It’s notoriously difficult to take the temperature of really hot things. Whether it’s the roiling plasma in our Sun, the extreme conditions at the core of planets or the crushing forces at play inside a fusion reactor, what scientists call “warm dense matter” can reach hundreds of thousands of degrees kelvin.
Image Credit: SLAC
Knowing precisely how hot these materials are is crucial for researchers to fully understand such complex systems, but taking these measurements has been, until now, virtually impossible.
“We have good techniques for measuring density and pressure of these systems, but not temperature,” said Bob Nagler, staff scientist at the Department of Energy’s SLAC National Accelerator Laboratory. “In these studies, the temperatures are always estimates with huge error bars, which really holds up our theoretical models. It’s been a decades-long problem.”
Now, for the first time, a team of researchers report in the journal Nature that they have directly measured the temperature of atoms in warm dense matter. While other methods rely on complex and hard-to-validate models, this new method directly measures the speed of atoms, and therefore the temperature of the system. Already, their innovative method is changing our understanding of the world: In an experimental debut, the team superheated solid gold far beyond the theoretical limit, unexpectedly overturning four decades of established theory.
Nagler and researchers at SLAC’s Matter in Extreme Conditions(MEC) instrument co-led this study with Tom White, associate professor of physics at University of Nevada, Reno. The group includes researchers from Queen’s University Belfast, the European XFEL (X-ray Free-Electron Laser), Columbia University, Princeton University, University of Oxford, University of California, Merced, and the University of Warwick, Coventry.
Taking the Temperature
For nearly a decade, this team has worked to develop a method that circumvents the usual challenges of measuring extreme temperatures – specifically, the brief duration of the conditions that create those temperatures in the lab and the difficulty of calibrating how these complex systems affect other materials.
“Finally, we’ve directly and unambiguously taken a direct measurement, demonstrating a method that can be applied throughout the field,” White said.
At SLAC’s MEC instrument, the team used a laser to superheat a sample of gold. As heat flashed through the nanometer-thin sample, its atoms began to vibrate at a speed directly related to their rising temperature. The team then sent a pulse of ultrabright X-rays from the Linac Coherent Light Source (LCLS) through the superheated sample. As they scattered off the vibrating atoms, the X-rays’ frequency shifted slightly, revealing the atoms’ speed and thus their temperature.
“The novel temperature measurement technique developed in this study demonstrates that LCLS is at the frontier of laser-heated matter research,” said Siegfried Glenzer, director of the High Energy Density Science division at SLAC and co-author on the paper. “LCLS, paired with these innovative techniques, play an important role in advancing high energy density science and transformative applications like inertial fusion.”
The team was thrilled to have successfully demonstrated this technique – and as they took a deeper look at the data, they discovered something even more exciting.
“We were surprised to find a much higher temperature in these superheated solids than we initially expected, which disproves a long-standing theory from the 1980s," White said. "This wasn’t our original goal, but that's what science is about – discovering new things you didn’t know existed.”
Surviving the Entropy Catastrophe
Every material has specific melting and boiling points, marking the transition from solid to liquid and liquid to gas, respectively. However, there are exceptions. For instance, when water is heated rapidly in very smooth containers – such as a glass of water in a microwave – it can become “superheated,” reaching temperatures above 212 degrees Fahrenheit (100 degrees Celsius) without actually boiling. This occurs because there are no rough surfaces or impurities to trigger bubble formation.
But this trick of nature comes with an increased risk: The further a system strays from its normal melting and boiling points, the more vulnerable it is to what scientists call a catastrophe – a sudden onset of melting or boiling triggered by slight environmental change. For example, water that has been superheated in a microwave will boil explosively when disturbed, potentially causing serious burns.
While some experiments have shown it is possible to bypass these intermediary limits by rapidly heating materials, "the entropy catastrophe was still viewed as the ultimate boundary," White explained.
In their recent study, the team discovered that the gold had been superheated to an astonishing 19,000 kelvins (33,740 degrees Fahrenheit) – more than 14 times its melting point and well beyond the proposed entropy catastrophe limit – all while maintaining its solid crystalline structure.
“It’s important to clarify that we did not violate the Second Law of Thermodynamics,” White said with a chuckle. “What we demonstrated is that these catastrophes can be avoided if materials are heated extremely quickly – in our case, within trillionths of a second.”
The researchers believe that the rapid heating prevented the gold from expanding, enabling it to retain its solid state. The findings suggest that there may not be an upper limit for superheated materials, if heated quickly enough.
Fusion and Beyond
Nagler noted that researchers who study warm dense matter have likely been surpassing the entropy catastrophe limit for years without realizing it, due to the absence of a reliable method for directly measuring temperature.
“If our first experiment using this technique led to a major challenge to established science, I can't wait to see what other discoveries lie ahead,” Nagler said.
As just one example, White and Nagler’s teams used this method again this summer to study the temperature of materials that have been shock-compressed to replicate the conditions deep inside planets.
Nagler is also eager to apply the new technique – which can pinpoint atom temperatures from 1,000 to 500,000 kelvins – to ongoing inertial fusion energy research at SLAC. “When a fusion fuel target implodes in a fusion reactor, the targets are in a warm dense state,” Nagler explained. “To design useful targets, we need to know at what temperatures they will undergo important state changes. Now, we finally have a way to make those measurements.”
This work was funded in part by the DOE National Nuclear Security Administration and Office of Science Fusion Energy Sciences. LCLS is a DOE Office of Science user facilities.