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Engr 313 Weeks 3 and 4

by: Andres Rodriguez

Engr 313 Weeks 3 and 4 Engr 313

Andres Rodriguez
GPA 3.47

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This set of notes includes examples that are included in a separate pdf file.
Introduction to Materials Science
Dr. Amrita Mishra
Class Notes
Material Science
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This 4 page Class Notes was uploaded by Andres Rodriguez on Saturday September 24, 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 21 views. For similar materials see Introduction to Materials Science in General Engineering at University of Mississippi.

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Date Created: 09/24/16
Chapter 3 (Continued): Atomic and Ionic Arrangements  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: λ sinӨ= 2d hkl ao dhkl √h +k +l 2 Where, h, k, l = Miller indices ao= Lattice parameters dhkl Interplanar spacing Ө = Bragg angle 2Ө = Diffraction angle


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