# Finding the concentrations of vacancies and interstitials

• Tom Weaver
In summary, at 300 K, the equilibrium concentration of vacancies and interstitials in a two-dimensional ionic crystal with a primitive hexagonal lattice is effectively zero, due to the high defect creation energies of 10eV and 8eV. This means that all defects in the crystal are intrinsic and do not contribute to the overall concentration. Despite this, defects still exist in crystals due to factors such as crystal growth conditions or external stresses.
Tom Weaver
Consider a two-dimensional ionic crystal with a primitive hexagonal lattice. The energy needed to create a Frenkel defect pair is 10eV, and Schottky defect formation costs 8eV.
Calculate the concentration of vacancies and interstitials in the crystal at 300 K, assuming that all defects are intrinsic.

n/N=e-(Edef/kbT)
Where: n = number of defects
N = number of atoms in the crystal
Edef = defect creation energy
kb = Boltzman's constant
T = temperature

I've tried using 10eV and 8eV as the defect creation energy however this equals to an answer smaller than *10-100, unsure how to progress.

That is correct. The equilibrium concentration for those defects at room temperature is effectively zero.

Why do we still have those defects in crystals?

## 1. What are vacancies and interstitials?

Vacancies and interstitials are types of defects in the crystal lattice of a material. Vacancies are empty spaces where an atom should be, while interstitials are atoms that are located in between the regular lattice positions.

## 2. Why is it important to find the concentrations of vacancies and interstitials?

Knowing the concentrations of vacancies and interstitials is crucial for understanding the properties and behaviors of materials. These defects can affect the strength, conductivity, and other physical and chemical properties of a material.

## 3. How can the concentrations of vacancies and interstitials be determined?

The concentrations of vacancies and interstitials can be determined through various experimental techniques, such as X-ray diffraction, transmission electron microscopy, and positron annihilation spectroscopy. These methods involve analyzing the changes in the crystal structure caused by the presence of defects.

## 4. What factors can affect the concentrations of vacancies and interstitials in a material?

The concentrations of vacancies and interstitials can be influenced by factors such as temperature, pressure, and the type of material. Increasing the temperature, for example, can lead to an increase in the number of vacancies and a decrease in the number of interstitials.

## 5. Can the concentrations of vacancies and interstitials be controlled?

In some cases, it is possible to control the concentrations of vacancies and interstitials in a material through processes such as annealing or doping. However, in most cases, these defects are inherent in the material and cannot be completely eliminated.

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