The selection of precipitate habit planes in Cr-32 Wt Pct Ni

Causes are investigated for the changes in precipitate crystal structure (fcc to 9R) and in morphology (degenerate plate to plate), which are observed to take place in Cr-Ni alloys as the reaction temperature decreases. Transmission electron microscopy (TEM) study is performed to determine the matrix/precipitate orientation relationship, habit plane, and growth ledge spacing. O-lattice modeling is used to show that it is likely that the metastable 9R phase forms as a transition phase at lower reaction temperatures because lattice matching at the bcc/9R habit plane is better than the matching at the bcc/fcc habit plane. The ability of the phenomenological theory of martensite crystallography (PTMC) to predict the habit plane of 9R plates precipitated by a diffusional mechanism is explained by the small lattice invariant deformation required to produce an invariant plane in Cr-Ni. Under this circumstance, the PTMC habit plane nearly coincides with the best-matching interface that presumably appears and is predicted by O-lattice theory. Formerly Graduate Student, Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University 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.     

The crystallography of hydride formation in zirconium: II. the δ → ε transformation

The phenomenological crystallographic theory of martensitic transformations has been applied to the transformation from δ (fcc) to ε (fct) zirconium hydride, using published lattice parameters. The habit plane, orientation relationship, lattice invariant shear, and interface characteristics were determined by transmission electron microscopy and diffraction. The shape strain was observed by interference microscopy. Good agreement between the predictions of the theory and the measured crystallography was obtained. The predicted and observed lattice invariant shear was twinning on 101. These twins which are found within alternating bands of hydride variants produce a herringbone morphology, and the bands produce a roof gable type of surface relief. For a given plate, the measured habit plane, twin plane, unique Bain contraction axis, and orientation relationship were mutually consistent with the respective predictions for a single variant. The magnitude of the lattice invariant shear was in excellent agreement with the predicted value. The interfaces separating the e hydride bands were found to be of two types, which alternated, often filling an entire grain. One of these, termed a spear interface, was found to be a twin plane, across which the twinned regions of the two bands “matched-up”. The other, termed an impingement interface, was found to have twin regions which did not “match-up”. This morphology can be explained as a pair of ε-hydride plates which share a spear interface. When two growing spears impinge, the resulting impingement interface is of the second type. Formerly with the University of Illinois.     

The crystallography of hydride formation in zirconium: I. The δ → γ transformation

The phenomenological theory of martensitic transformations has been applied to the transformation from δ (fcc) to γ (fct) zirconium hydride. The possibility of hydrogen diffusion prior to the transformation has been investigated by extrapolation of the published lattice parameters to lower hydrogen contents. The habit plane, orientation relationship, and lattice invariant shear were determined using transmission electron microscopy. Surface tilts were measured by interference microscopy and the direction and magnitude of the shape strain were determined from measurements of fiducial scratch displacements. The observed surface relief was indicative of an invariant plane strain. Good agreement between the predictions of the theory and the measured crystallographic features was obtained. The measured values of the direction of the shape strain and the habit plane were within 3.5 deg of the predicted values and the magnitude of the shape strain was in excellent agreement with the value predicted. The orientation relationship was near an identity, and the predicted and observed lattice invariant shear was twinning on (101)_γ. Formerly with the University of Illinois.     

Observation of cold-rolling texture and partially recrystallized texture in polycrystalline 3 pct Si-Fe by high-resolution electron backscattered diffraction

Cold-rolling texture and partially recrystallized texture of polycrystalline 3 pct Si-Fe were investigated using high-resolution electron backscattered diffraction (EBSD) method. From the measurement on a deformed grain with {211}〈011〉∼{111}〈011〉 orientations, deformation bands with {12 4 1}〈014〉 orientation were found. It turned out that the orientation rotation relationship between deformation bands and surrounding deformed grain can be explained by the activation of the slip system, which has a common slip plane with an adjacent grain. Oriented nucleation of recrystallized grains with {12 4 1}〈014〉 orientation was observed in a deformed grain with {211}〈011〉∼{111}〈011〉 orientation. Exactly the same orientation relationship that was observed between deformed grain and the deformation bands was also observed between the deformed grain and the recrystallized grain. A hypothesis that recrystallization nuclei are generated directly from the deformation bands formed by an activation of the slip system that has a common slip plane of neighboring deformed grains was proposed from the present experimental results.     

