Crystal formation is an increase in entropy?

February 6, 2008 4:51 PM

ScienceFilter: Creationists, crystals, and thermodynamics.

A common red herring argument that I've encountered as advanced by Creationists is that by Newton's Second Law of Thermodynamics evolution should not be possible. (According to Wikipedia that argument was originated by a biochemist named Duane Gish, incidentally.) My understanding is that among other things, one reason why this is an erroneous argument is that while it might apply to a closed system the environment on Earth is constantly being pumped full of heat via sunlight and other solar radiation.

But never mind that, that's just the context. I was thinking about it and it occurred to me that in terms of orderliness increasing, the formation of ice crystals in freezing-temperature water or quartz crystals in liquid hot magma that has cooled to the correct temperature both seem to represent an increase in orderliness of the matter in question.

Something I've heard is that formation of crystals isn't strictly due to loss of heat. Supposedly you can have a quantity of water at a static temperature around freezing and if it's turbulent it will remain liquid but when it becomes still the ice crystals will begin to form. (Although hmm, maybe loss of turbulence would be a loss of heat.)

So is an ice crystal actually a higher entropy state than the equivalent amorphous mass of water?

Water expands when it freezes. I don't know why, van der Waals bonds or something, right? But other substances become more dense when they change state to a solid, so a given mass would lose volume. Isn't this kind of like all the air molecules in a room leaping into one corner of it - just the example that's presented as absurd in explanations of statistical mechanics?

I know that orderliness isn't the same thing as heat and isn't really the opposite of entropy. I was hoping that anyone who feels they've got a thorough understanding of thermodynamics could expound on what a thermodynamic analysis of the formation of crystals would be. And anything you can say about the relationship of order to entropy and thermodynamics would be interesting too.

In an eerie coincidence there was this recent post about the second law. The crystals must be telling me things.

posted by XMLicious to science & nature (19 answers total)

Fundies Say the Darndest Things!

"One of the most basic laws in the universe is the Second Law of Thermodynamics. This states that as time goes by, entropy in an environment will increase. Evolution argues differently against a law that is accepted EVERYWHERE BY EVERYONE. Evolution says that we started out simple, and over time became more complex. That just isn't possible: UNLESS there is a giant outside source of energy supplying the Earth with huge amounts of energy. If there were such a source, scientists would certainly know about it. "

[emphasis added]
posted by Freen at 5:10 PM on February 6, 2008

Entropy isn't just about the order in the matter. It's about the order in the energy in the system too. You can increase the order in the matter in the system, have it crystallise or whatever, but there will be an appropriate increase in entropy in the distribution of energy in the system to keep things going as the second law prescribes. If you have something spontaneously crystallising it'll do something like produce a lot of heat, which goes off and spreads about the place and increases the entropy.
posted by edd at 5:29 PM on February 6, 2008

We need a couple of terms here: "open system" and "closed system". In a closed system, over time entropy will increase.

But in an open system, order can increase without violating the Second Law of Thermodynamics. The reason is that the open system can import ordered energy and export disordered heat. That's what living creatures do.

This specious argument about the Second Law also applies to reproduction. If you start with two rabbits and end up with twenty, isn' t that also an increase in order? Then the Second Law should also mean that having babies is impossible.

In a sense, an "open system" can be thought of as being a part of a "closed system". The Second Law doesn't require that entropy uniformly increase in every single part of a closed system, only that total entropy overall increase. Subsections of the closed system can increase in order, just as long as there's even more disorder somewhere else.

That's what's really happening when a baby grows up (yet another thing this specious argument about the Second Law should imply is impossible) or when babies are born, or when evolution creates more complex critters, or when crystals grow. All of it is an example of order being concentrated and disorder being exported elsewhere.
posted by Steven C. Den Beste at 5:35 PM on February 6, 2008

Umm... which is actually more complex, an ice crystal or a drop of water? Seems to me that crystals are a fairly simple structure, where as amorphous matter is much more complex. Of course, to the human mind matter with seemingly exact proportions or shapes appears more complex because we are accustomed to creating such structures ourselves, whereas the seemingly chaotic glass of water appears much more simple and.... uh... dilute. Perhaps the opposite is the case? It wouldn't be the first time something in nature turned out to be counter intuitive to human experience... (see also the heliocentric and religion thread a few posts up.)
posted by wfrgms at 5:40 PM on February 6, 2008

'Umm... which is actually more complex, an ice crystal or a drop of water?'
This encapsulates the problem by only talking about the ice crystal and the drop of water, and not what happens to everything else in the system when one changes to the other.
posted by edd at 5:51 PM on February 6, 2008

