Observed Habit Planes Research Articles

Comparative Study on the Crystallography of Isothermal and Athermal Precipitations in HCP-BCC System.

Due to the diversity of the lattice parameter ratio c/a of hexagonal structure and precipitation mechanism, a systematic overview of this transformation has not been fully established, which draws back the attempt to control crystallographic features of the precipitates and microstructures of applied metals and alloys. Here, a comparative investigation to the crystallography of isothermal and athermal precipitations occurring in the HCP-BCC system was demonstrated in a full range of the lattice parameter ratio by using an invariant deformation element (IDE) model. It was then proposed that a precipitation in the HCP-BCC system could be either of the isothermal type if the observed habit plane Miller index falls into a zone axis of BCC <11w>(w ≠ 0) or HCP 211¯0, or the athermal type when it is found to locate in a zone axis of BCC <11w](w = 0) or HCP [0001]. The crystallographic investigation on the precipitations in the HCP-BCC system in a full range of the lattice parameter may be a practical guide for computing material science when building a crystallographic interface model under an optimised orientation relationship, which is necessary to minimise the transformation system energy.

Possible Wave Processes Controlling the Growth of Martensite Crystals at B2-B19, B2-B19' and B2-R Transformations

Basic directions in the theory of martensitic transformations are briefly listed. Within the framework of the dynamic theory based on the synthesis of concepts of heterogeneous nucleation and wave growth of martensite crystals, the possibilities of description of morphological parameters during the В2→B19, В2→B19′, В2→R transformations are analyzed. It is demonstrated that the calculated and observed habit planes and orientation relationships can be matched.

Orientation Relationship, Habit Plane, Twin Relationship, Interfacial Structure, and Plastic Deformation Resulting from the δ → α′ Isothermal Martensitic Transformation in Pu-Ga Alloys

The orientation relationship, habit plane, parent-product interface at the atomic level, twin relationship, and plastic deformation resulting from the δ→α′ isothermal martensitic transformation in Pu-Ga alloys are examined using optical microscopy, transmission electron microscopy (TEM), and finite element calculations. The δ → α′ transformation exhibits a ∼20 vol pct collapse when the fcc δ phase transforms to the monoclinic α′ phase, which results in unique and intriguing crystallography and morphology. Here, we show that the orientation relationship is very close to that previously reported by Zocco et al. (1990), but has small rotational misalignments between the two phases both parallel and perpendicular to the $$ \left[ {110} \right]_\delta ||\left[ {100} \right]_{\alpha '} $$ direction. The amount of plastic deformation is exceedingly large due to the ∼20 vol pct collapse, and TEM is used to quantify the difference in dislocation density between untransformed δ matrix and regions of δ adjacent to the transformed α′. The twins contained in α′ plates are shown to have a (205) α orientation as the lattice invariant deformation and are found to be composed of two alternating variants that share a common α′ direction, but differ by a 60 deg rotation about α′ . A combination of electron diffraction and optical microscopy has been employed to examine the macroscopic habit plane, and the analysis suggests that a large fraction of the observed habit planes are on or near {111} δ . Finally, high resolution TEM reveals that the interface is faceted on {111} δ exhibiting a series of terrace and ledges.

Application of invariant plane strain (IPS) theory to γ hydride formation in dilute Zr–Nb alloys

The crystallographic aspects associated with the formation of the γ hydride phase (fct) from the α (hcp) phase and the β (bcc) phase in Zr–Nb alloys have been studied in two distinct situations, viz., in the α matrix in pure Zr and Zr–2.5Nb and in the β matrix in β stabilized Zr–20Nb alloy. The β–γ formation can be treated primarily as a simple shear on the basal plane involving a change in the stacking sequence. A possible mechanism for α–γ transformation has been presented in this paper. In this paper the β → γ transformation has been considered in terms of the invariant plane strain theory (IPS) in order to predict the crystallographic features of the γ hydride formed. The lattice invariant shear (LIS) (1 1 0) β [ 1 ¯ 1 0 ] β ||(1 1 1) γ [ 1 2 ¯ 1 ] γ has been considered and the crystallographic parameters associated with bcc → fct transformation, such as the habit plane and the magnitude of the LIS and the shape strain have been computed. The predictions made in the present analysis have been compared with experimentally observed habit planes. The α/γ and β/γ interface has been examined by high resolution transmission electron microscopy (HRTEM) technique to compare with the interfaces observed in martensitic transformations.

