From Strange Symmetry to Implicate Order: Unraveling the Mysteries of Quasicrystals

Introduction to Quasicrystals

Quasicrystals are a class of crystalline structures with unusual atomic ordering. Unlike traditional crystal lattices which exhibit periodic ordering, quasicrystals have an aperiodic arrangement of atoms. This aperiodic pattern does not repeat but still exhibits long-range order and symmetry.

The concept of quasicrystals was first proposed by mathematicians in the 1960s while studying aperiodic tilings. However, they were first discovered in 1982 by Dan Shechtman, an Israeli scientist who observed quasicrystalline structures in rapidly cooled alloys of aluminum and manganese. Initially met with skepticism by the scientific community, Shechtman’s discovery fundamentally transformed crystallography and overturned the assumption that crystals must have translational symmetry.

Shechtman was awarded the Nobel Prize in Chemistry in 2011 for his pioneering discovery. Since their initial discovery, hundreds of quasicrystal compositions have been synthesized in the laboratory. Natural quasicrystals have also been found in certain types of meteorites.

Quasicrystals have a number of unusual properties compared to periodic crystals. Their atomic structure gives rise to higher hardness, low surface energy, low friction and heat conduction, resistance to corrosion, and non-stick properties. This makes them promising materials for a wide range of applications.

Atomic Structure of Quasicrystals

Unlike traditional crystals, quasicrystals have an unusual aperiodic atomic structure that lacks translational symmetry. While normal crystals exhibit a repeating, ordered arrangement of atoms, the atoms in a quasicrystal are arranged in a pattern that never repeats itself. This aperiodic structure means there is no straightforward repetition of a unit cell that can be used to define the entire crystal lattice.

Quasicrystals violate traditional crystallographic restrictions on rotational symmetry, allowing their structure to have symmetry axes that are forbidden for periodic crystals, such as rotational symmetry of order 5, 8, 10 and 12. Their aperiodic arrangement gives them the symmetries of abstract mathematical quasiperiodic functions, rather than those of regular spatial lattices. Quasicrystalline patterns can continuously fill all space, but they lack the strict translational symmetry of classical crystals.

Mathematically, quasicrystals have been shown to exhibit self-similarity across different scales, as their aperiodic structure can be observed in progressively enlarged images of the atomic pattern. Their unusual atomic organization alters the typical physical properties found in most crystals, creating unique characteristics for quasicrystals. While their aperiodicity was initially thought impossible, the discovery of quasicrystals revealed revolutionary new possibilities for atomic structure.

Mathematical Principles Behind Quasicrystals

Quasicrystals exhibit a special type of order that had never been observed in nature before their discovery in 1982. This order is defined by aperiodic patterns and symmetries that have a mathematical foundation distinct from the translational symmetry seen in ordinary crystals. The discovery of quasicrystals revealed new possibilities for ordering matter and expanded scientific understanding of how atoms can be arranged.

The mathematical principles that define quasicrystalline order involve aperiodic tilings, which tile a plane by covering it completely without leaving gaps but also without repeating themselves periodically. British mathematician Roger Penrose pioneered such aperiodic tilings, now known as Penrose tilings, in the 1970s using pentagons, decagons, and the golden ratio. A key property of Penrose tilings is that they generate patterns that are ordered but non-periodic, allowing only certain symmetry orientations. Quasicrystalline materials are characterized by this special aperiodic order.

The discovery of quasicrystals demonstrated that Penrose tilings were not just mathematical curiosities but had real applications in physics and material science. The atoms in quasicrystals are arranged in patterns corresponding to Penrose tilings, providing an ordered structure despite the lack of translational symmetry. Mathematical principles governing aperiodic tilings, non-crystallographic symmetries, and irrational numbers like the golden ratio are thus essential to the structure and properties of quasicrystals. Ongoing research continues applying and expanding on these mathematical foundations to better understand quasicrystals and other aperiodically ordered systems.

Quasicrystal Formation

Quasicrystals can form naturally or be synthesized in the laboratory.

In nature, quasicrystals appear to form in conditions involving shock, such as meteorite impacts on extraterrestrial bodies. They have been discovered in a 4.5 billion-year-old meteorite and evidence suggests they may occur following meteorite strikes on Earth as well. The high pressures and temperatures produced by meteorite impacts can provide conditions suitable for quasicrystal formation.

Researchers have also synthesized quasicrystals in the laboratory under controlled conditions. Using a process called rapid quenching, a molten mixture of aluminum and transition metals like iron or nickel is cooled extremely quickly to form an amorphous solid. This solid is then annealed, or heated and slowly cooled again, allowing atoms to arrange themselves into an ordered quasicrystalline pattern.

Other methods like thin film deposition have also successfully produced quasicrystals on substrates in the lab. This involves carefully depositing layers of atoms on a surface and allowing their self-assembly into quasicrystalline structures. The starting materials, deposition method, and annealing conditions can be tailored to favor formation of specific quasicrystals.

