Superhard materials
Encyclopedia
A superhard material is a material with a hardness value exceeding 40 GPa (gigapascals) when measured by the Vickers hardness test
. They are highly 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, abrasive
s, polishing and cutting tools 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.
Superhard materials can be generally classified into two categories: intrinsic compounds and extrinsic compounds. The intrinsic group includes diamond
, cubic boron nitride (c-BN), 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.
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 (HPHT) 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 (sometimes half-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 an indenter
(usually made of diamond) 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. 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 (Vm) and cohesive energy (Ec) as B ~ Ec/Vm 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 metal
s (Pd, Ag) have anomalously high ratio of the bulk modulus to the Vickers of 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 sheer strain: G = stress/strain = F·L/(A·dx), 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 sharing forces. Therefore the shear modulus is a measure of rigidity. Shear modulus is related to bulk modulus as 3/G = 2B·(1–2v)·(1+v), 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 toughness
, which is a material's ability to resist breakage from forceful impact. A superhard material is not necessarily "supertough". For example, the toughness of diamond is about 7–10 MPa·m1/2, 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 (super)hard. While hard materials have high bulk moduli, a high bulk modulus does not mean a material is hard. Elastic 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
(fcc) structure known as "diamond lattice
". It is known for its hardness (see table above) and incompressibility and is targeted for some potential optical and electrical applications. The properties of individual natural diamonds are varying too widely for industry, and therefore synthetic diamond
became a major research focus.
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 (70–150 GPa) is very dependent on the relative purity of the crystal itself. The more perfect the crystal structure, the harder the diamond becomes. It has recently been reported that HPHT single crystals and nanocrystalline diamond aggregates (aggregated diamond nanorods) 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
(several atomic percent) makes it a superconductor.
s or their nitride
s, followed by spontaneous nucleation of c-BN under HPHT conditions. The yield of c-BN is lower and substantially slower compared to diamond's synthetic route due to the complicated intermediate steps. Its insolubility in iron and other metal alloys makes it more useful for some industrial applications than diamond.
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Pure cubic boron nitride is transparent or slightly amber. Different colors can be produced depending on defects or an excess of boron (less than 1%). Defects can be produced by doping solvent-catalysts (i.e. Li, Ca, or Mg nitrides) with Al, B, Ti, or Si. This induces a change in the morphology and color of c-BN crystals.
The result is darker and larger (500 μm) crystals with better shapes and a higher yield.
Cubic boron nitride is insoluble in iron, nickel, and related alloys at high temperatures, but it binds well with metals due to formation of interlayers of metal borides and nitrides. It is also insoluble in most acids, but is soluble in alkaline molten salts and nitrides, such as LiOH, KOH, NaOH/Na2CO3, NaNO3 which are used to etch c-BN. Because of its stability with heat and metals, c-BN surpasses diamond in mechanical applications. The thermal conductivity of BN is among the highest of all electric insulators. In addition, c-BN consists of only light elements and has low X-ray absorptivity, capable of reducing the X-ray absorption background.
s of c-BN is produced worldwide each year. By modification, Borazon, a US brand name of c-BN, is used in industrial applications to shape tools, as it can withstand temperatures greater than 2000 °C. Cubic boron nitride-coated grinding wheels, referred to as Borazon wheels, are routinely used in the machining of hard ferrous metals, cast irons, and nickel-base and cobalt-base superalloys. Other brand names, such as Elbor and Cubonite, are marketed by Russian vendors.
New approaches in research focus on improving c-BN pressure capabilities of the devices used for c-BN synthesis. At present, the capabilities for the production of c-BN are restricted to pressures of about 6 GPa. Increasing the pressure limit will permit synthesis of larger single crystals than from the present catalytic synthesis. However, the use of solvents under supercritical conditions for c-BN synthesis has been shown to reduce pressure requirements. The high cost of c-BN still limits its application, which motivates the search for other superhard materials.
Despite two decades pursuing this compound, no synthetic sample of C3N4 has validated the hardness predictions, that was attributed to the difficulty in material synthesis and C3N4's instability. Carbon nitride is only stable at a pressure that is higher than that of the graphite-to-diamond transformation. The synthesis conditions would require extremely high pressures because carbon is four- and sixfold coordinated. In addition, C3N4 would pose problems of carbide formation if they were to be used to machine ferrous metals. Although publications have reported preparation of C3N4 at lower pressure than stated, synthetic C3N4 was not proved superhard.
