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We investigated the behaviour of gallium inside carbon nanotubes (diameter, 40–150 nm) using a microscope equipped with a Gatan holder and twin heating system. Figure 1a–c shows a gallium column of diameter 75 nm and a continuous length of up to 7,560 nm. When the column temperature is increased or decreased in the range 50–500 °C, the gallium level rises or falls consistently.

Figure 1: Expansion of gallium inside a carbon nanotube with increasing temperature.
figure 1

a–c, Changing level of the gallium meniscus at 58 °C (a), 490 °C (b) and 45 °C (c); scale bar, 75 nm. d, Height of the gallium meniscus plotted against temperature, measured in steps of 30–50 °C; results are averaged (green curve) from closely similar measurements obtained during heating (red) and cooling (blue). The nanothermometer was synthesized in a vertical radiofrequency furnace (which differs from a one-step arc-discharge method). A homogeneous mixture of Ga2O3 and pure, amorphous, active carbon (weight ratio, 7.8:1) was reacted in an open carbon crucible under a flow of pure N2 gas: at 1,360 °C, the reaction Ga2O3(solid) + 2C(solid) → Ga2O(vapour) + 2CO(vapour) occurs. However, on the inner surface of a pure graphite outlet pipe at the top of the furnace, the temperature is lower (around 800 °C), causing the reaction Ga2O(vapour) + 3CO(vapour) → 2Ga(liquid) + C(solid) + 2CO2(vapour) to occur, during which the 'nanothermometers' are created.

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The variation with temperature of the height of the gallium meniscus in its carbon nanotube is plotted in Fig. 1d, using the level at 58 °C as a reference. Changes in the length and diameter of the carbon nanotube itself can be disregarded because of the minute linear expansion coefficient10 of graphite (about −1 × 10−6 per °C at 20–500 °C), so the height of the gallium column is determined by its volume at that temperature.

The volumetric change of liquid gallium in the macroscopic state upon heating is described by vt = v0(1 + α▵t), where vt and v0 are the volumes at temperatures t and t0 respectively, ▵t = t − t0, and α is the volumetric-expansion coefficient (0.1015 × 10−3 per °C at 30–977 °C, derived from measurements of density against temperature9). Our results indicate that this description also applies to nanoquantities of one-dimensional liquid gallium: calculations on the basis of its change in volume with temperature give a value for α of 0.095 ± 0.006 × 10−3 per °C, which is comparable to that for macroscopic liquid gallium. In this respect, the expansion coefficient differs from another basic thermal property, the melting point, which is greatly influenced by the surface effect11.

Because the gallium meniscus level in a carbon nanotube moves linearly and reproducibly with temperature in the range 50–500 °C, it meets the requirements of a filled-system thermometer in this range. For such a nanothermometer, the temperature can be measured as t = 58 + ▵h/0.753, where ▵h (in nm) is the difference in the height of the gallium column at t °C and 58 °C.

It should be feasible to read the temperature recorded by the nanothermometer in situ with the help of a scanning electron microscope, given that the walls of the carbon nanotube and the space inside, as well as the gallium level, can be clearly seen even using an instrument operated at 10 keV. Because it has a measuring range of 50–500 °C, our nanothermometer will extend temperature measurement beyond the 4–80 K range attainable by resistance micrometre-sized cryogenic thermometers12. It is easy to use, as the gallium meniscus is almost perpendicular to the inner surface of the carbon nanotube and the liquid column is continuous and long (up to 10 μm). The potential application proposed here follows on from several studies based on the discovery that carbon nanotubes can be filled with metal13.