You are here: Material Science/Chapter 1/Material Defects

You might have thought that, based on our previous discussion, that metal crystal structures are perfect, in the sense that every unit cell has the correct number of atoms, in the correct places. I’ve lead you astray, and for that I apologize. But I had to give you that impression, so that we could begin with the idealistic view and then begin to break it down to the real world.

Materials aren’t perfect; far from it. This section is dedicated to discussing some common defects, and why we’re bothering to investigate them. Actually, they’re quite important.  Materials can behave very, very differently if they’ve got some “errors” in their crystal structure –  what we call imperfections or impurities.  Most materials have a large number of imperfections.  But don’t get the wrong idea from the term imperfections; although that sounds negative, very often it can benefit the performance of the material and us humans will purposely add them to the material to suit our needs.

Point Defects

Vacancy Defect

What is the simplest defect that you can think of in a unit cell?  The simplest defect is just a missing atom.  An atom that simply is not present in the unit cell.  Vanished.  This type of defect is called a vacancy, and belongs to a category of defects called point defects.  Point defects are the type of defect when one (or two) atomic positions get bungled up.  We’ll also look at line defects (1D) and boundary defects (2D).  Not only are vacancies present in all crystalline solid materials, they are actually necessary – something to do with thermodynamics and entropy, or randomness – not important.  Just know that a vacancy is a missing atom, and there will always be vacancies.

Heating a metal will increase the number of vacancies.  How common are vacancies?  Imagine heating some metal to just below it’s melting temperature.  It’s still a solid, but it’s extremely hot.  On average, for every 10,000 atoms, only one will be missing.  Although all of the atoms are held into place and supported by neighbouring atoms, the missing atom doesn’t cause the crystal structure to collapse – it maintains it’s shape. In fact, neighbouring atoms may move away from the vacancy, closer to neighbouring atoms that they are bonded with.

Interstitial Defect

Just as there can be one missing, there can one too many. An extra atom can squeeze itself into one of the spaces between the other atoms in the unit cell. This is called an interstitial defect. Since it’s a defect concerning an atom, it’s categorized as a point defect, just like the vacancy. Of course, there isn’t supposed to be an atom in that space and it doesn’t really have room for it, so it creates a disruption in the crystal structure that affects neighbouring atoms.  Self-interstitials are interstitial atoms that are the same type as the rest of the crystal structure. If we were talking about Iron (Fe) then the extra atom would also be Iron.  Mostly, with self interstitials, the atoms are too big to squeeze into an empty space in the unit cell. So instead, the extra atom sort of shares a spot with an atom that was already in the crystal structure. So then both of the atoms are kind of in the wrong spot.  An example would be if two atoms share the same lattice center space in the BCC crystal structure. This is known as a split structure – the two atoms split, or share, the site.  The original lattice site is usually pretty much in the exact middle of the two atoms sharing the spot. Sort of like if you’re in a five seat car with six people, and you’re sharing a back seat with a friend, and you both take up half the seat.

Sometimes, the interstitial atom isn’t the same type. Often it is smaller, so it can squeeze into small spaces in the lattice without sharing a lattice site with an original atom. If we look at the car seat analogy again, it would be like having a cat in the car that is filled with 5 people. The cat could really fit in anywhere, but it wouldn’t take up a seat. It could sit on someone’s lap, or you could just, maybe, you know, put it in the trunk.  These atoms are located at true off-lattice sites, ‘in the middle of nowhere’.  These types of interstitials are called impurity interstitials.  There is also the case where the impurity interstitial atom is similar in size to the rest of the atoms in the structure but not the same type. In this case it will most likely have to share a lattice site instead of fitting into a small non-lattice site.

Although they are a type of defect, impurity interstitials can be extremely beneficial. We’ll see that impurity interstitials are of huge, huge importance in materials science. We use them all the time to change the properties of materials, and the big one is steel. We have so many different strengths of steel available to use, and impurity atoms play a huge role in this.

