Superhard material

A superhard material is a material with a hardness value exceeding 40 gigapascals when measured by the Vickers hardness test. They are virtually incompressible solids with high electron density and high bond covalency. As a result of their unique properties, these materials are of great interest in many industrial areas including, but not limited to, abrasives, polishing and cutting tools, disc brakes, and wear-resistant and protective coatings.
Diamond is the hardest known material to date, with a Vickers hardness in the range of 70–150 GPa. Diamond demonstrates both high thermal conductivity and electrically insulating properties, and much attention has been put into finding practical applications of this material. However, diamond has several limitations for mass industrial application, including its high cost and oxidation at temperatures above 800 °C. In addition, diamond dissolves in iron and forms iron carbides at high temperatures and therefore is inefficient in cutting ferrous materials including steel. Therefore, recent research of superhard materials has been focusing on compounds which would be thermally and chemically more stable than pure diamond.
The search for new superhard materials has generally taken two paths. In the first approach, researchers emulate the short, directional covalent carbon bonds of diamond by combining light elements like boron, carbon, nitrogen, and oxygen. This approach became popular in the late 1980s with the exploration of C₃N₄ and B-C-N ternary compounds. The second approach towards designing superhard materials incorporates these lighter elements, but also introduces transition metals with high valence electron densities to provide high incompressibility. In this way, metals with high bulk moduli but low hardness are coordinated with small covalent-forming atoms to produce superhard materials. Tungsten carbide is an industrially-relevant manifestation of this approach, although it is not considered superhard. Alternatively, borides combined with transition metals have become a rich area of superhard research and have led to discoveries such as ReB₂, OsB₂, and WB₄.
Superhard materials can be generally classified into two categories: intrinsic compounds and extrinsic compounds. The intrinsic group includes diamond, cubic boron nitride, carbon nitrides, and ternary compounds such as B-N-C, which possess an innate hardness. Conversely, extrinsic materials are those that have superhardness and other mechanical properties that are determined by their microstructure rather than composition. An example of extrinsic superhard material is nanocrystalline diamond known as aggregated diamond nanorods.

Definition and mechanics of hardness

The hardness of a material is directly related to its incompressibility, elasticity and resistance to change in shape. A superhard material has high shear modulus, high bulk modulus, and does not deform plastically. Ideally superhard materials should have a defect-free, isotropic lattice. This greatly reduces structural deformations that can lower the strength of the material. However, defects can actually strengthen some covalent structures. Traditionally, high-pressure and high-temperature conditions have been used to synthesize superhard materials, but recent superhard material syntheses aim at using less energy and lower cost materials.
Historically, hardness was first defined as the ability of one material to scratch another and quantified by an integer from 0 to 10 on the Mohs scale. This scale was however quickly found too discrete and non-linear. Measuring the mechanical hardness of materials changed to using a nanoindenter and evaluating bulk moduli, and the Brinell, Rockwell, Knoop, and Vickers scales have been developed. Whereas the Vickers scale is widely accepted as a most common test, there remain controversies on the weight load to be applied during the test. This is because Vickers hardness values are load-dependent. An indent made with 0.5N will indicate a higher hardness value than an indent made with 50N. This phenomenon is known as the indentation size effect. Thus, hardness values are not meaningful unless the load is also reported. Some argue that hardness values should consistently be reported in the asymptotic, as this is a more standardized representation of a material's hardness.

Material	Vickers hardness	Bulk Modulus
Diamond	115	440
c-BC₂N	76	282
c-BC₅	71
γ-Boron	58	227
c-BN	48, 62	400
OsB₂	37	395
B₄C	35, 38
WB₄	~30
AlMgB₁₄	26.7
ReB₂	~20

