A lock-in model for the atomic structure of interphase boundaries between metals and ionic crystals

The low energy interphase boundaries between noble metals (Au, Cu) and various ionic crystals (LiF, KCl, NaCl, MgO, A1₂O₃, mica) were determined at 550°C by means of the boundary energy induced rotation of small (~ 1 μm) spheres. The systems were chosen so that the effect of lattice mismatch (varied between 1.3 and 35.1%), the effect of lattice structure (cubic/cubic and hexagonal/cubic) and chemical effects could be studied. The results obtained suggest that boundary models based on the coincidence concept are not applicable to interphase boundaries between noble metals and ionic crystals because the low energy boundaries observed were not of the coincidence type and existing coincidence orientation relationships did not result in low energy boundaries. However, the atomic structure of the low energy interphase boundaries observed may be understood in terms of the following “lock-in model”. A low energy interphase boundary results if the close packed rows of atoms at the “surface” of the metal crystal fit into the “valleys” between close packed rows of atoms at the “surface” of the ionic crystal. This model seems to predict correctly the experimentally observed correlations between the interfacial energy and the boundary inclination, the lattice mismatch and the lattice structure of the two phases involved.     

Edge-to-edge plane matching as a criterion for interphase boundaries of low energy

As demonstrated by Aaronson and his colleagues over five decades or so, the structure, energy, and dynamic response of interphase boundaries in metallic systems are strongly correlated. It has also become clear that very few, if any, solid/solid transformation interfaces can be considered truly “incoherent.” Most treatments of the geometry of irrational interfaces (facet planes) have focused on the density of coincidence sites or near-coincidence sites (NCS); this naturally involves consideration of the matching of densely packed atomic planes lying parallel to the facet. Edge-to-edge plane matching represents an alternative and, perhaps, more general approach to the geometry of transformation interfaces. For diffusional transformations, growth ledges are required to displace and reproduce the structure of the facet plane; their geometrical properties are distinct from those of the interfacial facets. The role of local thermodynamic driving force in determining the migration mode is assessed. Several recent observations of the transient faceting of irrational interfaces, for which the density of NCS is relatively low, have stimulated considerations of the significance of the invariant-line condition and of edge-to-edge plane matching as criteria for local minima in interfacial free energy. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee.     

Edge-to-edge plane matching as a criterion for interphase boundaries of low energy

As demonstrated by Aaronson and his colleagues over five decades or so, the structure, energy, and dynamic response of interphase boundaries in metallic systems are strongly correlated. It has also become clear that very few, if any, solid/solid transformation interfaces can be considered truly “incoherent.” Most treatments of the geometry of irrational interfaces (facet planes) have focused on the density of coincidence sites or near-coincidence sites (NCS); this naturally involves consideration of the matching of densely packed atomic planes lying parallel to the facet. Edge-to-edge plane matching represents an alternative and, perhaps, more general approach to the geometry of transformation interfaces. For diffusional transformations, growth ledges are required to displace and reproduce the structure of the facet plane; their geometrical properties are distinct from those of the interfacial facets. The role of local thermodynamic driving force in determining the migration mode is assessed. Several recent observations of the transient faceting of irrational interfaces, for which the density of NCS is relatively low, have stimulated considerations of the significance of the invariant-line condition and of edge-to-edge plane matching as criteria for local minima in interfacial free energy. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee.     

Edge-to-edge plane matching as a criterion for interphase boundaries of low energy

As demonstrated by Aaronson and his colleagues over five decades or so, the structure, energy, and dynamic response of interphase boundaries in metallic systems are strongly correlated. It has also become clear that very few, if any, solid/solid transformation interfaces can be considered truly “incoherent.” Most treatments of the geometry of irrational interfaces (facet planes) have focused on the density of coincidence sites or near-coincidence sites (NCS); this naturally involves consideration of the matching of densely packed atomic planes lying parallel to the facet. Edge-to-edge plane matching represents an alternative and, perhaps, more general approach to the geometry of transformation interfaces. For diffusional transformations, growth ledges are required to displace and reproduce the structure of the facet plane; their geometrical properties are distinct from those of the interfacial facets. The role of local thermodynamic driving force in determining the migration mode is assessed. Several recent observations of the transient faceting of irrational interfaces, for which the density of NCS is relatively low, have stimulated considerations of the significance of the invariant-line condition and of edge-to-edge plane matching as criteria for local minima in interfacial free energy. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee.     

