Nanometer scale induced structure between amorphous layers and crystalline materials

US-NSF (00-18) # 1109644; EU: NANOAM GROW-2000 (GROW-200005,1)

US PIs (to be supported by NSF) Indicated by Bold in Proposal

W. Craig Carter, Massachusetts Institute of Technology

Yet-Ming Chiang, Massachusetts Institute of Technology

Wai-Yim Ching, University of Missouri, Kansas City

Roger H. French, University of Pennsylvania and Dupont CR&D

Stephen H. Garofalini, Rutgers University

US Group Members (Not supported by NSF) Indicated by Italic in Proposal

Paul F. Becher, ORNL

Rowland M. Cannon, LBNL

Thomas M. Shaw, IBM, T. J. Watson Laboratory

European PIs (to be supported by EU) Indicated by Underline in Proposal

David J. H. Cockayne, Oxford University

Martine Gautier-Soyer, CEA Saclay

Michael J. Hoffmann, University of Karlsruhe

Manfred Rühle, MPI Stuttgart

Adrian P. Sutton, Oxford University

Introduction

Because so many important properties depend upon them, interfaces have been and continue to be a research focus of the materials science community. Researchers in inorganic materials have recently discovered a rich variety of chemical, electronic, mechanical, and other properties that depend on often unrecognized thin interfacial or intergranular films [1,2,3]. Experiments have shown that these thin films typically have compositions that differ from the bulk phases with which they are in equilibrium [2,4,5,6,7,8,9]. Moreover, they can have compositions [4,5,6], electronic structures [10], and physical properties [11] that are neither observed nor necessarily stable in the bulk and they likely have through-thickness compositional and structural gradients. While the existence of stable thin films has a phenomenological explanation [12,13], no general or systematic understanding of the variety of interactions or possible structures exists. Similar 1-2 nm thick, equilibrium surface films of oxides on oxides, recently discovered by Chiang et al. [14,15], have a phenomenological correspondence with the intergranular films and may also have exploitable properties.

Examples where macroscopic polycrystalline properties depend critically on intergranular films include: increased toughness in ceramic materials [16,17,18,19,9], diminished creep resistance [1,20,21], tunable electrical conductivity [2,22], decreased thermal conductivity [23], and enhanced sintering behavior [24]. Equilibrium surface films exist in systems that also exhibit enhanced chemical and catalytic activity [14,15]. Not infrequently, the thin intergranular film properties differ significantly from bulk properties and corresponding differences are expected in the surface films.

Ostensibly, these novel properties derive either from interactions that are perturbed by the near proximity of the interface, or from constraints due to finite film dimensions. The thin-film effect involves both atomic and microscopic length scales. A systematic understanding of novel thin-film properties requires modeling and experiments that acquire and correlate data on several scales; integrating these approaches remains a major challenge of current scientific inquiry.

The establishment of a better understanding of these intergranular and surface films would yield important implications and technological applications. It would expedite the customization of structural ceramics with superior combinations of fracture toughness, low and high-temperature strength, and wear resistance via intergranular composition engineering. It would permit engineering of properties and processing for thick film resistors [2], varistors [22], and high-Tc superconductors [25]. A broad comprehension of stable surface films could lead to improved catalytic behavior [14,15]. Surface forces important in MEMS (e.g., avoiding stiction) and nanotechnology (e.g., self-assembly forces) could be meditated through surface and intergranular films. Electrochemical storage in high surface area nanomaterials, to date poorly understood, may well rely on adsorption mechanisms analogous to those occurring in multilayer films. In the microelectronics field, the search for high K gate dielectrics (useful at 3-5 nm thickness or less) necessary for sub-100 nm MOS [27] could benefit from the fundamental understanding sought in this research. Films with improved combinations of higher dielectric constant and breakdown voltage and lower leakage [26,27,28] are needed. A variety of strategies for the latter have been explored, specifically including amorphous Si-O-N materials with higher nitrogen contents and M-silicates, where M is a metal with higher polarizability, e.g., Zr or Hf. [28,29,30]. The existence of common features between these systems and the specific material systems proposed herein will lead to collateral benefits as the knowledge acquired from this work is applied to analogous systems.

We have assembled a group of researchers, from Europe and from the US, whose research expertise, as a group, spans experimental and theoretical length and time scales. Many of the principals have been active leaders in the exploration of thin intergranular film properties and all are committed to an integrated approach towards developing a fundamental understanding of stable thin intergranular films. The scope of this project requires a research collaboration of substantial breadth.

The existence of thin films stabilized by their proximity to an interface or a surface has been demonstrated in many systems. For example, 1-2 nm thick silicate based intergranular films have been observed in Si3N4 [1], SiC [19,31,32,33], and Pb-ruthenates in Pb-Al-silcates [2]. Silicon nitride is a prototype system [1,3] for which it has been well established, from work pioneered by Rühle and colleagues, that film thickness changes with the composition of the system but not with the amount of liquid forming material. The thickness is relatively less sensitive to grain boundary crystallography [34-37]. The films have enhanced nitrogen composition over that of bulk glasses [4,5,6]. In Al2O3 and MgO, silicate rich liquids may fully wet a high proportion of the grain boundaries such that the amorphous layers tend to be thicker [38,39,40,41,3]. Recently, nanometer-thick amorphous boundaries with about a monolayer of impurity adsorbate, in which silica is not involved, have been observed in several oxide materials, by Chiang and Rühle and colleagues, using combined techniques of high resolution and analytical transmission electron microscopy (TEM); these systems include ZnO/Bi2O3 [7,42,43], SrTiO3 with excess TiO2 plus Fe [44-46], and Al2O3/CaO [8]. The observed behavior may derive from general thermodynamic principles. These phenomena are remarkably similar to critical wetting transitions or the approach to perfect wetting [47-49].

In these situations, the films are a stable component of an interfacial thermodynamic system in equilibrium. In contrast, many materials made by chemical reaction, vapor deposition, or decomposition of polymers at temperatures below the glass transition temperature are not generally thermodynamic equilibrium phases. In these situations, it is possible to make materials, such as Si oxycarbide glasses [50], that are kinetically stabilized and have properties that are highly sensitive to formation conditions. For example, it is widely reported that amorphous Si-O-N materials containing up to 60 % N/(N+O) can be made by chemical reactions (e.g., references in [51,52]), or by various thin-film deposition methods (e.g., [53]). However, based upon the phase diagram for the Si3N4-SiO2 system [6], many of these compositions lie within a miscibility gap, and would rapidly phase-separate at temperatures where kinetic processes are not limited.

