Elastic Behavior of Tantalum Single Crystals Under <100> Tensile Loading: Temperature, Pressure, and Phase‑Transition Insights from Molecular Dynamics

Background

Tantalum crystallizes in a body‑centered‑cubic (BCC) lattice at ambient conditions and is renowned for its exceptional phase stability, high melting point (3269 K), and resistance to oxidation. These properties make Ta an ideal candidate for diffusion barriers in microelectronics, wear‑resistant coatings, and high‑temperature super‑alloys. Extensive experimental and theoretical work—using diamond‑anvil cells, density‑functional theory (DFT), and MD—has explored Ta’s behavior under high pressure and temperature, consistently confirming the persistence of the BCC phase up to 135 GPa and revealing increasing elastic moduli with pressure. Despite these advances, a systematic atomistic investigation of Ta’s dynamic response to tensile loading remains lacking. This work addresses that gap by evaluating size, strain rate, temperature, and pressure effects on Ta’s elastic properties during <100> tension and by probing the possibility of a tensile‑induced phase transition.

Methods and Experimental Details

Physical Modeling

We construct cubic Ta cells by replicating the BCC unit cell along the <001>, <010>, and <100> directions, using lattice constants a = b = c = 3.301 Å. Four cell sizes (12 a = 3.96 nm, 18 a = 5.94 nm, 24 a = 7.92 nm, 30 a = 9.90 nm) contain 3 456 to 54 000 atoms. Figure 1 illustrates the 3.96 nm model, which is the primary structure used in all simulations.

MD Simulation Protocol

All simulations were carried out with LAMMPS. Two EAM potentials—Zhou‑EAM and Ravelo‑EAM—were evaluated for their ability to reproduce elastic constants at 0 K and under hydrostatic pressure. The Ravelo‑EAM potential, developed by Ravelo et al. (Phys. Rev. B 2013, 88, 134101), outperformed Zhou‑EAM across the pressure range of interest. We used the direct method to compute C₁₁ and C₁₂ and derived the <100> elastic modulus via Eq. (1). Subsequent simulations employed a 1 fs time step, periodic boundary conditions in all directions, and a 50 ps NVT relaxation followed by NPT equilibration to impose hydrostatic pressures (0–140 GPa). Tensile loading along x was applied at strain rates from 5 × 10⁸ s⁻¹ to 7.5 × 10⁹ s⁻¹ until a 15 % elongation was reached.

Results and Discussion

Stretching Process

Figure 3 shows the stress–strain response and corresponding atomic configurations during <100> tension at zero pressure. Elastic deformation is linear up to ~7 % strain, after which a BCC→FCC transformation initiates at ~7.4 % and completes by ~9.8 %. The FCC phase persists until a surface fracture occurs near 13 %. The transformation and fracture mechanisms are consistent across all model sizes and strain rates, indicating negligible size or rate effects on the elastic modulus and yielding stress.

Size and Strain‑Rate Effects

Table 2 demonstrates that model size (3.96–9.90 nm) does not influence the elastic modulus (~139 GPa) or yielding stress. Similarly, Table 3 shows that strain rates between 5 × 10⁸ s⁻¹ and 7.5 × 10⁹ s⁻¹ produce no discernible changes in these properties. Consequently, a 3.96 nm cell and a strain rate of 5 × 10⁸ s⁻¹ were adopted for all subsequent analyses.

Temperature Dependence

Figure 4 illustrates the evolution of the stress–strain curves from 1 K to 1500 K. Both the elastic modulus E₁₀₀ and the yielding stress decrease monotonically with temperature. The modulus declines by ~42 % (136.5 → 76.7 GPa) and the yielding stress by ~51 % (≈8 → 4 GPa) over this range. A linear fit yields E₁₀₀ = 138.07 – 0.04094 T (GPa), valid up to 1500 K, while a quadratic fit captures the yielding stress dependence.

Pressure Dependence

Figure 6 presents E₁₀₀ versus hydrostatic pressure (0–140 GPa) at several temperatures. At 1 K, the dynamic results agree closely with static calculations based on Eq. (1). For temperatures ≤ 600 K, a concave region appears between 20–60 GPa, consistent with previous MD studies, whereas higher‑temperature curves remain monotonic. Across all temperatures, E₁₀₀ increases with pressure above ~40 GPa, confirming that Ta’s stiffness is enhanced under compression.

Conclusions

We performed a comprehensive MD investigation of Ta single crystals under <100> tension across a broad spectrum of temperatures (1–1500 K) and pressures (0–140 GPa). The Ravelo‑EAM potential proved reliable for high‑pressure simulations. Key findings include: (1) a BCC→FCC phase transition precedes fracture at low temperature; (2) elastic modulus and yielding stress decline linearly and quadratically, respectively, with temperature; (3) pressure enhances the elastic modulus above ~40 GPa; and (4) model size and strain rate exert negligible influence on the measured elastic properties.