# Explosion contained in the depths of a crystal: how would it work?

Far in the future, I have a bomb about to detonate in the skies above my city, a real city/province killer. A hero dramatically manages to enclose the bomb at the moment of detonation in a living crystalline metal matrix, saving the city...or maybe only part of the city, I haven't figured that out yet.

The heat, energies, shockwaves, radiation, everything (I think) are reflected on one another by the crystal metal. Like a hall of mirrors reflecting your image back on one another indefinitely. The detonation is contained and compressed inside this living crystal metal resulting in a small glowing crystal artifact or cocoon (yes, this will increase the yield of the explosion IF it does ever manage to finish exploding).

Having watched way too much Doctor Who, I have imagined something that looks like a 'White-Point Star Diamond' but with none of the dimensional time lock/link characteristics. Just literally an explosion contained in a crystal cocoon.

'Normal' physics applies, no magic. Which is why I used the science-based tag. The only thing 'strange' in this story-world is the living crystal metal (that also does have some quantum entanglement issues, i.e, spooky action at a distance)

• the living crystal metal is an alien symbiotic substance that will form an exceptionally strong (and malleable, not brittle) reflective cocoon around the explosion.
• the living crystal metal shape can only be destroyed by; the person who created it willing it to cease, the creator dying, being struck multiple times by another living crystal metal item, or a massive amount of energy (i.e the bomb blast itself, may wear down the crystal metal from the inside)
• to prevent accidental release of all the pent up energy, several individual's add several buffer layers of living crystal metal around the Cocoon - even if the explosion does break through one bond, there are still several more layers before the big badda boom.

First off, bearing in mind Far-future and advanced phlebotinum, What sort of explosion definitely would/wouldn't work in this situation? The bomb makers have a tendency to base their weapons on light but this particular bomb could always be new/old tech, so anything I should be aware of?

I imagine that with time the potential energy of the bomb will increase exponentially by being contained in a reflective substance. I have several ideas to help with this but am not sure which would actually help the most or do harm.

• constant 'feeding' of the crystal metal to replenish cocoon strength, or

• periodic 'feeding' of the crystal metal to replenish cocoon strength,

• occasional release of the pent up energy (this could be dangerous, and dramatic),

• the energy from the explosion actually provides the energy to maintain the cocoon rather than wear it down?

Secondly How will the energy from the explosion react to being constrained by a reflective surface?

and Thirdly (BONUS) How will the energy from the explosion react IF it were to be suddenly released? I'm thinking 'end of the world...'. How bad are we talking?

• You are far enough from real physics that, if I answer this "science based," you will find the answer is that not a single element of the story will work. It's just not how things work in real life. Is that useful to you, or should we try to change the tags to something which permits this to work better. Nov 7 '16 at 22:31
• As an example, "... the potential energy of the bomb will increase exponentially..." is simply not how potential energy works. The closest we can get to that is a nuclear explosion, where holding it together longer permits more of the material to undergo fission. Even then, there's a cap -- once all of the material has undergone fission, the energy is at a peak and no longer grows. Nov 7 '16 at 22:32
• Do you need the crystal to be holding onto some energetic remains afterwards? That's probably the most scientifically challenging part. What will end up happening in real physics is that the energy inside the bomb will slowly be converted to heat, which will be dissipated into the environment. Bombs don't have much energy, they just release it fast. For comparison, the bomb dropped on Hiroshima had the same amount of energy as the fuel in 6 Airbus A380s. Nov 7 '16 at 22:38
• Odd factoid that came out of looking at those numbers: Little Boy, the bomb dropped on Hiroshima put out 6*10^13J of energy. That's equal to the amount of solar energy which hits Costa Rica every second! Nov 7 '16 at 22:43
• Keep in mind that this much radiation will probably kill the alien organism, even if its body survives - and that many types of radiation can still permeate solids, reflective or not Nov 8 '16 at 2:09

Energy is an odd concept. By the current known laws of physics, energy cannot be created nor destroyed. However, "useful" energy can be destroyed by reducing it to thermal energy. Thermal energy is no different than any other form of energy, except that it is so unstructured that it tends to behave in very statistically boring ways. To make your story interesting, we're going to have to dig into some physics first. Bear with me.

When we start to look at bombs, it's important to understand stability and metastability. A material is "stable" when its energy is at its lowest. A rock is pretty darn "stable" by this definition. We can contrast this with an unstable material, which is at an elevated energy state. The flame burning around a candle is unstable. It must constantly tumble towards a lower energy state, and if it wants to remain around for a long period of time, it must find a fuel source. In the case of a candle, this fuel source is the vaporizing wax emitted from the wick. As long as there's wax to burn, the flame can stay. However, once there's no more fuel, it snuffs itself out.