The thermoelastic martensitic transformation inβ′ Ni-Al alloys: I. Crystallography and morphology

This investigation describes a study of the crystallographic features of the thermoelastic martensitic transformation inβ′ Ni-Al alloys. Experimental measurements of the habit plane, shape strain and orientation relationship have been made, and the results are found to be in good agreement with the predictions of the Bowles-Mackenzie phenomenological theory, assuming δ = 1.000, p₂', and {110}_β', and d₂ = <110> _β'. The martensite habit plane normals are close to {2, 14, 15}_β' and are typically clustered in self-accommodating groups of four crystallographically equivalent variants centered around {011}_β' poles. The experimental shape strain is found to be exactly an invariant plane strain with the displacement direction lying ∼92 deg from the habit plane normal.     

Application of the double-shear theory of martensite crystallography to the β → α′ transformation in an U(Ga) alloy

The phenomenological double-shear theory of martensite crystallography has been applied to the β → α′ martensitic transformation in the U-1.6 at. pct Ga alloy. A correspondence matrix for the β → α′ transformation was derived from the experimentally determined β/α′ orientation relationship, and the double lattice invariant shear was considered as a combination of the principal slip (010) [100]_a with one of the minor slips in the α-uranium structure. The theoretical predictions of the habit plane are in good agreement with the experimental observations. Formerly Graduate Student, Ben-Gurion University of the Negev.     

Crystallography of grain boundary α precipitates in a β titanium alloy

The crystallography of α(hcp) precipitates formed on the β(bcc) matrix grain boundaries has been studied with transmission electron microscopy (TEM) in a Ti-15V-3Cr-3Sn-3Al alloy. The α precipitates have a near-Burgers orientation relationship with respect to at least one of the adjacent β grains. Among the possible 12 variants in this orientation relationship, the variant that [11•20]_α is parallel to the 〈111〉_β closest to the grain boundary plane tends to be preferred by the α precipitates. Additionally, further variant selections are made so as to minimize the deviation of orientation relationship with respect to the “opposite“ β grain from the Burgers one. Such rules in variant selection often result in the formation of precipitates with a single variant at a planar grain boundary. Prior small deformation of β matrix changes the variant of α precipitates at the deformed portion of grain boundary. It is considered that the stress field of dislocations in the slip bands intersecting with the boundary strongly affects the variants of α precipitates. Discussion of these results is based upon a classical nucleation theory. Formerly Graduate Student, Department of Materials Science and Engineering, Kyoto University Formerly Graduate Student, Department of Materials Science and Engineering, Kyoto University 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.     

Characteristics of lath martensite: Part III. Some theoretical considerations

Using newly available experimental information, the phenomenological crystallographic theory of martensite transformations has been applied to lath martensite. Experimental observations on the habit plane, orientation relationship, and the interface dislocations are in agreement with the theory using the Bain strain and two lattice invariant shears, one on (lll)[?101]_f and the other on (100)[0?11]_f. The theoretical approach is based on the maintenance of a glissile interface when experimentally observed misfit dislocations are incorporated in the experimental habit plane. The predicted shape deformation magnitude is 0.96, which is comparatively quite large, but because of extensive accommodation deformation in the martensite, the experimentally observed shape strain magnitude may be considerably smaller than the true value. The large martensite shape deformation appears to be responsible for the intrinsic lath morphology and the restricted growth of the martensite in a direction parallel to the shape deformation. The high density of dislocations in the laths probably arises because of accommodation distortion. Theory predicts a highly coherent martensite/austenite interface consisting of one set of steps on (lll)_f with associated dislocations and one set of screw dislocations in the direction [0?11]_f.     

