron-doped, polycrystalline MgO was conducted. Creep regimes in which magnesium grain boundary, oxygen grain boundary, and magnesium-lattice diffusion were rate-controlling were identified. An analytical procedure was developed for the estimation of the diffusion constants for these three processes.

The steady state creep of polycrystalline (5–60 μm) rutile, which is doped with 1 cation % tantalum, is controlled by a Nabarro-Herring lattice diffusion process at 1100 to 1200° C. Doping with tantalum significantly depresses the steady state creep rate by lowering the concentrations of titanium interstitials and oxygen vacancies. The concentrations of these defects, and hence the steady state creep rate of doped rutile, can be increased by decreasing the oxygen partial pressure below 10−7 to 10−8 atm at 1200° C. Tentative evidence is presented in support of the hypothesis that the steady state creep of polycrystalline, undoped rutile at 950 to 1100° C is controlled by interfacial defect creation and/or annihilation at grain boundaries. Interfacial controlled deformation rates are probably due to the large concentrations (and perhaps high mobilities) of cation and anion lattice defects which are present in pure rutile equilibrated in both oxidizing and reducing atmospheres. The steady state creep rate was a very weak inverse function of the grain size and essentially independent of the oxygen partial pressure.

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.

Steady-state creep experiments were performed on hot-pressed polycrystalline MgO doped with Fe. Dead-load 4-point bend creep tests were conducted at stresses of 26 to 270 kg/cm2, at temperatures of 1250° to 1450°C, in O2 partial pressures of 1 to 10−9 atm, on specimens with grain sizes of 10 to 65 μm. Viscous steady-state creep was always observed when the grain size was stable. Experiments at variable PO2's and temperatures were used to identify regimes of high (117 ± 10 kcal/mol) and low (81 ± 5 kcal/mol) activation energy. In the latter, creep rates were nearly independent of Fe dopant concentration and PO2, whereas in the former creep rates were enhanced by increasing PO2's and Fe dopant levels. The high- and low-activation-energy regimes were interpreted as diffusional creep controlled primarily by Mg lattice diffusion and O grain-boundary diffusion, respectively.

The transient creep rate in polycrystalline Fe-doped MgO (grain size 4 to 19 μm) follows the exponential time relation The initial strain rate, , depends linearly on stress, and the relaxation time, τ, is thermally activated. Two mechanisms for the transient were considered, i.e. (1) viscous grain-boundary sliding with elastic accommodation and (2) transient diffusional creep. Although the results are not conclusive, transient diffusional creep appears to be the most promising mechanism.

Polycrystalline MgO and MgO-Fe2O3 solid solutions (0.10 to 8.08 wt% Fe2O3) were fabricated to almost theoretical density by vacuum hot-pressing. Specimens were creep-tested in air under four-point dead-load conditions between 1000° and 1400°C at stresses between 50 and 550 kg/cm2. Steady-state creep was never achieved in the experiments, which sometimes lasted more than 50 h. The strain rate vs time (t) data were described by an equation of the form =c1/(t+C2)p, which is consistent with the assumptions that creep occurs at least in part by a “viscous” mechanism and that grain growth occurs simultaneously. Doping MgO with Fe2O3 enhanced the viscous contributions to creep and inhibited the nonviscous ones. Creep rates in these specimens increased with increasing Fe2O3 additions. The occurrence of simultaneous grain growth during the high-temperature creep of magnesiowustite (i.e. MgO-Fe2O3 solid solutions) was used in establishing the strain rate vs grain size dependence. The results of this study are consistent with a transition between grain boundary and lattice diffusion mechanisms as the grain size increases (4 to 44 μan). The creep of polycrystalline MgO is a mixed process in that viscous and nonviscous (dislocation) contributions are present.

A mass transport equation which takes into account parallel diffusion paths for both anions and cations was derived and applied to the diffusional creep of polycrystalline ionic solids. From the results of the analysis, several limiting conditions were found for grain-boundary- and lattice-diffusion-controlled kinetics. These conditions depend on temperature, grain size, and type and concentration of cation impurities. Examples of these limiting situations are given for the creep of polycrystalline Fe-doped MgO and transition-metal-doped Al2O3. Summary A mass transport equation which takes into account parallel diffusion paths for anions and cations was derived and applied to the diffusional creep of polycrystalline ionic solids. The effect of grain size and cation impurities of variable valence in solid solution on the relative contributions of lattice and grain-boundary diffusion of different ionic species in polycrystalline MgO and Al2O3 was examined. Depending on the temperature, grain size, impurity level, and O2 partial pressure, several limiting conditions were found: Limit I: At very small grain sizes and reasonably small cation lattice diffusivities the creep rate will be controlled by the slower-moving ion in the grain-boundary regions (i.e. Coble creep). Limit II: For intermediate grain sizes and cation lattice diffusivities the creep rate will be controlled by cation lattice diffusion when anion transport is significantly faster near grain boundaries than in the lattice (i.e. Nabarro-Herring creep). Limit III: For an appropriate combination of large grain size and high cation lattice diffusivity the creep rate will be controlled by anion boundary diffusion (i.e. Coble creep). Well-defined examples of limits I and II have been observed in the creep of Fe-doped polycrystalline MgO, and tentative evidence exists for limit III. Most results of studies of creep in polycrystalline Al2O3 (doped and undoped) fall within limit II, with some overlap with limit III. The model developed in the present work explains much of the data in the literature in which creep rates correspond to cation lattice mobilities. It is concluded that in the creep of polycrystalline ionic solids anion transport near grain boundaries is rapid and can, in some circumstances, be rate-controlling. It should also be possible to apply this model to sintering and thermal-grooving data for such systems, particularly for Al2O3, in which cation lattice diffusion is frequently observed to be rate-controlling.32

