## What is atomic diffusion in solids?

In material science, diffusion can take place in solid, liquid, and gases. In solids, atomic diffusion can take place with the help of thermally activated and randomly vibrating atoms. The atomic diffusion in solids is complex and very slow in comparison to atomic diffusion in liquids and gases because the interatomic distance between the atoms is smaller in solids as compared to liquids and gases.

## What are the different types of atomic diffusion in solids?

There are different types of atomic diffusion mechanisms in solids: inter-diffusion, vacancy diffusion, interstitial diffusion, and self-diffusion. The phase transformations depend on the factor lattice site. The basic details about these types of atomic diffusion in solids are given below.

### Inter diffusion

In the formation of an alloy, atoms move from a region of higher concentration to lower concentration in a particular time period. The thermally activated atoms move randomly and occupy the interstitial position in the matrix of the lattice. The inter-diffusion in the alloy of copper and nickel is presented in the figure below:

### Vacancy diffusion

The term vacancy diffusion is also known as substitutional diffusion. It applies to substitutional impurities, and in this type of diffusion, substitutional atoms exchange with the vacancies in the lattice structure of the alloy. The rate of vacancy diffusion depends on various factors like the number of vacancies, activation energy of atoms, etc.

The term activation energy represents the amount of energy (minimum) required for a specific chemical reaction. If the activation energy is high, then the rate of atomic diffusion in solids is also high. The representation of vacancy diffusion is given in the diagram below:

### Interstitial diffusion

In this type of diffusion process solute atoms that are smaller in size occupy interstitial sites by jumping from one site to another. The rate of interstitial diffusion is faster than the vacancy diffusion because interstitial atoms are small and they move fast. The bonding between the interstitial atoms and surrounding atoms is weak. The representation of interstitial diffusion is given in the following diagram.

### Self diffusion

The term self-diffusion itself indicates the type of diffusion in which the diffusion of atoms in a solid matrix of material takes place by itself. Whenever the diffusion of atoms in a solid material takes place without any external means, this diffusion process is called as self-diffusion. Self-diffusion depends on the factor grain boundary. If the grain boundary allows smooth movement to atoms in the parent matrix then the rate of diffusion would be more.

The grain boundary of different materials is of different types.

## Steady state diffusion

The term steady-state diffusion indicates that the rate of diffusion is independent of time. Mathematically it can be represented in terms of the diffusion coefficient and concentration.

$J=-D\frac{dC}{dX}$

Here, $D$ represents the diffusion coefficient, $dC$ represents the change in concentration, and $dX$ represents the change in linear position.

The value of slope $\frac{dC}{dX}$ must be constant for steady-state diffusion. The profile of the diffusion rate in solids for steady-state diffusion is linear, representing the constant rate of diffusion of atoms in solids. The profile of the rate of diffusion for steady-state diffusion is represented in the steps below.

## Non steady state diffusion

The term non-steady-state diffusion indicates that the rate of diffusion is dependent on time. The governing equation of non-steady-state diffusion can be represented in the form of a mathematical expression.

$\frac{dC}{dt}=D\frac{{d}^{2}C}{d{x}^{2}}$

The concentration of diffusing atoms is a function of time as well as a function of position. As the time and position varies, the rate of diffusion in solids also varies. The profile of rate of diffusion in non-steady state diffusion in solids is not a linear one; it is a parabolic type. As the time increases, the slope of the profile of non-steady-state diffusion in solids starts to decrease.

## Factors affecting diffusion

Many factors affect the rate of atomic diffusion in solids. Some of the factors that affect the rate of atomic diffusion in solids are explained below.

### Diffusing atoms

If the diffusing atoms have a better ability to occupy interstitial sites, then the diffusing atoms can easily diffuse with the parent matrix or atoms. If the size of substitution atoms is approximately equal to the size of the parent atoms of the matrix, then the substitution diffusion would be an easier one.

### Temperature

The atomic vibrations in a metal matrix can be obtained with the help of temperature increment. If the temperature of the matrix increases, then the atomic vibration speeds up, resulting in an increment in the rate of atomic diffusion in solids.

