In my world I've created an alloy that can melt at low temperatures and solidify at high temperatures. This got me wondering, is something like this actually possible/does it exist. With most materials, of course, bonds are broken between individual molecules and atoms at high temperatures which creates a more liquid consistency. I did a bit of research but it appeared inconclusive.
Is there an element or alloy that melts at low temperatures, and solidifies at high temperatures?
I'm sure this is outside of the range of temperatures you were interested in, but in the spirit of "truth is stranger than fiction," Helium-3 actually does this:
The temperatures we are talking about are ridiculously small (fractions of degree above absolute zero), but note that the Solid region actually dips down around 0.3K. This means you can have a liquid at 3.1MPa at 0.01K, add heat to it to warm it up to 0.3K, and have it solidify on you!
The reason for this is beyond my expertise (I am told it has something to do with aligning spins), but yeah... Helium does it!
He delivers.
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Commented
Jan 17, 2017 at 10:44
Heat can drive moisture out of a substance. If some substance mixed with water is a very viscous fluid, then driving the water out with heat could leave you with a solid. According to various pottery blogs, moist clay is about 30% water, all of which is driven out in the process of firing.
A viscous mixture in solution (not necessarily a solution of water) could be heated in such a way as to drive off the solution and precipitate the results. I can think of a real life example of this: dissolve a pen's worth of ink in hair spray. Mixed together you have a black inky goo. When the alcohols in the hairspray evaporate, a hardened black mass is left. The alcohols in hairspray evaporate at room temperature, but just imagine instead a solvent that needs to be heated to be driven off.
The second possibility is if the substance underwent a chemical reaction at a high enough temperature and changed into something else that had a higher melting point, then it could theoretically solidify as the temperature went up. Clay doesn't quite undergo this reaction, but it does undergo chemical changes when fired.
Clay consists of a variety of minerals the most important of which for pottery are SiO$_2$ and Al$_2$O$_3$, both of which come from feldspars in the clay. Firing the clay burns off organic impurities, and removes the hydrated water and K$_2$O. Increasing the heat still further causes cross-link bonds to form between sheets of SiO$_2$ and Al$_2$O$_3$, forming a compound called kaolinite, which gives pottery its strength and hardness.
So it is plausible for a material to be heated and change its mechanical properties such that a fluid compound mixture precipitates into a solid material.
The caveat is, I can't think of any way this could be a metal, since metal alloys don't form the strong covalent bonds in the clay example. It would much more likely be some sort of ceramic like the clay example.
The other big caveat is that neither process is reversible. If you drive off a solvent with heat, then cooling down the resulting substance will not turn it liquid again. In the hairspray-ink example, you could re-dissolve the black mass by soaking it in rubbing alcohol, but it would take a long time (unless you ground the mass into powder first). Same with the clay example, cooling down the clay gives you hardened pottery, not lumps of crumbly minerals.
There are no such metal, alloy or pure element which does this within a reasonable temperature-pressure range2; but there are materials which can behave this way.
Why does stuff generally melt when heated and not when cooled down?3
All matter in our universe follow the bureaucracy founded within thermodynamics and, as part of that, all systems tries to reduce their internal energy to a minimum. A way to express the usable energy in a system is through Gibb's free energy, which tells how much energy can be extracted from a system. Gibb's free energy is commonly expressed as:
$\Delta G = \Delta H - T\Delta S$
in which $\Delta G $ is the Gibb's free energy, $\Delta H$ is the enthalpy (energy of the system, including the internal energy), $T$ is the absolute temperature, and $\Delta S$ is the entropy (the "disorder" of the system). If $\Delta G $ is negative, then it is a spontaneous process.
When atoms and molecules becomes highly organized, then they can usually lower their energy by a fairly decent amount, but they lose "disorder". This means that both $\Delta H$ and $\Delta S$ are negative for something which solidifies, but as $\Delta S$ is preceded a minus sign in the equation, a loss of disorder means that it adds to $\Delta G$. Luckily, it is multiplied by $T$, so it contributes less to the equation at low temperatures. The more negative $\Delta H$ can become for a system which is solidifying, the higher $T$ it can allow without $\Delta S$ taking overhand. As long as the sum is negative, then it will spontaneously solidify.
