Hubbry Logo
Diffusionless transformationDiffusionless transformationMain
Open search
Diffusionless transformation
Community hub
Diffusionless transformation
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Diffusionless transformation
Diffusionless transformation
Diffusionless transformation
View on Wikipedia
from Wikipedia
Diffusionless transformation classifications

A diffusionless transformation, commonly known as displacive transformation, denotes solid-state alterations in crystal structures that do not hinge on the diffusion of atoms across extensive distances. Rather, these transformations manifest as a result of synchronized shifts in atomic positions, wherein atoms undergo displacements of distances smaller than the spacing between adjacent atoms, all while preserving their relative arrangement. An example of such a phenomenon is the martensitic transformation, a notable occurrence observed in the context of steel materials.

The term "martensite" was originally coined to describe the rigid and finely dispersed constituent that emerges in steels subjected to rapid cooling. Subsequent investigations revealed that materials beyond ferrous alloys, such as non-ferrous alloys and ceramics, can also undergo diffusionless transformations. Consequently, the term "martensite" has evolved to encompass the resultant product arising from such transformations in a more inclusive manner. In the context of diffusionless transformations, a cooperative and homogeneous movement occurs, leading to a modification in the crystal structure during a phase change. These movements are small, usually less than their interatomic distances, and the neighbors of an atom remain close.

The systematic movement of large numbers of atoms led some to refer to them as military transformations, in contrast to civilian diffusion-based phase changes, initially by Charles Frank and John Wyrill Christian.[1][2]

The most commonly encountered transformation of this type is the martensitic transformation, which is probably the most studied but is only one subset of non-diffusional transformations. The martensitic transformation in steel represents the most economically significant example of this category of phase transformations. However, an increasing number of alternatives, such as shape memory alloys, are becoming more important as well.

Classification and definitions

[edit]

The phenomenon in which atoms or groups of atoms coordinate to displace their neighboring counterparts resulting in structural modification is known as a displacive transformation. The scope of displacive transformations is extensive, encompassing a diverse array of structural changes. As a result, additional classifications have been devised to provide a more nuanced understanding of these transformations.[3]

The first distinction can be drawn between transformations dominated by lattice-distortive strains and those where shuffles are of greater importance.

Homogeneous lattice-distortive strains, also known as Bain strains, transform one Bravais lattice into a different one. This can be represented by a strain matrix S which transforms one vector, y, into a new vector, x:

This is homogeneous, as straight lines are transformed into new straight lines. Examples of such transformations include a cubic lattice increasing in size on all three axes (dilation) or shearing into a monoclinic structure.

Shuffles, aptly named, refer to the minute displacement of atoms within the unit cell. Notably, pure shuffles typically do not induce a modification in the shape of the unit cell; instead, they predominantly impact its symmetry and overall structural configuration.

Phase transformations typically give rise to the formation of an interface delineating the transformed and parent materials. The energy requisite for establishing this new interface is contingent upon its characteristics, specifically how well the two structures interlock. An additional energy consideration arises when the transformation involves a change in shape. In such instances, if the new phase is constrained by the surrounding material, elastic or plastic deformation may occur, introducing a strain energy term. The interplay between these interfacial and strain energy terms significantly influences the kinetics of the transformation and the morphology of the resulting phase. Notably, in shuffle transformations characterized by minimal distortions, interfacial energies tend to predominate, distinguishing them from lattice-distortive transformations where the impact of strain energy is more pronounced.

A subclassification of lattice-distortive displacements can be made by considering the dilutional and shear components of the distortion. In transformations dominated by the shear component, it is possible to find a line in the new phase that is undistorted from the parent phase while all lines are distorted when the dilation is predominant. Shear-dominated transformations can be further classified according to the magnitude of the strain energies involved compared to the innate vibrations of the atoms in the lattice and hence whether the strain energies have a notable influence on the kinetics of the transformation and the morphology of the resulting phase. If the strain energy is a significant factor, then the transformations are dubbed martensitic, if not the transformation is referred to as quasi-martensitic.