Efficient progress toward developing a general foundation for the understanding and control of stable intergranular and surface films in ceramic systems is best achieved by focusing both experimental and modeling efforts on a limited set of material systems. We will adopt an integrated experimental and modeling approach to stabilized thin films in silicate and titanate based systems. We will focus on these two systems because stabilized amorphous intergranular films are present in both but could be considered to have different origins and attributes; therefore, it should be possible to draw general conclusions about thin-film behavior that are not specific to a single material class. The strontium-titanate based systems have a known grain boundary wetting transition and are a useful model for more complex perovskites used in a variety of device applications. These systems provide the highest probability of understanding and categorizing the combined effects of the following correlated phenomena on the properties of materials that contain interfacial phases: 1) spatially varying atomic order and composition; 2) bonding and electronic structure; 3) dispersion and steric forces mediated by the thin intergranular film; 4) bulk and gradient thermodynamic properties; and 5) transport properties).

Open scientific questions that will be addressed by the group are:

* Does "partial crystalline order" exist in the few nanometers of an amorphous film proximate to a crystalline material and how does it depend on adjoining crystallography?

* Can experiments and molecular models agree on the degree of induced ordering?

* What is the relative importance of dispersion forces vs. steric or osmotic forces in determining the composition dependent thickness of stable films?

* Can experiment and modeling together solve the electronic structure of nanoscale systems spatially varying in composition and order?

* Can molecular-based and ab initio calculations be used to infer thermodynamic coefficients in a continuum approach involving a small set of material properties?

* How is atomic transport modified in thin-film layers or confined systems in general?

* Can the structure and composition of a partially ordered film be correlated with its thermodynamic and often unique physical (creep, electrical) properties?

The collective group has a wide range of both experimental and modeling expertise and facilities so that questions such as those posed above-that could not be treated by a single group-can be successfully addressed.

Background

Although much literature treats monolayer and sub-monolayer adsorption to interfaces (See refs. in [3]), in only a few cases are any details related to the atomic structure and microscopic energetics of ceramic interfaces. Relatively thick interfacial phases, often having multilayer levels of adsorbate [2,4,5], that have been detected at ceramic interfaces have recently been observed as having classes of behavior substantially more complex than predicted by classical adsorption models [41,3]. Silicate and titanate-based materials both form non-crystalline intergranular films along grain boundaries. Evidence suggests that the observed interfacial phases can have compositions and structures that are not in equilibrium as an isolated bulk phase, e.g., compositions lie within a miscibility gap in certain instances [11,4,5,6]. Differences in composition and in structure have been observed between intergranular films and their adjacent multi-grain pockets [2,4,5,6,7,8,9,10]. Furthermore, the properties of the interfacial films are particular owing to the combined effects of their novel structure, imposed constraints, and compositions. A complete description of these interfaces has not yet been obtained nor has sufficient data been collected to categorize their behavior thoroughly.

While the presence of thin interfacial films may be deduced from theories of multilayer adsorption, existing theories cannot account for temperature dependence, structural transitions, and composition gradients within the film itself. Nor do existing theories treat the combined effects of space charges, polarization within the film, and dispersion forces resulting from polarization of the abutting media. Some insight into such thin-film behavior can be obtained from lattice gas models of fluid adsorption and prewetting [47-49] or diffuse interface theory of critical wetting [54]. Despite extensive evidence of roughening transitions on free surfaces, disorder transitions were largely discounted for years for pure metallic grain boundaries [55]. However, the TEM observations of nanometer thick amorphous boundaries combined with fact that transitions to complete wetting of the grain boundaries (( ( 0) by equilibrium liquid above a critical temperature have been reported for ZnO with Bi2O3 rich liquid [22] and TiO2-rich SrTiO3 [56] are strongly reminiscent of the prewetting behavior and wetting transitions predicted by various lattice gas or critical wetting theories for surfaces [47-49] and for grain boundaries [57,58]. These have utilized simpler interatomic potentials, especially for the latter. Although there is little unambiguous evidence from TEM, wetting transitions for multicomponent metallic grain boundaries have been inferred from diffusion anomalies [59,60], and a transition from monolayer to multilayer adsorption has been affirmed for Bi-doped Cu from Auger spectroscopy [61,62]. It is also clear that the large structural units in ceramic melts will form an important element for the explanation of stabilized amorphous films in some systems.

Cannon et al. [3] have noted a trend suggesting that thicker boundaries of similar oxides tend to correlate with lower dielectric constants. This implies that dispersion forces are important, which affirms a belief that the resistance to complete wetting is greater for internal interfaces. However, the lack of perfect correlation indicates that other phenomena must be taken into account. Similar complexities are indicated by evidence that surface oxide films exhibit thinner stable layers than would be expected were dispersion forces predominating [14,15]. The ability to quantify such a correlation has been advanced by recent work by French in developing procedures for applying the Lifshitz theory for dispersion forces accurately when data for the dielectric functions are available over a wide spectral interval [63,64,65]; however, this is subject to the proviso that the intergranular films are homogeneous of known composition or have very specific variabilities.

Aspects of existing theories yield guidance for understanding stable thin films, but a coherent framework that is sufficiently rich to capture all of the pertinent phenomena has yet to be established. Also as noted by Cannon et al. [3], the entire impurity adsorption spectrum has never been well documented for a single ceramic system. However, recent advances in ab initio computations as well as in molecular dynamical and phase field models persuade us that opportunities now exist for achieving significant improvements, especially when applied iteratively in concert with quantitative assessments of specially prepared materials using quantitative TEM for internal films plus spectroscopy and diffraction from surface films. It is crucial that materials with sufficient control of impurities be used. This has been illustrated by the situations where intergranular films in Si3N4 both with and without rare earth plus Al additions have been made with controlled and reproducible thickness by different groups when pure enough materials were used [20-21,34-37], plus the demonstrations that thicknesses vary markedly with small impurity levels [35,37].

Research Plan

This project is designed to create a complete computational and experimental description of the structure and basic properties of crystal/glass interfaces in several important materials systems, including:

* Spatially-varying atomistic structure and composition

* Bonding and electronic structure

* Dispersion, steric and osmotic forces across the interface

* Bulk and gradient thermodynamic quantities

* Transport properties

The model systems have been selected because they can be both modeled and studied experimentally at a high level of detail and because each system has clear technological relevance. In-depth study of these systems will result in an understanding applicable to broader classes of materials.

