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      Experimental pressure-temperature phase diagram of boron: resolving the long-standing enigma

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          Abstract

          Boron, discovered as an element in 1808 and produced in pure form in 1909, has still remained the last elemental material, having stable natural isotopes, with the ground state crystal phase to be unknown. It has been a subject of long-standing controversy, if α-B or β-B is the thermodynamically stable phase at ambient pressure and temperature. In the present work this enigma has been resolved based on the α-B-to- β-B phase boundary line which we experimentally established in the pressure interval of ∼4 GPa to 8 GPa and linearly extrapolated down to ambient pressure. In a series of high pressure high temperature experiments we synthesised single crystals of the three boron phases (α-B, β-B, and γ-B) and provided evidence of higher thermodynamic stability of α-B. Our work opens a way for reproducible synthesis of α-boron, an optically transparent direct band gap semiconductor with very high hardness, thermal and chemical stability.

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          Superconductivity in boron.

          Metals formed from light elements are predicted to exhibit intriguing states of electronic order. Of these materials, those containing boron are of considerable current interest because of their relatively high superconducting temperatures. We have investigated elemental boron to very high pressure using diamond anvil cell electrical conductivity techniques. We find that boron transforms from a nonmetal to a superconductor at about 160 gigapascals (GPa). The critical temperature of the transition increases from 6 kelvin (K) at 175 GPa to 11.2 K at 250 GPa, giving a positive pressure derivative of 0.05 K/GPa. Although the observed metallization pressure is compatible with the predictions of first-principles calculations, superconductivity in boron remains to be explored theoretically. The present results constitute a record pressure for both electrical conductivity studies and investigations of superconductivity in dense matter.
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            Thermodynamic stability of boron: the role of defects and zero point motion.

            Its low weight, high melting point, and large degree of hardness make elemental boron a technologically interesting material. The large number of allotropes, mostly containing over a hundred atoms in the unit cell, and their difficult characterization challenge both experimentalists and theoreticians. Even the ground state of this element is still under discussion. For over 30 years, scientists have attempted to determine the relative stability of alpha- and beta-rhombohedral boron. We use density functional calculations in the generalized gradient approximation to study a broad range of possible beta-rhombohedral structures containing interstitial atoms and partially occupied sites within a 105 atoms framework. The two most stable structures are practically degenerate in energy and semiconducting. One contains the experimental 320 atoms in the hexagonal unit cell, and the other contains 106 atoms in the triclinic unit cell. When populated with the experimental 320 electrons, the 106 atom structure exhibits a band gap of 1.4 eV and an in-gap hole trap at 0.35 eV above the valence band, consistent with known experiments. The total energy of these two structures is 23 meV/B lower than the original 105 atom framework, but it is still 1 meV/B above the alpha phase. Adding zero point energies finally makes the beta phase the ground state of elemental boron by 3 meV/B. At finite temperatures, the difference becomes even larger.
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              Imperfect crystal and unusual semiconductor: boron, a frustrated element.

              All elements, except for helium, appear to solidify into crystalline forms at zero temperature, and it is generally assumed that the introduction of lattice defects results in an increase in internal energy. beta-Rhombohedral boron, a thermodynamically stable form of elemental boron at high temperature, is known to have a large amount of partial occupied sites, seemingly in conflict with our common knowledge. By using lattice Monte Carlo techniques combined with ab initio calculations, we find that the beta-phase is stabilized by a macroscopic amount of intrinsic defects that are responsible not only for entropic effects but also for a reduction in internal energy. These defects enable the conversion of two-center to three-center bonds and are accompanied by the presence of localized, nonconductive electronic states in the optical gap. In addition we find that the ab initio Ising model describing the partial occupancy of beta-boron has macroscopic residual entropy, suggesting that boron is a frustrated system analogous to ice and spin ice.
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                Author and article information

                Journal
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                19 September 2011
                2011
                : 1
                : 96
                Affiliations
                [1 ]simpleBayerisches Geoinstitut, Universität Bayreuth , D-95440 Bayreuth, Germany
                [2 ]simpleMaterialphysik und Technologie, Lehrstuhl für Kristallographie, Physikalisches Institut, Universität Bayreuth , D-95440 Bayreuth, Germany
                [3 ]simpleGeoForschungsZentrum Potsdam, Experimental Geochemistry and Mineral Physics , 14473 Potsdam, Germany
                Author notes
                Article
                srep00096
                10.1038/srep00096
                3216582
                22355614
                843c81da-63a0-4d7b-aea6-7d3d906a29fe
                Copyright © 2011, Macmillan Publishers Limited. All rights reserved

                This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/

                History
                : 21 June 2011
                : 05 September 2011
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