Structural ledges in interphase boundaries

This article addresses the properties of stepped misfitting interfaces and their energetic preference to planar misfitting interfaces. It highlights: (a) the purely geometrical or rigidlike, (b) the rigid (unrelaxed) energetic, and (c) the relaxed energetic properties of stepped interfaces. In (a), we address (1) the accommodation of misfit by the step or ledge mode through the cancellation of the mismatch, that builds up along a terrace, by the forwardpattern advance effected by a step,i.e., the relative displacement of atomic patterns on either side of the interface as observed in crossing a structural ledge along the interface, (2) the sideways (shear) pattern advance which seems to be energetically undesirable, (3) the need for tilt-type misfit dislocations to accommodate the misfit normal to the interface, and (4) the fact that at {III}_fcc(face-centered cubic)/{110}_{bcc(body-centered cubic) interfaces with rhombic symmetries, the misfits, as well as the pattern advances, are interrelated through the ratior = b/a of nearest-neighbor distances in the crystals. In (b), we exploit the rigid model approach that (1) yields ideality criteria for minimum energy and provides energetic justification for the step mode of misfit accommodation, (2) confirms that the average terrace widthl[inx} defined by this mode also meets the condition for positive energy gain, and (3) defines the upper and lower energy bounds to provide a perspective of the system energetics. In (c), the foregoing considerations are refined by a transition to the harmonic (elastic) model to yield (1) the dependence of the mean energy per atom of a stepped interface on interfacial misfit and pattern advance, as well as the dependence of the mean energy per atom of a planar interface on misfit, (2) expressions for the stresses related to the atomic interaction between opposing terraces, (3) atomic displacements that might be probed by modern analytical techniques, and (4) resolved shear stresses and normal stresses that may facilitate the formation of glide dislocations in the presence of applied stresses. The boundary in a two-dimensional space—spanned by misfit and pattern advance—between regions where stepped interfaces are more stable than planar ones has been determined, suggesting that a critical misfit exists above which only planar interfaces are stable. Whereas the resolved shear stress related to the formation of structural ledges may facilitate the formation of dislocations in the presence of a subcritical applied stress, the corresponding displacements (bending) of atomic planes are probably observable only with strain contrast electron microscopy techniques. Formerly with the Physics Department, University of Pretoria. Formerly Visiting Scientist, Physics Department, University of Pretoria, Pretoria, South Africa. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

The cellular interlamellar and growth-front interphase boundaries in Cu-3 Wt pct Ti

Examination of the cellular colony interlamellar and growth-front interphase boundaries in Cu-3 wt pct Ti reveals an influence of crystallography at both of these interface types. Analysis of the interlamellar boundaries demonstrates that different arrangements of interphase misfit-compensating defects exist and combinations of misfit dislocations (MDs), structural ledges (SLs), or direction steps (DSs) were observed to dominate strain reduction between lamellae, even within the same colony. Detailed analysis also demonstrated that the actual interlamellar orientation relationship (OR) is (111) _α ‖ (010) _β with [-101] _α ‖ [501] _β , which is 0.28 deg in misorientation from the reported OR. The effect of crystallography was also apparent at the cellular growth front, as evidenced by the misfit-compensating structure observed with transmission electron microscopy (TEM) at the grain-boundary segments and the sharp faceting of all β precipitate-growth interfaces. This article is based on a presentation in the symposium “Interfacial Dislocations: Symposium in Honor of J.H. van der Merwe on the 50th Anniversary of His Discovery,” as part of the 2000 TMS Fall Meeting, October 11–12, 2000, in St. Louis, Missouri, sponsored under the auspices of ASM International, Materials Science Critical Technology, Sector, Structures.     

Comparison of interfacial structure-related mechanisms in diffusional and martensitic transformations

Some central problems in understanding the similarities of and the differences between ledgewise martensitic and ledgewise diffusional growth are examined. Martensitic growth can be described in terms of a lattic correspondence and a plane undistorted by the shear transformation. Diffusional growth can be similarly described in some cases but not in others. On the basis of the Sutton-Balluffi definitions of glissile and sessile boundaries, only misfit dislocations (on terraces or risers) or orthogonal sets of disconnections provide a truly sessile interface. When closely spaced structural ledges (now termed “structural disconnections”) are present during diffusional growth, they must have been glissile in the formation of a local equilibrium structure during the initial stages of growth. Once they are in local equilibrium and evenly spaced, however, they can only move synchronously because of their local strain interaction. Under these circumstances, extrinsic sources of growth ledges are required to move such interfaces in a diffusional manner. During martensitic growth, however, disconnections in the form of transformation dislocations can move freely in a synchronous manner. Also, on this basis, the apparent (undistorted) habit plane is generally useful in deducing the transformation mechanism during martensite formation, but is only occasionally so during diffusional growth, where only the terrace plane is generally useful. This article is based on a presentation in the symposium “Interfacial Dislocations: Symposium in Honor of J.H. van der Merwe on the 50th Anniversary of His Discovery,” as part of the 2000 TMS Fall Meeting, October 11–12, 2000, in St. Louis, Missouri, sponsored under the auspices of ASM International, Materials Science Critical Technology Sector, Structures.     