The rationale for specific computations and experiments is discussed later with respect to each materials system while an overview of the collaborative modeling and evaluation approach is presented here. Every intergranular film has several pertinent length scales. Modeling the behavior of thin films requires cooperation and communication among modelers, each of whom have expertise in a particular length scale and time domain. Ching and Sutton will produce ab initio energy and electronic structure calculations in silicate-based and strontium titanate films. Ching will also investigate related crystalline phases. These calculations will be compared to quantitative TEM experimental results, which can verify and help refine theory. These comparisons will include structural determinations by Cockayne and evaluation of electron energy loss near edge structure (ELNES) spectra, which are sensitive to local structure and composition, by Rühle and French. The latter will also measure and analyze valence electron energy loss spectroscopy (VEELS) spectra that can be used to deduce the dielectric response of the films and to compute full spectral Hamaker constants for the London dispersion forces. Ching will produce calculations of nanometer and interfacially resolved electronic excitations that can be compared directly to ELNES spectra. Ching will also investigate modeling predictions of optical excitation that can be used to guide or interpret experiments in specific systems. Similar iterations between theory and experiment for surface films will be accomplished based on x-ray photoemission spectroscopy (XPS), ultraviolet photoemission spectroscopy (UPS) and reflection electron energy loss spectroscopy (REELS) measurements by Gautier, TEM/STEM assessment by Chiang, plus ellipsometry and vacuum ultraviolet spectroscopy (VUV) spectroscopy on substrates by French.

The ab initio calculations will provide Garofalini with model structures to which to compare the molecular dynamics simulations for refinement of interatomic potentials. Garofalini will determine whether any additional structure or composition dependence can be inferred in stabilized films and also transport properties. Carter will adapt the image based structural determination of local atomic structure of Cockayne and Möbus to a method of extracting coarse-grained measures of induced order in psuedo-disordered states. These parameters will provide a self-consistent and quantifiable method of extracting thermodynamic data from molecular dynamics results or from experiments that directly access localized structural information. From stable amorphous film results, information regarding composition profiles and induced structural order from the abutting crystalline phases can be obtained. Such structural and compositional order will be reduced to bulk thermodynamic quantities by Carter and then modeled as a continuum thermodynamic system using a diffuse interface formalism that couples composition-induced crystalline order and crystallographic orientation fields through an expansion of a homogeneous free energy function in terms of gradient quantities that account for heterogeneous distributions of structure and composition. The continuum thermodynamics models allow general predictions of stable film behavior for a relatively small set of physical parameters that can be tested against specific experimental results. The diffuse interface model, as supplemented with kinetics (the so-called phase-field [66] model) can simulate the effects of temperature, composition, induced order, and orientation on microstructure and its evolution. These can be tested against predictions from statistical mechanics models based on ab initio computations from Sutton and molecular dynamics calculations from Garofalini performed on smaller arrays.

The experimental characterization of internal interfacial films will rely on carefully prepared samples, made by sintering/HIPing by Hoffmann that allows fabrication of dense material of prescribed purity, or doped SrTiO3 bicrystals. In addition, Hoffmann and Cannon will investigate dispersions of particles in silicate or titanate rich liquids. SEM quantification of the morphology changes of these will provide information about the growth kinetics and anisotropy; the colloidal behavior reveals information about the interparticle forces across intergranular films. TEM evaluation of the resulting samples by Rühle and Chiang will elucidate purity and temperature dependencies of film stability and character. The molecular dynamic and phase-field models should provide correlations regarding the impurity sensitive, anisotropic grain growth. Chiang will prepare surface films and study their stability using TEM/STEM and assess electrical properties in collaboration with French and Shaw. These experiments will provide trends of composition and temperature dependence of intergranular and surface film stability over a wider range of dopants than can be modeled in detail, thereby, providing rationale for selection of systems to be studied iteratively.

Finally, a goal will be to seek correlations with bulk properties such as creep or fracture resistance. Hoffmann will evaluate mechanical properties. In parallel, mechanical properties of these and similar Si3N4 and SiC based materials are being evaluated at ORNL by Becher and colleagues and at LBNL by Cannon and colleagues in ongoing DOE sponsored programs. Results will be available allowing correlation of mechanical behavior with the film structures and compositions to be evaluated in this program. Also, ab initio cluster computations by G. Painter, et al., at ORNL, that elucidate anion effects on toughness of these films [17], and synchrotron based evaluations of surface films on SiC at the ALS at LBNL will proceed. Collaboration between these DOE sponsored groups and those in the proposed EU/NSF program should be beneficial and stimulating.

1. Silicon-Based Crystals

Si3N4, SiC, and Si have in common a native siliceous (SiO2-based) surface layer that is modified by N, C, or other impurities and intentional additives. It is now well established that a nanometer-thick disordered glass film is present at most grain boundaries in polycrystalline Si3N4 and SiC containing oxygen. The induced structure and composition of the glass film play a crucial role in polycrystalline fracture and creep behavior. For silicon, the undoped native surface oxide is an indispensable component of microelectronic devices. The expectation is that the materials systems will evolve towards high performance oxides or oxynitrides as length scales shrink in future technology. In the search for new gate and memory oxides with high permittivity, low leakage, and high breakdown voltage, the phenomenology embodied by this proposal has not been utilized, although it is otherwise widely recognized that the structure and chemistry of the glass layer at its interface with the adjacent crystal has an important impact on electrical properties.

1.1 Silicon Nitride: Si-O-N and Si-O-N-M Intergranular Films

Pure silicon oxynitride films are the most basic that can be both experimentally fabricated and ab initio modeled in this system, and will be the starting model system. However, Si-O-N films do not provide increased fracture toughness in polycrystalline Si3N4 [67], whereas Si-O-N-Y and Si-O-N-La represent the simplest rare-earth doped films that do [9,20]. In well-studied systems also containing Al, the fracture and grain growth differ markedly with choice of lanthanide (rare earth) addition [20], as does the enrichment of La in the intergranular film [9]. Recently, Hoffmann and colleagues have made highly pure materials with only small levels of Y2O3 and SiO2 additions by sintering with a gas pressure HIP without need for encapsulation. It is deemed desirable to take advantage of this and concentrate the iterative modeling and evaluation on Si-O-N-M systems with only a single metallic additive, M being one of {Y, La, Lu, Yb}. Lutetium is of special interest since it results in similar microstructures yet significantly different high-temperature mechanical properties compared to other dopants, including ytterbium, which has similar ion size but differing electronic structure. Other co-doped materials being extensively characterized by Becher et al. at ORNL, for which composition effects on fracture resistance have been clearly documented, are also available for evaluation.

