Engr 313, Week 2 Notes
Engr 313, Week 2 Notes Engr 313
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This 4 page Class Notes was uploaded by Andres Rodriguez on Tuesday September 6, 2016. The Class Notes belongs to Engr 313 at University of Mississippi taught by Dr. Amrita Mishra in Fall 2016. Since its upload, it has received 39 views. For similar materials see Introduction to Materials Science in General Engineering at University of Mississippi.
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Date Created: 09/06/16
Chapter 3: Atomic and Ionic Arrangements Short-Range vs Long-Range Orders: No Order: Atoms or ions aren’t orderly arranged. For example, plasma created in fluorescent tubelight. Short-Range Order (SRO): Occurs when the atom’s extension only goes up to its nearest neighbors. One of the main factors for this to happen is covalent bonding. Water molecules are a good example short-range order because of the hydrogen-oxygen covalent bonding and because there is no specific arrangement with respect to molecules’ position (in the case of steam). Many polymers also have a short-range order. Long-Range Order (LRO): Occurs when the arrangement of atoms extends to larger scales than just the nearest neighbors (> 100nm). Atoms and ions are going to form regular repetitive patterns in three dimensions. Most metals and alloys, ceramic, semiconductors, and some polymers have a LRO. There are some techniques to measure LRO such as x-ray diffraction. NOTE: Some polymers undergo alignment and form small crystalline regions that are called “liquid crystals”. These regions behave as amorphous materials and they have an special type of order. Amorphous Materials: Definition: Material that only possesses a short-range order of atoms or ions. They tend to form when there isn’t formation of periodic arrangements in the kinetics of the process by which the material is produced. For example, glasses form in ceramic and polymer systems. Neutron scattering is a good technique to study the short-range order in amorphous materials. Glasses crystallization can be controlled by nucleating ultrafine crystals in amorphous glasses, process that creates glass-ceramics. These materials are highly crystalline and strong. Materials considered amorphous can still have some level of crystallinity. Metal and alloys tend to from crystals easily; therefore, additional efforts must be made to avoid the crystal production. One of the most common techniques is the rapid solidification, where metals and alloys are to be cooled very fast. 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 is a mathematical concept that doesn’t mention any atoms, ions, or molecules. For this reason, we can only describe a crystal structure when there is an association between a basis and a lattice. Different materials can have the same crystal structure. For example, copper and nickel have the face-centered cubic crystal structure (one atom associated with each lattice point). The main objective of choosing a unit cell for a crystal structure is to find the single unit that is later going to be duplicated in order to form the whole crystalline structure. 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. In the case of three-dimensional, each of the 8 corners has 1/8 of an atom for a total of one unit cell. The number of coordinates needed equals the number of atoms per unit cell. Number of atoms per unit cell = Number of atoms per lattice point x Number of lattice points per unit cell. There is a relationship between atomic radius and lattice parameters, which can be determined by calculating the length of the direction relative to the parameters and then adding the number of atomic radii along this direction. 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 structure6, BCC structure 8, and FCC structure12. 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). Metallic bond metals close-packing and large atomic mass whereas ceramics have less dense packing and polymers have even lower packing density. In other words: ρ metals < ρ ceramics < ρ polymers (Composites have intermediate values). Some engineering applications of single crystals are turbine blades, abrasives, among others. However, most engineering materials are polycrystals. Atomic Packing Factor: SC Structure: 4 3 ( )x(3 ᴨ x0.5a) APF= 3 a BCC Structure: 4 √3a/¿ 3 ¿ 4 ᴨ x¿ 3 2 x¿ ¿ APF=¿ FCC Structure: 4 √2a/¿ ¿ ¿3 4 3 ᴨ x¿ 4 x¿ ¿ APF=¿ NOTE: Check the bold sections to see the general formula for APF and the coordination number for each structure.
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