Among the different material shapes, cubes are particularly interesting at the nanoscale since cubic nanoparticles make up the building blocks of self-assembled structures such as bimetallic alloys. An example of one such alloy is the gold-copper (Au-Cu) system, which is especially attractive for a variety of applications because it is fully miscible over its entire composition range.

At low temperatures, this alloy has the ordered phases Au3Cu, AuCu and AuCu3, depending on the alloy composition. Such ordered structures are used in catalysts and researchers have indeed shown that intimate contact between Au and Cu can help in the catalytic conversion of CO to CO2. However, the problem is that the order-disorder transition temperature at which the alloy forms these superlattices is still unknown at the nanoscale.

Predicting the phase diagram of Au-Cu

Researchers led by Gregory Guisbiers at the University of Texas at San Antonio obtained results by first predicting the phase diagram of Au-Cu in the bulk using classical thermodynamics. They did this by minimizing the Gibbs potential of the system. To calculate the phase diagram on the nanoscale, they then considered the contribution of the surface of the nanoparticle (nanocube in this case) in the description of the Gibbs potential of the nanoparticle – and again minimized this potential.

They backed up their results with transmission electron microscopy observations of Au-Cu nanocubes that had been synthesized using wet chemistry.

EDX and diffraction patterns

“We investigated the crystalline structure of the nanocubes immediately after they had been synthesized,” explains Guisbiers. “We then heat-treated the alloys at various temperatures and looked at the samples just after the treatment, again using TEM, and measured the composition of the nanoparticles using EDX (energy-dispersive X-ray spectroscopy) at each temperature.”

In the final step to compare experimental observations with theory, the researchers took the diffraction pattern of the nanoparticles. “It is quite straightforward to determine if a nanoparticle is ordered or not using this technique,” says Guisbiers. “If the structure is ordered, we obtain extra reflections in the patterns obtained.”

Two size effects at play, not just one

The work is fundamentally important because we now have proof that there are two size effects at play during nanoscale phase transitions, not just one, he tells “In 2010, I predicted these two size effects and we now have the experimental evidence.

“The first effect is for fermions and the second for bosons. Indeed, the solid-liquid phase transition is driven by electrons (which are fermions) while the order-disorder phase transition is driven by phonons (which are bosons). If we were only to consider the size effect for fermions to describe order-disorder phase transitions at the nanoscale, we would not be able to explain our experimental observations.”

As for applications, Guisbiers says he is convinced that the new work will help researchers save time when synthesizing ordered nanostructures in the future because they will now know exactly which temperature they need to use when preparing a particular alloy composition. “This will be important for making catalysts, for example, since this approach is a way of controlling the chemical ordering at the nanoscale.”

The work is detailed in Nanoscale DOI: 10.1039/C7NR00028F.