High-resolution electron microscopy study of ledge structures and transition lattices at the austenite–martensite interface in Fe-based alloys

In order to clarify how the lattices of austenite and martensite are connected at the interface on the atomic scale in the region within the width of the transformation twins or between slipped planes, a high-resolution electron microscopy study of the austenite–martensite interface was performed for Fe–23.0Ni–3.8Mn, Fe–30.5Ni–10Co–3Ti and Fe–8.8Cr–1.1C (mass %) alloys. Martensitic transformations occur at a low temperature in these alloys and exhibit various transformation characteristics, such as isothermal and athermal transformations, Kurdjumow–Sacks and Nishiyama orientational relationships, and a reversible mobile interface and a non-reversible interface in the reverse transformation. There were three important findings: (1) the (121)f interface is made up of two component planes, i.e. the terrace plane (111)f (//(011)b) and the ledge (0 0)f, and the average numbers of atom rows of [ 01]f (//[ 1]b) on these planes are 2.7–4.9 on (111)f and 1.3–2.6 on (0 0)f. These are different depending on the alloy, but the ratio of the atom rows of the former to the latter is about 2:1, in accordance with the observed habit plane of (121)f; (2) the neighbouring (0 0)f ledges are separated by about five to ten planes of (112)b; and (3) transition lattices from fcc to bcc (or bct) exist at the interface and the thickness of this transition lattice region is 0.2–0.8 nm. It is reasonably assumed that screw dislocations with a Burgers vector of 1/2[ 01]f (//1/2[ 1]b) reside at the ledge of the interface, which produces the lattice invariant deformation when they move with the interface. The complete scheme for the relaxation of the strain at the interface is considered to be as follows. First, transformation twins are introduced to relax the strain at the interface on the macroscopic scale, in accordance with the phenomenological theory, then screw dislocations are brought in at the ledges to release the strain between each of the twin-related martensite crystals and the austenite, and, finally, transition lattices are generated at the interface to relax the strain on the most microscopic scale, i.e. at the atomic level.

Crystallography of nanometre-sized α′-martensite formed at intersections of mechanical γ-twins in an austenitic stainless steel

Nanometre-sized !′-martensites (bcc, denoted by α), a few nanometres in cross-sectional diameter, formed at intersections of deformation twins, have been found in a heavily deformed 316-type austenitic stainless steel (fcc, denoted by γ) and examined by high-resolution transmission electron microscopy (HRTEM). An orientation relationship was found to be close to the Kurdjumov-Sachs relationship, that is (111)γ//(101)α, [10amp;1macr;]γ//[11amp;1macr;]α. HRTEM observations were conducted with a beam direction parallel to [10amp;1macr;]γ//[11amp;1macr;]α. The observed nanometre-sized !'-martensites exhibited a (2amp;5macr;2)γ habit plane and the (10amp;1macr;)γ//(11amp;1macr;)α cross-section of the nanometre-sized !'-martensites were elongated along [545]γ. It has been revealed that the nanometre-sized !'-martensites of a few nanometres diameter formed at the intersections of deformation twins have a typical habit plane of (2amp;5macr;2)γ, which is identical with that reported for a fully grown plate such as !'-martensite. The origin of the observed habit plane is discussed on the basis of the ⟨112⟩{111}γ shear displacements assisting the γ → α′ transformation.

Crystallography of Hydride Formation in Zr-Nb Alloys

ABSTRACTThe crystallographic and morphological aspect associated with the formation of γ hydride phase (fct) from the β phase in β abilized Zr-20%Nb alloy has been reported. In this paper the βto γ transformation has been considered in the terms of the phenomenological theory of martensitic crystallography in order to predict the crystallographic features of the γ hydride in the β to γ transformation. The prediction made in the present analysis has been found to match very closely to the experimentally observed habit plane. The possibility of the α to γ transition through the formation of a transient β configuration has been examined.

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 e-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 e′- 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.

The invariant line and precipitation in a Ni-45 wt% Cr alloy

A three-dimensional invariant line strain model for f.c.c./b.c.c. phase transformations is developed and used to predict the growth direction and habit plane of lath-shaped precipitates. The results of this approach are shown to be essentially identical to those that can be derived from Bollmann's 0-lattice theory for a Kurdjumov-Sachs orientation relationship. Both theories are in excellent agreement with the experimental observations of Cr-rich (b.c.c.) precipitates in a Ni-Cr alloy. The growth direction of the lath precipitates lies ~5 1 2 ° from the common close-packed directions in the two lattices along an invariant (or near-invariant) line. The observed habit plane, {112} f is the unrolated plane of the phase transformation. The second facet plane of the precipitates, lying close to {313} f, is also predicted from the 0-lattice model.

A TEM study of α″-Fe 16N 2 and γ′-Fe 4N precipitation in iron-nitrogen

Precipitation of β″-Fe 16N 2 and γ′-Fe 4N in thin foil and bulk-aged nitrogen-ferrite was studied by in situ HVEM and conventional TEM techniques. Detailed analyses of the precipitate morphology, symmetry, and internal fine structure, have led to an improved understanding of the factors controlling the growth habits. The observed habit planes and orientation relationships for both types of precipitate are in good agreement with theoretical predictions. Evidence for various modes of strain accommodation was found, including formation of polytypes in the γ′ phase, and formation of groups of self-accommodating variants of both α″ and γ′ particles.

