Graphene is composed of sp2-bonded carbon atoms arranged in a two-dimensional honeycomb lattice.
The lattice can be seen as consisting of two interpenetrated triangular sub-lattices, for which the atoms of one sub-lattice are at the center of the triangles defined by the other with a carbon-to-carbon interatomic length, a(C–C), of 1.42A°. The unit
cell comprises two carbon atoms and is invariant under a rotation of 120 degree around any atom. Each atom has one s orbital and two in-plane p orbitals contributing to the mechanical stability of the carbon sheet. How they contribute to the mechanical properties?
Hi,
Frankly, I do not really understand specifically where is the question. Anyway, I will try to explain a bit along the paragraph, and hope it helps.
As you may already know that graphene is made of carbon atoms bonding in a honeycomb lattice, as in the attached image. Each carbon atom bonds to 3 neighbouring atoms. Regarding the "sub-lattice", the first thing you will need to notice is that the honeycomb is different from a close-packed hexagonal (where all atoms are equivalent). In a honeycomb lattice, two carbon atoms next to each other are not equivalent, in the sense that if you translate the lattice from one atom position to the one right next to it, you will not get the same lattice. The equivalent atoms in a honeycomb lattice are those located at the corners of the triangles (red or blue, in the attached image). Those within the red network are equivalent, and the same applied for those in the blue network. However, those in red and those in blue are not equivalent. This explains the two sub-lattices part of the paragraph.
The true lattice unit of graphene is the green diamond. If you rotate the diamond by 120 degree around any carbon atom, you will get the same lattice.
Regarding the mechanical properties, the each carbon atom has one s orbital and two p orbitals hybridising into three sp2 orbitals (plus one extra p orbital which does not participate in this hybridisation). The three hybridised orbitals are those that form the strong sigma covalent bonds amongs the carbon atoms to form the network, and provide the main mechanical strength to the lattice.
Regards,
Kien Cuong
Hi,
Frankly, I do not really understand specifically where is the question. Anyway, I will try to explain a bit along the paragraph, and hope it helps.
As you may already know that graphene is made of carbon atoms bonding in a honeycomb lattice, as in the attached image. Each carbon atom bonds to 3 neighbouring atoms. Regarding the "sub-lattice", the first thing you will need to notice is that the honeycomb is different from a close-packed hexagonal (where all atoms are equivalent). In a honeycomb lattice, two carbon atoms next to each other are not equivalent, in the sense that if you translate the lattice from one atom position to the one right next to it, you will not get the same lattice. The equivalent atoms in a honeycomb lattice are those located at the corners of the triangles (red or blue, in the attached image). Those within the red network are equivalent, and the same applied for those in the blue network. However, those in red and those in blue are not equivalent. This explains the two sub-lattices part of the paragraph.
The true lattice unit of graphene is the green diamond. If you rotate the diamond by 120 degree around any carbon atom, you will get the same lattice.
Regarding the mechanical properties, the each carbon atom has one s orbital and two p orbitals hybridising into three sp2 orbitals (plus one extra p orbital which does not participate in this hybridisation). The three hybridised orbitals are those that form the strong sigma covalent bonds amongs the carbon atoms to form the network, and provide the main mechanical strength to the lattice.
Regards,
Kien Cuong
Thanks Kien-Cuong Pham, you have nicely explained the hexagonal lattice structure of graphene.
but please explain this line "The true lattice unit of graphene is the green diamond"
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