I am trying to recreate King Arthur's the Sword in the Stone using chemistry.

I have a couple ideas how this could be done Would any of these work or how it might work?
Arthur removes the sword from the stone and is blessed by Archbishop Brice, from Le Livre de Merlin, France, N. (Arras), 1310, Add MS 38117, f. 73v." Caption via the British Library's Medieval Manuscripts Blog.

Unlike this answer: Making a sword in the stone, in a medieval world without magic I am interested how this could have been done with a substance available in 500AD.

What could be smelted or concreted then to allow a sword to be entered into it then allowed to cool or harden with no chemical bond to the sword?

The material of the stone would need to contract as it gets colder to release the sword at a certain temperature, not be so hot during insertion to effect the temper of the sword, and/or allow water or ice to permeate between the sword and stone.

Similar to using whiteout to create a barrier between the soft iron shell and the inside hard steel of a canister Damascus forge could the sword be coated with a whiteout/liquid paper like material that breaks down when wet over time?

Could water get between a designer stone and sword enough to erode or breakdown the bond between the sword and the stone?

The simplest way this could be done I can think of is thrusting the sword into a ball of lava rock that meets the edge of an ocean then moved and carved. Over time water and winter loosen the sword.

You could use Roman concrete

https://en.wikipedia.org/wiki/Roman_concrete

Roman concrete, also called opus caementicium, was a material used in
construction during the late Roman Republic until the fading of the
Roman Empire. Roman concrete was based on a hydraulic-setting cement.
Recently, it has been found that it materially differs in several ways
from modern concrete which is based on Portland cement. Roman concrete
is durable due to its incorporation of volcanic ash, which prevents
cracks from spreading... Further
innovative developments in the material, called the Concrete
Revolution, contributed to structurally complicated forms, such as the
Pantheon dome, the world's largest and oldest unreinforced concrete
dome.

The Pantheon is 2000 years old and looking very, very good. Roman concrete is poured and cast like modern concrete, but is chemically different from modern concrete in several ways. If you are materials-science inclined, recent studies of Roman concrete make for interesting reading. To release the sword the concrete does not contract, but the metallic sword does. It needs to get really cold.

Your sword is embedded in Roman concrete and has been since Roman-trained engineers put it there 150 years before your story. Dark ages medieval Britons would know of the Romans and be familiar with their works but would likely have lost the arts of reproducing their technology - which is what really happened.

I am trying to recreate King Arthur's the Sword in the Stone using chemistry

Chemical

You could use thixotropism and come up with a sword that cannot be removed from its stone scabbard no matter how hard you pull, unless the sword is rattled gently for a couple of minutes beforehand. However, this solution is almost surely bound to undergo degradation along the years.

Mechanical

The simplest way to reproduce the effect would be with a friction lock. Basically, the Stone has a wide hollow "sleeve" inside, not so large as to perceivably alter the Stone's mass or balance; the sleeve is drilled from the bottom side of the Stone and stops a few inches from the surface of the top side, where it narrows to the exact width and thickness of the Sword's blade. So, from above, the Sword is set in the Stone. If this was the whole setup, the Sword would be very easy to extract.

But inside the sleeve you have two steel prongs as long as the blade, covered with a layer of soft lead. Once pressed against the blade, the blade bites the lead and leaves its exact impression; if the rods are kept pressed hard against the blade, the friction is so high that you will never be able to extract the blade, not even using levers. You'd break the blade hilt first.

Now the prongs are kept in place by a counterweight mechanism hosted in a small chamber beneath the stone. The mechanism can work in several ways: it can be "remote-controlled" from a nearby cloister through a wire or light chain pulled through a tube, or it can be released by placing weight on specific stones. One could even devise a "combination lock" so that you'd need to put your weight on stone A, then B, then A, then C, then B to achieve release. Of course anyone would feel the pavement stones wobble slightly, but if most of the flagstones were equally wobbly, nobody would think twice about it. If the mechanism were controlled by pulling a pin attached to an underground chain in a tube, even the wielder of the Sword would never know how the trick was done.

Approximately:

Gypsum. Also known as drywall. Gypsum plaster has been used for millennia.
https://www.youtube.com/watch?v=tmbk8Pfau0I

With a little artistry, you could easily cast it into the shape of a big rock around a sword. Throw in some darker sand/gravel and maybe some bigger stones, to give the appearance of natural occlusions.

The big advantage gypsum has over concrete is that it's not all that strong. A big guy could possibly pull a sword out, whereas I'd think cement/concrete would be impossible. The sword in that case is basically rebar.

We can take advantage of the fact that when dissimilar materials are in contact, they will typically have differing coefficients of thermal expansion.

Basically, as solid objects get hotter, they expand, and they contract as they get cooler. The difference between the coefficients of the materials involved can be used to create a system that will release the blade under the appropriate thermal conditions.

Steel has a coefficient of expansion of around 12 nm/mK. Granite, a common, hard, weather-resistant stone has a coefficient of expansion of around 7.9 nm/mK.

This means that for every linear metre of the substance, for every degree Kelvin that its temperature increases, it will expand x nanometres.

The problem is that 7.9 and 12 are quite similar... the difference is only 4.1nm/mK, meaning that quite a large negative temperature differential would be required to cause the sword to release from the stone.

However!

The system need not be mechanically so simple as a sword in a blade-shaped hole in a solid block of granite requiring a significant, prolonged, drop in temperature to cause the blade to contract sufficiently to release from the stone.

If we were to have two blocks of granite, each forming half of a vertical cylinder split vertically through its diameter, with a blade-shaped notch in each side, so that with the sword between them, the stones don't quite meet, held together by a circular steel strap, like the steel tyre on a wooden wagon wheel, we would have a system where a relatively small increase in temperature would result in a relatively great expansion of the steel strap (because it is much longer, by a factor of Pi×Diameter than the gap between the stones). This would allow us to create a system where the sword would become loose at or above a specific temperature. By surrounding the stone with a fire, the strap could be made to expand enough, while ordinary daytime temperatures would not, or the strap could be sized to release only on the hottest of daytime temperatures.

This would also have the advantage that rhe sword would not become blunted by its compression in the stone(s), and it could be preserved from rust by filling the gap between stones with a resin.

All of this is easily achievable with iron age technology.

The steel strap could be embossed to make it look decorative, rather than the key piece of the lock, so only a wheelwright pr perhaps a blacksmith would likely consider the mechanism by which the sword might be released... and in the middle ages, knights didn't soil their hands with manual labour, or bother themselves to understand what it is that craftsmen do.

Knights guard the stone, and will allow only another knight to approach... so only a knight who actually thinks about the common people is likely to figure it out or be popular enough and receptive enough to be told and listen.