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Boron: a Hunt for Superhard Polymorphs


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Boron is a unique element, being the only element, all known polymorphs of which are superhard, and all of its crystal structures are distinct from any other element. The electron-deficient bonding in boron explains its remarkable sensitivity to even small concentrations of impurity atoms and allows boron to form peculiar chemical compounds with very different elements. These complications made the study of boron a great challenge, creating also a unique and instructive chapter in the history of science. Strange though it may sound, the discovery of boron in 1808 was ambiguous, with pure boron polymorphs established only starting from the 1950s-1970s, and only in 2007 was the stable phase at ambient conditions determined. The history of boron research from its discovery to the latest discoveries pertaining to the phase diagram of this element, the structure and stability of beta-boron, and establishment of a new high-pressure polymorph, gamma-boron, is reviewed.
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Boron: a Hunt for Superhard Polymorphs
A. R. Oganova,b and V. L. Solozhenkoc
aDepartment of Geosciences, Department of Physics and Astronomy, and New York
Center for Computational Sciences, Stony Brook University, Stony Brook, New York
11794-2100, USA
bGeology Department, Moscow State University, 119992 Moscow, Russia
cLPMTM-CNRS, Université Paris Nord, 93430 Villetaneuse, France
Received July 23, 2009
Abstract—Boron is a unique element, being the only element, all known polymorphs1 of which
are superhard, and all of its crystal structures are distinct from any other element. The electron-
deficient bonding in boron explains its remarkable sensitivity to even small concentrations of
impurity atoms and allows boron to form peculiar chemical compounds with very different
elements. These complications made the study of boron a great challenge, creating also a unique
and instructive chapter in the history of science. Strange though it may sound, the discovery of
boron in 1808 was ambiguous, with pure boron polymorphs established only starting from the
1950s–1970s, and only in 2007 was the stable phase at ambient conditions determined. The
history of boron research from its discovery to the latest findings pertaining to the phase diagram
of this element, the structure and stability of β-boron, and establishment of a new high-pressure
polymorph, γ-boron, is reviewed.
Keywords : boron, structure, polymorphism, phase diagram.
An element with a huge range of applications from nuclear reactors to superhard, thermoelectric
and high-energy materials, boron is also arguably the most complex element in the Periodic
Table. The history of boron research is full of disputes, with mistakes made even (or mainly?) by
great scientists. At times this history may even be read like a detective story. A story that we
briefly recount here, focussing on the most recent discovery – that of a high-pressure superhard
phase of boron called γ-B28 [1].
A boron-containing mineral borax, Na2 [B4O5(OH)4]·8H2O, has been known since ancient times
and its name derives from Arabic “buraq”, which means “white”. In 1702, starting from borax,
Wilhelm Homberg obtained a snow-white powder that he called “sedative salt”, now known as
metaboric acid, HBO2. The next stage, marked by the “double discovery” of this element, was at
the time of scientific rivalry between great English (Humphry Davy) and French (Louis Joseph
Gay-Lussac and Louis Jacques Thenard) chemists. On June 21, 1808 Gay-Lussac and Thenard
announced the discovery of the new element, which they called “bore” (the element is still called
this name in French). They obtained boron by reduction of boric acid with potassium2 [2].
1Rhombohedral α-B12 and β-B106 phases (with 12 and ~106 atoms in the unit cell, respectively), tetragonal T-192
(with 190-192 atoms/cell) and orthorhombic γ-B28 (with 28 atoms in the unit cell).
2 The story of how Gay-Lussac and Thénard obtained potassium is also quite instructive. Davy’s discovery of this
element by electrolysis caused a great excitement among chemists. Emperor Napoleon I, who awarded a prestigious
prize to English chemist Humphry Davy, wished to foster similar kind of research (discovery of new elements by
electrolysis) and presented Davy’s competitors, Gay-Lussac and Thénard, with a very large electric battery.
