In materials science and chemistry, diffusion is a very important phenomenon. Engineers must understand the general mechanisms and calculations of it to apply heat treatments and other kinds of things correctly. So, here we explain the general information about diffusion and diffusion mechanisms. You will be able to assess which kind of machine you will use in typical heat treatment. The general topics mentioned here;

Table of Contents ;

- Diffusion mechanism.
- Types of them.
- Fick’s Laws to make engineering calculations for practical applications.
- Factors that affect this phenomenon in the general systems.
- General practical applications and heat treatment applications that they use this phenomenon.

As you understand that you can have detailed information about diffusion at the engineering level.

## What is Diffusion?

Diffusion is the movement of atoms between solids, liquids, and gases at an atomic level over time. So, we are using this mechanism in different practical applications.

For example, if we place two solid materials at a specific temperature as touching to each other, atomic diffusion will take place over time. We call this phenomenon **interdiffusion** or **impurity diffusion.**

Also, there is another diffusion mechanism that occurs in the pure atoms that we call interdiffusion. The same atoms replace each other in the pure atoms which are very hard to observe.

You will see that these mechanisms are very important and complex mechanisms that a materials engineer and a mechanical engineer must understand.

## Mechanisms of Diffusion

There are different kinds of mechanisms that diffusion between the atoms takes place. After that, we will be able to assess the general structures and situations of the general heat treatment and other kinds of mechanisms.

In general, diffusion between solid materials takes place as the replacements of the atoms in lattice structures with other atoms from other solids. So, an atom must have sufficient energy to replace this atom. This energy is related to the temperature of the atoms. With the increasing temperature, the vibrations of atoms also increase. With this increment, the total energy increases to replace other atoms.

As you understand, with the increasing temperature, diffusion increases.

If we take a look from the mechanical view, diffusion takes place in two mechanisms; vacancy diffusion and interstitial diffusion. Also, this distinction is the same for atomic impurities and defects.

By understanding these mechanisms, you will be able to learn other important sections in detail.

### Interstitial Diffusion

This is the first type of mechanism that we need to understand. In interstitial diffusion mechanisms, the atoms take the interstitial places in the lattice structures of the host atoms or material. The atoms must be smaller than the lattice atoms to fit inside the interstitial places between the atoms.

The general atoms that interstitially diffuse in other atoms are; oxygen, hydrogen, nitrogen, and carbon. Because their atoms are smaller to fit inside the interstitial positions of the atoms.

Also, their interstitial diffusions take place in the structures of metals in general. This is because their structure has lots of interstitial places and very good host materials for the smaller atoms.

### Vacancy Diffusion

The vacancy mechanism is the general mechanism of the interdiffusion between different materials. So the vacancy diffusion takes place with the vacancies of the host lattices. With the increasing temperatures, the number of vacancies increases, and the energies of atoms increase. So, there is a proportion between the temperature and the vacancy diffusion mechanisms.

There is nearly no importance on the size of the atoms in these mechanisms. Because, with the vacancies, there is enough space for all sizes of atoms. Between the metals, the vacancy mechanism is very common.

## General Types of Diffusion

According to the situations and materials, there are different types of mechanisms that generally take place in most of the diffusions.

### Diffusion Through Grain Boundaries

Grain boundaries are the structures in the crystalline materials that form the boundaries of the crystallite regions. Also, these boundaries form because of the different orientations of the crystals in different sections.

Diffusion through the grain boundaries in crystalline structures is also a very common phenomenon. Because the activation energy of the grain boundaries is lower than the normal crystals.

### Volume Diffusion

We consider the general diffusion mechanisms that atoms go through the surface of the parts. But there is a mechanism that diffusion takes place as the atom migration through the bulk of the material. These kinds of diffusions are not common in general.

### Surface Diffusion

These are the most general types of them. In the surface type, diffusion takes place through a surface or interface between the materials. Also, most of the diffusion calculations are regarding surface diffusion.

## Important Terms about Diffusion Mechanisms

We use diffuson mechanisms in different kinds of engineering systems and practical applications. So, it is very important to have mathematical expressions to use in the different systems.

For example, we are using a term that we call **diffusion flux** which represents the total mass transfer in the number of atoms. We calculate it with the atoms passing through the cross-sectional area per unit of time. We divide it by the area and the total time.

But in some calculations, we consider diffusion as steady-state diffusions. Because most of the time, diffusion is a time-dependent phenomenon. The rate of diffusion can change with the changing time. But if the rate is not changing over time, we call this diffusion phenomenon **steady-state diffusion.**

Also, the concentration of the diffusing atoms decreases with the increasing distance from the contact point of the solids. We can plot **concentration profiles **over the solids to define the rate of diffusion in solids.

Furthermore, in mathematical calculations about diffusion, we use another term the diffusion coefficient which is the square meters per second or feet meters per second in** **English units.** **This is an important term for the direction of the diffusion mechanism.

### Fick’s First Law

We calculate the diffusion flux in diffusion mechanisms with Fick’s First Law of diffusion. With this law, we can calculate the concentrations over the distances in diffusion mechanisms. We use this equation;

In this equation;

- D is the diffusion coefficient which has the unit of m2/s
- C are the concentrations of the elements or atoms in each other which has the unit of kg/m3
- X is the total distance from the contact surface between the materials. The unit meters.