Beginning in 1990, a great interest has been put in studying the possibility to synthesize dense B-C-N phases. They are expected to be thermally and chemically more stable than diamond, and harder than c-BN, and would therefore be excellent materials for high speed cutting and polishing of ferrous alloys. These characteristic properties are attributed to the diamond-like structure combined with the sp3 σ-bonds among carbon and the heteroatoms. BCxNy thin films were synthesized by chemical vapor deposition
in 1972. However, data on the attempted synthesis of B-C-N dense phases reported by different authors have been contradictory. It is unclear whether the synthesis products are diamond-like solid solutions between carbon and boron nitride or just mechanical mixtures of highly dispersed diamond and c-BN. In 2001, a diamond-like-structured c-BC2N with was synthesized at pressures >18 GPa and temperatures >2200 K by a direct solid-state phase transition of graphite-like (BN)0.48C0.52. The reported Vickers and Knoop hardnesses were intermediate between diamond and c-BN, making the new phase the second hardest known material. Ternary B–C–N phases can also be made using shock-compression synthesis. It was further suggested to extend the B–C–N system to quaternary compounds with silicon included.
of these materials reveals their metallic nature, but the extensive covalent B-B and M-B bonding (M = metal) leads to high hardness. Metals such as osmium
, rhenium
, tungsten
, etc. are desirable due to the high electron density, small atomic radius, high bulk modulus, and highly controlled directional bonding with boron. The M-B bond contributes to this due to the overlapping of the transition metal d states and boron p states.
(OsB2) has a high bulk modulus of 395 GPa and therefore is considered as a candidate superhard material, but the maximum achieved Vickers hardness is 37 GPa, slightly below the 40 GPa limit of superhardness. A common way to synthesize OsB2 is by a solid-state metathesis reaction containing a 2:3 mixture of OsCl3:MgB2
. After the MgCl2
product is washed away, X-ray diffraction indicates products of OsB2, OsB and Os. Heating this product at 1000 °C for three days produces pure OsB2 crystalline product. OsB2 has an orthorhombic structure
(space group
Pmmn) with two planes of osmium atoms separated by a non-planar layer of hexagonally coordinated boron atoms; the lattice parameters are a = 4.684 Å, b = 2.872 Å and c = 4.096 Å. The b direction of the crystal is the most compressible and the c direction is the least compressible. This can be explained by the orthorhombic structure. When looking at the boron and osmium atoms in the a and b directions, they are arranged in a way that is offset from one another. Therefore, when they are compressed they are not pushed right up against one another. Electrostatic repulsion is the force that maximizes the materials incompressibility and so in this case the electrostatic repulsion is not taken full advantage of. When compressed in the c direction, the osmium and boron atoms are almost directly in line with one another and the electrostatic repulsion is therefore high, causing direction c to be the least compressible. This model implies that if boron is more evenly distributed throughout the lattice then incompressibility could be higher. Electron backscatter diffraction
coupled with hardness measurements reveals that in the (010) plane, the crystal is 54% harder in the <100> than <001> direction. This is seen by looking at how long the indentation is along a certain direction (related to the indentations made with a Vickers hardness test). Along with the alignment of the atoms, this is also due to the short covalent B-B (1.80 Å) bonds in the <100> direction, which are absent in the <001> direction (B-B = 4.10 Å).
Rhenium diboride
(ReB2) is a refractory compound which was first synthesized in the 1960s, using arc melting
, zone melting
, or optical floating zone furnaces. An example synthesis of this material is the flux method, which is conducted by placing rhenium metal and amorphous boron in an alumina crucible with excess aluminium. This can be run with a ratio of 1:2:50 for Re:B:Al, with the excess aluminum as a growth medium. The crucible is placed in an alumina tube, inserted into a resistively heated furnace with flowing argon gas and sintered
at 1400 °C for several hours. After cooling, the aluminium is dissolved in NaOH. Each ReB2 synthesis route has its own drawbacks, and this one gives small inclusions of aluminum incorporated into the crystal lattice.
Rhenium diboride has a very high melting point approaching 2400 °C and a highly anisotropic, layered crystal structure. Its symmetry is either hexagonal (space group P63mc) or orthorhombic (Cmcm) depending on the phase. There, close-packed Re layers alternate with puckered triangular boron layers along the (001) plane. This can be seen above on the example of osmium diboride. The density of states for ReB2 has one of the lowest values among the metal borides, indicating strong covalent bonding and high hardness.