Within days, on June 30, 1808, Humphrey Davy submitted to the Royal Society of London an
article on the discovery of a new element (which he called boracium)3 [3]. Faithful to his style,
which has led to the discovery of a whole pleiad of elements, Davy prepared boron by
electrolysis. The first detective twist, apart from the remarkably close dates of the two
independent discoveries, is that both discoveries did not produce a pure element. It is now clear
that both groups synthesized compounds containing no more than 50% of boron [4]. Should the
works of Gay-Lussac, Thenard and Davy be still considered as discoveries? It is hard to answer
positively, but if we answer negatively, then it will be exceedingly hard to say who actually
discovered the element, as we discuss below.
One of the prominent scientists, who proved that Gay-Lussac, Thenard and Davy did not deal
with a pure element, was Henri Moissan. In 1895 he prepared the element by reduction of B2O3
with magnesium in a thermite-type reaction [4]. However, even Moissan’s material was far from
being a pure element. It is often quoted that 99%-pure boron was synthesized by E. Weintraub [5]
in 1911, and while his methods were certainly advanced compared to the previous works, there
are reasons for doubt, as pure boron polymorphs are documented only after 1957.
a b c
Fig. 1. Discoverers of boron: (a) Joseph Louis Gay-Lussac (1778-1850), (b) Louis Jacques
Thenard (1777-1857), (c) Humphry Davy (1778-1829).
After the element itself got more or less established, a race for discovery of boron polymorphs
slowly began. And that race was equally complex and full of misdiscoveries. Already in 1857
Friedrich Wöhler and Henri Sainte-Claire Deville [6, 7] heating up boron oxide and aluminum
obtained three forms of boron. On the basis of hardness and luster, they drew an analogy with
carbon polymorphs and called these forms diamond-like, graphite-like, and charcoal-like
(amorphous). Amorphous form had the same properties as the material synthesized by Gay-
Lussac and Thenard (which, as we now know, was not pure boron), while the "diamond-like"
and "graphite-like" forms were later proven to be compounds containing no more than 70% of
boron [4]. Thus, many, if not most, of the great scientists who studied boron, fell victims of this
element’s extreme sensitivity to even small amounts of impurities. This sensitivity is evidenced
Disappointingly, the battery turned out to be not nearly as powerful as was expected. Gay-Lussac and Thénard,
however, managed to prepare potassium by heating up potash and iron.
3 The material obtained by Davy appears to have been metallic, whereas pure boron phases are all semiconducting.
by the existence of such very boron-rich compounds (with unique icosahedral structures) as
YB65.9, B6O, NaB15, B12P2, B13P2, B13C2, MgAlB14, AlC4B40, NiB50(?), B50C2, B50N2, PuB100(?)
(e.g., [8]). In particular, the structure of YB66 is an icon of structural complexity – it contains
1584 atoms in the unit cell [9].
It is fair to state that boron still remains a poorly understood element. At least 16 crystalline
polymorphs have been reported [8], but crystal structures were determined only for 4
modifications and most of the reported phases are likely to be boron-rich borides rather than pure
elemental boron [8, 10, 11]. Until 2007, it was the only light element, for which the ground state
was not known even at ambient conditions. And none of the polymorphs reported before 1957
actually correspond to pure boron. Most of the discoveries related to pure boron discoveries were
done in two “waves”, i.e. in 1957–1965 and 2001–2009.
The first wave was led by researchers from the Cornell University and General Electric (GE)
Corporation. The so-called I-tetragonal phase (or T-50, because it contains 50 atoms in the unit
cell), produced in 1943 jointly at Cornell and GE [12], was the first one, for which the structure
was solved – in 1951 [13, 14]. This structure appeared in many books, notably in Pauling’s
seminal The Nature of the Chemical Bond [15], where it was the only boron structure depicted4.
However, this “well-established” phase was proven to be a compound [10, 11, 16] of
composition B50C2 or B50N2.
The first pure boron phase discovered was β-B106 [17], the structure of which turned out to be
extremely complex and was solved only several years later [18]. This discovery was shortly
followed by the discoveries of α-B12 phase at GE in 1958 [19] and T-192 phase at Polytechnic
Institute of Brooklyn in 1960 [20] (the structure of the latter was so complex that it was solved
only in 1979 [21]). All these structures contain B12 icosahedra and are shown in Fig. 2.
a b c
4Although Pauling used a “wrong” phase for illustrating chemical bonding in boron, the ideas themselves were
largely correct.