In Si3N4-SiO2, the thickness of the glassy film is 1nm ± 1 Å irrespective of the amount of SiO2 present [1,21,35,37]. EELS applied to the glassy film in high purity Si3N4-SiO2 ceramics in [4,5] showed the chemical composition of the boundary film to be SiNxOy with x = 0.53 and y = 1.23. The constancy of the film thickness and composition is truly remarkable. The fact that the thickness and composition of the film depend only on the composition of the sintering aid, and not on the volume of sintering aid, indicates that the film exists as a consequence of chemical equilibrium. In other words, in Si3N4-SiO2 ceramics the film arises from equilibrium segregation of oxygen to grain boundaries. The observation that the film thickness and composition are less dependent on the boundary plane and misorientation indicates that these geometric variables do not strongly affect the equilibrium condition. Thus only three primary thermodynamic degrees of freedom govern the equilibrium of the glassy film. For example, once the temperature, pressure, and chemical potential of oxygen (i.e. p(O2)) have been specified, then the film thickness and composition are uniquely determined in Si3N4-SiO2 ceramics.

1.1.1 Theory

Sutton, Pettifor, and Kenney will conduct ab initio modeling of the thickness and composition of silicon oxynitride films sandwiched between two misoriented Si3N4 grains, beginning with Si-O-N compositions. Previously, Ching and Rühle [68] fitted effective interatomic potentials of ionic forms to ab initio calculations of the ground state total energies of (- and (-Si3N4 crystals. These potentials used ionic charged obtained from the ab initio calculations and, therefore, may not be transferable to other chemical environments where different ionic charges may pertain. Various approaches can be used to produce simple interatomic potentials for large-scale simulations that can be applied to specific chemical environments where different ionic charge may pertain, that will be based on ab initio computations by Sutton et al. and Ching et al. Yoshiya et al. [10] carried out discrete variational X-( calculations on Si-O-N clusters to interpret features appearing in the ELNES spectra from the silicon oxynitride boundary films. They proposed an atomic model for the film, having no dangling bonds. However, to date no simulations of the boundary film in Si3N4-SiO2 ceramics have treated the problem as one involving the establishment of chemical equilibrium through segregation of oxygen to the boundary. Since experiments indicate that the oxynitride films are a result of thermodynamic equilibrium, we believe that any credible model must guarantee this explicitly.

The computational approach will be as follows. We note that 3x + 2y = 4.05 in the SiNxOy oxynitride film, which is well within experimental error of 4. An ionic interpretation of this observation is that the composition of the film is such as to maintain overall charge neutrality if formal charges of +4, -2, and -3 are assigned respectively to the Si, O, and N ions. A covalent interpretation would be that each Si has four bonds, each nitrogen has three bonds, and each oxygen has two bonds. Then making the reasonable assumptions that N-N and O-O bonds do not arise, we could construct a simple network model of the oxynitride film, sandwiched between two misoriented Si3N4 grains. A Monte Carlo procedure could be devised to optimize the film structure using Keating type potentials to describe bent, stretched, and broken bonds with parameters fitted to ab initio calculations [69]. Thermodynamic equilibrium would be satisfied by carrying out the simulation within a grand canonical ensemble. The chemical potential for oxygen is determined by the experimental free energy of formation of SiO2 at the sintering temperature and pressure. In this way, the film thickness and composition will adjust through the course of the simulation, and equilibrium values, which can be compared with experimental measurements, will be predicted. The calculations will also be used as input for diffuse interface models of Carter/Cannon. The structure produced by this procedure could be further optimized with an ab initio relaxation to obtain a detailed picture of the interfacial bonding. The ab initio modeling will also enable EELS spectra to be predicted for comparison with experiments.

A more sophisticated strategy would be to construct analytic bond order potentials [70] for the oxynitride film, which would again involve some fitting to ab initio simulations. These potentials would have the advantages of allowing the assumptions about the local bonding topology to be relaxed and providing a much more realistic description of bonding than can be obtained with a Keating model. Grand canonical simulations would be conducted as before, to generate a structure for final optimization by an ab initio relaxation.

A variety of ab initio codes are available at Oxford University, including PLATO [71], an in-house localized-orbital DFT (density functional theory) code that is ideally suited to this system. The group has unique expertise in constructing bond-order potentials [70] and a long track-record in simulating interfaces [55]. Ching et al. have extensive experience and capability in using ab initio methods to study the electronic structure, bonding and optical properties of the crystalline Si3N4 and SiO2 phases [72]. The four crystalline phases of Si3N4, including the newly discovered spinel phase, were recently modeled with ab initio methods by Ching et al. [73] as were the (-SiAlON crystal [74] and crystalline phases in the Y-Al-O system [75,76].

Cockayne and Möbus will compare simulated structures with determinations of local structure in the silicon oxynitride films (see 1.1.2). Once the atomic structure is established, Ching will use the orthogonalized linear combination of atomic orbitals (OLCAO) method [77] based on DFT to calculate the electronic structure. This is an ab initio all-electron method particularly suitable for electronic structure calculation of complex structures. The use of atomic description in the basis set in the OLCAO method provides easy interpretation of the experimental data. Systems up to more than 1000 atoms can now be handled as was demonstrated in the calculation of a large amorphous-SiO2 model [78]. Comparisons of the calculated electronic structure with experiment will be to both ELNES and also VUV and VEELS results. Recent results using supercells and including core-hole effects have affirmed the detailed predictive power of ELNES calculations. Calculations on the ELNES edges in Si3N4, MgO, Al2O3, MgAl2O4, Y3Al5O12, ZnO, and Mg2SiO4, all yield excellent agreement with experimental data [79,80,81,82]. Such calculations can be applied to large structural models for the intergranular thin films and provide data that compares directly to spatially resolved ELNES spectra by selecting excited atoms individually across the interface. Here, ELNES calculations for the oxynitride films will be compared with model grain boundary measurements by Rühle and French. Ab initio calculations of the dielectric function and optical properties from the band structure then permits comparisons to the dielectric function determined from spatially resolved VEELS. It is anticipated that computations and measurements would be performed on bulk oxynitride glasses as well as for the thin intergranular films, in part out of interest in the properties. This would allow application of more standard experimental methods of VUV and ellipsometric spectroscopy to help validate the computational methods for amorphous materials.

