‘Surface of last screaming’

This has nothing to do with anything in the news. I was reading up about the Big Bang for a blog post when I came across this lucid explanation – so good it’s worth sharing for that reason alone – for the surface of last scattering, the site of an important event in the history of the universe. A lot happens by this moment, even if it happens only 379,000 year after the bang, and it’s easy to get lost in the details. But as the excerpt below shows, coming at it from the PoV of phase transitions considerably simplifies the picture (assuming of course that you’re comfortable with phase transitions).

To visualise how this effect arises, imagine that you are in a large field filled with people screaming. You are screaming too. At some time t = 0 everyone stops screaming simultaneously. What will you hear? After 1 second you will still be able to hear the distant screaming of people more than 330 metres away (the speed of sound in air, v, is about 330 m/s). After 3 seconds you will be able to hear distant screams from people more than 1 kilometre away (even though those distant people stopped screaming when you did). At any time t, assuming a suitably heightened sense of hearing, you will hear some faint screams, but the closest and loudest will be coming from people a distance v*t away. This distance defines the ‘surface of last screaming’ and this surface is receding from you at the speed of sound. …

When something is hot and cools down it can undergo a phase transition. For example, hot steam cools down to become water, and when cooled further it becomes ice. The Universe went through similar phase transitions as it expanded and cooled. One such phase transition … produced the last scattering surface. When the Universe was cool enough to allow the electrons and protons to fall together, they ‘recombined’ to form neutral hydrogen. […] photons do not interact with neutral hydrogen, so they were free to travel through the Universe without being scattered. They decoupled from matter. The opaque Universe then became transparent.

Imagine you are living 15 billion years ago. You would be surrounded by a very hot opaque plasma of electrons and protons. The Universe is expanding and cooling. When the Universe cools down below a critical temperature, the fog clears instantaneously everywhere. But you would not be able to see that it has cleared everywhere because, as you look into the far distance, you would be seeing into the opaque past of distant parts of the Universe. As the Universe continues to expand and cool you would be able to see farther, but you would always see the bright opaque fog in the distance, in the past. That bright fog is the surface of last scattering. It is the boundary between a transparent and an opaque universe and you can still see it today, 15 billion years later.

Where is the coolest lab in the universe?

The Large Hadron Collider (LHC) performs an impressive feat every time it accelerates billions of protons to nearly the speed of light – and not in terms of the energy alone. For example, you release more energy when you clap your palms together once than the energy imparted to a proton accelerated by the LHC. The impressiveness arises from the fact that the energy of your clap is distributed among billions of atoms while the latter all resides in a single particle. It’s impressive because of the energy density.

A proton like this should have a very high kinetic energy. When lots of protons with such amounts of energy come together to form a macroscopic object, the object will have a high temperature. This is the relationship between subatomic particles and the temperature of the object they make up. The outermost layer of a star is so hot because its constituent particles have a very high kinetic energy. Blue hypergiant stars, thought to be the hottest stars in the universe, like Eta Carinae have a surface temperature of 36,000 K and a surface 57,600-times larger than that of the Sun. This isn’t impressive on the temperature scale alone but also on the energy density scale: Eta Carinae ‘maintains’ a higher temperature over a larger area.

Now, the following headline and variations thereof have been doing the rounds of late, and they piqued me because I’m quite reluctant to believe they’re true:

This headline, as you may have guessed by the fonts, is from Nature News. To be sure, I’m not doubting the veracity of any of the claims. Instead, my dispute is with the “coolest lab” claim and on entirely qualitative grounds.

The feat mentioned in the headline involves physicists using lasers to cool a tightly controlled group of atoms to near-absolute-zero, causing quantum mechanical effects to become visible on the macroscopic scale – the feature that Bose-Einstein condensates are celebrated for. Most, if not all, atomic cooling techniques endeavour in different ways to extract as much of an atom’s kinetic energy as possible. The more energy they remove, the cooler the indicated temperature.

The reason the headline piqued me was that it trumpets a place in the universe called the “universe’s coolest lab”. Be that as it may (though it may not technically be so; the physicist Wolfgang Ketterle has achieved lower temperatures before), lowering the temperature of an object to a remarkable sliver of a kelvin above absolute zero is one thing but lowering the temperature over a very large area or volume must be quite another. For example, an extremely cold object inside a tight container the size of a shoebox (I presume) must be lacking much less energy than a not-so-extremely cold volume across, say, the size of a star.

This is the source of my reluctance to acknowledge that the International Space Station could be the “coolest lab in the universe”.

