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β-Rhombohedral Boron: At the Crossroads of the Chemistry of Boron and the Physics of Frustration [Boron: a frustrated element]

Journal Article · · Chemical Reviews
DOI:https://doi.org/10.1021/cr300356t· OSTI ID:1227014
 [1];  [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of California, Davis, CA (United States)

In the periodic table boron occupies a peculiar, crossover position: on the first row, it is surrounded by metal forming elements on the left and by non-metals on the right. In addition, it is the only non-metal of the third column. Therefore it is perhaps not surprising that the crystallographic structure and topology of its stable allotrope at room temperature (β-boron) are not shared by any other element, and are extremely complex. The formidable intricacy of β- boron, with interconnecting icosahedra, partially occupied sites, and an unusually large number of atoms per unit cell (more than 300) has been known for more than 40 years. Nevertheless boron remains the only element purified in significant quantities whose ground state geometry has not been completely determined by experiments. However theoretical progress reported in the last decade has shed light on numerous properties of elemental boron, leading to a thorough characterization of its structure at ambient conditions, as well as of its electronic and thermodynamic properties. This review discusses in detail the properties of β-boron, as inferred from experiments and the ab-initio theories developed in the last decade.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC52-07NA27344; FG02-06ER46262
OSTI ID:
1227014
Report Number(s):
LLNL-JRNL--609897
Journal Information:
Chemical Reviews, Journal Name: Chemical Reviews Journal Issue: 5 Vol. 113; ISSN 0009-2665
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English

References (249)

ON THE STRUCTURE OF ELEMENTARY BORON 1 journal April 1951
The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement journal December 1935
64. The structure of the boron hydrides journal January 1943
Electronic Requirements for Macropolyhedral Boranes journal December 2001
Boron Fullerenes: A First-Principles Study journal December 2007
On the Conductivity Mechanism of β-Rhombohedral Boron journal January 1970
Phase Stabilization through Electronic Tuning:  Electron-Poorer Alkali-Metal−Indium Compounds with Unprecedented In/Li Clusters journal January 2005
Canonical Configurational Interaction Procedure journal April 1960
Icosahedral boron frameworks. The structure of .gamma.-aluminum dodecarboride journal August 1977
Thermodynamic Stability of Novel Boron Sheet Configurations journal July 2008
Boron: Elementary Challenge for Experimenters and Theoreticians journal November 2009
Boron and Boron-based semiconductors journal January 1979
The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds journal January 1971
Partly occupied Wannier functions: Construction and applications journal September 2005
Electronic structures, total energies, and optical properties of α-rhombohedral B 12 and α-tetragonal B 50 crystals journal March 1992
Polyanionic Clusters and Networks of the Early p-Element Metals in the Solid State: Beyond the Zintl Boundary journal February 2000
The quantitative evaluation of the electron paramagnetic resonance anisotropy of β rhombohedral boron journal September 1979
Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures journal July 1959
C60: Buckminsterfullerene journal November 1985
Electrical conductivity measurements of β-boron under high pressure and temperature journal September 2007
Progress in the preparation and determination of the properties of boron journal August 1942
Transport properties of boron nanotubes investigated by ab initio calculation journal June 2009
Transformations of Ising Models journal February 1959
Low-temperature specific heat of isotopically modified boron single crystals journal July 2001
Partly Occupied Wannier Functions journal January 2005
Statistics of Kagome Lattice journal June 1951
Generalized gradient approximation for the exchange-correlation hole of a many-electron system journal December 1996
Metal cluster topology. 10. Polyhedral gallium cluster anions in intermetallic phases of gallium and alkali metals journal July 1989
Zone‐Refined Boron journal October 1959
Ab initio prediction of stable boron sheets and boron nanotubes: Structure, stability, and electronic properties journal January 2008
Ab initio equation of state of α - and β -boron: Possible amorphization of β -boron under high pressure journal June 2009
Phase transition in β-rhombohedral boron near 550 K journal November 2012
An Analysis of Polymorphism in Boron Based upon X-Ray Diffraction Results 1 journal January 1960
Electron Deformation Density in Rhombohedral α-Boron journal September 2001
The dependence of the internal friction of boron fibers on amplitude journal October 1979
Production of α-Rhombohedral Boron by Amorphous Boron Crystallization journal October 2000
