What is the packing efficiency of a body-centered cubic (BCC) structure? (2020)

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Q: What is the packing efficiency of a body-centered cubic (BCC) structure? (2020)

Solution: The packing efficiency of a body-centered cubic (BCC) structure is approximately 68%.

Steps: 8

Step 1: Understand what packing efficiency means. It is the fraction of volume in a crystal structure that is occupied by the atoms.
Step 2: Identify the structure type. In this case, we are looking at a body-centered cubic (BCC) structure.
Step 3: Know the arrangement of atoms in BCC. In BCC, there is one atom at each corner of the cube and one atom in the center.
Step 4: Calculate the total number of atoms in a BCC unit cell. There are 8 corner atoms (each contributing 1/8 of an atom) and 1 center atom, which gives a total of 2 atoms per unit cell.
Step 5: Calculate the volume occupied by the atoms. The volume of one atom can be calculated using the formula for the volume of a sphere (V = 4/3 * π * r^3). Multiply this by the number of atoms (2) to get the total volume occupied by the atoms.
Step 6: Calculate the volume of the unit cell. The volume of the cube is given by the formula (edge length)^3.
Step 7: Divide the total volume occupied by the atoms by the volume of the unit cell to find the packing efficiency.
Step 8: Convert the result into a percentage to express the packing efficiency.