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Defects in Crystals

© H. Föll


Hyperscripts of AMAT:
General Information

It has been my experience that folks who have no vices have very few virtues
A. Lincoln

Defects in crystals - are they of any relevance for life in general or materials science in particular?
Lets see: Diamonds are crystals and, as we are told, they are forever (a lie) and girls best friends (a lie, too, we (men) hope) - but if you buy one, it is mostly the defects in this carbon crystal that determine how much money you spent for a given size.
If you do not buy diamonds on a regular base, you are still exposed to defects in crystals in many ways. However, you may not be aware of this fact. So let's look at examples.
You are dealing with defects in crystals, whenever you
bent a piece of metal by applying some force (e.g. when you wrap your car around a tree) and when you do not bent a piece of metal (e.g. when you drive your car over a bridge that does not bent under the weight).
use any piece of electronic hardware.
complain about the high costs of solar energy, or the low mileage (= miles per gallon) of your car.
This needs explaining.
First we have to realize that all solid metals are crystals (like most other non-biological substances), even though they don't look like it. The shape of some piece of material does not necessarily say much about its atomic structure, and language can be deceiving. What in daily life is called "crystal" is often the exact opposite, namely amorphous glass.
Gemstones, which often are crystals and look like it by assuming some kind of geometric shape as, e.g. cubes, double pyramids etc., are very special crystals, called "single crystals".
The drawing below shows schematically what this means by comparing a perfect single crystal (very rare and very expensive) to the ubiquitous and humble poly crystal.

Model of a perfect single crystal Model of a poly-crystal with many defects.
This simple presentation does not only illustrate rather clearly the concept of "crystals" but gives an idea about defects in crystals as well.
The boundaries between the crystalline areas in the left-hand figure, the "grains"of the crystal, are obviously defects (appropriately termed "grain boundaries") in the regular lattice of a crystal, because in these areas the regular structure of the crystal lattice is disturbed. The atoms of the crystal are not were we would expect to find them. More defects are shown; e.g. "wrong" atoms, surplus atoms or missing atoms.
Metals, like practically all crystalline materials found in nature (e.g., most minerals, ores or salt), are poly-crystals full of defects. The same is true for most (but not all) man-made crystals, in particular metals and alloys.
If we look at those technical crystals, we find that a very large part of their interesting properties, including in particular many of their mechanical properties as, e.g. hardness, ductility, or brittleness, are controlled by the defects in their crystal lattice. A perfect single crystal of some metal would be void of technical interest, it would be rather useless. The metal industry (especially the so-called "metal-bending industry") lives exclusively from the manipulation of defects in the metals and alloys they use.
If you ever saw a smith doing its thing (remember "Under a spreading chestnut tree"), or at least saw a remotely natural performance of Wagners "Siegfried", you witnessed defect manipulation. Lets see:
Siegfried forges his sword. First he pours the molten "steel" into a form, he casts his sword. After cooling, he actually has a sword. The sword, in principal, exists after solidification, and a chemist, extracting a sample, would find a lot of iron (Fe), some carbon (C) and traces of everything else.
Siefried, however, is not yet done, he commences to forge his sword. He bangs it with a hammer, heats it up again, thrusts it into cold water (or oil?) heats it up again and bangs it up some more. Of course, he also does some magic (in the opera he does some heavy singing instead), before he is satisfied with his sword. And every smith in the world for the last 3000 or so years, has gone more or less through the same procedures.
The chemist is puzzled. Analyzing a sword sample after this rousing performance yields exactly the same result as before: the composition of the sword material has not changed at all.
Siegfried, however, is not a chemist but a material scientist. He knows that a freshly made sword is too soft or too brittle, and might bend or break in fights with dragons and other evildoers.
After the sword has been properly forged, however, it is strong and elastic, it will keep an edge and won't break - it is now perfectly suited to kill dragons and people.
Nowadays we prefer to use cars or guns to kill people.
But nothing has changed in principle. The car parts are still forged or treated in some way to obtain the required properties - without changing their composition. And we obtain the desired properties because by forging we manipulate the crystal defects in the steel, we introduce suitable defects in proper concentrations and structures and get rid of others.
So much for metals. Looking at the roots of the electronics and communications industry, we find semiconductor technology. Inside an integrated circuit (IC), the mainstay of the industry, we find a small Silicon (Si) crystal, a chip. The Si crystal from which the IC is made, is an extremely perfect single crystal - in contrast to metals. It was produced with an enormous amount of science, know-how, and machinery, and it is the most perfect object that can be found on this side of Pluto. It is also quite expensive.
Without a rather perfect Si crystal as starting material, advanced ICs and other semiconductor devices simply would not work. A transistor, the basic unit of a circuit, consists of small areas of the silicon where specific defects have been deliberately introduced (and others kept out) - again we are manipulating defects to make a product.
We are even using some specific defects, to get other defects to the places in the crystal where we want to have them. Being done, we have to get rid of our helper defects - you get a feeling for the complexity of the process.
There is, however, a major difference between forging a sword and making a chip:
Our smithies may have applied material science - but they certainly didn't know that! Until about 1930, nobody knew exactly what happened during forging or why it worked, but that did not keep our forefathers from making battleships, complicated watches, Eiffel towers and railways.
Metallurgy was an empirical science; the best materials, processes, and procedures were essentially found by trial and error through the millenniums. Of course, hard sciences like thermodynamics and analytical chemistry helped in the 19th century, but the basic theory of plastic deformation came long after the products.
Chips, on the other hand, are products of theory. Humans with 19th century knowledge could tinker around forever without ever coming close to making a transistor.
Solid state electronics, which includes everything made from Si, GaAs and the like, may be seen as the start of active materials science (as opposed to material knowledge), where understanding your materials and your product comes before making it. And understanding your materials means mostly understanding its defects, too.
But coming back to the questions asked above: How are the high costs of solar energy or the low mileage of your car related to defects? Easy:
Cheap Silicon is cheap because it contains many crystal defects - and makes lousy solar cells. Good solar cells need expensive Si with few defects - or cheap Si with "optimized" defects. How to optimize defects in cheap Si by some process akin to forging brittle iron into tough steel, is what materials scientists do in their research labs.
What do you need for the 100 miles per gallon car? Very useful would be a drastically reduced weight without loosing size, stability and comfort. So take Aluminum, or even better, Magnesium for making the body and other components.
Unfortunately, these metals are meeting most of the 50 or so requirements for structural car materials, but not all. Mg, for example, is prone to corrode too quickly (a little bit of corrosion is fine for selling new cars). Again, this is a property that can be tailored to some extent by introducing the right defects into the Mg crystal - but so far nobody knows how to do this without degrading some of the other properties or making it too expensive.
Of course, your mileage goes up, too, if the engine could work at higher temperatures and therefore with higher efficiency. But conventional metals have been pushed to their extremes, what we need to do now is to look for e.g. intermetallic compounds or ceramics that have the desired properties and are still affordable. Again, we are looking for the right kind of defect engineering as soon as we have selected a likely base material.
The list could be extended, but by now you get the idea why understanding and using defects in crystals leads you to the roots of human civilization.
To be sure, much has been achieved in the past, and much will be done in the future, by persons who do not know a lot about defects, but know their materials instead.
In the industrial practice you don't go to the roots, you start at a higher level. Hardly anybody among the practitioners of chip production worries about the defect situation in the Si crystals - you know that somebody else does and that you can buy near-perfect Silicon. You do your diffusion processes on the base of phenomenological theories or by using software packages that simulate whatever you want. But some are left who worry, and without them the others couldn't work.
The short history of Si technology and thus of microelectronics at large nicely illustrates this point.
Hardly anybody knows that the detailed mechanisms of the diffusion of substitutional elements - the mainstay of Si processes - are far less understood than in most other crystals. The first ICs were made with empirical knowlegde and a totally wrong theoretical picture of the atomic processes. Those ICs, however, worked anyway.
But todays ICs wouldn't be here without the results of much research conducted in the meantime, because the extremely fine structures encountered today would have been beyond the power of simple empirical equations.
Some materials scientists thus should know the basics about defects in crystals. This is knowledge that will not change much in the times to come and that always will help to understand what is going on an atomic scales when anything changes in crystals. This course tries to present that knowledge in a short and much abbreviated way. It covers all basic kinds of defects in one semester, which is a bit unusual. We will look at
Defect structures and geometries.
Some fundamental properties of defects.
Mechanisms of defect generation, manipulation, annihilation and interactions.
Experimental ways to observe defects and to measure defect properties.
In dealing with defects in crystals, we always must visualize some disorder in space, which for most people is not an easy thing to do. Whereas some scientists are perfectly happy with abstract mathematical description of objects including defects, most of us must have some spatial image of what is discussed to be able to grasp what is going on.
Visualization therefore is a must and this is where multimedia techniques may come into their own. Look at the schematic drawing of a dislocation below - can you see the dislocation?
You sure could when you would be able to rotate the image so you can view the dislocation from various angles, and you sure learn more by doing this compared to looking at a drawing that only shows one perspective that somebody else picked for you.