Fig. 2. Crystal structures of boron polymorphs: (a) α-B12, (b) β-B106, (c) T-192, (d) γ-B28.
Panels (a) and (d) are from [1].
Considering the wealth of different “boron polymorphs” reported in the literature, Amberger and
Ploog [10] even suggested that only two known phases correspond to pure boron, namely, α-B12
and T-192, and possibly β-B106. They obtained boron by CVD using a mixture of BBr3 and H2 at
temperatures of 1200–1600 K, by deposition on Ta wires in the absence of any foreign atoms.
This way they observed amorphous boron, α-B12 and T-192 phases, and occasionally β-B106.
T-50 phase (obtained earlier by a similar method [12]) was never synthesized. Because of the
sensitivity of boron to impurities different samples of the same polymorph show important
differences in structural and, as a result, in thermodynamic properties. The relative stability of
boron phases is still experimentally unresolved even at ambient conditions [22]. It was, for
instance, a matter of a debate (until 2007) whether α-B12 or disordered β-B106 is stable at ambient
As we mentioned, much of the progress was done at GE. At that time, GE amassed a unique
group of researchers with the aim of enabling industrial-scale synthesis of diamond. Furthermore,
GE researchers synthesized cubic BN, an advanced substitute for diamond in cutting and
abrasive tools. Both synthetic diamond and cubic BN (commercialized under the name
“borazon”) turned into multimillion-dollar industries. GE was interested in boron, because of its
extreme hardness and because of its highly tunable electrical conductivity. At least since the
works of Sainte-Claire Deville and Wöhler in 1850s, boron was known to be the second hardest
element after carbon (viz. diamond), and Weintraub [5] even entertained ideas that under certain
fabrication protocol boron could become harder than black diamond (variety of diamond called
In 1964, Robert Wentorf of GE, one of the pioneers of high-pressure synthesis of materials and
the main author of the synthesis of cubic BN, turned to study the behavior of boron under
pressure. At pressures above 10 GPa and temperatures of 1800-2300 K, he found that both β-
B106 and amorphous boron transformed into another, hitherto unknown, phase [23]. Wentorf
reported a qualitative diffraction pattern of the new material and described the changes of the
density and electrical conductivity across the phase transition. For that time, it was a state-of-the-
art work, but nevertheless it was not accepted by the community from the beginning. In a period
of 1965–2008 Wentorf’s paper was cited only 6 times (in spite of being published in a very
prestigious journal, Science) and only by papers dealing with boron indirectly. Classical papers
(e.g., the paper of Amberger and Ploog [10] on pure boron phases) never even mention
Wentorf’s paper! Furthermore, Wentorf’s diffraction data were deleted from Powder Diffraction
Files Database. One can speculate about the reasons for such a distrust, but almost certainly these
were (1) absence of chemical analysis in Wentorf’s paper (neither for the starting material, nor
for the product – and this in principle disqualifies any experimental work on boron, as we saw
5E.g., Weintraub wrote that “(pieces of boron) are very hard and scratch with ease the known hard substances except
diamond”, “in further continuation of the work additional toughness may be imparted to boron and the product
becomes a cheap substitute for black diamond” and “Will it be possible to approach the properties of diamond or
perhaps by combining boron and carbon even exceed diamond in its hardness? I can only say that we are working on
this problem.” [5]
above), (2) lack of crystal structure determination (there was a lasting doubt that Wentorf’s
material was a mixture of phases – which, indeed, it most likely was).
The second wave of boron studies was probably catalyzed by the 2001 unexpected discovery of
superconductivity in MgB2 [24]. It was clear from the beginning that superconductivity of this
compound is due to the graphite-like sublattice of boron atoms (e.g., [25]), and very soon
elemental boron was subjected to high pressures in search for superconductivity. In 2001,
compressing β-B106 at room temperature, Eremets et al. [26] indeed observed metallization at
160 GPa, and the metallic state displayed superconductivity (with the value of Tc reaching
11.2 K at 250 GPa). The structure of this metallic phase was not determined, but subsequent
experiments [27] suggested that room-temperature compression of β-B106 results in pressure-
induced amorphization at 100 GPa. This implies that there is a kinetically hindered phase
transition to some unknown crystalline phase below 100 GPa. The likely problem of room-
temperature experiments is metastability. Using laser heating to overcome kinetic barriers, Ma et
al. [28] have found that β-B106 transforms into the T-192 phase above 10 GPa at 2280 K. This
has proven that the T-192 phase is not only a pure boron phase, but also has a stability field at
high pressures and temperatures. Its stability field was further constrained in [1].
