Showing papers on "Grain boundary published in 1994"

A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes

Abstract: A new algorithm based upon a 2-dimensional Cellular Automaton (CA) technique is proposed for the simulation of dendritic grain formation during solidification. The CA model takes into account the heterogeneous nucleation, the growth kinetics and the preferential growth directions of the dendrites. This new CA algorithm, which applies to non-uniform temperature situations, is fully coupled to an enthalpybased Finite Element (FE) heat flow calculation. At each time-step, the temperature at the cell locations is interpolated from those at the FE nodal points in order to calculate the nucleation-growth of grains. The latent heat released by the cells and calculated using a Scheil-type approximation is fed back into the FE nodal points. The coupled CA-FE model is applied to two solidification experiments, the Bridgman growth of an organic alloy and the one-dimensional solidification of an Al-7wt% Si alloy. In the first case, the predicted boundaries between grains are in good agreement with experiment, providing the CA cell size is of the order of the dendrite spacing. For the second experiment, the quality of the coupled CA-FE model is assessed based upon grain structures and cooling curves. The columnar-to-equiaxed transition and the occurrence of a recalescence are shown to be in good agreement with the model.

Remanence and coercivity in isotropic nanocrystalline permanent magnets.

Abstract: Numerical micromagnetic calculations rigorously describe the correlation between the microstructure and the magnetic properties of nanocrystalline permanent magnets. In isotropic nanocrystalline permanent magnets exchange interactions override the anisotropy of the individual grains. Therefore the spontaneous magnetic polarization deviates from the easy axes in a region along the grain boundaries. For a fine grain structure with a mean grain size d20 nm the remanence is considerably enhanced, since the volume fraction of the boundary regions where the spontaneous magnetic polarization points towards the direction of the applied field becomes significantly high. The inhomogeneous ground state, however, favors the nucleation of reversed domains leading to a reduction of the coercive field with decreasing grain size. A uniform grain structure with a very small range in grain size avoids large demagnetizing fields and thus preserves a high coercivity. For a grain size of 10 nm isotropic two-phase permanent magnets based on ${\mathrm{Fe}}_{14}$${\mathrm{Nd}}_{2}$B and \ensuremath{\alpha}-Fe show remarkable high-energy products, because the volume fraction of the magnetically soft phase can be increased up to 50% without a significant loss of coercivity.

Deformation behaviour of ultra-fine-grained copper

Abstract: Mechanical behaviour and structural changes, such as the evolution of grain and dislocation structures and the formation of slip lines and grain-boundary-sliding traces, of a submicron-grained (SMG) copper during room-temperature compression have been studied. It is suggested that the absorption of dislocations into grain boundaries (GBs) is due to the migration and sliding of some highly non-equilibrium GBs during the deformation process and is influenced by high level internal stresses. From this point of view, the unusual behaviour of SMG copper, in particular, the high yielding and flow stresses, the absence of strain hardening, high plasticity and low strain rate sensitivity, are explained. Analogies of the mechanical behaviour of SMG copper with mechanical properties of metallic materials at large plastic strains in stage IV are discussed.

A unified approach to grain boundary sliding in creep and superplasticity

Abstract: Rachinger grain boundary sliding is a characteristic of high temperature deformation in both creep when the grain size is large ( d > λ ) and superplasticity when the grain size is small ( d λ ), where d and λ are the grain size and the subgrain size, respectively. An analytical procedure is used to determine the rate equation for Rachinger sliding when d > λ . Data for superplastic metals are examined to give the rate equation for Rachinger sliding when d λ . A unified model is developed for Rachinger sliding at all grain sizes, where the rate of sliding is controlled by the rate of accomodation through intragranular slip. It is demonstrated that the predictions of this model are in good agreement with experimental data under both creep and superplastic conditions.