Similarly, when you increase the temperature you start to add energy to the system in terms of heat and the molecules start to move around. This creates a positive $\Delta H$, but at the melting point they start to gain enough disorder ($\Delta S$ is now positive too) from the movement so that $T\Delta S$ becomes larger than $\Delta H$. Since the "disorder" gain contributes negatively, this causes $\Delta G$ to become negative again and the system will spontaneously melt and the "disorder" in the system will keep it melted for as long as $T$ is high enough.
Things can solidify when heated, but irreversibly
Polymerization is one method of creating solids by heating; it is what the reaction is called when you create plastics. You start of with monomers (the individual building blocks), which react through various means into polymers (i.e., plastics). There are several different ways for the monomers to react (e.g., free radical polymerization) and there are several ways to initiate the polymerization process (e.g., through light and heat). The polymerization process is also not limited to petrochemical plastics; similar processes also occur with biopolymers, such as milk proteins and wheat proteins However, this process is usually one way, meaning that once the polymer is created, then there is no melting of it, so it remains solid.
With exceptions
However, there is a novel material which breaks this rule and, seemingly, defies nature. It is an aqueous mixture of cyclodextrin and 4-Methylpyridine, which solidifies through gelation when heated above 45°C4 and is stable due to hydrogen bond formation between the two compounds. The bonds are created in a certain way as the cyclodextrin changes shape when heated and, when the mixture is cooled, the hydrogen bonds are broken and the cyclodextrin changes back to it's original shape and is, thus, prevented from forming the bonds required to solidify the solution.
So, while this example is not a metal alloy, it still shows that there is a material which can solidify when heated at a reasonable temperature range.
1: I misread the question and thought it said "any material" when writing my first version of my answer.
2: As Cort Ammon pointed out, Helium-3 does actually do this, but in a very small window at extremely low temperatures, which makes it highly impractical to use.
3: I'm trying to keep it simple and I am, thus, taking some liberties with the truth.
4: The article states "between 45°C and 75°C, which I interpret as that the compound is destroyed if heated more.
The examples of polymerization, evaporating water, and chemical reactions in other answers are usally irreversible. This is fundamentally different from reversible changes of physical state such as solid < > liquid < > gas.
If you don't mind some arm-waving about a technology that hasn't been discovered yet, there could be a few options that would be reversible:
Some sort of exotic shape memory alloy, which can be converted to a liquid by some means at low temperatures, but "remembers" is it a solid when it is heated, and returns to its original shape when it solidifies.
Some weird ferromagnetic material which behaves like a liquid below its Curie temperature when the magnetic effects are working, but like a solid at high temperatures when they are not.
Some sort of superconducting alloy, which only behaved like a liquid below its critical temperature.
You specified an alloy and you probably intend to mean anything that acts as a metal, including modern things like CPM so long as the bulk properties of the result seems metal-like rather than (say) ceramic.
Cort’s note on ultra-high pressure helium (“something to do with aligning spins”) gives me an idea that could be useful for realistic handwaving in your story.
You know what else has to do with aligning spins? Ferromagnetism and Ferrimagnetism allowing permanent magnets to exist.
A quirk of energy levels and atom spacing dependant on spin alignment means that it is favorable to have spins aligned because the energy associated with the different spacing more than make up for it.
Imagine a powerful magnet (like today’s rare-earth magnets) being developed (for electric vehicle motors) that incorporate molecules or nanoparticles that are dipoles (like water famously is). Water is anomolus in just about every way possible because of the dipole and hydrogen bonding. The researchers were trying to exploit the spin vs lattice spacing relationship to make powerful compact permanent magnets that don’t demagnetize when subjected to high-power fields in the motor.
But, above the Curie temperature, the situation changes. Without the influence of spin effects, a different lattice is preferred and the material changes state.
So, first the material melts at high temperature, but maintains the exotic structure at the nanoscale, like a liquid crystal. Keep heating, and the spin coupling effects drop out and it changes state, and the new state is solid at this temperature. As long as the nanoparticles are intact it’s reversable and will re-form the ferrimagnetic state when cooled. At sufficiently high temperature, though, you cook the nanoparticles or cause changes to those asymmetric molecules, and wind up with a mundane material (perhaps a ceramic).