Owing to the anisotropic nature of this material, the hardness depends on the crystal orientation. The (002) plane contains the most covalent character and exhibits a maximum Vickers hardness value of 40.5 GPa, while the perpendicular planes were 6% lower at 38.1 GPa. These values decrease with increased load, settling at around 28 GPa each. The nanoindentation values were found to be 36.4 GPa and 34.0 GPa for the (002) and perpendicular planes respectively. The hardness values depend on the material purity and composition – the more boron the harder the boride – and the above values are for a Re:B ratio of approximately 1.00:1.85. Rhenium diboride also has a reported bulk modulus of 383 GPa and a sheer modulus of 273 GPa. The hardness of rhenium diboride, and most other materials also depends on the load during the test. The above values of about 40 GPa were all measured with an effective load of 0.5–1 N. At such low load, the hardness values are also overestimated for other materials, for example it exceeds 100 GPa for c-BN. Other researchers, while having reproduced the high ReB2 hardness at low load, reported much lower values of 19–17 GPa at a more conventional load of 3–49 N, that makes ReB2 a hard, but not a superhard material.
Rhenium diboride exhibits metallic conductivity which increases as temperature decreases and can be explained by a nonzero density of states due to the d and p overlap of rhenium and boron respectively. At this point, it is the only superhard material with metallic behavior. The material also exhibits relatively high thermal stability. Depending on the heating method, it will maintain its mass up to temperatures of 600–800 °C, with any drop being due to loss of absorbed water. A small loss of mass can then be seen at temperatures approaching 1000 °C. It performs better when a slower heat ramp is utilized. Part of this small drop at around 1000 °C was explained by the formation of a dull B2O3 coating on the surface as boron is leeched out of the solid, which serves as a protective coating, thereby reducing additional boron loss. This can be easily dissolved by methanol to restore the material to it native shiny state.
is described by the Hall-Petch equation
Here σc is the critical fracture stress, d the crystallite size and σ0 and kgb are constants.
If a material is brittle its strength depends mainly on the resistance to forming microcracks. The critical stress which causes the growth of a microcrack of size a0 is given by a general formula
Here E is the Young's modulus
, kcrack is a constant dependent on the nature and shape of the microcrack and the stress applied and γs the surface cohesive energy.
The average hardness of a material decreases with d (crystallite size) decreasing below 10 nm. There have been many mechanisms proposed for grain boundary sliding and hence material softening, but the details are still not understood. Besides grain boundary strengthening, much attention has been put into building microheterostructures, or nanostructures of two materials with very large differences in elastic moduli. Heterostructures were first proposed in 1970 and contained such highly ordered thin layers that they could not theoretically be separated by mechanical means. These highly ordered heterostructures were believed to be stronger than simple mixtures. This theory was confirmed with Al/Cu and Al/Ag structures. After the formation of Al/Cu and Al/Ag, the research was extended to multilayer systems including Cu/Ni, TiN/VN, W/WN, Hf/HfN and more. In all cases, decreasing the lattice period increased the hardness. One common form of a nanostructured material is aggregated diamond nanorods, which is harder than bulk diamond and is currently the hardest (~150 GPa) material known.
Vickers hardness test
The Vickers hardness test was developed in 1924 by Smith and Sandland at Vickers Ltd as an alternative to the Brinell method to measure the hardness of materials. The Vickers test is often easier to use than other hardness tests since the required calculations are independent of the size of the...
. They are highly incompressible solids with high electron density and high bond covalency
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
. As a result of their unique properties, these materials are of great interest in many industrial areas including, but not limited to, abrasive
Abrasive
An abrasive is a material, often a mineral, that is used to shape or finish a workpiece through rubbing which leads to part of the workpiece being worn away...
s, polishing and cutting tools and wear
Wear
In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface....
-resistant and protective coatings.
Diamond
Diamond
In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...
is the hardest known material to date with a Vickers hardness in the range of 70–150 GPa. Diamond demonstrates both high thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
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
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
and forms iron carbides
Cementite
Cementite, also known as iron carbide, is a chemical compound of iron and carbon, with the formula Fe3C . By weight, it is 6.67% carbon and 93.3% iron. It has an orthorhombic crystal structure. It is a hard, brittle material, normally classified as a ceramic in its pure form, though it is more...
at high temperatures and therefore is inefficient in cutting ferrous materials including steel
Steel
Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...
. Therefore, recent research of superhard materials has been focusing on compounds which would be thermally and chemically more stable than pure diamond.
Superhard materials can be generally classified into two categories: intrinsic compounds and extrinsic compounds. The intrinsic group includes diamond
Diamond
In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...
