Note: This response was generated with the assistance of an AI tool (Claude) after this thread received no replies from other community members for over a week. AI-generated responses carry a real risk of error, particularly for narrow, domain-specific physics questions like this one. The methodology advice below is based on published literature, but please treat it as a starting point, not authoritative guidance, and validate against the primary references. We encourage human experts to correct or supplement this response.
On the core methodology question:
The standard approach in published large-scale atomistic grain boundary (GB) surveys (e.g., Olmsted, Foiles & Holm, Acta Materialia 57, 3694–3703, 2009; Tschopp & McDowell, Phil. Mag. 87, 3147–3173, 2007; Spearot & McDowell, JOM 2009) is to keep in-plane cell vectors fixed at the CSL-commensurate dimensions and relax only the atomic positions (and optionally the cell dimension in the normal/z direction). The key reason is thermodynamic consistency: the GB energy is defined as:
γ = (E_bicrystal − N · ε_bulk) / (2A)
where ε_bulk must be the energy per atom of a perfect crystal at the same in-plane lattice parameter as the bicrystal cell. If your bicrystal has a slight in-plane elastic strain due to the CSL construction, the reference single-crystal cells must be strained identically. Under this condition, the excess energy is dominated by the GB structural contribution and the bulk elastic artifact largely cancels.
Is in-plane box/relax ever appropriate?
Yes, with an important caveat: if you use fix box/relax x y xy to allow the in-plane dimensions to find a stress-free state, you must compute the reference single-crystal energy at those same relaxed in-plane dimensions (i.e., run the same box/relax on a pure single-crystal cell). Only then do the bulk elastic contributions cancel and you recover a physically meaningful GB energy. In practice this is rarely done in the published GB database literature, partly because it complicates the reference calculation and partly because for low- and moderate-Σ boundaries the residual in-plane elastic strain is tiny.
For high-angle, high-Σ tilt boundaries with large monoclinic xy tilt, residual in-plane compressive stress is a known issue. The standard workarounds in the literature are:
- Accept the fixed-cell convention and note that any residual in-plane stress contributes a small, nearly-identical elastic energy to both the bicrystal and the reference cells, so it largely cancels in the excess.
- Increase the GB-normal (z) dimension so the grains are thick enough that their core is elastically relaxed away from the GB; the in-plane stress is then genuinely confined to the boundary region and does not contaminate the bulk reference.
- Use a different supercell construction (e.g., rotating the periodic vectors so the xy tilt factor stays within LAMMPS’s |xy| ≤ 0.5·lx limit). This is what the warning about large triclinic skew is pointing to — LAMMPS is telling you that the simulation cell geometry is outside its efficient operating range.
On the large-skew LAMMPS warning:
LAMMPS requires |xy| ≤ 0.5·lx (and analogously for xz, yz). When fix box/relax changes lx and ly, the ratio xy/lx can exceed this bound, triggering the warning and eventually an error. The fix is either (a) to avoid box/relax on the in-plane dimensions for highly tilted cells, or (b) to choose a supercell with periodic vectors that have smaller tilt (many GB-construction tools, e.g. GBCode) offer this option).
Recommended references:
- D.L. Olmsted, S.M. Foiles, E.A. Holm, “Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy,” Acta Mater. 57, 3694 (2009). [link] — The canonical large GB database for FCC metals; fixed in-plane methodology.
- M.A. Tschopp, G.J. Tucker, D.L. McDowell, “Structure and free volume of <110> symmetric tilt grain boundaries with the E structural unit,” Acta Mater. 55, 3959 (2007). — Al/Cu tilt GBs with explicit description of the fixed-cell approach.
- H.S. Seung, D.R. Nelson, “Defects in flexible membranes with crystalline order,” Phys. Rev. A 38, 1005 (1988); and more practically, Ratanaphan et al., Acta Mater. 80, 96 (2014), “Grain boundary energies in body-centered cubic metals.” [link]
- Tschopp & McDowell 2015 (symmetric/asymmetric tilt GBs in Cu and Al, transferability to other FCC metals): [link]
- LAMMPS documentation for fix box/relax and triclinic box handling.