Why do dislocations assemble into interfaces in epitaxy as well as in crystal plasticity? To minimize free energy

Dislocations commonly form planar arrays that minimize the free interfacial energy between relatively mismatched crystal volumes. In epitaxy and phase transformations, the causative misfit is that between differences in lattice structure and/or orientations of different phases. In deformed homogeneous crystalline materials, the planar dislocation arrays are grain and mosaic block boundaries that accommodate relative misorientations within the same crystal structure. Thus, overwhelmingly, planar dislocation arrays have a basically common origin, namely minimization of interfacial energies. Consequently, they are all subject to the low-energy dislocation structures (LEDS) hypothesis. While the specific applications of the underlying general theory are well advanced in terms of epitaxy, phase, and grain boundaries, in connection with plastic deformation that very basis is widely overlooked, if not denied. The present article aims to (a) document the fact that, while being formed, dislocation structures due to plastic deformation are in thermodynamical equilibrium, (b) firmly establish the outlined connection between planar dislocation arrays of all types, and, thereby, (c) establish the kinship between epitaxy and plastic deformation of crystalline materials. This article is based on a presentation in the symposium “Interfacial Dislocations: Symposium in Honor of J.H. van der Merwe on the 50th Anniversary of His Discovery,” as part of the 2000 TMS Fall Meeting, October 11–12, 2000, in St. Louis, Missouri, sponsored under the auspices of ASM International, Materials Science Critical Technology Sector, Structures.     

The role of intruder dislocations in modifying the misfit dislocation structures and growth kinetics of precipitate plates

Intruder dislocations formed at θ’ and η plates in Al-4 pet Cu and Al-0.2 pct Au alloys respectively by a small plastic strain partially compensate the misfit by single arrays ; the Burgers vector of the dislocations has a component normal to the plate interfaces. On subsequently aging such deformed microstructures, little change takes place in θ’ where the misfit is low. In η, on the other hand, the large misfit is sufficient to nucleate other compensatory arrays which interact with the intruder dislocations to form the lowest energy dislocation network and to annihilate the Burgers vector component directed normal to the plates. The lengthening kinetics of θ’ plates are unaffected by the intruder dislocations, but the thickening kinetics are briefly accelerated, probably by means of vacancy-enhanced diffusion associated with the plastic deformation. The thickening enhancement later falls off as the defects are annealed. In Al-Au, an interesting morphological instability develops and leads to the formation of elongated plates. These we believe are caused by a mechanism of sympathetic nucleation. R. Sankaran, formerly Department of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, Pa. 19174     

Subnanometer-scale chemistry and structure of α-iron/molybdenum nitride heterophase interfaces

The local chemistry and structure of α-iron/molybdenum nitride heterophase interfaces is studied on a subnanometer scale by atom-probe field-ion microscopy (APFIM), three-dimensional atom-probe microscopy (3DAPM) and both conventional transmission electron microscopy (CTEM) and highresolution electron microscopy (HREM). Molybdenum nitride precipitates are generated by annealing Fe-2 at. pct Mo-X, where X=0.4 at. pct Sb or 0.5 at. pct Sn, at 550 °C or 600 °C, in an ammonia/hydrogen mixture. Internal nitridation at 550 °C produces thin, coherent platelet-shaped molybdenum nitride precipitates. Nitridation at 600 °C generates a much coarser structure with semicoherent thick plate-shaped and spheroidal precipitates in addition to the thin-platelet structure. The APFIM and 3DAPM analyses of the heterophase interfaces show substantial segregation of the solute species Sn and Sb only at the coarse precipitates, with Gibbsian interfacial excesses of up to 7±3 nm⁻², whereas the broad faces of the thin platelets have no detectable segregation. The TEM and HREM analyses show that the coarse precipitates are semicoherent, whereas the thin platelets are either coherent or have much fewer misfit dislocations than geometrically necessary. This demonstrates that Sn and Sb segregation is related to the presence of misfit dislocations at the interfaces of the coarse precipitates. This article is based on a presentation made at the symposium entitled “The Mechanisms of the Massive Transformation,” a part of the Fall 2000 TMS Meeting held October 16–19, 2000, in St. Louis, Missouri, under the auspices of the ASM Phase Transformations Committee.     

