Steel Unit Cell Phases and Behavior
My teacher showed us a wire (she used a piano wire) that
was heated (an electrical current). She was showing us that
electrical energy can be transferred to heat and light energy. She
then turned the current off. I watched carefully, and much to my
amazement, the wire sagged as it cooled! This would mean that as the
temperature went down, the atoms of steel (I guess it is really iron
and carbon atoms) get farther apart, not closer together. I asked
about that and she said it had to do with how the carbon and iron
interact in microscopic crystals. I tried researching this on the
web and ran into all sorts of things that did not make sense. The
sites talked about carburized steel, eutectoid temperatures, primary
phases, austenite, cementite, ferrite, and martensite. I looked
further and ended up in geological rocks (in other words, I got
lost). There was a link to NiTiNOL which looked interesting, but I
did not see the connection. It all looked very interesting and
exciting, but did not resemble my high school chemistry text. Throw
me the details (on the high school level) because I want to know all
about this! This is a long way to ask, "Why did the piano wire sag when it
You are observing an example of "rubber elasticity". Rubber bands behave the
same way. As you warm a rubber band that is under tension (hang a weight on the
rubber band attached fixed at the other end) the length of the rubber band
DECREASES. As the rubber band cools, it INCREASES in length. Put another way,
as the temperature of the rubber band increases, the force constant INCREASES.
This is all well understood. This is due to the change in entropy.
Entropy is a measure of how much energy is spread out over a system. Forget that
rubbish about a measure of disorder -- while true -- it is abstract, and widely
In the case of the rubber band and your piano string energy is spread out more
when the temperature decreases. Most substances exhibit the opposite behavior.
The explanation involves thermodynamics, which may involve some math you have
not yet had, but if you "Google" the term: "thermodynamics rubber elasticity"
you can find some simpler explanations that walk you through the math.
Nonetheless, a remarkable observation on your part.
This will be a bit long, so I hope you can bear with me. It will also get a bit
technical, but based on your last email, I am sure you will have little problem
in following it.
Before I get into discussing your comments and insights, I want to tell you how
impressed I am with your thoroughness, and just plain good scientific method.
I am especially impressed with your desire to follow up on something that most
people would dismiss as "not interesting".
It seems that I have misunderstood your previous description how the steel wire
was increasing in length. I understood you to mean that once it was fully cooled,
it was now a little longer. Your more detailed explanation makes it clear that,
once cooled, the wire length is not changed, and the "sagging" or "lengthening"
is only a temporary effect as the wire is still cooling. This makes much more
sense. Now, with this in mind, things are a good deal less "fishy" than I had
First off, a few general comments that may help to clarify things. Piano (or
more generically, "music") wire typically contains more than 0.83% carbon;
usually the amount is closer to 1%. This places it in the Hypereutectoid region
of the Iron / Iron-Carbide phase diagram. More on the significance of this below.
First, you asked about what the different "types of iron" meant. These are
allotropes of iron. That means that they are different crystal structures of
iron that have different properties. It may help to think of ordinary carbon.
Graphite and diamond are allotropes of carbon. They are both pure carbon, but
with different crystal structures, and vastly different properties.
Similarly, iron has several different allotropes at different temperatures. As
pure iron cools down from liquid, it undergoes several changes in crystal
structure. As liquid iron cools, it first crystallizes at 1538°C into its
so-called "delta" allotrope, or crystal structure. This crystal structure (that
is, arrangement of iron atoms) is called "Body Centered Cubic". As it cools
further and reaches 1394°C, the crystal structure rearranges to the "Face
Centered Cubic" structure, referred to as the Gamma phase, and commonly called
"Austenite". Then when it cools further to 912°C, the crystal structure once
again changes... this time back to "Body Centered Cubic" again. This is the
Alpha phase, commonly called "Ferrite", and which is stable at any temperature
Importantly, each of these different crystal structures has a different density.