, cubic boron nitride (c-BN), carbon nitrides
Beta carbon nitride
Beta carbon nitride is a material predicted to be harder than diamond.The material was first proposed in 1985 by Marvin Cohen and Amy Liu. Examining the nature of crystalline bonds they theorised that carbon and nitrogen atoms could form a particularly short and strong bond in a stable crystal...
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
Bulk modulus
The bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e...
and does not deform plastically
Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...
. 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 (HPHT) 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 (sometimes half-integer) from 0 to 10 on the Mohs scale
Mohs scale of mineral hardness
The Mohs scale of mineral hardness characterizes the scratch resistance of various minerals through the ability of a harder material to scratch a softer material. It was created in 1812 by the German geologist and mineralogist Friedrich Mohs and is one of several definitions of hardness in...
. This scale was however quickly found too discrete and non-linear. Measuring the mechanical hardness of materials changed to using an indenter
Nanoindenter
A nanoindenter is the main component for indentation hardness tests used in nanoindentation. Since the mid 1970’s nanoindentation has become the primary method for measuring and testing very small volumes of mechanical properties...
(usually made of diamond) and evaluating bulk moduli, and the Brinell
Brinell scale
The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece. It is one of several definitions of hardness in materials science....
, Rockwell
Rockwell scale
The Rockwell scale is a hardness scale based on the indentation hardness of a material. The Rockwell test determines the hardness by measuring the depth of penetration of an indenter under a large load compared to the penetration made by a preload. There are different scales, denoted by a single...
, Knoop
Knoop hardness test
The Knoop hardness test is a microhardness test - a test for mechanical hardness used particularly for very brittle materials or thin sheets, where only a small indentation may be made for testing purposes...
and Vickers
Vickers hardness test
The Vickers hardness test was developed in 1924 by Smith and Sandland at Vickers Ltd as an alternative to the Brinell method to measure the hardness of materials. The Vickers test is often easier to use than other hardness tests since the required calculations are independent of the size of the...
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. Bulk moduli, shear moduli, and elasticity are the key factors in the superhard classification process.
| Material | Diamond | c-BC2N | c-BN | B4C | OsB2 | ReB2 |
|---|---|---|---|---|---|---|
| Vickers hardness (GPa) | 115 | 76 | 48 | 30 | 37 | ~20 |
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
Hydrostatic stress
In continuum mechanics, a hydrostatic stress is an isotropic stress that is given by the weight of water above a certain point. It is often used interchangeably with "pressure" and is also known as confining stress, particularly in the field geomechanics...
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 (Vm) and cohesive energy (Ec) as B ~ Ec/Vm 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
Alkali metal
The alkali metals are a series of chemical elements in the periodic table. In the modern IUPAC nomenclature, the alkali metals comprise the group 1 elements, along with hydrogen. The alkali metals are lithium , sodium , potassium , rubidium , caesium , and francium...
and noble metal
Noble metal
Noble metals are metals that are resistant to corrosion and oxidation in moist air, unlike most base metals. They tend to be precious, often due to their rarity in the Earth's crust...
s (Pd, Ag) have anomalously high ratio of the bulk modulus to the Vickers of 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 sheer strain: G = stress/strain = F·L/(A·dx), 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 sharing forces. Therefore the shear modulus is a measure of rigidity. Shear modulus is related to bulk modulus as 3/G = 2B·(1–2v)·(1+v), 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 toughness
Fracture toughness
In materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications. The fracture toughness of a material is determined from the...
, which is a material's ability to resist breakage from forceful impact. A superhard material is not necessarily "supertough". For example, the toughness of diamond is about 7–10 MPa·m1/2, 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 (super)hard. While hard materials have high bulk moduli, a high bulk modulus does not mean a material is hard. Elastic 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
Diamond
In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...
is an allotrope of carbon where the atoms are arranged in a modified version of face-centered cubic
Cubic crystal system
In crystallography, the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals....
(fcc) structure known as "diamond lattice
Diamond cubic
The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group IV also adopt this structure, including tin, the semiconductors silicon and germanium, and silicon/germanium...
". It is known for its hardness (see table above) and incompressibility and is targeted for some potential optical and electrical applications. The properties of individual natural diamonds are varying too widely for industry, and therefore synthetic diamond
Synthetic diamond
Synthetic diamond is diamond produced in a technological process; as opposed to natural diamond, which is created in geological processes. Synthetic diamond is also widely known as HPHT diamond or CVD diamond, denoting the production method, High-Pressure High-Temperature synthesis and Chemical...
became a major research focus.