Garofalini will perform molecular dynamics (MD) simulations using variable charge and fixed charge multibody interatomic potentials. Large-scale atomistic systems relevant to intergranular films will be simulated in conjunction with the electronic structure calculations and the continuum-level phase field calculations [83,84]. Two of the major benefits of current MD simulations are: a) the ability to study relatively large system sizes so that relatively large coherence lengths can be included, and b) the ability to supplement ab initio calculations with experimentally important variables such as time, temperature, and pressure so that thermodynamic and kinetic behavior can be explored within the limits of current computational resources. MD lies at an intermediate length scale between the ab initio and electronic structure calculations, which offer greater accuracy at the atomistic level, and the phase field calculations, which provide a closer link to macroscopic experimental scales. While most MD simulations use fixed charge potentials, in the work proposed here, newer techniques that allow for variable charge potentials will be employed. While this may be a small modification for some simulations, it can be important in cases where the charges on an atom (ion) change significantly during simulation (i.e., during reactions).

The MD simulations will be used to create intergranular films and interface structures of silica and silicate glassy phases on silicon-based crystals as a function of crystal orientation and film composition in a manner similar to that used experimentally. High temperatures will be used to create a melt state from which the system is cooled to create the resultant film/crystal interfaces, similar to prior simulations of intergranular films in alumina [83,84]. Temperature dependent equilibrium film compositions and kinetic effects on the film structure and chemistry may, thereby, be revealed. Local structures generated from the MD simulations can be used in electronic structure calculations in order to evaluate the simulation results or be used as a feedback for optimizing the interatomic potentials being used. A link between theory and experiment will again be through ELNES calculations by Ching, applied to the MD simulated atomistic configurations and compared to experimentally determined ELNES data or REELS and related data for surface films. Interfacial energies will also be obtained from the simulations and compared to those from sufficiently large size DFT calculations (where system size can affect such energies). The exact values and compositions dependencies can be related iteratively to the diffuse interface calculations by Carter.

Another important aspect of the MD simulations is the study of transport properties. In the simulations, the migration of species in the molten films can be evaluated, as can the effect of interface trapping or channeling by the ordered interface structure as a function of crystal orientation and composition. With sufficiently large system sizes and long run times, the MD simulations can also be used to study dissolution or growth of dissimilar surface planes in contact with the same intergranular film at either double or triple points, or the film viscosity, i.e., rates of sliding bicrystals with an IGF at fixed shear load. While such large systems would not be amenable to electronic structure calculations, they would relate to the phase field calculations. These should also be directly correlated with the grain growth behavior to be investigated by Hoffmann, and can be correlated to inferred values of interfacial sliding rates being measured and reported on similar systems by G. Pezzotti et al [85] and others.

Previous constant pressure simulations of calcium silicate intergranular films between alumina crystals showed an increase in film thickness as a function of equilibrium bulk composition, even though the number of atoms in the interfacial region was constant [83,84]. No experimental data yet exists for direct comparison, but the simulation results yield a clear indication that those structural changes in the film caused by variations in the solute chemical potential affect thickness. Furthermore, the assortment of low energy structures admissible in an amorphous structure such as a silicate glassy phase requires the use of a computational technique that can kinetically sample many configurations. The MD technique can do this much more effectively than the ab initio techniques, especially when compositional effects are important. Thus, the MD technique links the ab initio calculations to the diffuse interface models and experimental data. Furthermore, because they correlate first principles calculations with experimental observations, the simulations would be kept reliably verifiable and realistic.

Carter will develop a diffuse interface (phase-field), model that addresses the thermodynamic stability of intergranular films in terms of thermodynamic parameters derived from atomic models of structure and steric forces [86]. Prior work has modeled the intergranular films using diffuse interface theories, motivated heuristically by supposing a steric term provides a disjoining force to offset the attractive London dispersion forces. This has been insightful, but it has been based on a single order parameter [87,88,89]. Thus, it cannot capture the variety of important phenomena associated with the formation of impurity induced amorphous grain boundaries, nor can it account for crystallographic orientation [86]. The treatment, to be co-developed with Cannon, would couple effects of order, composition, and crystallographic orientation and will correlate attributes from the theory of critical wetting. The model will utilize data obtained from ab initio calculations by Sutton and Ching and structures measured by Cockayne and Gautier. The structure analysis methods developed by Möbus will be utilized and adapted to infer order parameters from the ab-initio structures or from simulations by Garofalini.

1.1.2. Experiments

Hoffman will fabricate reference-standard quality high purity Si3N4-SiO2 polycrystals, thermally equilibrated at high temperatures, for electron microscopy and spectroscopy by Cockayne, Möbus, French, and Rühle. He has been involved in the production and characterization of Si3N4 materials for over a decade; studies of the grain boundary film thickness in several generations of materials he has made have proven to be consistent (see refs. in [3]). The samples recently made by high-pressure gas sintering/HIPing exhibit unexpectedly good creep resistance, apparently owing to reduction of hard-to-detect anion impurities. The experiments will provide results that can be directly compared with the calculations. Materials with various Al/Y ratios would also be available from Becher et al., but the Al complicates assessment, in part, as it dissolves in the Si3N4 grains.

Möbus and Cockayne will lead the characterization efforts for the following crystallographic key-quantities as accurately as possible in a series of grain boundaries for collective study:

* Orientation relationship and faceting statistics of the interfaces between volume crystals and interfacial phase ("internal surfaces" with respect to the crystal)

* High-precision assessment of the thickness of the interfacial phase/film

* Atomistic structure of the terminating crystal planes next to the amorphous films, including possible steps, reconstructions, and self-similarities of apparently random fluctuations along the interfaces

* Sub-nanometer localized examination of the terminating layers of amorphous materials, with respect to crystal-surface induced extra ordering mechanisms

* Full structural solution including all (relaxed) atomic coordinates and identification of the interface core structure for "reference segments" of grain boundaries with or without partially amorphous films

Möbus will make use of several new, problem-adapted, techniques, which were not available for previous major HREM studies of interfacial films in ceramics:

* Anisotropic Fourier spectral analysis of sub-nanometer sized interfacial segments [90]

* Geometric phase holography [91,92] for the sub-0.1nm tracking of displacements to be converted into 2D-strain maps

* Detection/rejection criteria for suspected partial order in apparently amorphous films [93]

* Focal series evaluation to obtain the aberration-free projected electron wave at the bottom side of the specimen, which reveals the atomic structure more reliably than do single HREM images [94]

* Iterative structure refinement to detect relaxations out of a (first guess) reference structure by matching simulated to experimental images heading for the best-fitting structure [95]

These recent techniques have turned HREM into a truly quantitative technique operating on digitized image data, in order to elaborate crystal structure data including confidence intervals for measurement precision by sophisticated methods of image processing.

