COMPOSITIONAL VARIATIONS OF TUNGSTEN MONOBORIDE

Abstract

Methods, devices, and systems include a composition for a metal alloy comprising tungsten (W), tantalum (Ta), and boron (B) crystallized in an orthorhombic phase, wherein the composition satisfies the formula W.sub.1-xT.sub.axB wherein x has a value within the range 0.01 to 0.99, inclusively.

Claims

1.-71. (canceled)

72. A metal composition of Formula (I) crystallized in an orthorhombic phase,
W.sub.1-xN.sub.xB Formula I wherein: N is a non-radioactive Group V Transition Metal; and x has a value within a range of 0.01 to 0.99, inclusively.

73. The composition of claim 72, wherein N is Tantalum (Ta), Vanadium (V), or Niobium (Nb).

74. The composition of claim 72, wherein x has a value within a range of 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively.

75. The composition of claim 72, wherein x has a value of about 0.5.

76. The composition of claim 72, wherein the metal composition has a bulk modulus of from about 336 GPa to about 346 GPa.

77. The composition of claim 72, wherein the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa.

78. The composition of claim 72, wherein the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

79. The composition of claim 72, wherein at least one plane of the metal composition further exhibits a discontinuous increase in directional incompressibility.

80. A metal composition of Formula (I):
W.sub.1-xN.sub.xB Formula I wherein: N is a non-radioactive Group V Transition Metal; and x has a value within a range of 0.01 to 0.99, inclusively; and wherein boron forms a plurality of chains within a crystal structure of the metal composition, and wherein each of the plurality of chains is aligned along a same axis of the crystal structure.

81. The composition of claim 80, wherein N is Tantalum (Ta), Vanadium (V), or Niobium (Nb).

82. The composition of claim 80, wherein x has a value within a range of 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively.

83. The composition of claim 80, wherein the metal composition is crystallized in an orthorhombic phase.

84. The composition of claim 80, wherein the axis is a c-axis.

85. The composition of claim 80, wherein the plurality of chains of boron do not alternate to form a perpendicular array within the crystal structure.

86. A method of making a stable metal composition comprising: introducing a plurality of additive particles into the interstices of a metal composition precursor to form a metal composition, wherein the plurality of additive particles is selected from vanadium, niobium, and tantalum; and subjecting the metal composition to a temperature and pressure at which the metal composition is stable at room temperature.

87. The method of claim 86, wherein the subjecting further comprises sintering the metal composition precursor with the plurality of additive particles to form the stable metal composition.

88. The method of claim 86, wherein the stable metal composition has a formula W.sub.1-xN.sub.xB, wherein N is an additive particle selected from vanadium (V), niobium (Nb), and tantalum (Ta) and x has a value within a range of 0.01 to 0.99, inclusively.

89. The method of claim 86, wherein at least one plane of the stable metal composition further exhibits a discontinuous increase in directional incompressibility.

90. The method of claim 86, wherein the metal composition has a crystalline structure, wherein boron forms a chain within the crystalline structure of the metal composition, and wherein the chain is aligned along a c-axis of the crystalline structure.

91. The method of claim 86, wherein the stable metal composition is an entropically stable metal composition.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings of which:

[0014] FIG. 1 shows a non-limiting example of a tungsten monoboride; in this case, a crystal structure of high-temperature, orthorhombic tungsten monoboride, WB, wherein the purple plane marks the location of a metallic tungsten bilayer.

[0015] FIG. 2 shows a non-limiting example of powder X-ray diffraction patterns of a W.sub.(1-x)Ta.sub.xB metal alloy; in this case, powder X-ray diffraction patterns of W.sub.(1-x)Ta.sub.xB (x=0.01, 0.05, 0.10, 0.25, and 0.50) with peaks indexed to orthorhombic WB (JCPDS Card #00-006-0541).

[0016] FIG. 3 shows a non-limiting example of energy-dispersive spectroscopy (EDS) plots of a W.sub.(1-x)Ta.sub.xB metal alloy; in this case, (EDS) plots demonstrate that tantalum (right) and tungsten (left) are evenly distributed throughout the alloy. (Scalebar=10 m.)

[0017] FIG. 4 shows a non-limiting example of a transmission electron microscopy of freshly fractured powder of a W.sub.(1-x)Ta.sub.xB metal alloy; in this case, the transmission electron microscopy of freshly fractured powder indicates that the majority of the grains are not nanostructured, ruling out extrinsic hardening mechanisms. (Scalebar=200 nm.)

[0018] FIG. 5 shows a non-limiting example of lattice parameters of a W.sub.(1-x) T.sub.ax B metal alloy; in this case, the a, b, c lattice parameters of W.sub.(1-x)Ta.sub.xB (x=0.01, 0.05, 0.10, 0.25, and 0.50), wherein the linear progression of the lattice parameters with respect to tantalum content, consistent with Vegard's law.

[0019] FIG. 6 shows a non-limiting example of Vickers indentation hardness of a W.sub.(1-x) Ta.sub.x B metal alloy; in this case, the Vickers indentation hardness of W.sub.(1-x) T.sub.ax B as a function of different loads (0.49 N/50 gram-force, 0.98 N/100 gram-force, 1.96 N/200 gram-force, 2.9 N/300 gram-force, and 4.9 N/500 gram-force), follows a linear trend. The hardness value of the 50% Ta composition under a load of 0.49 N is 42.82.6 GPa, and indicates that W.sub.0.5Ta.sub.0.5B is a superhard material.

[0020] FIG. 7 shows a non-limiting example of differential strain plot of a W.sub.(1-x) Ta.sub.x B metal alloy; in this case, differential strain plot of W.sub.0.5Ta.sub.0.5B with respect to the (200), (020), and (002) planes. The (020) plane supports the highest differential strain (t/G) and indicates that it is the load-bearing plane.

[0021] FIG. 8 shows a non-limiting example of thermogravimetric analysis (TGA) of a W.sub.(1-x) Ta.sub.x B metal alloy; in this case, thermogravimetric analysis (TGA) of W.sub.0.5Ta.sub.0.5B suggests that the onset of oxidation does not begin until 550 C.

[0022] FIG. 9 shows a non-limiting example of resistance/temperature relationship of a W.sub.(1-x) Ta.sub.x B metal alloy; in this case, the electrical resistance of the ingot increases with temperature, which suggests that W.sub.0.5Ta.sub.0.5B is metallic.

[0023] FIG. 10 shows a non-limiting example of deformation performance of a W.sub.(1-x) Ta.sub.x B metal alloy; in this case, the deformation in the unit cell volume is fitted to a Third-order Birch-Murnaghan equation of state, and shows that W.sub.0.5Ta.sub.0.5B is ultra-incompressible.

[0024] FIG. 11A and FIG. 11B illustrate representative synchrotron X-ray diffraction patterns for high HT phase WB (FIG. 11A) and LT phase WB (FIG. 11B) with increasing pressure. Pt was used for the in situ pressure calibration.

[0025] FIG. 12 illustrates selected d-spacings vs. pressure variations for HT WB and LT WB. Error bars that are smaller than the size of the symbol have been omitted.

[0026] FIG. 13A and FIG. 13B show dependence of d-spacings of HT WB (FIG. 13A) and LT WB (FIG. 13B) as a function of angle at highest pressure. The solid lines are the best linear fit to the data.

[0027] FIG. 14 shows ratio of differential stress to aggregate shear modulus (t(hkl)/G) of HT WB (black) and LT WB(red).

[0028] FIG. 15 shows evolution of peak broadening of (020) plane of HT WB and equivalent (004) plane of LT WB.

[0029] FIG. 16A and FIG. 16B show differential stress of selected lattice plane of HT WB (FIG. 16A) and LT WB (FIG. 16B) under Reuss (iso-stress) condition (open symbol) and Voigt (iso-strain) condition (close symbol).

[0030] FIG. 17 shows the calculated DFT energy change of the HT WB in response to shearing distortion.

[0031] FIG. 18 illustrates variation of the average differential stress of HT WB, LT WB and some other representative superhard materials as a function of pressure.

[0032] FIG. 19A and FIG. 19B illustrate evolution of unit cell volume of HT WB (FIG. 19A) and LT WB (FIG. 19B) as a function of pressure under non-hydrostatic compression. The volume was measured at =54.7. The inset is the Birch-Murnaghan equation-of-state for WB in terms of normalized pressure and Eulerian strain. The straight line yields an ambient pressure bulk modulus.

[0033] FIG. 20A and FIG. 20B illustrate exemplary crystal structures of orthorhombic WB (FIG. 20A) and Tetragonal WB (FIG. 20B).

[0034] FIG. 21 shows exemplary crystal structure of orthorhombic WB looking down the c axis (left panel) and a axis (right panel). The bicolor sticks denote the WB bonds.

[0035] FIG. 22 shows relevant bonding structures of the solid and a representative cluster. The top orbital had an energy displacement of 4.710.sup.4 eV during shearing in (020) and the bottom had an energy displacement of 3.510.sup.4. The cluster demonstrates more clearly the orbital interactions occurring in the solid; thus, we can attribute the solid state bonds to interactions between W's d.sub.xz and B's p.sub.x, and W's d.sub.z.sup.2 and B's p.sub.z, respectively.

[0036] FIG. 23A and FIG. 23B show fractional lattice constants of HT WB (FIG. 23A) and LT WB (FIG. 23B).

[0037] FIG. 24A and FIG. 24B show linear incompressibility of lattice constants of HT WB (FIG. 24A) and LT WB (FIG. 24B).

