Orientation‑Dependent Phase Transformations of B2 CuZr: Insights from Molecular Dynamics

Introduction

Bulk metallic glasses (BMGs) combine exceptional strength, elasticity, and corrosion resistance, yet their brittle failure through localized shear bands limits widespread application. Embedding ductile B2 CuZr particles has proven effective in mitigating this drawback, providing a toughening mechanism that is still under active investigation [1–11]. In CuZr‑based BMG composites, the B2 phase can form during crystallization under load, subsequently undergoing twinning and dislocation glide that alter the host matrix’s mechanical response [12]. Understanding the deformation behavior of the reinforcing CuZr particles is therefore critical for designing high‑performance BMGs.

The B2 CuZr alloy is a prototype shape‑memory alloy that recovers its original shape under specific thermo‑mechanical conditions, distinguishing it from conventional crystalline materials whose deformation is dominated by dislocation glide or twinning [13,14]. First‑principles calculations provide atomic‑scale insight into adsorption and interfacial phenomena [18–22], but they cannot capture the dynamic evolution of phase transformations at the relevant length and time scales. Molecular‑dynamics (MD) simulations, in contrast, offer a powerful approach to study mechanical properties and deformation mechanisms in detail [23–31]. Prior MD work has revealed cross‑sectional and temperature effects on Cu‑Zr nanowire phase transformations, as well as tension–compression asymmetry [32–34]. Moreover, the choice of interatomic potential influences the predicted martensitic transition from B2 to BCT [13,35–36].

Crystal anisotropy profoundly influences deformation mechanisms; different loading directions can activate distinct processes such as dislocation glide, twinning, or phase transformation [37–40]. For B2 CuZr, the atomic arrangement closely resembles a body‑centered cubic (BCC) lattice, but the presence of two distinct elements introduces additional complexity. In BMG composites, the reinforcing particles are randomly oriented, so the loading direction relative to the particle crystallography will modulate the toughening effectiveness. Consequently, a systematic investigation of the B2 phase under uniaxial tension and compression along multiple orientations is warranted.

In this study, we conduct a series of MD simulations of uniaxial tension and compression on B2 CuZr crystals oriented along [001], [110] and [111] to elucidate orientation‑dependent phase transformation pathways and the associated tension–compression asymmetry.

Methods

We employ the embedded‑atom method (EAM) potential developed by Mendelev et al. in 2016 [47], which accurately reproduces the stacking‑fault energies and crystallographic properties of CuZr. Three single‑crystal samples were constructed with the loading axis along [001], [110] and [111], as illustrated in Fig. 1. Prior to loading, a conjugate‑gradient (CG) energy minimization followed by a 20 ps NPT equilibration at 300 K (zero pressure) prepared a relaxed starting configuration.

Uniaxial strain was applied at a rate of 10⁹ s⁻¹, the typical range for nano‑scale MD studies where strain‑rate sensitivity is negligible [48,49]. The NPT ensemble with a Nose–Hoover barostat kept the lateral stresses at zero, ensuring constant volume in the transverse directions. Periodic boundary conditions were enforced in all directions.

Samples with axial z along a [001], b [110], and c [111], colored by atomic type.

Local crystal structures were identified using polyhedral template matching (PTM) [52], which remains robust under thermal fluctuations and strain. The PTM output was mapped to colors: blue (BCC/B2), green (FCC), red (HCP/stacking fault), purple (SC), and white (grain boundaries or dislocation cores). The centro‑symmetry parameter (CSP) was also calculated for each atom to quantify local disorder (Eq. 1) [53].

All MD data were visualized with Ovito [54].

Results and Discussions

Stress–Strain Curves

Figure 2 displays the σ–ε curves for the three orientations under tension and compression. The initial linear regime reflects elastic behavior; slopes yield Young’s modulus values (Table 1), showing that the [001] orientation is the softest and [111] the stiffest, consistent with BCC iron anisotropy [40]. Stress peaks and subsequent drops correspond to the onset of inelastic deformation. Three distinct post‑peak behaviors emerged: (I) rapid stress decline, (II) plateau followed by a secondary peak, and (III) zig‑zag fluctuations. These differences indicate orientation‑dependent transformation pathways.

σ–ε curves of samples under tension (T) and compression (C). a [001], b [110] and c [111].

