The melting point of germanium nanocrystals embedded in silica glass was measured inside a transmission electron microscope. Electron diffraction patterns from the crystalline lattice structure (bright rings) persist until the temperature is more than 200° K (−99° F)above the melting point of germanium in bulk, which is approximately 1,211° K (1,720°F). When the nanocrystal melts, the diffraction patterns disappear.

Germanium nanocrystals embedded in glass are hotter before they melt and colder before they freeze

Scientists at the Dept. of Energy's Lawrence Berkeley National Laboratory have discovered that germanium nanocrystals embedded in silica glass don't melt until the temperature rises almost 200°K (-99°F) above the melting temperature of germanium in bulk. What's even more surprising, these melted nanocrystals must be cooled more than 200°K below the bulk melting point before they resolidify. Such a large and nearly symmetrical "hysteresis" — the divergence of melting and freezing temperatures above and below the bulk melting point — has never before been observed for embedded nanoparticles.

Phase transitions between solid and liquid or liquid and vapor are familiar phenomena in the everyday world. Beyond scientific curiosity, the properties of germanium nanoparticles embedded in amorphous silicon dioxide matrices may have promising applications, says Eugene Haller, professor of materials science at the University of California at Berkeley.

"Germanium nanocrystals in silica have the ability to accept charge and hold it stable for long periods," Haller explains. "This property may help improve computer memory systems. Moreover, germanium dioxide (germania) mixed with silicon dioxide (silica) offers particular advantages for forming optical fibers for long-distance communication."

To exploit these properties, however, the melting/freezing transition of germanium (under a variety of conditions) needs to be better understood. Researchers at Berkeley's Materials Sciences Div., (MSD) embedded nanoparticles averaging 2.5 nm in diameter in silica. What they encountered when they heated and cooled this system was completely unexpected. Their results are published in the October 13, 2006 issue of Physical Review Letters.

How Materials Melt and Freeze

Researchers over the last hundred years have looked at how crystal size affects the transition between the liquid and solid state of a material. In general, smaller crystal size equates to lower melt temperatures. The melting temperature of a free-standing metal or semiconductor nanocrystal, typically comprised of a few hundred to a few thousand atoms, may be more than 300 degrees Kelvin below the melting temperature of the same material in bulk.

The reason for this, says Joel Ager of MSD, a coauthor of the Physical Review Letters report, is that "The smaller a solid object gets, the larger the percentage of its atoms reside at the surface. If it keeps shrinking, eventually the object's practically all surface." Inside a crystalline solid the atoms are constrained by the crystal lattice, Ager explains. "But at the surface the atoms have more freedom to move. As temperature rises, they begin to vibrate. And when the vibration of surface atoms reaches a certain percentage of the bond length between them, melting begins and then starts to propagate through the solid."

"Melting and freezing begin at the interface between the surface of the solid and its surroundings," says theorist Daryl Chrzan, also of MSD and a professor of materials science at UC Berkeley. "The solid phase has a certain free energy, the liquid another, vapor yet another, and interfaces between these phases have their own characteristic energies. The likelihood of a phase transition occurring in one direction or the other can be calculated based on the free energies of the material phases themselves and their interface energies, taking into account volume, geometry, density, and other factors."

For most materials, interface energies between solid and vapor favor the formation of a liquid surface layer as the temperature increases. This surface liquid layer will continue to grow until the entire object melts. The liquid layer forms more readily at lower temperatures as the proportion of surface-to-volume increases. Haller notes that, "If you make free-standing nanoparticles of gold, small enough, for example, they melt at room temperature."

Embedded nanocrystals occasionally behave differently, however. Superheating has been observed in the case of nanocrystals embedded in a crystalline matrix, for example nanoparticles of lead embedded in an aluminum matrix. This is attributed to the lattice structures of the two crystals "locking up," suppressing the vibration of the nanoparticles' surface atoms that would lead to melting.

But germanium nanocrystals in silica glass are quite a different matter. The glass matrix has no lattice structure to lock with the germanium crystal surface. Ager says that "Because there was no lattice structure in the matrix, we had naively expected the germanium crystals to behave more like free-standing nanoparticles i.e., we expected the melting temperature to be much less than in bulk germanium. Instead, to our surprise, germanium nanocrystals in glass had to be superheated to melt."

Additionally, in bulk materials, the interface energy responsible for the transition from solid to liquid at the melting temperature creates a roadblock in the opposite direction and acts as an energy barrier to freezing.

"It takes energy to form a surface," says Chrzan. "It's possible to supercool bulk materials and keep them in a liquid state well above their normal freezing/melting point. To freeze, a material must overcome that slight energy barrier to form a critical solid nucleus."

In the case of germanium nanocrystals embedded in glass, the large interface-energy barrier that leads to superheating before the solid crystal can melt also means the melted inclusions must be supercooled before they freeze.

"While these results were unexpected," Chrzan says, "it turns out they can be explained in a straightforward way. We modified the traditional theory of nucleation developed by David Turnbull in the 1950s. Though in our system, the ratio of surface-to-volume is far greater than in the bulk materials Turnbull was working with — and though, instead of a solid-vapor interface, we are working with a solid-glass interface — we saw we could apply his theory in this new regime."

Says Chrzan, "Typically in bulk materials, surface premelting means there's no need for nucleation before melting occurs. But in our case, the large proportional surface area of the germanium nanoparticles, plus the interface energy of the solid-glass interface, creates a calculable nucleation barrier in both directions."

As the nanoparticle heats up, a liquid nucleus, its lens shape partly determined by the confining spherical cavity in the glass, must hit a critical size before it can spread and entirely melt the nanocrystal. Conversely, as the temperature drops, a solid nucleus forms and starts to grow from the surface of the liquid sphere — a nucleus that will eventually make the entire nanometer-sized liquid globule freeze into a solid crystal. The Turnbull theory as modified by Chrzan correctly predicted the temperatures at which both events would occur.

Manipulation Under the Microscope

To perform these experiments, the researchers made silica glass samples 500-nm thick by oxidizing pure silicon in steam. They implanted germanium ions in the amorphous silicon and then annealed the sample at 900° C (1,652° F) to form nanocrystals. The transparent glass allowed characterization of the embedded nanocrystals by Raman spectroscopy; the glass was also readily etched away for examination of the nanocrystals with an atomic force microscope.

Heating and cooling of the samples took place in situ in a transmission electron microscope at the Dept. of Energy's National Center for Electron Microscopy, based at Berkeley Lab. By thinning the samples to less than 300 nm and looking straight through them with the microscope's electron beam (with the beam itself masked off so as not to hit the camera), the researchers could observe the electron diffraction rings produced by the crystal lattices of the embedded particles. When the particles began to melt, the diffraction rings weakened and finally vanished, allowing precise measurement of the temperature at which the embedded particles melted. As the temperature was lowered again, the appearance of the diffraction rings signaled resolidification.

"Melting and freezing points for materials in bulk have been well understood for a long time," says Haller, "but whenever an embedded nanoparticle's melting point goes up instead of down, it requires an explanation. With our observations of germanium in amorphous silica and the application of a classical thermodynamic theory that successfully explains and predicts these observations, we've made a good start on a general explanation of what have until now been regarded as anomalous events."

The Office of Science of the DOE and the National Science Foundation helped fund the research.

More information:
Berkeley Lab, a U.S. DOE national laboratory