Interface effects in superplastic deformation of alumina containing zirconia,titania or hafnia as a second phase

The superplastic properties of alumina can be changed in interesting ways by small additions of transition metals zirconium, hafnium, or titanium. All three introduce a “leaky” threshold stress of 5–20 MPa. Above the threshold the flow rate is linearly related to the applied stress. A similar threshold is observed in sinterforging experiments. The additions also have the effect of enhancing the superplastic ductility and the fracture strength, presumably by increasing interfacial cohesion. This higher interfacial cohesion appears to correlate to the higher activation energy for boundary diffusion and to a lower interfacial energy. The threshold is explained in terms of a roughening transition of interfaces that are faceted. Below the transition the flow rate is interface limited, while above it, it is diffusion limited. The stress for the roughening transition is obtained from a model that describes the transition in terms of a barrier for the nucleation of interface dislocations. The barrier is shown to depend on the change of the interface energy with misorientation. It is estimated that dγ/dθ = 1 mJ m⁻²/degree can give rise to a threshold stress of 10 MPa.     

Atomistic modelling of the metal/oxide interface with image interactions

We calculate the interfacial energy and lowest energy relative position for an Ag (001)/MgO (001) interface. The dominant image terms and short-range repulsions are included in full, and the MgO ions are relaxed to equilibrium using the MIDAS code. An essential new feature is the suppression of charge density fluctuations with wave-vectors greater than a (Fermi wavevector) cutoff. Our results show that the powerful methods based on interatomic potentials, widely used for ionic systems, can be extended to metal/ionic interfaces.     

On the Unavailability of Universal Glass Forming Ability Criterion

The present work examines different glass forming ability criteria (GFA), which distribute into four major categories based on different theories for glassy alloys. Four major categories are based on (i) characteristics transformation temperatures, (ii) Miedema approach, (iii) internal atomic configuration, and (iv) kinetic constraints (viscosity, diffusivity, etc.). Twelve alloys of widely different origin and nature (with respect to number of constituent elements, base element, critical casting thickness, etc.) have been selected for studying the applicability of different GFA criteria of different categories. The experimentally determined critical casting thickness (Z_max) of each alloy has been taken to be the measure of GFA. The best criterion of each category has been identified. Finally, it has been observed that no single criterion of any category alone shows satisfactory correlation with Z_max. However, two criteria of two different categories do not simultaneously fail. It has been concluded that to determine GFA of any random glass forming material, two different criteria of two different categories should be checked. If both results do not indicate similarity in them, GFA must be checked with third criteria of third category.     

Theory of metal—Ceramic adhesion

Fully self-consistent, all-electron density functional calculations were carried out for MgO/Ag(100) and MgO/Al(100) interfaces with and without interfacial monolayers of C and S impurities. These first-principles results indicate that both Ag and Al atoms favor the site on top of the O atom. Electron density distributions in the interface regions suggest a significant ionic component to the metal—ceramic bond. There were indications of a metallic/covalent component as well. All adhesion curves were found to accurately obey the universal energy relation. Impurities were found to cause substantial changes in adhesion energies, ranging from 9 to 61%. The contribution of misfit dislocation networks to the work of adhesion was found to be large. Excellent agreement with experiment was found for our computed work of adhesion and contact angle. Finally, application of the Harris functional was found to be accurate, opening the way to systems currently beyond the capability of the fastest computers.     

