代写ENGR 145 MIDTERM REVIEW代写留学生数据结构程序

ENGR 145 MIDTERM REVIEW

Quantum mechanics

-Electrons can be represented as waves where the electrons surrounding a nucleus are considered to be an electron cloud. The cloud represents the region where the electrons might be.

-There is still a distance that the electron is highly likely to exist from the nucleus which is a multiple of the Bohr radius (which has a value of 0.0529 nm). This radius is only for hydrogen, where other atoms are likely to be bigger than this number, or some multiple constant.

 

Bondings

-Depending on the materials, there are a few types of interatomic bonding that you need to know. These are covalent bonding: due to the sharing of electrons (over overlapping of electron clouds), metallic bonding: due to the free electrons roaming the entire structure, where the metal shares a big electron cloud, ionnic bonding: due to the attraction between positive and negative  ions, dipole bonding: due to dipoles attraction (dipole are molecules that has the negative and positive part separated to two side). An important thing to remember is that a hybrid of

bond is very common so a structure can have both covalent and ionic bonds.

 

Interatomic Potential

-The interatomic bonding as listed above also has an underlying repelling force beyond the attractive force we mention. This repelling force is due to ionization energy, electron affinity, and importantly, Pauli’s exclusion principle which states that two electrons can not have the same state. This results in an interatomic potential energy curve as shown below.

  

Unit Cell

-Structure: The unit cell is the smallest building block that represents the crystal. Go any smaller and we lose information. We are identifying the different types of crystal structures e.g. BCC, SC, FCC, and crystal systems e.g. cubic, hexagonal. We also have interposed crystal structures like diamond which are two FCCs of carbon, or zinc blende which is similar to diamond but for compound structure.

-Lattice sites: The sites in a unit cell that are equivalent (thus, different elements can not be counted to be the same lattice site, but rather they are interposed of two different crystal structures. In that case, just count one of the elements). The rule applies as ⅛ for a corner, ½ for a face, and 1 for inside the cell.

Understanding important definitions to characterize the unit cell of a crystal:

-Atomic packing factor (APF): How closely packed the unit cell is. This is different from the mass density

-Nearest neighbor: Closest atoms to a given atom. These are the atoms the given atom will have bonding with.

-Hard sphere model: Imaging each lattice site being expanded to become big spheres, as soon as the sphere touches each other, these spheres will represent the electron cloud of the

atom and thus the atomic radius.

-Mass density: The mass of the atoms in the unit cell over the entire volume of the unit cell. 

-Linear and planar density: Remember to differentiate the different types of density, LD and PD have units of # of atoms over (length or area) while mass density is mass over volume.

Also, the way you identify the number of atoms for these number densities is not the

same when you are doing the lattice sites. To do so, draw out the lines and the plane in 2D,  where the lines and plane stop at the center of the atom. For line, if they cover the entire atom   diameter -> 1 atom, if they cover half of the diameter -> ½ atom. For plane, it is the area of the  atom covered by the plane that determines the number of atoms. (Ex: Two atoms covered from

the [110] line)

  

-Miller indices: How to characterize a plane or a line in a unit cell. For a plane, use parenthesis, for a line, use square brackets, with negative numbers having a bar over the head. For the line, please write down the end and starting coordinates to get partial credits in case you get it wrong. For the planar indices, if there is a 0, that means the plane is parallel   to the corresponding axis. Also, different planar indices can be equivalent (either through symmetry or changing the coordinate system, where the origin is). I suggest looking through the possible plane and their respective indices if you are not confident with identifying one.

 

Polymer

-Polymer is any of a class of natural or synthetic substances composed of very large molecules, called macromolecules, that are multiples of simpler chemical units called monomers. The monomer is the repeating unit and is typically made up of C, H, and O (with occasions of F, N, Cl,...). Remember that the main line of the polymer is called the backbone.

-Polymers of a monomer type can vary in length, geometry, and formation leading to different abilities to form. crystallization. One of these factors is stereoisomerism which is split into three components: isotactic, syndiotactic, and atactic (tacticity). This tacticity characteristic involves how the side group is orientated along the chain, whether it is periodic and on the same side, periodic but alternating between sides, or completely random. We also have the stereoisomerism of cis and trans isomers, however, for these, we do not care that much about how they affect the crystallization effect.

 

-Another factor is the bulkiness of the side group of the monomer. If one monomer has CH3 as the side group while the other has a benzene ring, then the CH3 monomer will have a higher chance of crystallization.

-We also need to care about how the polymer chain looks like. If the chain is linear, then it has a higher chance than branched, which is higher than cross-linked, which is higher than network. However, for the more complex polymer structure, it is a grey area and whether a polymer has a higher chance to crystallize requires your decision-making. We also care about the structure of a copolymer made from two or more monomers. Block has a higher crystallizing chance than graft, and alternating has a better chance than random one.

Defects

-Point defects cause energy and disrupt the symmetry of the crystalline structure. On a bigger scale, we have dislocations where the crystalline structure has been bent, or shifted, creating boundaries differing in phase, or orientation.

-Back to defects, we have different types of defects, mainly interstitial and substitutional point defects. Interstitial defects are when there is an atom located in the crystal structure position that it should not be (say in a unit cell of a SC, atoms should only lie on the vertices). The substitutional defect is when the crystal structure is replaced by another atom of a different type. This interstitial defect often leaves a vacancy in the crystal structure which is also a defect.

-Broader, we have Frenkel defect and Schottky defect where Frenkel defect has an interstitial and vacancy while Schottky defect, we are having a missing of both a cation and anion.

-We can calculate the number of defects in a volume through the formula

-Remember that Qv is often given in eV so use the Boltzman constant for eV. If not, you can always convert eV to Joules.

Diffusion

-Diffusion is the movement of particles from a high concentration to a lower concentration reaching equilibrium eventually. For that to happen, we need a gradient in concentration that pushes the diffusion.

-Diffusion can be for substitutional defects or interstitial defects. For substitutional defects, the movement of the substitutional to vacancy sites can often be look at the movement of vacancies instead. We can calculate the diffusion coefficient as

 

where R here is the gas constant. This formula and the formula for the vacancies site can be plotted in linear form. where y is the ln(D) (ln(Nv)) and x is (1/T) where the slope is respectively (-Qd/R) and (-Qv/k).

-Here, we see the slope is dependent on the constant of Qd and Qv which is material dependent.

-Remember to use Kelvin and not Celcius always.

[Remember: Try to look at the formulas studied in the past, understand what each variable means in the formulas, and how these variables are correlated to one another e.g. thermal expansion coefficient is inversely proportional to the melting point. Why? This document is not  extensive as it does not covers all the equation talked about in class. For such, just a brief look and understanding what they mean is sufficient]

[Please remember that for a question if they ask you why e.g. Quiz 6 regarding solubility, the correct answer will yield you almost no point, so have explanations or some written words with your answers (depending on the point distribution).]

[The exam will not be math heavy so focus on remembering and understanding concepts, look through all the recitation slides, and lecture slides, and email me if you have any last-minute questions. Also, do not mix up equations e.g. planar density and mass density of a unit cell]