Perspective view of the most simple dislocation in a cubic lattice.
The dislocation line has been marked by differently colored spheres.
In view of this, the course "Defects in Crystals" was used as a vehicle to try out for the first time the possibilities of the new media in teaching a non trivial subject. A "Hyperscript" was collated on a "lecture note base", i.e. there are no long verbal descriptions.
This hyperscript is an English version of the original German hyperscript, but includes advancements made in the meantime; it is also formatted in a slightly different (and hopefully) improved way.
It is now the "real" thing; the German version, while still kept, will no longer be updated.
The hyperscript consists of 5 major parallel "strings" which are:
Here you will find some basic background knowledge about subjects that should be known, but can bear to be repeated.
Backbone 1
This is the main part - it would be the "book" in a conventional format.
Backbone 2
Additional "chapters of the book" that are not in the top priority of the course, but may be used on occasions.
All those pictures, graphs, movies and other materials that would drive your book editor up the wall if you would try to include it in a conventional book.
Typical exercise questions together with typical solutions
Everything you do not have to know, but may take an interest in. This may include hard-core science or interesting recent developments in the field, but also anecdotes or historical notes.
I sincerely believe that hyperscripts will replace classical text books in years to come. But I also believe that nobody (including myself) knows at present how to produce the perfect, defect-free hyperscript. Only time will tell.
Being willing to learn, I do invite comments and suggestion for improvements. Please get in touch via e-mail:

e-mail an H. Föll


Footnote to "molten steel"

Wagner got it totally wrong! Siegfried does not pour anything - simply because he could not melt iron or steel (nor could anybody else); his fire was simply not hot enough.

That he (and other smiths, too) nevertheless could obtain iron and forge a sword for more than 2000 years before melting it became possible, is one of the less well known marvels of ancient history. A glimpse of the underlying technology can be obtained by jumping to "history of steel" or to "Damascene technique in Metal Working"; from there you may enter the fascinating world of magical swords or otherwise remarkable issues of metal working (and thus defect manipulations).