While we regularly equate heat with temperature without much consequence to our judgment, the latter can be described by a single number pertaining to a single object whereas the former – heat – is energy flowing from a hotter to a colder region of space (or the other way with the help of a heat pump). In essence, the amount of heat is a function of two differing temperatures. In turn it could matter, when looking for the “coolest” place, that we look not just for low temperatures but for lower temperatures within warmer surroundings. This is because it’s harder to maintain a lower temperature in such settings – for the same reason we use thermos flasks to keep liquids hot: if the liquid is exposed to the ambient atmosphere, heat will flow from the liquid to the air until the two achieve a thermal equilibrium.

An object is said to be cold if its temperature is lower than that of its surroundings. Vladivostok in Russia is cold relative to most of the world’s other cities but if Vladivostok was the sole human settlement and beyond which no one has ever ventured, the human idea of cold will have to be recalibrated from, say, 10º C to -20º C. The temperature required to achieve a Bose-Einstein condensate is the temperature required at which non-quantum-mechanical effects are so stilled that they stop interfering with the much weaker quantum-mechanical effects, given by a formula but typically lower than 1 K.

The deep nothingness of space itself has a temperature of 2.7 K (-270.45º C); when all the stars in the universe die and there are no more sources of energy, all hot objects – like neutron stars, colliding gas clouds or molten rain over an exoplanet – will eventually have to cool to 2.7 K to achieve equilibrium (notwithstanding other eschatological events).

This brings us, figuratively, to the Boomerang Nebula – in my opinion the real coolest lab in the universe because it maintains a very low temperature across a very large volume, i.e. its coolness density is significantly higher. This is a protoplanetary nebula, which is a phase in the lives of stars within a certain mass range. In this phase, the star sheds some of its mass that expands outwards in the form of a gas cloud, lit by the star’s light. The gas in the Boomerang Nebula, from a dying red giant star changing to a white dwarf at the centre, is expanding outward at a little over 160 km/s (576,000 km/hr), and has been for the last 1,500 years or so. This rapid expansion leaves the nebula with a temperature of 1 K. Astronomers discovered this cold mass in late 1995.

(“When gas expands, the decrease in pressure causes the molecules to slow down. This makes the gas cold”: source.)

The experiment to create a Bose-Einstein condensate in space – or for that matter anywhere on Earth – transpired in a well-insulated container that, apart from the atoms to be cooled, was a vacuum. So as such, to the atoms, the container was their universe, their Vladivostok. They were not at risk of the container’s coldness inviting heat from its surroundings and destroying the condensate. The Boomerang Nebula doesn’t have this luxury: as a nebula, it’s exposed to the vast emptiness, and 2.7 K, of space at all times. So even though the temperature difference between itself and space is only 1.7 K, the nebula also has to constantly contend with the equilibriating ‘pressure’ imposed by space.

Further, according to Raghavendra Sahai (as quoted by NASA), one of the nebula’s cold spots’ discoverers, it’s “even colder than most other expanding nebulae because it is losing its mass about 100-times faster than other similar dying stars and 100-billion-times faster than Earth’s Sun.” This implies there is a great mass of gas, and so atoms, whose temperature is around 1 K.

All together, the fact that the nebula has maintained a temperature of 1 K for around 1,500 years (plus a 5,000-year offset, to compensate for the distance to the nebula) and over 3.14 trillion km makes it a far cooler “coolest” place, lab, whatever.

The imperfection of strontium titanate

When you squeeze some crystals, you distort their lattice of atoms just enough to separate a pair of charged particles and that in turn gives rise to a voltage. Such materials are called piezoelectric crystals. Not all crystals are piezoelectric because the property depends on what the arrangement of atoms in the lattice is.

For example, the atoms of strontium, titanium and oxygen are arranged in a cubic structure to form strontium titanate (SrTiO3) such that each molecule displays a mirror symmetry through its centre. That is, if you placed a mirror passing through the molecule’s centre, the object plus its reflection would show the molecule as it actually is. Such molecules are said to be centrosymmetric, and centrosymmetric crystals aren’t piezoelectric.

In fact, strontium titanate isn’t ferroelectric or pyroelectric either – an external electric field can’t reverse their polarisation nor do they produce a voltage when they’re heated or cooled – for the same reason. Its crystal lattice is just too symmetrical.

The strontium titanate lattice. Oxygen atoms are red, titanium cations are blue and strontium cations are green.