At the same time, the stable phase at ambient conditions remained unknown, putting XX and
XXI century chemists in shame. The debate whether α-B12 or β-B106 is stable at ambient
conditions, was finally resolved in 2007-2009 by ab initio calculations of three different groups
[29–31], which used different approaches, but all concluded in favor of β-B106 and against
common intuition that favored the much simpler α-B12 structure.
Another major result came up from Chen (experiments done in February 2004 at Stony Brook
University) and Solozhenko (experiments done in April 2004 at the Université Paris Nord and
HASYLAB-DESY, and in July 2004 at the Bayerisches Geoinstitut). Both groups found a new
phase of boron at pressures above 10-12 GPa and temperatures above 1500 K. Further evolution
of ideas and events completed the “second wave of boron research”, resolved many old problems
and by itself could deserve a detective novel.
Although Chen and collaborators managed to determine the unit cell parameters of the new
phase, neither group succeeded in solving its structure, in spite of intense research and repeated
experiments during several years. In 2006 Chen posed this problem to Oganov, whose method
for predicting crystal structures [32] could be used for solving this problem. The structure was
solved within one day6, and its simulated diffraction pattern coincided with the experimental one
(to make the test challenging and unbiased, Oganov and his team of theoreticians did not have
access to experimental diffraction data and thus, the comparison was done in a “blind” way). The
structure, thus confirmed by experiment, was indeed unique – it is a NaCl-type arrangement of
two types of clusters, B12 icosahedra and B2 pairs7 [1]. Detailed investigations showed that these
6But it took much longer to publish these results. The paper, originally submitted to Science on December 8, 2006,
was turned down and submitted to Nature on January 27, 2007. It took 2 years for Oganov’s team to publish their
manuscript in Nature (the paper came out on January 28, 2009). During this period, Oganov learned about
Solozhenko’s independent work and the two parallel teams merged.
7Only in compounds, such as B4C, B6P, B6O, etc., there are roughly similar structures – but there, the two sublattices
are occupied by chemically different atoms.
two clusters have very different electronic properties (Fig. 3) and there is a charge transfer (of
~0.5 e) from B2 to B12 [1], and this is correlated with the strong IR absorption and high
dynamical charges on atoms. This partially ionic phase was named γ-B28 [1]. Our measurements
[33] showed that γ-B28 is superhard, with Vickers hardness of 50 GPa, which makes it the
hardest phase of boron (the best estimates of the hardness of β-B106 and α-B12 are 45 GPa [34]
and 42 GPa [35], respectively). Comparison of the diffraction data on γ-B28 with older data of
Wentorf [23] shows a great deal of similarity; given also quite similar conditions of synthesis, it
is very likely that what Wentorf observed was indeed γ-B28 (in a mixture with some other
This discovery has attracted much attention. Very recently Zarechnaya et al. [36, 37] confirmed
the structure and superhardness of γ-B28. Their main achievement was the synthesis of micron-
sized single crystals, though conditions of synthesis were suboptimal (e.g., the capsules reacted
with boron sample) and their papers unfortunately contained serious errors (see [38] for details)
and confusions (e.g., tetragonal T-192 and B50C2 are incorrectly implied to be the same phase).
Their equation of state, measured to 30 GPa [36], shows large deviations from theory [1] and
independent experiment [39]. Later calculations found that (i) the electronic spectra of the
different atomic sites are indeed very different [40], confirming the charge-transfer model [1]
and (ii) during deformation of the structure, the first bonds to break are those between the most
charged atoms [41].