Synthetic diamond
The high-pressure synthesis of diamond in 1953 in Sweden and in 1954 in the USA, 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 nitrideBoron nitride
Boron nitride is a chemical compound with chemical formula BN, consisting of equal numbers of boron and nitrogen atoms. BN is isoelectronic to a similarly structured carbon lattice and thus exists in various crystalline forms...
c-BN was obtained and found to be the second hardest solid.
Synthetic diamond
Synthetic diamond
Synthetic diamond is diamond produced in a technological process; as opposed to natural diamond, which is created in geological processes. Synthetic diamond is also widely known as HPHT diamond or CVD diamond, denoting the production method, High-Pressure High-Temperature synthesis and Chemical...
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 (70–150 GPa) is very dependent on the relative purity of the crystal itself. The more perfect the crystal structure, the harder the diamond becomes. It has recently been reported that HPHT single crystals and nanocrystalline diamond aggregates (aggregated diamond nanorods) 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
Boron
Boron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...
(several atomic percent) makes it a superconductor.
History
Cubic boron nitride or c-BN was first synthesized in 1957 by Robert H. Wentorf at General Electric, shortly after the synthesis of diamond. The general process for c-BN synthesis is the dissolution of hexagonal boron nitride (h-BN) in a solvent-catalyst, usually alkali or alkaline earth metalAlkaline earth metal
The alkaline earth metals are a group in the periodic table. In the modern IUPAC nomenclature, the alkaline earth metals are called the group 2 elements. Previously, they were called the Group IIA elements . The alkaline earth metals contain beryllium , magnesium , calcium , strontium , barium and...
s or their nitride
Nitride
In chemistry, a nitride is a compound of nitrogen where nitrogen has a formal oxidation state of −3. Nitrides are a large class of compounds with a wide range of properties and applications....
s, followed by spontaneous nucleation of c-BN under HPHT conditions. The yield of c-BN is lower and substantially slower compared to diamond's synthetic route due to the complicated intermediate steps. Its insolubility in iron and other metal alloys makes it more useful for some industrial applications than diamond.
The result is darker and larger (500 μm) crystals with better shapes and a higher yield.
Structure and properties
Cubic boron nitride adopts a sphalerite crystal structure, which can be constructed by replacing every two carbon atoms in diamond with one boron atom and one nitrogen atom. The short B-N (1.57 Å) bond is close to the diamond C-C bond length (1.54 Å), that results in strong covalent bonding between atoms in the same fashion as in diamond. The slight decrease in covalency for B-N bonds compared to C-C bonds reduces the hardness from ~100 GPa for diamond down to 48 GPa in c-BN. As diamond is less stable than graphite, c-BN is less stable than h-BN, but the conversion rate between those forms is negligible at room temperature.Cubic boron nitride is insoluble in iron, nickel, and related alloys at high temperatures, but it binds well with metals due to formation of interlayers of metal borides and nitrides. It is also insoluble in most acids, but is soluble in alkaline molten salts and nitrides, such as LiOH, KOH, NaOH/Na2CO3, NaNO3 which are used to etch c-BN. Because of its stability with heat and metals, c-BN surpasses diamond in mechanical applications. The thermal conductivity of BN is among the highest of all electric insulators. In addition, c-BN consists of only light elements and has low X-ray absorptivity, capable of reducing the X-ray absorption background.
Research and development
With great chemical and mechanical robustness, c-BN has wide applications as abrasives, cutting tools, and even one of the popular X-ray membranes – here the good mechanical properties allow to minimize the membrane thickness without breaking it, thereby decreasing the X-ray absorption. Several hundred tonneTonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...
s of c-BN is produced worldwide each year. By modification, Borazon, a US brand name of c-BN, is used in industrial applications to shape tools, as it can withstand temperatures greater than 2000 °C. Cubic boron nitride-coated grinding wheels, referred to as Borazon wheels, are routinely used in the machining of hard ferrous metals, cast irons, and nickel-base and cobalt-base superalloys. Other brand names, such as Elbor and Cubonite, are marketed by Russian vendors.
New approaches in research focus on improving c-BN pressure capabilities of the devices used for c-BN synthesis. At present, the capabilities for the production of c-BN are restricted to pressures of about 6 GPa. Increasing the pressure limit will permit synthesis of larger single crystals than from the present catalytic synthesis. However, the use of solvents under supercritical conditions for c-BN synthesis has been shown to reduce pressure requirements. The high cost of c-BN still limits its application, which motivates the search for other superhard materials.