Determination of the crystallographic parameters of cubic-to-tetragonal martensitic transformation using the infinitesimal deformation approach and wechsler, lieberman, and read theory

The aim of the present study is to discuss the infinitesimal deformation (ID) approach’s application and practical applicability. Therefore, ID theory was reformulated and applied to the face centered cubic (fcc) to body centered tetragonal (bct) martensitic transformation for the case of the (110) slip system as the lattice invariant shear (LIS). The analytical solutions for the habit plane orientation, the magnitude of the lattice invariant shear, the orientation relation between parent and product phases, etc. were derived for fcc to bct martensitic transformation in an Fe-7 pct Al-2 pct C alloy. In order to compare with phenomenological theory’s results, crystallographic parameters were also calculated by using Wechsler, Lieberman, and Read (W-L-R) phenomenological theory. Agreement between the two results obtained from ID approach and W-L-R theory was found to be excellent.     

Crystallographic and mechanistic aspects of growth by shear and by diffusional processes

Growth by shear and by diffusional processes, both taking place predominantly by means of ledge mechanisms, are reviewed for the purpose of distinguishing critically between them at the atomic, microscopic, and macroscopic levels. At the atomic level, diffusional growth is described as individual, poorly coordinated, thermally activated jumps occurring in the manner of biased random walk, whereas growth by shear is taken to be tightly coordinated “glide” of atoms to sites in the product phase which are “predestined” to within the radius of a shuffle. Obedience to the invariant plane strain (IPS) surface relief effect and the transformation crystallography prescribed by the phenomenological theory of martensite is shown to be an unsatisfactory means of distinguishing between these two fundamentally different atomic growth mechanisms. In substitutional alloys, continuous differences in compositionand in long-range order (LRO) from the earliest stages of growth onward are concluded to be the most useful phenomenological approach to achieving differentiation. At a more fundamental level, however, the details of interphase boundary structure are the primary determinant of the operative mechanism (when the driving force for growth is sufficient to permit either to occur). In the presence of a stacking sequence change across the boundary, terraces of ledges are immobile irrespective of their structural details during diffusional growth. Kinks on the risers of superledges are probably the primary sites for diffusional transfer of atoms across interphase boundaries. In martensitic transformations, on the other hand, terraces containing edge dislocations in glide orientation or pure screw dislocations are mobile and accomplish the lattice invariant deformation (LID), though probably only after being overrun by a transformation dislocation. Risers associated with transformation dislocations are also mobile and cause the crystal structure change during growth by shear. The successes achieved by the invariant line (IL) component of the phenomenological theory of martensite in predicting precipitate needle growth directions and precipitate plate habit planes (Dahmen and co-workers) are here ascribed to the rate of ledge formation usually being a minimum at an interface containing an IL, primarily because nuclei formed sympathetically at this boundary orientation are likely to have the highest edge energies. Since martensite plate broad faces also contain the IL, the ability of the phenomenological theory to predict the habit plane and the orientation relationships of both precipitate and martensite plates is no longer surprising. The IPS relief effect at a free surface can be generated by precipitate plates when growth ledges are generated predominantly on only one broad face and only one of several crystallographically equivalent Burgers vectors of growth ledges is operative. Both pReferences probably result from larger reductions in transformation strain energy for the particular geometry with which a given plate intercepts the free surface. Precipitate morphology often differs significantly from that of martensite even if precipitates are plate-shaped and can readily differ very greatly. Whereas martensite morphology is determined by the need to minimize shear strain energy, that of precipitates derives from the more flexible base of the interphase boundary orientation-dependence of the reciprocal of the average intergrowth ledge spacing, as modified by both the orientation-dependence of interkink spacing on growth ledge risers and the spacing/ height ratio dependence of diffusion field overlap upon growth kinetics. This paper is based on a presentation made in the symposium “Interface Science and Engineering” presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26–29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee.     

Comparison between the invariant line and structural ledge theories for predicting the habit plane,orientation relationship and interphase boundary structure of plate-shaped precipitates

A comparison is made between the invariant line and structural ledge theories for predicting the habit plane, orientation relationship and (misfit) dislocation structure at interphase boundaries for various transformation strains. It is shown that the fundamental approaches of the invariant line and structural ledge theories are significantly different and that this can lead to the same or different predictions for the habit plane, orientation relationship and dislocation structure between two crystals depending on the type of transformation strain. It is also shown that the structural ledge theory is not applicable to transformations that involve expansion or contraction between orthogonal lattices.     