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 Po2 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 Po2, temperature, and grain size, it was concluded that the steady-state creep of transition-metal-doped Al2O3 is controlled by cation lattice diffusion.

An analysis of strains and stresses in four-point bending creep tests in the limit of small beam deflections resulted in a general equation which relates the load-point deflection, the applied load, the creep exponent (N), and the geometrical parameters of the loading system. Measurements of load-point deflection rates, which are experimentally easy to accomplish in ceramic systems, vs the applied load lead to the direct determination of the creep exponent and the creep compliance in a steady-state creep test. The creep compliance is a function of the temperature, grain size, and all other factors except stress. The elastic equation relating the load-point deflection and the outer fiber strain is strictly valid for viscous creep and approximately valid for nonviscous creep (i.e. N>1) if the ratio of the distance between the support points to the distance between the load points is not very large.

A mixed diffusional creep mechanism in a polycrystalline ceramic can cause the apparent activation energy to vary with temperature and grain size. For mechanisms involving parallel transport paths for the same ion (e.g., cation lattice and grain-boundary diffusion), the process with the lowest activation energy will be dominant (i.e., rate-limiting) at low temperatures and the process with the highest activation energy will dominate at high temperatures. However, for mechanisms involving coupled and parallel diffusional steps (e.g., cation lattice and anion grain-boundary diffusion), the process with the lowest activation energy will be dominant at high temperatures whereas the high-activation-energy process will dominate at low temperatures. Examples of these effects are presented for the diffusional creep of polycrystalline MgO and Al/sub 2/O/sub 3/ doped with Fe. Variations in creep activation energy with grain size and temperature are only significant when the difference in activation energies for the competing processes is significant and the temperature range investigated is large.

It is well known that under conditions of small stress, fine grain size and enhanced lattice and/or grain boundary diffusion polycrystalline ceramics will deform at elevated temperatures by one or more diffusional creep mechanisms.[1–9] In this paper creep deformation maps will be utilized to illustrate the role of soluble (aliovalent) dopants, grain size, and oxygen fugacity on the relative contributions of (1) lattice diffusion, (2) grain boundary diffusion, (3) interfacial defect reactions at grain boundaries, and (4) power law or dislocation deformation mechanisms on the creep deformation of polycrystalline magnesium and aluminum oxides.

Steady-state creep experiments were performed on hot-pressed polycrystalline MgO doped with Fe. Dead-load 4-point bend creep tests were conducted at stresses of 26 to 270 kg/cm2, at temperatures of 1250° to 1450°C, in O2 partial pressures of 1 to 10−9 atm, on specimens with grain sizes of 10 to 65 μm. Viscous steady-state creep was always observed when the grain size was stable. Experiments at variable PO2's and temperatures were used to identify regimes of high (117 ± 10 kcal/mol) and low (81 ± 5 kcal/mol) activation energy. In the latter, creep rates were nearly independent of Fe dopant concentration and PO2, whereas in the former creep rates were enhanced by increasing PO2's and Fe dopant levels. The high- and low-activation-energy regimes were interpreted as diffusional creep controlled primarily by Mg lattice diffusion and O grain-boundary diffusion, respectively.

Steady state, constant load, creep experiments have been conducted on pure and doped, polycrystalline magnesium and aluminum oxides to determine: 1) the effect of solid solution impurities (e.g. Fe, Cr, Ti) on deformation mechanisms, particularly as they relate to the concentration of lattice defects 2) the effects of impurities, atmosphere, and grain size on the relative contribution to viscous deformation of lattice and grain boundary diffusion of both cationic and anionic species 3) the relative roles of viscous and non-viscous deformation mechanisms.

The high temperature deformation of iron-doped polycrystalline aluminum and magnesium oxides was studied by stress relaxation and dead-load creep. Linear and non-linear anelastic effects, which are important in stress relaxation, can lead to significant differences in apparent creep rates and strain rate-stress relationships which are inferred from dead-load creep and stress relaxation data. In the low stress regime, the effects of the major variables, such as temperature and grain size, are similar for both modes of deformation and are consistent with diffusional creep controlled by various combinations of lattice and grain boundary diffusion. In the non-viscous deformation of magnesium oxide, dead-load creep and stress relaxation testing yielded similar results in terms of the grain size effect and activation energy for deformation. However, in the case of iron-doped aluminum oxide, the stress relaxation is apparently athermal and strongly influenced by non-linear anelasticity.