DETAILED DESCRIPTION OF THE DISCLOSURE

[0038] Superhard compounds can be compounds that have a Vickers hardness value of about or greater than 40 gigapascals (GPa). In some instances, superhard compounds can be designed rather than discovered by following, for example, two rules. The first rule or step can be to start with a starting material of high valence electron density, leading to a large bulk modulus and high incompressibility. The second rule or step can be to add short, strong covalent bonds to prevent shear and slipping of planes. For example, diamond is both the hardest and stiffest single-phase material known with a hardness of 70-110 GPa, a bulk modulus of 442 GPa, and a valence electron density of 0.71 e.sup..sup.3 (8). Similarly, utilizing the aforementioned design rules to generate superhard metals comprising for example tungsten and boron can result in high borides in a tungsten metal composition and/or heavy covalent tungsten compounds with less metallic characteristics relative to a WB composition. For example, to generate a heavy metal tungsten, one method can be by introducing at least four molar equivalents of boron to yield WB.sub.4. In such cases, this can increase covalent bonding, and can result in a superhard composition.

[0039] With the lower borides of tungsten, a lower level of covalent bonding in some instances results in a softer material. For example, pristine tungsten tetraboride, the highest boride in the WB system, is superhard with a Vickers Hardness of 43 GPa under a load of 0.5 N. Experimental hardness measurements have shown that pristine WB is not naturally superhard, with single crystals exhibiting a Vickers Hardness of 26 GPa under a load of 1 N and polycrystalline materials 36 GPa. Computational studies have shown that WB can have a high shear modulus, although lower than those found in superhard materials such as WB.sub.4. Furthermore, in tungsten monoboride, the tungsten-tungsten bond distance (2.8 angstroms) approaches that of pure tungsten metal (2.7 angstroms), which suggests a stronger metallic character. This brings with it some of the malleability and toughness found in conventional metals. Indeed, WB is suggested to be a balance between hardness and ductility, which can lead to high wear resistance.

[0040] Because of the higher metallic character, metallic bonding can play a greater role in the mechanical properties of tungsten monoboride. However, metallic bonding can be weak. For example, metals, while possessing high electron density and incompressibility, possess metallic bonds which are non-directional. Lack of directional bonding allows for bonds to break and dislocations to form, leading to a ductile and malleable metal. In some instances, one method of increasing the hardness of metallic tungsten monoboride can be to add more equivalents of boron to yield a more covalent tungsten tetraboride.

[0041] In some embodiments, described herein is an alternative approach of generating a tungsten monoboride with superhard metal properties. In some instances, this is achieved by selectively tuning specific crystallographic planes to increase the hardness of tungsten monoboride to become superhard. More specifically, this can be accomplished through solid-solution strengthening of the metallic tungsten planes of tungsten monoboride with a non-radioactive Group V Transition Metal (e.g., tantalum).

[0042] In certain embodiments, provided herein is a metal composition of Formula (I) crystallized in an orthorhombic phase,

W.sub.1-xN.sub.xB Formula I

[0043] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively.

[0044] In some embodiments, N is Tantalum (Ta). In some embodiments, N is Vanadium (V). In some embodiments, N is Niobium (Nb). In some embodiments, x has a value within the range 0.05 to 0.95, inclusively. In some embodiments, x has a value within the range 0.1 to 0.9, inclusively. In some embodiments, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some embodiments, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In some embodiments, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively. In some embodiments, x has a value of about 0.5. In some embodiments, the metal composition is a metal composition of Formula (Ia) crystallized in an orthorhombic phase,

W.sub.1-xTa.sub.xB Formula Ia

[0045] wherein x has a value within the range 0.01 to 0.99, inclusively.

[0046] In some embodiments, x has a value within the range 0.05 to 0.95, inclusively. In some embodiments, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some embodiments, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In some embodiments, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively. In some embodiments, x has a value of about 0.5. In some embodiments, the metal composition has a bulk modulus of from about 336 GPa to about 346 GPa. In some embodiments, the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa. In some embodiments, the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening. In some embodiments, at least one plane of the metal composition further exhibits a discontinuous increase in directional incompressibility. In some embodiments, boron forms a chain within the crystalline structure of the metal composition, and the chain is aligned along a c-axis of the crystalline structure. In some embodiments, the chain of boron does not alternate to form a perpendicular array within the structure.

[0047] In some embodiments, the metal composition is a metal composition of Formula (Ib) crystallized in an orthorhombic phase,

W.sub.1-xNb.sub.xB Formula Ib

[0048] wherein x has a value within the range 0.01 to 0.99, inclusively.

[0049] In some embodiments, the metal composition is a metal composition of Formula (Ic) crystallized in an orthorhombic phase,

W.sub.1-xNb.sub.xB Formula Ic

[0050] wherein x has a value within the range 0.01 to 0.99, inclusively.

[0051] In certain embodiments, provided herein is a metal composition of Formula (I):

W.sub.1-xN.sub.xB Formula I

[0052] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively; and wherein the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

[0053] In some embodiments, N is Tantalum (Ta). In some embodiments, N is Vanadium (V). In some embodiments, N is Niobium (Nb). In some embodiments, x has a value within the range 0.05 to 0.95, inclusively. In some embodiments, x has a value within the range 0.1 to 0.9, inclusively. In some embodiments, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some embodiments, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In some embodiments, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively. In some embodiments, x has a value of about 0.5. In some embodiments, at least one plane of the metal composition further exhibits a discontinuous increase in directional incompressibility. In some embodiments, the metal composition is crystallized in an orthorhombic phase. In some embodiments, the metal composition has a bulk modulus of from about 336 GPa to about 346 GPa. In some embodiments, the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa. In some embodiments, boron forms a chain within the crystalline structure of the metal composition, and the chain is aligned along a c-axis of the crystalline structure. In some embodiments, the chain of boron does not alternate to form a perpendicular array within the structure.

[0054] In certain embodiments, provided herein is a metal composition of Formula (I):

W.sub.1-xN.sub.xB Formula I

[0055] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively; and wherein boron forms a plurality of chains within a crystal structure of the metal composition, and wherein each of the plurality of chains is aligned along a same axis of the crystal structure.

[0056] In some embodiments, N is Tantalum (Ta). In some embodiments, N is Vanadium (V). In some embodiments, N is Niobium (Nb). In some embodiments, x has a value within the range 0.05 to 0.95, inclusively. In some embodiments, x has a value within the range 0.1 to 0.9, inclusively. In some embodiments, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some embodiments, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In some embodiments, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively. In some embodiments, x has a value of about 0.5. In some embodiments, the metal composition is crystallized in an orthorhombic phase. In some embodiments, the metal composition has a bulk modulus of from about 336 GPa to about 346 GPa. In some embodiments, the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa. In some embodiments, the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening. In some embodiments, at least one plane of the metal composition further exhibits a discontinuous increase in directional incompressibility. In some embodiments, the axis is the c-axis. In some embodiments, the chain of boron does not alternate to form a perpendicular array within the structure.

[0057] In certain embodiments, provided herein is a method of making a stable metal composition comprising (a) introducing a plurality of additive particles into the interstices of a metal composition precursor to form a metal composition, wherein the plurality of additive particles is selected from vanadium, niobium, and tantalum; and (b) subjecting the metal composition to a temperature and pressure at which the metal composition is stable at room temperature. In some embodiments, the metal composition precursor comprises a tungsten and boron molecule of formula WB. In some embodiments, the subjecting further comprises sintering the metal composition precursor with the plurality of additive particles to form the stable metal composition. In some embodiments, the stable metal composition has the formula W.sub.1-xN.sub.xB, wherein N is an additive particle selected from vanadium, niobium, and tantalum and x has a value within the range 0.01 to 0.99, inclusively. In some embodiments, x has a value within the range 0.05 to 0.95, inclusively. In some embodiments, x has a value within the range 0.1 to 0.9, inclusively. In some embodiments, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some embodiments, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In some embodiments, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively. In some embodiments, x has a value of about 0.5. In some embodiments, the additive particle is tantalum. In some embodiments, the stable metal composition is crystallized in an orthorhombic phase. In some embodiments, the stable metal composition has a bulk modulus of from about 336 GPa to about 346 GPa. In some embodiments, the stable metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa. In some embodiments, the stable metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening. In some embodiments, at least one plane of the stable metal composition further exhibits a discontinuous increase in directional incompressibility. In some embodiments, boron forms a chain within the structure of the metal composition and is aligned along one axis of the structure. In some embodiments, the axis is the c-axis. In some embodiments, the chain of boron does not alternate to form a perpendicular array within the structure. In some embodiments, the stable metal composition is an entropically stable metal composition.

[0058] In certain embodiments, provided herein is a tool comprising a surface for cutting or abrading, said surface being a surface of a metal composition disclosed above.

[0059] In certain embodiments, provided herein is an abrasive material comprising a plurality of abrasive particles, each being a metal composition disclosed above.

[0060] In certain embodiments, provided herein is a method of making a tool, comprising (a) providing a powder comprising a plurality of metal composition particles, wherein the plurality of metal composition particles comprise metal compositions disclosed above; and compressing said powder to form a self-supporting structure.

[0061] In some embodiments, described herein is a metal composition of Formula (I) crystallized in an orthorhombic phase,

W.sub.1-xN.sub.xB Formula I

[0062] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively.

[0063] In some embodiments, also described herein is a metal composition of Formula (I):

W.sub.1-xN.sub.xB Formula I

[0064] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively; and wherein the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

[0065] In some embodiments, further described herein is a metal composition of Formula (I):

W.sub.1-xN.sub.xB Formula I

[0066] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively; and wherein boron forms a chain within the structure of the metal composition and is aligned along one axis of the structure.

