What are Crystalline Imperfections?

The crystalline imperfections are described as the geometrical defects in the crystal due to incorrect arrangement of atoms, impurity, vacancy, and many more. It is not possible to achieve a perfect or ideal crystal, practically.

Classification of crystalline Imperfections

The crystalline imperfections based on dimensionality are classified as:

• Point defect
• Line defect
• Surface or area defect
• Volume defect

Point defect

The point defect is a zero-dimensional defect that indicates a point irregularity in a crystalline substance. The point defect mainly occurs due to the fast crystallization process. It occurs due to the false arrangement of particles in crystalline solid.

What is the formula for the number of imperfections in a crystal?

The formula for the number of imperfections in a crystal is as follows:

$n=N{e}^{\left(\frac{-{E}_{d}}{{k}_{b}T}\right)}$

Here, n is the number of imperfections, N is the number of atomic sites per mole,

${E}_{d}$ is free energy required to form defects,

${k}_{b}$ is the Boltzmann's constant, and T is the absolute temperature.

Following are the various types of point defects:

• Vacancy defect
• Interstitial defect
• Schottky defect
• Frenkel defect

Vacancy defect

The vacancy defect is developed in a crystalline substance due to the vacant atomic site inside the crystal. It mainly occurs due to imperfect packing during crystallization. The vacancy defect results in decreasing the density of the material. The number of vacancy defects is a function of temperature. The representation of vacancy defect is shown as:

Interstitial defect

The interstitial defect is developed in a crystalline substance due to the extra atom in the atomic site of the crystal. The interstitial defect causes atomic distortion, increasing the system's density. The interstitial defect is also called the inverse of a vacancy defect.

The representation of interstitial defect is shown as:

Schottky defect

In the Schottky defect, an equal pair of cations and anions is absent inside the crystal lattice, creating an equal number of cation and anion vacancies in the crystal. The Schottky defect also decreases the density of atomic crystal. In the Schottky defect, the atomic crystal is electrically neutral because of an equal number of cations and anions missing.

The diagrammatical representation of the Schottky defect is shown as:

Frenkel defect

In Frenkel defect, cations dislocate from their lattice site to the interstitial site in the crystal structure. In the Frenkel defect, there is no change in the density of the crystal structure. It is observed when cations and anions differ in their sizes. Frenkel defect is commonly found in ionic solids of low co-ordinate number.

The diagrammatical representation of the Frenkel defect is shown as:

Line defect

The line defect is a one-dimensional defect that indicates a line of atoms' irregularity in a crystalline substance. In the line defect, the interatomic bonds are distorted near the dislocation line, which directly affects the crystal structure's mechanical properties.

Following are the various types of line defects:

• Edge dislocation
• Screw dislocation
• Mixed dislocation

Edge dislocation

In edge dislocation, an extra plane of atoms is added to the crystal structure. The burger vector and dislocation line are perpendicular to each other in edge dislocation.

The diagrammatical representation of edge dislocation is shown as:

Screw dislocation

In screw dislocation, one crystal region is shifted one atomic distance to another region caused by shear stress. The burger vector and dislocation line are parallel to each other in screw dislocation.

The diagrammatical representation of screw dislocation is shown as:

Mixed dislocation

In mixed dislocation, both edge dislocation and screw dislocation is present in the crystal structure. In mixed dislocation, the line direction and Burger vector are neither perpendicular nor parallel to each other.

The diagrammatical representation of mixed dislocation is shown as:

What are surface and volume defects?

Surface defect

The surface defect is a two-dimensional crystal defect that occurs mainly due to variation in stacking of atomic plane on or across the crystal structure boundary.

Following are the various types of surface defects:

• External Surface Imperfection
• Internal Surface Imperfection

External surface imperfection

The imperfection shown by the boundary of the crystal structure is known as external surface imperfection. In external surface imperfection, the surface atoms are not surrounded by any other atoms; therefore, they have higher energy than the internal atoms of the crystal.

Internal surface imperfection

The imperfection that occurs inside the crystal structure is known as internal surface imperfection. Internal surface imperfection is occurred due to grain boundaries, tilt & twin boundaries, and stacking faults.

Volume defect

The volume defect is a three-dimensional imperfection in the crystal structure. It occurs due to small dissimilarities between stacking sequence, presence of large vacancy or voids, inclusions or impurity present, and others.

Common Mistakes

• Sometimes, students forget the dimensions of various defects or imperfections in the crystalline structure.
• Sometimes, students get confused that either a pair of ions or a single ion varies in crystal structure rather than an ideal crystal structure.
• Sometimes, students get confused between the dislocation line and burger vector directions in edge and screw dislocation.

Context and Applications

• Bachelors of Technology in Mechanical Engineering
• Bachelors of Technology in Civil Engineering
• Bachelors of Technology in Material Engineering
• Masters in Technology in Material Science
• Doctor of philosophy in Material Science
• Defects in Solids
• Properties of Solid based on crystal structure
• Relationship of dislocation and Plasticity
• Nature of Solid

Practice Problems

Q1. Which of the following imperfection is called 3-dimensional imperfection?

1. Point Defect
2. Line Defect
3. Surface Defect
4. Volume Defect

Correct option- (d)

Explanation: The volume defect is also known as a three-dimensional defect. On the other hand, the point defects and line defects are one and two-dimensional (2D) defects, respectively.

Q2. The defect in which equal number of ion pairs are absent in crystal structure is known as ______?

1. Schottky defect

2. Frenkel Defect

3. Edge Dislocation

4. Mixed Dislocation

Correct option- (a)

Explanation: In the Schottky defect, an equal pair of cations and anions is absent inside the crystal lattice, creating an equal number of cation and anion vacancies in the crystal.

Q3. Which of the following dislocation, the direction of dislocation line and burger vector is perpendicular to each other?

1. Screw Dislocation

2. Edge Dislocation

3. Mixed Dislocation

4. None of these

Correct option- (b)

Explanation: The direction of the dislocation line and burger vector is perpendicular to each other in edge dislocation, while in screw dislocation, they are parallel to each other.

Q4. The formula for the number of imperfections in crystal lattice is?

1. $n=N{e}^{\left(\frac{-{E}_{d}}{{k}_{b}T}\right)}$

2. $n=N\mathrm{ln}\left(\frac{-{E}_{d}}{{k}_{b}T}\right)$

3. $n=N{e}^{\left(\frac{-2{E}_{d}}{{k}_{b}T}\right)}$

4. $n=2N{e}^{\left(\frac{-{E}_{d}}{{k}_{b}T}\right)}$

Correct option- (a)

Explanation: The relation of the number of imperfections in crystal lattice is given by,

$n=N{e}^{\left(\frac{-{E}_{d}}{{k}_{b}T}\right)}$

Q5. Which of the following imperfection is produced by grain boundaries?

1. Point Imperfection

2. Internal Surface Imperfection

3. External Surface Imperfection

4. None of these

Correct option- (b)

Explanation: Internal surface imperfection occurs due to grain boundaries, tilt & twin boundaries, and stacking faults.

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Crystalline Imperfections

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