Iron-carbon martensitic transformation

[edit]

The distinction between austenitic and martensitic steels is subtle in nature.[4] Austenite exhibits a face-centered cubic (FCC) unit cell, whereas the transformation to martensite entails a distortion of this cube into a body-centered tetragonal shape (BCT). This transformation occurs due to a displacive process, where interstitial carbon atoms lack the time to diffuse out.[5] Consequently, the unit cell undergoes a slight elongation in one dimension and contraction in the other two. Despite differences in the symmetry of the crystal structures, the chemical bonding between them remains similar.

The iron-carbon martensitic transformation generates an increase in hardness. The martensitic phase of the steel is supersaturated in carbon and thus undergoes solid solution strengthening.[6] Similar to work-hardened steels, defects prevent atoms from sliding past one another in an organized fashion, causing the material to become harder.

Pseudo martensitic transformation

[edit]

In addition to displacive transformation and diffusive transformation, a new type of phase transformation that involves a displacive sublattice transition and atomic diffusion was discovered using a high-pressure X-ray diffraction system.[7] The new transformation mechanism has been christened pseudo martensitic transformation.[8]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Diffusionless transformation

View on Grokipedia
from Grokipedia
A diffusionless transformation, also referred to as a displacive transformation, is a solid-state phase change in crystalline materials where the atomic rearrangement occurs without long-range atomic diffusion, relying instead on coordinated shear displacements and shuffles of atoms over distances typically less than one interatomic spacing, thereby preserving the local atomic neighborhood relationships. These transformations are characterized by rapid kinetics, often producing macroscopic shape changes through mechanisms like invariant plane strain, where the interface between parent and product phases remains undistorted on a macroscopic scale. The most prominent example of diffusionless transformations is the martensitic transformation, first identified in quenched steels where (face-centered cubic) converts to (body-centered tetragonal) via a shear-dominated process, resulting in a hard, brittle microstructure without compositional change. Other variants include shuffle transformations, such as the second-order transition in driven by vibrational instabilities, and omega transformations in , both of which involve lattice distortions without diffusion. Crystallographically, these processes are governed by theories like the of Wechsler, Lieberman, and Read (1953), which accounts for lattice deformation (e.g., Bain strain), rigid-body rotation, and lattice-invariant shear (e.g., twinning or slip) to predict orientation relationships and habit planes. In materials engineering, diffusionless transformations play a critical role in enhancing properties such as and strength; for instance, medium-carbon steels (0.4 wt.% C) can achieve yield strengths up to 2240 MPa through formation. They also enable functional behaviors like the shape-memory effect in thermoelastic of Ni-Ti alloys, used in medical stents and actuators, where reversible transformations occur with minimal . Additionally, these transformations contribute to high damping capacity in alloys and the transformation-induced plasticity (TRIP) effect in advanced steels, improving and energy absorption under deformation. Overall, their diffusion-free nature allows for athermal or thermally activated processes that are (discontinuous) or second-order (continuous), influencing through factors like shear and interfacial coherency.

Fundamentals

Definition and characteristics

A diffusionless transformation is a solid-state phase change in which the atoms rearrange collectively through coordinated shear or displacive motions over distances shorter than the interatomic spacing, without involving long-range atomic diffusion and thus preserving the local composition across the interface. These transformations are characterized by their displacive , where the parent and product phases maintain a specific crystallographic orientation relationship, enabling the process to occur via homogeneous or heterogeneous . Initiation typically requires undercooling below the equilibrium transformation (such as T0T_0 or MsM_s), and there is no partitioning or redistribution of solute atoms during the process. Key features include the extremely rapid transformation speed, often approaching or exceeding 10510^5 cm/s—near the in —allowing the interface to advance almost instantaneously across the . The transformation can be athermal, progressing with decreasing without time dependence, or isothermal, occurring at a constant over time. A defining geometric aspect is the presence of a habit plane, which corresponds to an invariant plane strain where the lattice remains undistorted in one plane, minimizing overall strain. These processes frequently result in the formation of metastable phases, such as supersaturated solid solutions, due to the kinetic constraints that prevent equilibrium compositions from being achieved. To accommodate the resulting lattice distortions, internal mechanisms like twinning or plastic slip often operate within the transformed regions, alongside elastic strains. Additionally, such transformations are associated with a volume change upon completion; for instance, the formation of typically involves a shear-induced expansion of about 3-4% in volume. Martensitic transformations exemplify these traits as the archetypal diffusionless process.

