The conditions for structural transitions at the core of a grain boundary separating two crystals was investigated with a diffuse interface model that incorporates disorder and crystal orientation ͓Kobayashi et al., Physica D 140, 141 ͑2000͔͒. The model predicts that limited structural disorder near the grain boundary core can be favorable below the melting point. This disordered material is a precursor to a liquid phase and therefore the model represents grain boundary premelting. This model is shown to be isomorphic to Cahn's critical point wetting theory ͓J.W. Cahn, J. Chem. Phys. 66, 3667 ͑1977͔͒ and predicts first-and higher-order structural grain boundary transitions. A graphical construction predicts the equilibrium grain boundary core disorder, the grain boundary energy density, and the relative stability of multiple grain boundary "complexions." The graphical construction permits qualitative inference of the effect of model properties, such as empirical homogeneous free energy density and assumed gradient energy coefficients, on properties. A quantitative criterion is derived which determines whether a first-order grain boundary transition will occur. In those systems where first-order transition does occur, they are limited to intermediate grain-boundary misorientations and to a limited range of temperatures below the melting point. Larger misorientations lead to continuously increasing disorder up to the melting point at which the disorder matches a liquid state. Smaller misorientation continuously disorder but are not completely disordered at the melting point. Characteristic grain boundary widths and energies are calculated as is the width's divergence behavior at the melting point. Grain boundary phase diagrams are produced. The relations between the model's predictions and atomistic simulations and with experimental observations are examined.

A thermodynamic diffuse interface analysis predicts that grain boundary transitions in solute absorption are coupled to localized structural order-disorder transitions. An example calculation of a planar grain boundary using a symmetric binary alloy shows that first-order boundary transitions can be predicted as a function of the crystallographic grain boundary misorientation and empirical gradient coefficients. The predictions are compared to published experimental observations.

o f G e r m a n y 94720 kawrence Herkelcy IAoratory, Ilniversity of California, Herkeley, California Silicon nitride materials typically reveal thin amorphous intergranular films along grain boundaries, with only the exception of special boundaries. It is known that such grainboundary films strongly affect the high-temperature properties of the bulk material. High-resolution electron microscopy (HKEM) was used to study these amorphous films in different Si,N, ceramics. The observed film thicknesses at grain boundaries in these materials varied between 5 and 15 #. It was shown that the grain-boundary film thickness strongly depends on film chemistry. Careful inspections of film-thickness measurements across grain boundaries in a given material suggest that the film widths vary on the order of 1 A. Therefore, a quantitative evaluation should allow for the determination of the standard deviation of the film thickness. The amorphous film widths along grain boundaries in four materials were measured over the entire length (up to 1 pm) of the grain boundary between two triple points. Forty to fifty data points were evaluated for each boundary, giving a Gaussian-like distribution of the film thickness around a median value, which corresponded well with the film width measured from single HREM micrographs. The accuracy achieved by the statistical method was better than 4 1 A.

Two different electron energy loss spectroscopy (EELS) quantitative analytical methods for obtaining complete compositions from interface regions are applied to ultrathin oxide-based amorphous grain boundary (GB) films of ∼ 1 nm thickness in high-purity HIPed Si3N4 ceramics. The first method, 1, is a quantification of the segregation excess at interfaces for all the elements, including the bulk constituents such as silicon and nitrogen; this yields a GB film composition of SiN0.49±1.4O1.02±0.42 when combined with the average film thickness from high resolution electron microscopy (HREM). The second method, II, is based on an EELS near-edge structure (ELNES) analysis of the Si–L2,3 edge of thin GB films which permits a subtraction procedure that yields a completeEELS spectrum, e.g., that also includes the O–K and N–K edges, explicitly for the GB film. From analysis of these spectra, the film composition is directly obtained as SiN0.63±0.19O1.44±0.33, close to the one obtained by the first method but with much better statistical quality. The improved quality results from the fewer assumptions made in method II; while in method I uniform thickness and illumination condition have to beassumed, and correction of such effects yields an extra systematic error. Method II is convenient as it does not depend on the film thickness detected by HREM, nor suffer from material lost by preferential thinning at the GB. In addition, a chemical width for these films can be deduced as 1.33 ± 0.25 nm, that depends on an estimation of film density based on its composition. Such a chemical width is in good agreement with the structural thickness determined by HREM, with a small difference that is probably due to the different way in which these techniques probe the GB film. The GB film compositions are both nonstoichiometric, but in an opposite sense, this discrepancy is probably due to different ways of treating the surface oxidation layers in both methods.