The exotic material is metal-like in bulk because it is a conductor of electricity and an excellent conductor of heat, even if not via the same mechanism of a natural metal. These are desirable properties for its original purpose to make motors.
Tin might fit the bill in some respects.
https://en.wikipedia.org/wiki/Tin
In warm temperatures it is metal and you can make stuff out of it. In cold weather it shifts to a different configuration which is nonmetallic, nonconductive and does not hold together - not melting but coming apart into powder (tin pest). Close to what you want in that the warm version has structural integrity and the cold has not. But not liquid / solid.
video of tin pest in action found https://www.youtube.com/watch?v=Q9zdt-rOB0Y
This goes against the laws of physics, it's like inventing a light bulb that sucks away darkness to reveal the light hidden "underneath".
It's about heat and pressure, these are the two things that force matter to change its state.
Granted, there are some weird states of matter, but if you want to actually melt and solidify matter there is only one way.
As stated in the comments and other answer, there are ways to have "matter" become "hard" and then "soft" again in other ways, but that has nothing to do with the state of matter as you describe it.
OP has said "alloy" but what about a compound of nanobots? It could be programmed to perform in the way desired, against Thermodynamics. Nanobots might not fit in with the rest of the World though.
Just 1¢ addition to other answers
Melting temperature may depend on a size of nanoparticles, and it is one of the problems in making them, as it begins to be too low.
As size of particles begins to be smaller, surface tension of the droplets begins to be more significant part of the total energy of the particle, as volume of the particle reduces proportionally $\sim r^3$ and surface $\sim r^2$
Dependence is not linear, an example with tungsten, from Melting tungsten nanoparticles: a molecular dynamics study
Such particles, in theory, may contain shells with different properties - oxide layers to prevent agglutination for longer period of time, other metals to form solutions with lower or higher melting point than original metals like Wood's metal or changing melting point of a nanoparticle, or creating solid-liquid mix, shapes of nanoparticles embedded in metal nanoparticles (like CNT, monocrystals - hedgehog style) etc etc.
Shells are not necessary it may be a mix of different sizes nanoparticles of the same metal of different metals etc.
All that may allow creating of interesting mixes of metal and(or) nonmetal nanoparticles with different time-temperature-phase dependencies of the mix.
It will be(probably most of the time) one-time one-way mixtures - but with creating different macro objects it will be most likely one would wish.
With increasing temperature, we get increasing disorder, so it would be very strange for a substance to solidify with increasing temperature (unless water vapour or or other liquid is driven off as mentioned by Kingledion.)
However such substances do exist, as mentioned by Mrkvicka. Similarly, and equally counterintuitively, ice gets denser when it melts.
The thing that must increase as temperature increases is disorder. In the case of the density of water/ice, it just so happens that ice's most ordered structure has a lot of empty space in it, which explains why it is less dense than the more disordered liquid form of water.
As you asked for an "element" or alloy that solidifies when heated, it is worth mentioning pure sulphur, which comes close, in a way. It has a vast increase in viscosity as it is warmed. It starts off as an ordered crystalline solid of S8 rings, which melts into a runny liquid of S8 rings. At a certain temperature, these ordered rings break open and a highly viscous polymer develops, with lots of different chain lengths. On further heating, this breaks down into a runny liquid of formula S2 and finally into gas.
Mrkvicka's example is similar in that molecules have an ordered sysem of intramolecular hydrogen bonding at low temperature, which becomes a disordered system of intermolecular hydrogen boning at high temperature. However there are also big differences: In Mrkvicka's example I understand the ring itself is not disturbed, and the bonds broken are hydrogen bonds rather than covalent bonds.
Another interesting and counterintuitive property is found in sulphur produced by the desulphurization process of the oil industry, which has hydrogen sulphide dissolved in it. The hydrogen sulphide caps the polymeric chains, so this sulphur does not become viscous like pure sulphur. But what is interesting is that when it cools and forms a more ordered structure of S8 rings, it expels the hydrogen sulphide. Thus it "boils" when the temperature is reduced!