Metastability is a strange hybrid of the two. A metastable compound is mostly stable, but can be pushed into a unstable regime. Consider a cup on a table next to your favorite feline. The cup is rather stable. It's not going anywhere; the table is flat and solid. However, if the cat merely nudges the cup in the wrong direction (and they only nudge them in the wrong direction), the cup will become unstable, fall to the ground, and break.

Explosives are like that. They are metastable. They are designed to be very stable while working with them, and remain stable until an initiator sets them off. At that time, they become unstable and... well... blow up.

So, with those scientific terms covered, let's get back to your story. It is reasonable to contain an explosion inside a container. On one of the recent nuclear tests done by North Korea, they contained their bomb underground. There's no exponential power gains or anything like that. Being contained simply means that the container has to dissipate the energy. The ground is very good at...well... not moving very much. It happily contained that nuclear explosion. Of course, the energy has to go somewhere. Some of it went into heating the ground locally. Other portions of the energy were turned into seismic waves which echoed around the world. This was actually what the western world used to validate North Korea's claims about the test. We looked at the seismic waves and compared them to what we expected to see given their announced data!

Now there's something interesting about these two ways of dissipating energy. Thermal energy is highly random, and generally uncontrolled. The nature of the seismic energy, on the other hand, is highly structured. It's structured enough that we can detect it on the other side of the world and make inferences. Its structure is based on the materials of the earth. Some frequencies naturally translate well, and some do not. For example, typically high frequencies attenuate quickly and lower frequencies do not. That's why shutting the door on your brother's loud music blots out the high parts, but the low bass rumbles through the door. Your door is transmitting the low frequency sounds, but its turning the high frequency sounds into heat. (You just don't notice the heat because it's tiny in the case of audio energy... but it is there).

Now one solution is to have the crystal simply convert everything to heat. This is easy -- because the bomb already wants to heat things up. You don't have to do anything special. All you have to do is have the structural integrity to not blow up under the intense pipe-bomb style pressures that the bomb will generate. Once you're done holding the bomb in, you're going to have a very hot inner surface. That heat will then propagate outward towards the outer surface. The crystal can then simply "cool off" for a while, dissipating all of that heat energy.

How much heat energy is it going to have to deal with? It turns out not very much. As I pointed out in comments, bombs don't depend on massive amounts of energy. They depend on sudden localized impulses. The sun puts far more energy on the earth every second than your city-killer would ever emit. For a real life data point I love to turn to Wikipedia's page Orders of Magnitude (Energy) and find interesting coincidences. Today's coincidence: Little Boy (the bomb we dropped on Hiroshima) outputted $6.3\cdot 10^{13}J$. That's the amount of solar energy that falls on Costa Rica in a single second! The amount of energy in these sorts of weapons is nothing compared to what our planet experiences every day from the sun!

Now this isn't quite the ringing crystal effect you are looking for. If we did everything with thermal energy, your crystal would be done with its job in days (weeks at most), and once it was done with the few few seconds of the job, we could all be pretty confident that the risk is over. You want a bit more thrill. For that, we're going to need to harness the energy of the weapon, similar to the seismic waves through the earth.

The big difference between this case and the thermal case is that, in this case, we want to capture all of that energy as potential energy. Eventually, we want to re-emit that energy slowly to dissipate it. Think of your crystal metal kinda like a tuning fork. The bomb gives it a really really hard thump. It elastically responds, and then springs back into a vibrating state that we use to tune a piano. In this case, much of the energy of the original explosion remains pent up inside the structure of your crystal/tuning fork. If you want to see how much energy is in one of those tuning forks, give one a rap and then hold it up to your teeth. Like your crystal, tuning forks have a lot of energy that you don't want going in the wrong directions!

Now in a realistic setting, the energy dissipates. It'd be very loud, but doable. You'd probably want to structure the crystal metal such that the outside is a "node" for the sound, meaning none of the energy actually escapes. In this case, you'd simply find the crystal metal flexes back and forth until that movement eventually turns all of the energy to heat (like before). This is getting closer, but we still don't have too much thrill. Again, it would be easy enough to dissipate most of the energy fast enough to be boring. We need something to make it more interesting.

What if the weapon that was set off was a new weapon, and there was a pressing need to understand it better. In such a case, there would be a strong desire to not destroy any information you have about the weapon, and turning meaningful energy into heat energy destroys information. There might be a desire to intentionally keep all of the energy pent up. In such a case, your magical crystal metal might try to hold onto as much of the information from the blast without destroying anything. Naturally, this would require keeping all of that energy pent up while the powers at be decide what to do with it.