On the role of interphase-boundary structure in plate growth by diffusional mechanisms

The structures of planar phase interfaces and of interfacial defects responsible for their diffusional migration are discussed in terms of extensions of the O-lattice concept, in which the intersection of the two structures is treated analytically. Two cases are considered and illustrated with well-characterized experimental examples: one in which two-dimensional structural matching leads to O-planes, and a second in which linear matching yields an array of O-lines. It is suggested that growth ledges moving normal to the O-lines will often require lateral kink formation and motion for their propagation. The misfit associated with transformation ledges is modeled in terms of real (screened) dislocations, which may coexist with virtual (unscreened) dislocations representing a residual component of misfit. A macroscopic shear can result from the cumulative action of transformation ledges with shear components parallel to the habit plane. This article is based0 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.     

The Effect of β Stabilizers on the Structure and Energy of α/β Interfaces in Titanium Alloys

The structure and energy associated with interfaces between the BCC and HCP lattices (β and α phase, respectively) in titanium alloys with commonly used β stabilizers were analyzed. For this purpose, the crystallographic structure of the matching facets of broad, side and end faces was described using misfit dislocations and structural ledges which compensate the mismatch in atomic spacing of the α and β phases. The effect of the β/α transformation temperature due to various concentration of β stabilizers on periodicity of misfit dislocations and structural ledges was estimated. The van der Merwe approach was used to calculate energy of different matching facets. An increase in the percentage of β-stabilizing elements was found to result in a decrease in the lattice-parameter ratio (a_β/a_α) and an increase in the energy of all faces. The dependence of the interface energy on the a_β/a_α ratio was for the first time quantified, and insight into the preferred shape of α-phase precipitates was obtained.

     

Heterogeneous nucleation of σ′ on dislocations in a dilute aluminum-lithium alloy

The nucleation of S on dislocations with small undercooling in binary aluminum-lithium alloys has been examined. The study of related microstructures was performed using transmission electron microscopy (TEM), which demonstrates that σ′ preferentially nucleates on dislocations with a strong edge character and locates at the side where the stress field is compressive without destroying the dislocation core structure. This qualitatively justifies the theoretical prediction by Larché on coherent heterogeneous nucleation on edge dislocations. Following the evaluation of the volume free energy change for the binary system by the ideal solution model and the mean-field model by Khachaturyan, the nucleation barrier and the nucleation rate were calculated and compared with experimentally determined data based on Larché's model. Specifically, the back-calculated interfacial energies from the experimentally determined nucleation rate data are in good agreement with the interfacial energy temperature dependence predicted by the related interfacial energy model. The effects of misfit strain, volume diffusion, interfacial energy, and nucleation sites are discussed. Formerly Graduate Student This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,” organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3–5. 1994 in Rosemont, Illinois.     

Correlation of microstructure and creep stages in the 〈100〉 oriented superalloy SRR 99 at 1253 K

The microstructure of creep specimens tested at 1253 K is analyzed in the three stages of the creep curve by TEM investigations. Stage I is characterized by the glide of screw dislocations in the matrix, while the transition to stage II is the beginning of γ′ rafting. Throughout stage II, the γ′ phase is not cut by dislocations. From these and other metallographic results, the mechanism of creep in the single-crystal alloy can be deduced. The misfit stress at the γ/γ′ interfaces proved to be of special importance for this type of alloy containing a high volume fraction of γ′.     

Influence of crystallography and bonding on the structure and migration of irrational interphase boundaries