All the transformations mentioned here are reversible which I assume is what you are looking for.
Unfortunately, these properties are due to the molecular nature of the substance, so as metals do not generally form molecules it would be much less likely to find such properties in a metal.
That said, it is concievable that a zintl phase could have the properties you are looking for at some temperature range. These are compounds containing positively charged alkali metal ions and negatively charged ions consisting of clusters of silicon, tin or lead atoms. Being ionically bonded they are not conductive in the solid state. It is not out of the question that there could exist a zintl phase where heating to some (very high) temperature could cause the molecular negative ions to break down into a more disordered polymeric state. But the atoms in negative ions are not behaving like "metals" so to call this an "alloy" would be a bit of a stretch.
I'm late to the party but I did find some info on inverse melting in a Ti-Cr metal alloy.
In inverse melting, a metastable supersaturated alloy transforms polymorphously to the amorphous or undercooled liquid state. This transformation is thus like melting, except that the resulting phase is the undercooled liquid or an amorphous phase near the glass temperature (Ts),as opposed to high temperature equilibrium melt.
It is found that upon spontaneous vitrification the hardness of the material increases by about 40% whereas the longitudinal sound velocity decreases by about 10% indicating an elastic softening. The mechanical properties of partially vitrified material were found to be independent of the amount of crystalline inclusions indicting that they are dominated by the amorphous matrix.
The bad news:
However, it does bring up something interesting, which is the idea that in some cases an crystal phase could actually have MORE entropy than an amorphous one. This has also found to be the case for a Zirconium Tungstenate alloy at high temperatures and pressures.
I was skeptical, but that paper seems to end with a small glimmer of hope for you!
Our findings point to an entire class of materials that should behave similarly to ZrW2O8 and constitute direct experimental evidence for an overall entropy increase in an amorphous-to-crystalline transition.
If you're willing to accept a "certain point of view" answer:
There's no such thing as a melting/freezing temperature. A substance changes state continuously, solid<->liquid<->gas. As temperature increases, the rate at which it changes from solid to liquid increases, while the rate of the reverse process decreases. At some point, given other things remain the same, the melting and freezing rates are the same, and we call that temperature the melting/freezing point for that material under that set of conditions. That means, if the conditions change, you can, in fact have a substance remain liquid at a temperature lower than its melting point, or solid at temperatures above its freezing point, provided that conditions are different. This is far less likely than the liquid to gas change, as that is easy enough to achieve with pressure and concentration changes, but there is no reason why it's impossible.
Alternately, consider that melting/freezing happens over a range of temperatures. Depending on how you define "melting" or "liquid", you could claim it to occur at various temperatures, not the conventional value. A metal that has just softened enough that you can make an impression with a knife could be declared a very viscous liquid. Similarly, a metal, just cooled enough to form a crystalline outer skin could be declared a solid.
Your "alloy" is suffused with nanobots or perhaps made almost entirely of nanobots. Thus, you can give it any properties you want, including one that makes it solid at higher temperatures and liquid at lower temperatures.
You can even use the mechanics of another answer for one direction, such as driving liquids from a solution leaving behind the solids. In the case of the nanobots, they take the liquid within themselves or just help evaporate the liquid. In the reverse, they release the liquid or extract liquid from the air (or a combination of both).
In most cases, you've got a snowball's chance in the Sahara at midday of getting that to happen at conventional temperatures. Nature doesn't like it when people try to invert Physics. At the same time, a trick of Chemistry might get you what you want. Suppose you create an alloy molecule whose core was a fully (-)ionized semiconductor. The core would be surrounded by a shell made from the desired elements of your target alloy, neutrally charged.
Since the whole molecule would have a net negative charge, a large mass of this molecule would tend to be liquid if not cooled sufficiently. Oddly, when heated to within a certain range (depending on the structure of the molecule) the semiconductors in the core would tend to release their excess electrons and make it possible for ionic bonds to form between the molecules. As long as the strength of those ionic bonds is enough to hold up against the heat applied, you'd get a solid while hot.
It's a wierd molecule, probably expensive to fabricate, and doesn't actually exist, but it is theoretically possible.