Fig. 3. Electronic structure of γ-B28. The total density of states is shown, together with the
electron density corresponding to four different energy regions denoted by letters A, B, C, D.
Note that lowest-energy electrons are preferentially localized around the B12 icosahedra, whereas
highest-energy electrons are concentrated near the B2 pairs.
The discovery of γ-B28 provided the missing piece of a puzzle of the phase diagram of boron [1].
The stability field of this phase is larger than the fields of all other known boron polymorphs
combined (Fig. 4). The diagram shown in Fig. 4 describes all known data in a satisfactory
manner. The upper pressure limit of stability of γ-B28 remains to be tested. Theoretical
predictions of an α-Ga-type metallic phase above 74 GPa [42, 43] were confirmed [1] using
crystal structure prediction tools [32], except that the predicted pressure of this phase transition
was shifted to a higher value, 89 GPa, by the presence of a new phase, γ-B28 [1]. α-Ga-type
boron has been predicted to be a superconductor [44]. This structure does not contain B12
icosahedra and heralds a new type of boron chemistry under pressure. A chemistry that remains
to be probed by future experiments.
Fig. 4. Phase diagram of boron. This diagram is based on theoretical and experimental data from
[1], as well as data from earlier works. Reproduced from [1].
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... Since molecular properties depend greatly on their geometry [32,33], boron clusters exhibit a large number of molecular properties that have potential applications in medicine [34][35][36][37], molecular motors [21,223,38], superhard materials [39], hydrogen storage [40], batteries [41][42][43][44], catalysis [45], and energy materials [46], among many others. ...
... In these pairs of planar enantiomers, chirality arises due to the hexagonal hole and its position. A year later, the lowest-energy structures of the B 39 − borospherene were reported as chiral due to their hexagonal and pentagonal holes [17]. Similarly, the B 44 cluster was reported as a chiral structure due to its nonagonal holes [20]. ...
... If an electron has high energy, then the inner electrons of the target are used to generate characteristic X-rays, and numbers of target materials (Cu, Fe, Mo, Cr) are used to produce the X-rays spectra for studies. Boron is a unique element that is super hard with unique crystal structures than others [1]. ...
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This work aims to study the XRD of 5 Boron oxides crystal with different X-ray sources using Quantum Expresso. When XRD was done with angle vs. intensity, a pretty exciting observation was observed: the single high-intensity peak was observed for each source. The high intensity with large Bragg’s angle is observed with Fe-sources among the considered source (Cu, Ag, Mo, and Fe). This shows lower atomic mass sources have higher Bragg’s angle when incidence on a sample of Boron oxides. The high-intensity peak when Fe-sources is used for XRD of B6O, BO3, B2O, B8O, B2O3 was observed at an angle of 44.3, 37.5, 11, 44.3, 39.8 degrees, respectively.
... 3,5 Boron electron deficiency gives origin to vast number of allotropic forms and uncommon geometries 2,6,7 such as nanotubes, 8,9 borospherenes, 10 borophene, 7 cages, 9,11 planar, 12 quasi planar, 13 rings, 14,15 chiral, 13,16-20 boron-based helix clusters, 16,21 and fluxional boron clusters 2,21-31 that have recently attracted the interest of experimental and theoretical researchers. Since the molecular properties depend greatly on their geometry and temperature; 32,33 boron cluster exhibit a large number of molecular properties that yield potential applications in medicine, [34][35][36][37] molecular motors, 21,23,38 superhard materials, 39 hydrogen storage, 40 batteries, 41-44 catalysis, 45 and energy materials 46 among many others. ...
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The lowest-energy structure, distribution of isomers, and their molecular properties depend significantly on the geometry and temperature. The total energy computations under DFT methodology are typically carried out at zero temperature; thereby, entropic contributions to total energy are neglected, even though functional materials work at finite temperature. In the present study, the probability of occurrence of one particular Be$_4$B$_8$ isomer at temperature T is estimated within the framework of quantum statistical mechanics and nanothermodynamics. To locate a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surface is done by employing a multilevel multistep global genetic algorithm search coupled to DFT. Moreover, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The computed VCD/IR spectrum of each isomer is multiplied by their corresponding Boltzmann weight at temperature T; then, they are summed together to produce a final Boltzmann weighted spectrum. Additionally, we present chemical bonding analysis using the Adaptive Natural Density Partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer-enantiomer and enantiomer-achiral activation energies as a function of temperature, evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.
