Presentation on theme: "Linear and Planar Atomic Densities"— Presentation transcript:
1Linear and Planar Atomic Densities Linear Density:Directional equivalency is related to the atomic linear density in the sense 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 the linear density.Planar Density:Crystallographic planes that are equivalent have the same atomic planar density. The plane of interest is positioned so as to pass through atom centers.Planar density is the fraction of total crystallographic plane area that is occupied by atoms.Linear and planar densities are one- and two-dimensional analogs of the atomic packing factor.
2FCC: Linear Density 3.5 nm a 2 LD = Linear Density of Atoms LD = Number of atomsUnit length of direction vectoraex: linear density of Al in  direction a = nm# atomslength13.5 nma2LD-=Adapted fromFig. 3.1(a),Callister & Rethwisch 8e.
3P 3.53 (a): Linear Density for BCC Calculate the linear density for the following directions in terms of R:
4Planar Density of (100) Iron Solution: At T < 912ºC iron has the BCC structure.2D repeat unitR34a=(100)Radius of iron R = nmAdapted from Fig. 3.2(c), Callister & Rethwisch 8e.=Planar Density =a21atoms2D repeat unitnm212.1m2= 1.2 x 1019R34area
5P 3.55 (a): Planar Density for BCC Derive the planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R.
6Planar Density of BCC (111) Iron Solution (cont): (111) plane1 atom in plane/ unit surface cell2aatoms in planeatoms above planeatoms below plane2D repeat unit3h=a232R164aaharea=øöçèæ1=nm2atoms7.0m20.70 x 101932R16Planar Density =2D repeat unitarea
7P 3.54 (a): FCCDerive planar density expressions for FCC (100), (110), and (111) planes.
8P 3.563.56 (a) Derive the planar density expression for the HCP (0001) plane in terms of the atomic radius R.(b) Compute the planar density value for this same plane for magnesium. (atomic radius for magnesium is nm)