Materials scientist awarded the 2011 Nobel Prize in Chemistry

The 2011 Nobel Prize in Chemistry went to Daniel Shechtman for his discovery that atoms in metals can arrange themselves in non-periodic, quasicrystalline structures with fivefold symmetry. But what exactly does this mean, and what makes this discovery such a remarkable achievement in materials science?

A change of perspective helps us understand it.

A thought experiment with tiles

Imagine that we are tilers. During training, we soon learn that a surface can be covered without gaps using triangular, square or hexagonal tiles. This produces periodic patterns that repeat regularly:

• A triangular tile can be rotated three times through 120° and still fit the pattern. This is known as threefold symmetry.
• A square tile can be rotated four times through 90°: fourfold symmetry.
• A hexagonal tile can even be rotated six times through 60°: sixfold symmetry.

In every case, a surface can be filled without gaps and in a periodic pattern: tile after tile after tile.

The old dogma of crystallography

Materials scientists find similar structures in metals. The atoms arrange themselves in periodic crystal structures whose symmetries may, for example, be threefold, fourfold or sixfold.

One form of symmetry, however, was long considered impossible: fivefold symmetry. The reason is the same as in our tiling example. Regular pentagons cannot cover a surface without gaps in a periodic pattern.

How can atomic symmetries be identified?

The atomic structure of a metal cannot, of course, be observed directly with the naked eye: the distances between atoms are far too small. Materials scientists therefore use indirect methods, such as electron diffraction and X-ray diffraction. The resulting diffraction patterns allow conclusions to be drawn about the symmetry of the atomic arrangement. Typical metals with a cubic structure, for instance, show fourfold diffraction patterns.

Daniel Shechtman, however, observed something entirely unexpected: diffraction patterns with fivefold symmetry. According to the scientific understanding of the time, this was simply “forbidden”.

Facing resistance from the scientific community

Let us return to our tiling example. Suppose there were an unshakeable rule in the tilers’ guild: “Fivefold patterns are impossible.”

Then a tiler came along and claimed: “I have found such a pattern.”

The guild’s response would probably be less than enthusiastic. Daniel Shechtman’s experience was much the same. Parts of the scientific community initially expressed serious doubts about his findings or even dismissed them as an error. It took several years for his work to be published and accepted. He eventually received the Nobel Prize around 30 years after his original discovery.

How are fivefold structures possible?

How can atoms form fivefold symmetry if pentagons cannot be fitted together periodically? The solution is to use other geometric shapes. Two particular types of rhombus with equal sides can be combined:

• a rhombus with an acute angle of 72°
• a rhombus with an acute angle of 36°

Arranging these shapes appropriately produces a gap-free structure that is not periodic. The pattern does not repeat regularly, yet it still has a clear order and five preferred directions. Precisely these structures were later found in certain metallic alloys.

Materials scientists call them quasicrystals. Their structure has no periodic repetition, but is nevertheless ordered and contains no gaps.

In brief: why did Shechtman receive the Nobel Prize?

The significance of the discovery can be understood from several perspectives:

• It demonstrated for the first time that fivefold symmetries are possible in atomic structures.
• It challenged a central dogma of crystallography.
• It opened up a new field of research in materials science.

And not least:

• because Shechtman discovered something unique,
• because he pursued a revolutionary idea,
• because he defended his findings in the face of considerable resistance,
• and because his discovery fundamentally changed our understanding of crystalline materials.

Quasicrystals also have a number of unusual and sometimes highly useful properties, such as high hardness, low friction and distinctive electrical properties, which remain the subject of intensive research.