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