Remember the earlier topic of metastability? Your crystal just became metastable. In theory, it is perfectly containing the energy of the explosion inside of its structure. However, if mishandled, it may cease to be able to contain that energy, and unleash it as though it was an explosive itself!

In this case, the destruction of the crystal metal would never exceed the original explosion, but it would keep the threat looming for as long as your magical metal can avoid turning those sound waves to heat. It would encourage "care and feeding" to help it maintain the constantly shifting effects.

• Thanks. That is very helpful. You have taken my inaccurate deductions on what would happen and made them seem plausible. You deserve more than +1. Nov 8 '16 at 7:05
• How hot do you think the crystal would get: Burning hot or a warm glow?Turning all that energy to heat...Would you still be able to hold it in your hand? Nov 10 '16 at 8:50
• @EveryBitHelps That depends greatly on thermal properties. In particular how well it holds the energy in. The bomb is going to release on the order of 10^13J of energy to be released over time. A 1kW space heater outputs 1000J of heat every second, so if it dissipated the heat over 1 second, it would be as hot as 10,000,000,000 space heaters. If it dissipated it over 1,000,000 seconds, it would be as hot as 10,000 space heaters. If it dissipated it over 10,000,000,000 seconds (317 years), it would be exactly as hot as a space heater. Nov 10 '16 at 15:15
• As an example of a surprising insulator, take a look at aerogels.. They're not about to hold onto that heat for years like you might need, but they are an example of an insulator that slows the transmission of heat remarkably. Nov 10 '16 at 15:16
• Oh, and note that those numbers I just threw around are for the Hiroshima sized bomb. If your weapon is more powerful than that, you can scale those numbers accordingly. The nice thing about energy is that it is conserved, so you can multiply and divide and generally not be surprised by it. A bomb releasing 10x more energy takes 10x longer to cool! Nov 10 '16 at 15:20

Now, How does an explosion work? It has mainly 2 foundations:

1. setting free thermal energy by destroying covalent bonds
2. changing the state of the solid explosive to expanding gas

As it does both, the result is a shock wave, which in turn is what destroys items.

The basic physics behind stable, unstable and metastable objects was very well explained by Cort Ammon, but he did not look into the gas part too much.

## Thermodynamics of explosions

Now, let's take our metastable compound, for example 2-Methyl-1,3,5-trinitrobenzene. We know very well about the behavior of this when it becomes unstable, and we know pretty well that it produces a "standard gas volume" of $$975 \frac l{kg}$$. So if we just convert 1 kg of TNT to gas at standard conditions (20°C, 1 atm, V=22.5 l/mol) the gas formula $$pV=nRT$$ will give us a V of 975 liters, or in reverse, the correct number of molecules n.

Now, our TNT doesn't turn gas in an instant, it doesn't turn so at 20°C either, something has to happen: first of all, the reaction takes time and starts somewhere. Then the block "burns through" with a speed of $$6900 \frac ms$$ from our initial detonator to the edges, so it is finished within a really tiny fraction of a second. Doing so, it sets free a lot of heat $$(3725 - 3612 \frac{kJ}{kg})$$ and the kown ammount of gas molecules n (which is not a number that is really well to handle, let's keep it that way).

Now, we have our formula above, we know standard condition volume and pressure, so we can recalculate with our known n... Obviously we stumble about a factor that isn't the same as before: T aka temperature has increased by those more than 3600 kJ for 1 kg. We have a temperature of at least 300°C now and maybe much more, so our gas will have to do something to compensate for the increased T as n will stay the same. The first step any gas does to compensate increased temperature is always the same: it expands, increasing the V part of the term.

Once it can't expand freely anymore (because there is something like solid objects or other gases in the way), it will start to put itself and the 'barrier' under pressure and increases the p part too (actually, it starts so the very moment V increases, but not so fast as it will once hitting solid object). This puts stress on the objects it hits, creating a shockwave.

Luckily for us, the art of blowing up things provides us with an indicator how strong this shockwave is via the Trauzl test: TNT creates a cavity of $$30 \frac {cm^3} g$$, so our 1 kg block above makes a cavity of 30000 cm³, or about 30 liters, in a similar lead cylinder. Compressing 975 liters to a 30 liters cavity is a factor of 32.5, so we have a pressure of roughly 32.5 atmospheres.

That is our shockfront: 32.5 atm or 477.6 psi (under ignorance of the thermal factor again) at the very end of the expansion (in the lead block), and much more in some of the steps to get there.