Dissociation of asymmetric ∑9, ∑27a and ∑81d 〈110〉 tilt boundaries

∑9, ∑27a and ∑8ld〈110〉 tilt boundaries in annealed bulk polycrystals of a Cu + 6 at.% Si alloy are shown to dissociate, and in each case a new intermediate grain is formed which is separated from one of the original grains by a ∑3 coherent twin interface. For ∑9 dissociation, the other two interfaces bounding the intermediate grain are lower valued ∑ interfaces i.e. coherent and incoherent ∑3 boundaries; for ∑27a dissociation, the other interfaces bounding the intermediate grain are higher valued ∑ interfaces, i.e. ∑81d boundaries; and for ∑81d dissociation the other interfaces bounding the intermediate grain are also higher valued ∑ interfaces, i.e. ∑243a boundaries. A mechanism is proposed which describes the atom movements involved in the dissociation of a ∑9 boundary, and it is suggested that similar types of mechanism may account for the observed dissociation of ∑27a and ∑81d boundaries to higher valued ∑ boundaries. The primary GBD structure of a ∑243a〈110〉 tilt boundary is determined and shown to correspond to a 7.36 low angle tilt boundary.     

Ceramic/metal interfacial crack growth: Toughening by controlled microcracks and interfacial geometries

Toughening of ceramic/metal interfaces through the use of controlled interfacial geometries and non-coplanar microcrack-like pores is examined with respect to both critical and subcritical crack growth. Patterned uniform arrays of inclined interfacial steps and of “microcracks/voids” (with width 22 μm and spacing 10 μm), out-of-plane to the main interfacial crack, were produced for glass/copper interfaces by photo-lithographic techniques combined with evaporation and diffusion bonding processes. Significant toughening and improved stress corrosion crack-growth resistance is achieved through the promotion of crack-tip shielding primarily from crack bridging. Specifically, plastic void growth within the copper is seen to generate bridged ligaments of metal film between the glass substrates; the resulting mechanical crack bridging leads to plastic stretching of the film and provides the dominant toughening mechanism, with a smaller contribution from crack deflection. Correspondingly, subcritical (pre-instability) crack-growth rates with the patterned arrays in “wet” and “dry” gaseous atmospheres are retarded by orders of magnitude compared to rates for plain interfaces. The toughness with the various patterned interfaces exhibits marked resistance-curve (R-curve) behavior with fracture toughness values increased by factors of 4–9 compared to intrinsic fracture toughness, G₀, values of ∼2 J/m² for these plain glass/copper interfaces. Surface roughness of the glass substrate is reasoned to be a controlling parameter for the shape and magnitude of such crack-resistance curves.     

Selective segregation at grain boundaries

Abstract

Experimental observations provide support for two different types of solute enhancement at interfaces, namely equilibrium and non-equilibrium segregation. It is shown that these segregation processes are dependent upon the structures of different large-angle grain boundaries. Experimental data clearly indicate that this selective grain boundary segregation influences the mobility and energy of grain boundaries.

A fundamental relationship is found to exist between the energy of coincidence boundaries and the density of shared atom sites (or the size of the periodic unit) in the boundary. The energy and mobility results provide strong support for the boundary coincidence and “relaxed” coincidence models of grain boundary structure.

A selective solute segregation to grain boundaries can lead to the formation of preferred orientations in annealed materials and enhanced corrosion at grain boundaries.

Résumé

Les études expérimentales apportent des arguments aux deux types differents d'enrichissement en soluté aux interfaces, c'est-à-dire la ségrégation d'équilibre et la ségrégation de non-équilibre. Ces deux modes de ségrégation dépendent de la structure des différents joints de grains à forte désorientation. Les résultats expérimentaux indiquent clairement que cette ségrégation sélective aux joints de grains influence la mobilité et l'énergie des joints de grains.

Une relation fondamentale existe entre L'energie des joints en coincidence et la densité des sites atomiques partagés (ou la taille des unités périodiques) dans le joint. Les résultats relatifs à l'énergie et à la mobilité amènent de fortes preuves au modèle de joints de grains basé sur la coincidence ou la coincidence «relaxée».

Une ségrégation sélective du soluté aux joints de grains peut conduire à la formation d'orientations préférentielles dans les matériaux recuits et favoriser la corrosion aux joints de grains.     

