LECTURE 21 Crystal properties

LECTURE 21 Crystal - SUMMARY FROM LAST CLASS Miller indices • • • • • • • A set of atomic planes entirely defines a crystal structure

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Dr. P. Lucas U of A MSE 110 Miller indices A set of atomic planes entirely defines a crystal structure and we can identify these planes based on their orientation in the unit cell using the Miller indices . The plane orientation is specified by the intercept with each axes of the unit cell. This defines a set of Miller indices (hkl) determined as follow: Find an origin for which the plane intercepts all axes. Except for parallel axes. Find the intercepts on the three axes in fraction of the cell parameter. Except for parallel axes where intercept is . Determine the reciprocal of these numbers. Reduce the reciprocals to the smallest integers having the same ratio. Cite the three integers in parenthesis placing bars over negative indices. Using Bragg’s equation λ = 2d sin θ a set of d-spacings is obtained from the θ values on the XRD pattern. Each d correspond to a plane of orientation (hkl) . SUMMARY FROM LAST CLASS 2 2 2 ) ( l k h a d hkl + + = For a cubic cell, the geometric relationship between a , d and (hkl) is By inspection, we can calculate a and obtain the set of (hkl) for each d-spacing. This determines the structure entirely. a , d and (hkl) from all known minerals are compiled in a database.
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Dr. P. Lucas U of A MSE 110 The effect of structure on the properties of materials: Mechanical, electrical, optical and other properties are affected by the structure of a material. A solid with the same composition but different structures can have very different properties. A prime example is graphite and diamond. Graphite is a fragile, opaque electrical conductor while diamond is a very hard transparent insulator. These two allotropic form of carbon are both made of pure carbon atoms arranged in a different structure. CRYSTAL PROPERTIES
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Dr. P. Lucas U of A MSE 110 Graphite: The graphite structure consists of stacked rigid layers of carbon atoms. Carbons are covalently bonded within a layer with alternating double bond creating both a rigid structure and an extended π system contributing to the electrical conductivity. Layers are bonded through weak Van der Waals forces. CRYSTAL PROPERTIES Extended π system.
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Dr. P. Lucas U of A MSE 110 Graphite: Because of the weak Van der Waals bonding, the layers can easily shift passed each other and graphite powder is commonly used as a dry lubricant. This 2-D character also explain why graphite is such a soft and brittle solid in comparison to diamond. The bonding within a layer however is very strong and confer graphite a very high melting point of 3825ºK. Graphite crucibles are often used for high temperature synthesis. The delocalized
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This note was uploaded on 10/06/2009 for the course MSE 110 taught by Professor Lucas during the Spring '08 term at University of Arizona- Tucson.

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LECTURE 21 Crystal - SUMMARY FROM LAST CLASS Miller indices • • • • • • • A set of atomic planes entirely defines a crystal structure

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