Carbon nitride
The structure of carbon nitride (C3N4) was proposed in 1985. This compound, isostructural with Si3N4, was predicted to be harder than diamond. The calculated bond length was 1.47 Å, 5% shorter than the C-C bond length in diamond. Later calculations indicated that the shear modulus is 60% of that of diamond, and carbon nitride is less hard than c-BN.Despite two decades pursuing this compound, no synthetic sample of C3N4 has validated the hardness predictions, that was attributed to the difficulty in material synthesis and C3N4's instability. Carbon nitride is only stable at a pressure that is higher than that of the graphite-to-diamond transformation. The synthesis conditions would require extremely high pressures because carbon is four- and sixfold coordinated. In addition, C3N4 would pose problems of carbide formation if they were to be used to machine ferrous metals. Although publications have reported preparation of C3N4 at lower pressure than stated, synthetic C3N4 was not proved superhard.
Boron carbon nitride
The similar atomic sizes of boron, carbon and nitrogen, as well as the similar structures of carbon and boron nitride polymorphs, suggest that it might be possible to synthesize diamond-like phase containing all three elements. It is also possible to make compounds containing B-C-O, B-O-N, or B-C-O-N under high pressure, but their synthesis would expect to require a complex chemistry and in addition, their elastic properties would be inferior to that of diamond.Beginning in 1990, a great interest has been put in studying the possibility to synthesize dense B-C-N phases. They are expected to be thermally and chemically more stable than diamond, and harder than c-BN, and would therefore be excellent materials for high speed cutting and polishing of ferrous alloys. These characteristic properties are attributed to the diamond-like structure combined with the sp3 σ-bonds among carbon and the heteroatoms. BCxNy thin films were synthesized by chemical vapor deposition
Chemical vapor deposition
Chemical vapor deposition is a chemical process used to produce high-purity, high-performance solid materials. The process is often used in the semiconductor industry to produce thin films. In a typical CVD process, the wafer is exposed to one or more volatile precursors, which react and/or...
in 1972. However, data on the attempted synthesis of B-C-N dense phases reported by different authors have been contradictory. It is unclear whether the synthesis products are diamond-like solid solutions between carbon and boron nitride or just mechanical mixtures of highly dispersed diamond and c-BN. In 2001, a diamond-like-structured c-BC2N with was synthesized at pressures >18 GPa and temperatures >2200 K by a direct solid-state phase transition of graphite-like (BN)0.48C0.52. The reported Vickers and Knoop hardnesses were intermediate between diamond and c-BN, making the new phase the second hardest known material. Ternary B–C–N phases can also be made using shock-compression synthesis. It was further suggested to extend the B–C–N system to quaternary compounds with silicon included.
Metal borides
Contrary to carbon-based systems, metal borides can be easily synthesized in large quantities under ambient conditions, which is an important technological advantage. A few examples of these metal borides include RuB2, OsB2 and ReB2. The electronic density of statesDensity of states
In solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...
of these materials reveals their metallic nature, but the extensive covalent B-B and M-B bonding (M = metal) leads to high hardness. Metals such as osmium
Osmium
Osmium is a chemical element with the symbol Os and atomic number 76. Osmium is a hard, brittle, blue-gray or blue-blacktransition metal in the platinum family, and is the densest natural element. Osmium is twice as dense as lead. The density of osmium is , slightly greater than that of iridium,...
, rhenium
Rhenium
Rhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. With an average concentration of 1 part per billion , rhenium is one of the rarest elements in the Earth's crust. The free element has...
, tungsten
Tungsten
Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...
, etc. are desirable due to the high electron density, small atomic radius, high bulk modulus, and highly controlled directional bonding with boron. The M-B bond contributes to this due to the overlapping of the transition metal d states and boron p states.
Osmium diboride
Osmium diborideOsmium borides
Osmium borides are compounds of osmium and boron. Their most remarkable property is potentially high hardness. It is thought that a combination of high electron density of osmium with the strength of boron-osmium covalent bonds will make osmium borides superhard materials. This has not been...
(OsB2) has a high bulk modulus of 395 GPa and therefore is considered as a candidate superhard material, but the maximum achieved Vickers hardness is 37 GPa, slightly below the 40 GPa limit of superhardness. A common way to synthesize OsB2 is by a solid-state metathesis reaction containing a 2:3 mixture of OsCl3:MgB2
Magnesium diboride
Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...
