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# section%2040.2 - Chapter 4 Atomic Arrangements in Solids...

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Chapter 4: Atomic Arrangements in Solids 4.2 Unit Cells Objectives Draw and identify common unit cells. Calculate quantities associated with unit cells. In a crystal, the atoms form a repeating, periodic array. What is meant by a periodic array? We will start by looking at some art. M.C Escher was an Dutch artist who lived from 1898 to 1972. He is mostly famous for his pictures that depict physically impossible situations. One example is shown in Figure 4.2.1 Figure 4.2.1: Waterfall, created in 1961 by M.C. Escher. Follow the path of the water to see why this image depicts a physically impossible situation. Escher is also famous for his tessellations, which are images which show a regular repeating pattern. Figure 4.2.2 shows an example of a tessellation. One way to create a tessellation is to make a stamp of the smallest unique piece of the pattern and then use that stamp to make the whole picture (although this is not how Escher did it). The red box in Figure 4.2.2 shows one possible stamp, although there are many others. The green box shows how the stamp can be used to create the whole image. You should notice that what is in the two boxes is identical. Also notice how some of the lizards are not in a single box. Instead they are shared by several boxes. A periodic array is just an arrangement of objects that repeats in this way. You can create the entire group of objects by creating a stamp of the smallest unique piece of the group and then using that stamp to create the entire group. At the atomic level a crystal is just like Escher’s tessellations, except that it is in three dimensions and the objects are atoms. The unit cell of a crystal is a piece of the crystal that repeats throughout the whole material. We can think of the unit cell as a three dimensional stamp that can be used to create the entire

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