Quasicrystals

Quasicrystals are a unique form of solid matter that exhibit an ordered yet non-periodic atomic structure. Unlike conventional crystals, which have repeating and periodic arrangements of atoms, quasicrystals possess an ordered atomic arrangement that does not repeat periodically but still produces distinct diffraction patterns, revealing a high degree of structural organisation.
The discovery of quasicrystals revolutionised the understanding of solid-state physics, challenging the long-held belief that all crystals must have periodic atomic structures. They combine properties of both crystalline and amorphous solids, displaying symmetry and order without regular repetition.

Discovery and Historical Background

Quasicrystals were first discovered in 1982 by Dr. Dan Shechtman, an Israeli materials scientist, while examining rapidly cooled aluminium–manganese alloys under an electron microscope. He observed diffraction patterns with five-fold symmetry, which was previously thought impossible for crystals because five-fold rotational symmetry cannot fill space periodically.
His discovery faced intense scepticism from the scientific community, as it contradicted established crystallographic principles. However, after further verification and theoretical explanation, quasicrystals were accepted as a new state of matter. For this pioneering work, Dan Shechtman received the Nobel Prize in Chemistry in 2011.

Structure and Characteristics

1. Ordered but Aperiodic Structure:

• Traditional crystals exhibit periodicity — their atomic patterns repeat regularly in three-dimensional space.
• Quasicrystals, in contrast, are aperiodic yet deterministically ordered. This means their atomic arrangement follows a fixed mathematical rule but does not repeat periodically.

2. Symmetry:

• Conventional crystallography allows rotational symmetries of 2-, 3-, 4-, or 6-fold.
• Quasicrystals can exhibit forbidden symmetries, such as 5-fold, 8-fold, 10-fold, or 12-fold rotational symmetry.
• These symmetries are similar to those seen in Penrose tiling — a mathematical model that inspired much of the understanding of quasicrystalline order.

3. Diffraction Patterns:

• Despite their aperiodicity, quasicrystals produce sharp diffraction patterns with well-defined spots, indicating long-range order.
• The patterns exhibit symmetries forbidden to conventional crystals, confirming their distinct structural category.

4. Composition:

• Quasicrystals are typically metallic alloys composed of elements such as aluminium (Al), manganese (Mn), nickel (Ni), copper (Cu), and iron (Fe).
• Common examples include Al–Mn, Al–Cu–Fe, Al–Ni–Co, and Ti–Zr–Ni systems.

Mathematical Description and Models

Quasicrystals can be described mathematically using higher-dimensional geometry:

• They can be viewed as projections of periodic structures from higher dimensions (such as 4D, 5D, or 6D space) onto 3D space.
• Penrose tiling, developed by mathematician Roger Penrose, is a two-dimensional analogue that illustrates a non-repeating but ordered pattern using a combination of shapes such as rhombi or kites.
• These models help explain how quasicrystals achieve order without translational periodicity.

Physical Properties

Quasicrystals display a fascinating combination of metallic and non-metallic characteristics:

1. Low Thermal and Electrical Conductivity:
   • They conduct heat and electricity poorly compared to regular metals, behaving more like semiconductors.
2. High Hardness and Brittleness:
   • Quasicrystals are extremely hard but also brittle, making them resistant to deformation but difficult to shape.
3. Low Friction and Non-Stick Properties:
   • Their surface structure gives them low coefficients of friction, making them useful in coatings and surface treatments.
4. Corrosion Resistance:
   • Many quasicrystalline alloys exhibit strong resistance to oxidation and corrosion.
5. Unique Optical Properties:
   • Some quasicrystals reflect light in unusual ways due to their complex internal structure, making them interesting for photonic applications.

Classification of Quasicrystals

1. Icosahedral Quasicrystals:
   • Exhibit icosahedral symmetry (20 faces, with 5-fold rotational axes).
   • Example: Aluminium–Manganese (Al–Mn) alloy.
2. Decagonal Quasicrystals:
   • Show 10-fold symmetry in one direction and periodicity along another.
   • Example: Aluminium–Nickel–Cobalt (Al–Ni–Co).
3. Dodecagonal Quasicrystals:
   • Display 12-fold symmetry, typically found in transition metal alloys.
   • Example: Aluminium–Cobalt–Nickel systems.
4. Octagonal and Other Quasicrystals:
   • Some rare quasicrystals exhibit 8-fold or other non-crystallographic symmetries.

Formation and Synthesis

Quasicrystals are typically formed under rapid solidification conditions, such as:

• Melt quenching: Rapid cooling of molten alloys to prevent atoms from forming a periodic lattice.
• Vapour deposition and sputtering: Thin-film techniques that produce aperiodic atomic arrangements.
• Mechanical alloying: Repeated fracturing and welding of metal powders to create metastable quasicrystalline phases.

Natural quasicrystals have also been discovered in meteorites, suggesting that they can form under high-pressure and high-temperature cosmic conditions. The first natural quasicrystal, icosahedrite (Al₆₃Cu₂₄Fe₁₃), was identified in 2009 in a meteorite from Siberia’s Khatyrka region.

Applications of Quasicrystals

Due to their unique combination of structural and physical properties, quasicrystals have found practical and emerging uses in several fields:

1. Industrial Coatings:
   • Used in non-stick cookware, anti-corrosive layers, and wear-resistant coatings due to their hardness and low friction.
2. Aerospace and Automotive Industry:
   • Quasicrystalline materials are used in lightweight and durable coatings for engine components.
3. Electronics and Photonics:
   • Their unusual electronic and optical properties make them candidates for photonic band-gap materials and semiconductor applications.
4. Biomedical Applications:
   • Due to biocompatibility and corrosion resistance, they are being explored for surgical instruments and implants.
5. Hydrogen Storage:
   • Quasicrystalline alloys have been studied for their ability to absorb and release hydrogen efficiently.
6. Catalysis:
   • Some quasicrystals serve as catalysts for chemical reactions due to their large surface area and unique atomic arrangement.

Significance in Science

The discovery of quasicrystals fundamentally altered the definition of a crystal. In 1992, the International Union of Crystallography (IUCr) redefined a crystal as:

“Any solid having an essentially discrete diffraction diagram.”

This definition removed the requirement for periodicity, thus formally including quasicrystals within the family of crystalline solids.
Quasicrystals have also provided deeper insights into:

• The nature of atomic order and symmetry in solids.
• The relationship between mathematics (tiling theory) and material science.
• The complexity and diversity of solid-state phases in nature.

Challenges and Limitations

Despite their fascinating properties, the large-scale application of quasicrystals faces several challenges:

• Brittleness: Limits their use in structural applications.
• Production Cost: Complex synthesis processes hinder commercial scalability.
• Stability: Some quasicrystals are metastable and transform into simpler crystalline phases at high temperatures.