Gold can remain solid at temperatures of over 14 times its melting point, far beyond a long-assumed theoretical limit dubbed the “entropy catastrophe”. This finding is based on temperature measurements made using high-resolution inelastic X-ray scattering, and according to team leader Thomas White of the University of Nevada, US, it implies that the question “How hot can you make a solid before it melts?” has no good answer.
“Until now, we thought that solids could not exist above about three times their melting temperatures,” White says. “Our results show that if we heat a material rapidly – that is, before it has time to expand – it is possible to bypass this limit entirely.”
Gold maintains its solid crystalline structure
In their experiments, which are detailed in Nature, White and colleagues heated a 50-nanometre-thick film of gold using intense laser pulses just 50 femtoseconds long (1fs = 10-15 s). The key is the speed at which heating occurs. “By depositing energy faster than the gold lattice could expand, we created a state in which the gold was incredibly hot, but still maintained its solid crystalline structure,” White explains.
The team’s setup made it possible to achieve heating rates in excess of 1015 K s –1, and ultimately to heat the gold to 14 times its 1064 °C melting temperature. This is far beyond the boundary of the supposed entropy catastrophe, which was previously predicted to strike at 3000 °C.
To measure such extreme temperatures accurately, the researchers used the Linac Coherent Light Source (LCLS) at Stanford University as an ultrabright X-ray thermometer. In this technique, the atoms or molecules in a sample absorb photons from an X-ray laser at one frequency and then re-emit photons of a different frequency. The difference in these frequencies depends on a photon’s Doppler shift, and thus on whether it is propagating towards or away from the detector.
The method works because all the atoms in a material exhibit random thermal motion. The temperature of the sample therefore depends on the average kinetic energy of its atoms. Higher temperatures correspond to faster-moving atoms and a bigger spread in the velocities of the photons moving towards away or from the detector. Hence, the width of the spectrum of light scattered by the sample can be used to estimate its temperature. “This approach bypasses the need for complex computer modelling because we simply measure the velocity distribution of atoms directly,” White explains.
A direct, model-independent method
The team, which also includes researchers from the UK, Germany and Italy, undertook this project because its members wanted to develop a direct, model-independent method to measure atom temperatures in extreme conditions. The technical challenges of doing so were huge, White recalls. “We not only needed a high-resolution X-ray spectrometer capable of resolving energy features of just millielectronvolts (meV) but also an X-ray source bright enough to generate meaningful signals from small, short-lived samples,” he says.
A further challenge is that while pressure and density measurements under extreme conditions are more or less routine, temperature is typically inferred – often with large uncertainties. “In our experiments, these extreme states last just picoseconds or nanoseconds,” he says. “We can’t exactly insert a thermometer.”
White adds that this limitation has slowed progress across plasma and materials physics. “Our work provides the first direct method for measuring ion temperatures in dense, strongly driven matter, unlocking new possibilities in areas like planetary science – where we can now probe conditions inside giant planets – and in fusion energy, where temperature diagnostics are critical.”
Fundamental studies in materials science could also benefit, he adds, pointing out that scientists will now be able to explore the ultimate stability limits of solids experimentally as well as theoretically, studying how materials behave when pushed far beyond conventional thermodynamic boundaries.
The researchers are now applying their method to shock-compressed materials. “Just a few weeks ago, we completed a six-night experiment at the LCLS using the same high-resolution scattering platform to measure both particle velocity and temperature in shock-melted iron,” White says. “This is a major step forward. Not only are we tracking temperature in the solid phase, but now we’re accessing molten states under dynamic compression, that is, at conditions like those found inside planetary interiors.”
White tells Physics World that these experiments also went well, and he and his colleagues are now analysing the results. “Ultimately, our goal is to extend this approach to a wide range of materials and conditions, allowing for a new generation of precise, real-time diagnostics in extreme environments,” he says.
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