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Ionic bonding: between metallic & nonmetallic elements (on horizontal extremities) [NaCl] XA,XB are electronegativities Covalent bonding: sharing of electrons between two atoms; [CH 4,H2O,HNO3] Metallic bonding: in metals and alloys; have 1-3 valence electrons, float around in molecule electrons float around in sea (Ionic & covalent=insulators; metallic bonds=conductors, electrons flow easily) Amorphous: non-crystalline structure / Crystalline: atoms are orderly and in repeating patterns-long range Polycrystalline: crystalline materials of more than one grain Lattice: infinite array of points in a solid / Unit cell: smallest repeating unit FCC: (n)=4 Coordination #=12,nearest neighbors APF= .74 (for all FCC & HCP) APF= BCC: (n)=2 f General density equation Coordination #=8 APF=.68 (for all BCC) In a ceramic: structure determined by relative charge and size of anion/cation Cation: gives up electrons to anion / Anion: takes electrons from cation (larger) Using the coordination number we can find geometry [2-linear;3-triangular;4-tetrahedral;6-octehedral;8-square] Cation to Anion Ratio=rC/rA Rock Salt Structure: coordination #=6 [from FCC, 2 lattices together]; (NaCl) 4Na, 4Cl <.155 2 Cesium Chloride Structure: coordination #=8 [from BCC, but not all same size]; (CsCl) Zinc Blende: coordination #=4 (ZnS, ZnTe, SiC) .155 - .225 3 Diamond Cubic Crystal Structure: variant of zinc blende but all atoms are carbons .225 - .414 4 .414 - .732 6 .732 - 1.0 [Rock Salt] [Cesium Chloride] Density computations for ceramics: [Zinc Blende] 8 [Diamond] where n′ = the number of formula units2 within the unit cell ΣAC = the sum of the atomic weights of all cations in the formula unit ΣAA = the sum of the atomic weights of all anions in the formula unit VC = the unit cell volume (Will have to calculate with lattice constants) 1. 2. 3. 4. Crystalline Directions Redraw coordinate system @ origin of interested vector r= aux + bvy +cwz [a,b,c lattice dimensions] / [u,v,w coefficiants] Multiply by common factor to reduce u,v,w to integers Call direction [u v w] Note: (-) indicated by bar above # (Linear atomic density) (Planar atomic density) 1. 2. 3. 4. 5. Crystalline Planes Redraw coordinate system so origin is not on plane of interest Note axis intercepts (hax, iby, jcz) [h,i,j = coefficients] Replace h,i,j with reciprocals!! Multiply by common factor to reduce to integers Call plane (h i j) = also called Miller indices Note: -1 1 Number Average X-Ray Diffraction: Mi= mean molecular weight xi=fraction of total # of chains wi= weight fraction of molecules m = mer molecular weight m = Σfimi f=chain fraction, m=mol. wt repeat unit Weight Average Degree of Polymerization **watch for diffraction angles on chart, may need to divide by 2 %Crystalinity will increase when: slow cooling vs. fast cooling/linear>branched>cross-linked, network/ Isotactic, syndiotactic>atactic polymers/simple mer unit>bulky side chains/copolymers>simple polymer ρs =sample density ρa =density of totally amorphous ρc =density of totally crystalline Polymers: made by connecting large number of hydrocarbon molecules together “mer”: individual repeating hydrocarbon unit / “polymer’: Created by the chain of repeating ‘mers’ **polymers can crystallize w/ very specific conditions; very rare for 100% crystalline. Polymer Structure: linear=end to end in long chain/branched=main chain with side branches/cross-linked= adjacent linear chains are joined one to another at various positions by covalent bonds/network=complex 3-D structure Polymer Order: isotactic=R-groups positioned on same side of chain/syndiotactic=R-groups alternate sides/atactic: random grouping Isomerism: 2 compounds with same formula, different structures. cis=same side of chain/trans=opposite sides of chain Copolymer: composed of 2 repeating unitsrandom=randomly dispersed/alternating=2 units alternate/block=repeat units are clustered in blocks along chain/graft=one chain with other polymer chains off the main one Imperfections: maximizing disorder causes imperfections/self-intestinal: found in hole (atom squeezed in) [rare] Point Defects: T=temperature (K) N=# atomic sites/unit volume Nv=# vacancies/unit volume Qv=Activation Energy k= Boltzman’s constant (8.62x10-5 eV/K) = Boltman’s constant (1.38x10-23 J/K) In a Ceramic Material: Anion vacancy: if many, crystal will be positively charged Cation vacancy: if many, crystal negatively charged Frenkel defect: cation leaving its position and goes to interstitial site Schottky defect: removing cation/ion pair, and placing both on external surface **Same formula for Frenkel and Schottky defects as on left. Substitutional Impurity: impurity atom replaces host atom Interstitional Impurity: An atom just thrown in the mix Solid Solution: 2 elements randomly distributed in one crystal Phase separation:2 metals separate like oil & water Intermetallic Compound: 2 metals having directional bonds (Mg2Pb) Interstitial: “extra” atoms between atomic sites Hume-Rothery Rules (solid solutions): 1) Atomic radius difference <15% 2) Electronegativity similar will form solid/if greatly different Intermetallic Compound 3) Same crystal structure (FCC,BCC,etc) 4) Two species must have similar valence **If one doesn’t work will not form solid solution Weight % m1 and m2 = weight (or mass) of elements Atom % where = the mass (in grams) A1 =atomic weight Edge dislocation= extra portion of a plane of atoms, or half-plane, the edge of which terminates within the crystal. b ┴ to dislocation line Screw Dislocation= formed by a shear stress that is applied to Weight % Atom % produce the distortion b ║to dislocation line Mixed Dislocation= neither pure edge nor pure screw, but exhibit components of both types Grain Boundary= Low angle: few degrees angular dismatch/ High angle: larger angular dismatch Weight % Mass/Volume(Density) Twin Boundary= mirror symmetry across plane Burgers vector (b)= magnitude and direction of lattice distortion Microscopy: N = 2n-1 Atomic Weight (2 metal alloy) N= #grains/in2 at 100x n=grain size # Aave= 100/((C1/A1)+(C2/A2)) ρ ave =100/((C1/ρ1)+(C2/ρ2))