Diamond is the allotrope of carbon in which the carbon atoms are arranged in the specific type of cubic lattice called diamond cubic. Diamond is an optically isotropic crystal that is transparent to opaque. Diamond is the hardest naturally occurring material known. Yet, due to important structural weaknesses, diamond's toughness is only fair to good. The precise tensile strength of bulk diamond is unknown;however, compressive strength up to 60 GPa has been observed, and it could be as high as 90–100 GPa in the form of nanometer-sized wires or needles (~100-300 nanometers in diameter),with a corresponding local maximum tensile elastic strain in excess of 9%. The anisotropy of diamond hardness is carefully considered during diamond cutting. Diamond has a high refractive index (2.417) and moderate dispersion (0.044) properties that give cut diamonds their brilliance. Scientists classify diamonds into four main types according to the nature of crystallographic defects present. Trace impurities substitutionally replacing carbon atoms in a diamond's crystal structure, and in some cases structural defects, are responsible for the wide range of colors seen in diamond. Most diamonds are electrical insulators and extremely efficient thermal conductors. Unlike many other minerals, the specific gravity of diamond crystals (3.52) has rather small variation from diamond to diamond. Known to the ancient Greeks as ἀδάμας – adámas ('proper', 'unalterable', 'unbreakable') and sometimes called adamant, diamond is the hardest known naturally occurring material, scoring 10 on the Mohs scale of mineral hardness. Diamond is extremely strong owing to the structure of its carbon atoms, where each carbon atom has four neighbors joined to it with covalent bonds. The material boron nitride, when in a form structurally identical to diamond (zincblende structure), is nearly as hard as diamond; a currently hypothetical material, beta carbon nitride, may also be as hard or harder in one form. It has been shown that some diamond aggregates having nanometer grain size are harder and tougher than conventional large diamond crystals, thus they perform better as abrasive material. Owing to the use of those new ultra-hard materials for diamond testing, more accurate values are now known for diamond hardness. A surface perpendicular to the crystallographic direction (that is the longest diagonal of a cube) of a pure (i.e., type IIa) diamond has a hardness value of 167 GPa when scratched with a nanodiamond tip, while the nanodiamond sample itself has a value of 310 GPa when tested with another nanodiamond tip. Because the test only works properly with a tip made of harder material than the sample being tested, the true value for nanodiamond is likely somewhat lower than 310 GPa. The precise tensile strength of diamond is unknown, however strength up to 60 GPa has been observed, and theoretically it could be as high as 90–225 GPa depending on the sample volume/size, the perfection of diamond lattice and on its orientation: Tensile strength is the highest for the crystal direction (normal to the cubic face), smaller for the and the smallest for the axis (along the longest cube diagonal). Diamond also has one of the smallest compressibilities of any material. Cubic diamonds have a perfect and easy octahedral cleavage, which means that they only have four planes—weak directions following the faces of the octahedron where there are fewer bonds—along which diamond can easily split upon blunt impact to leave a smooth surface. Similarly, diamond's hardness is markedly directional: the hardest direction is the diagonal on the cube face, 100 times harder than the softest direction, which is the dodecahedral plane. The octahedral plane is intermediate between the two extremes. The diamond cutting process relies heavily on this directional hardness, as without it a diamond would be nearly impossible to fashion. Cleavage also plays a helpful role, especially in large stones where the cutter wishes to remove flawed material or to produce more than one stone from the same piece of rough (e.g. Cullinan Diamond). Diamonds crystallize in the diamond cubic crystal system (space group Fd3m) and consist of tetrahedrally, covalently bonded carbon atoms. A second form called lonsdaleite, with hexagonal symmetry, has also been found, but it is extremely rare and forms only in meteorites or in laboratory synthesis. The local environment of each atom is identical in the two structures. From theoretical considerations, lonsdaleite is expected to be harder than diamond, but the size and quality of the available stones are insufficient to test this hypothesis. In terms of crystal habit, diamonds occur most often as euhedral (well-formed) or rounded octahedra and twinned, flattened octahedra with a triangular outline. Other forms include dodecahedra and (rarely) cubes. There is evidence that nitrogen impurities play an important role in the formation of well-shaped euhedral crystals. The largest diamonds found, such as the Cullinan Diamond, were shapeless. These diamonds are pure (i.e. type II) and therefore contain little if any nitrogen. The faces of diamond octahedrons are highly lustrous owing to their hardness; triangular shaped growth defects (trigons) or etch pits are often present on the faces. A diamond's fracture may be step-like, conchoidal (shell-like, similar to glass) or irregular. Diamonds which are nearly round, due to the formation of multiple steps on octahedral faces, are commonly coated in a gum-like skin (nyf). The combination of stepped faces, growth defects, and nyf produces a 'scaly' or corrugated appearance. Many diamonds are so distorted that few crystal faces are discernible. Some diamonds found in Brazil and the Democratic Republic of the Congo are polycrystalline and occur as opaque, darkly colored, spherical, radial masses of tiny crystals; these are known as ballas and are important to industry as they lack the cleavage planes of single-crystal diamond. Carbonado is a similar opaque microcrystalline form which occurs in shapeless masses. Like ballas diamond, carbonado lacks cleavage planes and its specific gravity varies widely from 2.9 to 3.5. Bort diamonds, found in Brazil, Venezuela, and Guyana, are the most common type of industrial-grade diamond. They are also polycrystalline and often poorly crystallized; they are translucent and cleave easily. Because of its great hardness and strong molecular bonding, a cut diamond's facets and facet edges appear the flattest and sharpest. A curious side effect of diamond's surface perfection is hydrophobia combined with lipophilia. The former property means a drop of water placed on a diamond will form a coherent droplet, whereas in most other minerals the water would spread out to cover the surface. Similarly, diamond is unusually lipophilic, meaning grease and oil readily collect on a diamond's surface. Whereas on other minerals oil would form coherent drops, on a diamond the oil would spread. This property is exploited in the use of so-called 'grease pens,' which apply a line of grease to the surface of a suspect diamond simulant. Diamond surfaces are hydrophobic when the surface carbon atoms terminate with a hydrogen atom and hydrophilic when the surface atoms terminate with an oxygen atom or hydroxyl radical. Treatment with gases or plasmas containing the appropriate gas, at temperatures of 450 °C or higher, can change the surface property completely. Naturally occurring diamonds have a surface with less than a half monolayer coverage of oxygen, the balance being hydrogen and the behavior is moderately hydrophobic. This allows for separation from other minerals at the mine using the so-called 'grease-belt'. Unlike hardness, which denotes only resistance to scratching, diamond's toughness or tenacity is only fair to good. Toughness relates to the ability to resist breakage from falls or impacts. Because of diamond's perfect and easy cleavage, it is vulnerable to breakage. A diamond will shatter if hit with an ordinary hammer. The toughness of natural diamond has been measured as 2.0 MPa m1/2, which is good compared to other gemstones, but poor compared to most engineering materials. As with any material, the macroscopic geometry of a diamond contributes to its resistance to breakage. Diamond has a cleavage plane and is therefore more fragile in some orientations than others. Diamond cutters use this attribute to cleave some stones, prior to faceting.