Materials Science/Useful Formulas

Table of Formulas

Name	Equation	Notes	Subject
Attractive Force	$F_{A}$= ${\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}$ = $k_{0}{\frac {e^{2}Z_{1}Z_{2}}{r^{2}}}$		Bonding Forces and Energies
Repulsive Force	$F_{R}{=}{\frac {-b^{n}}{r^{n+1}}}$		Bonding Forces and Energies
Net Energy	$E_{net}$ = $\int F_{A}dr+\int F_{R}dr$ = ${\frac {-A}{r}}+{\frac {B}{r^{n}}}$	Where A= $k_{0}e^{2}Z_{1}Z_{2}$ and B is found using an empirical plot	Bonding Forces and Energies
% Ionic Character	$\%IC{=}$ $(1-e^{-(.25)(X_{A}-X_{B})^{2}})*100\%$	A ionic B Covalent X electronegativity	Bonding
Density, Metal	$\rho {=}{\frac {nM}{V_{C}N_{A}}}$		Density of Metals and Ceramics
Density, Ceramic	$\rho {=}{\frac {n'(\sum A_{C}+\sum A_{A})}{V_{C}N_{A}}}$		Density of Metals and Ceramics
Atomic Packing Factor	APF= ${\frac {Volumeofatomsinaunitcell}{TotalUnitCellvolume}}=$ $N{\dot {\frac {{\frac {4}{3}}\pi R^{2}}{a^{3}}}}{=}{\frac {V_{s}}{V_{C}}}$	Ceramic Crystal Structures
Degree of Polymerization	$DP={MolarWeightofpolymer({\bar {M_{n}}}) \over Molarweightofsubstituent({\bar {m}})}$		Polymer Structures
Molar Weight Polymer	${\bar {M_{n}}}{=}\sum x_{i}M_{i}$		Polymer Structures
Molar weight substituent	${\bar {M_{w}}}{=}\sum w_{i}M_{i}$		Polymer Structures
number repeat units/ cell	$n{=}{\rho V_{C}N_{A} \over A}$		Crystallinity
% Crystallinity	${\rho _{c}(\rho _{s}-\rho _{a}) \over \rho _{s}(\rho _{c}-\rho _{a})}\times 100\%$		Crystallinity
Number of Vacancies	$N_{v}{=}Nexp\left({-Qv \over kT}\right)$		Defects
Error function	${\frac {2}{\sqrt {\pi }}}\int _{0}^{x}e^{-t^{2}}\,dt$		Diffusion

Glossary

Term	Definition	Notes	Subject
Bonding Energy	Energy required to separate two atoms to and infinite separation	Example	Bonding
Polymer	Having Many Mer		Polymer Structures
Mer	Base atom or structure that repeats		Polymer Structures
Ceramic	nonmetallic, w/ %IC		Bonding
Covalent	Shares electrons		Bonding
Ionic	Gives up/ gains electrons		Bonding
Electronegativity	How much electrons wanted		Bonding
Crystal	single ordered form		Crystallinity
Linear Density			Ceramic Crystal Structures
Planar Density			Ceramic Crystal Structures
Number-average	based off size of chain		Polymer Structures
Weight-average	based off weight of chain		Polymer Structures
Thermoplastics	Linear+branched w/ minimal cross linking, heat malliable		Polymer Structures
Thermoset	network w/ crosslinks, covalent bonds, decomposes under heat		Polymer Structures
Copolymer	Different repeat units		Polymer Structures
Monopolymer	Same repeat units		Polymer Structures
Atomic Packing Factor	Atoms/ unit cell		Ceramic Crystal Structures
Unit Cell	Smallest crystal pattern constituent		Ceramic Crystal Structures
Cation	Positive ion		Bonding
Anion	Negative ion		Bonding
Coordination number	Number of nearest neighbors		Ceramic Crystal Structures
Stacking Sequence			Ceramic Crystal Structures
Ceramic			Bonding
Degree of Polymerization	Average number of repeat units per chain		Polymer Structures
crystalline material	periodic array of atoms over large atomic distances		Ceramic Crystal Structures
unit cells	small, repeating entities of crystalline material	Example	Ceramic Crystal Structures
mer	unit cell of a polymer		Polymer Structures
Polymorphism	when metal or nonmetal may have more than one crystal structure	see: allotropy	Ceramic Crystal Structures
Allotropy	polymorphism for elemental solids specifically	see: Polymorphism	Ceramic Crystal Structures
Random copolymers	No pattern	AABABBABBBABAA	Polymer Structures
Alternating copolymers	Directly alternating units	ABABABABA	Polymer Structures
Block copolymers	One block identical, block other	AAAABBBBAAAA	Polymer Structures
Graft copolymers	Main homopolymer chain with grafted homopolymer side branches		Polymer Structures
Homopolymer			Polymer Structures
Linear Polymer	repeat units joined end-to-end in one chain		Polymer Structures
Branched Polymer	Has side-branch chains connected to main chains		Polymer Structures
Crosslinked Polymer	Adjacent linear chains connected at various positions by covalent bonds		Polymer Structures
Network Polymer	3D network of multifunctional monomers		Polymer Structures
Isotactic Polymer	All substituents on same side of monomolecular backbone		Polymer Structures
Syndiotactic Polymer	alternating positions along chain (down/up)		Polymer Structures
Atactic Polymer	substituents placed randomly on chain		Polymer Structures
Tacity			Polymer Structures
Interdiff