Thick-film resistors are electrical composites containing ultrafine particles of ruthenate conductor (Pb,Ru,O, in the present materials) distributed in a highly modified silicate glass. We show that conductor particles remain flocced in the absence of any applied or capillary pressures, but are separated at equilibrium by a nanometer-thick film of glass. Microstructures show evidence for liquid-phase sintering, i.e., contact flattening of particles, under van der Waals attraction alone. Titania addition, which in dilute concentrations markedly increases the resistivity, decreases the temperature coefficient of resistance, and improves voltage stability and noise, is found to increase the equilibrium film thickness between particles by a few angstroms. STEM analyses show that the added titania preferentially concentrates in the silicate-rich grain boundary film, as well as at particle-glass interfaces. The roles of interparticle forces and adsorption on the glass film thickness with and without titania are discussed. The large increase in resistivity caused by titania additions is attributed to the increase in film thickness as well as to local chemical changes of two possible types. Titania enrichment within the glass film itself is expected to decrease the local ruthenium ion solubility, and this along with the possible formation of a more insulating titania-substituted surface layer on ruthenate grains will decrease the tunneling conductivity between conductor grains.

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The mechanical behavior of four rare earth (RE)‐Mg‐doped Si3N4 ceramics (RE=La, Lu, Y, Yb) with varying grain‐boundary adhesion has been examined with emphasis on materials containing La and Lu (which represent the extremes of RE ionic radius). Fracture‐resistance curves (R‐curves) for all ceramics rose very steeply initially, giving them exceptional strength and relative insensitivity to flaw size. The highest strength was seen in the Lu‐doped material, which may be explained by its steeper initial R‐curve; the highest “apparent” toughness (for fracture from millimeter‐scale micronotches) was seen in the lowest strength La‐doped material, which may be explained by its slowly rising R‐curve at longer crack lengths. Excellent agreement was found between the predicted strengths from R‐curves and the actual strengths for failures originating from natural flaws, a result attributed to careful estimation of the early part of the R‐curve by deducing the intrinsic toughness, K0, and the fact that this portion of the R‐curve is relatively insensitive to sample geometry. Finally, it was found that RE elements with relatively large ionic radius (e.g., La) tended to result in lower grain‐boundary adhesion. This implies that there is a small window of optimal grain‐boundary adhesion which can lead to the fastest rising R‐curves (for short cracks) and the highest strengths. The importance of this work is that it reinforces the notion that factors which contribute to the early part of the R‐curve are critical for the design of ceramic microstructures with both high strength and high toughness.

Quantitative analyses of the local chemistry of amorphous films at the grain boundary (GB) were taken on hot isostatically pressed high-purity Si 3 N 4 doped with various amounts of calcium (up to 450 ppm). This work was mainly accomplished by using spatially resolved electron energyloss spectroscopy (EELS) in a dedicated scanning transmission electron microscope. The amount of calcium segregation, quantified in terms of GB excess, saturated in the films at a bulk-doping level of ∼220 ppm. Extra additives did not stay at the triple-point glass pockets, where the calcium was almost expelled completely; instead, the additives stayed at intersections between the films and pockets. Otherwise, the calcium distribution was uniform along and across GB films. The latter was determined from simulations of EELS profiling. At grain/pocket interfaces, a much-lower segregation level occurred, ranging from one-half to one-tenth of the level at the GB. This observation indicates different segregation mechanisms in the two cases. Also, the calcium segregation in GB films changed the film composition dramatically, because more N 3− ions were introduced and replaced O 2− ions, to maintain the local stoichiometry. Reduction of the Van der Waals force has been proposed as being the origin of the film expansion with increasing calcium content.