## What does this tell us about our 'container'?

### Stress on the Crystal

Now, our crystalline structure will have not only to endure the thermal energy that was previously stored in the covalent bonds of the explosive, it also has to endure the pressure the expanding gas puts upon it. To do so, our structure is better highly ductile, allowing it to deform with the expanding shockwave and lessening the impact due to longer exposure time: Force is always mass times acceleration, and acceleration is speed change over time. or, as a formula: $$\vec F = m \times \vec a = m \times \frac {\text d \vec v}{\text dt}$$. Let's assume m (mass of crystal) and v (speed of the shockwave} are constant, then by taking 1 second instead of 0.1 second to stand in the way of the shockwave will put only 1/10th of the stress upon the crystal. So our "crystal" better be mallable to some degree to increase its potential at containing the explosion by expanding. Think about this like... a baloon or a tire.

### Path of least resistance

Now, we always assumed our crystal would have to contain the whole detonation. What if we only placed the barrier on one side, and kept open sky above or put the detonation between two crystal disks? Now we face very interesting effects: shockwaves and expanding gasses take the "way of least resistance". Partly this is because it is much "easier" to increase volume by applying pressure to push away gas than applying pressure to indent solids, partly this is because in indenting solids causes some of the particles that were sent against the solid are reflected. The result is pretty simple:

If you detonate something against a solid surface, and don't take care to apply pressure on it, you get a loud bang and a little bit scorched ground. Also, Detonation shockwaves don't get around barriers very well (they can, but it is more difficult). This is used as a trick to create directed charges: a strong barrier and a weak barrier encase an explosive, forcing the detonation to deform the weak barrier (usually copper) and turn it into a cutting edge.

## Solution

Should the bomb not contain harmful materials to the city underneeth it (nuclear devices, dirty bombs, chemical compounds), the way to go would not be encasing the bomb fully, but to encase the lower half of it. This will direct the shockwave upwards in a flat cone (or to make it mathematically correct: spherical cone), minimize the stress on the crystal and at the same time maximise the protection. A detonation at the very 'horizon' of a half-sphere reflector will expand to the non-shielded half-sphere. If it detonates lower, the stress gets bigger, but the resulting effected cone is much more focussed.

• Ah, so I was correct that the crystal barrier and compression would affect the explosion dynamics? I have toyed with some of the explosion being directed skyward when first being covered by the hero (they just couldn't get there in time). I was thinking it would be in a focused beam, but a flat cone as you described it actually makes more sense. Nov 8 '16 at 13:05
• @EveryBitHelps A focused beam would be the result of a long cylinder with one open end. Think of the resulting shockwave 'shape' a bit like the 'cone' of a flashlight - depending on where the detonation is in the reflector, the cone is wider or flatter. with the detonation happening at the height of the edge of the reflector, you get a half sphere, anything lower gets the conical sphere cutout. Nov 8 '16 at 13:15
• "in time" is an interesting choice of words. Look at a mythbusters explosion sometime. Things just vanish. The entire explosion is over in a fraction of a second. There is no way for a human to react after the explosion has started and before they have been blown to smithereens. Nov 8 '16 at 13:25
• @TimB, ah but that's why I say explosion inside a crystal and not a bomb. The hero attempts to cover the entire bomb, managing to shield say 90% surface area. The bomb then goes off, can't stop that as you say, it's a fraction of a second, but the blast is directed towards the opening in the already formed crystal (and probably deforming the existing shape in the process). Then the 10%missing coverage is added and the crystal compacted to result in the 'white-point star' size... Nov 8 '16 at 14:19
• @TimB in time is meant as "before the detonation" not really "during it", but then again, Flash or Superman might be fast enough to still react, especially when they move at relative speeds. Nov 9 '16 at 9:16

Don't overthink this:

You basically just build a pipe-bomb; A explosion is just a sudden release of stuff (heat, air, radiation) into the surounding environment. If the "stuff" can't escape, it stays under pressure until the time the containment fails. Basically you just bottled the explosion, delaying it's effect.

This would work on anything we classicallly consider an explosion.

The explosion wouldn't get stronger, because you are not adding any additional energy, but it could potentially be more focused (e.g. when you contained all the energy of a aerated fuel explosion (meter wide dispersion of the explosion "fuel") into a few centimeters, the core of the explosion would of course be more energetic, even when releasing the same amount of explosive yield).

• Yeah. I think I used the wrong word. I was thinking more the intensity increasing than the actual energy amount increasing. Nov 8 '16 at 10:47