Stability and Strength of Transition-Metal Tetraborides and Triborides

Zhang, Ruifang; Legut, Dominik; Lin, Zheng‐Zhe; Zhao, Yusheng; Mao, Ho‐kwang; Vepřek, S.

doi:10.1103/physrevlett.108.255502

Cited by 147 publications

(128 citation statements)

References 29 publications

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“…[20][21][22][23][24][25][26] Zhang et al [24] reopened the question on the correct crystal structure of WB 4 or WB 3 , as the calculated indentation hardness of WB 4 is lower than that of ReB 2 in contrast to the experimental result and the calculated normalized c/a ratio of WB 3 exhibits a negative pressure dependence, inconsistent with the observed trend. Li et al [25] in their latest study presented new thermodynamically stable structures for WB 3 (R 3m-''6u'') and WB 4 (P6 3 /mmc-''2u'').…”

Section: Introductioncontrasting

confidence: 42%

“…However, more recent theoretical calculations of band structure and physical properties (density functional theory calculations DFT) of this compound have inferred some confusion on the true crystal structure of ''WB 4 ''. [20][21][22][23][24][25][26] Whereas the first studies by Chretien and Helgorsky [15] reported a tetragonal unit cell for ''WB 4 '' (a = 0.634 nm, c = 0.450 nm), Rudy et al [16] claimed a hexagonal cell (a = 0.3004 nm, c = 0.3174 nm) but proposed ''WB 12 '' as a more appropriate composition. A first structure model was derived by Romans and Krug [17] from x-ray powder data backed by single crystal Laue and precession photographs indexed on a hexagonal lattice (a = 0.5200 nm, c = 0.6340 nm).…”

Section: Introductionmentioning

confidence: 99%

“…The theoretical DFT studies on the structural assignment and stability of WB 4 or MoB 4 (WB 3 or MoB 3 ) [20][21][22][23][24][25][26] claimed that WB 3 (MoB 3 ) with a two-dimensional boron net is thermodynamically more stable than WB 4 (MoB 4 ) with a three-dimensional boron skeleton. [20][21][22][23][24][25][26] Zhang et al [24] reopened the question on the correct crystal structure of WB 4 or WB 3 , as the calculated indentation hardness of WB 4 is lower than that of ReB 2 in contrast to the experimental result and the calculated normalized c/a ratio of WB 3 exhibits a negative pressure dependence, inconsistent with the observed trend.…”

Section: Introductionmentioning

confidence: 99%

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Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

Zeiringer

Rogl

Grytsiv

et al. 2014

J. Phase Equilib. Diffus.

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The crystal structure of W 12x B 3 has been reinvestigated by x-ray single crystal diffraction and revealed isotypism with the Mo 12x B 3 structure type (space group P6 3 /mmc; a = 0.52012(1), c = 0.63315(3) nm; R F = 0.040). As a characteristic feature of the structure, planar hexagonal metal layers (1/3 of atoms removed from ordered positions) sandwich planar boron honeycomb layers. One of the two W-sites shows a random defect of about 73%. Strong metal boron and boron-boron bonds are responsible for high mechanical stability. Although W 12x B 3 at about 80 at.% B is the metal boride richest in boron, it contains no directly linked three-dimensional boron framework. The solubility of Rh, Ir, Ni, Pd and Pt in W 12x B 3 as well as of Rh in Mo 12x B 3 has been investigated in as cast state and after annealing. Furthermore, phase equilibria in the boron rich part of the corresponding isothermal sections W-TM-B (TM = Rh, Ir at 1100°C, TM = Ni, Pd at 900°C and TM = Pt at 800°C) and Mo-Rh-B (at 1100°C) have been established. A ternary compound only forms in the system W-Ir-B: s 1 -W 12x Ir x B 2 with ReB 2 structure type (space group P6 3 /mmc; a = 0.2900, c = 0.7475 nm). The type of formation and crystal structure of diborides W 12x TM x B 2 (TM = Ru, Os, Ir) isotypic with ReB 2 were studied by x-ray powder diffraction and electron probe microanalysis in as cast state and after annealing at 1500°C. Accordingly, W 0.5 Os 0.5 B 2 (a = 0.29127(1), c = 0.7562(1) nm) forms directly from the melt, whereas W 0.4 Ru 0.6 B 2 (a = 0.29027(1), c = 0.74673(2) nm) and W 0.6 Ir 0.4 B 2 (a = 0.29263(1), c = 0.75404(8) nm) are incongruently melting. Annealing at 1500°C leads in case of the iridium compound to an almost single-phase product but the same procedure does not increase the amount of the ruthenium diboride.