[0067] In some embodiments, additionally described herein include a method of making a stable metal composition comprising: (a) introducing a plurality of additive particles into the interstices of a metal composition precursor to form a metal composition, wherein the plurality of additive particles is selected from vanadium, niobium, and tantalum; and (b) subjecting the metal composition to a temperature and pressure at which the metal composition is stable at room temperature.

[0068] In some embodiments, the metal compositions of the present disclosure are easy to synthesize. In addition, these metal compositions can be made at ambient pressure and thus can be cast from the melt like common metals. Furthermore, their metallic character allows them to be easily cut and shaped post-synthesis by electric discharge machining.

[0069] In some embodiments, described herein also include tools and abrasive materials comprising a metal composition described herein and methods of making such tools.

Metal Compositions

[0070] In certain embodiments, disclosed herein include metal compositions, stable metal compositions, methods of making the metal compositions, tools for cutting or abrading, or abrasive materials comprising the metal compositions. In some embodiments, described herein include a metal composition of Formula (I) crystallized in an orthorhombic phase,

W.sub.1-xN.sub.xB Formula I

[0071] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively.

[0072] Sometimes, x can have a value within the range 0.05 to 0.95, inclusively. Sometimes, x can have a value within the range 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0073] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6.

[0074] In some embodiments, N is selected from Tantalum (Ta), Vanadium (V), and Niobium (Nb). In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0075] In some embodiments, a metal composition described herein is a metal composition of Formula (Ia) crystallized in an orthorhombic phase,

W.sub.1-xTa.sub.xB Formula Ia

[0076] in which x has a value within the range 0.01 to 0.99, inclusively.

[0077] Sometimes, x can have a value within the range 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0078] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6.

[0079] In some embodiments, a metal composition described herein is a metal composition of formula W.sub.0.5Ta.sub.0.5B crystallized in an orthorhombic phase.

[0080] Sometimes, the metal composition can have a bulk modulus from about 336 GPa to about 346 GPa. Bulk modulus (K or B) can measure a material's resistance to uniform compression. In some cases, bulk modulus refers to the elastic modulus (also known as Young's modulus and tensile modulus) or elastic deformation behavior of a metal composition described herein.

[0081] In some instances, the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa. Hardness can be described as a measurement of how resistant a material is to permanent deformation when a compressive force is applied. Hardness can be modulated by factors such as for example, ductility, plasticity, elastic stiffness, strain, viscoelasticity, viscosity, or a combination thereof. In some instances, a hardness measurement comprises scratch, indentation, or rebound measurement. In some cases, a hardness measurement is an indentation measurement with an indentation hardness scale of Rockwell, Vickers, Shore, or Brinell. In some cases, an indentation measurement is a Vickers hardness test.

[0082] In some cases, the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening. Strain hardening (also known as work hardening or cold working) can be described as the strengthening of a material by plastic deformation. Plastic deformation can be an irreversible deformation of a material under an applied force.

[0083] In some cases, at least one plane of the metal composition further exhibits a discontinuous change (e.g, increase) in directional incompressibility. Compressibility can be a measure of the relative volume change of a material as a response to a pressure change. In the current case for example, a directional discontinuous change in incompressibility can refers to a change along one of the crystal lattice of a metal composition described herein. In some instances, a discontinuous change in directional incompressibility can be a discontinuous increase along one of the crystal lattice of a metal composition described herein. In some cases, a discontinuous increase in directional incompressibility can be along one of the crystal lattice of a metal composition described herein crystallized in an orthorhombic phase.

[0084] In some instances, boron forms a chain within the structure of the metal composition of Formula (Ia) and is aligned along one axis of the structure. For example, the axis can be the c-axis or the a-axis. In some cases, the axis is the c-axis. In some cases, the axis is the a-axis.

[0085] In some instances, the chain of boron does not alternate to form a perpendicular array within the structure, as can be observed in the tetrahedral phase.

[0086] In some embodiments, N is Vanadium (V) and the metal composition is a metal composition of Formula (Ib) crystallized in an orthorhombic phase,

W.sub.1-xV.sub.xB Formula Ib

[0087] in which x has a value within the range 0.01 to 0.99, inclusively.

[0088] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0089] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

[0090] Sometimes, the metal composition can have a bulk modulus that is higher than the bulk modulus of a metal composition of Formula (Ib) crystallized in a tetragonal phase. Other times, the metal composition can have a bulk modulus that is lower than the bulk modulus of a metal composition of Formula (Ib) crystallized in a tetragonal phase. In additional times, the metal composition can have a bulk modulus that is similar to the bulk modulus of a metal composition of Formula (Ib) crystallized in a tetragonal phase.

[0091] In some instances, the metal composition has a hardness that is higher than the hardness of a metal composition of Formula (Ib) crystallized in a tetragonal phase. Other times, the metal composition can have a hardness that is lower than the hardness of a metal composition of Formula (Ib) crystallized in a tetragonal phase. In additional times, the metal composition can have a hardness that is similar to the hardness of a metal composition of Formula (Ib) crystallized in a tetragonal phase.

[0092] In some cases, the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

[0093] In some cases, at least one plane of the metal composition further exhibits a discontinuous increase in directional incompressibility.

[0094] In some instances, boron forms a chain within the structure of the metal composition of Formula (Ib) and is aligned along one axis of the structure. For example, the axis can be the c-axis or the a-axis. In some cases, the axis is the c-axis. In some cases, the axis is the a-axis.

[0095] In some instances, the chain of boron does not alternate to form a perpendicular array within the structure, as can be observed in the tetrahedral phase.

[0096] In some embodiments, N is Niobium (Nb) and the metal composition is a metal composition of Formula (Ic) crystallized in an orthorhombic phase,

W.sub.1-xNb.sub.xB Formula Ic

[0097] in which x has a value within the range 0.01 to 0.99, inclusively.

[0098] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0099] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

[0100] Sometimes, the metal composition can have a bulk modulus that is higher than the bulk modulus of a metal composition of Formula (Ic) crystallized in a tetragonal phase. Other times, the metal composition can have a bulk modulus that is lower than the bulk modulus of a metal composition of Formula (Ic) crystallized in a tetragonal phase. In additional times, the metal composition can have a bulk modulus that is similar to the bulk modulus of a metal composition of Formula (Ic) crystallized in a tetragonal phase.

[0101] In some instances, the metal composition has a hardness that is higher than the hardness of a metal composition of Formula (Ic) crystallized in a tetragonal phase. Other times, the metal composition can have a hardness that is lower than the hardness of a metal composition of Formula (Ic) crystallized in a tetragonal phase. In additional times, the metal composition can have a hardness that is similar to the hardness of a metal composition of Formula (Ic) crystallized in a tetragonal phase.

[0102] In some cases, the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

[0103] In some cases, at least one plane of the metal composition further exhibits a discontinuous increase in directional incompressibility.

[0104] In some instances, boron forms a chain within the structure of the metal composition of Formula (Ic) and is aligned along one axis of the structure. For example, the axis can be the c-axis or the a-axis. In some cases, the axis is the c-axis. In some cases, the axis is the a-axis.

[0105] In some instances, the chain of boron does not alternate to form a perpendicular array within the structure, as can be observed in the tetrahedral phase.

[0106] In some embodiments, described herein include a metal composition of Formula (I):

W.sub.1-xN.sub.xB Formula I

[0107] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively; and wherein the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

[0108] In some embodiments, N is selected from Tantalum (Ta), Vanadium (V), and Niobium (Nb). In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0109] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0110] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

[0111] In some embodiments, a metal composition described herein is a metal composition of formula W.sub.0.5Ta.sub.0.5B in which the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening.

[0112] Sometimes, at least one plane of the metal composition can further exhibit a discontinuous increase in directional incompressibility.

[0113] In some instances, the metal composition is crystallized in an orthorhombic phase or a tetragonal phase. In some instances, the metal composition is crystallized in an orthorhombic phase. In other instances, the metal composition is crystallized in a tetragonal phase.

[0114] In some cases, the metal composition has a bulk modulus of from about 336 GPa to about 346 GPa.

[0115] In some cases, the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa.

[0116] Sometimes, boron can form a chain within the structure of the metal composition and is aligned along one axis of the structure. The axis can be the c-axis or the a-axis. Sometimes, boron can form a chain along the c-axis of the structure and the structure is in an orthorhombic phase. Sometimes, boron can form a chain along the a-axis of the structure and the structure is in an orthorhombic phase.

[0117] Sometimes, the chain of boron does not alternate to form a perpendicular array within the structure.

[0118] In some embodiments, described herein include a metal composition of Formula (I):

W.sub.1-xN.sub.xB Formula I

[0119] wherein N is a non-radioactive Group V Transition Metal; and x has a value within the range 0.01 to 0.99, inclusively; and boron forms a chain within the structure of the metal composition and is aligned along one axis of the structure.

[0120] In some embodiments, N is selected from Tantalum (Ta), Vanadium (V), and Niobium (Nb). In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0121] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0122] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

[0123] In some embodiments, a metal composition described herein is a metal composition of formula W.sub.0.5Ta.sub.0.5B in which boron forms a chain within the structure of the metal composition and is aligned along one axis of the structure.

[0124] In some instances, the metal composition is crystallized in an orthorhombic phase or a tetragonal phase. In some instances, the metal composition is crystallized in an orthorhombic phase. In other instances, the metal composition is crystallized in a tetragonal phase.

[0125] In some cases, the metal composition has a bulk modulus of from about 336 GPa to about 346 GPa.

[0126] In some cases, the metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa.