Ongoing research aims to better understand quasicrystal nucleation and growth in natural systems. This could enable synthesizing novel quasicrystals in the laboratory that do not normally occur in nature.

Properties and Applications

Quasicrystals possess some unique properties that make them potentially useful for various applications. Here are some of the key properties and potential uses of quasicrystals:

Mechanical Properties

• High hardness and strength – Quasicrystals are typically harder and stronger than conventional metallic alloys. The increased hardness comes from the aperiodic arrangements of the atoms. This makes quasicrystals attractive for applications requiring high wear resistance.
• Low surface energy – The surfaces of quasicrystalline materials have low energy. This reduces adhesion, friction, and wear when quasicrystals come into contact with other materials. This property is useful for non-stick coatings and low-friction surfaces.
• Brittleness – Although strong, quasicrystals tend to be brittle. This limits their applicability in situations requiring ductility and toughness. The brittleness results from the unconventional structure which makes plastic deformation difficult.

Optical Properties

• Low thermal conductivity – Quasicrystals are poor conductors of heat due to their aperiodic structure. This property allows their use as thermal insulating materials.
• Low electrical conductivity – The unusual atomic structure also results in low electrical conductivity. This can be advantageous for electrical insulation applications.
• Optical diffraction – Quasicrystals can selectively diffract certain wavelengths of light based on their spacings. This enables uses in coatings and paints requiring specific optical effects.

Potential Applications

• Surface coatings – Quasicrystalline coatings provide hardness, low friction, non-stick, and corrosion resistance. They are suitable for cookware, mechanical parts, and optical equipment.
• Reinforcements – Adding quasicrystalline particles to composite materials can increase their strength, hardness, and wear resistance. The composites maintain better mechanical properties at high temperatures.

-Thermal insulation – The low thermal conductivity of quasicrystals allows their use as a thermal barrier coating material. They can provide insulation in appliances, vehicles, and aerospace applications.

• Catalysts – The unusual atomic structure gives quasicrystalline materials catalytic properties. Their catalytic activity depends on their specific composition.
• Photonic applications – The optical diffraction properties of quasicrystals can be useful for photonic crystals, filters, and other optical devices.

Overall, the combination of hardness, strength, low-friction, insulation, and optical characteristics make quasicrystals promising materials for a wide range of applications. More research is still needed to fully develop commercial products utilizing quasicrystalline materials.

Quasicrystals and the Implicate Order

Quasicrystals have a unique structure that does not follow traditional crystallographic rules. The aperiodic, fractal patterns found in quasicrystals resonate with physicist David Bohm’s concept of the implicate order.

Bohm proposed that what we perceive as reality is an explicate order that unfolds from an underlying implicate order. This implicate order contains the totality of existence enfolded within it. Through a process of enfoldment and unfoldment, the explicate order of reality manifests.

The self-similar, non-repeating patterns seen in quasicrystals can represent how the implicate order enfolds information. Just as a quasicrystal pattern has complexity and richness that cannot be seen at a glance, the implicate order contains depths of meaning and interconnection.

As an alternative to viewing the universe as composed of separate objects, Bohm’s implicate order suggests an interconnected wholeness. Quasicrystals demonstrate how matter itself can take on structures reflecting this worldview. Their aperiodic patterns challenge assumptions that the universe should obey predictable physical laws.

Quasicrystal geometry shows how higher dimensional forms can unfold into physical reality. This relates to how Bohm believed the implicate order contains many dimensions enfolded within it. The strange beauty of quasicrystals hints at the possibilities for understanding reality in new ways that connect science, mathematics and metaphysics.

Quasicrystals in Nature

Quasicrystals occur naturally, though they are quite rare. The first naturally occurring quasicrystal was discovered in 2009 in a rock sample from Russia’s Khatyrka River. Analysis showed the quasicrystal composition matched that of synthetic quasicrystals. Further study found evidence that the natural quasicrystal likely formed during an impact event billions of years ago.

While that first discovery came from a rock, other naturally occurring quasicrystals have since been found in various metallic meteorites. The extraterrestrial origins of those samples point to quasicrystal formation in early solar system processes. Some researchers theorize they may have formed as a result of collisions between asteroids early in the solar system’s history.

There are also indications that quasicrystals may form through natural geological processes on Earth. Some mineral samples, such as those containing aluminum, iron, and nickel, have shown evidence of naturally formed quasicrystalline regions. However, conclusive proof remains elusive. The harsh conditions of most geological processes make preservation of quasicrystals unlikely. Further research is needed to fully understand if and how natural terrestrial processes can create quasicrystals.