Calculation of Fermi Surface and Its Application to Li-Doped α-Boron journal December 2009
Temperature dependence of the internal friction in fine-grained boron journal November 1981
Study of the ? to ? transformation in boron journal May 1972
Icosahedral B12, macropolyhedral boranes, β-rhombohedral boron and boron-rich solids journal September 2006
Dielectric loss in boron journal September 1979
Principles of Thermodynamics book August 2002
Ionicities of Boron-Boron Bonds in B 12 Icosahedra journal January 2005
Boron. I. Preparation and Properties of Pure Crystalline Boron journal October 1943
No Cage, No Tube: Relative Stabilities of Nanostructures journal August 2008
Electronic distributions and local range order in crystals and quasicrystals journal December 1995
Crystal stability of α - and β -boron journal March 2006
Metallic Hydrogen: A High-Temperature Superconductor? journal December 1968
Raman effect in icosahedral boron-rich solids journal February 2010
Rietveld analysis of LiB13 with β-rhombohedral boron structure journal April 1995
Heat Content and Heat Capacity of Crystalline Boron from 298° to 1700° K. journal January 1962
β-Boron and a1b12 as quasi-amorphous semiconductors and thermoelectrical materials journal June 1976
Phase stability in α - and β -rhombohedral boron journal March 2007
Thermodynamics book January 1996
First-principles study of superconductivity in high-pressure boron journal May 2002
A new intermetallic phase K4Na13Ga49.57: Synthesis and X-ray crystal structure journal August 1986
Structural and Thermodynamic Explanations of Ostwald's Rule journal November 2003
Superconductivity in boron under pressure: A full-potential linear muffin-tin orbitals study journal November 2005
A new polymorph of boron journal March 1960
Electronic structures of boron nanoribbons journal July 2008
The Valence Structure of the Boron Hydrides journal June 1954
Thermoelectric power in crystalline boron journal May 1971
Polymorphism of Two-Dimensional Boron journal April 2012
Maximally localized Wannier functions for entangled energy bands journal December 2001
The Pressure Dependence of Solid Boron journal November 2004
Linear-Scaling Quantum Monte Carlo Calculations journal November 2001
Comparison of solid-state crystallization of boron polymorphs at ambient and high pressures journal March 2012
Recherches récentes sur les borates et sur le bore journal January 1933
Rhombohedral Elemental Boron journal October 1957
Complex alloy structures regarded as sphere packings. I. Definitions and basic principles journal March 1958
First-Principles Prediction of Vacancy Order-Disorder and Intercalation Battery Voltages in Li x CoO 2 journal July 1998
The Unusually Stable B 100 Fullerene, Structural Transitions in Boron Nanostructures, and a Comparative Study of α- and γ-Boron and Sheets journal March 2010
Ground State of the Electron Gas by a Stochastic Method journal August 1980
Structure and electronic properties of Mg-doped β -rhombohedral boron constructed from icosahedral clusters journal January 2008
Antiferromagnetism. The Triangular Ising Net journal July 1950
The high-pressure phase of boron, γ-B28: Disputes and conclusions of 5 years after discovery journal December 2011
New boron barrelenes and tubulenes journal July 2008
High pressure synthesis of single crystals of α-boron journal April 2011
Thermodynamic Stability of Boron:  The Role of Defects and Zero Point Motion journal March 2007
Structure and bonding in crystalline boron and B 12 C 3 journal January 1982
Zur bildung der tetragonalen modifikation des bors journal June 1968
Beitrag zur Theorie des Ferromagnetismus journal February 1925
Confusion and clarification: Albert Einstein and Walther Nernst's Heat Theorem, 1911–1916 journal March 2006
TEMPERATURE AND FREQUENCY DEPENDENCE OF MICROWAVE ELASTIC LOSSES IN β‐RHOMBOHEDRAL BORON FOR LONGITUDINAL WAVES ALONG THE c AXIS journal May 1969
Superconductivity in Boron journal July 2001
States of Thermal Equilibrium in β-Rhombohedral Boron and Their Alteration by Optical Excitation journal October 1984
Optical and magnetic properties of boron fullerenes journal January 2009
Optische und photoelektrische Eigenschaften von β-rhomboedrischem Bor. I. Optische Konstanten, Bandkante und Absorption freier Landungsträger journal January 1969
Polyhedral skeletal electron pair approach. A generalised principle for condensed polyhedra journal January 1983
Low temperature phase transition in β-rhombohedral boron journal March 1986
Magnetic susceptibility of pure boron journal November 1973
EPR investigation of paramagnetic centres in β-rhombohedral boron journal October 1973
Pressure-induced metallization in solid boron journal September 2002
Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another journal April 1960
Model for Configurational Thermodynamics in Ionic Systems journal March 1995
The crystal structure of tetragonal boron journal September 1979
