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Engr 313 Test 1 Study Guide

by: Andres Rodriguez

Engr 313 Test 1 Study Guide Engr 313

Andres Rodriguez
GPA 3.47

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Material covered from chapters 1 through 4
Introduction to Materials Science
Dr. Amrita Mishra
Study Guide
Material Science
50 ?




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This 10 page Study Guide was uploaded by Andres Rodriguez on Sunday September 25, 2016. The Study Guide belongs to Engr 313 at University of Mississippi taught by Dr. Amrita Mishra in Fall 2016. Since its upload, it has received 74 views. For similar materials see Introduction to Materials Science in General Engineering at University of Mississippi.


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Date Created: 09/25/16
Test 1 Study Guide (Chapters 1-4)  Chapter 1:  General Classification of Materials:  Metal and Alloys: First, an alloy is formed when a metal is mixed with one or more metals and non-metals. Metals and alloys are good electrical and thermal conductors, very strong, very stiff, and ductile (flexible). Useful for load-bearing purposes. Some common metals are: Fe, Al, Cu, Ti, Ni, Mg, among others.  Ceramics: Inorganic crystalline materials that are bad heat conductors due to their porosity. They are very hard and strong, but brittle at the same time (breaks without important deformations). Since very high temperatures must be reached to melt ceramics, they are used to make the tiles for space shuttles. Some popular ceramics are: Al O2, 3iO 2 (Silica), MgO, etc.  Glasses: Amorphous (not a defined structure) materials that are thermal and electrical insulators (bad conductors). They can become stronger by thermal treatments. They play a key role in fiber optics since this industry is based on silica glass. Silicates and optical glass fiber are the most common glasses.  Polymers: Non-crystalline organic materials that are good electrical and thermal insulators; however, there are some of them that are semiconductors. Not very strong, but good in resisting corrosion. Even though they are long chains of molecules, they are very ductile. Polymers have a lot of applications going from clothes to compact disks. Nylon and polyethylene are two very popular polymers.  Semiconductors: Also known as electronic materials, they have an electrical conductivity capacity that ranges between the ones of metallic conductors and ceramic insulators. Used to enable electric devices such as transistors, which are employed integrated circuits. Some common semiconductors are: Si, Ge, Sn GaAs, among others.  Composite: Formed from the combination of two or more materials, usually with the purpose of creating properties that cannot be found in a single material. The advantage of composites is that you can have a material that is lightweight but strong and ductile at the same time, which is very useful in industrial applications such as the production of aircraft and aerospace vehicles (carbon fiber). Concrete, plywood, and fiberglass are some of the most common composite materials. Fiberglass and Kevlar fiber are some well-known composites. Strength Order: Metals and Alloys > Composites > Ceramics > Polymers  Classification of Materials Based on Structure:  Crystalline: Long range order materials which atoms are arranged in a periodic fashion  Amorphous: Short range order materials that are randomly arranged.  Single Crystals: Crystalline materials that have the form of one crystal.  Polycrystalline: Crystalline materials that have many crystals or grains.  Grain Boundaries: Regions between individual crystals in a polycrystalline material that can be seen since the crystals do not follow a pattern, they are oriented in different directions (non-uniform structures). NOTE : Refer to the structure classification in order to have a better understanding of the general classification.  Chapter 2:  Periodic Table:  Rows refer to quantum shells  Columns refer to the number of electrons in the outer s and p energy levels. They correspond to the most common valence  Carbon based polymers appear on Group 4B  Groups 1 through 5B contain ceramics, which are usually based on the mixture of many elements. Oxygen, carbon, and nitrogen are also ceramics  Groups 1 and 2 contain metallic materials. Transition metal elements are also considered metallic materials  Groups 2B and 6B contain the elements that can be mixed to form semiconductors. Some elements in Groups 3B and 5B can also be combined to create semiconductors  Trends (Arrows indicate increase):  Atomic Bonding:  Metallic Bond: Metallic elements donate their valence electrons, so atoms can be surrounded by electrons (electron sea). Valence electrons move freely in the electron sea and associate with atom cores. The bond is produced by the mutual attraction of the positively charged ion cores to electrons. Metallic bonds are non-directional; therefore, metals tend to show good ductility.  