The intrinsic stress of polycrystalline and epitaxial thin metal films

Abstract: It is well known that thin films develop large intrinsic stress during their preparation. The intrinsic stress either originates from strained regions within the films (grain boundaries, dislocations, voids, impurities, etc.) or at the film/substrate (lattice mismatch, different thermal expansion, etc) and film/vacuum interfaces (surface stress, adsorption, etc.) or is due to dynamic processes (recrystallization, interdiffusion, etc). Since the magnitude of most of these stress contributions is directly related to film morphology, important structural information can be extracted from measurements of the intrinsic stress. This article presents a thorough discussion of today's understanding of the growth of thin films and reviews the related atomistic mechanisms responsible for intrinsic stress. On the basis of these ideas recent experimental results on the intrinsic stress of UHV deposited polycrystalline and epitaxial thin metal films are discussed. Depending on the respective growth mode of the films-Volmer-Weber, Stranski-Krastanov and Frank-Van der Merwe modes-characteristic stress behaviours are observed. In situ intrinsic stress measurements are therefore a promising new technique to gain additional insight into film growth.

Mechanical properties of nanophase metals

Abstract: Nanophase metals have grain-size dependent mechanical properties that are significantly different than those of their coarse-grained counterparts. Pure metals are much stronger and apparently less ductile than conventional ones; intermetallics are also strengthened, but they tend toward increased ductility at the smallest grain sizes. These property changes are primarily related to grain size limitations, but they are also affected by the large percentage of atoms in grain boundaries and other microstructural features. Strengthening appears to result from a limitation of dislocation activity, while increased ductility probably relates to grain boundary sliding. A brief overview of our present understanding of the mechanical properties of nanophase metals is presented.

Hardness-grain-size relations in ceramics

Abstract: 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.

First Principles Determination of the Effects of Phosphorus and Boron on Iron Grain Boundary Cohesion

Abstract: Toward an electronic level understanding of intergranular embrittlement and its control in steels, the effects of phosphorus and boron impurities on the energy and electronic properties of both an iron grain boundary and its corresponding intergranular fracture surface are investigated by the local density full potential augmented plane wave method. When structural relaxations are taken into account, the calculated energy difference of phosphorus in the two environments is consistent with its measured embrittlement potency. In contrast to the nonhybridized interaction of iron and phosphorus, iron-boron hybridization permits covalent bonding normal to the boundary contributing to cohesion enhancement. Insights into bonding behavior offer the potential for new directions in alloy composition for improvement of grain boundary-sensitive properties.

Investigation of Pt/Ti bilayer metallization on silicon for ferroelectric thin film integration

Abstract: The stabilities of Pt/Ti bilayer metallizations in an oxidizing atmosphere have been investigated with several thicknesses of interfacial Ti‐bonding layers. Reactions in the Pt/Ti/SiO2/Si interface were examined as a function of various annealing conditions in the temperature range 200–800 °C by using Rutherford backscattering spectrometry, Auger electron spectroscopy, x‐ray diffraction, and transmission electron microscopy. Thermal treatment in oxygen was found to cause rapid oxidation of the Ti layer, accompanied by the migration of Ti into the Pt film. Diffusion of oxygen through the Pt grain boundaries was mainly responsible for the adverse reactions at the interface and loss of mechanical integrity. Thin Ti (10 nm) layers resulted in the depletion of the interfacial bonding layer causing serious adhesion problems, whereas thicker Ti films (100 nm) caused the formation of TiO2−x in the Pt‐grain boundaries, ultimately encapsulating the Pt surface with an insulating TiO2 layer. Improved stability and adhesion in the Pt/Ti bilayer metallization compatible with ferroelectric thin film processing, were achieved by incorporating well reacted thin TiO2 layers in situ, and depositing Pt films at a high temperature.

