Diamond batteries? Unlikely.

The start of the academic year at Rice has been very time-intensive, leading to the low blogging frequency.  I will be trying to remedy that, and once some of the dust settles I may well create a twitter account to point out as-they-happen results and drive traffic this way.  

In the meantime, there has been quite a bit of media attention this week paid to the claim by NDB that they can make nanodiamond-based batteries with some remarkable properties.  This idea was first put forward in this video.  The eye-popping part of the news release is this:  "And it can scale up to electric vehicle sizes and beyond, offering superb power density in a battery pack that is projected to last as long as 90 years in that application – something that could be pulled out of your old car and put into a new one."

The idea is not a new one.  The NDB gadget is a take on a betavoltaic device.  Take a radioactive source that is a beta emitter - in this case, ¹⁴C which decays into ¹⁴N plus an antineutrino plus an electron with an average energy of 49 keV - and capture the electrons and ideally the energy from the decay.  Betavoltaic devices produce power for a long time, depending on the half-life of the radioactive species (here, 5700 years).  The problem is, the power of these systems is very low, which greatly limits their utility.  For use in applications when you need higher instantaneous power, the NDB approach appears to be to use the betavoltaic gizmo to trickle-charge an integrated supercapacitor that can support high output powers.

To get a sense of the numbers:  If you had perfectly efficient capture of the decay energy, if you had 14 grams of ¹⁴C (a mole), my estimate of the total power available is 13 mW. (((6.02e23 *49000 eV *1.602e-19 J/eV)/2)/(5700 yrs*365.25 days/yr*86400)). If you wanted to charge the equivalent of a full Tesla battery (80 kW-h), it would take (80000 W-hr*3600 s/hr)/(0.013 W) = 2.2e10 seconds. Even if you had 10 kg of pure ¹⁴C, that would take you 180 days.

Now, the actual image in the press release-based articles shows a chip-based battery labeled "100 nW", which is very reasonable.  This technology is definitely clever, but it just does not have the average power densities needed for an awful lot of applications.

Black Si, protected qubits, razor blades, and a question

The run up to the new academic year has been very time-intense, so unfortunately blogging has correspondingly been slow.  Here are three interesting papers I came across recently:

• In this paper (just accepted at Phys Rev Lett), the investigators have used micro/nanostructured silicon to make an ultraviolet photodetector with an external quantum efficiency (ratio of number of charges generated to number of incoming photons) greater than 100%.  The trick is carrier multiplication - a sufficiently energetic electron or hole can in principle excite additional carriers through "impact ionization".  In the nano community, it has been argued that nanostructuring can help this, because nm-scale structural features can help fudge (crystal) momentum conservation restrictions in the impact ionization process. Here, however, the investigators show that nanostructuring is irrelevant for the process, and it has more to do with the Si band structure and how it couples to the incident UV radiation.  
• In this paper (just published in Science), the authors have been able to implement something quite clever that's been talked about for a while.  It's been known since the early days of discussing quantum computing that one can try to engineer a quantum bit that lives in a "decoherence-free subspace" - basically try to set up a situation where your effective two-level quantum system (made from some building blocks coupled together) is much more isolated from the environment than the building blocks themselves individually.  Here they have done this using a particular kind of defect in silicon carbide "dressed" with applied microwave EM fields.  They can increase the coherence time of the composite system by 10000x compared with the bare defect.
• This paper in Science uses very cool in situ electron microscopy to show how even comparatively soft hairs can dull the sharp edge of steel razor blades.  See this cool video that does a good job explaining this.  Basically, with the proper angle of attack, the hair can torque the heck out of the metal at the very end of the blade, leading to microfracturing and chipping.

And here is my question:  would it be worth joining twitter and tweeting about papers?  I've held off for a long time, for multiple reasons.  With the enormous thinning of science blogs, I do wonder, though, whether I'd reach more people.

The energy of the Beirut explosion

The shocking explosion in Beirut yesterday was truly awful and shocking, and my heart goes out to the residents.  It will be quite some time before a full explanation is forthcoming, but it sure sounds like the source was a shipment of explosives-grade ammonium nitrate that had been impounded from a cargo ship and (improperly?) stored for several years.

