Ultra Low K = Good Science

Last summer at ICT2006 in Vienna David Johnson of the University of Oregon presented a paper (Johnson et al, "Engineering Low Thermal Conductivity in Novel Thermoelectric Materials", presented at ICT2006 but does not appear in the Proceedings) which is of interest both for the scientific results, but also because it represents an excellent example of how Good Science is done. Sadly, the paper does not appear in the Conference Proceedings, but that work (and more) has now appeared in Science [1] (see below for a link to the Science manuscript). I've waited until now to comment, to give Johnson and his collaborators time to publish their results. But much of my commentary is based on his presentation in Vienna, some of which does not appear in the Science article.

Breifly, WSe_2 has a hexagonal sheet-like structure with strong bonds within the a-b plane and weak bonds perpendicular to the plane. When prepared by the by modulated elemental reactants (MER) method, the crystalline orientation in the a-b plane appears to be completely random. Johnson et al reports thermal conductivity in the c-direction (normal to the a-b plane) at 300 K is about 0.05 W/m-K. 30 times lower than a single crystal and 6 times lower than the 'theoretical minimum'. As the Science article reports, the "lowest thermal conductivity
ever observed in a fully dense solid". Indeed, one astonished observer in Vienna remarked that it was "lower than still air".

A dense solid that conducts heat as badly as a gas. All I can say is "neat".

No, it will not likely win a Nobel Prize, spark another "Woodstock of Physics", or garner headlines in the New York Times or Wall Street Journal. It will probably not even lead to a breakthrough in ZT, although that possibility is certainly not zero.

Still, Johnson's paper is a model of Good Science because, among other
things:
- the expected result did not happen
- an unexpected result did and they recognized the difference
- they checked their work by gathering good statistics on multiple samples
- and they performed corroborating estimates and measurements.

The first characteristic (that the expected result did not happen) is neither necessary nor sufficient for Good Science, but if you always get what you expect one worries that you may be delusional or not trying hard enough.

I'll elaborate a bit on his experiment, as I understand it. I say 'his', but this is merely shorthand because the team consists of collaborators from several institutions. For some years he has been developing a synthesis method known as 'modulated elemental reaction', MER. This preparation method involves chemical deposition of layers of elements followed by annealing at fairly low temperatures.

The annealing triggers chemical reactions which, however, are inhibited from going to full completion by the slow kinetics of diffusion. Pretty high quality metastable superlattices can result, with distinct superlattice XRD peaks.

With this nice synthesis method in hand, he set out to make
'nanolaminates' with layers of the wide band gap semiconductor WSe2
(tungsten diselenide) and layers of a titanium metal between. The idea
was that the nanolaminate, with such different bonding, would lead to very low thermal conductivity values across the laminate.

Initial results were encouraging in that very low thermal conductivity
values did indeed result: indeed, nearly an order of magnitude lower than the lowest expected result, the so-called 'minimum lattice thermal
conductivity'. Since low values were sought and found, many studies
would have happily published their results as 'proof' that the Ti metal
layers were the cause of the low k values.

Something, I know not what, motivated Johnson to look further. After all, at this stage one does not actually have proof of anything. You do have a recipe (for making a certain type of sample) and some observations, but you do not know if the recipe is causally connected only incidental to the result. So Johnson made what amounts to 'control' samples: samples prepared by essentially the same method but without the Ti metal layers.

This gave surprise number 1: the thermal conductivity was just as low
without the Ti layers. It is not easy, psychologically, to abandon one's hypothesis even when the evidence points elsewhere. Good Science sometimes demands you do so, even if it means admitting your initial hunch was wrong.

At the same time the stubbornly low k values was surprise number 2: it
was not immediately obvious that these 'control' samples should have such low k. Was it true, and if so why? So they measured many samples, with various experimental parameters and they were all uniformly low, some lower than others. They also measured some of the samples more than once.

Repeated measurements on the same sample speaks to the precision of the
measurements, which was quite good. Measurement of multiple samples speaks to the reproducibility, which was also good. One sample had a k value (confirmed by repeated measurements) well below the population of the others, but all were quite low. That one sample has yet to be explained, but including it in the report is much in the spirit of the "warts and all" principle I've discussed previously.

At face value these experimental results appear to challenge the 'minimum thermal conductivity' (kmin) idea introduced most lucidly by G.A. Slack (although the idea has roots going back to Einstein). The kmin idea is that phonons are waves, which travel with some velocity (vs) for some distance (d) at which point they are scattered. Slack's idea for kmin is to imagine that each phonon travels exactly one wavelength, putting a lower limit on 'd'. Slack's formula for kmin is proportional to vs and d, and has a factor for the number of atoms per unit cell which accounts for the number of heat carrying acoustic phonon modes per unit cell. There are several other formulas one can choose from to estimate kmin and they can give answers differing by a factor of 2 or so.

Johnson's results, which were much lower than the classical kmin estimate
for the compositions in question, presents some challenge to the whole
idea. So Johnson measured the sound velocity, vs, in his samples and
found it to be much lower than the corresponding bulk values. Sound
velocity is often a fairly robust proxy for the bonding in a material,
typically correlating well with properties like hardness and melting point.

The low vs values in Johnson's nanolaminates qualitatively accounts for
the low k values and also suggests the layers are only weakly bonded to
each other. One wit in a hallway conversation referred to such materials
as 'crackers', which one is not surprised to find have low thermal
conductivity.

I'll be surprised (pleasantly so, and not for the first time) if good
electrical proper can be achieved across these crackers (aka
nanolaminates). But the work remains really Good Science in any case.
You may not be able to control what the answer turns out to be, but the
most efficient path to good and useful results must be through doing Good
Science. And doing Good Science is in your control.

Be like Johnson:
- question your hypothesis, even when initial results superficially
support it
- be alert to interesting results not imagined in your philosophy
- check your results with controls and statistics
- do BOTEC estimates and corroborating measurements

These things are neither sufficient nor necessary to Good Science. But
they help.

Reference:
1. Chiritescu, C., Cahill, D. G., Nguyen, N., Johnson, D., Bodapati, A., Keblinski, P., and Zschack, P., Ultralow Thermal Conductivity in Disordered, Layered WSe2 Crystals, Science, 1136494, 2006.

To access a pdf of the article, go to David Cahill's publication page:
http://users.mrl.uiuc.edu/cahill/pubs.html

and scroll to bottom of the page. Click on the link to Reference 124.