Source: D. Raabe, Z. Li, D. Ponge, “Metastability alloy design”, MRS Bulletin 44 (2019), pp. 266–272, doi:10.1557/mrs.2019.72. Max-Planck-Institut für Eisenforschung, Germany.

Most materials are thermodynamically metastable at some stage during synthesis, processing, and service. The microstructure — interfaces, dislocations, stacking faults, composition gradients, dispersed precipitates — is precisely the collective ensemble of all features in a material that are not in thermodynamic equilibrium. These defects are retained because of their local mechanical stability and their slow relaxation and annihilation kinetics, and they endow metallic alloys with their load-bearing properties. Thermodynamic metastability is therefore a desired material state and the main target of practically all processing steps after primary synthesis; alloys in true thermodynamic equilibrium are a rare exception with little relevance for applications.

Metastability alloy design (MAD) goes one step further. Instead of accepting metastable phases that are coincidentally inherited from processing, they are engineered: compositional (partitioning), thermal (kinetics), and microstructural (size effects and confinement) tuning of metastable phases so that they trigger athermal transformation effects when the material is mechanically, thermally, or electromagnetically loaded. The concept works both at the bulk scale and at a spatially confined microstructure scale, such as at lattice defects. In the latter case, local stability tuning works primarily through elemental partitioning to dislocation cores, stacking faults, interfaces, and precipitates. Depending on stability, spatial confinement, misfit, and dispersion, both bulk and local load-driven athermal transformations equip alloys with substantial gains in strength, ductility, and damage tolerance. Examples include self-organized metastable nanolaminates, austenite reversion steels, metastable medium- and high-entropy alloys, and steels and titanium alloys with martensitic phase transformation and twinning-induced plasticity (TRIP and TWIP) effects.

An interesting feature of metastable alloy systems is that the thermodynamic weakness of a phase — its lack of stability — triggers deformation mechanisms that lead to higher strength and damage tolerance. Athermal deformation mechanisms are often not commensurate: they require the activation of additional mechanisms such as dislocation slip and secondary twinning to accommodate and compensate local shape and volume mismatch upon deformation.

Athermally triggered deformation also introduces a size effect into strain hardening, because it occurs in confined regions with high deformation activity, in particular at the interfaces between the host matrix and the transformed volume portion. High populations of geometrically necessary dislocations — dislocations accommodating local lattice curvature — are associated with this confinement.

When metastability is spatially confined, a double size effect appears: both the athermally transformed volume and the accommodation plasticity surrounding it are size dependent. Athermal transformation can be triggered at dimensions as small as a few atomic layers.

Because the athermal transformation of a (partially) metastable microstructure is activated through deformation, the host phase’s degree of metastability can be shifted into a load range where local material weakening sets in. The onset of athermal transformation events then provides additional strain hardening precisely in those regions and at those load stages where the material is most highly deformed and stressed, such as shear bands, crack tips, and notches. Metastability alloy design can lend a certain self-healing capacity to metallic materials, because the associated athermal transformations become active first in the locally softened regions that experience high peaks in deformation and load.

Athermal transformation also creates volume mismatch. The volume occupation of the athermally formed new phase can be either larger or smaller than that of the matrix phase, creating local compressive or tensile stress fields. Compressive stresses in particular can assist in closing, blunting, or branching crack tips. This applies specifically to alloys that contain interstitial elements which, when frozen-in upon transformation, create a tunable volume mismatch between the host and the product phase.

Athermal deformation mechanisms and the role of stacking-fault energy

Materials in which metastability is successfully utilized for microstructure design include alloys undergoing spinodal decomposition, metallic glasses and crystal-glass composites, bulk TWIP and TRIP steels, shape-memory alloys, and TRIP titanium alloys. In TWIP, TRIP, and quench-partitioning steels, face-centered-cubic (fcc) phase stability is typically tuned by adjusting the Mn, Ni, C, N, Al, and Si content. Interestingly, a harmful impurity element such as hydrogen (H) can also be used for metastability design: it reduces the stacking-fault energy in Ni and in high-entropy alloys.

Depending on the stacking-fault energy, or more generally on the free energy difference between the matrix phase and the next available stable or metastable phase state accessible through athermal transformation, a wide variety of deformation mechanisms triggered under load can be observed. Among these are the formation of hexagonal-close-packed (hcp, ε phase) or body-centered-tetragonal (bct, α′ phase) martensite variants in an fcc host matrix, mechanical twin formation, planar slip through dislocation core expansions, stacking faults, formation of crystallographic slip bands and their successive dynamic refinement, and partial dislocations, including stair-rod dislocations.

Of particular interest is the recently observed bidirectional TRIP effect: deformation-driven forward and reverse (bidirectional) martensitic transformation. It occurs when the stacking-fault energy approaches near-zero values and is realized for the fcc–hcp case by the forward and reverse motion of dissociated Shockley partial dislocations. In this situation the bulk matrix no longer has a preference as to which structure to assume; local transformation events and microstructure scaling are dominated by the specific barriers of the lattice defects that carry the respective transformation mechanism. The fcc and hcp phases can then coexist and athermally transform into each other upon loading, even in a reversible fashion. If a bcc/bct phase has a similar free energy, up to three of these phases can occur simultaneously, as observed in several stainless duplex steels and TRIP steels, where the fcc phase athermally transforms into hcp regions and further into the bcc or bct phase, preferably at the intersection of two hcp bands. In some of these metastable alloys, deformation via athermal transformations leads to complex cascades of metastable transition states, with some phenomenological similarity to microstructure formation in spinodally decomposing alloys.

For many fcc alloys (γ), the most frequently occurring adjacent, more stable phases are ε (hcp), α (bcc), and α′ (bct). The reduction of stacking-fault energy can therefore be used as an approximate measure and guideline for designing alloys with a desired metastability.