From wikipedia: Phase transition
A phase transition or, phase change, describes when a substance changes its state of matter - ex. ice melting to water is a phase change because a solid changed to a liquid. For a phase change to occur, energy must be added or removed from the substance. Normally adding or removing energy will change the temperature of the substance as the kinetic energy of the particles will increase or decrease. During a phase change however, the potential energy of the substance changes as the particles are moved further apart or closer together. There is no change in kinetic energy o

entropy of ice crystal
posted by francesca too at 5:53 PM on February 6, 2008

Phase transitions occur when the free energy of the system is minimized by that transition. The concept of free energy is an important one. Consider, for example, the Gibbs Free Energy of a system, which is given by G=H-TS, where H is the enthalpy, T is temperature (in absolute units; generally Kelvin), and S is entropy. This expression should clarify why things tend to freeze at cold temperatures; the decrease in free energy from the enthalpy term (which is approximately, but not exactly, a measure of bond strength) is larger than the effect of the increase in free energy caused by the entropy term. Again, keep in mind the difference between an open and closed system which was explained above.

Creationists who make this argument are, to be frank, blatantly misinterpreting the 2nd law of Thermodynamics.
posted by JMOZ at 6:24 PM on February 6, 2008 [1 favorite]

There's quite a bit going on thermodynamically in the solidification of a liquid, and you've touched on a few ideas here already, but I'll try to fill in some of the gaps here.

Basically, for any system, you can define a quantity called "free energy" which is defined as:

U-TS

where U is the energy term (also called enthalpy), T is the temperature, and S is the entropy.

Systems will always behave in a way that lowers the "free energy"

The temperature term is important because it determines just how the system goes about lowering the free energy. So at a high temperature, the system can decrease the free energy more effectively by increasing entropy, but at low temperature it is more effective to lower the enthalpy. This is why we have solid ice at lower temperatures and liquid water at higher temperatures. From an energy standpoint, water molecules are attracted to each other and want to clump together. Bringing two water molecules close together lowers the energy of the system (releases energy) and separating them raises the energy (requires energy to be input). But when water molecules clump together, they are more ordered than when they are floating about freely, so there is a competing entropy cost. At low temperatures (because entropy is multiplied by temperature in the free energy term), solid ice occurs spontaneously because crystal ice is a lower energy structure than liquid water. It is more ordered, but this is OK because the temperature is low, so the entropy contribution is low. When the temperature is higher, crystal ice is still generally a lower energy structure than water, but entropy becomes more and more important to the point where even though it requires energy to remove a water molecule from the ice crystal and put it into the liquid phase, the increase in entropy makes it thermodynamically favorable.

Something I've heard is that formation of crystals isn't strictly due to loss of heat. Supposedly you can have a quantity of water at a static temperature around freezing and if it's turbulent it will remain liquid but when it becomes still the ice crystals will begin to form. (Although hmm, maybe loss of turbulence would be a loss of heat.)

What you're talking about here is called supercooling and it is due to the problem of nucleation. If you've got pure water in a container and you gently lower the temperature below the freezing point, the water will remain liquid even though the free energy argument above would seem to indicate that the water should freeze. Why does this happen? Well, in order for ice to form, the water molecules need a seed crystal to latch on to. If you drop a small seed crystal into supercooled water, the water will freeze around the seed. If not, the water will stay liquid until a seed crystal develops spontaneously. It would seem that this should happen immediately, since the molecules thermodynamically "want" to crystallize, but what happens is when you have solid ice floating in liquid water, there is an interface which has an energy cost per unit area. Because the surface area-to-volume ratio goes down as a sphere increases radius, small seed crystals are unstable (they require too much energy to expand the surface area), but when they reach a critical size, they will grow spontaneously. This is because more energy is released in the volume-dependent phase transformation (liquid to solid) than is required to increase the area of the interface. So in supercooled water, there are often small seed crystals forming randomly (just due to liquid water molecules arranging themselves into small seed crystals by chance) but because they are below the critical size, they will not expand and freeze the rest of the water. Agitation of the water as well as smooth walls in the container also inhibit the formation of crystal seeds.
posted by SBMike at 6:41 PM on February 6, 2008 [5 favorites]

Umm... which is actually more complex, an ice crystal or a drop of water? Seems to me that crystals are a fairly simple structure, where as amorphous matter is much more complex.

Water droplets are not really amorphous because water molecules are polarized and therefore interact with one another in very specific ways, even when in liquid form.
posted by oneirodynia at 6:44 PM on February 6, 2008

Thanks guys! Who knew all that was going on when I was a little kid making rock candy.