Effect of Grain Size on Hertzian Contact Damage in Alumina

Abstract: The role of microstructural scale on deformation-microfracture damage induced by contact with spheres is investigated in monophase alumina ceramics over a range 3--48 [mu]m in grain size. Measurement of a universal indentation stress-strain curve indicates a critical contact pressure [approx] 5 GPa, above which irreversible deformation occurs in alumina. A novel sectioning technique identifies the deformation elements as intragrain shear faults, predominantly crystallographic twins, within a confining subsurface zone of intense compression-shear stress. The twins concentrate the shear stresses at the grain boundaries and, above a threshold grain size, initiate tensile intergranular microcracks. Below this threshold size, classical Hertzian cone fractures initiate outside the contact circle. Above the threshold, the density and scale of subsurface-zone microcracks increase dramatically with increasing grain size, ultimately dominating the cone fractures. The damage process is stochastic, highlighting the microstructural discreteness of the initial deformation field; those grains which lie in the upper tail of the grain-size distribution and which have favorable crystallographic orientation relative to local shear stresses in the contact field are preferentially activated. Initial flaw state is not an important factor, because the contact process creates its own flaw population. These and other generic features of the damage process will be discussedmore » in relation to microstructural design of polycrystalline ceramics.« less

Grain Boundary Defect Chemistry of Acceptor‐Doped Titanates: Space Charge Layer Width

Abstract: The grain boundary space charge depletion layers in acceptor-doped SrTiO3 and BaTiO3 ceramics were investigated by impedance spectroscopy in the time and frequency domain. Based on the layer width and its dependence on the acceptor concentration, the temperature, and the oxygen partial pressure during annealing, a suggestion for a refined Schottky model is proposed. The local distribution of the donor-type grain boundary states causing the depletion layer and the resulting band bending are discussed.

An evaluation of the strain contributed by grain boundary sliding in superplasticity

Abstract: Grain boundary sliding is an important mode of deformation in superplasticity. Measurements of the contribution of sliding to the total strain generally give values of about 50–70% so that there is an apparent “missing strain” of about 30–50%. It is demonstrated that the experimental method used to measure the sliding contribution will lead to estimates in the range of about 45–90% even when all the deformation is by grain boundary sliding and the associated accommodation process. Since the problem of accommodation is less severe at the specimen surface, it is shown that estimates of the sliding contribution from surface marker lines will tend to lie at the lower end of this predicted range. It is concluded that grain boundary sliding accounts for essentially all the deformation under optimum superplastic conditions and there is no “missing strain” of about 30–50%.

High Li+ Conducting Ceramics

Abstract: In this Account, the authors describe one of the most suitable ways for preparing a high Li+ conducting polycrystalline material An excellent conductivity was realized by detailed studies of both the lattice size in the Li+ migrating bulk (intragrain) and the condition of the grain boundaries (integrain) 55 refs, 8 figs, 1 tab

Structure and properties of nanocrystalline materials

Abstract: The present article reviews the current status of research and development on the structure and properties of nanocrystalline materials. Nanocrystalline materials are polycrystalline materials with grain sizes of up to about 100 nm. Because of the extremely small dimensions, a large fraction of the atoms in these materials is located at the grain boundaries, and this confers special attributes. Nanocrystalline materials can be prepared by inert gas-condensation, mechanical alloying, plasma deposition, spray conversion processing, and many other methods. These have been briefly reviewed. A clear picture of the structure of nanocrystalline materials is emerging only now. Whereas the earlier studies reasoned out that the structure of grain boundaries in nanocrystalline materials was quite different from that in coarse-grained materials, recent studies using spectroscopy, high-resolution electron microscopy, and computer simulation techniques showed unambiguously that the structure of the grain boundaries is the same in both nanocrystalline and coarse-grained materials. A critical analysis of this aspect and grain growth is presented. The properties of nanocrystalline materials are very often superior to those of conventional polycrystalline coarse-grained materials. Nanocrystalline materials exhibit increased strength/hardness, enhanced diffusivity, improved ductility/toughness, reduced density, reduced elastic modulus, higher electrical resistivity, increased specific heat, higher thermal expansion coefficient, lower thermal conductivity, and superior soft magnetic properties in comparison to conventional coarse-grained materials. Recent results on these properties, with special emphasis on mechanical properties, have been discussed. New concepts of nanocomposites and nanoglasses are also being investigated with special emphasis on ceramic composites to increase their strength and toughness. Even though no components made of nanocrystalline materials are in use in any application now, there appears to be a great potential for applications in the near future. The extensive investigations in recent years on structure-property correlations in nanocrystalline materials have begun to unravel the complexities of these materials, and paved the way for successful exploitation of the alloy design principles to synthesize better materials than hitherto available.

