The preprint asks how a relaxed beta-gallium oxide film can form on c-plane sapphire without observed dislocations. Its focus is the interface between a thin alpha-gallium oxide wetting layer and beta-gallium oxide islands. The modeled answer is a local rearrangement of gallium within a single atomic plane, while the beta oxygen framework expands and retains long-range crystallinity.
To investigate the idea, the authors combine three scales of calculation: density functional theory for slab energies, continuum nucleation theory for competition between the alpha and beta forms, and large-scale molecular dynamics using a machine-learned interatomic potential. Together, the models follow the problem from what first coats the sapphire to how strain is distributed through an island and how atoms move at the interface.
The clue is in the first layer
The sequence begins with a strong calculated preference for alpha-gallium oxide to wet the sapphire. The surface energy of bare sapphire was about 113 meV/Ų. A single alpha bi-layer reduced it, and stabilization saturated after approximately three bi-layers, approaching strained alpha bulk. The calculation reported no further gain beyond that thickness.
That preference changed as the modeled island volume increased. On bare sapphire, the alpha form remained favored across all modeled volumes. With one to three alpha wetting-layer bi-layers, alpha was favored at small volumes, but beta became favorable above a critical volume. That threshold decreased slightly as the wetting layer became thicker.
Taken together, the calculations suggest a two-stage energetic picture: an alpha layer can cover the substrate first, while beta becomes favorable only after the deposited volume passes a threshold. Increasing the wetting layer from one to three bi-layers nudged that threshold down without changing the overall sequence.
Strain moves before the atoms do
The researchers next estimated how mismatch strain would be distributed through a beta island. Their finite-element model used a truncated-cone beta-gallium oxide island on a planar alpha-gallium oxide substrate, with a top radius of 22 nanometres, a bottom radius of 28 nanometres and a height of 18 nanometres. The calculation showed substantial relaxation, particularly along the direction with the larger mismatch.
Elastic minimization alone relieved strain near the island’s free surfaces, while the core remained compressed. The outer regions relaxed toward those surfaces without structural rearrangement, leaving a partially relieved but still elastically strained island.
The atomistic test used approximately 88,000 atoms in a cell about 180 Å by 180 Å across. The beta islands shared an oxygen interface with a strained alpha wetting layer; in-plane boundaries were periodic, and only the upper six bi-layers were mobile. After elastic minimization, the model was heated from 0 K to 500 K over 200 ps, held for 200 ps, then quenched to 0 K over 200 ps with a 1 fs time step.
At 500 K, the molecular-dynamics model produced a collective atomic rearrangement. In the represented case, the total potential energy was approximately 100 eV lower than in the purely elastic configuration. The beta lattice expanded laterally, the alpha wetting layer remained constrained, and the strain map showed almost complete release of the initial compression.
A one-plane change at the boundary
The important structural change was concentrated at the interface. After plastic relaxation, the modeled boundary contained a single atomic plane with alternating alpha-like and beta-like gallium coordination: octahedral sites beside tetrahedral sites. Meanwhile, the beta oxygen framework expanded toward the modeled L direction while preserving long-range oxygen crystallinity.
The reconstruction also remained compatible in the model with beta rotational domains separated by about 120 degrees. Their in-plane orientation relationships did not change, even as the interface accommodated the mismatch.
The authors interpret this localized interfacial reconstruction as a potentially general, underexplored relaxation channel in complex oxide heteroepitaxy. The proposed idea shifts attention toward rearrangements of cations at an interface, rather than assuming that strain relief must appear through conventional dislocations.
A prediction still waiting for a test
Because the document is a preprint and the evidence described here comes from calculations, the one-plane reconstruction is a model prediction rather than a direct experimental finding. The reported energy difference belongs to the represented case, while the continuum calculation identifies a crossover above a critical volume without giving an exact value in the supplied account.
The atomistic result also reflects a defined computational setup: periodic in-plane boundaries, a constrained alpha layer, a selected island geometry and a 600 ps thermal schedule. Those choices make the mechanism concrete, but leave open how it changes with island size, wetting-layer thickness, temperature, growth conditions or defects.
For now, the study offers a focused candidate mechanism for the modeled gallium-oxide and sapphire system. The calculations link alpha wetting, beta nucleation and interfacial gallium rearrangement while retaining oxygen order and rotational-domain relationships. Whether related reconstructions occur in other polymorphic oxides remains an open question.
Paper data and sources
Original title: Plastic Relaxation without Dislocations in $β$-Ga$_2$O$_3$ Heteroepitaxy: A Structural Peculiarity of Ga$_2$O$_3$ Polymorphs
Authors: I. Bertoni, A. Marzegalli, A. Ugolotti et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
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