An atomistic-statistical thermodynamic evaluation of grain boundary embrittlement

A theory of intergranular brittle fracture at low temperature is presented. The intergranular crack nucleation process is modelled by utilizing the stress-concentrating effect of the double slip bands coincident on the boundary plane. The criterion of propagation is based upon an examination of such nucleated crack against blunting by nucleated dislocations. The resulting nucleation stress and the propagation stress are shown to depend critically upon the interfacial cohesion γ. The interfacial cohesion is expressed in terms of the interfacial cohesion of the boundary in pure state, γ₀, and a term involving a statistical-thermodynamic decohesion parameter Λ which is a measure of the ratio of the fracture surface activities to the grain boundary surface activities due to the segregant. γ₀ is determined by an atomistic model while Λ is obtained from experimental data. The model is applied to the analysis of coincidence tilt boundaries in Cu and Al. The internal energies, entropies, free energies, and the interfacial cohesions of these boundaries at temperatures of 1200 K for Cu and 1073 K for Al are presented and discussed. The calculated specific surface energies are in reasonable agreement with measured values. The separation process of these boundaries at 300 and 0 K has also been simulated for the analysis of the observed low temperature intergranular fracture stress. The predicted variation of fracture stress with the bulk concentration of Bi for the CuBi alloys is in good agreement with the experimental observations.     

Nucleation of a second solid phase along dislocations

A model for the nucleation of a second solid phase along dislocations is proposed and analyzed. The elastic distortions caused by the difference in the specific volume of the two phases in the elastic field of a dislocation are calculated following Eshelby’s transformation problem and assuming that both phases have the same moduli, but some modifications are introduced to account for the presence of the dislocation. The nucleation rateJ is expressed in terms of the dislocation density π, the free energy of formation of the critical embryo δG _d ^* and other quantities. It is found that the nucleation barrier δG _d ^* is only slightly shape dependent and therefore the critical shape can be approximated by that of the family with the lowest nucleation barrier. Then δG _d ^* andJ are calculated numerically for incoherent nucleation along edge and screw dislocations. It is found that: i) the nucleation barrier is smaller for edge than for screw dislocations, ii) the higher the shear modulus, the stronger the catalytic effect of dislocations, iii) metastable embryos may exist in undersaturated systems.     

The role of structural ledges at phase boundaries—III. F.C.C.-B.C.C. interfaces in Kurdjumov-Sachs orientation

The ledge mode of misfit accommodation is extended to {111} f.c.c.∥{110} b.c.c. interfaces with the Kurdjumov-Sachs (KS) orientation relationship. As with the Nishiyama-Wassermann (NW) relationship the geometric quantities are uniquely related by the misfit ratio r of atomic diameters. A rigid lattice analysis shows that the driving forces for a KS orientation relationship are significantly larger than those for the NW-x and even more so than those for the NW-y relationships. The rigid analysis also predicts that the terrace width which satisfies the periodicity conditions for a stepped interface are well within the terrace widths which allow significant energy gains. The models developed for the NW analysis are modified for KS configurations and employed to sum energies for the terrace patches, tilt misfit dislocations and the riser interface energy. Comparing this energy with that of a planar interphase boundary comprised of only misfit compensating dislocations shows that a stepped interphase boundary is energetically favored at r values near and greater than r_KS but less than r_NW-y.     

Cyclic fatigue-crack propagation along ceramic/metal interfaces

The integrity of ceramic/metal joints is investigated under mechanically applied cyclic stresses using double-cantilever-beam, and compact-tension, sandwich test specimens. Specifically, fatigue-crack propagation rates for interfacial cracks are characterized over a range of velocities from 10⁻⁹ to 10⁻⁴m/s for glass/copper and alumina/aluminum-alloy interfaces tested in moist air. Compared to corresponding (stress-corrosion) results under sustained loading, it is found that true interfacial cracks in glass-copper joints are significantly accelerated under cyclic loads. In addition, crack extension force (G) thresholds for interfacial crack growth under cyclic loads are some 46% lower than under sustained loads and are typically over six times lower than the interface toughness (G_c). For the alumina/aluminum-alloy system, conversely, fracture never occurs in the interface; under monotonic loading cracking progresses near the interface in the ceramic layer whereas under cyclic loading failure may occur either in the ceramic or in the metal. Based on a comparison with fatigue-crack growth data in bulk alumina and bulk aluminum alloys, it is found that near interfacial crack-growth rates in the metal are much lower than those of the bulk ceramic and show a far higher dependency on the range of G than behavior in the bulk metal.     