Boron is located just before carbon in the periodic table. It has very similar atomic weight and electron structure as carbon, with just one less electron. Planar boron structures have long been a topic of intensive interest both experimentally and theoretically. With the experimental realization of borophene in 2015, there have been a surge of researches in this fascinating new 2D material. Borophene is 2D metal, with a predicted conductivity even higher than graphene. Combined with the strong chemical bonds and light atomic mass, borophene can be regarded as the thinnest, and lightest metal in nature. Moreover, intriguing properties such as structural anisotropy, high in-plane elasticity, Dirac fermions, visible range plasmonics, and even phonon-mediated superconductivity have been predicted in borophene. However, like silicene, borophene is unstable in air. Although different strategies have been proposed to overcome this problem, there is still a long way to go before useful borophene-based devices can be realized in the future.
As the lightest two-dimensional material discovered so far, borophene exhibits rich physical properties, including high flexibility, optical transparency, high thermal conductivity, one-dimensional nearly free electron gas, Dirac fermions, and superconductivity. However, due to the strong interlayer covalent bonding force of bulk boron, it is difficult to obtain the monolayer borophene via mechanical exfoliation. In addition, due to the electron-deficient property of boron atoms, its chemical properties are relatively active, and its bonding is complex, resulting in different boron allotropes, which is different from other two-dimensional materials. For a long time, the research on borophene has been limited to theoretical exploration, and it has been difficult to make breakthroughs in the experimental synthesis of two-dimensional borophene. It has been only successfully prepared by a few research groups in recent years. However, there is still huge space for exploration on the growth, structure and electronic properties of borophene. This paper systematically reviews the preparation methods and different structures of borophene under different substrates, and its growth mechanism is discussed. It provides a research platform for further expanding the physical properties of borophene, and provides ideas for exploring the preparation of borophene nanodevices. It has great potential application prospects in high energy storage, optoelectronic devices, high detection sensitivity, and flexible nanodevices.
Finding allotropes with novel structures and intriguing properties is of great interest from both fundamental and applicable standpoints. Here, we propose a hitherto unknown boron allotrope, possessing intrinsic superconductivity and...
The abnormal brittle failure of superhard boron carbide (B4C) and other icosahedral solids arises from the shear-induced amorphization. Mitigating the amorphization in these materials remains challenging due to the lack of other deformation mechanisms such as mobile dislocations. This paper illustrates the shear-induced amorphization process of B4C from molecular dynamics (MD) simulations using quantum-mechanics-derived machine-learning force field. The amorphization in B4C initiates from the disintegration of icosahedral clusters, and then this icosahedral deconstruction propagates and merges to form an amorphous region with 2–3 nm in width, leading to the following cavitation and brittle failure. More interesting, the deformation mechanism transforms from amorphization to stacking fault (SF) formation by microalloying aluminum (Al) into B4C. This SF formation originates from the enhanced icosahedral slip as the Al is incorporated into the C-B-C chain to form a C-Al-C chain. This paper illustrates a deformation mechanism of superhard icosahedral solids and provides a strategy for suppressing the amorphization and brittle failure of B4C.
Two-dimensional (2D) boron monosulfide (BS) nanosheets are predicted to have several stable phases and unique electronic structures, endowing them with interesting attributes, including superconducting, thermoelectric, and hydrogen storage properties. In...
The intrinsic and electronic properties of elemental two-dimensional (2D) materials beyond graphene are first introduced in this review. Then the studies concerning the application of gas sensing using these 2D materials are comprehensively reviewed. On the whole, the carbon-, nitrogen-, and sulfur-based gases could be effectively detected by using most of them. For the sensing of organic vapors, the borophene, phosphorene, and arsenene may perform it well. Moreover, the G-series nerve agents might be efficiently monitored by the bismuthene. So far, there is still challenge on the material preparation due to the instability of these 2D materials under atmosphere. The synthesis or growth of materials integrated with the technique of surface protection should be associated with the device fabrication to establish a complete process for particular application. This review provides a complete and methodical guideline for scientists to further research and develop the hazardous gas sensors of these 2D materials in order to achieve the purpose of environmental protection.