Covalent Bond: Very strong bonds that are formed when two or more atoms share valence electrons, where each sharing represents one covalent bond. Bonds must have a directional relationship (formation of angles between bonds). Polymers are a great example of covalently bonded materials.  Ionic Bond: Formed when oppositely charged ions (cations and anions) are attracted to one another. This happens when there is more than one type of atom in a material because an atom may donate its valence electron to another atom. This take us to the situation where both atoms have filled or emptied their outer energy levels and have acquired an electrical charge. The one that donates the electron is going to become positively charged (cation) whereas the one that receives the electron is going to become negatively charged (ion). Now, the attraction previously explained occurs. Ionic bonds are non- directional because an ion has the same attraction from all directions for an ion of opposite charge. Glasses and ceramics are good examples of ionic bonding.  Binding Energy and Interatomic Spacing:  Binding Energy: Energy required to create o break a bond. Ionically bonded materials have high binding energy (electronegativity difference) whereas metals have a low binding energy (similar electronegativity).  There is a relation between modulus of elasticity (Young’s modulus) and the slope of the force-distance curve. A material has a high modulus of elasticity when having a steep slope (higher binding energy and melting point). This means that a greater force is required to stretch the bond.  The modulus of elasticity does not highly depend on the microstructure. On the other hand, it can be related to the stiffness of bonds between atoms. NOTE: Check examples 2-1 and 2-2 in the book to review atomic structure calculations. They are pretty simple, just follow the steps. Section 2-7 has drawings of the structure of the four different types of carbon (diamond, graphite, buckyballs, and carbon nanotubes).  Chapter 3:  Lattice, Basis, Unit Cells, and Crystal Structures:  Lattice: One-, two-, or three-dimensional collection of points that are arranged in a periodic pattern. This allows that the surroundings of each point are pretty much identical. In one dimension, the only possible lattice is a line of points, where there is an equal separation between them.  Basis: Group of one or more atoms that are positioned in a specific way respect to each other. They are also associated with every lattice point.  Crystal Structure: Combination of lattice and basis.  Unit Cell: Subdivision of a lattice that still possesses the overall qualities of the main lattice, which points are either placed at the corner if the unit cells or at the faces or center of the unit cell.  There is five different ways to arrange two-dimensional points while there are fourteen ways to arrange three-dimensional points (Bravais lattices). The latest ones are grouped into seven crystal systems: cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, and triclinic (Figure 3-6). These names are a description of the points’ arrangement in the unit cell.  Lattice Parameters: Axial dimensions of the unit cell. By convention, they are denoted as a, b, and c.  Interaxial Angles: Angles between the axial positions. By convention, they are denoted by the Greek letters α, β, and ɣ. Figure 3-8 shows the combination of these two previous definitions using the established convention.  All lattice parameters, interaxial angles, and atomic coordinates must be specified in order to fully determine an unit cell. For example, for a two-dimensional unit cell the axial lengths are a=b, the interaxial angle is ɣ=90°, and the atomic coordinate is (0,0). Go to Table 3-1 to see each type of structure.  Coordination Number: Number of atoms touching a particular atom. In other words, it is the number of nearest neighbors for a particular atom. For ionic solids, the coordination number of cations is the number of nearest anions and viceversa. In the case of unit cells, the coordination numbers are the following: SC structure6, BCC structure 8, and FCC structure12.  Packing Factor = ((Number of atoms/cell) x (Volume of each atom)) / Volume of unit cell FCC Close-packed SC and BCC Relatively open. Metallic bonding metals are packed as efficiently as possible whereas mixed-bond metals may have unit cells that are lower than the maximum packing factor.  Density (ρ) = ((Number of atoms/cell) x (Atomic mass)) / ((Volume of unit cell) x (Avogadro constant))  Hexagonal Close-Packed Structure (HCP): There are two atoms associated with every lattice point; therefore, there are two atoms per unit cell (Figure 3-13).  Atomic Packing Factor:  SC Structure: 4 3 ( )x( ᴨ x0.5a) APF= 3 a3  BCC Structure: 4 √3a/¿ ¿3 ¿ 4 3ᴨ x¿ (2)x¿ ¿ APF=¿  FCC Structure: 4 √2a/¿ ¿ ¿3 4 ᴨ x¿ 3 (4)x¿ ¿ APF=¿ NOTE: Check the bold sections to see the general formula for APF and the coordination number for each structure.  Points, Directions, and Planes in the Unit Cell:  Directions in the Unit Cell: There is a shorthand notation called Miller indices (h, k, l) used to describe directions. 1. Use a three dimensional coordinate system (Make sure it is properly labeled). 