Interphase boundary structure developed during precipitation from solid solution and during massive transformations is considered in diverse alloy systems in the presence of differences in stacking sequence across interphase boundaries. Linear misfit compensating defects, including misfit dislocations, structural disconnections, and misfit disconnections, are present over a wide range of crystallographie when both phases have metallic bonding. Misfit dislocations have also been observed when both phases have covalent bonding (e.g., US: β US₂ by Sole and van der Walt). These defects are also found when one phase is ionic and the other is metallic (Nb∶Al₂O₃ by Rühleet al.), albeit when the latter is formed by vapor deposition. However, when bonding is metallic in one phase but significantly covalent in the other, the structure of the interphase boundary appears to depend upon the strength of the covalent bonding relative to that in the metallically bonded phase. When this difference is large, growth can take place as if it were occurring at a free surface, resulting in orientation relationships that are irrational and conjugate habit planes that are ill matched (e.g., ZrN: α Zr−N by Liet al. and Xe(solid):Al−Xe by Kishida and Yamaguchi). At lower levels of bonding directionality and strength, crystallography is again irrational, but now edge-to-edge-based low-energy structures can replace linear misfit compensating defects (γ_m:TiAl:αTi−Al by Reynoldset al.). In the perhaps still smaller difference case of Widmanst?tten cementite precipitated from austenite, one orientation relationship yields plates with linear misfit compensating defects at their broad faces whereas another (presumably nucleated at different types of site) produces laths with poorly defined shapes and interfacial structures. Hence, Hume-Rothery-type bonding considerations can markedly affect interphase boundary structure and thus the mechanisms, kinetics, and morphology of growth. H.I.Aaronson, deceased, was R.F. Mehl University Professor Emeritus in the, Department of Materials Science and Engineering at Carnegie Mellon University, Pittsburgh, PA, 15213-3890, U.S.A. He was also Visiting Professor in the School of Physics and Materials Engineering at Monash University, Victoria, 3800, Australia, and Adjunction Professor in the Department of Materials Science and Engineering at the University of Virginia, Charlottesville, VA 22904-4745, U.S.A. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occured 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.     

influence of crystallography and bonding on the structure and migration of irrational interphase boundaries

Interphase boundary structure developed during precipitation from solid solution and during massive transformations is considered in diverse alloy systems in the presence of differences in stacking sequence across interphase boundaries. Linear misfit compensating defects, including misfit dislocations, structural disconnections, and misfit disconnections, are present over a wide range of crystallographie when both phases have metallic bonding. Misfit dislocations have also been observed when both phases have covalent bonding (e.g., US: β US₂ by Sole and van der Walt). These defects are also found when one phase is ionic and the other is metallic (Nb∶Al₂O₃ by Rühle et al.), albeit when the latter is formed by vapor deposition. However, when bonding is metallic in one phase but significantly covalent in the other, the structure of the interphase boundary appears to depend upon the strength of the covalent bonding relative to that in the metallically bonded phase. When this difference is large, growth can take place as if it were occurring at a free surface, resulting in orientation relationships that are irrational and conjugate habit planes that are ill matched (e.g., ZrN: α Zr−N by Li et al. and Xe(solid):Al−Xe by Kishida and Yamaguchi). At lower levels of bonding directionality and strength, crystallography is again irrational, but now edge-to-edge-based low-energy structures can replace linear misfit compensating defects (γ_m:TiAl:αTi−Al by Reynolds et al.). In the perhaps still smaller difference case of Widmanst?tten cementite precipitated from austenite, one orientation relationship yields plates with linear misfit compensating defects at their broad faces whereas another (presumably nucleated at different types of site) produces laths with poorly defined shapes and interfacial structures. Hence, Hume-Rothery-type bonding considerations can markedly affect interphase boundary structure and thus the mechanisms, kinetics, and morphology of growth. H.I.Aaronson, deceased, was R.F. Mehl University Professor Emeritus in the, Department of Materials Science and Engineering at Carnegie Mellon University, Pittsburgh, PA, 15213-3890, U.S.A. He was also Visiting Professor in the School of Physics and Materials Engineering at Monash University, Victoria, 3800, Australia, and Adjunction Professor in the Department of Materials Science and Engineering at the University of Virginia, Charlottesville, VA 22904-4745, U.S.A. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occured 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.     

Origins of internal structure in massive transformation products

The internal structure in massive phases formed during six massive transformations has been reviewed. A counterpart review has also been made for the proeutectoid ferrite reaction, mainly in alloy steels in which bulk partition of alloying elements between austenite and ferrite has not occurred. Both dislocations and twins comprise this structure unless the stacking fault energy is too high to permit twin formation. Volume and shape changes associated with transformation can explain dislocation loops through stress-induced displacement and multiplication of misfit dislocations into the softer phase by means of either a dissociation reaction followed by Ashby-Johnson prismatic looping or emanation of glide loops from Frank-Reed sources. Following Gleiter et al., the “growth accidents” concept used to explain dislocation and twin formation during grain growth proves equally suitable for explaining formation of the same features during the massive and other diffusional transformations. Climb of interfaces produced by edge-to-edge rather than the usual plane-to-plane matching, introduced by Kelly and Zhang and experimentally supported by Nie and Muddle and by Howe et al. for the α → γ _m transformation in near-TiAl alloys, is proposed as another source of dislocations in the product phase. This paper was prepared following participation of its authors in the symposium “The Mechanisms of the Massive Transformation,” held Oct. 9–11, 2000. during the Fall 2000 TMS/ASM Meeting in St. Louis, MO, under the sponsorship of the ASM INTERNATIONAL Phase Transformations Committee.     