Characteristics of lath martensite: Part I. crystallographic and substructural features

This investigation, using an Fe-20 pct Ni-5 pct Mn (wt pct) alloy, was carried out to provide more detailed and accurate information on the crystallographic features of ferrous lath martensite than is presently available. The martensite observed was typical of that found in low carbon steels, but with the present alloy substantial amounts of retained austenite are found, which can be used as a crystallographic reference basis. Analysis of some twenty laths showe_d_the average austenite-martensite orientation relationship to be (lll)_f ‖ (011)_b: [•101]_f 3.9 deg from [•1•1l]_b, using an electron diffraction method involving an error of only a fraction of a degree. Adjacent laths within a packet of lath martensite were found to exhibit the same variant of the orientation relationship although such laths may be misoriented relative to each other by up to 2 deg. Thick layers of austenite found between adjacent laths indicate that the laths do not form by self-accommodation. The lath martensite habit plane is irrational, close to (575)_f [equivalently (•154)_b], but since the habit plane is of the type hkh, 12 apparent habit planes are observed although 24 variants of the orientation relationship may be found. The martensite-austenite interface on one side of a given lath is relatively planar, while that on the opposite side is irregular, suggesting that the laths thicken mainly in one direction. The martensite laths contain screw dislocations in all four ( 111 )_b directions, but one set of the four with Burgers vector α/2 [•111]_b is clearly dominant as a result of accommodation deformation imposed by the large lath martensite shape strain. Austenite dislocation arrays associated with the straight and irregular lath interfaces are very different, again suggesting that the thickening of a lath takes place mainly in one direction away from the initial straight interface.     

Edge-to-edge interfaces in Ti?Al modeled with the embedded atom method

The atomistic structure and energies of high-index interphase boundaries are explored using a combination of molecular statics and dynamics simulations with embedded atom potentials. We investigate planar boundaries between the α₂ and γ phases in the Ti−Al system. The class of boundaries considered has a high-index boundary orientation; the orientation relationship between the α₂ and γ phases also is high index, and a set of planes from each phase meet edge to edge at the boundary plane. For the particular case of a boundary that is commensurate in one direction and coincides with a moiré plane given by the so-called “Δg” diffraction condition, the boundary is not structurally singular, but it is energetically stable and does not appear to dissociate into other low-energy configurations. Misfit compensating defects are not observed; misfit in directions other than the commensurate one appears to be distributed uniformly. The boundary energy is evaluated as a function of the orientation of the boundary plane, and the edge-to-edge (moiré) boundary is found to lie in an energy cusp. 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 interfaces in Ti?Al modeled with the embedded atom method

The atomistic structure and energies of high-index interphase boundaries are explored using a combination of molecular statics and dynamics simulations with embedded atom potentials. We investigate planar boundaries between the α₂ and γ phases in the Ti−Al system. The class of boundaries considered has a high-index boundary orientation; the orientation relationship between the α₂ and γ phases also is high index, and a set of planes from each phase meet edge to edge at the boundary plane. For the particular case of a boundary that is commensurate in one direction and coincides with a moiré plane given by the so-called “Δg” diffraction condition, the boundary is not structurally singular, but it is energetically stable and does not appear to dissociate into other low-energy configurations. Misfit compensating defects are not observed; misfit in directions other than the commensurate one appears to be distributed uniformly. The boundary energy is evaluated as a function of the orientation of the boundary plane, and the edge-to-edge (moiré) boundary is found to lie in an energy cusp. 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.     