This is similar to the situation with pure carbon; as you probably know, diamond
has a different density than graphite, even though they are both just pure
So, as you correctly pointed out, if the weight of the wire hasn't changed, and
its density does change when transitioning from one crystal structure to another
as it cools, then clearly its dimensions must therefore change.
But things get more complicated! All the above relates to pure iron only. Steel
(an iron-carbon alloy, with small amounts of other metals like manganese) is a
more complex situation. But the principles are similar.
Have a look at the Iron / Iron-Carbon phase diagram shown on this website....
It looks complicated, but I'll try to explain. This diagram shows what happens
as a mixture of liquid iron and dissolved carbon is cooled to room temperature.
Temperature increases as you move vertically upward on the diagram, and carbon
content is higher as you move to the right.
Notice there are several vertical dashed lines. Each vertical line represents
what happens when you cool a mixture with a specific percentage of carbon.
Let's look at the dashed vertical line marked "E". Note that at the bottom,
it crosses the horizontal axis of the diagram at the point where carbon content
of the original molten mixture is 0.83%. This is what is called the Eutectoid
point (more on that at later).
As this mixture of 99.17% iron and 0.83% dissolved carbon cools, it first enters
the region labeled "Austenite in Liquid". Here, gamma iron (Austenite) starts to
precipitate out, and there is a slushy mix of solid particles of Austenite and
Next, as you cool further (that is, you go down the dashed "E" line), more and
more Austenite precipitates out, and there is less and less liquid iron. Once
you cool enough that you cross the border into the large area called "Austenite
solid solution of carbon in gamma iron", all the liquid iron has now "frozen"
into solid Austenite, together with that original 0.83% carbon mixed into what
is called a "solid solution" of carbon in Austenite.
Upon cooling further, when the Austenite (with carbon in solid solution) drops
to a critical temperature of 723°C (1333°F), it changes to Pearlite, which is
microscopic layers of pure ferrite ("alpha Iron") and Cementite (a compound of
iron and carbon with the formula Fe3C).
The mixture of iron and 0.83% carbon is the "Eutectoid" point. This means that
the 0.83% carbon contained, is exactly the right amount to form 100% Pearlite
in the zone below 723°C. If there was less than 0.83% carbon, the result would
be a mixture of Pearlite with some Ferrite left over. If there was more than
0.83% carbon, there would be Pearlite with some Cememtite left over.
Have I confused you yet?!
Notice the "V" shaped lower borderline at the bottom of the "Austenite solid
solution of carbon in gamma iron" area of the diagram. Following the "E" dashed
line down, you will notice that the transition at 723°C from one allotrope to
another, the change occurs suddenly.
But if the original carbon content is higher than the 0.83% carbon (such as with
the dashed line "B"), things get a bit more complex. The Austenite first passes
through an intermediate area labeled "Austentite ledeburite and cementite",
before finally crystallizing as Pearlite and Cementite below 723°C.
Since piano wire typically contains a little more carbon than 0.83%, its cooling
curve will be slightly to the right of the Eutectoid curve "E".
So what does all this mean? I believe this is what happens....
- Your piano wire (with close to 1% carbon content) starts off at a temperature
lower than the melting point, and somewhere in the upper area labeled "Austenite
solid solution of carbon in gamma iron".
- Then as it cools, it passes though several "zones" where its crystal structure
- When it enters a new "zone", its changed crystal structure causes a change in
density, and therefore a small change in the wire's length.
The phase diagram of steel is (as you can see) rather complex, resulting in
several phase changes as the wire cools. You might try wires made of other
metals such as copper or brass or heating wire (nichrome), etc. I suspect these
materials with their more simple phase diagrams, will not exhibit the
"shrink-lengthen-shrink" effect you have detected.
Other methods of measurement:
You might try hanging a weight from the test wire, directly in front of a ruler.
Best would be to use relatively thin wire, and a weight that is heavy enough to
ensure the wire is held straight, but not so heavy as to stretch the wire when
it is red hot. This way, as the wire expands and shrinks, you can directly see
the weight rise and fall slightly.
Hope this lengthy explanation has helped. Keep up the good work!
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Update: June 2012