Computer simulation of grain growth—I. Kinetics

The addition of reactive elements can have a significant effect on the oxidation behavior of alumina- and chromia-forming alloys. A model has been developed to explain the effects associated with the addition of reactive elements that is based on the segregation of reactive-element ions to scale grain boundaries and the metal-oxide interface. Reactive-element ions use these interaces as pathways for diffusion from the metal substrate to the gas interface of the scale. The driving force for this outward diffusion is the oxygen potential gradient across the scale. Doping of the scale grain boundaries results in scale growth primarily by inward oxygen diffusion, while doping at the metal-oxide interface slows the growth of interfacial voids and thus improves scale adhesion.

Experimental observations in support of the dynamic-segregation theory to explain the reactive-element effect

Creep of ceramics: Part 1 Mechanical characteristics

The oxidation behavior of an Fe-27%Cr-4%Al alloy and similar alloys containing 0.023% and 0.82% Y in 1 atm oxygen at 1200°C has been examined. The oxide formed on the yttrium-free alloy develops a highly convoluted configuration, apparently resulting from lateral growth of the oxide. The latter leads to oxide detachment from the alloy at temperature and extensive spalling during cooling. It is postulated that lateral growth results from the formation of oxide within the existing oxide layer by reaction between oxygen diffusing inward down the oxide grain boundaries and aluminum diffusing outward through the bulk oxide. Additions of yttrium to the alloy apparently prevent the formation of oxide within the oxide layer, the oxide-forming reaction occurring as the alloy-oxide interface. Thus lateral growth is prevented and spalling during cooling does not occur. Secondary advantages conferred by the addition of 0.82% Y to the alloy are the prevention of void formation at the alloy-oxide interface, the avoidance of alloy grain growth during oxidation, and the creation of an oxide “keying” or “pegging” effect.

The influence of yttrium additions on the oxide-scale adhesion to an iron-chromium-aluminum alloy

Computer modelling has been carried out to study normal grain growth in three dimensions. The approach consists of digitizing the microstructure by dividing the polycrystalline material into small volume elements and storing the spatial location and crystallographic orientation of each element. An energy is assigned between each element and its neighbours, such that neighbours having unlike orientations provide weaker bonding than neighbours of like orientations. The annealing treatment during which grain growth occurs is simulated using a Monte Carlo technique in which elements are selected at random and thermally activated transitions to other orientations are attempted. With time, the system evolves so as to reduce the total grain interface area. The microstructures produced are in good correspondence to observations of pure metals and ceramics which have undergone grain growth. Power-law kinetics ([Rbar] = ct n) are observed, with a growth exponent in three dimensions of n = 0·48 ±0·04 in the...

Computer simulation of normal grain growth in three dimensions

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.

Calculation of Stresses and Strains in Four-Point Bending Creep Tests

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.

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

Grain growth was studied at 1300°, 1400°, and 1500°C in nearly theoretically dense (0.1 to 0.8% porosity) hot-pressed magnesium oxide (99.99+%) and magnesiowustite (0.10 and 0.48 wt% Fe2O3). Small amounts of porosity had large effects on the kinetics of grain growth. Grain growth is probably porosity-controlled in MgO at all temperatures and in magnesiowustite at 1400° and 1500°C if pores remain on grain boundaries or at grain intersections. The tendency for the entrapment of porosity is enhanced as the temperature is increased and as the dopant (Fe2O8) concentration is decreased. Small amounts of porosity (<1%) can cause limiting growth situations at grain sizes well below 100 μm. The Fe2O3 dopant stabilizes squared grain growth kinetics at 1300°C and decreases the rate of grain growth at all three temperatures.

Effect of Small Amounts of Porosity on Grain Growth in Hot‐Pressed Magnesium Oxide and Magnesiowustite

Origin of Anomalously High Activation Energies in Sintering and Creep of Impure Refractory Oxides

Das stationare Kriechverhalten von fast zu theoretischer Dichte heisgeprestem Al2O3 mit Fe, Ti oder Cr-Dotierungen 1% wird untersucht.

G. W. Hollenberg

Papers

Calculation of Stresses and Strains in Four-Point Bending Creep Tests

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

Effect of Small Amounts of Porosity on Grain Growth in Hot‐Pressed Magnesium Oxide and Magnesiowustite

Origin of Anomalously High Activation Energies in Sintering and Creep of Impure Refractory Oxides

Einfluss des sauerstoffpartialdrucks auf das kriechen von mit cr, fe oder ti dotiertem polykristallinen al2o3