Atomic Mobility in Solids
Here is the confusion that I have. I
thought that in a solid, the atoms vibrate (heat
energy) around fixed positions. I am studying the
cooling of allotropes of carbon steel. If I
understand correctly, the atoms in a SOLID rearrange
themselves on cooling. But they are not melting or
evaporating. How can they do this? From what I am
reading, it seems that the atoms in a solid move
around, not just vibrate over a fixed position. How
can that be? Also, it should take energy to change
from one allotrope to another, just like changing
from a liquid to a solid. With the liquid-solid
change it is called heat of fusion. Is there a heat
of "allotropism?" Are there ways of measuring this
I understand your puzzlement! Yes, many solid substances have multiple
allotropes, and can "morph" (for want of a better word) from one to
another. As you know, steel has several allotropes that are stable
only within specific temperature ranges. Steel that has 0.83% carbon
content, for example, exists as the solid gamma crystal structure
(called "Austenite") above the transition temperature of 1333°F. (By
the way, please note that in a previous reply I incorrectly stated
this temperature was 1333°C). As the Austenite cools below this
transition temperature, its "Face Centered Cubic" crystal arrangement
becomes unstable, and changes to "Body Centered Cubic". Steel with
this so-called alpha crystal structure is called Ferrite. To answer
your question, yes, the atoms of iron and carbon actually rearrange in
the solid state. If you look up Body Centered Cubic, and Face Centered
Cubic on a search engine, you can see the crystal cell structure of
each. They are very similar, but nonetheless different.
As bizarre as all this sounds, it is more common than you may think.
Phosphorous exists as several allotropes. White phosphorous is
somewhat unstable at room temperature and its crystal structure slowly
changes to that of red phosphorous. Diamond and graphite are just
different allotropes of carbon. Contrary to popular belief, diamonds
are not "forever"! In fact, diamonds are slightly unstable at room
temperature, and very (very!) slowly change their crystal structure to
that of graphite. At very high temperature, this "morphing" from one
allotrope (diamond) to another (graphite) occurs quite quickly.
Changing from one allotrope to another can also result in a
significant change in density and dimensions. In the case of steel,
the change is small, but when diamond reverts to graphite, there is a
very substantial change in density and volume.
The thermal vibration (heat) of atoms you refer to is only a secondary
factor here. Over the temperature range where a specific crystal
structure in a specific material is stable, the bonds between
individual atoms in a crystal are strong enough to overcome the
instability caused by thermal atomic vibration.
To my knowledge, there is no "heat of allotropism" as such. In many
cases external energy is indeed needed to drive this change. For
example, heat and extreme pressure are needed to change graphite into
diamond. In many other cases, the change from one allotrope to another
is often spontaneous or triggered by temperature change. In the latter
case, changes in temperature drive the change from one allotrope to
another, since many allotropes are only stable within a specified
temperature range. Iron and steel are examples of how one allotrope
changes to another, as the temperature gradually cools.
I hope this has helped you to get your head around what is a puzzling
Atoms in a solid can rearrange. This may occur as a single atom
repositioning itself with respect to its neighbors, or it may occur as a
molecule if the solid is a molecular solid. Associated with first order
transitions, there is indeed a "heat of allotropism". Some substances even
have multiple melting points, depending upon which phase is melting.
Perhaps the champion of allotropes is the element Plutonium with six
allotropes. The temperatures of the transitions are, in increasing order:
395, 473, 583, 725, and 753 kelvins. The "normal" melting point of Pu is 914
kelvins. Despite this the heat of fusion of Pu is a mere 2.8 k-J/mol. Just
for comparison, sodium with a melting point of 371 kelvins, has a comparable
heat of fusion of 2.6 kJ/mol. One would "expect" the heat of fusion of Pu to
be much higher, given its high melting temperature. A common method for
observing allotropism is the molar heat capacity as a function of
temperature, although there are other methods such as x-ray diffraction, and
It is true, atoms can move around in a solid. They diffuse, just like they
might in gas or liquid -- just at a much slower rate. The difference is that
in liquids and gases, they can also convect (moving eddies and currents),
which does not occur in solids.
When you heat something up, its rate of diffusion increases. So with hot
metals, atoms can diffuse and move around in the solid at measurable rates.
At colder temperatures, diffusion might be so slow that it cannot be measured
(hence the impression that it is not occurring).
To find the enthalpy (heat) difference between different allotropes (e.g.
graphite vs. diamond) all you have to do is find the difference between
their heats of formation. You will find that graphite is in fact the reference
state for carbon (e.g. enthalpy of formation is zero by definition), and the
heat of formation of diamond is around 2 kJ/mol, meaning it is slightly
higher energy state than graphite. This method is applicable for more than
just allotropes, too -- it is very useful for chemical reactions for example.
Hope this helps,
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Update: June 2012