Average Grain Size in Polycrystalline Ceramics

A model is proposed which realistically characterizes the grain structure of polycrystalline ceramics. The average grain size of a log-normal distribution of grain sizes with tetrakaidecahedral (truncated octahedral) shape is related to the average intercept size by a proportionality constant. This result can be used to determine the average grain size of a sintered powder compact composed of nontextured grains which shows no discontinuous grain growth.     

Strength-Grain Size-Porosity Relations in Alumina

Experimental measurements of the coincident effects of grain size G and porosity P on the transverse bend strength S of alumina at 25° and 120°C are shown to follow the relations

respectively. Brittle fracture in bending appears to be controlled at both temperatures by a Griffith-Orowan mechanism in which preexisting surface defects, produced during grinding, are propagated to fracture at a critical level of stress

The effects of grain size and temperature on strength may be interpreted largely in terms of changes in the parameters E , γ, and c₀. The effect of porosity on strength is complicated by the apparently beneficial role played by relatively large pores. Such pores appear to interfere with crack propagation by locally reducing the elastic stress concentration at the crack front. This porosity-crack interaction produces characteristic patterns on the fracture surface and appears to become more significant with increasing grain size. It is considered to be responsible for the decreasing porosity dependence of strength with increasing grain size and the decreasing grain size dependence with increasing porosity.     

Surface Finish Effects and the Strength-Grain Size Relation in SiC

The effect of surface finish on the strength-grain size relation was investigated for dense hot-pressed SiC. Failure initiated predominantly via the propagation of extrinsic machining-induced flaws for the range of grain sizes and machining grit sizes studied. These results are consistent with the region of large-grain-size flaw control as delineated by Prochazka and Charles. The severity of machining-induced flaws, relative to the machining grit size, decreased with increasing machining grit size and decreasing SiC grain size.     

Chemical Strengthening of Polycrystalline Ceramics

The feasibility of strengthening polycrystalline ceramic bodies by low-expansion solid solution surface layers was established. Failure, by shearing of the surface layers, was prevented by establishing gradual variations in composition and in thermal expansion coefficient which, in turn, resulted in gradual variations in stresses and reduction of the maximum shear stress. Titania ceramics were strengthened by TiO₂-SnC₂ surface layers and alumina ceramics were strengthened by Al₂O₃-Cr₂O₃ surface layers.     

Impurity Distribution in Polycrystalline Aluminum Nitride Ceramics

Convergent-beam electron diffraction and diffuse darkfield imaging of transmission electron microscopy were used to obtain qualitative information regarding the distribution of impurities in polycrystalline AIN. Impurities are distributed homogeneously within the grains of a given ceramic, but an amorphous grain-boundary phase on the order of 1 to 2 nm in thickness is observed between the AIN matrix grains.     

Oxygen Grain-Boundary Diffusion in Polycrystalline Mullite Ceramics

Oxygen tracer diffusivities of low- and high-alumina mullite ceramics (72 wt% Al₂O₃, 28 wt% SiO₂ and 78 wt% Al₂O₃, 22 wt% SiO₂, respectively) were determined. Gas/solid exchange experiments were conducted in an atmosphere enriched in the rare stable isotope ¹⁸O, and the resulting ¹⁸O isotope depth distributions were analyzed using SIMS depth profiling. The investigation showed that grain-boundary diffusivities for both mullite ceramics were several orders of magnitude higher than mullite volume diffusivity. Activation enthalpies of oxygen diffusion were 363 ± 25 kJ/mol for the low-alumina and 548 ± 46 kJ/mol for the high-alumina materials. Because the glassy grain-boundary films were not identified, the differences between the low- and high-alumina materials might be explained by different impurity concentrations in the grain boundaries of the two materials.     

Thermal Conditioning of Polycrystalline Alumina Ceramics

High-alumina ceramics, thermally conditioned by reheating to a temperature near the normal maturing temperature and cooling rapidly in forced air, showed significant increases in physical and dielectric strengths over as-fired specimens. A mechanism for the strength increase is proposed as the prevention of exsolution of components soluble in either a major or minor crystalline phase. Experimental evidence is presented to support this theory. Reheating a polycrystalline, polyphase alumina ceramic relieves internal stresses caused by volume changes associated with exsolution that occurs during slow kiln cooling. Rapid cooling, following the reheating, inhibits exsolution. Spinel cell size and strength of an alumina ceramic containing spinel are correlated. Evidence is presented to show that the dominant thermal-conditioning mechanism is a volume effect and not the surface effect present in tempered glass.     

