Low temperature phase transition in β-rhombohedral boron

Werheit, H.; Franz, R.

doi:10.1016/0022-5088(86)90026-3

Cited by 7 publications

(1 citation statement)

References 14 publications

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“…7 In particular, the calculated energy of the ␣ form lies below the reported calculated energies of the ␤ form. 7-10 Some researchers propose a finite-temperature phase transition, 11 including one proposal that vibrational entropy drives an ␣ to ␤ transition at finite temperature. 7 Quantum mechanical zero-point vibrational energy has been proposed as a mechanism to stabilize the ␤-rhombohedral form at absolute zero.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-broken crystal structure of elemental boron at low temperature

2008

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The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report the beta-rhombohedral (black) form is stable over all temperatures from absolute zero to melting. However, early calculations found its energy to be greater than the energy of the alpha-rhombohedral (red) form, implying beta cannot be stable at low temperatures. Furthermore, beta exhibits partially occupied sites, seemingly in conflict with the thermodynamic requirement that entropy vanish at low temperature. Using electronic density functional theory methods and an extensive search of the configuration space we find a unique, energy minimizing pattern of occupied and vacant sites that can be stable at low temperatures but that breaks the beta-rhombohedral symmetry. Even lower energies occur within larger unit cells. Alternative configurations lie nearby in energy, allowing the entropy of partial occupancy to stabilize the beta-rhombohedral structure through a phase transition at moderate temperature.Comment: 12 pages, 5 figure

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Section: Introductionmentioning

confidence: 99%