[0127] In some instances, the metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening. Sometimes, at least one plane of the metal composition can further exhibit a discontinuous increase in directional incompressibility.

[0128] Sometimes, the axis can be the c-axis or the a-axis. Sometimes, boron can form a chain along the c-axis of the structure and the structure is in an orthorhombic phase. Sometimes, boron can form a chain along the a-axis of the structure and the structure is in an orthorhombic phase.

[0129] Sometimes, the chain of boron does not alternate to form a perpendicular array within the structure.

[0130] Methods of Use

[0131] In certain embodiments, described herein include methods of making metal compositions and methods of using the same. In some embodiments, described herein is a method of making a stable metal composition comprising: (a) introducing a plurality of additive particles into the interstices of a metal composition precursor to form a metal composition, wherein the plurality of additive particles is selected from vanadium, niobium, and tantalum; and (b) subjecting the metal composition to a temperature and pressure at which the metal composition is stable at room temperature.

[0132] In some embodiments, the metal composition precursor comprises a tungsten and boron molecule of formula WB.

[0133] In some embodiments, the subjecting further comprises sintering the metal composition precursor with the additive particles to form the stable metal composition. Sintering is the process of compacting and forming a solid mass of a material by heating and/or pressure without liquefaction.

[0134] In some embodiments, the stable metal composition has the formula W.sub.1-xN.sub.xB, wherein N is an additive particle selected from vanadium, niobium, and tantalum and x has a value within the range 0.01 to 0.99, inclusively. In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0135] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0136] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

[0137] In some embodiments, a metal composition described herein is a metal composition of formula W.sub.0.5Ta.sub.0.5B.

[0138] In some instances, the stable metal composition is crystallized in an orthorhombic phase or a tetragonal phase. In some instances, the stable metal composition is crystallized in an orthorhombic phase. In other instances, the stable metal composition is crystallized in a tetragonal phase.

[0139] In some cases, the stable metal composition has a bulk modulus of from about 336 GPa to about 346 GPa.

[0140] In some cases, the stable metal composition has a hardness of about 33, about 34, about 35, about 36, about 37, or about 38 GPa.

[0141] In some instances, the stable metal composition has at least one plane that exhibits a strain hardening effect when subjected to a pressure sufficient to induce strain hardening. Sometimes, at least one plane of the stable metal composition can further exhibit a discontinuous increase in directional incompressibility.

[0142] Sometimes, boron can form a chain within the structure of the stable metal composition and is aligned along one axis of the structure. The axis can be the c-axis or the a-axis. Sometimes, boron can form a chain along the c-axis of the structure and the structure is in an orthorhombic phase. Sometimes, boron can form a chain along the a-axis of the structure and the structure is in an orthorhombic phase.

[0143] Sometimes, the chain of boron does not alternate to form a perpendicular array within the structure.

[0144] In some cases, the stable metal composition is an entropically stable metal composition.

[0145] In some embodiments, described herein include a method of making a tool, comprising: (a) providing a powder comprising a plurality of metal composition particles, wherein the plurality of metal composition particles comprise metal compositions described herein; and (b) compressing said powder to form a self-supporting structure. In some embodiments, the metal composition has the formula W.sub.1-xN.sub.xB, wherein N is selected from vanadium, niobium, and tantalum and x has a value within the range 0.01 to 0.99, inclusively. In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0146] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0147] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

Tools and Abrasive Materials

[0148] In some embodiments, also included herein are tools and abrasive materials that comprise a metal composition described herein. In some instances, described herein include a tool which comprise a surface for cutting or abrading, said surface being a surface of a metal composition described herein. In some embodiments, the metal composition has the formula W.sub.1-xN.sub.xB, wherein N is selected from vanadium, niobium, and tantalum and x has a value within the range 0.01 to 0.99, inclusively. In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0149] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0150] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

[0151] In additional embodiments, further described herein include abrasive materials that comprise a plurality of abrasive particles, each being a metal composition described herein. In some embodiments, the metal composition has the formula W.sub.1-xN.sub.xB, wherein N is selected from vanadium, niobium, and tantalum and x has a value within the range 0.01 to 0.99, inclusively. In some instances, N is Tantalum (Ta). In some cases, N is Vanadium (V). In other cases, N is Niobium (Nb).

[0152] Sometimes, x can have a value within the range 0.05 to 0.95, 0.1 to 0.9, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, or 0.45 to 0.5, inclusively. In some cases, x has a value within the range 0.1 to 0.9, inclusively. In some instances, x has a value within the range 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, or 0.4 to 0.6, inclusively. In some instances, x has a value within the range 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, or 0.45 to 0.55, inclusively. In additional instances, x has a value within the range 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, or 0.4 to 0.5, inclusively.

[0153] In some cases, x has a value of about 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, or about 0.95. In some cases, x has a value of about 0.1. In some cases, x has a value of about 0.2. In some cases, x has a value of about 0.3. In some cases, x has a value of about 0.4. In some cases, x has a value of about 0.41. In some cases, x has a value of about 0.42. In some cases, x has a value of about 0.43. In some cases, x has a value of about 0.44. In some cases, x has a value of about 0.45. In some cases, x has a value of about 0.46. In some cases, x has a value of about 0.47. In some cases, x has a value of about 0.48. In some cases, x has a value of about 0.49. In some cases, x has a value of about 0.5. In some cases, x has a value of about 0.51. In some cases, x has a value of about 0.52. In some cases, x has a value of about 0.53. In some cases, x has a value of about 0.54. In some cases, x has a value of about 0.55. In some cases, x has a value of about 0.56. In some cases, x has a value of about 0.57. In some cases, x has a value of about 0.58. In some cases, x has a value of about 0.59. In some cases, x has a value of about 0.6. In some cases, x has a value of about 0.7. In some cases, x has a value of about 0.8. In some cases, x has a value of about 0.9.

Certain Terminology

[0154] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It is to be understood that the general description and the detailed description are exemplary and explanatory only and are not restrictive of any subject matter claimed. As used in this specification, the singular forms a, an, and the include plural references unless the context clearly dictates otherwise. Any reference to or herein is intended to encompass and/or unless otherwise stated.

[0155] As used herein, ranges and amounts can be expressed as about a particular value or range. About also includes the exact amount. Hence about 5 GPa means about 5 GPa and also 5 GPa. Generally, the term about includes an amount that would be expected to be within experimental error.

[0156] The section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

EXAMPLES

[0157] These examples are provided for illustrative purposes only and not to limit the scope of the claims provided herein.

Example I

[0158] In some embodiments, the composition for a metal alloy, the tool for cutting or abrading, the abrasive material, and the method of making and using the same as described herein include experimental procedures to test the hardness of a material, including indent diagonals, radial diffraction, differential strain, thermal stability, among others.

[0159] Tungsten (Strem, 99.95%), tantalum (Roc/Ric, 99.9%), and boron (Materion, 99%) powders were stochiometrically ground in an agate mortar and pestle (typical total loadings were 1 gram). Some samples had a slight excess of boron due to boron sublimation from the high temperatures of arcing. The homogeneous powders were pressed into a pellet, arced, turned over, and re-arced to ensure homogeneity. Samples were arced under high-purity argon under ambient pressure. The ingots were then bisected, with one half crushed for powder X-ray diffraction, high pressure radial diffraction, and thermal gravimetric analysis. The other half was mounted in epoxy and polished, for hardness and scanning electron microscopy (SEM), and for phase analysis. Mounted samples were polished with a SouthBay Technologies Polishing Station using polishing papers from 120 to 1200 grit (Allied High Tech Products Inc.).

[0160] Samples were analyzed by powder X-ray diffraction on a Panalytical X'Pert diffractometer using a Cu k.sub.1 source (=1.5418 ). The as-collected spectra were compared against JCPDS Card #00-006-0541 using X'Pert HighScore Plus as the processing software. Powder samples were then refined by size using a solvent suspension method, and imaged under a TF-20 transmission electron microscope (TEM) for size analysis. Size-refined powders were then used for high pressure radial diffraction.

[0161] Polished samples were imaged under backscatter SEM using a Nova 230 electron microscope with electron dispersive spectroscopy (EDS) used to determine homogeneity. Polished samples were measured for hardness on a Micromet 2103 equipped with a pyramid diamond indenter tip. With a dwell time of 15 s, the samples were indented under loads of 0.49, 0.98, 1.96, 2.9, and 4.9 N. Indent diagonals were measured using a Zeiss Axiotech 100HD optical microscope (Carl Zeiss Vision GmbH, Germany). Vickers hardness is determined from Equation 1.1 using the arithmetic mean of H randomly chosen indents:

[00001]$\begin{array}{cc}{H}_v=\frac{1854.4.Math.P}{d^2}& \left[1.1\right]\end{array}$

where P is the applied load and d is the average of the diagonals.

[0162] Radial diffraction was performed at the Advanced Light Source at Lawrence Berkeley National Labs using a diamond anvil cell (DAC). Incompressibility was determined using the third-order finite strain Birch-Murnaghan equation of state (Equation 1.2):

[00002]$\begin{array}{cc}P=\frac{3}{2}.Math.K_0\left[{\left(\frac{V}{V_0}\right)}^{-\frac{7}{3}}-{\left(\frac{V}{V_0}\right)}^{-\frac{5}{3}}\right].Math.\left\{1-\frac{3}{4}.Math.\left(4-K\right)\left[\left({\left(\frac{V}{V_0}\right)}^{-\frac{2}{3}}-1\right)\right]\right\}& \left[1.2\right]\end{array}$

where P is the applied load, K.sub.0 is the bulk modulus, V is the deformed unit cell volume, V.sub.0 is the undeformed unit cell volume, and K.sub.0 is the derivative of the K.sub.0 with respect to P. Here, K.sub.0 is fixed to 4.