Frenkel Defect

Now here’s something interesting. An atom originally in the crystal structure can actually move into an interstitial site – thereby simultaneously creating a vacancy and an interstitial defect.  This called a Frenkel defect.

Line Defects (1D)

Discussed above were point defects, or 1D defects, because they just involved an atom or two. Now we can discuss line defects, which are 2D. They are defects involving an entire row of atoms.  What I think is the simplest line defect is called an edge dislocation. This is basic – just an extra half sheet of atoms that causes the crystal structure to be uneven.  A drawing easily explains this one. Because there shouldn’t be this extra half sheet, the atoms tend to be a bit squished on the half where the extra sheet occurs. And then in the other half that doesn’t contain the extra sheet, the crystal structure is kind of stretched as the atomic structure tries to make room.  So the crystal structure ‘bends’ around the extra sheet to make room for it. Think of a stack of 10 pieces of paper. Then cut a sheet in half and insert it into the stack. On the top edge, there will be 11 sheets, and on the bottom, 10 sheets. In the middle, the papers bend to accommodate the extra half sheet – and you’ll notice a bulge in the middle of the stack, at the ‘edge’ of the half-sheet of atoms. Thus, an edge dislocation.

The length of the dislocation can be measured. Essentially, it’s the width of the row of atoms. This length is called the Bergers vector. Materials science textbooks will try to confuse you about this. It’s not hard. Here, I’ll draw you one right now:

Another type is called a screw dislocation, which is a little bit more difficult to explain, but again, drawings will help. The short explanation is that within the crystal structure, a region of atoms shift over an atomic distance while the others stay in the same spot.  It’s like the two regions have been pulled in opposite directions – a shear stress has been applied.  Again, we can describe the magnitude and direction of the dislocation using the handy Bergers vector.

We can also introduce the concept of a dislocation line. This is simply the 1D line (which makes sense considering we’re talking about 1D defects) where the dislocation is located. For example, with the edge dislocation, the dislocation line is located at the edge of dislocation – at the edge of the half sheet of paper located in the middle of the stack. In the case of an edge dislocation, the bergers vector is perpendicular to the dislocation line. With the screw dislocation, it is parallel.  Now, both edge and screw dislocations can be found in crystal structures.  In fact, usually the dislocation is neither pure edge or pure screw, it’s sort of a hybrid between the two – or what is formally called a mixed dislocation.

 

Interfacial Defects (2D)

We’ll talk about 2D defects here – defects that deal with 2 dimensions in the material. Another fancier term is interfacial defects (or, ‘defects between faces’).  Remember how earlier we discussed how a metal actually crystallizes?  First it is liquid, and the bonds between atoms are broken so everything is flowing, and as it cools the bonding begins. But it doesn’t cool into one perfect crystal – it’s made up of regions of crystal structures, or grains, and they all crash into each other to form grain boundaries. These are 2D defects. 2D Defects.

Surface Energy

Here’s something that may seem obvious but you may haven’t given much thought: what happens at the external surface of a material?  Obviously, there comes a point where the crystal structure stops, and it drops off into thin air.  Clearly, at the surface, the atoms are not bonded to the maximum number of neighbouring atoms, since there are no neighbouring atoms on one side.  Not all of the bonds are completed, and this actually results in a surface energy – an excessive energy that can be measured in units of energy per unit area (J/m^2).  Why does this happen?  Since the atoms on the surface are bonded to atoms on one side only, they tend to get pulled into the material.  There is a net force inward.  You can think of this as a surface energy, or force.  The atoms in the bulk of the material don’t have this excess energy, since they are evenly bonded to their neighbours.  What happens is that this inward force created tries to ‘minimize’ the surface of the material.  Or, you could think of it like this: the material is attempting to reduce this excess surface energy by reducing the amount of surface area.  Clever!  This mechanism is at work with liquids.  A carefully place water droplet on some smooth, non-absorbing surface will assume a spherical shape, to reduce its surface area.  Obviously, this doesn’t work for solids; they are rigid and this inward force isn’t enough to change the shape in any way.  Imagine a block of steel reassembling itself into a sphere to reduce surface energy: not going to happen.

