# What causes the latent heat of solidification?

Every explanation that I read says:

"When a crystal (solid state) forms from a liquid, heat is being produced."

This seems rather weird, why would the production of something as ordered as ice crystals also produce heat as they are being assembled?

I understand that there is an explanation in thermodynamics that goes as follows:

The change from liquid to solid is a process that makes a less ordered system in to a more ordered system (potential violation of the Second law). But nature avoided that with the fact that the Gibbs free energy during a phase change stays constant, so:

$$G_{solid} = G_{liquid}$$

$$dG=dH-TdS=0$$

$$dH=TdS$$

$$H_{{liquid}}-H_{{solid}}=T({S_{liquid}}-{S_{solid}})$$

and as stated above $$S_{liquid} > S_{solid}$$

$$dH_{freezing}=TdS_{freezing}=\delta Q > 0$$

So, heat is being produced and given to the environment because $$dG=0$$.

I am interested in the more microscopic explanation of this process. Can this be explained with statistical (quantum) mechanics? What is the mechanism that produces heat when crystal structures are being formed?

It is possible to lower the temperature of water below the freezing temperature (at given pressure) and for it to still not go through a phase transition. That happens if there are no starting points of nucleation, or no sudden impacts and if the water is very pure.

Lets imagine liquid water at $$\vartheta=-10°C$$ (metastable state) and now we insert one ice crystal to initiate crystallization.

The water now almost immediately goes to the freezing temperature $$\vartheta = 0°C$$, now stable state (that is dictated by the phase diagram), and ice is being formed.

Now how did the water heat up for $$10°C$$ from the metastable state to the stable state? I presume that the ice formation produced latent heat to heat it up.

• Does the reverse process also seem weird? Eg, melting ice absorbs heat. Commented May 31 at 22:24
• Of course not. But I don't want the explanation to be: "You input energy when you melt stuff, now just think in reverse." That doesn't make the concept more clear and it doesn't explain the underlying mechanism. Commented May 31 at 22:32
• You form stronger bonding interactions when the lattice solidifies. There is your extra energy. Commented May 31 at 22:47
• You are falling into a really common error students make in chemistry. The formation of bonds does not use energy, it creates energy. This is because when you take two less stable individual atoms of relatively high energy, they form more favorable interactions. They will then release energy as light when they form a bond because the excess energy of the original atoms that is greater than their bound energy has to go somewhere. Commented May 31 at 22:56
• It's an unfortunately common misconception that bonds store energy. Bonds release energy when they form, and bonds sit at a relatively low energy level; stronger bonds release more energy, and energy is needed to break bonds. Scenarios described by the shorthand of "bonds store energy" correspond to an implicit assumption that they're broken in some way or another, and then that the reaction products have a still lower energy such that the energy penalty is paid for, and then some; thus, the total process is exothermic. A common example is metabolism. Commented Jun 1 at 5:36

Think of the atoms in a solidifying liquid as being like magnets snapping together. Magnets starting even at rest (with no kinetic energy) can, as they come together, develop quite a bit of speed. The kinetic energy of their motion comes from the potential energy released by "satisfying" the force of magnetic attraction. When the magnets do collide, the kinetic energy is transferred to other phenomena (heat, sound, potentially even into breaking the magnets), so that the magnets can't bounce back to their original positions.

The same idea applies to the molecules in a crystallizing liquid. A molecule in the liquid phase near the solid-liquid interface is at a higher potential energy there than it will be in its final position in the solid phase. The forces attracting the molecule into the solid do work on the molecule (i.e. add to its kinetic energy) whenever it moves towards its final position (remember that the force on a particle points down its potential energy gradient). If the crystal is growing, so more molecules are entering the solid than leaving it, then there is net kinetic energy being added to the system by the attractive forces. As this energy dissipates, it appears macroscopically as the heat of fusion.

A fuller description of where the heat of fusion comes would therefore require answering the question "why are atoms attracted to each other in chemical bonds?". In the most high-level terms, atoms are attracted to one another because they are made of charges. When two atoms approach each other, the nucleus of each atom is able to pull on the electrons of the other, so the electrons (if allowed by the Pauli exclusion principle) pool in between the nuclei and in turn hold the nuclei together. So, in fundamental physics terms and with much handwaving, the heat of fusion generally originates as the work done by electrostatic forces between the atoms of the liquid. Making precise quantitative predictions of the forces on molecules is the realm of quantum chemistry and molecular dynamics. Here's a random paper I found documenting a calculation of a heat of fusion starting from quantum mechanics principles, just to show that it's possible.

• The last paragraph was the most helpful. The analogy with magnets helps to paint the picture, but it doesn't explain anything about the exact mechanism, because it is an analogy. I was looking for a more under the hood explanation, like the paper you linked (although there is a paywall, so I couldn't read it). Nonetheless, I was the most curious as to weather scientists in general were able to describe latent heat from QM or similar theories, rather than just from the thermodynamics perspective. Commented Jun 1 at 21:05
• I will link this question, as it is about bonding in general, and is of similar flavour. physics.stackexchange.com/questions/664825/… Commented Jun 1 at 21:07

Maybe the thing seems weird to your physical intuition because you are muddling cause and effect. It's not that configuring the atoms causes heat to be produced, it's that if heat is removed then the atoms have to find an arrangement with less entropy. The cause of the heat flow is that something nearby (and in thermal contact) has a lower temperature. The entropy of that other thing goes up as it receives the heat.

• I see the reasoning in this approach. Its similar as to how electrons when they lose energy, fall to a lower configuration state. That seems like a reasonable explanation. But than I encountered the example I added in the addendum to my question, and than I can not seem to explain that situation with this approach. Commented May 31 at 22:45
• This is wrong/confusing the point, it is exactly the rearranging of the atoms and the resulting stronger bonds between them that is causing the latent heat to be produced. These stronger bonds reduce the atoms potential energy, this energy has to go somewhere (it is conserved after all) and is what is released as heat. There is also the global lessening of temperature (which we can roughly equate with the atoms kinetic energy) that causes freezing but even without this (say for instance causing freezing as a function of pressure) heat would still be released on freezing.
– Max
Commented Jun 1 at 13:55
• Thanks for that; I think a combination of my answer and your comment gives the right overall message. Cause and effect are often hard to separate (or even a matter of opinion) in quasistatic processes. My point is that the atoms are free to find those states of lower potential energy at any time, so why don't they do so? The cause (that which drives the direction of the process) is entropy increase overall. Commented Jun 1 at 15:10
• @AndrewSteane there are these bags with a meta-stable liquid you can trigger to become solid – they heat up quite a bit, and can be used as a heat source to keep hands warm. So at least in some cases the phase change comes first. Commented Jun 1 at 22:36
• @PaŭloEbermann I had a think about that. The statement 'they heat up quite a bit' is a statement about temperature not heat flow. Once there is a temperature difference the heat will flow. So now the question is 'why does the temperature rise?' It rises because potential energy is being converted into kinetic energy, but the reason the process does not immediately reverse is, as ever, owing to entropy considerations. Commented Jun 3 at 12:43

The crystal arrangement is the lowest energy arrangement at that temperature. During the phase transition, think about one atom that is not part of the crystal yet. When it finds its spot in the cristal net, it falls in a lower energy state, releasing its additional energy by providing vibration (heat) to the crystal itself.
If you keep taking away this heat from the cristal, it will continue to form.
Imagine not taking away the heat: the vibration energy distributed among the cristal can (statistically speaking) reorganize itself to provide the detachment energy to the atom and separate it again from the cristal.

This is at least how I picture this stuff independently from abstractions like the Gibbs energy and the intent of nature.