[0163] Differential strain was interpreted using lattice strain theory from the high-pressure radial diffraction using Equation 1.3:

d.sub.meas(hkl)=d.sub.hydro(hkl)[1+(13 cos.sup.2 )]Q(hkl)[1.3]

where is the angle between the diffracting plane normal and the maximum stress axis, d.sub.hydro(hkl) is the hydrostatic d-spacing (measured when =54.7), and d.sub.meas(hkl) is the measured d-spacing under pressure. Q(hkl), the orientation dependent differential strain, can be written as:

[00003]$\begin{array}{cc}\frac{t\left(\mathrm{hkl}\right)}{G}=6.Math.Q\left(\mathrm{hkl}\right)& \left[1.4\right]\end{array}$

where G is the aggregate shear strain, and t is the differential stress (18). The differential stress, t, can be rewritten using the Tresca yield criterion,

t=.sub.axial,max.sub.radial,min2=.sub.y[1.5]

where .sub.axial, max is the maximum stress along the axial direction, .sub.radial, min is the minimum stress along the radial direction, and .sub.y is the yield strength. The elastically-supported differential stress, t, enables one to estimate the lower-bound of the material's yield strength, .sub.y.

[0164] Thermal stability in air of the materials is determined using a Pyris Diamond thermogravimetric/differential thermal analyzer. Powder samples were heated in air up to 200 C. at a rate of 20 C./min, held for 20 min to remove residual moisture, and then heated up to 1000 C. at a rate of 2 C./min.

Results and Discussion

[0165] Tungsten monoboride crystallizes in either a low temperature tetragonal or a high temperature orthorhombic unit cell. The primary difference between these two phases is found in the layer of boron chains, where in the tetragonal (low temperature) form, the boron chains alternate orthogonally, while in the orthorhombic (high temperature) form the boron chains are all aligned along the a-axis. Similarly, both structures possess a bilayer of tungsten atoms as can be seen in FIG. 1. In a particular embodiment, a tungsten monoboride demonstrates a crystal structure of high-temperature, orthorhombic tungsten monoboride, WB, wherein the plane 100 marks the location of a metallic tungsten bilayer, as shown in FIG. 1.

[0166] Inspection of the tungsten monoboride unit cell has shown that it possesses a bilayer of tungsten atoms separated by boron chains. Because tungsten monoboride (unlike tungsten tetraboride, WB.sub.4) is a lower boride, it should not possess a substantial degree of covalent bonding which can prevent the formation or movement of dislocations. Combined with the WW bond lengths approaching that of tungsten metal, it infers that the majority of the materials strength is supported in this system through the metal atoms, and thus, the hardness of tungsten monoboride is determined by its metallic bonding. If dislocations can be prevented in this metallic plane, it should increase the overall hardness of tungsten monoboride.

[0167] Therefore, solid-solution strengthening is a real possibility. By substituting tungsten with larger atoms, the slipping of the metallic planes can be prevented through dislocation pinning, and with the higher resistance to dislocations, the overall hardness should increase. As such, the subject matter described herein, in certain embodiments, substitutes tantalum onto the tungsten sites because tantalum has a similar valence, electronegativity, and atomic radii when compared to tungsten. Furthermore, tantalum monoboride crystallizes into the same phase as the high temperature form of tungsten monoboride, which satisfies the Hume-Rothery rules for solid solutions. It should be noted that the end members of W.sub.1-xTa.sub.xB are not known to be superhard, and as such this is an excellent system to study.

[0168] Tantalum monoboride crystallizes in an orthogonal unit cell, and when combined with the fast cooling rate of the copper hearth of the arc melter, it is expected that all W.sub.1-xTa.sub.xB compositions (where x=0.01 to 0.5) will crystallize in the orthorhombic phase. Indeed, powder X-ray diffraction suggest that even at 1% Ta concentration, as seen in W.sub.0.99Ta.sub.0.01B, the favored phase is the high temperature orthorhombic modification. Moreover, TaB is miscible in WB at high concentrations with no secondary phases as observed by powder X-ray diffraction (FIG. 2). In a particular embodiment, powder X-ray diffraction patterns of W.sub.(1-x)Ta.sub.xB (x=0.01, 0.05, 0.10, 0.25, and 0.50) with peaks indexed to orthorhombic WB (JCPDS Card #00-006-0541) are described, as shown in FIG. 2.

[0169] There is a noticeable shift towards larger lattice parameters with increased tantalum concentration, and this is expected because tantalum (1.343 ) has a slightly larger atomic radius when compared to tungsten (1.299 ). As shown in FIG. 5, these lattice parameters increase linearly as expected from Vegard's Law. In a particular embodiment, lattice parameters of a W.sub.(1-x) Ta.sub.x B metal alloy are described to show the a, b, c lattice parameters of W.sub.(1-x)Ta.sub.xB (x=0.01, 0.05, 0.10, 0.25, and 0.50), wherein the linear progression of the lattice parameters with respect to tantalum content is consistent with Vegard's law, as shown in FIG. 5.

[0170] This suggests a well-behaved alloy system with tantalum randomly distributed across the tungsten sites. Backscatter scanning electron microscopy confirms that there are no secondary phases, and elemental mapping with electron dispersive spectroscopy (EDS) suggests that both tantalum and tungsten are well dispersed (FIG. 3). As shown in FIG. 3, in a particular embodiment, energy-dispersive spectroscopy (EDS) plots of a W.sub.(1-x)Ta.sub.xB metal alloy are described to demonstrate that tantalum (right) and tungsten (left) are evenly distributed throughout the alloy. (Scalebar=10 m.) Transmission electron microscopy of freshly fractured and crushed powder suggests that the samples are highly crystalline and not nanostructured, as seen in FIG. 4. In a particular embodiment, as shown in FIG. 4, a transmission electron microscopy of freshly fractured powder of a W.sub.(1-x)Ta.sub.xB metal alloy indicates that the majority of the grains are not nanostructured, ruling out extrinsic hardening mechanisms. (Scalebar=200 nm.) The lack of a secondary phase rules out extrinsic hardening mechanisms such as precipitation hardening or dispersion hardening.

[0171] Vickers hardness was then measured under loads of 0.49, 0.98, 1.96, 2.9, and 4.9 N (FIG. 6). In a particular embodiment, as shown in FIG. 6, Vickers indentation hardness of a W.sub.(1-x) Ta.sub.x B metal alloy is described as a function of different loads (0.49 N/50 gram-force, 0.98 N/100 gram-force, 1.96 N/200 gram-force, 2.9 N/300 gram-force, and 4.9 N/500 gram-force), follows a linear trend. The hardness value of the 50% Ta composition under a load of 0.49 N is 42.82.6 GPa, and indicates that W.sub.0.5 Ta.sub.0.5B is a superhard material. Under a low load of 0.5 N, the tungsten monoboride sample containing 1% tantalum has a Vickers hardness of 35.1 GPa, well in agreement with pristine, polycrystalline WB of 36 GPa. As the tantalum concentration is increased, there is an across-the-board increase in hardness. This trend is linear; reaching 42.8 GPa at 50% composition. This breaks the threshold for superhard materials deigned as H.sub.v40 GPa; therefore, W.sub.0.5Ta.sub.0.5B can be considered a new superhard metal. Aside from WB.sub.4, this is the only other superhard composition in the tungsten-boron system. And unlike the covalent WB.sub.4, superhardness in tungsten monoboride has been achieved through optimization of the metallic planes.

[0172] This linear hardness trend that peaks at a 50% concentration is quite unusual amongst the borides. For example, WB.sub.4 forms solid solutions with tantalum, chromium, and manganese, but the hardness trend for WB.sub.4 solid solutions is not linear. Likewise, the hardness of Os.sub.1-xRu.sub.xB.sub.2 solid solutions is linear, but it does not peak at 50% concentration. Such a unique correlation in W.sub.1-xTa.sub.xB, combined with inspection of the orthorhombic crystal structure, suggests that the metallic bilayer is responsible for the material's strength. By substituting tungsten with larger tantalum atoms, plane slipping will be diminished through dislocation pinning. At 50% concentration, pinning will be maximized, and this is reflected in the hardness measurements. This chemical tuning of the structure shows that the hardness of tungsten monoboride can be increased through solid solution hardening.

[0173] To confirm the hardening effects of substituting tantalum into the metallic bilayer, high-pressure diffraction studies are used to correlate macroscopic hardness with microscopic deformations. By compressing samples under non-hydrostatic stress in a high-pressure diamond anvil cell, conditions similar to those found under the indenter tip can be controllably produced in a geometry that can be readily probed using X-ray diffraction. Such experiments can provide a lattice specific measure of yield strength and the predominant slip systems available in the material. High-pressure radial diffraction is a well-known technique that has been satisfactorily used previously to determine the amount of load each plane supports in nanocrystalline WB.

[0174] Here, high-pressure radial diffraction is used to determine which planes in tungsten monoboride are responsible for the superhardness. This enables an understanding of the slip system in the material. Planes that have a low differential strain (t/G) value tend to dislocate and slip, while planes that have a high t/G value can support greater force and pressure. For W.sub.0.99Ta.sub.0.01B, the planes (200), (020), and (002) were chosen for study because they represent the anisotropy of the unit cell. Dislocations in the (200) cut between the boron-boron chains, while the (020) cut through the tungsten bilayer, and the (002) cuts through the boron-boron bonds (FIG. 1). In other words, the (200) and (020) represent more covalent/boron bonding, while the (020) possesses more metallic/tungsten bonding.