I’ll try to explain another way to think about surface energy, because it seems like a bit of strange concept.  Imagine taking a material and splitting it into two.  This would take some energy to do.  For example, pulling apart an eraser.  So you’ve put energy in to break bonds and create two new surfaces.  Well, this energy doesn’t just evaporate – conservation of energy means that the energy that you put into breaking those bonds will be equal to the energy inherent in the two new surfaces you created (under perfect conditions, and with except for energy lost to, for example, sound).   These new surfaces now have an energy associated with them, because you needed to put in energy to create them.  So we can actually define surface energy as the work per unit area done by the force that creates the new surface.  The more difficult it is to pull that eraser apart, the higher the surface energy is going to be.  Surface energy also depends on the crystallographic orientation at the surface.  If at the surface, the exposed plane isn’t the one with the highest atomic density, then the surface energy will be less because there are fewer atoms with unsatisfied bonds.  Conversely, if the atomic packing factor is maximum at the surface, then there will be more atoms on the surface with unsatisfied bonds, and the surface energy will be higher.

Grain Boundaries

We briefly discussed grain boundaries earlier.  We can actually measure the severity of the boundary, or the degree of crystallographic alignment in fancier terms.  We can draw a line along a row of atoms in the first grain, and then do the same for the other grain.  When the lines intersect, we can measure the angle.  If the angle is small – less than about 15 degrees – then it is termed a small-angle grain boundary.  If the mismatch between the grains is larger, then it is a high-angle grain boundary.

Now we can tie the concepts of grain boundaries and surface energy together.  When the grain boundary is high-angle, the mismatch is greater, and it is more difficult for atoms to “reach” across the divide and bond with neighbouring atoms.  What results, then, is atoms that don’t bond with neighbouring atoms across that grain boundary, and we end up with a surface (or you could call it a  grain boundary, which you can think of as  an internal surface) energy again, just like we had for the external surface.  It makes sense too that the magnitude of the energy is directly tied to the severity of the mismatch between the two grains.  If it is a low-angle grain boundary, then the mismatch between the two grains is slight, meaning that more atoms will bond, resulting in less surface energy.  And now we have these high-energy grain boundaries, with atoms that aren’t completely bonded, and they are more chemically reactive than the bulk of the material.  Impurity atoms like to hang out in these high energy grain boundary locations, and because of the impurity atoms, they become prime sites for the onset of corrosion.  The total energy due to the internal surfaces in large grain materials is lower compared to fine grained materials, because in large grain materials there are less grain boundaries.

This isn’t to say that these materials aren’t still quite strong in spite of all their flaws at the grain boundaries.  Actually, the grain boundaries can actually increase the strength of a material, which may seem odd at first, but later sections will explore this.  What’s also interesting is that the density of these polycrystalline specimens is more or less the same as a perfect single crystal material.  I suppose this isn’t too surprising, considering that these grain boundaries are pretty small and don’t really take up much space at all in the material.

Twin Boundaries

There are more 2D defects that I’ll mention briefly.  One type of grain boundary is called a twin boundary.  This is when the atoms are mirrored across the grain boundary, and the region of material between the boundaries is called a twin.  Twins can be produced either by mechanical forces or during heat treatments.

Here’s a question for you.  Can you ever recall seeing a grain boundary?  You may have seen metals before that seem to have random shapes on them that appear slightly different colours or shades.  Commonly this occurs with certain applications of aluminum – guardrails, such as those on the sides of roads, often exhibit this.  These would be called macroscopic grains, since you can see them.  Most materials, the grains are microscopic, where they are so small (on the order of microns) that a good microscope would be necessary to investigate them.

This was a brief introduction to material defects, and the concepts will become very important in later sections, when we talk about material properties such as the yield strength of a material.

You are here: Material Science/Chapter 1/Material Defects
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