So, does a solid object of any substance that was created through phase transition (as opposed to sedimentation or something) contain crystals? Do some substances form crystals more readily and some less readily, and is there a name for that property?

Lipids, for example, don't look like they have crystals when they're solid. I realize that hamburger grease is often proteins congealing, or whatever proteins like in eggs do when you cook them, but I'm thinking more about something like candle wax.
posted by XMLicious at 7:58 PM on February 6, 2008

There are amorphous solids. Glass is an example, and there is a whole class of solids that are called glasses because they have a similar non-crystalline structure. Often glass happens because you cool the liquid too quickly for its molecules to rearrange into a crystal lattice. (If you cool window-glass more slowly, you get quartz, I think, and the other components would crystallize out separately as little inclusions or grain boundaries or something.)
posted by hattifattener at 9:26 PM on February 6, 2008

Good point about glass! So is candle wax like glass that way, I wonder?

Spelunking through Wikipedia came up with this article on the glass transition ❲named after glass but it's describing a sort of 2nd melting point for amorphous solids.❳:

Consider a molecular liquid which is slowly cooling down. At a certain temperature, the average kinetic energy of molecules no longer exceeds the binding energy between neighboring molecules and growth of organized solid crystal begins. Formation of an ordered system takes a certain amount of time since the molecules must move from their current location to energetically preferred points at crystal nodes. As temperature falls, molecular motion slows down further and, if the cooling rate is fast enough, molecules never reach their destination — the substance enters into dynamic arrest and a disordered, glassy solid (or supercooled liquid) forms.

That makes me think of it like musical chairs - as the liquid cools the molecules begin wandering around looking for chairs / energetically preferred binding points, but if the music stops / the transition point is reached too soon they just bind to whatever is nearby.

It sounds as though the reason why commonly-used plastics are useful is because at room temperature they're in between their glass transition temperature and their melting point?

Here's something interesting and relevant from the glass article itself:

Some people believe glass is a liquid due to its lack of a first-order phase transition where certain thermodynamic variables such as volume, entropy and enthalpy are continuous through the glass transition temperature. However, the glass transition temperature may be described as analogous to a second-order phase transition where the intensive thermodynamic variables such as the thermal expansivity and heat capacity are discontinuous. Despite this, thermodynamic phase transition theory does not entirely hold for glass and hence the glass transition cannot be classed as a genuine thermodynamic phase transition.

Am I right that this is implying that volume, entropy, and enthalpy are discontinuous at the phase transition point in a substance forming a crystal? So there's a crack! as the molecules come together into a crystalline structure, like breaking the rack to start a game of pool but in reverse? Oh my arrow of time!

Also of interest, a table in this Wikipedia article lists some (first-order?) melting and boiling points of common substances. Ethyl alcohol freezes at -114 °C.

Go Wikipedia! A++++, would learn again. For some reason this stuff is much more interesting to me right now than it ever was in school.
posted by XMLicious at 11:06 PM on February 6, 2008 [1 favorite]

For some reason this stuff is much more interesting to me right now than it ever was in school.


That's because you weren't motivated to learn it then. Now you are. In college I flunked Art History twice. (Embarrassing for a Graphic Design major to admit!) But it's come to fascinate me, and I have learned a great deal about it.
posted by Guy_Inamonkeysuit at 6:19 AM on February 7, 2008

You can create amorphous ice if you cool water quickly enough (from above 0°C to below -137°C in milliseconds, if Wikipedia is to be believed).
posted by DevilsAdvocate at 6:39 AM on February 7, 2008

Don't forget about all 17 crystaline forms of ice

and of course my favorite is Vonnegut's version of Ice IX
posted by Black_Umbrella at 7:24 AM on February 7, 2008

Lattice vibrations are quantized? ❊brain asplodes❊
posted by XMLicious at 12:45 PM on February 8, 2008

XMLicious: "Lattice vibrations are quantized? ❊brain asplodes❊"

Yes, in fact, and there's a simple model which works quite nicely to describe phonon behavior. If you imagine atoms to be hard balls and the bonds between them to be springs, you will likely quickly realize that there are "modes" (that is, particular frequencies/patterns) of vibration which occur.

XMLicious- it sounds like you might really enjoy a solid-state physics course if you have the option. They do tend, however, to be quite mathematical, and the difference between a good teacher and a bad teacher in solid state is enormous.
posted by JMOZ at 5:29 AM on February 11, 2008

I'm a bit beyond the usual college age but I'll check out what's available locally.
posted by XMLicious at 10:42 AM on February 11, 2008

Regarding the ice/water question, it may be handy to know that the higher-temperature phase is always the higher-entropy phase.
posted by Mapes at 5:44 PM on April 28, 2008