Materials Science/Structure of Matter

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. $$ Z_1 $$ and $$ Z_2 $$ are the valences of the ions

Where A= $$ k_0 e^2 Z_1 Z_2 $$ 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

$$ \%IC = $$ $$ (1-e^{-(.25)(X_A-X_B)^2} )*100\% $$

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In order of increasing intermolecular force strength:

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

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 $$ \frac{r_{cation}}{r_{anion}} $$

Atomic Packing Factor
APF= $$ \frac{Volume of atoms in a unit cell}{Total Unit Cell volume} =$$ $$ N \dot \frac{ \frac{4}{3} \pi R^2 }{a^3} = \frac{V_s}{V_C} $$

Miller Indices for Points, Vectors, and Planes
For points and Vectors:

Simpler form:


 * 1) find $$ \Delta x, \Delta y, \Delta z $$ 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 $$\infin$$

(b) If plane parallels an axis the value is $$\infin$$


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

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

Degree of Polymerization
DP=average number of repeat units per chain

$$ DP= {Molar Weight of polymer ( \bar{M_n}) \over Molar weight of substituent (\bar{m})} $$

$$ \bar{M_n} = \sum x_i M_i

\bar{M_w} = \sum w_i M_i \bar{m} $$ = average molecular weight of repeat unit

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

$$ n = { \rho V_C N_A \over A} $$

% Crystallinity = $$ { \rho_c (\rho_s-\rho_a) \over \rho_s(\rho_c-\rho_a)} \times 100\% $$

$$ \rho_c = density perfectly crystalline polymer \rho_a = density totally amorphous polymer \rho_s = density of sample polymer $$

Crystal Structure
Some of the properties of crystalline solids depends on the crystal structure of the material, the manner in which atoms, ions or molecules are spatially arranged.

Defects
Defects are the small gaps that develop between crystal layers where the continuation of the layer is interrupted by a boundary of a different crystal layer. Because the crystals do not perfectly align, small gaps are created in between the crystals where they meet. These gaps are called defects. Defects of materials are subject to intense study. However there are some methods to determine the source of defects and, if occurred, the size, shape and position of defects in the materials. There are: destructive testing methods and Non destructive testing methods (NDT).


 * material permanently deformed
 * can be mixed, many are
 * metals many slip planes


 * covalent, ionic ceramic motion hard
 * high force to break bonds
 * ionic ceramics have repulsion when move

Metals:
 * move in close packed planes
 * FCC many close packed planes, directions
 * HCP only 1 plane, 3 directions
 * many planes-> more plastic
 * one plane, more brittle
 * move by breaking, remaking atomic bonds
 * plastic deformation produce dislocation motion

Diffusion
When one substance moves into another