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Updated: Jun 25, 2026

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Imperfect crystal and unusual semiconductor: boron, a frustrated element
Tadashi Ogitsu1, François Gygi, John Reed
1Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
Beta-rhombohedral boron is stabilized by intrinsic defects, which reduce internal energy and create unique electronic states. This finding challenges common assumptions about lattice defects in crystalline solids.
Area of Science:
- Solid-state physics
- Materials science
- Computational chemistry
Background:
- Crystalline solids typically increase internal energy with lattice defects.
- Beta-rhombohedral boron exhibits unusual partial site occupancy at high temperatures.
Purpose of the Study:
- Investigate the stabilization mechanism of beta-rhombohedral boron.
- Understand the role of intrinsic defects in its structure and properties.
Main Methods:
- Ab initio calculations
- Lattice Monte Carlo simulations
- Ising model analysis
Main Results:
- Beta-boron is stabilized by a significant concentration of intrinsic defects.
- These defects reduce internal energy and introduce localized, nonconductive electronic states within the optical gap.
- The system exhibits macroscopic residual entropy, indicating frustration.
Conclusions:
- Intrinsic defects are crucial for the stability of beta-rhombohedral boron.
- Boron behaves as a frustrated system, similar to ice and spin ice.
- The study redefines the understanding of lattice defects in crystalline materials.
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