Cockayne will use primarily energy-selected electron diffraction to attempt a detailed structural determination of the intergranular glassy phases within these boundaries. Energy selected electron diffraction [96,97] is now well established as a means for studying the structure of small volumes of amorphous material. The technique gives the pair correlation function to high accuracy (0.02Å first nearest neighbor), which provides a fingerprint to differentiate between possible structural models. It has, for example, demonstrated the existence of thin foil tetrahedrally coordinated amorphous carbon (amorphous diamond). Furthermore, by comparing the experimental pair correlation function with that derived from a model structure, structural refinement is possible [98]. However, to study intergranular phases, further refinement of the technique will be required, because, to obtain the small size of electron probe necessary to analyze material of the dimension of the intergranular phase, a highly convergent probe will be needed. Pilot studies [99] have shown that deconvolution of the probe function from the diffraction pattern can be achieved satisfactorily.

EXELFS can be used to give the pair correlation function for specified atomic species; this technique will be used to give results for comparison with the energy-selected diffraction results described above. Si3N4-SiO2 ceramics are ideal for this study. Thin specimens can be prepared by PIPS and ion beam milling, and the elements Si, O, and N have relatively low scattering power, so that the need for single scattering can be more easily attained. Moreover, the dependence of the scattering factors (f(s)) on scattering angles for these elements are sufficiently similar to allow interpretation of peak positions in G(r) (the reduced density function) in terms of nearest neighbors. The experimental diffraction data will be compared with the simulated data obtained from models. This comparison will lead to selection between possible alternative structures and refinement of structural models, and possibly clarification of the growth processes.

Rühle will obtain ELNES data from the intergranular films as well as for bulk intergranular glassy phases for comparison with calculations based on the electronic structure and in collaboration with French will acquire spatial-resolved VEELS spectra. Prior work has used EELS to quantify the chemical compositions of intergranular films in various Si3N4 materials [4,5], and to correlate these with composition dependent film thickness [35]. More recently insights were gained about the film chemistry based upon semi-quantitative analysis of the ELNES spectra [4]. With a new microscope, SESAM, (Sub-E-volt Sub-Ångstrom-Microscope) having better energy resolution and potentially superior spatial resolution, it should be possible to obtain improved spectral data while avoiding the beam damage that, in part, limits the ability to probe the intergranular films in detail. The interpretation of these spectra can be quantified by iterative simulations and computations of the ELNES spectra as demonstrated by Ching in a grain boundary model of _-Al2O3 [100] and SrTiO3 [101]. This will provide a verification of key aspects of the structure and composition for amorphous films. If the spatial resolution can be improved relative to that achievable recently, it may be possible to make deductions about the through-thickness chemical gradients in these films, which were just beyond resolution in recent measurements with a VG microscope [5].

The VEELS spectra will be analyzed to provide the dielectric function and optical properties for the intergranular films. This latter information is a direct counterpart to the VUV and ellipsometric spectroscopic information taken for bulk materials [102], which has been used extensively to validate and guide refinement of computation of the electronic structure of bulk ceramics [103]. With spatially resolved methods, the VEELS analyses should give similar information for films [65]. Having the electronic structure information for the grain and intergranular material also allows a direct computation of the dispersion forces across interfacial films [65,64]. Although effects of through-thickness gradients on the dispersion forces are hard to account, this will make the assessment of the dispersion forces an accurate part of the simulation of the forces that control equilibrium.

Hoffmann, Becher, and Cannon and colleagues have previously conducted low and high-temperature crack growth and creep experiments, as well as fracture toughness and indentation-based crack deflection measurements on polycrystalline silicon nitride [16,19,9,20]. Such measurements will be carried out to compare the model materials of this study with each other and with other (generally more complex) doped systems, by Hoffmann and, in parallel efforts, in the DOE laboratories.

A complementary set of experiments by Hoffmann and Cannon will explore the colloidal behavior of Si3N4 particles suspended in appropriately doped silicon oxynitride liquids. These experiments reveal the degree to which particles are attracted and form clusters or not and provide a complement to the observations of wetting versus multilayer adsorption from polycrystalline samples. They also yield information about the interparticle forces acting across intergranular films [3,41]. Composition or temperature-induced changes of behavior should reveal wetting transitions for the grain boundaries. Such samples can also be used to determine grain growth morphoglies and kinetics. SEM quantification of the morphology changes of these will provide information about the growth kinetics and anisotropy [104,105].

1.2. Silicon Carbide: Si-O-C and Si-O-C-Al Intergranular and Surface Films

Silicon carbide grain boundaries films are an exemplar for amorphous films that are reported to crystallize upon heat treatment (e.g., as reported in the Al-doped case [32,33]). The modeling of oxycarbide glass films could be similar to that described for oxynitride films and involves some of the same investigators in an extant DOE program on SiC. It is expected that similarities between the oxynitride and SiC systems will be mutually beneficial in modeling, sample preparation, and characterization techniques.

Chiang will study the thermal stability of the oxycarbide films on SiC free surfaces (made possible by the availability of large single SiC crystals, e.g., from Cree, Inc.), and determine whether this system exhibits surface films of constant thickness as do certain binary oxides [14,15]. Thin films of oxycarbide glasses will be deposited by PVD techniques (magnetron sputtering, laser ablation) from SiC/SiO2 targets. The suite of surface spectroscopies and REELS (described in the next section) will be applied. Also, this system is suited for characterization of surface film structure and chemistry by techniques not applicable to intergranular films. The higher electrical conductivity of SiC relative to Si3N4 facilitates use of methods such as XPS and grazing-angle synchrotron X-ray scattering (to observe ordering and gradients in order). Especially in the Si-O-C-Al case, structural order in the surface film may be induced by heat treatment. Stable surface films in this system are also of potential interest for SiC-based electronics. If such films are identified, Chiang and Shaw will conduct capacitance, leakage current, and breakdown voltage measurements. French will do VUV spectroscopy and ellipsometry.