Crystallographic theories,interface structures,and transformation mechanisms

The structure and properties of an idealized planar interface that traverses a single crystal of the parent phase are first discussed. A (macroscopic) coherent interface is defined in terms of a relatively coarse-grained Larché-Cahn network related to the observed shape deformation. Reconstructive and displacive transformations are distinguished, and a new category of “ diffusional-displacive” transformations is introduced. The crystallographic theory of martensite requires that the habit plane interface is atom conserving (or “glissile”), but nonconservative (”epitaxial”) interfaces may form in some diffusional-displacive transformations. A modified Eshelby procedure is used to discuss the strain energy of particles of a new phase forming, by any mechanism, inside a constraining matrix. It is shown that the effective Burgers vector of a step (or ledge) in a fully or partly coherent interface is dependent on the parameters of the shape deformation and increases with the ledge height. Multiple height ledges (”superledges”) should only be observed if their fields have been effectively neutralized, either by averaging over displacement directions that are spatially distinct but crystallographically equivalent or by combining with lattice dislocations through processes essentially equivalent to emissary slip or climb. In the latter case, the shape discontinuity is effectively transferred from the interface into the matrix or to a surface. The use of invariant line theories and the concepts of growth, structural, and misfit ledges are also examined. 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.     

Edge-to-edge interfaces in Ti-Al modeled with the embedded atom method

The atomistic structure and energies of high-index interphase boundaries are explored using a combination of molecular statics and dynamics simulations with embedded atom potentials. We investigate planar boundaries between the α₂ and γ phases in the Ti-Al system. The class of boundaries considered has a high-index boundary orientation; the orientation relationship between the α₂ and γ phases also is high index, and a set of planes from each phase meet edge to edge at the boundary plane. For the particular case of a boundary that is commensurate in one direction and coincides with a moiré plane given by the so-called “Δg” diffraction condition, the boundary is not structurally singular, but it is energetically stable and does not appear to dissociate into other low-energy configurations. Misfit compensating defects are not observed; misfit in directions other than the commensurate one appears to be distributed uniformly. The boundary energy is evaluated as a function of the orientation of the boundary plane, and the edge-to-edge (moiré) boundary is found to lie in an energy cusp. 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.     

Brass-type shear bands and their influence on texture formation

The issues of brass-type shear band formation and the evolution of band microtexture components are addressed. The analysis is based on bands developed by plane strain compression in twinned {112}〈111〉 oriented copper single crystals deformed at 77 K. Substantial progress in understanding the formation of the bands was possible thanks to systematic local orientation measurements using transmission electron microscopy (TEM). The TEM orientation maps allowed investigation of the way in which unstable behavior of twin-matrix layers leads to the brass-type shear bands. It has been found that several important transitions of the deformation textures are correlated with shear banding. Early stages of shear band formation are the result of the equally effective operation of two coplanar slip systems on the {111} slip planes. This process leads to the lattice rotation about the 〈110〉 axis and to the rise of Goss orientation. For well-developed shear bands, a second rotation about the 〈112〉 direction is observed. It is accompanied by activation of new slip systems. The observed disappearance of matrix components from the shear band microtexture is the result of twinning within reoriented matrix lamellae. In the twin-oriented areas, the dominance of one of two coplanar slip systems ultimately leads to the formation of the brass texture component.     

Carbide precipitation during stage I tempering of Fe-Ni-C martensites

Microstructural changes which accompany the first stage of tempering have been studied by transmission electron microscopy (TEM) and electrical resistometry in two Fe-Ni-C alloys that form platelike martensite. The ε-carbide transition phase in these alloys adopts a platelike shape with a habit plane near {012=_α. Electron diffraction data indicate that the carbide may be partially ordered, resulting in orthorhombic symmetry, and therefore, this phase is designated as ε′- carbide. The carbide particles contain a fine internal substructure which appears to represent an internal accommodation deformation (faulting) on the carbide basal plane. Detailed analysis of the kinematics of carbide precipitation suggests that the observed habit plane and accommodation deformation permit an invariant-plane strain transformation which minimizes elastic strain energy. The apparent selection of only a limited number of possible orientation variants is explained in terms of the symmetry of the parent martensitic phase, which is known to undergo spinodal decomposition prior to the nucleation of the transition carbide. The martensitic substructure is not found to exert any significant influence on this overall precipitation behavior. formerly with the Massachusetts Institute of Technology formerly with the Massachusetts Institute of Technology