. After the MgCl2
Magnesium chloride
Magnesium chloride is the name for the chemical compounds with the formulas MgCl2 and its various hydrates MgCl2x. These salts are typical ionic halides, being highly soluble in water. The hydrated magnesium chloride can be extracted from brine or sea water...
product is washed away, X-ray diffraction indicates products of OsB2, OsB and Os. Heating this product at 1000 °C for three days produces pure OsB2 crystalline product. OsB2 has an orthorhombic structure
Orthorhombic crystal system
In crystallography, the orthorhombic crystal system is one of the seven lattice point groups. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base and height , such that a,...
(space group
Space group
In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...
Pmmn) with two planes of osmium atoms separated by a non-planar layer of hexagonally coordinated boron atoms; the lattice parameters are a = 4.684 Å, b = 2.872 Å and c = 4.096 Å. The b direction of the crystal is the most compressible and the c direction is the least compressible. This can be explained by the orthorhombic structure. When looking at the boron and osmium atoms in the a and b directions, they are arranged in a way that is offset from one another. Therefore, when they are compressed they are not pushed right up against one another. Electrostatic repulsion is the force that maximizes the materials incompressibility and so in this case the electrostatic repulsion is not taken full advantage of. When compressed in the c direction, the osmium and boron atoms are almost directly in line with one another and the electrostatic repulsion is therefore high, causing direction c to be the least compressible. This model implies that if boron is more evenly distributed throughout the lattice then incompressibility could be higher. Electron backscatter diffraction
Electron backscatter diffraction
Electron backscatter diffraction , also known as backscatter Kikuchi diffraction is a microstructural-crystallographic technique used to examine the crystallographic orientation of many materials, which can be used to elucidate texture or preferred orientation of any crystalline or polycrystalline...
coupled with hardness measurements reveals that in the (010) plane, the crystal is 54% harder in the <100> than <001> direction. This is seen by looking at how long the indentation is along a certain direction (related to the indentations made with a Vickers hardness test). Along with the alignment of the atoms, this is also due to the short covalent B-B (1.80 Å) bonds in the <100> direction, which are absent in the <001> direction (B-B = 4.10 Å).
Rhenium borides
Rhenium was targeted as a candidate for superhard metal borides because of its desirable physical and chemical characteristics. It has a high electron density, a small atomic radius and a high bulk modulus. When combined with boron, it makes a crystal with highly covalent bonding allowing it to be incompressible and potentially very hard. A wide array of rhenium borides have been investigated including Re3B, Re7B3, Re2B, ReB, Re2B3, Re3B7, Re2B5, ReB3 and ReB2. Each of these materials has their own set of properties and characteristics. Some show promise as superconductors and some have unique elastic and electronic properties, but the most relevant to superhard materials is ReB2.Rhenium diboride
Rhenium diboride
Rhenium diboride is a synthetic superhard material. It was first synthesized in 1962 and re-emerged recently due to hopes of achieving high hardness comparable to that of diamond...
(ReB2) is a refractory compound which was first synthesized in the 1960s, using arc melting
Electric arc furnace
An electric arc furnace is a furnace that heats charged material by means of an electric arc.Arc furnaces range in size from small units of approximately one ton capacity up to about 400 ton units used for secondary steelmaking...
, zone melting
Zone melting
Zone melting is a group of similar methods of purifying crystals, in which a narrow region of a crystal is molten, and this molten zone is moved along the crystal...
, or optical floating zone furnaces. An example synthesis of this material is the flux method, which is conducted by placing rhenium metal and amorphous boron in an alumina crucible with excess aluminium. This can be run with a ratio of 1:2:50 for Re:B:Al, with the excess aluminum as a growth medium. The crucible is placed in an alumina tube, inserted into a resistively heated furnace with flowing argon gas and sintered
Sintering
Sintering is a method used to create objects from powders. It is based on atomic diffusion. Diffusion occurs in any material above absolute zero, but it occurs much faster at higher temperatures. In most sintering processes, the powdered material is held in a mold and then heated to a temperature...
at 1400 °C for several hours. After cooling, the aluminium is dissolved in NaOH. Each ReB2 synthesis route has its own drawbacks, and this one gives small inclusions of aluminum incorporated into the crystal lattice.
Rhenium diboride has a very high melting point approaching 2400 °C and a highly anisotropic, layered crystal structure. Its symmetry is either hexagonal (space group P63mc) or orthorhombic (Cmcm) depending on the phase. There, close-packed Re layers alternate with puckered triangular boron layers along the (001) plane. This can be seen above on the example of osmium diboride. The density of states for ReB2 has one of the lowest values among the metal borides, indicating strong covalent bonding and high hardness.
