Lecture 24 - A crystalline solid holds atoms, molecules,...

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A crystalline solid holds atoms, molecules, ions together in a regular long-range pattern called a lattice. The smallest repeating unit in this lattice is called a unit cell . An analysis of the crystal structure and the size of the unit cell gives valuable information relating density and molar mass of the substance. X-ray diffraction data gives us such information about the crystal structure and size of the unit cell. The distance between atoms in a lattice is roughly the same as X-ray wavelengths, resulting in a special scattering pattern called diffraction. When the reflected and incident rays reinforce each other, a diffraction pattern emerges. The Bragg equation can be used to determine the distance d between atomic layers in a lattice. n λ = 2d sin θ where λ = wavelength of the incoming X-rays, d = distance between layers θ = the angle of incidence between the incoming X-rays and the line of atoms in the crystal. n = the order of the diffraction, usually taken as 1. Example: X-rays having wavelength of 154 pm produce a diffraction pattern when aimed at a layer in the lattice at an angle of 19.3. Calculate d, the distance between the layers. Assuming first order diffraction pattern (n = 1): d = By changing the incident angle, we aim the X-rays at different layers, and can infer the crystal structure. In practice, this can be a complex process, not as easy as just using one simple equation such as the Bragg equation shown above. Some common unit cells are:
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Simple cubic: atom in each corner of a cube Face-centered cube: atom in each corner of a cube and an atom in the center of each face. Body-centered cube: atom in each corner of a cube, and an atom in the center of the cube. A diagram of these unit cells are shown below. A good recommended website is:
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http://www.molsci.ucla.edu/pub/explorations.html Then take the link to crystalline solids, and then to download setup program. The downloaded program will give excellent three-dimensional views of different unit cells and crystal structures. Students should learn to do problems relating:
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This note was uploaded on 02/15/2010 for the course CHEMISTRY 160:161 taught by Professor Paulkimmel during the Fall '09 term at Rutgers.

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Lecture 24 - A crystalline solid holds atoms, molecules,...

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