1.3. Silicon: Si-O-M and Si-O-N-M Surface Films

An enormous prior research exists on the properties of gate and thin-film dielectric oxides. Recent studies of gate alternatives to SiO2 have focused on systems such as Si-O-Hf and Si-O-Zr [29,30], selected with the rational expectation that a high Z constituent of fixed valence will raise permittivity without introducing defect levels (contrary to d or f transition metals). Thermodynamic compatibility with silicon at processing temperatures (up to 1000(C) is also required [106]. Since crystallization of the gate oxide is generally expected to introduce undesirable interface states, the compositions studied have been highly siliceous, for example, Zr4Si31O65 [30].

The proposed work will address the question of whether surface amorphous films on silicon can exhibit a self-regulating (equilibrium) thickness and composition. The specific questions we will address are: 1) Do the selection criteria that have been applied to identifying binary oxide systems with equilibrium-thickness disordered films [14,15] pertain to doped silicates on Si? (It is recognized that that can only pertain at a p(O2) range in which finite thickness films are stable) 2) If so, can film compositions that are more highly doped than predicted by bulk equilibrium [29,30] be stabilized in a disordered state via surface forces? 3) If varying degrees of induced order are obtained in such films, what is the effect on electrical properties pertinent to gate and thin-film dielectric oxides? We also note that while Zr is a classical nucleating agent in silicate glasses, lanthanide additives satisfy dielectric and thermodynamic stability criteria for gate oxides [106] and are more benign from the crystallization viewpoint. These considerations, combined with the fact that sub-2-nm thicknesses are ultimately desired, create a prospect for new gate oxides based on the concept of equilibrium-thickness, disordered surface films. These considerations apply equally to high permittivity amorphous films for DRAM technology. Although much recent work has focused on perovskites such as (Ba,Sr)TiO3 (BST), reactivity with silicon at the high processing temperature necessary in fabrication limits their introduction and raises interest in a stable, high permittivity siliceous film.

The specific systems to be studied are Si-O-M and Si-O-N-M surface films on silicon, where again M is (Y, La, Lu, Yb). While gate oxide compositions involving rare-earth doping are under study in other laboratories as well, here we will investigate specific compositions that have directly analogous counterparts being simultaneously studied as intergranular films in Si3N4. Nitrogen is of interest as a dopant since it may suppress crystallization, in part, by raising viscosity. In this way, an intellectual and collaborative link is formed to that part of the program, and the understanding that emerges from the collective work on those intergranular films can be applied to this class of surface films.

In the course of the above experiments, wetting and reactions between silicate melts and silicon will also be studied. Amorphous SiO2 is known to dewet silicon grain boundaries [107], and it may be that native SiO2 surface films are largely kinetically stabilized. Both equilibrium and nonequilibrium films can clearly be of practical relevance. However, to understand the tendency towards wetting or dewetting, and because the higher temperature range of silicon processing (1000(C) may well allow equilibration, high temperature experiments will first be examined. The anion composition of films will be controlled using two approaches: 1) closed-system experiments in which the oxygen/nitrogen content of the film is determined by deposition; and 2) open-system experiments in which the oxygen activity is controlled to maintain a stable film composition in equilibrium with silicon. Chiang and Shaw will collaborate to prepare thin (1-5 nm) Si-O-M and Si-O-N-M films on silicon using magnetron sputtering or laser ablation facilities at MIT and IBM, and use TEM to characterize wetting/dewetting, interfacial reactions, and crystallization as a function of film composition, thickness, and temperature. Stable films will be further studied. The permittivity, breakdown voltage, and leakage current will be measured in order to correlate film structure and composition with electrical parameters. More detailed theoretical and experimental study of specific stable films will follow in collaboration with other team members.

These films will also be investigated by Gautier using a complement of surface spectroscopies (XPS and UPS) possibly including XAS (x-ray adsorption spectroscopy) and XANES (X-ray adsorption near edge structure)as well as REELS (reflection electron energy loss spectroscopy). The interpretation for the amorphous films is less well understood than for ordered surfaces in which the surface structure and electronic states can be characterized with extensive detail [108,109,110]. The REELS data will be evaluated using Kramers-Kroning based techniques in concert with French; the object is the development of methods that deduce the dielectric function of the thin amorphous films analogous to those recently developed for VEELS in the TEM [65]. In parallel, French will conduct VUV and ellipsometry studies of bulk crystals of interest to this program [102], which can be used to determine the electronic structure, and optical properties as well as the dispersion forces across surface and intergranular films. He will similarly investigate silicon oxynitride glasses. The bulk electronic structures will serve as a reference for the results for the thin amorphous interfacial and surface films. Complementary information will also be obtained from ellipsometry. This work will be performed in collaboration with Dawn Bonnell of the University of Pennsylvania and compared with the calculations on the same system by Ching.

2. SrTiO3

Strontium titanate is a non-silicate system that is representative of a broad range of complex perovskites with interesting ferroelectric, dielectric, magnetoresistive, and superconducting properties. It is included here as a model system on account of observations of a grain boundary wetting transition in polycrystals sintered with titania excess which produces a eutectic liquid [56] and the amorphous intergranular films found at silicate-free boundaries [44-46]. These data suggest that a systematic progression from "dry" to "moist" (multilayer-adsorbed) grain boundaries to boundaries fully-wetted by a titania-rich eutectic liquid occurs in strontium titanate, when considered over a range of temperature. The atomic structure and composition of various special boundaries in SrTiO3, with and without dopants, have recently been experimentally characterized and modeled at Northwestern University, Oak Ridge National Laboratory, University of Illinois-Chicago [111,101,112], and Max-Planck Institute [44-46]. Here the goal will be to identify whether and where multilayer adsorption and wetting transitions occur, and to understand the criteria for such transitions. Cannon will conduct grain boundary penetration experiments in which bicrystals of known misorientation (available as substrates for high Tc films) will be heat-treated in contact with pre-equilibrated titania rich melts at various temperatures. The behavior will be contrasted with that found from colloid-like suspensions of particles in eutectic melts. PbO and Bi2O3 dopants will be studied; the former is known to lower the wetting transition temperature [56]. Silicate additions will be used to affirm that the transitions are not due to impurities. Hoffmann will prepare polycrystalline materials of similar doping. These samples will be characterized by Rühle and Chiang using TEM and STEM in order to determine whether adsorption and wetting transitions do occur, and their dependence on misorientation, temperature, and doping. It is expected that a clear experimental determination of the composition and structure of the Ti-enriched intergranular films will provide the impetus for modeling and additional experiments amongst the collaborators, as in the case of the other materials systems.

