Energetic Origins of Competing Deformation Modes in Metastable Titanium Alloys

TL;DR

This study investigates why competing deformation modes emerge in metastable beta-Ti alloys under varying temperature, composition, and loading. Molecular dynamics simulations reveal that both {112} and {332} twinning pathways proceed through reversible beta-to-alpha'' transformations, with mode selection governed by two energetic parameters: the free-energy barrier for the beta↔alpha'' transformation and the misfit-strain energy along the phase boundaries. The authors define a twin-nucleation metric that combines these contributions and develop a flowchart to predict when TRIP, TWIP, or dislocation slip will dominate, providing a physically grounded framework for alloy design. The approach offers a pathway to high-throughput screening and can be extended to refractory high-entropy alloys, emphasizing energetics over simple phase-stability descriptors for deformation-mode control.

Abstract

Metastable alloys, such as $β$-phase titanium (Ti) alloys with a body-centered cubic (BCC) lattice, can exhibit exceptional mechanical properties through the interplay of multiple deformation mechanisms -- diffusionless phase transformations, deformation twinning, and conventional dislocation slip. However, understanding how these mechanisms compete or cooperate across a wide range of metastable alloys and loading conditions remains a fundamental challenge. Here, we employ molecular dynamics (MD) simulations to investigate the nucleation behavior of competing deformation modes in metastable $β$-Ti alloys as a function of temperature, composition, and loading conditions. We reveal that twinning pathways emerge through reversible transformations between the $β$ phase and the orthorhombic $α"$ phase, in agreement with crystallographic theories. Quantitative analyses demonstrate that the dominant deformation mechanisms and preferred twinning-plane orientations are governed by two key energetic parameters: the free energy barrier for homogeneous $β\leftrightarrow α"$ transformations and the misfit strain energy along specific phase boundaries. These energetic quantities vary systematically with thermodynamic and mechanical conditions, thereby rationalizing the deformation mode transitions observed in both simulations and experiments. These energetic metrics offer a physically grounded and computationally tractable basis for designing next-generation metastable alloys.

Figures (8)