The precipitation of γ-hydride plates in zirconium

On slow cooling high purity zirconium containing 40 ppm hydrogen, γ-hydride (ZrH) precipitates as acicular plates. This paper considers the possibility that such plates form by a displacive or shear transformation. The habit planes and orientation relationships of hydrides have been determined and related to possible dislocation mechanisms for the transformation. It is shown that habit planes close to {10–17} Zr are predicted for hydrides having a [l1̄0] γ ∥[12̄10] Zr, (111̄) γ~ ∥(0001) Zr orientation relationship. Hydrides with {10-10} habit planes have a [11̄0] γ or [101̄] γ ∥[12̄10] Zr and [001] γ or [010] γ ∥[0001] Zr orientation relationship. In this case, the observed habit plane can only be invariant if the pure lattice strain is succeeded by a pure shear shape change. Experimentally, internal twinning in the plates and dislocation arrays at the interface are observed and it is suggested that these accomplish the required shape change. In the final section of the paper, these results are related to the problem of hydride reorientation and hydride cracking in zirconium alloys.

A check of the I.P.S. theory with the aid of an accurate determination of habit planes and orientation relationships in bainitic steels

With the aid of a new method of habit plane determination, which has been described earlier [1,2], it is possible to determine the orientation relationship in specimens of a commercial 35NiCr18 steel within a deviation of 1°, despite the fact that the orientations of the bainite plates are measured by means of electron diffraction. This new method is based on the orientation determination of the austenite prior to the bainite transformation at 365°C using annealing twin traces on a surface of the crystal. The observed habit planes relative to the f.c.c. and b.c.c. structure are irrational but the mean values are close to {569}γ and {2 7 10}λ respectively, while the orientation relationship is of the type Kurdjumov-Sachs. The I.P.S. theory can not account for the observed habit planes and orientation relationships because the choice of the shear elements of the lattice invariant strain is not unrestricted, and twinned bainite has never been observed in the present investigation as required by the double shear theory.

On a martensitic phase transformation in zirconia (ZrO 2)—II. Crystallographic aspects

Crystallographic aspects of the martensitic tetragonal → monoclinic phase transformation in zirconia single crystals have been studied experimentally and compared with predictions of the phenomenological theory of martensite crystallography. Two different orientation relationships have been observed between the high and low temperature phases. Above 1000°C, the transformation occurs according to the orientation relations (100) m∥~(100) t and [010] m∥~[001] t, while below 1000°C, (100) m~(100) t and [001] m∥~[001] t were observed. These results indicate that the habit planes of the plate-like martensite products reported in the first paper of this series [ Acta Met. 20, 1281 (1972)] had been incorrectly indexed; this occurred because of an incorrect assumption that a single crystal undergoing a monoclinie → tetragonal → monoclinic cycle would return to its original orientation at the end of the cycle. Application of the phenomenological theory of martensite crystallography indicates that the observed habit planes can be predicted using a single Bain correspondence, implied by the lower temperature orientation relations, combined with different lattice invariant deformation modes.

Theoretical and experimental aspects of the “(225)” austenite-martensite transformation in iron alloys

Measurements of the habit plane, p 1′, the direction of the shape strain, d 1; and the orientation relationship, R, were made for an Fe-Cr-C alloy. The classical “(225)” hahit plane is believed to be non-existent; allowing for experimental errors, all of the habit plane measurements obtained to date and all of the present p 1′ determinations do not lie on the boundary between (001) f and (111) f. The shape strain results indicate that a uniform dilatation (δ > 1 ) is more consistent with observations than the case where the interface is one of zero-average distortion (δ = 1). Particular states of interface strain such as that proposed by Frank and Suzuki, and an ad hoc δ-δ-δ∗ strain were studied for consistency. An anisotropic interface distortion is considered to be unlikely. The phenomenological theory does not permit the orientation relationship to be deduced from first principles. Within the framework of the theory, a dilatation is needed, but it is the required dilatation which produces the discrepancy between the observed and predicted orientation relationships. The theory in its present form, it is concluded, cannot account for all aspects of the “(225)” transformation: for example, the observed habit plane and orientation relation can be predicted, but the predicted direction of the shape strain differs from the observed one; alternatively the observed habit plane and direction of the shape strain can be successfully predicted, but the predicted orientation relationship is not consistent with that observed.

Metallographic Study of the Martensite Transformation in Lithium

1. Techniques have been developed for the metallographic examination of lithium and the microstructural characteristics of lithium martensite are described. 2. The lithium habit plane has been shown to be approximately {441}. This is not in agreement with Burgers’ prediction of {112} but is closely similar to the habit planes utilized in other martensite transformations in body-centered cubic metals. 3. The atom movements proposed by Burgers are probably correct for they are consistent with the observed superlattice in Cu−Al martensite. To modify Burgers’ mechanism so that it becomes consistent with the observed habit plane and relief effects, it will be necessary to find out how the “Burgers’ unit distortion” is repeated throughout the lattice.