Modelling the effect of deformation-induced vacancies on segregation and precipitation

Abstract: The influence of deformation-induced excess vacancies on segregation and on precipitation is discussed within a phenomenological framework. During high temperature deformation, vacancies are mainly generated by the non-conservative movement of thermal jogs. Sinks for these vacancies are dislocations and grain boundaries. The excess vacancy concentration increases with strain rate and inverse temperature. Stronger effects are expected in f.c.c. materials because of their comparatively low diffusivities; in austenitic steels, the concentrations of deformation-induced vacancies are predicted to be significant, even at temperatures as high as 0.75 of the melting temperature. At the high strain rates (> 10 s −1 ) used in industrial rolling, the vacancy concentration may attain levels 2–3 orders-of-magnitude higher than the equilibrium one. One consequence of the presence of deformation-induced vacancies is the non-equilibrium segregation of boron observed e.g. in austenitic Nb-B steels, where it stimulates the nucleation of Nb borocarbonitrides.

Equilibrium pore surfaces, sintering stresses and constitutive equations for the intermediate and late stages of sintering—II. Diffusional densification and creep

Abstract: Constitutive equations for the intermediate and late stages of sintering are derived assuming grain boundary diffusion to be the controlling transport mechanism. The surface of the pore space is assumed to be in equilibrium. Numerical results for the shape of equilibrium surfaces are taken from a companion paper [J. Svoboda, H. Riedel and H. Zipse, Acta metall. mater.42, 435 (1994)]. For open porosity the contacts between grains turn out to be nearly circular in all cases, so that the diffusion problem in the contact areas can be solved readily. The macroscopic response of the powder compact can then be built up of the mechanical and the surface tension forces acting across the contacts. The analysis is carried out for a random, or homogeneous distribution of contacts around each particle, and for simple cubic, body-centered cubic, and face-centered cubic grain arrangements. The cubic viscosities are averaged using various methods, the best of which appears to be the self-consistent method.

Direct Determination of Grain Boundary Atomic Structure in SrTiO3

Abstract: An atomic structure model for a 25° [001] symmetric tilt grain boundary in SrTiO3 has been determined directly from experimental data with the use of high-resolution Z-contrast imaging coupled with electron energy loss spectroscopy. The derived model of the grain boundary was refined by bond-valence sum calculations and reveals candidate sites for dopant atoms in the boundary plane. These results show how the combined techniques can be used to deduce the atomic structure of defects and interfaces without recourse to preconceived structural models or image simulations.

Equilibrium pore surfaces, sintering stresses and constitutive equations for the intermediate and late stages of sintering—I. computation of equilibrium surfaces

Abstract: The intermediate stage of sintering is characterized by equilibrium surfaces of the open pore space between the grains. These doubly curved surfaces are determined numerically for the three cubic arrangements of grains (simple cubic, b.c.c. and f.c.c). The numerical program constructs surfaces of constant mean curvature connected via the dihedral angle to grain boundaries having zero mean curvature. The pore morphologies resulting from the analysis are different from the conventional picture of interconnected pore channels along grain edges. According to the present results, open porosity rather consists of interconnected pillow-shaped gaps between next-nearest grain neighbors. The transition to closed porosity occurs when the connections between these gaps close, a process which leads to relatively large isolated pores on two-grain junctions between former next-nearest neighbors. The numerical results for the contact areas between grains and for the sintering stress are approximated by quadratic functions of the pore volume fraction and of the dihedral angle, and the best-fit coefficients are tabulated. The results are used in a companion paper in which constitutive equations for the mechanical behavior during sintering are derived.

