Chpter 3: The Structure of Crystlline Solids ISSUES TO ADDRESS... How do toms ssemble into solid structures? Exmples of dependence of mteril property on its crystl structure Chpter 3-1
Crystlline mterils... toms pck in periodic, 3D rrys with long-rnge trnsltionl symmetry typicl of: Crystlline vs. Noncrystlline (Amorphous) Mterils - Most metls - Mny cermics - Some polymers Noncrystlline mterils... toms hve no long-rnge periodic pcking occurs for: - All glsses - Some polymer "Amorphous" = Noncrystlline crystlline SiO2 Adpted from Fig. 3.23(), Cllister & Rethwisch 8e. Si Oxygen noncrystlline SiO2 Adpted from Fig. 3.23(b), Cllister & Rethwisch 8e. Chpter 3-2
Energy & Pcking for Crystlline vs. Noncrystlline (Amorphous) Mterils Crystlline mteril Ordered pcking, higher density Energy typicl neighbor bond length typicl neighbor bond energy r Amorphous mteril: Rndom pcking, lower density Energy typicl neighbor bond length typicl neighbor bond energy r Orderly pcked crystlline structures tend to hve higher density nd lower energies (more stble) Chpter 3-3
Single Crystl Mterils Periodic rrngement of toms throughout the entire mteril -- dimond single crystls for industril brsives (Courtesy Mrtin Dekins, GE Superbrsives, Worthington, OH. Used with permission.) -- Single crystl silicon wfer for semiconductor -- turbine bldes Fig. 8.33(c), Cllister & Rethwisch 8e. (Fig. 8.33(c) courtesy of Prtt nd Whitney). http://www.sumcosi.com/english/products/lineup.html Chpter 3-4
Polycrystlline Mterils Most engineering mterils re polycrystlline, i.e., they contin mny individul grins or smll crystls Nb-Hf-W plte with n electron bem weld. 1 mm Adpted from Fig. K, color inset pges of Cllister 5e. (Fig. K is courtesy of Pul E. Dnielson, Teledyne Wh Chng Albny) Csted polycrystlline Si Polycrystlline Si wfer Ech "grin" is single crystl Grin size rnges from ~1 nm to ~1 cm http://pveduction.org Chpter 3-5
Polycrystlline Mterils Chpter 3-6
Hrd Sphere Model for Crystl Structures Hrd-sphere model Atoms re hrd spheres Atoms touch nerest neighbors Periodic with trnsltionl symmetry Exercise: Drw 1D rrngement Drw 2D rrngement Chpter 3-7
Crystl Lttice, Unit Cell, & Coordintion Number (CN) Crystl lttice: n rry of points coincide with toms (or certin set of toms or molecules) representing geometric configurtion in crystls Unit cell: Smllest (simplest) repeting unit in lttice tht stisfy the followings: Represent/reflect symmetry in crystl Trnsltionl Rottionl Mirror Opposite fces (for 3D)/edges re prllel Ech point is identicl in its environment Coordintion Number (CN) Number of nerest (or touching) neighboring toms for n tom within crystl srinivseduction.blogspot.com Chpter 3-8
Unit cell in 3D typiclly prllelepipeds Crystl Systems 4 3-fold xis of rottion 7 Crystl Systems 1 4-fold xis of rottion 3 2-fold xis of rottion Cubic Tetrgonl Orthorhombic Fig. 3.4, Cllister & Rethwisch 8e., b, nd c re the lttice constnts α, β, γ re ngles Monoclinic 1 mirror plne Triclinic None Rhombohedrl (Trigonl) 1 3-fold xis of rottion Adpted with chnges from http://crystlineheling.blogspot.com/2014/06/blog-post_11.html Hexgonl Chpter 3-9 1 6-fold xis of rottion