2. Trace a vector (line) from the origin to your point in the x-axis. 3. Locate your point in the y-axis, but before tracing a vector, you have to adjust the location of that point since you will be tracing the line from the head of the previous vector, not from the origin. Once you adjust your point, you can trace the vector. 4. Locate your point in the z-axis and go through the same adjusting process just explained. Once done, trace your vector from the head of the y-axis vector to your z-axis point. 5. Finally, trace a vector from the origin to the head of the vector just traced (z-axis). This is going to be the direction of your coordinates. An example will be attached in a picture (Ex 1) NOTE: If you have direction vector coordinates that are higher than one you can divide the whole vector by a common factor, so that way your highest point is and your direction vector fits in a single unit cell. Example will be attached (Ex 2). Also, if you there is a negative point, you can change your origin location so the vector fits in one unit cell (Ex 3). The number one represents the distances between the corners of the unit cell (cube), that is why the coordinate points cannot be higher than 1 if you want to use a single unit cell.  Planes in the Unit Cell: The same miller indices in this case 1. Use a three dimensional coordinate system (Make sure it is properly labeled). 2. Mark a point on the x-axis in the place that your coordinate indicates with respect to he origin. 3. Do the same thing for the y-axis and the z-axis. 4. Trace lines that join each point with the subsequent marked point, creating some sort of area. 5. Shade such area and that is your unit cell plane. (Ex 4) NOTE: The same modifications performed in the unit cell directions can also be applied to the unit cell planes. Also, when one of the coordinate points is 0, you just mark the other two points and then mark parallel points two each of them. This allows you to create an area, which will be your plane (Ex 5). In the case of having just one coordinate point, the area is going to be the face of the unit cell (cube) that corresponds to the axis (Ex 6).  Close Pack Planes and Directions: Structure Directions Planes SC <100> None BCC <111> None FCC <110> {111} HCP <100>, <110>, <11-20> (0001), (0002)  Linear and Planar Densities and Packing Density (LD, PD, LDP, PPD), and Packing Fraction:  LD = Number of atoms centered on a direction vector / Length of the direction vector  PD = Number of atoms centered on a given plane / Area of the plane  LDP = Number of radii along a direction vector / Length of the direction vector  PPD = Area of atoms centered on a given plane / Area of the plane  Packing Fraction = 2*r*LD  Diffraction Technique for Crystal Structure Analysis:  Bragg Law: sinӨ= λ 2dhkl a d = o hkl √h +k +l 2 Where, h, k, l = Miller indices a = Lattice parameters o d = Interplanar spacing hkl Ө = Bragg angle 2Ө = Diffraction angle  Chapter 4:  Types of Defects:  Point Defects: Localized disruptions in perfect atomic or ionic configurations in a crystal structure. There are different types of point defects. - Vacancies: Produced when an atom is missing from its normal site in the crystal structure. −Q v nv=nexp? (RT ) Where 3 nv= Number of vacancies per cm 3 n = Number of atoms per cm Q v Energy required to one mole of vacancies (cal/mol or J/mol) R = Gas constant T = Temperature in K - Interstitial Defects: Formed when an extra atom or ion is inserted into the crystal structure at a usually unoccupied position. - Schottky Defect: When vacancies occur in ionically bonded materials, a stoichiometric number of anions and cations must be missing from regular atomic positions if electrical neutrality is to be preserved. Occurs in ionic materials, especially ceramics. - Frenkel Defect: Formed when an ion jumps from a normal lattice point to an interstitial site, leaving a vacancy behind.  Linear Defects (Dislocations): - Edge Dislocations: The perfect way to describe it to picture slicing partway through a perfect crystal, spreading the crystal apart, and partly filling the cut with an extra half plane of atoms. - Screw Dislocations: The best way to illustrate it is by cutting partway through a perfect crystal and then skewing the crystal by one atom spacing. - Mixed Dislocations: Posses edge and screw characteristics with a transition region between them. Burgers Vector: Direction and distance that a dislocation moves in each step. Also known as the slip vector. In edge dislocations, the burgers vector is perpendicular to the dislocation line, while it is parallel to the dislocation line in the screw dislocation.  Planar Defects: - Twin Boundary: There is a mirror image misorientaion of the crystal structure. - Surface Defects: Boundaries or planes that separate a material into regions. - Grain Boundary: Surface that separates the individual grains, where atoms are not properly spaced. NOTE: Recommended numerical problems for this chapter are 4-1 and 4-2, which are explained step by step in the book.


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