# 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= ${\frac {Volumeofatomsinaunitcell}{TotalUnitCellvolume}}=$ $N{\dot {\frac {{\frac {4}{3}}\pi R^{3}}{a^{3}}}}{=}{\frac {V_{s}}{V_{C}}}$ | 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 |