PROBLEM SET 7

# PROBLEM SET 7 - CRYSTALLINE LATTICES Crystal systems: There...

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MSE 110 -- U of A Crystal systems: CRYSTALLINE LATTICES • There are seven possible shape for the unit cell. • Every possible crystalline structure can be described using one of the seven following crystal system. • The position of atoms in these unit cells then differ for every crystalline structures.

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MSE 110 -- U of A Bravais Lattices: CRYSTALLINE LATTICES It can be shown that there are only fourteen ways to arrange points in space so that each point has identical surrounding. Because every atom is repeated along each repeatable lattice points, all these points are symmetrically identical and indistinguishable from another. Again, the lattice points do not necessarily correspond to atom positions but are rather a geometrical reference to describe their position. These correspond to the 14 Bravais lattices. Each of these lattice points are surrounded by the same atoms in the same geometrical arrangement. All crystals can be described using one these Bravais lattices
MSE 110 -- U of A CRYSTALLINE LATTICES Ans: The black atom is ½ along x, ½ along z and 0 or 1 along y. The rule is to state the coordinate involving 0 rather than 1 hence the proper way of stating the coordinates of the black atom is (½ ½ 0) Problem 1 What is the proper way to state the coordinates of the black atoms in the cell A- (½ 0 0) B- (½ 1 ½) C- (½½0) D- (½ 0 1)

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MSE 110 -- U of A CRYSTALLINE LATTICES Ans: The black atom is 0 or 1 along x, ½ along y and 0 or 1 along z. The rule is to state the coordinate involving 0 rather than 1 hence the proper way of stating the coordinates of the black atom is (0 ½ 0) Problem 2 What is the proper way to state the coordinates of the black atoms in the cell A- (½ 1 0) B- (½ 1 ½) C- (0 ½ 0) D- (0 ½ 1)
MSE 110 -- U of A CRYSTALLINE LATTICES Ans: The eight corner atoms correspond to the position of the origin (0 0 0). The black atoms are all equivalent and correspond to the coordinates (0 ½ 0). Hence only two coordinates are necessary to describe all the atoms position in this structure. Problem 3 How many atomic coordinates should be specified to describe all the atoms in the following structure?

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MSE 110 -- U of A CRYSTALLINE LATTICES Ans: The eight corner atoms correspond to the position of the origin (0 0 0). The black atoms are all equivalent and correspond to the coordinates (0 0 ½). The two green atoms are equivalent and correspond to the position (½ ½ 0). Hence only Three coordinates are necessary to describe all the atoms position in this structure. Problem 4 How many atomic coordinates should be specified to describe all the atoms in the following structure?
MSE 110 -- U of A • For a stacking sequence ABCABC. .. The unit cell is FCC and the octahedral (O) sites can be easily visualized using the ball and stick model.

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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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PROBLEM SET 7 - CRYSTALLINE LATTICES Crystal systems: There...

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