Lecture 3

Lecture 3 - EEE 352: Lecture 03 Crystal Structure * Diamond...

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EEE 352: Lecture 03 Crystal Structure * Diamond Crystal * Basis of the FCC * Bonds * Tetrahedral coordination * X-Ray Diffraction * Laue and Braggs
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Here we consider some important crystal structures encountered in nature * The first of these is the DIAMOND crystal structure Which is one of the crystal forms of CARBON In crystallography it is typical to break crystals down to their PRIMITIVE CELL * A basic BUILDING BLOCK that can be used to construct the crystal * The cell of the diamond structure, shown below, IS NOT THE PRIMITIVE CELL THE NORMAL CELL OF DIAMOND FOUR ATOMS ARE CONTAINED WITHIN THIS CELL MAKING IT EXTREMELY COMPLEX ! Crystal Structure of Diamond The PRIMITIVE CELL is formed by the primitive vectors and the basis. The normal cell is larger, but is more suitable for building the lattice.
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Recall that when describing lattice structures we used TRANSLATION VECTORS * That allow us to MAP from one lattice point to another We must also introduce translation vectors to describe the BASIS unit of the crystal * These vectors indicate the spatial relation of atoms WITHIN the basis unit * The translation vectors for the basis unit of diamond are shown below Where we have assumed the primitive cell size is a Crystal Structure of Diamond d Relative to each lattice point: * The FIRST atom of the basis is located at: * The SECOND atom of the basis is located at:
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Crystal Structure of Diamond The “basis” results in 4 new atoms in the face-centered cubic cell (BUT only 4 as the new structure is not “close packed” but rather open) :
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Crystal Structure of Silicon, Diamond, Germanium,… These two bonds form a plane, which is a (110) plane The two back bonds form a plane, which is at right angles to the first plane—THE PLANE OF THE BONDS ROTATE TO FORM THE TETRAHEDRON.
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Crystal Structure of Silicon, Diamond, Germanium,… These two bonds form a plane, which is a (110) plane
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Crystal Directions We have referred to various directions in the crystal as (100), (110), and (111). What do these mean? How are these directions determined? Consider a cube- and a plane- 1/2 1 2/3 The plane has intercepts: x = 0.5 a , y = 0.667 a , z = a .
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Crystal Directions We want the NORMAL to the surface. So we take these intercepts (in units of a ), and invert them: Then we take the lowest common set of integers: These are the MILLER INDICES of the plane. The NORMAL to the plane is the (4,3,2) direction, which is
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This note was uploaded on 09/28/2009 for the course EEE 352/333 taught by Professor Allee during the Fall '09 term at ASU.

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Lecture 3 - EEE 352: Lecture 03 Crystal Structure * Diamond...

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