Bulk moduli, shear moduli, and elasticity are the key factors in the superhard classification process. The incompressibility of a material is quantified by the bulk modulus B, which measures the resistance of a solid to volume compression under hydrostatic stress as B = −Vdp/dV. Here V is the volume, p is pressure, and dp/dV is the partial derivative of pressure with respect to the volume. The bulk modulus test uses an indenter tool to form a permanent deformation in a material. The size of the deformation depends on the material's resistance to the volume compression made by the tool. Elements with small molar volumes and strong interatomic forces usually have high bulk moduli. Bulk moduli was the first major test of hardness and originally shown to be correlated with the molar volume and cohesive energy as B ~ E_c/V_m.
Bulk modulus was believed to be a direct measure of a material's hardness but this no longer remains the dominant school of thought. For example, some alkali and noble metals have anomalously high ratio of the bulk modulus to the Vickers or Brinell hardness. In the early 2000s, a direct relationship between bulk modulus and valence electron density was found as the more electrons were present the greater the repulsions within the structure were. Bulk modulus is still used as a preliminary measure of a material as superhard but it is now known that other properties must be taken into account.
In contrast to bulk modulus, shear modulus measures the resistance to shape change at a constant volume, taking into account the crystalline plane and direction of shear. The shear modulus G is defined as ratio of shear stress to shear strain: G = stress/strain = F·L/, where F is the applied force, A is the area upon which the force acts, dx is the resulting displacement and L is the initial length. The larger the shear modulus, the greater the ability for a material to resist shearing forces. Therefore, the shear modulus is a measure of rigidity. Shear modulus is related to bulk modulus as, where v is the Poisson's ratio, which is typically ~0.1 in covalent materials. If a material contains highly directional bonds, the shear modulus will increase and give a low Poisson ratio.
A material is also considered hard if it resists plastic deformation. If a material has short covalent bonds, atomic dislocations that lead to plastic deformation are less likely to occur than in materials with longer, delocalized bonds. If a material contains many delocalized bonds it is likely to be soft. Somewhat related to hardness is another mechanical property fracture toughness, which is a material's ability to resist breakage from forceful impact. A superhard material is not necessarily "supertough". For example, the fracture toughness of diamond is about 7–10 MPa·m^1/2, which is high compared to other gemstones and ceramic materials, but poor compared to many metals and alloys – common steels and aluminium alloys have the toughness values at least 5 times higher.
Several properties must be taken into account when evaluating a material as hard. While hard materials have high bulk moduli, a high bulk modulus does not mean a material is hard. Inelastic characteristics must be considered as well, and shear modulus might even provide a better correlation with hardness than bulk modulus. Covalent materials generally have high bond-bending force constants and high shear moduli and are more likely to give superhard structures than, for example, ionic solids.

Diamond

is an allotrope of carbon where the atoms are arranged in a modified version of face-centered cubic structure known as "diamond cubic". It is known for its hardness and incompressibility and is targeted for some potential optical and electrical applications. The properties of individual natural diamonds or carbonado vary too widely for industrial purposes, and therefore synthetic diamond became a major research focus.

Synthetic diamond

The high-pressure synthesis of diamond in 1953 in Sweden and in 1954 in the US, made possible by the development of new apparatus and techniques, became a milestone in synthesis of artificial superhard materials. The synthesis clearly showed the potential of high-pressure applications for industrial purposes and stimulated growing interest in the field. Four years after the first synthesis of artificial diamond, cubic boron nitride c-BN was obtained and found to be the second hardest solid.
Synthetic diamond can exist as a single, continuous crystal or as small polycrystals interconnected through the grain boundaries. The inherent spatial separation of these subunits causes the formation of grains, which are visible by the unaided eye due to the light absorption and scattering properties of the material.
The hardness of synthetic diamond is very dependent on the relative purity of the crystal itself. The more perfect the crystal structure, the harder the diamond becomes. It has been reported that HPHT single crystals and nanocrystalline diamond aggregates can be harder than natural diamond.
Historically, it was thought that synthetic diamond should be structurally perfect to be useful. This is because diamond was mainly preferred for its aesthetic qualities, and small flaws in structure and composition were visible by naked eye. Although this is true, the properties associated with these small changes has led to interesting new potential applications of synthetic diamond. For example, nitrogen doping can enhance mechanical strength of diamond, and heavy doping with boron makes it a superconductor.
In 2014, researchers reported on the synthesis of nano-twinned diamond with Vickers hardness values up to 200 GPa. The authors attribute the unprecedented hardness to the Hall-Petch effect, which predicts that smaller microstructural features can lead to enhanced hardness due to higher density of boundaries that stop dislocations. They achieve twins with an average thickness of 5 nm using a precursor of onion carbon nanoparticles subjected to high temperature and pressure. They also simultaneously achieve an oxidation temperature that is 200 °C higher than that of natural diamond. Higher thermal stability is relevant to industrial applications such as cutting tools, where high temperatures can lead to rapid diamond degradation.