The study of naturally formed quasicrystals provides clues about the conditions and elements needed for quasicrystal genesis. While unusual atomic structure makes laboratory formation challenging, nature seems to stumble upon the recipe through meteorite collisions, lightning strikes, and extreme geological environments. Further discoveries of natural quasicrystals will reveal more about how these enigmatic structures can spontaneously emerge through natural processes.

History of Quasicrystal Research

In 1982, Israeli chemist Daniel Shechtman reported discovering crystals with forbidden rotational symmetries in aluminum-manganese alloys containing approximately 10 percent manganese. This went against accepted crystallographic theory that crystals can only have rotational symmetries in specific ratios. Shechtman initially met resistance from the scientific community, but his discovery was validated over time as other researchers found examples of quasicrystals in nature and laboratory settings.

Some key events in the history of quasicrystal research include:

• 1984 – Leading crystallographer and Nobel laureate Linus Pauling publishes a letter stating Shechtman’s crystals are impossible and not “scientific evidence”. Pauling refuses to retract his statements even after quasicrystals are accepted.
• 1985 – French materials scientist Denis Gratias provides early mathematical models explaining forbidden symmetries in quasicrystals.
• 1987 – Princeton theoretical physicist Paul Steinhardt and graduate student Dov Levine develop the first theoretical model of quasicrystal atomic structure and formation.
• 1988 – Steinhardt and others report discovery of first natural quasicrystal mineral icosahedrite. This validates quasicrystals as naturally occurring.
• 1994 – Quasicrystals observed forming in laboratory experiments, providing insight into their formation process.
• 2011 – Nobel Prize in Chemistry awarded to Dan Shechtman for his discovery of quasicrystals.
• 2012 – Largest ever natural quasicrystal discovered in eastern Russia. Named decagonite, it has almost perfect decagonal symmetry.
• 2018 – Engineers 3D print stable macroscale quasicrystals for potential applications like heat insulation.
• 2021 – Machine learning algorithm developed that can rapidly scan materials data and predict undiscovered quasicrystal structures.

The initial controversy around quasicrystals gave way to broad acceptance and accelerated research once their existence was confirmed. Mathematical models, laboratory studies and natural quasicrystal discoveries have all expanded our understanding of these unique materials. While many questions remain, the field continues to progress rapidly over 40 years after their initial discovery.

Unanswered Questions and Current Research

Quasicrystals are a relatively new field of study with many open questions and active areas of research. Some key unresolved issues and frontiers include:

• Synthesis of stable quasicrystals: Many discovered quasicrystals are unstable and decompose at moderately high temperatures. Improving quasicrystal stability through alloying or other techniques is an active goal.
• Bulk scale production: Methods for economically producing bulk quantities of quasicrystalline materials are lacking but could enable more applications. Most production is limited to coatings or small samples.
• Fundamental growth mechanisms: The processes governing quasicrystal nucleation and growth during solidification are not fully understood. Both thermodynamic and kinetic factors seem to play a role.
• Effects of defects and disorder: Real quasicrystals contain imperfections, but how defects affect properties is unclear. Reducing defects could improve potential applications.
• Strengthening mechanisms: The strengthening effects from quasicrystalline atomic structures are not fully explained. Research into dislocation movements or other dynamics could provide insight.
• New applications: Most commercial applications are limited today. But properties like low friction, scratch resistance, and non-stick nature show promise in surface coatings. Expanding real-world uses is an active research frontier.
• Natural quasicrystals: Recent discoveries of naturally occurring quasicrystals raise questions about how they form in geological environments. Further study of natural samples could provide hints about stability.

Overall, many foundational questions around quasicrystal formation, behavior, properties and practical applications remain unsettled. The uniqueness of their atomic structure continues to drive new research to better understand quasicrystals and harness their full potential.

Conclusion

The discovery of quasicrystals in 1982 fundamentally changed our understanding of crystallography and solid state materials. Once thought impossible, these aperiodic structures have Atomic arrangements previously unimaginable in nature. The mathematical principles behind their formation reveal deep connections between seemingly disparate fields like geometry, abstract algebra, and materials science.

Quasicrystalline substances possess unique properties of low friction, low heat conduction, and resistance to corrosion. Their applications in advanced coatings and reinforced composites continue to expand. Research also shows quasicrystals naturally occurring in minerals and metallic alloys. This demonstrates nature’s innate capacity for generating highly ordered complexity through self-assembly.

While much has been learned over the past 40 years, quasicrystals remain an active area of research. Key questions remain about their growth mechanisms, physical properties, and prevalence in natural systems. Ongoing studies explore photonic, electronic, and quantum properties for potential breakthroughs in quantum computing.

The discovery of quasicrystals transformed crystallography and materials science. Their aperiodic order reveals nature’s ingenuity in structuring matter. While many mysteries remain, quasicrystals will continue inspiring mathematical insights and novel applications through multidisciplinary research. Their unique structure challenges conventional notions of order, demonstrating there is still much to learn at the frontiers of quantum matter.