The Application of Molecular Dynamics Simulation in Determining the Diffusivity of Boron in Molten Slag

(Simulating boron transport in molten slag using high-performance computing)

By: Andreas Diga Pramata Putera, Héléna Verbeeck, Akbar Rhamdhani, Inge Bellemans

In silicon-based photovoltaic cells, boron is introduced as a dopant to enhance electrical properties. However, during silicon recycling, all impurities—including boron—must be removed into a CaO–Al₂O₃–SiO₂ slag to recover high-purity silicon. In high-temperature pyrometallurgical recycling processes, the reaction chemistry is typically fast, and the mass transfer in the slag is often the true rate limiter. Getting a trustworthy value for boron’s diffusivity helps distinguish pure diffusion from convection-aided mass transport, improving how we design and interpret diffusivity experiments, and eventually industrial reactors.

Figure 1: Illustration of a CaO-Al₂O₃-SiO₂-B₂O₃ slag system with a composition of 44.25 wt% CaO, 44.25 wt% SiO₂, 0.1 wt% Al₂O₃, and 1.5 wt% B₂O₃, represented by 20k atoms.

Using large-scale molecular dynamics (MD), our team computed the boron self-diffusivity in a CaO–SiO₂–Al₂O₃ slag with 1–10 wt% B₂O₃ at 1773–1873 K. Systems of 10k to 20k atoms were simulated in LAMMPS with long (25 ns) production runs, performing three repetitions for each composition and temperature, from which the boron diffusivities were extracted. The boron diffusivities, averaged over the three independent repetitions, were then modeled as a function of temperature and composition with (i) a full Thibodeau–Jung composition model, (ii) a reduced (Si,Al) network-former model, and (iii) a simplified B₂O₃-only model. These models allowed us to extrapolate the diffusivities for even lower boron concentrations, typically encountered during silicon recycling.

Figure 2: Illustration of the MD results for the boron diffusivity and comparison of the fitting approaches and their extrapolation results.

Key findings:

• The boron diffusivity (D_B) is firmly in the 10⁻¹⁰ m²·s⁻¹ range. Across temperatures and B₂O₃ contents, boron diffusivity varies between 5 and 11 × 10⁻¹⁰ m²·s⁻¹. Extrapolations to 100–300 ppmw B at 1773–1873 K remain in the same order of magnitude.

• All three fitting strategies (full, reduced, simplified) agree closely for the studied compositions, indicating low-B systems don’t require explicit B-pair terms to capture trends.

• The MD-derived D_B values align with earlier diffusion-controlled experimental estimates, but are 1–2 orders of magnitude lower than some kinetics-derived measurements. This gap suggests that in large-crucible or agitated laboratory setups, convective flows likely enhance mass transport, inflating the apparent diffusivity compared to the purely diffusive mechanism captured by MD.

  
  

How did VSC contribute to the research?

"VSC Tier-1 resources made it possible to run long, statistically robust MD simulations (10k–20k atoms, 25 ns) across multiple compositions and temperatures. The paper explicitly acknowledges VSC for providing the computational resources."

Research team & affiliations:A.D.P. Putera (Swinburne University of Technology), H. Verbeeck (KU Leuven), M.A. Rhamdhani (Swinburne University of Technology), I. Bellemans (Ghent University).

Read the full publication in Springer Nature here

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