So, if we know the diffusion coefficient and diffusion flux of a mechanism, we can calculate the total concentrations at different distances with Fick’s First Law. But this is only valid for the steady-state diffusion mechanisms.

We generally deal with the transient diffusion mechanisms in engineering. And this First law is only for the theoric applications. To obtain more real calculations and accurate results, it is better to use transient calculations.

## Transient Diffusion Mechanisms

This is the real law of diffusion. The rate of diffusion changes with the changing time. So, we generally deal with the transient diffusion mechanisms in general in our calculations.

The diffusion flux and concentration gradient change with time. For the calculations, we use Ficks’s Second Law.

### Fick’s Second Law

With Fick’s Second Law, we calculate the diffusion characteristics of transient diffusion mechanisms. We use this formula;

This is the approximated equation from the transient equation. We use the error function for the calculation of this value;

You need to choose the equivalent value from the error function table below;

erf(X) | X |
---|---|

0.0282 | 0 |

0.0564 | 0.025 |

0.1125 | 0.05 |

0.1680 | 0.1 |

0.2227 | 0.15 |

0.2763 | 0.20 |

0.3286 | 0.25 |

0.3794 | 0.30 |

0.4284 | 0.35 |

0.4755 | 0.40 |

0.5205 | 0.45 |

0.5633 | 0.50 |

0.6039 | 0.55 |

0.6420 | 0.60 |

0.6778 | 0.65 |

0.7112 | 0.70 |

0.7421 | 0.75 |

0.7707 | 0.80 |

0.7970 | 0.85 |

0.8209 | 0.90 |

0.8427 | 0.95 |

0.8802 | 1 |

0.9103 | 1.0 |

0.9340 | 1.1 |

0.9523 | 1.2 |

0.9661 | 1.3 |

0.9763 | 1.4 |

0.9838 | 1.5 |

0.9891 | 1.6 |

0.9928 | 1.7 |

0.9953 | 1.8 |

0.9981 | 1.9 |

0.9993 | 2 |

0.9998 | 2.4 |

0.9999 | 2.6 |

In this equation, the C0 is the beginning concentration of the solute atoms in the solid. Cs is the surface concentration. And Cx is the concentration at the x distance.

D is the diffusion coefficient and t is the time.

So, you can easily calculate the solutions at the x distance in t time with Fick’s Second Law. For example in the case of hardening and age hardening applications, engineers are using Fick’s Second Law to calculate the concentrations accurately.

## Important Factors on Diffusion

There are different kinds of factors that affect the rate of diffusion. In assessing the general structures of these mechanisms, we need to delve into the factors that affect diffusion.

### Temperature

Temperature is one of the most important factors that affect diffusion. Because, with the increasing temperature, the diffusion increases. Once the temperature increases, the total amount of vacancies and interstitials increases. Also, the energies of the atoms are increases.

The total vibration of atoms increases with the increasing temperatures. So, they are the effects that increase the total mechanism in these systems.

In general, they apply heat treatment applications in elevated temperatures. Because, at elevated temperatures, the diffusion of the materials inside the solids becomes more effective.

### Types of Atoms

There are different kinds of mechanisms between the different atoms. The main importance is the size of the atom. If the size of the atom is small enough, interstitial diffusion takes place with the vacancy mechanism. Also, if the atoms are big enough or nearly same in the size, the general diffusion mechanism is vacancy diffusion.

For example, the size differences between the iron and carbon atoms are very high. Because of it, this mechanism can occur very easily between them. So, iron-carbon alloys are so common in engineering.

### Activation Energy

Activation energy is also a very important value to obtain diffusion motions. As we stated above, with the increasing energies of atoms, the total energies of the atoms increase. Also, there is an activatiıon everywhere the replacements of atoms take place. If the energy of the atoms does not exceed this activation energy, diffusion will not take place.

So with the lower activation energies of atoms in solids, the diffusion will be more effective and at higher rates. And also, with the increasing activation energies, exceeding this energy will be harder and the mechanism will be slower.

Also, we call the substances that decrease the activation energies the catalyzers. With the decreasing activation energy, the mechanism will much more rapid.

### Concentrations of Atoms

The concentration of atoms of the diffusing species is very important also. Because with the increasing concentrations, the diffusing mechanisms increase. The general reason for this, with the increasing concentration, the possibility of placing atoms as vacancies and interstitials increases.

For example in the nitriding and carburizing applications, the atom concentrations are very high. So, it is very important to have very high concentrations to obtain the required surface characteristics.

### Crystal Structures

The type of crystal structure has an şmmense effect on diffusion. It is because of the atomic packing factor. With the increasing atomic packing factor like in FCC and HCP crystalline structures, the mechanism decreases. Because there are lower vacancies between the atoms. This means lower amounts of atoms will diffuse into another one.

Also in the lower atomic packing, the diffusion will be much easier. For example in BCC structures, the packing factor is lower than the other ones.