The impact of grain boundary character distribution on fracture in polycrystals

Abstract: The importance of structural effects on intergranular fracture is discussed in order to understand, predict and control fracture in polycrystals. The heterogeneity of fracture in a polycrystal has been found to be due to the difference in structure-dependent propensity to intergranular fracture among grain boundaries. The grain boundary character distribution (GBCD) which describes the type and frequency of grain boundaries is shown to be one of important microstructural factors affecting fracture processes and characteristics. A recent prediction of GBCD-controlled toughness and brittle-ductile transition is introduced. The importance of the connectivity of grain boundaries, the so-called grain boundary correlation number, is also discussed. Recent successful achievement of the control of intergranular brittleness is presented as an application of the result of basic research on fracture to the control of intergranular brittleness by grain boundary design and control in advanced materials.

The study of grain size dependence of yield stress of copper for a wide grain size range

Abstract: Room temperature yield strength of copper has been measured by means of miniaturized disk-bend test as a function of grain size ranging from about 30 nm to 180 μm. It has been established that grain size dependence of strength does not obey the Hall-Petch relation in the entire range of grain sizes studied. The results obtained suggest that a gradual change of deformation mechanism takes place with decreasing grain size. Nanostructured samples appear to be rather ductile.

Polycrystalline silicon thin films processed with silicon ion implantation and subsequent solid-phase crystallization: Theory, experiments, and thin-film transistor applications

Abstract: A review is presented of the self‐implantation method which has been developed to achieve high‐quality polycrystalline silicon thin films on insulators with enhanced grain sizes and its applications to thin‐film transistors (TFTs). In this method, silicon ions are implanted into an as‐deposited polycrystalline silicon thin film to amorphize most of the film structure. Depending on ion implantation conditions, some seeds with 〈110〉 orientation remain in the film structure due to channeling. The film is then thermally annealed at relatively low temperatures, typically in the range of 550–700 °C. With optimized process conditions, average grain sizes of 1 μm or greater can be obtained. First, an overview is given of the thin‐film transistor technology which has been the greatest motivation for the research and development of the self‐implantation method. Then the mechanism of selective amorphization by the silicon self‐implantation and the crystallization by thermal annealing is discussed. An analytical mode...

Fundamental Aspect of Texture Formation in Low Carbon Steel.

Abstract: The mechanism of the texture formation in low carbon steels is not fully understood as yed. To clarify this, a series of systematic investigations has been made. Summarizing these results and comparing these with those of other investigations, possible mechanisms of texture formation are discussed. In polycrystalline iron, deformation and recrystallization in grain boundary regions play the most important role in the texture formation. In this respect, results obtained on single and bi-crystals do not provide much informations. In polycrystals, crystal rotation occurs during rolling along different paths from that observed in single crystals, affected by grain boundary constraints significantly. Approaches to the stable end orientation seems to be closely related with the development of the stable dislocation substructures. The development of the rolling texture is therefore strongly affected by the metallurgical factors that influence the evolution of the dislocation substructures. {111} recrystallized grains seem to be formed from the grain boundary regions of the same orientation through the subgrain growth mechanism.

Alloy thermodynamics in nanostructures

Abstract: The importance of the interactions between alloy atoms and topological defects for the thermodynamic properties of nanostructured alloys is pointed out. The McLean model for grain boundary segregation is extended to yield an expression for the total Gibbs free energy of an alloy polycrystal. This provides a simple conceptual basis for a qualitative discussion of the thermodynamic properties of nanocrystalline alloys. It is demonstrated that certain alloy poly- or nanocrystals may reach a metastable state, where the alloy is stable with respect to variation of its total grain boundary area.

Improvement of grain size and deposition rate of microcrystalline silicon by use of very high frequency glow discharge

Abstract: The influence of the plasma excitation frequency on the growth conditions and the material properties of microcrystalline silicon prepared by plasma enhanced chemical vapor deposition at low deposition temperature is investigated. It is found that an increase of the plasma excitation frequency leads to a simultaneous increase of the growth rate, the grain size, and the Hall mobility of microcrystalline silicon. This is attributed to an effective selective etching of disordered material creating more space to develop crystalline grains, while also more species for faster growth of the crystallites are available.

