Reference no: EM132554248
Crystal Structures Use the visualization tool found at https://atom.calpoly.edu/crystal/
Drawing Z-diagrams
Drawing in 3D is difficult, so scientists use z-diagrams to represent different layers of the crystalline arrangement on the paper, in 2D. A Z-diagram is a 2D representation of the 3D shape of the unit cell. Each layer is labeled as z = #, where # is a value between 0 and 1 to distinguish the ordering of the layers. The number is going up in evenly divided increments until reaching the z = 1 layer. For example, if the pattern has 5 layers, they would be labeled z = 0, z = ¼, z = ½, z = ¾, z = 1. To come up with the layers, the unit cell is imagined to be on the axis system and is then cut perpendicularly to the z-axis. The lowest layer z=0 represents the lowest plane where the centers of the lower plane of spheres lie, z=1 represents the upper plane of spheres.
You will notice that if drawn correctly every z-diagram, z = 0 and z = 1 layers are exactly the same. There might be others as well. So, instead of drawing these repeat layers twice, we label one layer to represent both the top and the bottom one. The bottom/top layer would thus be labeled z = 0, 1.
1. How many distinct layers does the smallest repeated cube for SC have?
2. How many distinct layers does the smallest repeated cube for BCC have?
3. How many distinct layers does the smallest repeated cube for FCC have? Your LAs should have a model of this, be sure to check with them before moving on.
4. For each layer of the SC pattern, draw the z-diagram projection. Be sure to label the layers.
5. For each layer of the FCC pattern, draw the z-diagram projection. Be sure to label the layers.
6. For each layer of the BCC pattern, draw the z-diagram projection. Be sure to label the layers.
7. The picture below is the simplest repeating pattern for a lattice structure. Draw the z-diagram for it.
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