_______ layering pattern will have a void fraction of 0.260?

Answer

To determine which layering pattern has a void fraction of 0.260, we can follow these steps:

### Step 1: Understand Void Fraction
The void fraction is defined as the fraction of volume that is not occupied by the solid particles in a packing arrangement. It can be calculated using the formula:
\[ \text{Void Fraction} = 1 - \text{Packing Efficiency} \]

### Step 2: Identify the Packing Efficiency
The packing efficiency is the fraction of volume occupied by the particles. For different types of packing, the packing efficiencies vary:
- Simple cubic packing: 52%
- Body-centered cubic (BCC): 68%
- Face-centered cubic (FCC) or cubic close packing (CCP): 74%

### Step 3: Calculate the Void Fraction for FCC
Since we are looking for a void fraction of 0.260, we can rearrange the void fraction formula:
\[ \text{Void Fraction} = 1 - \text{Packing Efficiency} \]
Substituting the packing efficiency for FCC:
\[ 0.260 = 1 - 0.74 \]

### Step 4: Verify the Calculation
Calculating the right side:
\[ 1 - 0.74 = 0.26 \]
This confirms that the void fraction of 0.260 corresponds to a packing arrangement with a packing efficiency of 74%.

### Step 5: Identify the Layering Pattern
The layering pattern that corresponds to a packing efficiency of 74% is the cubic close packing (CCP) or face-centered cubic (FCC). The arrangement typically follows the ABCABC... pattern.

### Conclusion
The layering pattern that will have a void fraction of 0.260 is **cubic close packing (CCP)**.

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