Computer simulation of ledge migration under elastic interaction

The diffusional growth of a phase by the motion of disconnections (ledges which contain transformation or misfit dislocations) was studied by a finite difference computer model. The elastic stress of these dislocations is considered to alter the (local equilibrium) solute concentration at the riser of ledges and cause a complex diffusion field interaction among ledges as they migrate. In some cases, however, the ledges forming a train can migrate all at the same speed in the presence of elastic interaction. The condition under which ledges overcome the elastic barrier and form a multipleheight ledge was determined. The model was applied to the migration of ledges/Shockley partial dislocations at γ′-plate interfaces in Al-Ag alloys. This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,” organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3–5, 1994, in Rosemont, Illinois.     

Mobile dislocations at the α2/γ phase boundaries in intermetallic TiAl/Ti3Al-alloys

Ti₃Al/TiAl interfaces of four titaniumaluminium alloys with and without chromium additions were examined in detail by tilting experiments using conventional transmission electron microscopy (TEM). Careful adjustment of weak beam conditions showed that the TiAl- as well as the Ti₃Al- phase contain interfacial dislocations which accommodate the lattice misfit between both phases. In the most ductile TiAl47Cr1Si0.2 alloy only one set of 〈10〉 interfacial dislocations in the TiAl phase was found. Most of them possess screw character and will leave the interface during plastic deformation. Consequently, this alloy exhibits remarkable ductility at room temperature.     

Deformation processes related to interfacial boundaries in two-phase γ-titanium aluminides

The deformation behaviour of two-phase (α₂ + γ) titanium aluminide alloys with a lamellar microstructure was investigated by conventional and high resolution electron microscopy. With regard to the mechanical properties, the structures of the interfacial boundaries occurring in these materials are characterized and the interaction mechanisms of the deformation processes with these interfaces is investigated. Accordingly, the misfit dislocations present at semicoherent α₂/γ and γ/γ interfaces assist the generation of dislocations and deformation twins. On the other hand, the semicoherent interfaces act as very effective barriers impeding the propagation of slip across the lamellae.     

Interfacial ledge structures in Ni3 Al-Ni3Cb eutectic composites

The interfacial structure of Ni₃Al-Ni₃Cb directionally solidified eutectic composites has been investigated by transmission electron microscopy. These interfaces contain at least three distinguishable arrays of features. Two of the arrays, misfit dislocations, have been discussed previously by Nakagawa and Weatherly. The third set, ledges which can fulfill both structural and kinetic growth functions, may interact with the dislocation arrays through strain-energy mechanisms. The interaction is manifested both as a local alteration of the line vector of the dislocation in certain circumstances, and as a change in the response of the dislocation image to ±g electron-microscope image-contrast experiments. A simple model of the strain field of a ledge based on that of an edge dislocation is formulated to rationalize the behavior of a misfit dislocation lying in close proximity to a ledge. The interaction of ledges and dislocation segments is expected to have significance in physical processes of practical interest such as production of matrix slip dislocations, misfit dislocation rearrangement, boundary sliding, and coarsening, and these processes are discussed in some detail.     

Defects in Ni and Co silicide: Si interfaces

Silicide formation has been studied by deposition of Ni and Co on (001) and (111) Si substrates, followed by annealing. NiSi₂ and CoSi₂, exhibiting both the A (parallel lattices) and B (twin related lattices) type epitaxial relationships, and also CoSi (lattices rotated by 30° about a coincident [111] direction), have been investigated. Observations, using transmission electron microscopy, have been interpreted in the framework of a topological theory of interfacial discontinuities, and extensive agreement has been found between theory and experiment. In NiSi₂Si A-type specimens, crystal dislocations were observed to accomodate misfit, although this was not completely relieved in general. In addition, irregular arrangements of dislocations with b=1/4<111> were observed on (001) interfaces and at the intersection of obtuse pairs of {111} facets. (001) interfaces were frequently found to facet on {111} planes, sometimes on a fine scale with facet spacings as small as 6 nm. NiSi₂Si and CoSi₂Si (111) type B specimens exhibit arrays of interfacial dislocations with b=1/6<211>, partially accommodating misfit. On theoretical grounds, these dislocations are thought to exhibit interfacial steps at their cores. Direct confirmation of this was obtained in plan view ultra-thin specimens by using a contrast technique based on a method for revealing steps on crystal surfaces. Arrays of interfacial dislocations were also observed in CoSiSi (111) specimens. The components of their Burgers vector parallel to the interface were determined to be close to 1/3<110>, in agreement with theory. Possible evidence of disclination formation was also found in these samples.