Linear and Planar Atomic DensitiesLinear Density:Directional equivalency is related to the atomic linear density in thesense that equivalent directions have identical linear densities.The direction vector is positioned so as to pass through atom centers.The fraction of line length intersected by these atoms is equal to thelinear density.Planar Density:Crystallographic planes that are equivalent have the same atomic planardensity. The plane of interest is positioned so as to pass through atomcenters.Planar density is the fraction of total crystallographic plane area that isoccupied by atoms.Linear and planar densities are one- and two-dimensionalanalogs of the atomic packing factor.
2ex:linear density of Al in directiona= 0.405 nmFCC: Linear Density•Linear Density of AtomsLD =aUnit length of direction vectorNumber of atoms# atomslength13.5 nma22LD-==Adapted fromFig. 3.1(a),Callister &Rethwisch 8e.
Linear Density for BCCCalculate the linear density for thefollowing directions in terms of R:a. b. c.