Dislocations 2

This piece is a continuation of my previous article on the same subject. The aim of this article is to overcome some of the shortcomings of the previous articles in terms of the lack of illustrations (which we all know are more effective, since “A picture is worth a

thousand words.”) and also, I will try to go beyond the level at which the other writing stopped.

First, I would like to explain, with the help of pictures, the structures of the edge and the screw dislocation. The pictures below show what they look like.

 Sample ImageSample Image

Fig 1 An Edge (left) and a Screw Dislocation

The image on the left is an edge dislocation, while the one on the right is a screw dislocation. These are two extreme kinds of dislocations, other dislocations, and most dislocations we observe are of a mixed character, that is they have both an edge and a screw component.

As you can easily observe in the pictures, the edge dislocation is formed from the insertion of an extra half plane into the crystal lattice, while the screw dislocation is made by the relative shearing of the atoms within the crystal.

As is evident from the pictures, the disturbance in the atomic positions is localized, and the crystal adopts the normal atomic position at a large distance from the dislocation. How does a dislocation then arise within a crystal? Well, in our universe, where the laws of physics as we know them are valid, any system reaches equilibrium when it attains a state of minimum potential energy. The presence of potential energy in a system indicates an ability to do work, and whenever that ability is present, the system does work. However, there are present, almost always, certain physical, and thus energetic barriers to the doing of this work. If the system has adequate potential energy to overcome this barrier, it is able to do work. Otherwise, it remains in its state of equilibrium. The formation of a dislocation is also a method of minimizing the energy of the crystal system. When the crystal formed from a melt, or some other amorphous or crystalline form, there may have been some stresses. If the formation of a dislocation would relieve this stress, then a dislocation would form, and thus reduce the total potential energy of the system.

In my previous article, I also mentioned that the presence of dislocations causes a reduction in the strength of metals, and thus renders them ductile enough that we may form them easily. I will now explain, partly though analogy, how this happens. Even though the dislocation was formed in order to reduce the strain energy of the crystal, the dislocation has, associated with itself, a certain amount if strain energy. A perfect crystal lattice, on the other hand has none. Therefore, when an external stress is applied, a perfect crystal lattice requires a higher stress to reach the energy level at which deformation can start occurring. However, the presence of the dislocation increases the internal strain energy of the crystal, and a relatively small stress is enough to start the movement of atoms within the crystal to cause deformation.

The previous paragraph may be somewhat difficult to follow for those readers who are not that comfortable with this concept of potential and strain energy. If you are such a reader, then I hope that this analogy will serve to form a good picture of the situation. In crystals, the mechanism by which deformation occurs is known as slip. The simple reason for this name is that we consider the dislocations to slip over a certain plane and this results in an overall deformation. To explain with the help of an analogy, take the example of a heavy carpet lying on the floor. In order to move this carpet by two inches, you try to pull it one of its ends. From common experience we know that this is quite difficult because of the friction that the carpet has with the floor. Moving it by even a small distance requires a large amount of effort. Instead of pulling it so, you could also just pinch the carpet a little bit and create a small hump which extends throughout the length of the carpet, parallel to one of its sides. Now you may push this hump easily from one side to the other, and if the span of the hump was two inches, then viola! Your carpet has moved by the required two inches, and you’re not too tired at the end of the exercise too. The crystal is like the carpet and the dislocation is exactly like this hump. The plane of the crystal over which the slip occurs is called the slip plane.

The above analogy is also very useful in forming a very handy definition of a dislocation. A dislocation is also defined as the boundary between a slipped and unslipped region in a crystal. By using this definition, we arrive at several useful properties of a dislocation. One of the very useful results of this definition is that a dislocation cannot end abruptly within a crystal. It must end either at a foreign particle within the crystal, or at the grain boundary, or even at another dislocation, but never abruptly within the crystal. The dislocation may even form a loop, and these dislocations loops are observed quite often. These loops often act as sources of more dislocations. The most commonly quoted dislocation loop is the Frank-Read source, which keeps generating more dislocations, while it remains intact.

Most of the other results are out of the scope of this article, but the interested reader may refer to the book by Johannes and Julia Weertman, “Elementary Dislocation Theory” to learn more. For the more mathematically inclined reader, I would suggest “Theory of Dislocations” by John Price Hirth.

Read Dislocation 1 at https://medhajournal.com/content/view/267/83/

 

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