Researchers from MaX advanced the predictive design of tantalum-based components, significantly enhancing the ability to model and understand how tantalum behaves under extreme conditions such as high temperatures, intense pressures, and corrosive environments.
Application sectors: Health – Medical devices, Energy – Electronics, Mobility – Aerospace
Keywords: Tantalum, thermoelasticity, quasi-harmonic approximation, DFT, high-pressure materials
Tantalum is a refractory metal prized for its high melting point (3269 K), corrosion resistance, and mechanical stability. It is a backbone material in electronics, chemical processing, medical devices, and metallic alloys. Components built from tantalum often face extreme temperatures and pressures, making it essential to understand how the material behaves elastically under these conditions.
While tantalum has been studied experimentally and computationally, high-pressure and high-temperature elastic data remain sparse. In particular, temperature-dependent elastic constants (TDECs) display unusual trends, like slope changes at elevated temperatures, that standard computational methods struggle to reproduce. This knowledge gap limits the predictive design of tantalum-based components for aerospace, medical, or energy applications.
The research carried out in this study combined density functional theory (DFT) with the quasi-harmonic approximation (QHA) to capture tantalum’s thermoelastic behaviour. QHA reproduces experimental TDECs accurately up to ~500 K and predicts a linear decrease in elastic constants at higher temperatures, highlighting anharmonic effects. Comparisons with the quasi-static approximation (QSA) show that QHA captures low-temperature trends better, while QSA aligns more with high-temperature slopes. Pressure-dependent calculations at 5, 300, 1000, and 1500 K provide predictive data for conditions that are experimentally challenging to reach. Overall, the study establishes reliable benchmarks for tantalum’s elastic behaviour in extreme environments, informing design decisions in electronics, aerospace, and medical devices.
Methods & computing resources
The team used DFT within a plane-wave pseudopotential framework, employing PAW potentials and LDA, PBE, and PBEsol functionals. Calculations involved harmonic and quasi-harmonic contributions, demanding high plane-wave cutoffs and dense k- and q-point meshes for convergence. The quasi-harmonic approximation (QHA) is computationally intensive because it requires multiple volumes, distorted geometries, and electronic excitations. To handle this, simulations were performed on the Leonardo supercomputer at CINECA, leveraging GPU-optimized workflows to manage workloads efficiently.
The study relied on the MaX lighthouse code Quantum ESPRESSO, specifically using the thermo_pw module for quasi-harmonic free energies, phonon dispersions, and temperature-dependent elastic constants. This enabled accurate interpolation of Helmholtz free energies across distorted geometries and temperatures.
The MaX team provided essential guidance in optimizing QHA workflows and interpreting complex thermoelastic trends. Their expertise ensured reliable predictions even in regions with scarce experimental data, allowing the research to go beyond traditional computational limits and explore extreme pressure–temperature regimes with confidence.
Predicting tantalum’s elastic constants at low temperatures
This work demonstrates that the combination of DFT and QHA accurately predicts tantalum’s elastic constants at low temperatures, while also highlighting where anharmonic effects become significant above ~500 K. Pressure-dependent predictions extend the known thermoelastic landscape of tantalum, providing critical data for extreme-environment applications.
These findings offer insights for designing electronic components, medical devices, and aerospace materials where tantalum must endure high pressures and temperatures. By filling experimental gaps, this research supports safer, more reliable material selection and predictive modeling in industries that rely on refractory metals.
Advanced HPC workflows are now enabling insights into extreme-condition material behavior that were previously inaccessible. Talk to us about applying MaX lighthouse codes to your material challenges, or explore the Quantum ESPRESSO repository to reproduce and extend these simulations.
Reference paper
High-pressure and high-temperature thermoelasticity of tantalum: An ab initio study.