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Section: Introductioncontrasting

confidence: 42%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

Zeiringer

Rogl

Grytsiv

et al. 2014

J. Phase Equilib. Diffus.

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“…Within the past five years, there has been a rapid succession of computational papers with the goal of identifying the structural origin of the properties of WB 4 (18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28). Although the correctness of the Romans and Krug model was initially assumed (24), it was quickly noticed that such a structure should be unstable (26).…”

mentioning

confidence: 99%

Structure of superhard tungsten tetraboride: A missing link between MB ₂ and MB ₁₂ higher borides

Lech

Turner

Mohammadi

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

113

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Superhard metals are of interest as possible replacements with enhanced properties over the metal carbides commonly used in cutting, drilling, and wear-resistant tooling. Of the superhard metals, the highest boride of tungsten-often referred to as WB 4 and sometimes as W 1-x B 3 -is one of the most promising candidates. The structure of this boride, however, has never been fully resolved, despite the fact that it was discovered in 1961-a fact that severely limits our understanding of its structure-property relationships and has generated increasing controversy in the literature. Here, we present a new crystallographic model of this compound based on refinement against time-of-flight neutron diffraction data. Contrary to previous X-ray-only structural refinements, there is strong evidence for the presence of interstitial arrangements of boron atoms and polyhedral bonding. The formation of these polyhedra-slightly distorted boron cuboctahedra-appears to be dependent upon the defective nature of the tungsten-deficient metal sublattice. This previously unidentified structure type has an intermediary relationship between MB 2 and MB 12 type boride polymorphs. Manipulation of the fractionally occupied metal and boron sites may provide insight for the rational design of new superhard metals.A s demand increases for new superhard materials, the introduction of transition metal borides as candidate compounds has recently attracted a great deal of attention (1-4). This trend is at least partially driven by a need for greater efficiency in cutting tools compared with tungsten carbide (which is not superhard), as well as the shortcomings of the traditional superhard compounds-diamond (which is unusable for cutting ferrous materials) (5) and cubic boron nitride (which is very expensive to synthesize and difficult to shape) (6). Within the rapidly growing family of superhard borides, tungsten tetraboride (or WB 4 ) is of specific interest due to its excellent mechanical properties and its relatively lower cost compared with borides such as ReB 2 , OsB 2 , RuB 2 , and RhB 2 , which contain platinum group metals (3, 7-11). For instance, tungsten tetraboride demonstrates an extremely high indentation hardness of ∼43 GPa by the Vickers method (under an applied load of 0.49 N) (8) and ∼41.7 GPa by nanoindentation (maximum, at a penetration depth of 95.25 nm; Fig. 1), and can sustain a differential stress (a lower-bound estimate of compressive yield strength) of up to ∼19.7 GPa (12). More dramatically, it is like ReB 2 (2), capable of scratching natural diamond (11). We have, furthermore, previously shown that the hardness of this compound may be enhanced by the creation of solid solutions with other transition metals (9). However, to understand the underlying mechanisms for the hardness enhancements observed in WB 4 solid solutions, as well as to guide the design of new superhard borides with tailored mechanical properties, it is crucial to understand the crystal structure of this compound.Perhaps surprisingly for a simple binary ...

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“…In comparison with the bulk moduli, it has been demonstrated that the correlation between the hardness and the compressibility has become particularly important for the prediction of the super-hard materials. 1,14,29,30,33,35,37,38 Based on our results as listed in Table II compressibility is proven to be inversely proportional to the hardness. For example, the compressibility increases from 2.38 TPa -1 to 3.91 TPa -1 with decreasing of the hardness from 96.0 GPa to 18.0 GPa in cubic materials as plotted in Figure 5 (black curve).…”

Section: The Relationship Between the Compressibility And The Hardmentioning

confidence: 96%

Anisotropic elasticity and abnormal Poisson’s ratios in super-hard materials

Huang

Chen

2014

AIP Advances

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We theoretically investigated the variable mechanical properties such as Young's modulus, Poisson's ratios and compressibility in super-hard materials. Our tensorial analysis reveals that the mechanical properties of super-hard materials are strongly sensitive to the anisotropy index of materials. In sharp contrast to the traditional positive constant as thought before, the Poisson's ratio of super-hard materials could be unexpectedly negative, zero, or even positive with a value much larger than the isotropic upper limit of 0.5 along definite directions. Our results uncover a correlation between compressibility and hardness, which offer insights on the prediction of new super-hard materials. C

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Stability and Strength of Transition-Metal Tetraborides and Triborides

Cited by 147 publications

References 29 publications

Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

Structure of superhard tungsten tetraboride: A missing link between MB ₂ and MB ₁₂ higher borides

Anisotropic elasticity and abnormal Poisson’s ratios in super-hard materials

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Stability and Strength of Transition-Metal Tetraborides and Triborides

Cited by 147 publications

References 29 publications

Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

Structure of superhard tungsten tetraboride: A missing link between MB 2 and MB 12 higher borides

Anisotropic elasticity and abnormal Poisson’s ratios in super-hard materials

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Product

Resources

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Structure of superhard tungsten tetraboride: A missing link between MB ₂ and MB ₁₂ higher borides