Symmetry breaking in Prussian Blue Analogues via growth–guided local ordering of hexacyanometallate vacancies

Symmetry is the silent architect of the material world. It is the reason a snowflake has six identical arms and why a diamond sparkles with such uniform brilliance. In the laboratory, scientists often look for symmetry to understand how a material behaves, assuming that if a crystal looks the same from every angle, its internal structure must be perfectly balanced. However, nature is rarely so simple. Sometimes, the most interesting properties emerge when that perfect balance is broken. When a crystal loses its symmetry, it can gain new abilities, such as the capacity to bend light in specific ways or to conduct electricity only in one direction. For decades, researchers have tried to force crystals to break their symmetry, usually by looking for subtle shifts in the positions of atoms or by cooling materials to extreme temperatures. These methods are often difficult to control, leaving scientists with a desire for a more reliable way to shape the internal order of a crystal.

A team of researchers at ETH Zurich and several international partners has discovered a surprisingly simple way to guide this process. They found that the direction in which a crystal grows can dictate how its internal imperfections arrange themselves, effectively breaking the crystal's symmetry without changing its average shape. They demonstrated this using a family of materials known as Prussian Blue Analogues. These are colorful, sponge-like crystals made of metal ions connected by cyanide bridges, with plenty of empty spaces, or vacancies, scattered throughout their structure. While these materials are already known for their potential in gas storage and battery technology, their internal disorder has usually been seen as a random mess. The researchers realized that this randomness was not entirely random; it was being guided by the very act of the crystal growing.

The story begins with a set of perfectly formed, cube-shaped crystals of a manganese-cobalt Prussian Blue Analogue. To the naked eye, and even under a standard microscope, these cubes look like they possess perfect cubic symmetry, meaning they should look identical no matter how you turn them. Yet, when the researchers placed these cubes between two crossed polarizing filters, a strange pattern appeared. Instead of remaining dark, the crystals lit up with a distinct, four-triangle contrast that resembled a pyramid. This optical effect, known as birefringence, only happens in materials that are not perfectly symmetrical. It suggested that inside these seemingly perfect cubes, the internal structure was actually stretched or squashed in a specific direction, making them behave like a lower-symmetry material.

This observation created a puzzle. When the scientists used high-resolution X-ray diffraction to look at the average position of every atom in the crystal, the data confirmed the old view: the atoms were arranged in a perfect cubic pattern. The standard tools of crystallography saw no evidence of the distortion that the light was revealing. The average structure was indeed cubic. However, the researchers knew that the light was telling the truth about the local reality. To solve this, they turned their attention to the "fuzzy" parts of the X-ray data, known as diffuse scattering. Unlike the sharp spots that reveal the average atomic positions, this diffuse scattering reveals how atoms and vacancies are correlated with one another over short distances.

When they analyzed this diffuse scattering, the hidden order was revealed. The vacancies in the crystal were not scattered randomly. Instead, they were lined up in a very specific way, forming strong chains along the direction in which the crystal had grown. The researchers found that the crystal grew layer by layer, and as new layers formed, the vacancies were forced to align with the growth direction. This alignment created a local structure that was tetragonal, meaning it had a different symmetry than the overall cubic shape. The crystal was essentially a mosaic of six different regions, or domains, each growing outward from a face of the cube. In each of these six pyramid-shaped regions, the vacancies were ordered along the direction of growth, creating a local symmetry that was lower than the global average.

To confirm this, the team used a computer simulation to model how the vacancies might arrange themselves. They found that if the vacancies were simply random, the scattering would look different. But when they programmed the simulation to make the vacancies avoid each other in the immediate neighborhood while encouraging them to line up along the growth axis, the result matched the experimental data perfectly. The simulation showed that the vacancies formed long, ordered chains along the growth direction, while remaining more disordered in the perpendicular directions. This confirmed that the growth process itself was the architect of the symmetry breaking. The crystal did not need to be cooled or chemically altered to achieve this state; it simply needed to grow in a specific direction.

The researchers then took this idea a step further to see if they could control the symmetry by changing the growth direction. They grew crystals that were not perfect cubes but were shaped like cubeoctahedra, which have both square faces and triangular faces. By adjusting the chemical concentration during the growth, they could make the triangular faces larger or smaller. When they examined these crystals with a special type of polarized light microscope, they saw a new pattern. The square faces still showed the tetragonal symmetry associated with growth along the cube edges. However, the triangular faces showed a different kind of symmetry, one that was trigonal, corresponding to growth along the diagonal of the cube. This proved that by simply choosing which way the crystal grows, they could dictate whether the internal disorder would arrange itself into a tetragonal or a trigonal pattern.

This discovery offers a new way to think about engineering materials. For a long time, scientists believed that controlling the symmetry of a disordered crystal was a nearly impossible task, requiring precise manipulation of atomic forces. This work suggests that the solution is much more accessible. By controlling the growth direction, perhaps by using specific chemicals or shaping the container in which the crystal forms, scientists can now guide the internal order of a material. This method works because the crystal locks in the arrangement of its defects as it grows, preserving the memory of the growth surface. The result is a material where the average structure remains high-symmetry and robust, but the local structure is tailored to have specific, useful properties like birefringence or altered pore connectivity.

The implications of this finding extend beyond just these blue crystals. The mechanism relies on fundamental aspects of how crystals grow, suggesting that this "growth-guided local ordering" could be a common feature in many disordered materials that have been overlooked. Because the symmetry breaking is driven by the growth process rather than the specific chemistry of the material, it could be applied to a wide range of substances used in energy storage, catalysis, and electronics. The researchers have shown that the path to new functional properties does not always require breaking the laws of physics or discovering new elements. Sometimes, it simply requires understanding the direction in which the material is growing and letting that direction do the work of organizing the chaos within.