# L17 - SUMMARY FROM LAST CLASS Crystalline lattices The unit...

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Dr. P. Lucas U of A MSE 110 Crystalline lattices SUMMARY FROM LAST CLASS The unit cell is the smallest repeatable building block that is replicated in three dimensions to generate the periodic crystalline structure. The space lattice is as a three dimensional net of straight line dividing all space into equal size parallelepiped corresponding to the crystal unit cell. All crystals can be described using one of 7 different unit cell geometry (7 crystalline systems). The unit cell edges defines a coordinate system with its origin at the cell corner. This coordinate system specifies the atoms position in the cell. When stating the position of an atom that has several equivalent positions, the coordinates that involve zero rather than ones are chosen. Specifying the unit cell and the atoms coordinates fully defines the crystal structure. Some crystals are conveniently described using a unit cells with repeatable lattice positions in the center of the cell or in the middle of faces. These lattice positions will have the exact same surrounding in the cell and everywhere else in the crystal. They are therefore indistinguishable. There are only 14 ways to arrange such indistinguishable lattice sites. These correspond to the 14 Bravais lattices. In a cell with n lattice sites an atom must therefore be repeated n times to produce the same atomic surrounding around each site. Example NaCl: 4 sites, 4 Na, 4 Cl.

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Dr. P. Lucas U of A MSE 110 Lattice planes: MILLER INDICES Each different crystalline structure generate different planes in different directions. Each crystalline structure will actually generate a unique set of planes with specific orientations. Because of the periodic nature of crystalline structures, many planes of atoms can be identified in different directions in the crystal lattice.
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