[0175] In a particular embodiment, a differential strain plot of a W.sub.(1-x) Ta.sub.x B metal alloy is shown in FIG. 7 and described herein. Furthermore, differential strain plot of W.sub.0.5 Ta.sub.0.5B with respect to the (200), (020), and (002) planes are demonstrated. The (020) plane supports the highest differential strain (t/G) and indicates that it is the load-bearing plane. As can be seen in FIG. 7, the (200) and (002) planes support a significantly lower differential strain as compared to the (020) set of planes. Under high pressure, the (020) supports up to 5.0% differential strain, while the (200) and (002) supports 4.8% and 3.8% strain, respectively. Therefore, the purely metal (020) planes are the least likely to slip, so this metallic bilayer can be considered responsible for the high hardness of tungsten monoboride, rather than the more covalent (200) or (002) planes. Since the (002) plane possesses more covalent character than the (020), one would ordinarily expect that the (002) would support higher differential strain than the (020), as it should be more difficult to break boron-boron bonds than to break metal-metal bonds. However, contrary to conventional theory, the results here suggest that metallic bonding can be tuned to pin dislocations so that even ductile metals can prevent shear as well as, if not better than, many covalent materials. Since the tantalum was directly substituted into the load-bearing plane, this led to a linear correlation between tantalum concentration and increasing hardness in tungsten monoboride.

[0176] More intriguingly, the behavior of the (020) plane reveals key insights into the nature of the bonding. As can be seen in FIG. 7, the (020) plane strain hardens up to a maxima of 5.1% differential strain at 35 GPA, then strain softens. This behavior of strain-strengthening followed by strain-softening is reminiscent of pure niobium metal. These results suggest that the tungsten bilayer, represented by the (020) plane, supports the bulk of the differential strain and behaves like a pure metal. Combined with the linear relationship found in the Vickers hardness testing, W.sub.1-xTa.sub.xB may indeed behave as a true superhard metal, where the strength of the material comes from the metallic bonding.

[0177] In a particular embodiment, deformation performance of a W.sub.(1-x) Ta.sub.x B metal alloy indicates that the deformation in the unit cell volume is fitted to a Third-order Birch-Murnaghan equation of state, as shown in FIG. 10, and shows that W.sub.0.5Ta.sub.0.5B is ultra-incompressible. From the high-pressure studies, the bulk modulus of W.sub.0.5Ta.sub.0.5B was determined to be 3373 GPa using a second order Birch-Murnaghan equation of state. This demonstrates that W.sub.0.5Ta.sub.0.5B is not only superhard, but also ultra-incompressible. This is slightly lower than the theoretical prediction for bulk modulus of 350 GPa, which is expected because tantalum contains fewer electrons than tungsten. Tungsten monoboride is therefore even more incompressible than tungsten tetraboride (3263 GPa), the other superhard boride in the tungsten-boron system. This was expected, since incompressibility is related to high electron density which comes from the tungsten. With a high tungsten content and tungsten-tungsten bonds approaching that of tungsten metal, tungsten monoboride should have a high bulk modulus. Therefore, optimization for an even more incompressible material, using the lower borides in the tungsten-boron system, is warranted.

[0178] Oxidation resistance was measured using thermal gravimetric analysis. In practical applications, high oxidation resistance is needed because the act of machining generates high temperatures from friction. In a particular embodiment, thermogravimetric analysis (TGA) of W.sub.0.5 Ta.sub.0.5B suggests that the oxidation of W.sub.0.5Ta.sub.0.5B begins at 550 C. in air, as shown in FIG. 8. This suggests that W.sub.0.5Ta.sub.0.5B has a higher resistance to oxygen than tungsten carbide, which begins oxidizing at 500 C. Tungsten carbide is one of the most useful materials for cutting tools. The added oxidation resistance provided by adding tantalum is likely due to formation of a protective oxide coating, which prevents further oxidation until 550 C.

[0179] The greatly increased role of metallic bonding in the hardness of WB offers an intriguing line of inquiry into superhard materials. Typically, non-directional metallic bonds are prone to slipping and thus, conventional wisdom would suggest that the best way to make a superhard metal would be to add boron until covalent bonding dominates and prevents dislocations from motion. As such, superhardness should generally be found in strongly covalent materials such as diamond or tungsten tetraboride. In a particular embodiment, resistance/temperature relationship of a W.sub.(1-x) Ta.sub.x B metal alloy indicates that the electrical resistance of the ingot increases with temperature, which suggests that W.sub.0.5Ta.sub.0.5B is metallic, as shown in FIG. 9. As described herein, it is demonstrated that metallic bilayers can be strengthened to yield a completely new superhard material. Solid solution strengthening can be used to increase the hardness of tungsten monoboride. Furthermore, high-pressure radial diffraction experiments confirm that the metallic bilayer of tungsten monoboride supports the majority of the differential strain and that the behavior of this plane is metallic. This suggests that metallic bonding can contribute as much, if not more towards hardness than conventional covalent bonding. In conclusion, W.sub.0.5Ta.sub.0.5B may be the first superhard metal that derives its strength from metallic bonding.

Example II

[0180] Volumetric Deformation and Strength Anisotropy of Orthorhombic Tungsten Monoboride Under Non-Hydrostatic Compression

[0181] As the world's hardest natural material, diamond has limited applications in cutting and drilling since it reacts with ferrous materials to form brittle carbides. Alternative superhard materials such as rhenium diboride (ReB.sub.2) and cubic boron nitride (c-BN) both have hardness values close to that of diamond and are chemically stable relative to diamond. However, the stringent manufacturing requirements and/or expensive raw materials lead to high manufacturing costs. In some instances, tungsten tetraboride (WB.sub.4) is a less expensive superhard material. WB.sub.4 has a Vickers hardness that reaches 43.32.9 GPa under an applied load of 0.49 N and a bulk modulus of 3243 GPa. Its hardness results from the high valence electron density of tungsten and short strong covalent bonds introduced by boron. In some instances, pure WB.sub.4 is thermodynamically unfavorable, and WB.sub.4 samples prepared by an arc melting process have a W:B molar ratio of about 1:12, which is a composite of WB.sub.4 and crystalline boron, and thereby introduces non-uniformity within the structure. In some cases, lower borides of transition metals are studied.

Experimental Procedure and Lattice Strain Theory

[0182] Orthorhombic WB and tetragonal WB were synthesized by arc melting. Tungsten powder and boron powder with a 1:1 molar ratio were mixed together followed by pressing into pellets. Subsequently, the pellets were arc melted and cooled in argon gas. In order to stabilize the HT-orthorhombic phase of WB at room temperature, 5 at. % Ta was added because TaB is known to crystallize in an orthorhombic structure. Tetragonal WB and orthorhombic stabilized WB pellets were then crushed and ground to powder respectively with a particle size of <20 m. Non-hydrostatic in situ high pressure angle-dispersive X-ray diffraction experiments were performed to characterize the strength and deformation behavior at synchrotron beamline 12.2.2 of the Advanced Light Source (ALS, Lawrence Berkeley National Lab). A prepared polycrystalline WB sample was loaded into a laser drilled hole (60 m in diameter) in a boron gasket (400 m in diameter and 70 m in thickness). A small circle of Pt foil (15 m in diameter) was placed on top of the sample to serve as a pressure internal standard. No pressure-transmitting medium was used in order to create a non-hydrostatic environment in the DAC. A monochromatic X-ray beam with a wavelength of 0.4959 , and size of 2020 m was passed through the sample perpendicular to the loading axis. The 2D diffraction image was collected with program FIT2D (Hammersley, et al., High Pressure Research 14, 235 (1996)) at a step of 4 GPa after calibration of the detector distance and orientation using a LaB.sub.6 standard. The combination of radial X-ray diffraction and lattice strain theory enabled studying of the stress state of samples under non-hydrostatic compression in a DAC.

[0183] The stress state in a compressed sample under uniaxial loading in a DAC is characterized by .sub.3, the maximum stress along the axial direction, and .sub.1, the minimum stress in the radial direction. The difference between .sub.1 and .sub.3 is the macroscopic differential stress t, which can be defined by the Tresca yield criterion:

t=.sub.3.sub.12=.sub.y,[2.1]

[0184] where is the shear strength and .sub.y is the yield strength of the material (Ruoff, A. L. J. Appl. Phys. 46, 1389 (1975)). A measurement of the elastically-supported differential stress enables one to estimate the lower-bound of the material's yield strength, .sub.y. According to lattice strain theory, the measured d-spacing, d.sub.m(hkl) is a function of d.sub.p(hkl), d-spacing under the hydrostatic pressure, and , angle between the diffracting plane normal and the maximum stress axis,

d.sub.m(hkl)=d.sub.p(hkl)[1+(13 cos.sup.2)Q(hkl)],[2.])