A parallel set of experiments will be done on TiO2 rich surfaces of SrTiO3 with various dopants by Gautier and French. Again these will explore conditions under which stable equilibrium films form, and seek conditions for wetting transitions. A subset of the compositions giving surfaces and intergranular films will become candidates for extensive, iterative modeling and evaluation by the procedures described for Si based systems.

An objective of studying titanate systems, in addition to silicate systems, is to develop a unified description of intergranular films in terms of adsorption theory, wetting and prewetting behavior, and colloidal approaches to interparticle interactions. Correlations of thermodynamical and materials properties with interfacial film behavior and wetting transitions will be sought. Diffuse interface models will be invoked and used to explore or describe prewetting and wetting behavior of silicate or titanate rich intergranular and surficial films.

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78 M.-Z. Huang, L. Ouyang and W. Y. Ching "Electron and Phonon States in an Ideal Continuous Random Network Model of a-SiO2 Glass," Phys. Rev., B59, 3540-50 (1999).

79 M. Gülgün, W. Y. Ching, Y.-N. Xu and M. Rühle, "Electron States in YAG Probed by Electron Loss Near Edge Spectroscopy and Ab-initio Calculations," Philos. Mag. B, 79 [6] 921-40 (1999).

80 S.-D. Mo and W. Y. Ching, "Ab-inito Calculation of Core-Hole Effect in the Electron Energy Loss Near Edge Spectra", Phys. Rev., B62 7901-07 (2000).

81 I. Tanaka, T. Mizoguchi, T. Sekine, H. He, K. Kimoto, S.-D. Mo and W. Y. Ching, "Electron Energy Loss Near Edge Structures of Cubic Si3N4," submitted Appl. Phys. Lett.

82 W. Y. Ching, et al. to be published

83 S. Blonski and S. H. Garofalini, "Atomistic Structure of Calium Silicate Intergranular Films in Alumina Studied by Molecular Dynamics Simulations," J. Am. Ceram. Soc., 80 1997-2004 (1997).

84 D. A. Litton and S. H. Garofalini, "Molecular Dynamics Simulations of Calcium Aluminosilicate Intergranular Films on (0001) Al2O3 Facets," J. Am. Ceram. Soc., 83 2273-81 (2000).

85 G. Pezzotti, T. Wakasugi, T. Nishida, R. Ota, H.-J. Kleebe, K. Ota, "Chemistry and Inherent Viscosity of Glasses Segregated at Grain Boundaries of Silicon Nitride and Silicon Carbide Ceramics,"J. Non-Cryst. Solids, 271 79-87 (2000).

86 R. Kobayashi, J. A. Warren and W. C. Carter, "A Continuum Model of Grain Boundaries," Physica D, 140 141-50 (2000).

87 D. R. Clarke, "The Intergranular Film in Silicon Nitride Ceramics: A Diffuse Interface Approach," in Tailoring of Mechanical Properties of Si3N4 Ceramics, ed. M. J. Hoffmann and G. Petzow, Kluwer Academic Publ, Dordrecht, The Netherlands, pp. 291-301 (1994).

88 H. D. Ackler and Y.-M. Chiang, "Effect of Initial Microstructure on Final Intergranular Phase Distributions in Liquid-Phase-Sintered Ceramics," J. Am. Ceram. Soc., 82 183-89 (1999).

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95 G. Möbus, R. Schweinfest, T. Gemming, T. Wagner and M. Rühle, "Iterative Structure Retrieval Techniques in HREM: a Comparative Study and a Modular Program Package," J. Microsc. - Oxf., 190 109-30 (1998).

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98 D. G. McCulloch, D.R., McKenzie, C. M., Goringe, D.J.H. Cockayne, W. E. McBride and D. C. Green, "Experimental and Theoretical Characterization of Structure in Thin Disordered films," Acta Cryst., A55 178-187 (1999).

99 W. E. McBride, D. J. H. Cockayne, D.J.H. and C. M. Goringe,"Reduced Density Function Analysis using Convergent Electron Illumination and Iterative Blind Deconvolution," Ultramcroscopy, 76 115-123 (1999).

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101 S. D. Mo, W. Y. Ching, M. F. Ching and G. Düsher, "Electronic Struture of a Grain-Boundary Model in SrTiO3,"Phys Rev B-Cond Matter, 60 2416-24 (1999).

102 R. H. French, D. J. Jones, H. Müllens, S. Loughin, A. D. Dorneich and P. F. Carcia, "Optical Properties of Alumnum Nitride: Determined from Vacuum Ultraviolet Spectroscopy and Spectroscopic Ellipsometer," J. Mater. Res., 14 4337-44 (1999).

103 R. H. French, S. J. Glass, F. S. Ohuchi, Y.-N. Xu, F. Zandiehnadem and W. Y. Ching, "Experimental and Theoretical Studies on the Electronic Structure and Optical Properties of Three Phases of ZrO2," Phys. Rev. B Conds. Matter, 49 5133-42 (1994).

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108 M. Descostes, F. Mercier, N. Thromat, C. Beaucaire, M. Gautier-Soyer, "Use of XPS in the Determination of Chemical Environment and Oxidation State of Iron and Sulfur Samples:.," Appl. Surf. Sci., 165 288-302 (2000).

109 S. Gota, E. Guiot, M. Henriot, M. Gautier-Soyer, "Atomic-Oxygen Assisted MBE Growth of (-Fe2O3 on (-Al2O3 (0001): Metastable FeO (111)-like Phase Subnanometer Thicknesses," Phys. Rev B-Cond, Matter., 60 14387-95 (1999).

110 M. Gautier-Soyer, "X-ray Adsorption Spectroscopy: A Tool to Study the Local Atomic and Electronic Structure of Ceramics," J. Eur. Ceram. Soc., 18 2253-61 (1998).

111 S. J. Pennycook, M. F. Chisholm, Y. Yan, G. Düscher and S. T. Pantelides, "A Combined Experimental and Theoretical Approach to Grain Boundary Structure and Segregation," Physica B, 274 453-57 (1999).

112 N. D. Browing, J. P Buban, H. O. Moltaji, S. J. Pennycook, G. Düsher, K. D. Johnson, R. P. Rodrigues and V. P. Dravid, "The Influence of Atomic Strucutre on the Formation of Electrical Barriers at Grain Boundaries in SrTiO3," Appl. Phys. Lett. 74 2638-40 (1999).