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The compressive strength and hardness of diamond and various other materials, such as boron nitride, [10] (which has the closely related zincblende structure) is attributed to the diamond cubic structure. Example of a diamond cubic truss system for resisting compression. Similarly, truss systems that follow the diamond cubic geometry have a ...
In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type.Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group.
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
The unit tesseract in a Cartesian coordinate system for 4-dimensional space has two opposite vertices at coordinates [0, 0, 0, 0] and [1, 1, 1, 1], and other vertices with coordinates at all possible combinations of 0 s and 1 s. It is the Cartesian product of the closed unit interval [0, 1] in each axis.
When a coordinate system is chosen in the Euclidean space, this defines coordinates on : the coordinates of a point of are defined as the coordinates of (). The pair formed by a chart and such a coordinate system is called a local coordinate system , coordinate chart , coordinate patch , coordinate map , or local frame .
The diamond cubic crystal structure occurs for example diamond , tin, and most semiconductors. There are 8 atoms in the cubic unit cell. There are 8 atoms in the cubic unit cell. We can consider the structure as a simple cubic with a basis of 8 atoms, at positions
Diamond is extremely strong owing to its crystal structure, known as diamond cubic, in which each carbon atom has four neighbors covalently bonded to it. Bulk cubic boron nitride (c-BN) is nearly as hard as diamond. Diamond reacts with some materials, such as steel, and c-BN wears less when cutting or abrading such material. [4]
In diamond, all the carbon-to-carbon bonds, both within a layer of rings and between them, are in the staggered conformation, thus causing all four cubic-diagonal directions to be equivalent; whereas in lonsdaleite the bonds between layers are in the eclipsed conformation, which defines the axis of hexagonal symmetry.