[0185] where Q (hkl) is the orientation dependent lattice strain (Singh, A. K. J. Appl. Phys. 106, 043514 (2009)), which is defined by

[00004]$\begin{array}{cc}Q\left(\mathrm{hkl}\right)=\left(\frac{t}{3}\right).Math.\left\{{\left[2.Math.G_R\left(\mathrm{hkl}\right)\right]}^{-1}+\left(1-\right).Math.{\left(2.Math.G_v\right)}^{-1}\right\}.& \left[2.3\right]\end{array}$

[0186] Here G.sub.R (hkl) is the lattice dependent Reuss shear modulus under an iso-stress condition while the Voigt shear modulus, G.sub.V, is independent of hkl under iso-strain condition. The G.sub.V is given by

15G.sub.V=(c.sub.11+c.sub.22+c.sub.33)(c.sub.12+c.sub.23+c.sub.31)+3(c.sub.44+c.sub.55+c.sub.66)[2.4]

[0187] For orthorhombic and tetragonal systems, the expressions of G.sub.R(hkl) in terms of elastic compliance, [S.sub.ij] can be found in Singh, et al., J. Appl. Phys. 83, 7567 (1998). The actual shear modulus of a randomly oriented polycrystalline sample is neither G.sub.R (hkl) nor G.sub.V, but a weighted average of them. Approximately, the differential stress can be given by

t=6G<Q(hkl)>,[2.5]

[0188] where <Q (hkl)> stands for the average value of lattice strain observed for the diffraction peaks and G is the aggregate shear modulus. According to Equation 2.2, one could find that d.sub.m(hkl) is a linear function of (13 cos.sup.2) with a slope of d.sub.p(hkl)Q(hkl) and an intercept of d.sub.p(hkl) (at =54.7). The Q(hkl) resolved from the slope can be used to evaluate and describe contributions of both plastic and elastic deformation. While the pressure dependent d-spacing at =54.7 reflects the compression behavior due to hydrostatic component of stress, namely, the equivalent hydrostatic compression curve can be derived from non-hydrostatic data. The zero pressure bulk modulus, K.sub.0, can be determined by fitting the compression curve to the Birch-Murnaghan equation-of-state (EOS),

P=1.5K.sub.0[(V/V.sub.0).sup.7/3(V/V.sub.0).sup.5/3].[2.6]

[0189] Here, the pressure, P, and the unit cell volume, V, is measured at =54.7.

Computational Methods:

[0190] The bulk modulus was calculated by isotopically scaling the unit cell by small increments. The external pressure and volume were extracted from the calculation and then fit to a polynomial, the linear coefficient of this polynomial is the calculated Bulk Modulus. The experimental unit cells were used for this calculation. Dispersion interactions were approximated using the D2 Grimme scheme. PAW PBE basis sets and pseudopotentials applied to all atoms. All calculations carried out using the PBE/PBE functional in VASP except for the energy differences, which used the RPBE functional (Adamo, C., and Barone, V. J. Chem. Phys. 110, 6158 (1999); Hafner, J. Comput. Chem. 29, 2044 (2008)). The HT phase was calculated with a 24824 k-mesh to assess the dependence on k-point density, results were found to be consistent with a smaller k-mesh of 626. DOS and Band calculations were performed with the 24824 mesh while the shearing calculations used the 626 mesh. (Shearing removes symmetry making larger meshes less feasible). An energy cutoff of 320 eV was used.

[0191] The stress testing of electronic states procedure was developed in-house and has been demonstrated to characterize the strength of bonds along different distortions. The Bloch state visualizations were generated with quantum espresso. Using the PBE/PBE functional, and using a PBE scalar relativistic corrected basis for B, and the ultra soft scalar relativistic corrected basis for W. Once again, the cutoff energy was set to 320 eV. The isosurfaces had isovalues of 0.005. The cluster models were run in Gaussian 09 using PBEPBE and the lanl2dz basis set.

HT-Orthorhombic WB Exhibits Different Properties than LT-Tetragonal WB

[0192] In some instances, tungsten monoboride possesses two distinct phases with a B:W molar ratio of 1:1, an orthorhombic high temperature (HT) and tetragonal low temperature (LT) phase with a phase transition temperature of 2170 C. Both of these phases share the same alternating BCC tungsten bilayer/boron chain superstructure, but differ in the arrangement of the borons. In the LT-tetragonal phase, the boron chains alternate to form perpendicular arrays (FIG. 20B), but in the HT-orthorhombic phase, the boron chains are aligned along the c-axis (FIG. 20A) and this is responsible for the subtle orthorhombic distortion. In some instances, it has been reported that LT tetragonal WB is an ultraincompressible material with a bulk modulus of 4284 GPa (Yeung, et al., Annu. Rev. Mater. Res. 46, 1 (2016)) and a maximum differential stress of 14 GPa (Dong et al., J. Appl. Phys. 111, 123514 (2012)). In some instances, the orthorhombic phase WB is unstable at high temperature. In some cases, Ta is used to stabilize the HT orthorhombic phase of WB. In such cases based on the Vickers microindentation hardness measurement, the HT-orthorhombic WB has a hardness of 35.52.5 GPa and is comparable with LT-tetragonal WB (313.0 GPa).

[0193] In some instances, additional properties such as elastic deformation behavior, e.g., bulk modulus and crystal lattice strain response to a large applied non-hydrostatic stress and phase differences are further studied herein.

[0194] Synchrotron-based angle dispersive X-ray diffraction (XRD) experiments in radial geometry using a diamond anvil cell (DAC) were performed to examine the volumetric deformations and anisotropic lattice deformations of orthorhombic and tetragonal WB under applied pressures up to 52 GPa and 36 GPa respectively. The diffraction patterns were collected at steps of 4 GPa and analyzed using lattice strain theory (Singh et al, Phys. Rev. Lett. 80, 2157 (1998); Singh, J. Appl. Phys. 73, 4278 (1993); and Singh, et al, J. Appl. Phys. 83, 7567 (1998)). In the radial experimental geometry, the anisotropic stress condition in a DAC during compression is similar to that under an indenter's tip in a microindentation hardness test. In such cases, it provides insights for understanding the microscopic response of a crystal lattice to differential stress and the macroscopic response to applied loads. Additionally, radial XRD enables in situ observations of deformation behavior in a lattice specific manner as a function of pressure.

[0195] Representative XRD patterns for HT-orthorhombic WB are shown in FIG. 11A. The stick reference pattern given below the experimental diffraction peaks is from the Joint Committee on Powder Diffraction Standards (JCPDS Card #00-006-0541). A shift towards higher angles with increasing pressure can be seen due to the decreased lattice constants. Note that no Ta peaks appear in the pattern across the entire pressure range, meaning the added Ta forms solid solution with W, e.g., Ta.sub.0.05W.sub.0.95B, and the dopants do not extrude from the sample during compression. In some instances, although solid solution formation may influence mechanical properties, for example, the low doping amount and the small difference in atomic size (5%) between Ta (1.49 ) and W (1.41 ), however, the structural (orthorhombic VS. tetragonal) induced change in mechanical properties is greater than that from chemical doping. The LT-tetragonal WB was compressed up to 36.4 GPa and its representative XRD patterns are shown in FIG. 11B. The pressure at each point was determined at =54.7 by fitting the equation-of-state of Pt to its lattice parameter (Fei, et al., Proc. Nat. Acad. Sci. USA 104, 9182 (2007)).

[0196] The pressure dependence of d-spacings and lattice constants is summarized in FIG. 12 and Tables 1 and 2. There are no signs of phase transformations upon compression. For HT-orthorhombic WB, the diffraction planes (200), (020) and (002) were studied. The three orthogonal planes reflect the anisotropic deformation behavior of lattice constants a, b and c. As LT WB is tetragonal, the (200) and (020) are symmetrically the same, and thus the diffraction planes (200) and (004) were studied. FIGS. 13A and 13B shows the dependence of d-spacing as a function of (13 cos.sup.2) for the selected planes at the highest pressure, which presents an expected linear variation according to Equation 2.2. The slope of each line gives the corresponding (hkl) and the intercept yields the d-spacing under the mean normal stress. The ratio of differential stress to aggregate shear modulus (t(hkl)/G) of HT-orthorhombic WB (black) and LT-tetragonal WB (red) was plotted as a function of pressure in FIG. 14. As can be seen in the figure, the HT-orthorhombic WB shows larger variations in the t(hkl)/G ratio than the LT-tetragonal WB phase, which is an indication of higher elastic anisotropy in differential strain. This may arise from the distinct crystal structure between the HT-orthorhombic phase and the LT-tetragonal phase. When comparing their structures (FIGS. 20A and 20B), it was noted that the boron zigzag chains are in the same direction in the HT-orthorhombic phase, while they are along the perpendicular directions in the LT-tetragonal phase.

[0197] For HT-orthorhombic WB, the t(200)/G ratio shows an almost linear variation with pressure achieving the highest value of 4.7% at 52 GPa. This suggests that along the [200] direction/a-axis, the HT-orthorhombic WB phase can support a higher differential stress than the other directions. The t(020)/G ratio increases linearly with pressure at the beginning, but then levels off and increases more slowly above 15 GPa, ending with a plateau value of 4.4% at 26 GPa. The plateau is an indication of the onset of plastic deformation by a slip system. As shown in FIGS. 20A and 20B, the (020) of HT-orthorhombic WB is equivalent to the (004) of LT-tetragonal WB, which is the plane parallel to the metal bilayers. Since the metal-metal metallic bond is likely weaker than the metal-boron and boron-boron bonds; therefore, it appears that at pressures higher than 15 GPa, the (020) plastically deforms and starts to slip. Diffraction profile analysis was conducted to confirm this assumption. One source for broadening of the peaks in high pressure experiments is the inhomogeneous strain caused by the local deviatoric stresses among crystallites under non-hydrostatic compression. FIG. 15 displays the evolution of the (020) peak broadening as a function of pressure, and a similar trend to that of t(020)/G is observed. The peak broadening in the linear regime mainly results from the inhomogeneous elastic strain. Upon further compression, it deviates from linearity and approaches a limiting value of 0.17, indicating that no more local stress can be stored in the sample and it has relaxed by slipping. The data with open symbol at 0 GPa was taken upon decompression. The irreversible peak broadening reflects the residual stress effect in the quenched sample, which also suggests the sample deformed plastically under compression.

