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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)
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2.
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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.
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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 unitsrandom=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))