• Figure 1: Coexistence of {112} twin and {332} twin in 5$\%$ cold-rolled Ti2448 (Ti–24Nb–4Zr–8Sn) sample.A is the TEM figure illustrating morphology of {112} twin and {332} twin, red circle mark the boundary of {332} twin, and orange circle mark the boundary of secondary {112} twin located inside the {332} twin region. B-C are the diffraction patterns at the boundary of{112} twin and {332} twin. D-E are schematic draws for the {112} twin boundary and {332} twin boundary.F show an example of formation of BCC twin phase via reversible $\beta$-$\alpha"$ phase transformations.
• Figure 2: Atomistic structural evolution and deformation modes of Ti-Nb alloys under varying temperature, composition, and stress/strain conditions by MD simulations. In all cases, the shear loading is along [311] direction on ($\bar{2}$33) planes. Temperature, composition and stress/strain conditions are fixed in each row: (A-C) is Ti$_{5}$Nb under 77 K, non-confined simple shear condition; (D-F) is Ti$_{5}$Nb under 77 K, confined simple shear condition; (G-I) is Ti$_{4}$Nb under 300 K, non-confined simple shear condition; (J-L) is Ti$_{2}$Nb under 300 K, non-confined simple shear condition. From top to down, (A,D,G,J) are snapshots of atomistic structures before loading applied; (B,E,H,K) are snapshots of atomistic structures when applied shear strain is 0.12 and different deformation modes produced; (C,F,I,L) illustrate nucleation of different metastable phases during shear loading and dynamic volume fraction change. Color interpretation of atoms in the MD snapshots locating at the top of the figure. dominant deformation mode of each row is different: (A-C) is $\alpha"$ martensite; (D-F) is {332} twin; (G-I) is {112} twin and (J-L) is dislocation slip.
• Figure 3: Temperature and composition conditions for {332} twin nucleation for Ti-Nb alloys in experiments hanada1986effecthanada1985deformationyang2010evolutionzhan2016dynamicshin2017phasechen2018transitionalliang2020rolezhang2019plasticgordin2020newyang2020plasticgao2025manipulatingzhan2015deformationbertrand2016deformation. In A, data points marked in pink rectangle (Nb concentration is less than 24 wt$\%$) indicates that dominant deformation mode is $\alpha"$ martensite and {332} twin. {332} twin (and small volume of {112} twin) can form insensitive to temperature and loading condition when Nb concentration is between 25 wt$\%$ and 36 wt$\%$ (data points in light green circle). {332} twin can form by carefully controlling loading condition under cryogenic temperatures (Nb concentration is between 36 wt$\%$ and 47 wt$\%$). Within this region, {112} twin and slip can also form and compete with {332} twin nucleation. When Nb concentration is larger than 47 wt$\%$, shown in purple region, {332} twin can not form in any condition and dislocation slip is the dominant deformation mode. As for alloys that marked with "*", Nb is the dominant $\beta$ stabilizer element in the composition but the alloy is not binary, they also include small amount of neutral elements and oxygen in addition. In B, we also present the predicted deformation modes of samples in A by $\overline{\text{Bo}}-\overline{\text{Md}}$ diagram. The definition of colors of data points in B are consistently based on the deformation modes observed in experiments in A.The experimental-fitted boundaries for different deformation modes are from Morinaga morinaga2018molecular. Clearly, compared to experimental observations of deformation modes in the samples shown in A, there are large deviation compared to $\overline{\text{Bo}}-\overline{\text{Md}}$ prediction, especially those marked in red rectangles.
• Figure 4: $\beta$-$\alpha"$ energy landscape for Ti alloys, including unstable BCC Ti-alloy ($\alpha$-Ti alloys), metastable BCC Ti-alloys and stable BCC Ti-alloy. Here we choose two collective variables: shuffle magnitude between (011) planes along $[0\bar{1}1]$ directions and "b/a" ratios ("b" is the length of $\langle0\bar{1}1\rangle$ in BCC and "a" is the length of $\langle100\rangle$ in BCC phase). Positions of BCC and $\alpha"$/$\alpha$ phase are marked in the figure. A is for Ti$_{15}$Nb at 300 K, an example of unstable BCC Ti-alloy ($\alpha$-Ti alloys). In this case, only one global minima located near $\alpha$ (HCP) phase and no local minima at BCC. B-C are cases of metastable BCC Ti-alloys: Ti$_{5}$Nb at 77 K and Ti$_{4}$Nb at 300 K. In this case, there are two minima corresponding to $\alpha"$ and BCC phase.D is the case of stable BCC Ti-alloys, which we can only observe one global minima at BCC phase and no local minima for $\alpha"$ phase.
• Figure 5: Facted interfaces of BCC and nucleated $\alpha"$ phase before nucleation of different deformation modes.(A) is illustration on the all conventional coherent $\text{$\beta$}$$\parallel$$\alpha"$ interfaces (marked in orange and blue) consistent with the BOR and defined by {211} planes with in-plane $\langle\bar{1}11\rangle$ directions, lying in the [311]–[$\bar{2}$33] zone. We also mark the ($\bar{2}$33) plane along [311] direction (green line) that closely align to the {332} twin boundary formed under shear loading. The coordinate system in (A) is consistent with that of initial state of simulation box in (B-H). (B) is the snapshot when the system close to the stage of $\alpha"$ phase nucleation saturation. Corresponding setting is consistent with the case in Figure \ref{['fig:Structural']} (A-D). (C-D) are snapshots of critical stage of {112} twin nucleation in the case of Figure \ref{['fig:Structural']} (I-L). (E-H) are the snapshots of {332} twin nucleation process in the case of Figure \ref{['fig:Structural']} (E-H). Here we want to present how the interfaces of $\text{$\beta$}$$\parallel$$\alpha"$ (bottom of the figures) tilt from blue lines to green lines that closely align with {332} twinning plane. Definitions on the colors of atoms are consistent with the definition in Figure \ref{['fig:Structural']}. Lines in (B-H) mark some facted interfaces between BCC and nucleated $\alpha"$ phase. Lines with the same color as A) correspond to closely related orientation.