The number of phonon branch in graphite, with four atoms in the primit...
Phonon Branches in GraphitePhonons are quantized lattice vibrations in a crystalline material. They are important in understanding the thermal, electrical, and mechanical properties of materials. Graphite is a layered material with a hexagonal crystal structure. There are four carbon atoms in the primitive unit cell of graphite. The number of phonon branches in graphite can be determined from its crystal structure and symmetry.
Crystal Structure of GraphiteGraphite has a hexagonal crystal structure with a layered arrangement of carbon atoms. The carbon atoms are arranged in a flat hexagonal lattice with each atom bonded to three neighboring atoms in the same layer. The layers are stacked on top of each other along the c-axis with a distance of approximately 0.34 nm between adjacent layers. The distance between carbon atoms in the same layer is approximately 0.142 nm.
Phonon Branches in GraphiteThe number of phonon branches in graphite can be determined from its crystal structure and symmetry. Graphite has a hexagonal crystal structure with a space group of P6/mmc. The irreducible representations of the space group are Γ1u, Γ2u, Γ3u, Γ4u, Γ5u, Γ6u, Γ7u, Γ8u, Γ9u, Γ10u, Γ11u, Γ12u, Γ13u, Γ14u, Γ15u, Γ16u, Γ17u, Γ18u, Γ19u, Γ20u, Γ21u, Γ22u, Γ23u, Γ24u, Γ25u, Γ26u, Γ27u, Γ28u, Γ29u, Γ30u, Γ31u, Γ32u, Γ33u, Γ34u, Γ35u, Γ36u, Γ37u, Γ38u, Γ39u, Γ40u, Γ41u, Γ42u, Γ43u, Γ44u, Γ45u, Γ46u, Γ47u, Γ48u, Γ49u, Γ50u, Γ51u, Γ52u, Γ53u, Γ54u, Γ55u, Γ56u, Γ57u, Γ58u, Γ59u, Γ60u, Γ61u, Γ62u, Γ63u, Γ64u, Γ65u, Γ66u, Γ67u, Γ68u, Γ69u, Γ70u, Γ71u, Γ72u, Γ73u, Γ74u, Γ75u, Γ76u, Γ77u, Γ78u, Γ79u, Γ80u, Γ81u, Γ82u, Γ83u, Γ84u, Γ85u, Γ86u, Γ87u, Γ88u, Γ89u, Γ90u, Γ91u, Γ92u, Γ93u, Γ94u, Γ95u, Γ96u, Γ97u, Γ98u, Γ99u, Γ100u, Γ101u, Γ102u, Γ103u, Γ104u, Γ105u, Γ106u, Γ107u, Γ108u, Γ109u, Γ110u, Γ111u, Γ112u, Γ113u,