Current-voltage characteristics of ultrafine-grained ferroelectric Pb(Zr, Ti)O 3 thin films

Abstract: Room-temperature current-voltage dependence of ultrafine-grained ferroelectric Pb(Zr, Ti)O3 thin films has been investigated. Both strong varistor type behavior and space charge limited conduction (SCLC) were observed. Differences in the current-voltage characteristics are attributed to differences in the nature of the grain boundaries resulting from variations in processing conditions. The strong varistor type behavior is believed to be due to the presence of highly resistive grain boundaries and thus may be termed grain boundary limited conduction (GBLC). A double-depletion-layer barrier model is used to describe the origin of high resistivity of the grain boundaries. It is suggested that the barrier height varies significantly with the applied field due to the nonlinear ferroelectric polarization, and that the barrier is overcome by tunneling at sufficiently high fields. In some other cases, the resistivity of the grain boundaries is comparable to that of the grains, and therefore the intrinsically heterogeneous films degenerate into quasi-homogeneous media, to which the SCLC theory is applicable. As such, a unified grain boundary modeling reconciles different types of conduction mechanisms in the ultrafine-grained ferroelectric thin films. This grain boundary modeling also well accounts for some other dc-related phenomena observed, including abnormal current-voltage dependencies, remanent polarization effect, electrode interface effect, and unusual charging and discharging transients. In addition, many other electrical properties of the ferroelectric films may be better understood by taking the effect of grain boundaries into account.

Thin Glass Film between Ultrafine Conductor Particles in Thick-Film Resistors

Abstract: Thick-film resistors are electrical composites containing ultrafine particles of ruthenate conductor (Pb[sub 2]Ru[sub 2]O[sub 7] in the present materials) distributed in a highly modified silicate glass. The authors 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 moremore » insulating titania-substituted surface layer on ruthenate grains will decrease the tunneling conductivity between conductor grains.« less

Fabrication and mechanical behaviour of Al2O3/Mo nanocomposites

Abstract: Two types of Al2O3/Mo composites were fabricated by hot-pressing a mixture of γ- or α-Al2O3 powder and a fine molybdenum powder. For Al2O3/5 vol% Mo composite using γ-Al2O3 as a starting powder, the elongated molybdenum layers were observed to surround a part of the Al2O3 grains, which resulted in an apparent high value of fracture toughness (7.1 Mpa m1/2). In the system using α-Al2O3 as a starting powder, nanometre sized molybdenum particles were dispersed within the Al2O3 grains and at the grain boundaries. Thus, it was confirmed that ceramic/metal nanocomposite was successfully fabricated in the Al2O3/Mo composite system. With increasing molybdenum content, the elongated molybdenum particles were formed at Al2O3 grain boundaries. Considerable improvements of mechanical properties were observed, such as hardness of 19.2 GPa, fracture strength of 884 MPa and toughness of 7.6 MPa m1/2 in the composites containing 5, 7.5, 20 vol% Mo, respectively; however, they were not enhanced simultaneously. The relationships between microstructure and mechanical properties are also discussed.

Effect of atmosphere on the PTCR properties of BaTiO3 ceramics

Abstract: The influence of low-temperature annealing, at < 360 °C, in various reducing and oxidizing atmospheres for a series of BaTiO3 ceramics with a positive temperature coefficient of resistance (PTCR) is discussed. Combined impedance and modulus spectroscopy is used to analyse a.c. impedance data and shows that the total resistance of the sample can be composed of up to three components, dependent on the cooling rate from the sintering temperature. For quickly cooled samples the PTCR response is dominated by an outer shell on individuals grains, whereas for slowly cooled samples the grain boundary resistance dominates. Annealing in reducing atmospheres destroys the grain boundary PTCR effect whereas the outer-shell grain PTCR effect is relatively insensitive to the reducing atmosphere. It is proposed that the acceptor states responsible for the outer-grain and grain-boundary PTCR effects are predominantly intrinsic metal vacancies, i.e. Ba and/or Ti, and adsorbed oxygen, respectively.