The chemical and geometrical genesis of quasicrystals: Relationship of icosahedral aluminum alloy quasicrystal structures to icosahedral structures in elemental boron journal March 1991
Skeletal electron counting in cluster species. Applications to metal-hydrocarbon π-complexes journal June 1972
Li- and Mg-doping into icosahedral boron crystals, α- and β-rhombohedral boron, targeting high-temperature superconductivity: structure and electronic states journal February 2004
Residual Entropy of Square Ice journal October 1967
Structural Study of α-Rhombohedral Boron at High Pressures journal August 2011
Theory of Superconductivity journal December 1957
The electronic structure of an icosahedron of boron atoms
  • Longuet-Higgins, Hugh Christopher; Roberts, M. De V.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 230, Issue 1180, p. 110-119 https://doi.org/10.1098/rspa.1955.0115
journal June 1955
Electronic structures and mechanical properties of boron and boron-rich crystals (Part 2) journal October 2010
Polyhedral skeletal electron pair approach journal September 1984
Metal-Nonmetal Transition in the Boron Group Elements journal February 2003
High-pressure lattice dynamics and thermoelasticity of MgO journal April 2000
Semiconductor Properties of Boron book January 1965
Ideal Polyhedral Model for Boron Nanotubes with Distinct Bond Lengths journal October 2009
Chemical applications of group theory and topology. 7. A graph-theoretical interpretation of the bonding topology in polyhedral boranes, carboranes, and metal clusters journal November 1977
Valence control and metallization of boron by electronic doping journal December 2007
B48B2C2 und B48B2N2, zwei Nichtmetallboride mit der Struktur des sog. I tetragonalen Bors journal October 1972
Tetrahedral Stars as Flexible Basis Clusters in sp-Bonded Intermetallic Frameworks and the Compound BaLi 7 Al 6 with the NaZn 13 Structure journal April 1998
Electronic Structure and Electrical Resistivity of α-Boron under High Pressure journal August 2009
Correlation between structural defects and electronic properties of icosahedral boron-rich solids journal August 1999
Stability and Electronic Properties of Atomistically-Engineered 2D Boron Sheets journal January 2007
Antiferromagnetism. The Triangular Ising Net journal June 1973
Structure and Bonding of γ-B 28 : Is the High Pressure Form of Elemental Boron Ionic? journal December 2010
Spectral analysis of the electronic structure of γ-B28 journal December 2011
The intermetallic phases of gallium and alkali metals. Interpretation of the structures according to Wade's electron-counting methods journal June 1983
Efficient method for Li doping of α -rhombohedral boron journal September 2011
Thermal expansion of boron and boron carbide journal March 1986
Hydrogen-Bond Topology and the Ice VII / VIII and Ice I h / XI Proton-Ordering Phase Transitions journal April 2005
Theoretical Study of the Stability of Lithium Atoms in α-Rhombohedral Boron journal November 2005
X-ray diffraction analysis of B50C2 and B50N2 crystal-lizing in the “tetragonal” boron lattice journal June 1976
Maximally localized Wannier functions for simulations with supercells of general symmetry journal April 1999
Structure of B 13 C 2 journal January 1991
Experimental pressure-temperature phase diagram of boron: resolving the long-standing enigma journal September 2011
Imperfect Crystal and Unusual Semiconductor: Boron, a Frustrated Element journal February 2009
Apparent low-frequency charge capacitance of semiconducting boron journal January 2009
Verfeinerung des β-rhomboedrischen Bors journal November 1970
A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions journal August 1933
Boron: a hunt for superhard polymorphs journal October 2009
Ionic high-pressure form of elemental boron journal January 2009
Phase transition in KOH-doped hexagonal ice journal October 1982
Fused and linked deltahedral clusters in the chemistry of the Group 13 elements journal September 1990
First approach to the band structure of α -rhombohedral boron journal February 1981
First-principles calculations of elemental crystalline boron phases under high pressure: Orthorhombic B28 and tetragonal B48 journal April 2011
Large shear strength enhancement of gamma-boron by normal compression journal December 2011
Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets journal September 2007
Convergent real-space cluster expansion for configurational disorder in ionic systems journal May 1995
The Structure of β-Rhombohedral Boron journal February 1963
A determination of the crystal structure of ice XI journal April 1989
A new Crystalline Modification of Boron journal May 1958
The α–β phase boundary of elemental boron journal November 2012
A new approach to bonding in transition metal clusters: Theory journal December 1980
Electron-phonon coupling of α − Ga boron journal December 2004
A Unifying Electron-Counting Rule for Macropolyhedral Boranes, Metallaboranes, and Metallocenes
  • Jemmis, Eluvathingal D.; Balakrishnarajan, Musiri M.; Pancharatna, Pattath D.
