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# section%204.4 - 4.4 Planes and Directions in Crystals...

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4.4 Planes and Directions in Crystals. Objectives Calculate linear density. Calculate planar density. List members of families of directions and planes. Identify close-packed directions, close-packed planes. Many properties of materials depend on the packing of the atoms. Bulk properties, like density, depend on the packing in three dimensions, as we saw in Section 4.2. However, other properties depend on the packing in a particular plane or along a particular direction. For example, the stiffness of a perfect single crystal of copper depends on which direction the modulus is measured in: it varies from 67 GPa in the [100] direction, to 130 GPa in the [110] direction, to 191 GPa in the [111] direction – the stiffness triples just by changing which way we pull on it! The packing of atoms in a direction is called the linear density ; the packing of atoms on a plane is the planar density . The next sets of questions will guide you on how to calculate these quantities. Figure 4.4.1: Example for GI questions 4.4.1-4.4.5. GI 4.4.1 How long is the line shown in Figure 4.4.1 in terms of the lattice parameter?

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section%204.4 - 4.4 Planes and Directions in Crystals...

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