### Lattice Structure

The rate of diffusion is faster in open lattice structures in comparison to the closed lattice structure. In the closed lattice structure, the gap between the atoms is much less than that in an open lattice structure. In the open lattice structure, the movement of atoms is easier, whereas the movement of atoms in a closed lattice structure is difficult.

### Defects

The presence of defects like dislocations, grain boundaries, etc., provides a path to the diffusing atoms with the parent matrix atoms. The rate of diffusion is fast if the lattice structure has defects. So, if a material's lattice structure has many defects then the rate of atomic diffusion in the lattice structure would be more.

### Annealing

Whenever a solid object is annealed, a fine refinement of atoms takes place, resulting in a decrement in the inter atomic gap between the atoms of the material's lattice. It reduces the rate of atomic diffusion in solids.

### Impurity

Impurity provides passage for the movement of atoms in solids. If the impurity is more in a lattice structure, then the rate of atomic diffusion in solids would be more.

## Diffusivity

The term diffusivity is used for the measurement of the rate of diffusion of atoms in any medium. The rate at which an atom spreads or distributes into a medium is referred to as diffusivity. The measurement of diffusivity varies with respect to different mediums. Generally, two types of diffusivity are mass diffusivity and thermal diffusivity. For the atomic diffusion in solids, mass diffusivity are used.

## Common Mistakes

- Sometimes students get confused about the possibility of atomic diffusion in solids because the students consider that the atoms in solids can not move. They assume that the diffusion process can happen in liquids and gases. However, diffusion in solids is also possible with the help of thermal activation.

- Sometimes students may be confused about the strength of matrix/alloy after atomic diffusion compared to the strength of alloy/matrix before atomic dislocation.

- In the context of the rate of diffusion in solids and the rate of diffusion in liquids and gasses, students get confused about why the rate of diffusion is faster in liquids and gases compared to solids. However, in liquids and gas, the inter atomic gap between the atoms is larger compared to those of solids. So, the rate of diffusion in solid is slower.

## Context and Applications

The topic of atomic diffusion in solids is very much significant in the several professional exams and courses for undergraduate, Diploma level, graduate, postgraduate. For example:

- Bachelor of Technology in Materials Engineering
- Bachelor of Technology in Mechanical Engineering
- Bachelor of Technology in Civil Engineering
- Master of Technology in Mechanical Engineering
- Doctor of Philosophy in Mechanical Engineering
- Diploma in Mechanical and Civil engineering

## Related Concepts

- Diffusion in liquids
- Diffusion in gases
- Fick's law
- Concentration Profile
- Diffusion mechanism
- Grain boundary formation
- Lattice site
- Phase transformations
- Crystal lattice
- Activation Energy

## Practice Problems

Q1. What is the rate of diffusion in solids in comparison to diffusion in liquids and gases?

- Slower
- Faster
- Same
- None of these

**Correct option: (a)**

Explanation: The rate of diffusion in solids is slower, when compared to that in liquids and gases.

Q 2. What is the governing equation for steady-state atomic diffusion in solids?

a. $J=-D\frac{dC}{dx}$

b. $J=D\frac{dC}{dx}$

c. $J=\frac{1}{D}\frac{dC}{dx}$

d. $J=-\frac{1}{D}\frac{dC}{dx}$

**Correct option: (a)**

Explanation: 𝐽=–𝐷(𝑑𝐶/𝑑𝑋) is the equation which represents the steady-state atomic diffusion in solids.

Q.3 What is the mode of atomic diffusion in solids?

- Ionic atoms
- Thermally activated atoms
- Both (a) and (b)
- None of these

**Correct option: (b)**

Explanation: Atomic diffusion in solids is a result of thermally activated atoms.

Q.4 What is the slope of the concentration profile of the steady state diffusion in solids?

- Parabolic
- Cubic
- Linear
- None of these

**Correct option: (c)**

Explanation: The slope of the concentration profile of the steady state diffusion in solids is linear.

Q.5 What is/are the variables at which non-steady state diffusion in solids depends?

- Time and position
- Time and concentration
- Concentration and position
- Only position

**Correct option: (a)**

Explanation: Non-steady state diffusion in solids depends on time and position.

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