Simple Cubic Structure (SC) Cubic crystl system Simple Rre for metls (only Po hs this structure) Close-pcked directions re cube edges Coordintion number (CN, or the # nerest/touching neighbors) = 6 R (Courtesy P.M. Anderson) If sme types of toms (e.g., pure metl) Edge length Atom rdius R = 2R On verge: 1 toms per unit cell: 8 corners x 1/8 = 1 Chpter 3-10
Crystl Structure Appliction Problem 2 Atomic Pcking Fctor (APF) for Simple Cubic Structure APF = Volume of toms in unit cell* Volume of unit cell APF for simple cubic structure = 0.52 *ssume hrd spheres close-pcked directions R=0.5 # of toms per unit cell APF = The unit cell contins 8 x 1/8 = 1 tom 1 4 3 p (0.5) 3 3 Volume of ech tom Volume of n unit cell Adpted from Fig. 3.24, Cllister & Rethwisch 8e. Chpter 3-11
Visulizing Simple Cubic (SC) Lttice Filling blls for SC lttice Bll-Stick model for SC lttice Unit cell for SC lttice srinivseduction.blogspot.com http://www2.ucdsb.on.c/tiss/stretton/chem2/rch19.htm Chpter 3-12
Body Centered Cubic (BCC) Structure Atoms touch ech other long cube digonls. --Note: All toms re identicl; the center tom is shded differently only for ese of viewing. ex: Cr, W, Fe ( ), Tntlum, Molybdenum Coordintion number CN = 8 https://www.ndeed.org/eductionresources/communitycolleg e/mterils/structure/metllic_structures.htm Adpted from Fig. 3.2, Cllister & Rethwisch 8e. On verge, 2 toms per unit cell: 1 center + 8 corners x 1/8 Chpter 3-13
Crystl Structure Appliction Problem 2 Atomic Pcking Fctor (APF) for BCC APF for body-centered cubic structure = 0.68 3 Adpted from Fig. 3.2(), Cllister & Rethwisch 8e. # of toms per unit cell APF = R 2 4 3 p ( 3 /4 ) 3 3 2 Along close-pcked direction: 4R = 3 Volume of ech tom Volume of n unit cell Chpter 3-14 2
Fce Centered Cubic (FCC) Structure Atoms touch ech other long fce digonls. --Note: All toms re identicl; the fce-centered toms re shded differently only for ese of viewing. A? B https://www.ndeed.org/eductionresources/com munitycollege/mterils/structure/ metllic_structures.htm ex: Al, Cu, Au, Pb, Ni, Pt, Ag Coordintion number CN = 12 A E 2 2 B C D Adpted from Fig. 3.1, Cllister & Rethwisch 8e. On verge: 4 toms per unit cell: 6 fce x 1/2 + 8 corners x 1/8 Chpter 3-15
Crystl Structure Appliction Problem 2 Atomic Pcking Fctor (APF) for FCC APF for fce-centered cubic structure = 0.74 mximum chievble APF 2 Close-pcked directions: 4R = 2 Adpted from Fig. 3.1(), Cllister & Rethwisch 8e. # of toms per unit cell APF = 4 4 3 p ( 2 /4 ) 3 3 Volume of ech tom Volume of n unit cell Chpter 3-16
Densities of Mteril Clsses In generl r metls > r cermics > r polymers Why? Metls hve... close-pcking (metllic bonding) often lrge tomic msses Cermics hve... less dense pcking often lighter elements Polymers hve... low pcking density (often morphous) lighter elements (C,H,O) Composites hve... intermedite vlues r (g/cm 3 ) 30 2 0 10 5 4 3 2 1 0.5 0.4 0.3 Metls/ Alloys Pltinum Gold, W Tntlum Silver, Mo Cu,Ni Steels Tin, Zinc Titnium Aluminum Mgnesium Grphite/ Cermics/ Semicond Polymers Dt from Tble B.1, Cllister & Rethwisch, 8e. Composites/ fibers B sed on dt in Tble B1, Cllister *GFRE, CFRE, & AFRE re Glss, Crbon, & Armid Fiber-Reinforced Epoxy composites (vlues bsed on 60% volume frction of ligned fibers in n epoxy mtrix). Zirconi Al oxide Dimond Si nitride Glss - sod Concrete Silicon G rphite PTFE Silicone PVC PET PC H DPE, PS PP, LDPE Glss fibers GFRE* Crbon fibers CFRE * A rmid fibers AFRE * Wood Chpter 3-17