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What is the coordination number and the packing efficiency of copper atoms in a face-centered cubic (FCC) crystal structure?

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In a face-centered cubic  FCC  crystal structure, each atom is surrounded by 12 other atoms. Therefore, the coordination number for copper atoms in an FCC structure is 12.To calculate the packing efficiency, we need to determine the volume of atoms in the unit cell and divide it by the total volume of the unit cell. In an FCC structure, there are 4 atoms per unit cell  1/8 of an atom at each corner and 1/2 of an atom on each face .The atomic radius  r  of copper is 1.28 . The edge length  a  of the unit cell can be related to the atomic radius through the following equation:a = 22 * rSubstituting the value of r:a = 22 * 1.28   3.61 Now, we can calculate the volume of the unit cell  V_cell :V_cell = a =  3.61    47.19 The volume of one copper atom  V_atom  can be calculated using the formula for the volume of a sphere:V_atom =  4/3 r =  4/3  1.28    8.77 Since there are 4 atoms per unit cell, the total volume of atoms in the unit cell  V_atoms  is:V_atoms = 4 * V_atom = 4 * 8.77   35.08 Finally, we can calculate the packing efficiency:Packing efficiency =  V_atoms / V_cell  * 100 =  35.08  / 47.19   * 100  74.4%So, the coordination number of copper atoms in an FCC crystal structure is 12, and the packing efficiency is approximately 74.4%.
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