Effect of interatomic potential on the calculated energy and structure of high-angle coincident site grain boundaries—II. (100) Twist boundaries in Cu,Ag and Au

Earlier calculations on (100) high-angle twist boundaries in Al are extended to Cu, Ag and Au. Recent pseudopotentials of Dagens together with three empirical potentials for Cu are applied. Boundaries with values of Σ, the inverse density of coincidence sites, ranging between 5 and 73 are considered. In contrast to our earlier results for the Al pseudopotential of Dagens et al., the relaxed grain-boundary energy, E_Σ, is found to increase smoothly as function of the twist angle, θ, for all six potentials considered here; i.e. “cusps” in the E_Σ(θ) curve are not observed. Rather similar boundary structures are obtained for the noble-metals; these differ drastically from those derived by means of the pseudopotential for Al. From a comparison with (100) twist boundaries in ionic crystals with NaCl structure it is concluded that also in the f.c.c. metals a volume expansion at the interface which increases smoothly with θ should be present. Interfacial structures determined without consideration of this expansion are hence concluded to be systematically in error. The article concludes with a summary of the properties of (100) twist boundaries in the f.c.c. and NaCl structures which are thought to be valid independent of the detailed form of the interatomic potential chosen.     

Delamination Failure of RC Beams Strengthened with FRP Strips—A Closed-Form High-Order and Fracture Mechanics Approach

An analytical model for the prediction of the interfacial delamination failure of reinforced concrete (RC) beams strengthened with externally bonded fiber-reinforced plastic strips (FRPs) is presented. The analysis is conducted through a comprehensive stress analysis of the strengthened member and a failure criterion based on fracture mechanics concepts. The stress analysis follows the closed-form high-order approach for the analysis of deformations, stresses, and stress resultants in the multilayered structure. The model is based on equilibrium and compatibility requirements in and between all constituents of the strengthened beam, i.e., the concrete beam, the FRP strip, and the adhesive layer. The governing equations of the bonded and the delaminated regions are derived, and along with a unique set of boundary and continuity conditions that model the cracking of the RC beam, they are solved in a closed form. The results provide the basis for the fracture analysis stage in which a criterion for the initiation and stable or unstable growth of the interfacial delaminations is derived. This criterion is based on the fracture mechanics concept of the elastic energy release rate and replaces the classical stress-based criteria. The energy release rate is evaluated through the path independent J-integral over the stress, deformation, and energy fields determined by the stress analysis. Three numerical examples concerning interfacial delamination triggered by cracking of the concrete and by the stress concentration at the edge of the FRP strip are presented. The emphasis is put on the development of the internal stress resultants in the RC beam and the FRP strip, the stresses at the adhesive layer, and the energy release rate with the growth of the delamination. The paper is concluded with a summary and some recommendations for the design of such strengthened beams.     

Intrinsic ledges at interphase boundaries and the crystallography of precipitate plates

The structure of intrinsic ledges at interphase boundaries has been interpreted with extended O-lattice/DSC-lattice approaches. The distribution of structural ledges can be predicted if the spacing difference between parallel matrix and product planes is treated as a measure of the relaxed coincidence condition. A small rotation away from the low-index planar parallelism introduces a series of interfacial dislocations that cancels the spacing difference, resulting in a lattice invariant line. Misfit-compensating ledges at bcc: hcp interfaces are produced as a ledged interface intersects additional O-points that are recognized with the incorporation of previously omitted bcc atom positions into the O-lattice construction. Energetic consideration suggests that structural interfacial energy may decrease when a flat interface becomes ledged with misfit-compensating ledges. Burgers vectors associated with structural ledges and misfit-compensating ledges are displacement shift complete (DSC) lattice vectors. Precipitate and martensite crystallography may both include a lattice invariant line, but they are involved in different interphase boundary characteristics. Assumptions and implications in precipitate and martensite crystallography are discussed in the framework of the O-lattice theory and phenomenological theory of martensite crystallography. This article is based on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.