Bulk metastability alloy design for medium- and high-entropy alloys

Medium- and high-entropy alloys represent a material class particularly well suited for compositional tuning with the aim of rendering it thermodynamically metastable. Their stacking-fault energy can be adjusted over a wide range, especially by dropping the entropy maximization rule, which opens access to a nearly infinite range of nonequimolar compositions.

Several new materials have recently been introduced in which substantial strain hardening is observed due to athermal transformation of the metastable massive solid-solution matrix. For example, the phase stability of high- and medium-entropy materials pertaining to the FeCrMnCoNi system, as well as of interstitially doped high-entropy alloys, can be well tuned by modifying the ratio among Fe, Mn, Ni, Cr, and Co. Beyond fcc phase-stability trimming, hydrogen was also observed to reduce the stacking-fault energy of certain high-entropy alloys with these solid-solution element ratios. This effect opens the opportunity to exploit this otherwise harmful impurity element for metastability tuning of alloys that are exposed to harsh hydrogen-containing environments.

Several studies on these alloy systems revealed that their prevalent deformation mechanisms change when reducing the stacking-fault energy:

• Stacking-fault energy ≥ 50 mJ/m²: deformation by dislocation shear.
• 20 mJ/m² ≤ stacking-fault energy ≤ 40 mJ/m²: additional mechanical twinning.
• Stacking-fault energy ≤ 20 mJ/m²: dislocation shear plus hcp martensite formation.

Another interesting deformation phenomenon was recently observed when approaching the limit of near-zero stacking-fault energy in fcc high-entropy alloys: a bidirectional transformation induced plasticity (B-TRIP) effect. This mechanism describes the joint occurrence of athermal forward transformation from an fcc matrix phase into an hcp nanolamellar structure and the partial dynamic reverse transformation back from hcp to fcc.

Similar athermal effects can be achieved in TiZrHf-based medium- and high-entropy alloy systems when blending them with bcc-stabilizing elements such as Nb, V, Ta, Mo, W, Cr, and Fe, rendering them metastable bcc alloys. Athermal transformation sequences in such metastable bcc high- and medium-entropy alloys include formation of bcc twins, athermal bcc-to-hcp phase transformation, hcp twins, and omega phase formation. Chemical ordering and cluster formation may also play a role.

Spatially confined metastability: segregation engineering at lattice defects

Segregation engineering is a concept that renders not the entire host matrix, but only certain regions or phases of an alloy metastable through a corresponding heat treatment and elemental partitioning. For some engineering alloys this approach is well established and has been applied to adjust the stability of adjacent mesoscopic phases, such as in quench-partitioning, medium Mn, and duplex stainless steels. In such cases, several size and confinement effects apply. While composition-dependent stacking-fault energy, temperature, and strain rate are the most influential parameters for triggering athermal deformation mechanisms and their activation sequence, specific additional features can be tuned through local chemical partitioning, grain size, texture, and the dislocation substructure.

It should be emphasized that compositional partitioning generally occurs not only among adjacent mesoscopic phases, but also between the bulk matrix and its lattice defects. Such local chemical decoration effects at lattice imperfections such as dislocations, stacking faults, and grain boundaries can be readily engineered due to the self-organizing nature of the mean-field McLean or Fowler–Guggenheim isotherms. Isotherms are thermodynamic models describing element partitioning between a lattice defect and its adjacent matrix region: the McLean isotherm assumes statistical decoration without any chemical interaction among the segregating atoms, while the Fowler–Guggenheim isotherm assumes interaction among the segregating atoms.

Typical metallic microstructures represent an array of sinks for trapping solute elements. Each type of lattice defect provides a characteristic density of trapping states and an associated distribution of characteristic trapping energies. When exposed to a heat treatment, the solute elements redistribute among these multiple traps, which leads to characteristic chemical compositions at the different lattice defects. These individual local decoration states can then lead to individual local metastability states at the defects, capable of producing local phase states that can undergo athermal transformation when exposed to loads. Compositional adjustment of such local partitioning effects to lattice defects can be readily achieved by adjusting the corresponding heat treatments.

An example is the local chemical partitioning of Mn to the low-angle lath interfaces of a Fe–Mn-based cubic martensite, which promotes local metastable martensite-to-austenite reversion at these interfaces. These metastable nanolaminate layers undergo spatially confined transformation from austenite back to bcc martensite under mechanical fatigue loading, triggered by an approaching crack. This confined phase transformation reduces the crack propagation rate through compressive stresses, crack branching, or blunting — an effect phenomenologically resembling the micromechanics of bone.

Summary and outlook

Thermodynamic phase metastability can be utilized to make metallic alloys stronger and more ductile. Two types of approach are covered: first, mechanisms and examples of bulk metastability alloy design known from transformation- and twinning-induced steels, Ti-alloys, and high-entropy alloys; and second, spatially confined metastability created by heat treatments in which elemental partitioning between the matrix and its lattice defects leads to local metastable phases, a concept also referred to as segregation engineering.

Three trends seem particularly promising for further work along these lines:

1. Bidirectional athermal transformation, occurring when the stacking-fault energy approaches near-zero values, leads to an ongoing refinement of the microstructure down to the nanometer regime. The resulting high density of interfaces and stacking faults reduces the mean free dislocation path and thus provides high strength and ductility.
2. Well-targeted segregation at lattice defects, exploiting their usually high density, with the aim to render them metastable and thus amenable for athermal phase transformation when mechanically loaded.
3. The use of less expensive alloying elements. Most of the currently developed metastable high- and medium-entropy alloys use expensive alloying elements such as Co and Ni. These could be replaced by much less costly elements, such as Mn, C, or N, which create similar thermodynamic trends.