Measuring the temperature of extremely hot materials has long been a challenge for scientists. From the plasma inside the Sun to the crushing forces at the core of planets and fusion reactors, these states of matter—known as “warm dense matter”—can reach hundreds of thousands of kelvins. Until now, researchers have lacked a reliable way to determine their exact temperature.
“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 (Stanford Linear Accelerator Center) 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.”
A team of researchers has now reported in Nature that they have directly measured the temperature of atoms in warm dense matter for the first time. Unlike earlier methods that depended on complex models, this new approach measures the speed of atoms, which directly reveals their temperature.
The study was co-led by Nagler at SLAC’s Matter in Extreme Conditions (MEC) instrument and Tom White, associate professor of physics at the University of Nevada, Reno. The collaboration included scientists from several institutions, including Queen’s University Belfast, the European XFEL, Columbia University, Princeton University, the University of Oxford, the University of California, Merced, and the University of Warwick.
At SLAC, the team used a laser to superheat a thin sample of gold. As the atoms vibrated faster with rising temperature, ultrabright X-rays from the Linac Coherent Light Source (LCLS) were sent through the sample. The scattered X-rays shifted slightly in frequency, revealing the atoms’ speed and thus their temperature. This technique, based on high-resolution inelastic X-ray scattering, allowed the researchers to directly track the lattice temperature during ultrafast heating.
The results went beyond the team’s expectations. The gold was superheated to about 19,000 kelvins (33,740 degrees Fahrenheit or ~18726.85 °C), more than 14 times its melting point, while still retaining its crystalline structure. This finding far exceeded the theoretical stability boundary known as the “entropy catastrophe,” first described by Fecht and Johnson.
The entropy catastrophe marks the point where the entropy of a superheated crystal equals that of its liquid state, typically occurring at around three times the melting point. The entropy catastrophe is a theoretical limit in physics that describes when a superheated solid becomes as disordered as its liquid form. At this point, the entropy, or measure of disorder, of the crystal equals that of the liquid, meaning the solid should no longer remain stable. It has long been considered the ultimate stability limit for solids.
In practice, however, solids usually destabilize at much lower temperatures due to a hierarchy of intermediate catastrophes, such as surface melting or defect formation. These events have prevented experimental exploration of the entropy catastrophe itself. By heating the gold samples on ultrafast timescales—within trillionths of a second—the researchers bypassed these intermediate instabilities. The inability of the material to expand under such rapid heating conditions appears to have been a key factor in maintaining its solid state.
The findings suggest that the entropy catastrophe may not represent a strict upper limit for superheating, and that solids can remain stable at far higher temperatures if heated quickly enough. This challenges four decades of theoretical assumptions and provides new insights into the dynamics of melting under extreme conditions.
Nagler noted that scientists may have unknowingly exceeded the entropy catastrophe limit in past experiments but lacked a way to confirm it. “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,” he said.
The team has already applied the method to study shock-compressed materials that mimic planetary interiors. They also plan to use it in inertial fusion research, where knowing precise temperatures is essential for designing fuel targets. With this new technique, researchers can now measure atom temperatures ranging from 1,000 to 500,000 kelvins, opening the door to more accurate studies of extreme matter.
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