### Defects and Impurities

Defects and impurities such as dislocations have a very important effect on diffusion. For example, with the increasing angle of tilt between the grains, the diffusion increases.

Also, there are other impurities in the host material, and the mechanism decreases. They are important effects of the impurities.

Furthermore, the grain boundaries provide extra crystal imperfections which provide higher vacancies and higher interstitials. This is the other effect that increases diffusion.

### Grain Size

Grain size is also very important in diffusion. With the increasing grain boundaries in the crystalline structures, the total mechanism increases. This is because the activation energy at the grain boundaries is lower than in the other portions.

So, if the grain size decreases to be finer grains, the total number of grain boundaries increases. And the total diffusion increases.

## Applications of Diffusion

We use diffusion mechanisms in general engineering applications. Because of it, the application of them is very important in terms of engineering. So, it is very important to know the general applications.

### Welding and Brazing

In the welding applications, we combine different metals with the application of very high temperatures and filler materials. In general, welding takes place in the molten situation of the metals. And also, the diffusion between the combined metals is very important in welding. It has a very big effect on the combination of different metals.

Brazing application is also the same as welding operations. These mechanisms are also very important in these joining applications.

### Carburization and Nitriding Heat Treatments

In general, the applications of heat treatments are so common in metallurgy. So, we obtain the materials with desired properties in heat treatment applications. There are lots of kinds of heat treatment applications out there. But we will talk about the most important applications in terms of diffusion.

In the carburization processes or heat treatments, we use carbon gas. The material at high temperatures is held inside the carbon gas environment. And carbon atoms diffuse inside the material interstitially. So, we obtain very hard surface structures in their systems.

For hard gear applications, they apply carburization processes in general. The external teeth of the gears are harder than the internal sides because of the higher carbon concentrations. So, they obtain more wear-resistant structures on the outer surfaces.

Also for low alloy steels, application of the nitriding heat treatment is very common. The principle is the same with the carbon application. And harder surfaces were again obtained with the nitriding.

These two mechanisms are very important in terms of this phenomenon.

### Metal Oxidations

This is not an application, it is a natural phenomenon for the metals that stays in the atmosphere. Furthermore, over time, the oxygen atoms diffuse into the structures of metals, and they form metal oxide layers.

### Semiconductor Production

Semiconductor production is also a very important example. In the production of semiconductors, impurities increase or decrease the electrical resistances of these materials. So, they use diffusion techniques to impart these impurities.

They need strict calculations for the application of the impurities to obtain accurate electrical resistance values.

In electronic circuits, semiconductor technologies are very important. In general, Silicone-based materials are used in the semiconductor industry.

### Age Hardening Processes

Age hardening heat treatment processes are very important to increase the yield strength of malleable metal alloys. So, they become structural materials that we use in mechanical applications.

Diffusion mechanisms are very important in age-hardening processes. This is because there is the application of impurities and precipitates on the volume of the material. So, the strength of the material increases with the application of diffusion.

## Conclusion

As you see above, this topic is a very complex topic that we need to learn about all aspects. There are different types of mechanisms in which the sizes of the atoms have prime importance. And also, these types of them occur in different situations such as in the grain boundaries.

We use Fick’s laws in the strict calculations of compositions and the depths of the compositions. Because in heat treatment applications, we need to know the general types and applications of Fick’s law. Time is also a very important factor. And we define the mechanisms as time-dependent or transient or steady-state. But in most of the practical applications, we use a transient approach.

Also, there are a bunch of factors that affect the mechanisms. We can make changes to these factors to see their effects on practical applications. Among these factors, the most important one is the temperature. With the increasing temperatures, the total energies, and vibrations of atoms increase. So, the ability to replace the atoms increases with the increasing energy.

There are also other effects such as concentrations and activation energies.

As we stated above, there are important practical engineering applications that we use the diffusion mechanisms. Around these applications, heat treatments are the most common ones.

These are the general points about diffusion in mechanical engineering.

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## FAQs

**What is diffusion?**It is a general mechanism that atoms or molecules take the places of other atoms in other materials in different ways. We use them in different kinds of practical applications. The replacement of the atoms takes place with two mechanisms; interstitial and vacancy.

**Why is diffusion important in materials?**Because, in most of the practical applications, we use these mechanisms. For example in the carburizing processes, we apply carbon atoms in a gas environment to the steel parts at high temperatures. So, the carbon atoms diffuse inside the iron that takes the place of the iron atoms. And we obtain harder surface structures.

**How is diffusion used in engineering?**The most important example that we use that phenomenon is heat treatment applications. Applications of nitride and carbon atoms are a very common practice in hardening heat treatment applications. Diffusion of these atoms takes place. Also, welding and brazing are very important mechanisms for the diffusion of the metals between each other take place. Diffusion is a very important mechanism in welding and brazing applications.

**How does diffusion occur in materials?**Diffusion takes place in materials in two different ways. The first one is the interstitial type. In this mechanism, the smaller atoms such as carbın and oxygen are placed in the little places of crystal lattices of metals. Because their sizes are smaller than the metals. And also, the second way is a vacancy. There are vacancies in the lattice structures of materials, and other atoms are placed in these vacancies.

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