Activation Energies in the Diffusional Creep of Polycrystalline Ceramics

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 A1₂O₃ 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.     

Hardness–Grain-Size Relations in Ceramics

Both Vickers and Knoop hardness ( H ), measured at two or more loads in the range of 100–2000 g (most commonly 100 and 500 g) for a variety of dense oxide and non-oxide materials, covering a range of grain sizes ( G ), including single crystals where possible, were shown to generally be consistent with (often more limited) literature data. Apparently, conflicting trends of H (1) showing either no G dependence, (2) decreasing from single-crystal or large G values with decreasing G , or (3) having the generally accepted increase with decreasing G are shown to be due to the combination of the limited extent of data and H generally heing determined by two basic trends. These two trends are (a) the normal inverse G (i.e., H–G ^−1/2) dependence at finer G , (b) a variable G minimum at intermediate G , and (c) H increasing with increasing G at larger G (to. single-crystal values). The H minimum is due to local cracking around the indent (mostly along grain boundaries), generally reaching a maximum effect, e.g., minimum in H , when the indent and grain sizes are similar, and tends to be greater for Vickers vs Knoop indents, higher loads and probably greater grain boundary Impurity, additive contents, and stresses.     

A Diffuse Interface Description of Intergranular Films in Polycrystalline Ceramics

The thermodynamic equilibrium between a thin liquid phase and adjoining grains of a co-existing solid phase is treated, using a diffuse interface formulation applied to a multilayer of liquid and solid phases. The analysis leads to spatial variation in composition, which minimizes the overall free energy. The overall energy includes a gradient-energy contribution. For a fixed overall composition, the equilibrium concentration profile is dependent on the thicknesses of the two phases, relative to the interface width (a characteristic-length scale in the analysis). When the thickness of the liquid phase approaches the characteristic length, its composition can deviate markedly from the bulk liquid-phase composition. In the absence of any stabilizing interactions, such as repulsive structural and electrostatic forces, the analysis indicates that there is a driving force for thinning of the film and a minimum thickness exists at which it becomes favorable for the film to dissolve. Therefore, the observations of equilibrium film thicknesses in certain ceramics imply that, in those materials, additional stabilizing forces must exist between the grains.     

Stress Measurement in Single-Crystal and Polycrystalline Ceramics Using Their Optical Fluorescence

A general methodology is developed for determining the state of stress and the numerical value of the stresses from observed shifts and broadening of optical fluorescence lines. The method is based on the piezospectroscopic properties of single crystals. We present general relationships between the measured fluorescence shifts and the stress state for a number of illustrative cases, pertinent to both polycrystalline and single-crystal ceramics under stress. These include measuring the stresses applied to polycrystalline ceramics, the residual stress distribution due to crystallographically anisotropic thermal expansion, and the stresses applied to single crystals. Using the recently implemented technique of performing the fluorescence measurements in an optical microprobe, we also provide experimental tests of the relationships derived.     

Resistivity-Microstructure Relations in Lithia-Stabilized Polycrystalline β"-Alumina

The sodium ion resistivity of lithia-stabilized polycrystalline β"-alumina was measured as a function of temperature for fine-grained and coarse-grained specimens with a chemical composition of 8.80 Na₂0-0.75 Li₂O-90.45 A1₂O₃ (wt%). A model is presented which explains the dependence of sodium ion resistivity on grain size. Using the model the activation energy was determined for the transport of sodium ions across a grain boundary in this form of sodium β"-alumina.     

Strength-Anisotropy-Grain Size Relations in Ceramic Oxides

On the basis of high strengths observed at small grain size and crack formation observed at moderate grain size, a large grain-size dependence of the strength of rutile ceramics was predicted. This dependence was investigated by experiment, and a grain-size exponent greater than -1/3 was found. Tabulating literature data on the grain-size dependence of strength and the degree of anisotropy of several oxide ceramics demonstrated a correlation between the degree of anisotropy and the grain-size exponents; the grain-size exponent increases with increasing anisotropy. The mechanism of fracture of single-phase ceramics composed of anisotropic crystals is discussed.     