[0198] FIG. 14 shows that the t(002)/G also presents a plateau in the 20-40 GPa range, but after that it resumes increasing, a finding which was not observed in higher, more covalent borides such as WB.sub.4 and ReB.sub.2. Such behavior may arise from strain hardening effects. Considering that the elastic regime for HT WB is quite large in (200), the HT-orthorhombic tungsten monoboride may bring a desirable property-ductility to the superhard materials family. In some cases, strain hardening behavior was not observed in the LT-tetragonal WB in FIG. 14, which suggests that the arrangement of boron chains play a role on ductility. In contrast to HT-orthorhombic phase, the LT-tetragonal phase is more isotropic in differential strain. Given that the (004) shows a plateau in t/G ratio and FWHM, it is likely that (004) starts to slip at 20 GPa (as seen with the (020) for the HT phase).

[0199] Unlike the differential strain, the differential stress (t) can be correlated to hardness. The differential stress under Reuss (Reuss, A, Angew. Z., Math. Mech. 9, 49 (1929)) and Voigt (Voigt, W. Lehrbuch der Kristallphysik (Teubner, Leipzig, 1928)) conditions for HT-orthorhombic WB and LT-tetragonal WB was calculated by using the elastic stiffness constants provided by Liang, et al., Comput. Mater. Sci. 68, 222 (2013) and Cheng, et al., Act. Crystallogr. 70, 85 (2014), respectively. As shown in FIGS. 16A and 16B, the anisotropic nature of HT WB is preserved under both conditions. The plateau in the differential stress supported by the (020) plane suggests that it has reached its actual yield strength (9-11 GPa) at pressures achieved in this experiment. In contrast, the t(200) shows no plateau across the pressure range under both conditions; therefore, its corresponding yield strength was not estimated. However, considering that (200) supported the highest value (11-13 GPa) among the selected planes at 52 GPa, it can be concluded that its true yield strength should be even higher, indicating that the a axis is the hardest direction, followed by b axis and then the c axis. As shown in FIG. 21, the a-axis is dominated by the strong WB bonds, while the c-axis involves the least WB bonding. Therefore, the occurrence of covalent bonding between the W and B caused by the zigzag topology in the HT WB structure is responsible for the large differential stress supported along a-axis.

[0200] In order to confirm the anisotropy in strength, the DFT energy shifts in response to small shearing distortions were calculated. As shown in FIG. 17, it is energetically unfavorable to shear a (dominated by WB bonds) along c, suggesting that (200) is able to support a large shear stress. In contrast, shearing b (involves the least WB bonding) along c costs the least energy, suggesting that the (002) might support the least shear stress, which is consistent with our experimental results. Note that (020) supports the highest t until 50 GPa (FIG. 16). In some instances, the WB bond also plays a role in the observed strength. The change in energy of individual electronic states exposed the ones that are most energetically affected by geometric distortions. In this way, the bonds that were most active in resisting shear movement were determined. FIG. 22 shows two bonding structures with the highest energy displacement corresponding to WB bonds crossing the (020) plane during shear deformation. To gain an insight into the underlying electronic behavior leading to this strength, the electronic structure of a small model cluster, W.sub.2B.sub.2, were examined. The molecular orbitals corresponding to the WB bonds shown in FIG. 22 correlates to the bond strength. The HOMO-4, in addition to WB bonding, also corresponds to donation from the d-orbital on W to the apx bonding orbital in B2, thereby strengthening the BB interaction. Hence, the slip between W.sub.2 and B.sub.2 in the cluster disrupts both WB and BB bonding. The cluster clearly replicates the bonding patterns seen in the solid, thereby indicating that the BW interaction correlates to the strength of the composition.

[0201] To estimate the macroscopic differential stress (t) for polycrystalline sample, the contribution from each diffraction plane is considered. For example, t was obtained by taking the average of t(200)/G, t(020)/G and t(002)/G followed by multiplying to theoretical shear modulus of 198 GPa. Similarly, the differential stress of LT-tetragonal WB was obtained by using the shear modulus of 199 GPa. The shear modulus at high pressure were extrapolated using dG/dP=1.5. The hardness test shows that HT-orthorhombic WB and LT-tetragonal WB are comparable in hardness. As seen in FIG. 18, the maximum differential stress that they can support is quite close with a value of 11 GPa, suggesting that they have a similar macroscopic yield strength according to Equation 2.1, which is consistent with our hardness measurement. The differential stress of WB is lower than that of WB.sub.4 but higher than that of ReB.sub.2.

[0202] Note that although the LT-tetragonal and HT-orthorhombic phases show similar maximum differential stresses, they present different slopes. This may result from the difference in incompressibility between the two structures. The unit cell volume of HT-orthorhombic WB at elevated pressures ranging from 1.7 GPa to 52 GPa is shown in FIG. 19A. The compression curve was then fit to the second order Birch-Murnaghan equation-of-state (Birch, F. J. Geophys. Res. 83, 1257 (1978)) yielding a bulk modulus of 3415 GPa. The LT-tetragonal WB was found to be more incompressible than the HT phase with a bulk modulus increased to 3813 GPa (FIG. 19B). Because the orthorhombic phase is only thermodynamically favorable at high temperature, the HT WB is proposed to be an entropically stabilized phase. Upon compression, the enthalpy of the LT and HT probably behave similarly (because of the same bonding), while the entropy of HT should rapidly drop, suggesting that HT WB may have a lower incompressibility.

[0203] In addition to the volume deformation behavior, the lattice incompressibility was also examined. The fractional lattice constants of HT WB present a discontinuous change as can be seen in FIGS. 23A and 23B. At pressures lower than 20 GPa, the a axis is more compressible than the b axis, but upon further compression, the a axis becomes more incompressible. Due to the differences in pressure dependence of the lattice constants, an equation-of-state in terms of normalized pressure and Eularian strain was applied to the unit cell parameters, which yields K.sub.a(1)=92710.5 GPa (using data measured at pressures lower than 20 GPa), K.sub.a(2)=11009 GPa (using data measured at pressures higher than 20 GPa), K.sub.b=102018 GPa and K.sub.c=97212 GPa (FIGS. 24A and 24B). It is known that the incompressibility is directly related to the valence electron density. Given that the (020) plane starts to deform plastically at pressures around 15-20 GPa, one reason is that the discontinuous increase in directional incompressibility may result from a dislocation induced electronic structure rearrangement. There might be a charge density transfer between the WW bonds and WB bonds under compression in a similar manner to what has been observed in CrN (Rivadulla, et al., Nature Mater. 8, 947 (2009)). For LT WB, c axis (K.sub.c=12156 GPa) was found to be more incompressible than the a axis (K.sub.a=112813.5 GPa).

[0204] The high pressure behavior of WB in two different phases was compared using synchrotron based X-ray diffraction under non-hydrostatic compression up to 52 and 36 GPa, respectively. The bulk modulus for each phase was determined and the LT-tetragonal phase was found to be more incompressible than the HT-orthorhombic phase. Moreover, a discontinuous change in directional compressibility in HT-orthorhombic WB was observed. Although the two phases show similar harnesses, they present a distinct anisotropic nature in strength. The peak profile and lattice strain was examined, showing that the (200) is likely the strongest plane that supports the highest differential stress over other selected planes. The (020) was found to start slipping at 15 GPa and the (002) shows a strain hardening effect. In contrast to the HT-orthorhombic phase, LT-tetragonal WB is more isotropic in strength and seems more brittle since no strain hardening was observed. The two phases were found to support a similar maximum differential stress of 11 GPa. If it was assumed that t reflects the lower bound of the yield strength, then it is consistent with the microindentation hardness measurements. Additionally, the computation results suggest that WB bonds contribute the most to the strength of the material.

TABLE-US-00001 TABLE 1 Compression data for HT WB. P (GPa) a () b () c () 0 3.144 3.0793 1.682 3.137 8.4674 3.0734 2.907 3.136 8.4614 3.0704 4.437 3.129 8.4488 3.0664 11.077 3.115 8.4002 3.0506 15.098 3.099 8.3726 3.0398 19.716 3.087 8.3378 3.0258 24.053 3.078 8.3022 3.0118 26.918 3.074 8.2871 3.0044 29.715 3.069 8.2702 2.9981 32.842 3.065 8.2561 2.9902 35.171 3.059 8.2391 2.9862 39.505 3.052 8.2136 2.9772 41.943 3.046 8.2002 2.9718 44.309 3.040 8.1861 2.9671 48.102 3.036 8.1734 2.9618 49.491 3.029 8.1654 2.9578 52.251 3.024 8.1428 2.9511 *The data at 0 GPa was collected upon decompression.

TABLE-US-00002 TABLE 2 Compression data for LT WB sample. P (GPa) a () c () 0 3.1159 16.9056 2.719 3.1078 16.8888 6.411 3.1021 16.8548 8.773 3.0944 16.8116 12.798 3.0858 16.7712 16.045 3.0762 16.7384 18.521 3.0686 16.6952 26.918 3.0514 16.6121 28.193 3.0430 16.5947 36.389 3.0296 16.5022

[0205] The embodiments illustrated and discussed in this specification are intended only to teach those skilled in the art how to make and use the invention. In describing embodiments of the invention, specific terminology is employed for the sake of clarity. However, the invention is not intended to be limited to the specific terminology so selected. The above-described embodiments of the invention may be modified or varied, without departing from the invention, as appreciated by those skilled in the art in light of the above teachings. It is therefore to be understood that, within the scope of the claims and their equivalents, the invention may be practiced otherwise than as specifically described.