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Name: Justin
Status: student
Grade: 9-12
Location: IL
Country: USA



Question:
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 heating curve?


Replies:
Hi Justin

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 subject!

Regards,
Bob Wilson


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 optical properties.

Vince Calder


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,
Burr Zimmerman



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