Interestingly, it is possible in principle to get a good estimate of the total energy yield of the explosion from cell phone video of the event.  The key is a fantastic example of dimensional analysis, a technique somehow more common in an engineering education than in a physics one.  The fact that all of our physical quantities have to be defined by an internally consistent system of units is actually a powerful constraint that we can use in solving problems.  For those interested in the details of this approach, you should start by reading about the Buckingham Pi Theorem.  It seems abstract and its applications seem a bit like art, but it is enormously powerful.  

The case at hand was analyzed by the British physicist G. I. Taylor, who was able to take still photographs in a magazine of the Trinity atomic bomb test and estimate the yield of the bomb.  Assume that a large amount of energy \(E\) is deposited instantly in a tiny volume at time \(t=0\), and this produces a shock wave that expands spherically with some radius \(R(t)\) into the surrounding air of mass density \(\rho\).  If you assume that this contains all the essential physics in the problem, then you can realize that the \(R\) must in general depend on \(t\), \(\rho\), and \(E\).  Now, \(R\) has units of length (meters).  The only way to combine \(t\), \(\rho\), and \(E\) into something with the units of length is \( (E t^2/\rho)^{1/5}\).  That implies that \( R = k (E t^2/\rho)^{1/5} \), where \(k\) is some dimensionless number, probably on the order of 1.  If you cared about precision, you could go and do an experiment:  detonate a known amount of dynamite on a tower and film the whole thing with a high speed camera, and you can experimentally determine \(k\).  I believe that the constant is found to be close to 1.  

Flipping things around and solving, we fine \(E = R^5 \rho/t^2\).  (A more detailed version of this derivation is here.)  

This youtube video is the best one I could find in terms of showing a long-distance view of the explosion with some kind of background scenery for estimating the scale.  Based on the "before" view and the skyline in the background, and a google maps satellite image of the area, I very crudely estimated the radius of the shockwave at about 300 m at \(t = 1\) second.  Using 1.2 kg/m³ for the density of air, that gives an estimated yield of about 3 trillion Joules, or the equivalent of around 0.72 kT of TNT.   That's actually pretty consistent with the idea that there were 2750 tons of ammonium nitrate to start with, though it's probably fortuitous agreement - that radius to the fifth really can push the numbers around.

Dimensional analysis and scaling are very powerful - it's why people are able to do studies in wind tunnels or flow tanks and properly predict what will happen to full-sized aircraft or ships, even without fully understanding the details of all sorts of turbulent fluid flow.  Physicists should learn this stuff (and that's why I stuck it in my textbook.)

How long does quantum tunneling take?

The "tunneling time" problem has a long, fun history.  Here is a post that I wrote about this issue 13 years ago (!!).  In brief, in quantum mechanics a particle can "tunnel" through a "classically forbidden" region (a region where by simple classical mechanics arguments, the particle does not have sufficient kinetic energy to be there).  I've written about that more recently here, and the wikipedia page is pretty well done.  The question is, how long does a tunneling particle spend in the classically forbidden barrier?  

It turns out that this is not a trivial issue at all.  While that's a perfectly sensible question to ask from the point of view of classical physics, it's not easy to translate that question into the language of quantum mechanics.  In lay terms, a spatial measurement tells you where a particle is, but doesn't say anything about where it was, and without such a measurement there is uncertainty in the initial position and momentum of the particle.  

Some very clever people have thought about how to get at this issue.  This review article by Landauer and Martin caught my attention when I was in grad school, and it explains the issues very clearly.  One idea people had (Baz' and Rybochenko) is to use the particle itself as a clock.  If the tunneling particle has spin, you can prepare the incident particles to have that spin oriented in a particular direction.  Then have a magnetic field confined to the tunneling barrier.  Look at the particles that did tunnel through and see how far the spins have precessed.  This idea is shown below.

"Larmor clock", from this paper

This is a cute idea in theory, but extremely challenging to implement in an experiment.  However, this has now been done by Ramos et al. from the Steinberg group at the University of Toronto, as explained in this very nice Nature paper.  They are able to do this and actually see an effect that Landauer and others had discussed:  there is "back-action", where the presence of the magnetic field itself (essential for the clock) has an effect on the tunneling time.  Tunneling is not instantaneous, though it is faster than the simple "semiclassical" estimate (that one would get by taking the magnitude of the imaginary momentum in the barrier and using that to get an effective velocity).  Very cool.