Failure Behavior

Under compression along [110] and [111], the σ–ε curves exhibit a sharp drop coinciding with the appearance of mixed‑phase regions (Fig. 3). Radial distribution functions (RDFs) confirm that these regions are amorphous, while the remaining B2 domains remain crystalline. No dislocation nucleation was detected, indicating that localized amorphization is the primary failure mechanism. Similar behavior occurs in tension along [001] and [110] and compression along [001] (Fig. 4), where mixed regions are surrounded by FCC or HCP phases, suggesting a transformation of the B2 lattice into these structures before amorphization.

Atomic configurations and RDFs of samples under compression. a–d Along [110] and e–h along [111].

Atomic configurations in samples at failure strain. a Under tension along [001], b under tension along [110], and c under compression along [111].

Phase Transformations

Figure 5 tracks the evolution of the [001] tensile test. Initially, the B2 lattice is intact (ε = 0.079). At ε ≈ 0.082, a localized B2→FCC transition initiates, causing the first stress drop. As deformation continues, the FCC phase grows, and by ε = 0.242 the entire sample has transformed to FCC (Fig. 5). The transition is accompanied by a ~5° lattice rotation and the gradual disappearance of Cu–Zr layer separation. CSP analysis (Fig. 6) shows that the number of atoms with low CSP (<1) increases with strain, indicating a progression from imperfect to perfect FCC. Upon unloading (Fig. 8), the FCC region partially reverts to B2, underscoring the superelastic nature of the transformation.

σ‑ε curve of the sample under tension along [001], colored by local structure (blue = B2, green = FCC, red = amorphous).

a RDF, b N–CSP plots of sample under tension along [001]. c–e CSP distribution at different strains.

Figure 7 visualizes the lattice evolution through yz slices at increasing strain. The initial B2 lattice (ε = 0) displays orthogonal atom arrays. At ε ≈ 0.079–0.119, partial FCC nucleation occurs with a ~5° deviation. As strain increases, the FCC region expands and reorients, ultimately aligning with the <110> plane (ε = 0.267). This rotation further supports the martensitic character of the B2→FCC transition.

yz slices of [001] sample under tension at different strains, colored by local lattice (blue = B2, green = FCC, red = amorphous).

Upon unloading from various maximum strains (ε_max = 0.1, 0.2, 0.3), the stress–strain paths (Fig. 8) exhibit hysteresis loops that do not fully overlap the loading curves, yet they return to the elastic line, confirming a reversible, superelastic response. The hysteresis originates from the forward B2→FCC transition and its reverse path.

Loading and unloading σ‑ε curves tension along [001] from different strains.

Compression along [001] follows a distinct path (Fig. 9). After an initial elastic rise, stress drops to a plateau, then rises again to a second peak before a final sharp decline. PTM analysis shows that most atoms remain B2 until the second peak, indicating a B2→BCT transition driven by differential bond elongation (Fig. 10). The BCT phase, with lattice parameters a = b > c, forms through uniform deformation and Cu–Zr layer separation. Subsequent stress decrease corresponds to localized amorphization.

Responses of the sample [001] under compression. a σ‑ε curve and typical atomic configurations, with atoms colored by PTM-identified local structures. b N–CSP plots.

Evolution of bond length for the sample [001] under compression, with bonds colored by their length.

Under tension along [110] (Fig. 11), the initial yield peak is followed by a rapid drop as local B2 transforms to HCP, driven by Cu–Zr layer separation. As strain increases, the HCP phase grows until the sample fully converts (point C), after which further deformation leads to local amorphization and a final stress decline. X‑OY slices (Fig. 11b–c) reveal the key atomic rearrangement: at ε = 0.150 the Cu and Zr layers decouple, initiating the B2→HCP transition.

a Deformation behavior of tension along [110], colored by PTM. b, c Atomic slices on X‑OY plane at ε = 0 and 0.150.

Conclusions

Our MD investigation of B2 CuZr under uniaxial loading along [001], [110] and [111] reveals four key findings:

1. Mechanical responses exhibit a clear tension–compression asymmetry; failure is dominated by localized amorphization.
2. Three distinct orientation‑dependent phase transformations occur: B2→FCC and B2→BCT under [001] tension/compression, and B2→HCP under [110] tension.
3. Each transformation follows a unique mechanism: ~5° lattice rotation for B2→FCC, uniform deformation and Cu–Zr layer separation for B2→BCT, and Cu–Zr layer decoupling for B2→HCP.
4. The transformed region can partially recover upon unloading before amorphization, demonstrating superelasticity.

These insights clarify the deformation pathways of nanocrystalline CuZr and guide the design of BMG composites with tailored toughness.

Availability of Data and Materials

The datasets generated during this study are available from the corresponding author upon reasonable request.