The search of new superhard materials has received a strong impulse by industrial demands for low-cost alternatives to diamond and c-BN, such as metal borides. In this Letter we introduce a new family of superhard materials, “fused borophenes” (FBs), containing 2D boron layers that are interlinked to form a 3D network. These materials, identified through a high-throughput scan of BxC1−x structures, exhibit Vicker's hardness comparable to those of the best commercial metal borides. Due to their low formation enthalpies, FBs could be synthesized by high-temperature methods, starting from appropriate precursors, or through quenching of high-pressure phases.
Crystallographers have an elegant system using definitive notation for describing crystal structures, but it does not serve as well the needs of many others working with crystalline solids. Most chemists, metallurgists, mineralogists, geologists and materials scientists need a simple system and notation for describing crystal structures. Structure and Chemistry of Crystalline Solids presents a widely applicable system with simple notation giving important information about the structure and the chemical environment of ions or molecules. It is easily understood and used by those concerned with applications dependent on structure-properties relationships. Early chapters provide an introduction to crystal structures and symmetry for readers with a variety of backgrounds. Insight into crystal structures, including some complex silicates, is aided by the use of the CrystalMaker computer program. The bundled CD-ROM, which uses CrystalMaker for instruction and demos on both Windows and Macintosh platforms, allows the user to manipulate the structures. Key Features: Understandable by anyone concerned with crystals or solid state properties dependent on structure Presents a general system using simple notation to reveal similarities and differences among crystal structures Depicts more than 300 selected and prepared figures illustrating structures found in thousands of compounds Includes a CD-ROM with CrystalMakerTM data files to allow the reader to view and manipulate the structures on both Windows and Macintosh platforms.
Using ab initio techniques we have calculated the electron energy loss near edge structure (ELNES) of a new high pressure phase of boron (γ-B28) and the structurally similar allotrope, α-B12. The total ELNES spectra are presented as weighted sums of the site specific spectra of the constituent non-equivalent B atoms. The five different non-equivalent B sites in γ-B28 all show rich ELNES spectra and their similarities and differences to the simpler α-B12 case are detailed. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Commentary on errors in an earlier article on the nature of the chemical bond. Keywords (Audience): First-Year Undergraduate / General
Through the use of perturbation theory, in this work we develop a method which allows for a substantial reduction in the size of the plane-wave basis used in density-functional calculations. This method may be used for both pseudopotentials and all-electron calculations and is particularly beneficial in the latter case. In all cases, the approach has the advantage of allowing accurate predictions of transferability errors for any environment. Finally, this method can be easily implemented into conjugate-gradient techniques, and it is therefore computationally efficient. In this work, we apply this method to study high-pressure phases of boron. We find that boron undergoes a phase transition from the α12-B structure to the αga-B structure, both of which are semiconducting. The αga-B structure has lower energy than traditional monoatomic structures, which supports the assertion that the metallic, and hence superconducting phase, for boron is much more complicated than a simple monoatomic crystal.
On the pyrolysis of BBr3 and H2 on tantalum wires at 900 °–1300 °C under very clean conditions, elementary boron is formed with the II-tetragonal or α-rhombohedral structure in a reproducible manner. These lattices of pure boron disappear when very small quantities of CH4 or CHBr3 are added to the BBr3-H2 mixture (maximalCH4: BBr3 = 0.003:1 Mol-%). By increasing the small carbon supply, the following lattices are induced:First the β-rhombohedral boron (which probably contains carbon) is obtained and then the new boron-rich borides (B12)4B2C and (B12)4B2C2 are formed. In these two borides with the lattice constants a = 8.77 and the unstable lattice (B12)4B2 of the so-called “I-tetragonal boron” is stabilized by occupying one or two more tetrahedral holes in the icosahedron framework by single carbon atoms. When the carbon supply is further increased the two known rhombohedral phases B13C2 and B4C are obtained.