  • Journal of the American Chemical Society, Vol. 123, Issue 18 https://doi.org/10.1021/ja003233z
journal May 2001
Orientation-dependent effects of EPR-measurements on β-rhombohedral boron journal June 1976
A New Class of Boron Nanotube journal December 2009
Answer to Question #34. What is the third law of thermodynamics trying to tell us? journal April 1997
Coordination Number Pattern Recognition Theory of Carborane Structures book January 1976
Molecular Rotation in Ice at 10°K. Free Energy of Formation and Entropy of Water journal January 1933
An exact polyhedral model for boron nanotubes journal January 2009
Geometrical Frustration in the Ferromagnetic Pyrochlore Ho 2 Ti 2 O 7 journal September 1997
Pressure-induced isostructural phase transformation in γ -B 28 journal November 2010
Superconductivity in α-boron at Mbar pressure journal December 2010
Preparation and Crystal Structure Determination of the New Intermetallic Compound RbGa3 journal September 1981
The structure analysis of β-rhombohedral boron journal January 1970
Low Temperature Heat Capacities of Inorganic Solids. 1 V. The Heat Capacity of Pure Elementary Boron in Both Amorphous and Crystalline Conditions between 13 and 305°K. Some Free Energies of Formation journal March 1951
New pecularities of the conductivity and photoconductivity mechanisms in β-rhombohedral boron journal February 2004
Symmetry-broken crystal structure of elemental boron at low temperature journal February 2008
Spin Ice State in Frustrated Magnetic Pyrochlore Materials journal November 2001
Low frequency non-stabilities of photocurrent in β rhombohedral boron at low temperatures journal November 1981
Order-disorder in hexagonal lattices journal May 1950
Optical and Photoelectrical Properties of β-Rhombohedral Boron II. Photoeffects journal January 1970
High-pressure route to superhard boron-rich solids journal March 2011
The crystal structure of a simple rhombohedral form of boron journal July 1959
Wannier-function description of the electronic polarization and infrared absorption of high-pressure hydrogen journal December 2000
X-ray study of transition-metal dopants in β-boron journal September 1988
Thermally activated hopping in β rhombohedral boron journal October 1979
Phase relations in boron at pressures up to 18 GPa and temperatures up to 2200 ∘ C journal January 2012
Icosahedron Oligomerization and Condensation in Intermetallic Compounds. Bonding and Electronic Requirements journal April 2000
On the nature of chemical bonding in γ-boron journal December 2011
Computational search for the real tetragonal B 50 journal February 1992
Ab initio transport properties of nanostructures from maximally localized Wannier functions journal January 2004
Band-calculation of the electronic densities of states and the total energies of boron–silicon system journal December 2002
First-principles statistical mechanics of structural stability of intermetallic compounds journal July 1991
Probing Properties of Boron α-Tubes by Ab Initio Calculations journal May 2008
First-principles study on metal-doped icosahedral B 12 solids journal November 1996
Geometrical Frustration book January 2010
Boron fullerenes: From B 80 to hole doped boron sheets journal April 2009
Linear-programming method for obtaining effective cluster interactions in alloys from total-energy calculations: Application to the fcc Pd-V system journal January 1995
Aspects of anionic framework formation journal December 1998
Polyhedral Boranes and Elemental Boron:  Direct Structural Relations and Diverse Electronic Requirements journal May 2001
THE ISOLATION OF THE ICOSAHEDRAL B 12 H 12 -2 ION journal June 1960
High-pressure high-temperature synthesis and structure of α-tetragonal boron journal October 2011
The crystal structure and density of β-rhombohedral boron journal September 1988
The Statistics of Honeycomb and Triangular Lattice. I journal March 1950
Crystal structure of tetragonal boron related to α-AlB12 journal June 1979
Electronic Requirements of Polycondensed Polyhedral Boranes journal May 2000
Generalized Gradient Approximation Made Simple journal October 1996
Ca-Coated Boron Fullerenes and Nanotubes as Superior Hydrogen Storage Materials journal May 2009
The Entropy of Water and the Third Law of Thermodynamics. The Heat Capacity of Ice from 15 to 273°K. journal July 1936
Ionic high-pressure form of elemental boron journal July 2009
Factors influencing the morphologies of boron deposited by chemical vapour deposition journal March 1980
Self-compensation property of β-rhombohedral boron doped with high Li concentration journal November 2012
Wannier functions characterization of floating bonds in a-Si journal March 2001
Electrical and optical properties of amorphous boron and amorphous concept for ß-rhombohedral boron journal November 1974