Owing to the anisotropic nature of this material, the hardness depends on the crystal orientation. The (002) plane contains the most covalent character and exhibits a maximum Vickers hardness value of 40.5 GPa, while the perpendicular planes were 6% lower at 38.1 GPa. These values decrease with increased load, settling at around 28 GPa each. The nanoindentation values were found to be 36.4 GPa and 34.0 GPa for the (002) and perpendicular planes respectively. The hardness values depend on the material purity and composition – the more boron the harder the boride – and the above values are for a Re:B ratio of approximately 1.00:1.85. Rhenium diboride also has a reported bulk modulus of 383 GPa and a sheer modulus of 273 GPa. The hardness of rhenium diboride, and most other materials also depends on the load during the test. The above values of about 40 GPa were all measured with an effective load of 0.5–1 N. At such low load, the hardness values are also overestimated for other materials, for example it exceeds 100 GPa for c-BN. Other researchers, while having reproduced the high ReB2 hardness at low load, reported much lower values of 19–17 GPa at a more conventional load of 3–49 N, that makes ReB2 a hard, but not a superhard material.
Rhenium diboride exhibits metallic conductivity which increases as temperature decreases and can be explained by a nonzero density of states due to the d and p overlap of rhenium and boron respectively. At this point, it is the only superhard material with metallic behavior. The material also exhibits relatively high thermal stability. Depending on the heating method, it will maintain its mass up to temperatures of 600–800 °C, with any drop being due to loss of absorbed water. A small loss of mass can then be seen at temperatures approaching 1000 °C. It performs better when a slower heat ramp is utilized. Part of this small drop at around 1000 °C was explained by the formation of a dull B2O3 coating on the surface as boron is leeched out of the solid, which serves as a protective coating, thereby reducing additional boron loss. This can be easily dissolved by methanol to restore the material to it native shiny state.
Other boron-rich superhard materials
Other hard boron-rich compounds include B4C and B6O. Amorphous a-B4C has a hardness of about 50 GPa, which is in the range of superhardness. It can be looked at as consisting of boron icosahedra-like crystals embedded in an amorphous medium. However, when studying the crystalline form of B4C, the hardness is only about 30 GPa. This crystalline form has the same stoichiometry as B13C3, which consists of boron icosahedra connected by boron and carbon atoms. Boron suboxide (B6O) has a hardness of about 35 GPa. Its structure contains eight B12 icosahedra units, which are sitting at the vertices of a rhombohedral unit cell. There are two oxygen atoms located along the (111) rhombohedral direction.Nanostructured superhard materials
Nanosuperhard materials fall into the extrinsic category of superhard materials. Because molecular defects affect the superhard properties of bulk materials it is obvious that the microstructure of superhard materials give the materials their unique properties. Focus on synthesizing nano superhard materials is around minimizing microcracks occurring within the structure through grain boundary hardening. The elimination of microcracks can strengthen the material by 3 to 7 times its original strength. Grain boundary strengtheningGrain boundary strengthening
Grain-boundary strengthening is a method of strengthening materials by changing their average crystallite size...
is described by the Hall-Petch equation
- σc = σ0 + kgb/√d
Here σc is the critical fracture stress, d the crystallite size and σ0 and kgb are constants.
If a material is brittle its strength depends mainly on the resistance to forming microcracks. The critical stress which causes the growth of a microcrack of size a0 is given by a general formula
- σc = kcrack√(2Eγs/πa0) ∝ 1/√d
Here E is the Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...
, kcrack is a constant dependent on the nature and shape of the microcrack and the stress applied and γs the surface cohesive energy.
The average hardness of a material decreases with d (crystallite size) decreasing below 10 nm. There have been many mechanisms proposed for grain boundary sliding and hence material softening, but the details are still not understood. Besides grain boundary strengthening, much attention has been put into building microheterostructures, or nanostructures of two materials with very large differences in elastic moduli. Heterostructures were first proposed in 1970 and contained such highly ordered thin layers that they could not theoretically be separated by mechanical means. These highly ordered heterostructures were believed to be stronger than simple mixtures. This theory was confirmed with Al/Cu and Al/Ag structures. After the formation of Al/Cu and Al/Ag, the research was extended to multilayer systems including Cu/Ni, TiN/VN, W/WN, Hf/HfN and more. In all cases, decreasing the lattice period increased the hardness. One common form of a nanostructured material is aggregated diamond nanorods, which is harder than bulk diamond and is currently the hardest (~150 GPa) material known.