However, scientists haven’t been deterred by this limitation (such as it is) because its perfect symmetry indicates that messing with the symmetry can introduce new properties in the material. There are also natural limits to the lattice itself. A cut and polished diamond looks beautiful because, at its surface, the crystal lattice ends and the air begins – arbitrarily stopping the repetitive pattern of carbon atoms.

An infinite diamond that occupies all points in the universe might look good on paper but it wouldn’t be nearly as resplendent because only the symmetry-breaking at the surface allows light to enter the crystal and bounce around. Similarly, centrosymmetric strontium titanate might be a natural wonder, so to speak, but the centrosymmetry also keeps it from being useful (despite its various unusual properties; e.g. it was the first insulator found to be a superconductor at low temperatures, in 1967).

Tausonite, a naturally occurring mineral form of strontium titanate. Credit: Materialscientist/Wikimedia Commons, CC BY-SA 3.0

So does strontium titanate exhibit pyro- or piezoelectricity on its surface? Surprisingly, while this seems like a fairly straightforward question to ask, it hasn’t been straightforward to answer.

A part of the problem is the definition of a surface. Obviously, the surface of any object refers to the object’s topmost or outermost layer. But when you’re talking about, say, a small electric current originating from the material, it’s difficult to imagine how you could check if the current originated from the bulk of the material or just the surface.

Researchers from the US, Denmark and Israel recently reported resolving this problem using concepts from thermodynamics 101. If the surface of strontium titanate is pyroelectric, the presence of electric currents should co-exist with heat. So if a bit of heat is applied and taken away, the material should begin cooling (or thermalising) and the electric currents should also dissipate. The faster the material cools, the faster the currents dissipate, and the faster the currents dissipate, the lower the depth to which the material is pyroelectric.

In effect, the researchers induced pyroelectricity and then tracked how quickly it vanished to infer how deeply inside the material it existed.

Both the bulk and the surface are composed of the same atoms, but the atomic lattice on the surface also has a bit of surface tension. Materials scientists have already calculated how deeply this tension penetrates the surface of strontium titanate, so the question was also whether the pyroelectric behaviour was contained in this region or went beyond, into the rest of the bulk.

The team sandwiched a slab of strontium titanate between two electrodes, at room temperature. At the crystal-electrode interface, which is a meeting of two surfaces, opposing charged particles on either side gather and neutralise themselves. But when an infrared laser is shined on the ensemble (as shown above), the surface of strontium titanate heats up and develops a voltage, which in turn draws the charges at its surface away from the interface. The charges in the electrode are then left without a partner so they flow through a wire connected to the other electrode and create a current.

The laser is turned off and the strontium titanate’s surface begins to cool. Its voltage drops and allows the charged particles to move away from each other, and some of them move towards the surface to once again neutralise oppositely charged particles from the other side. This process stops the current. So measuring how quickly the current drops off gives away how quickly the voltage vanishes, which gives away how much of the material’s volume developed a voltage due to the pyroelectric effect.

The penetration depth the group measured was in line with the calculations based on surface tension: about 1.2 nm. To be sure the effect didn’t involve the bulk, the researchers repeated the experiment with a thin layer of silica (the major component of sand) on top of the strontium titanate surface, and there was no electric current when the laser was on or off.

In fact, according to a report in Nature, the team also took various precautions to ensure any electric effects originated only from the surface, and due to effects intrinsic to the material itself.

… they checked that the direction of the heat-induced current does not depend on the orientation of the crystal, ruling out a bulk effect; and that the local heating produced by the laser is very small…, which means that the strain gradients induced by thermal expansion are insignificant. Other experiments and data analysis were carried out to exclude the possibility that the induced current is due to molecules … adsorbed to the surface, charges trapped by lattice defects, excitation of free electrons induced by light, or the thermoelectric Seebeck effect (which generates currents in semiconductors that contain temperature gradients).

Now we know strontium titanate is pyroelectric, and piezoelectric, on its surface at room temperature – but this is not all we know. During their experiments (with different samples of the crystal), the researchers spotted something odd:

The pyroelectric coefficient – a measure of the strength of the material’s pyroelectricity – was constant between 193 K and 225 K (–80.15º C to –48.15º C) but dropped sharply above 225 K and vanished above 380 K. The researchers note in their paper, published on September 18, that others have previously reported that the strontium titanate lattice near the surface changes from a cubic to a tetragonal structure at around 150 K, and that a similar transformation could be happening at 225 K.

In other words, the surface pyroelectric effect wasn’t just producing a voltage but could in fact be altering the relative arrangement of atoms itself. What the precise mechanism of action could be we don’t know – nor any other features that might arise in the material as a result. The researchers hope future studies can resolve these questions.