Elastoresistance of β-Rhombohedral Boron Crystals journal January 1970
Antiferromagnetism. The Kagome Ising Net journal August 1953
Self-doping in boron sheets from first principles: A route to structural design of metal boride nanostructures journal October 2009
Growth of single crystals of B28 at high pressures and high temperatures journal November 2010
Ordering and Antiferromagnetism in Ferrites journal May 1956
Crude Boron. Analysis and Composition journal November 1942
Calculations of the superconducting properties of 32 metals with Z ≤ 49 journal May 1977
Exact Solution of the Problem of the Entropy of Two-Dimensional Ice journal April 1967
Electronic structures and mechanical properties of boron and boron-rich crystals (Part I) journal June 2010
Superhard Semiconducting Optically Transparent High Pressure Phase of Boron journal May 2009
Self-consistent calculations of the energy bands and bonding properties of B 12 C 3 journal July 1990
Maximally localized generalized Wannier functions for composite energy bands journal November 1997
Electron-Deficient and Polycenter Bonds in the High-Pressure γ − B 28 Phase of Boron journal May 2011
Incoherent inelastic neutron scattering measurements on ice XI; the proton-ordered phase of ice Ih doped with KOH journal January 1998
Thermodynamics and Introductory Statistical Mechanics journal August 2004
The transport properties of boron nanostructures journal May 2009
Crystal structure of I-tetragonal boron journal October 1974
Phonons and related crystal properties from density-functional perturbation theory journal July 2001
An accurate refinement of the β-rhombohedral boron structure journal June 1977
The Structure of Tetragonal Boron 1 journal September 1958
Theoretical study of the stability of A B 12 ( A = H − Ne ) icosahedral clusters journal July 1999
Bonding with boron journal April 2009
Geometrical frustration in an elemental solid: An Ising model to explain the defect structure of β -rhombohedral boron journal January 2010
Frameworks of clusters in alkali metal-gallium phases: Structure, bonding and properties journal January 1993
Boron Crystals journal July 1966
Thermally Stimulated Current in Boron journal January 1969
High Temperature Superconductivity in Metallic Hydrogen: Electron-Electron Enhancements journal January 1997
Peculiarities of changes of some physicomechanical characteristics of monoisotopes 10B, 11B and natural β-boron journal September 2006
Comparative review of theoretical and experimental equations of state of orthorhombic boron γ-B28 journal December 2011
Maximally localized Wannier functions: Theory and applications journal October 2012
Electronic structure and bonding of β -rhombohedral boron using cluster fragment approach journal November 2005
The Mechanism and Quantitative Description of the Photoconductivity and Photo-EPR in Beta-rhombohedral Boron Single Crystals at 77 K journal June 1973
Role of large but defective deltahedra in the structural chemistry of very complex solid borides and gallides journal May 1991
Synthesis of Uniform Diameter Boron-Based Nanostructures Using a Mesoporous Mg−Al 2 O 3 Template and Tests for Superconductivity journal September 2009
Electronic Structures of Newly Predicted Intercalation Compounds “Lithium Intercalated α-Boron” journal July 1993
Density-Functional Perturbation Theory for Quasi-Harmonic Calculations journal January 2010
Self-interaction correction to density-functional approximations for many-electron systems journal May 1981
High-pressure properties and phase diagram of boron journal January 2007
Impact of lattice vibrations on equation of state of the hardest boron phase journal April 2011
Synthesis of an orthorhombic high pressure boron phase journal December 2008
Superconductivity in Li-doped α -rhombohedral boron journal May 2011
The competition of double-, four-, and three-ring tubular B3n (n=8–32) nanoclusters journal July 2008
A General Theory for Cluster and Ring Compounds of the Main Group and Transition Elements journal April 1972
Boron: Another Form journal January 1965
Synthesis and crystal structure determination of the new ternary intermetallic phase Na17Cu6Ga46.5 (Na102Cu36Ga279) journal October 1992
Interband and Gap State Related Transitions in β-Rhombohedral Boron journal April 1993
Defects and physicomechanical properties of polycrystalline β-rhombohedral boron journal March 1986
Boron and Boron Carbide Materials: Nanostructures and Crystalline Solids book January 2009
Preparation, structure and some properties of boron crystals with different content of 10B and 11B isotopes journal February 2004
High-pressure metallic phases of boron journal November 1990

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