Comparison with diffusional transformations

Diffusional transformations in involve long-range atomic diffusion, where atoms move over distances comparable to atomic spacings via thermally activated jumps, leading to the formation of equilibrium phases such as and in iron-carbon alloys. These processes require solute redistribution and partitioning to achieve compositional differences between parent and product phases, resulting in slower kinetics primarily governed by diffusion coefficients that follow an Arrhenius dependence on temperature. Interface migration during these transformations occurs gradually through diffusion-controlled mechanisms, with energy barriers arising from gradients and the for atomic diffusion, typically in the range of 45–65 kcal/mol for substitutional solutes. In contrast, diffusionless transformations lack any significant solute partitioning or long-range atomic , preventing the formation of equilibrium compositions and instead producing non-equilibrium structures with uniform solute distribution inherited from the parent phase. Rather than relying on diffusive interface migration, these transformations proceed via coordinated shear mechanisms that maintain an invariant plane strain, where the transformation interface glides without disrupting the lattice on a specific habit plane, enabling rapid and uniform shape changes. This shear-dominated process contrasts sharply with the reconstructive nature of diffusional transformations, as diffusionless ones are displacive, involving and synchronized movements of groups of atoms rather than random, independent atomic jumps. A key distinction in activation lies in the energy barriers: for diffusionless transformations, these stem primarily from elastic strain energy associated with lattice distortions and volume changes during the shear process, contributing to the total change alongside chemical driving forces. Diffusional transformations, however, face barriers dominated by chemical diffusion across interfaces, without the prominence of elastic strains. Kinetically, diffusionless transformations are characterized by athermal behavior defined by specific temperatures—Ms (martensite start, where transformation begins) and Mf (martensite finish, where it completes)—independent of time, unlike the time-dependent isothermal nature of diffusional ones depicted by the C-shaped nose in time-temperature-transformation (TTT) diagrams, where transformation rates peak at intermediate undercoolings due to balanced driving force and diffusion mobility.

Mechanisms and thermodynamics

Crystallographic theory

The phenomenological theory of martensite crystallography (PTMC) provides a framework for understanding the structural changes in diffusionless transformations by modeling the transformation as a sequence of homogeneous lattice deformation, , and lattice-invariant shear, resulting in an overall invariant plane strain where the habit plane remains undistorted and unrotated. This theory, independently formulated by Wechsler, Lieberman, and Read in 1953 and by Bowles and Mackenzie between 1952 and 1954, emphasizes that the transformation proceeds without atomic , ensuring that the martensite inherits the exact composition of the parent phase. Central to PTMC are specific orientation relationships between the parent and product lattices, such as the Kurdjumov-Sachs relation, where {111} planes in face-centered cubic (FCC) align parallel to {110} planes in body-centered cubic (BCC) , and <110> directions in FCC align with <111> in BCC, or the Nishiyama-Wassermann relation, featuring {111} FCC parallel to {110} BCC but with <211> FCC parallel to <100> BCC. The habit plane, typically denoted as {225} or {259} in for Kurdjumov-Sachs, serves as the undistorted interface, while the interface structure often involves a glide plane (close to the habit plane) or the martensite plane, with any residual mismatch accommodated by arrays of dislocations. A key component of the lattice deformation in FCC-to-BCC transformations is the Bain strain, proposed by Bain in , which involves a homogeneous tetragonal : contraction along two orthogonal axes in the {001} plane and expansion along the third, transforming the FCC cube into a BCC structure while preserving the nearest-neighbor distances approximately. To achieve the invariant plane strain, the shape change from this is accommodated by lattice-invariant shear, often via twinning in low-stacking-fault-energy materials or slip in others, forming transformation twins that minimize overall . The total deformation is described by the deformation gradient tensor F=RBP\mathbf{F} = \mathbf{R} \mathbf{B} \mathbf{P}, where R\mathbf{R} is the rotation matrix, B\mathbf{B} represents the Bain strain matrix (e.g., for FCC-to-BCC in iron: B=(200020001/2)\mathbf{B} = \begin{pmatrix} \sqrt{2} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & 1/\sqrt{2} \end{pmatrix}
Add your contribution
Related Hubs
User Avatar
No comments yet.