No free passage for heat
(appeared in Feb 2017)

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A metal that does not conduct heat in the usual way could have many new applications, says S.Ananthanarayanan.

The experience has been that metals, which are good conductors of electricity, are also good conductors of heat. And non-metals, like most gases, carbon, phosphorus, sulphur, iodine, bromine, are poor or not good conductors of either electricity or of heat. Applications have thus been adapted to available materials and the fact that a good conductors of electricity must also, usually, be a conductor heat, has been a constraint or a restriction. There is, all the same, a class of substances that behaves in a different way, by conducting electricity well, but not conducting heat – but this property shows up only when the substances are cooled to extremely low temperatures, and is hence of little practical value.

A team of researchers, Sangwook Lee, Kedar Hippalgaonkar, Fan Yang, Jiawang Hong, Changhyun Ko, Joonki Suh, Kai Liu, Kevin Wang, Jeffrey J. Urban, Xiang Zhang, Chris Dames, Sean A. Hartnoll, Olivier Delaire and Junqiao Wu, from South Korea, Singapore, Jeddah, Beijing, Oak Ridge National Laboratory, Lawrence Berkeley National Laboratory, Duke University, Stanford University and the Universities of California at Berkeley now report their studies of one of these materials, that shows the same behaviour at ordinary temperatures.

The property of conducting electricity depends on the availability of relatively free electrons to transfer electric charge from one part of a material to another. The outer-most electron shells of atoms of metals have just one or two electrons, and the remaining electrons, which are in nearer orbits, shield the outer shell electrons from the central positive charge of the atoms. These outer electrons are hence not strongly bound, and are free to transport charges. Metals are thus generally good conductors of electricity. The atoms of non-metals, in contrast, have six or seven electrons, just short of a stable count of eight, in the outer orbit. There are fewer inner shell electrons to shield the centre and the economy in packing is to acquire electrons, to complete the count of eight. The electrons are hence not free and non-metals, generally, are poor conductors of electricity.

Transfer of heat can take place through a gas or a liquid or through solid material. In gases or liquids, the usual means is by convection, where molecules of the gas or liquid transfer heat by moving about. In a solid, the atoms are not free to move long distances but can vibrate. A vibration is more pronounced at a warmer end of the solid and this is a means of transfer of energy to the cooler end. As solids are denser than gases, solids are better conductors of heat. In crystalline solids, the vibration motion can get enhanced as waves and it is possible to think of the waves behaving like particles, or wave packets, which are known as ‘phonons’ (a material equivalent of ‘photons’).

This process of transfer of heat by lattice vibrations is similar in the case of metallic or non-metallic solids. Metals, however, pass heat much more readily than most non-metals and this is because of their free electron content. The free electrons in metals behave like the molecules of gases and play an important role in transporting heat and lattice vibration energy. This leads to metals becoming vastly better conductors of heat than non-metals (diamond is a notable exception because its extreme hardness makes lattice transfer most efficient), just as they are vastly better conductors of electricity. The efficiency of heat transfer by metals is connected to the efficiency of electrical conduction by a law called the Wiedemann-Franz law, which says good conductors of electricity should be good conductors of heat.

Transition metals

In the progression of atoms, from the smallest of the atoms to the heavier ones, along with increase in the number of the positive particles in the nucleus and the electrons in orbit, the outer electron shells keep adding to their number. This increase continues till they reach the number eight, or the ‘octet’, which represents a stage of economy. Once the number eight is reached, the next electron is not added to this shell, but starts a new shell, which grows till it has eight occupants. This is till we reach the third shell, with the element, calcium. After the third shell, the outer shell first takes in two electrons and then the penultimate shell accommodates additions, till it holds 18 electrons, before the next one spills over to the outermost shell. This results in a number of elements, whose outer shell should have had 3 to 8 electrons, continuing with fewer electrons in the outer shell, which makes them metals, and these elements are called the transition metals.

Atoms of such metals have the unusual composition of a small number of electrons in the outermost shell and a penultimate shell with more than the eight electrons of usual metals. These metals display unusual properties, by remaining insulators at low temperatures but transforming to conductors when the temperature is raised beyond a critical temperature, which is known as the ‘transition temperature’. The temperature at which this change takes place is exceedingly low in most of the cases, but in the case of one material, vanadium dioxide, or VO2, it is as high as 67°C.

The manner in which electrons participate in conducting heat is linked to the fact that electrons are charged and that, unlike molecules of a gas, they interact with one another through electric and magnetic forces. The transport of heat, as well as charge, by electrons is thus understood as transport by not just electrons, but by groupings of electron states, which can behave like particles, somewhat in the manner that oscillations of the atoms in a crystal can come together as wave packets, the phonons. The movement of electrons, which mutually interact, has thus been explained by a theory that considers their movement as a small departure from what it would be if they did not interact and normal electrical conduction and the part of thermal conduction that arises from movement of electrons is explained by considering the movement to be a stream of relatively constant combinations of electron states.

The reason that Vanadium dioxide shows anomalous behaviour is hence explained as linked to the conducting electrons in the material being strongly correlated so that the approximation to a small departure from an ordinary gas, where the molecules do not interact, no longer holds. The team of researchers carried out experiments to estimate the non-electronic, or lattice based contribution to thermal conduction and hence to work out the electronic contribution, at different temperatures. The result of the trials has been that around the temperature that the structure of VO2 undergoes changes to transform it from an insulator to an electrical conductor, there is a drastic fall in the electronic contribution to thermal conduction.

We thus now have a material that behaves in the opposite way, compared to normal metals, in the changes of conduction of electricity and heat with the change in temperature. And along with this change, there is a peaking of the efficiency with which VO2 can be used to harvest electricity from temperature differences. This can have applications – in finding ways to extract electricity from waste heat, or as a solid state refrigerator, for instance. The effect can even be tuned, with the help of selected impurities. Another property of VO2 is that at just about the temperature at which it changes from insulator to conductor, it also changes from being transparent to opaque. This property could lead to applications of controlling lighting levels, apart from thermal conduction, by changes in temperature.

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