Calculate the fraction of atom sites that are vacant.

Understand the Problem

The question is asking to determine the proportion of atom sites that do not have atoms, meaning we need to calculate the fraction of vacancies in a given lattice or structure. This typically involves knowing the total number of sites and the number of vacancies.

Answer

The fraction of vacancies is given by $ \frac{N_{\text{vacancies}}}{N_{\text{total}}} $.

Steps to Solve

Identify the total number of sites
First, we need to identify the total number of atomic sites in the lattice structure. Let's denote this as $N_{\text{total}}$.
Determine the number of vacancies
Next, we need the number of vacancies present in the lattice, which we will denote as $N_{\text{vacancies}}$.
Calculate the fraction of vacancies
We can find the fraction of vacancies by dividing the number of vacancies by the total number of sites. This can be represented as:
$$ \text{Fraction of vacancies} = \frac{N_{\text{vacancies}}}{N_{\text{total}}} $$
Express as a percentage (if needed)
If the problem requires the result to be expressed as a percentage, multiply the fraction by 100:
$$ \text{Percentage of vacancies} = \left( \frac{N_{\text{vacancies}}}{N_{\text{total}}} \right) \times 100 $$

The proportion of atom sites that do not have atoms (vacancies) is given by
$$ \text{Fraction of vacancies} = \frac{N_{\text{vacancies}}}{N_{\text{total}}}. $$

More Information

The fraction of vacancies is essential in materials science, helping in understanding the properties of materials such as strength, conductivity, and diffusion. High vacancy concentrations can affect the structural integrity of materials.

Tips

Not correctly identifying the total number of sites and vacancies can lead to incorrect calculations of the fraction. It's crucial to double-check these values.
Forgetting to convert the fraction to a percentage when specified in the question.

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