Solid-State Reactive Sintering of Transparent Polycrystalline Nd:YAG Ceramics

Transparent polycrystalline Nd:YAG ceramics were fabricated by solid-state reactive sintering a mixture of commercial Al₂O₃, Y₂O₃, and Nd₂O₃ powders. The powders were mixed in methanol and doped with 0.5 wt% tetraethoxysilane (TEOS), dried, and pressed. Pressed samples were sintered from 1700° to 1850°C in vacuum without calcination. Transparent fully dense samples with average grain sizes of ∼50 μm were obtained at 1800°C for all Nd₂O₃ levels studied (0, 1, 3, and 5 at.%). The sintering temperature was little affected by Nd concentration, but SiO₂ doping lowered the sintering temperature by ∼100°C. Abnormal grain growth was frequently observed in samples sintered at 1850°C. The Nd concentration was determined by energy-dispersive spectroscopy to be uniform throughout the samples. The in-line transmittance was >80% in the 350–900 nm range regardless of the Nd concentration. The best 1 at.% Nd:YAG ceramics (2 mm thick) achieved 84% transmittance, which is equivalent to 0.9 at.% Nd:YAG single crystals grown by the Czochralski method.     

Stress Relaxation of Polycrystalline Ceramics with Grain-Boundary Sliding and Grain Interlocking

The stress relaxation of two-phase polycrystalline ceramics has been examined. A two-dimensional array of elastic hexagonal grains embedded in a contiguous fluid has been used as a model for grain-boundary sliding and grain interlocking. The viscoelastic constitutive equation, in a phenomenological sense, is of a nonlinear Maxwell type; the model is composed of a strain-dependent dashpot and an elastic spring connected in series. The squeezing-in/out processes and mechanisms of grain-boundary fluid essentially result in the rheological nonlinearity. The experimental results in stress-relaxation tests of a β-spodumene glass-ceramic under simple shear are characterized from the standpoint of the nonlinear constitutive equation. It is emphasized that the stress-relaxation test is one of the important test techniques that enables one to study quantitatively the rheological behavior of polycrystalline ceramics with grain-boundary sliding and grain interlocking without any of the difficulties and ambiguities that are accompanied by stress-induced grain-boundary cavities, which so often appear in conventional creep tests.     

Fracture Toughness of Polycrystalline Ceramics in Combined Mode I and Mode II Loading

Fracture of Polycrystalline alumina and zirconia ceramics in combined mode I and mode II loading was studied using precracked disk specimens in diametral compression. Fracture toughness was assessed in different stress states (including pure mode I, combined mode I and mode II, and pure mode II) by aligning the center crack at specific angles relative to the loading diameter. The resulting mixed-mode fracture-toughness envelope showed significant deviation to higher fracture toughness in mode II relative to the predictions of the linear elastic fracture mechanics theory. Critical comparison with corresponding results on soda–lime glass and fracture-surface observations showed that crack-surface resistances arising from grain interlocking and abrasion were the main sources of the increased fracture resistance in mode II loading of the polycrystalline ceramics. Quantitative fractography confirmed an increased percentage of transgranular fracture of the grains in mode II loading.     

Ex-Situ Stress Measurements in Polycrystalline Ceramics Using Photo-Stimulated Luminescence Spectroscopy and High-Energy X-Rays

The photo-stimulated luminescence spectroscopy (PSLS) technique provides the means to establish stress dependencies of the well-known R -line peak positions in polycrystalline alumina. The uniaxial compression tests presented in this paper, which determine the coefficients describing this piezospectroscopic (PS) behavior, tackle two previously unexplored areas. Firstly, the vibronic band peaks in the emission spectrum are introduced here, and the PS coefficients of several peaks within these bands are established. These results set the foundation for the exploitation of vibronic band peakshifts, along with the R -lines, in order to provide the non-symmetric components of the stress tensor and therefore the measurement of the complete stress state in polycrystalline alumina. Secondly, high-energy X-rays serve as an ex-situ stress measurement method upon which the optical fluorescence shifts are based, thereby advancing the accuracy of PS coefficient determination in a unique approach. The results of PSLS and synchrotron X-ray experiments are presented here and used in conjunction to reveal new information on the PS behavior of polycrystalline alumina.