Atomic Structure and Bonding

Fundamentally, two types of bonding exist- bonds between atoms and bonds between ions. Bonds between atoms of nonmetals are covalent, meaning that they share a pair of electrons in the space between them. These two atoms are bound together and cannot be separated by simple physical means. If these two atoms have similar electronegativity, neither atom has more pull on the electron pair than the other. This type of covalent bond is called Non Polar. Examples of non polar covalent compounds are methane, carbon dioxide and graphite. In graphite, all atoms are identical and so no atom has stronger pull than any of the others. In methane, the carbon-hydrogen bonds are very slightly polar, and the polarities are cancelled because the bonds all point to the same locus. Further there exists a weaker type of bond called hydrogen bonds important in complex molecules such as proteins. These form weak bonds that give complex molecules like Chlorophyll its specific shape and properties. The kinds of bonds and the structure of the molecules affect the microscopic properties of substances.

Bonding Forces and Energies

Attractive Coulombic Force between charges.
${\displaystyle Z_{1}}$ and ${\displaystyle Z_{2}}$ are the valences of the ions

	Attractive Forces	Repulsive Forces	Energy
Formula	${\displaystyle F_{A}}$= ${\displaystyle {\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}}$ = ${\displaystyle k_{0}{\frac {e^{2}Z_{1}Z_{2}}{r^{2}}}}$	${\displaystyle F_{R}{=}{\frac {-b^{n}}{r^{n+1}}}}$	${\displaystyle E_{net}}$ = ${\displaystyle \int F_{A}dr+\int F_{R}dr}$ = ${\displaystyle {\frac {-A}{r}}+{\frac {B}{r^{n}}}}$
F/E plot vs r	F vs r -> modulus (stiffness	See left	Thermal expansion coefficiant melt temperature binding energy minimum is equilibrium distance

Where A= ${\displaystyle k_{0}e^{2}Z_{1}Z_{2}}$ and B is found using an empirical plot

Bonding

-Percent Ionic Character - Tells how much of the bond between element A and B is ionic and covalent, based on electronegativity X

${\displaystyle \%IC{=}}$ ${\displaystyle (1-e^{-(.25)(X_{A}-X_{B})^{2}})*100\%}$

In order of increasing intermolecular force strength:

fluctuating induced dipole < polar molecule induced dipole < hydrogen bonding (permanent dipole moment)

Density of Metals and Ceramics

	Metals	Ceramics
Density	${\displaystyle \rho {=}{\frac {nM}{V_{C}N_{A}}}}$	${\displaystyle \rho {=}{\frac {n'(\sum A_{C}+\sum A_{A})}{V_{C}N_{A}}}}$
How dense	More Dense	Less dense
Why dense	metallic bond -> close packing large atomic mass	covalent bonds lighter mass

Ceramic Crystal Structure

• In ceramics with ionic charachter, the magnitude of the electrical charge on each ion and the relative sizes of the ions partly determines the structure
• The charges of ions shows the ratio- the crystal must be neutral
• The number of ion neighbors of opposite charge is maximized
• Number of large anions that are able to surround small cation fixed by cation/anion radius ratio
• coordination number increases with ${\displaystyle {\frac {r_{cation}}{r_{anion}}}}$

Table of Major types of Ionic Ceramic Crystal Structures

Ceramic Structure	geometry	Anion Packing	Coordination number, anions	Coordination number, cations	Structure Stoichiometry
Sodium chloride	linear	FCC	6	6	AX
Zincblende	tetrahedral	FCC	4	4	AX
Cesium chloride	tri-planar	Simple Cubic	8	8	AX
Fluorite	Octohedral	Simple Cubic	4	8	${\displaystyle AX_{2}}$

Table of Metal Crystal Structures

	Body-Centered Cubic	Face-Centered Cubic	Hexagonal Close Packed	Simple Cubic
Coordination Number	8	12	12	6
Unit cell-radius relationships	${\displaystyle 4r=a_{0}{\sqrt {3}}}$	${\displaystyle 4r{=}a_{0}{\sqrt {2}}}$	${\displaystyle 2r=a_{0}}$ ${\displaystyle c/a_{0}=1.63}$	${\displaystyle a_{0}=2r}$
Volume	${\displaystyle a^{3}}$	${\displaystyle a^{3}}$	${\displaystyle a^{2}c\cos {(30)}}$	${\displaystyle a^{3}}$
Stacking Sequence	N/A	A-B-C	A-B
Atoms/ unit cell	2	4	6	1
Atomic Packing Factor	.68	.74	.74
Close-packed planes	[0001]	[111]	none
Close-packed directions	${\displaystyle <{\bar {1}}120>}$	<110>	<111>
Ceramic Structure		NaCl, Zincblende		(Simple cubic)CsCl, Fluorite

Miller Indices for Points, Vectors, and Planes

For points and Vectors:

Simpler form:

1. find ${\displaystyle \Delta x,\Delta y,\Delta z}$ scale them to the nearest integer

For Planes:

1. If the plane in question passes through the origin, create new origin
2. Note the incercepts of the plane in terms of x,y,z

(a) if intersection is entire axis the value is ${\displaystyle \infty }$

(b) If plane parallels an axis the value is ${\displaystyle \infty }$

1. Take reciprocals of found intercepts
2. Reduce to smallest integers
3. Enclose in parentheses without commas

[info] [list of directions] [comparison table]

Linear and Planar densities

Degree of Polymerization

DP=average number of repeat units per chain

${\displaystyle DP={MolarWeightofpolymer({\bar {M_{n}}}) \over Molarweightofsubstituent({\bar {m}})}}$

${\displaystyle {\bar {M_{n}}}{=}\sum x_{i}M_{i}<br/>{\bar {M_{w}}}{=}\sum w_{i}M_{i}<br/>{\bar {m}}}$ = average molecular weight of repeat unit

Molecular Structure and Tacity

Thermal Behavior

Copolymers

• Homopolymers are the term for pure polymers
• Copolymers have differing repeat units

Ex: PVC-C-PE is a copolymer (C stands for copolymer)

Crystallinity

• Crystalline regions of polymers charachterized by chain folded structures
• Higher indices of refraction than amorphous
• Electrical insulators
• Mechanically light
• Chemically inert
• Solid at STP
• Low density Polymers --> high optical transparency
• High density Polymers --> opaque
• Higher molecular weight--> less crystalization, longer chains more difficult to align to array
• Heat treating increases % crystallinity
• n= number of repeat units per cell

${\displaystyle n{=}{\rho V_{C}N_{A} \over A}}$

% Crystallinity = ${\displaystyle {\rho _{c}(\rho _{s}-\rho _{a}) \over \rho _{s}(\rho _{c}-\rho _{a})}\times 100\%}$

${\displaystyle \rho _{c}=densityperfectlycrystallinepolymer<br/>\rho _{a}=densitytotallyamorphouspolymer<br/>\rho _{s}=densityofsamplepolymer}$