Crystal Science


The Definition of a Crystal

One morning in 1982 Daniel Shechtman observed a sample mixture of Aluminum and Manganese under an Electron Microscope. Initially, he didn't believe what he saw: The scattering pattern of the x-ray crystallographic image indicated 5-fold symmetry, a crystal formation never documented previously and thought impossible according to established science [2]. Shechtman's skillful manipulation of the electron microscope and detailed examination of the data ensured his certainty in his own work, but led to persistent doubt in the scientific community for many years.

Crystals mimic a cut-and-polished diamond with all its facets reflecting the brilliance of the world around it. A diamond is a crystal made of carbon atoms, the same carbon atoms that makeup the lead of a graphite pencil and our bodies use for fuel. Diamonds differ from pencil lead in the arrangement of their carbon atoms, packed together in what is called a crystal lattice.

To illustrate this concept, imagine a group of carbon atoms as connected styrofoam balls. Connect four of them together by sticking chop sticks in them to create a 3-dimensional cube. If you then attached many of these forms together, you would have a model resembling the arrangement of carbon in a diamond. This configuration of atoms has symmetry in four dimensions, allowing rotation by 90 degrees 4 times before arriving back to its original orientation. However, each time
Icosahedron (A Platonic Solid with 2-Dimensional 5-Fold Symmetry)
we rotate the grouping, it remains essentially the same. These geometric units can be stacked to infinity. Most importantly, if you take any portion of pattern and shift it around inside of this infinite structure, it can be aligned with an identical arrangement anywhere else in the lattice. This is called Translational Symmetry.

The historical definition of crystals comes from an examination of this type of structure. Ancient Greeks described these types of organizations in terms of geometry as mathematically complex 3-dimensional shapes. Philosophers such as Plato posited that the elements of life are made up these regular geometric arrangements. The Icosahedron to the right is an example of a Platonic Solid , with all of its faces consisting of the same repeating polygon. Both these and Archimedian Solids are types of highly geometric structures that were (and still are) studied extensively in geometric and mathematical applications. Platonic solids are especially interesting because of the presence of the Golden Ratio in the relationships between the lengths of their sides and the angles between them. This ratio governs a particular relationship between parts of a whole that appears repeatedly in nature and is aesthetically pleasing to the human eye. A common example is the spiral of a Nautilus shell [11].

For many years, naturally occurring crystalline solids had a narrow definition. Scientists agreed on a 3-dimensional arrangement of atoms with infinite repeating structural units that had translational symmetry in all dimensions. Constraints in 3-dimensional packing orders led to assumptions that crystalline structures could only exist with 2, 3, 4 and 6 fold symmetry. This theory was reinforced by research that proved the inability of other types of symmetry to pack together without leaving any "void" areas, or spaces, between repeating units. This would create gaps in the structure of the crystal and these gaps were thought to lead to instability in the solid structure of the material. Observations made using X-Ray Crystallography of documented naturally occurring crystals supported this idea for many years.

What Is A Quasicrystal?

The defraction pattern of an Icosahedral ZnMgHo Quasicrystal with 10-Fold Symmetry

In the 1970s, crystal scientists investigated non-periodic 2-dimensional tiling patterns. Non-periodic patterns are repeating units that could not be shifted within the larger pattern. These types of tilings, while displaying no unit piece or translational symmetry, seemed to follow an overarching, or long range pattern. When viewed from a distance there appeared to be some regularity to the layout of the shapes, even though it was never repeating the same pattern twice. An example of this type of tiling can be seen below in the form of a Penrose, or 2-dimensional tiling with long range 5-fold symmetry. The insights gained from 2-dimensional modeling did not begin to penetrate into examinations of 3-dimensional crystal structures until Daniel Shechtman made his unusual observation on an electron microscope in the morning of 1982. While occasional observations of such structures were in fact made prior to Shechtman's observations, due to the accepted definition of a crystal at the time, they were not pursued.

An examination of the electron diffraction image to the right illustrates Shechtman's quasicrystal observations. This image is generated by shining a concentrated electron beam through a crystal of the test material. The electron microscope bends light in differing but predictable ways, scattered by the arrangement of atoms within lattice. This scattered light is then reflected onto an electron sensitive material (Originally a type of film, now typically a digitized photoelectric array). Scientists identify the atomic structure by examining the distribution of captured points of scattered light.

The symmetry of the structure can be observed by drawing lines through consecutive points in the image and counting the number of resulting lines. This corresponds to the number of dots in the inner-most circle, in this case revealing 10-fold symmetry. This quantity is also observed in the dominant scatterings (the larger and brighter points) in each consecutive circle moving out from the center of the image.

Another type of dimensional symmetry can also be observed by examining repeating patterns in the defraction image. For example, in this image we can observe repeated pentagrams throughout the image by imagining lines between certain arrangements of the points. Since 10 is a multiple of 5, the structure of the material reveals both 5-fold and 10-fold symmetry.

Quasicrystals typically consist of a ratio of metalic elements, frequently some sort of Aluminum alloy. They can also exist with some polymer structures. Despite being made predominately of metals (which we typically think of as conductive) quasicrystals are relatively poor conductors and only exhibit di-polar magnetic fields in certain conditions. These properties have important implications for their potential applications [1].

Quasicrystals exhibit long range order that appears similar to the tiling patterns mentioned earlier, but in three dimensions. This long range order follows strict mathematical regularity, even without translational symmetry. The golden ratio is involved in the shape of the atoms occurring in the "void" areas [12]. Just as in non-periodic tiling patterns, these gaps are filled by an atom of a complementary shape. Depending on how a quasicrystal is made, these in-between portions are able to stabilize the structure of the quasicrystal to different degrees. Initial quasicrystal structures were metastable, and degraded with time [1]. This contributed to doubt about Shectman's work since he was initially unable to produce the sample used to produce his electron diffraction patterns.

Redefinition of a Crystal

Before Shechtman's discovery, 5 and 7 fold symmetries were unaccepted in
An example of pentagonal symmetry
crystalline structures with no scientific proof to justify their existence. After many in the science community accepted Shectman's quasicrystal, the definition of a “crystal” had to be revised from the.original definition given by the International Union of Crystallography: “a substance in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating 3-dimensional pattern.”[2]

Now, with the concept of “quasi-crystallinity”, scientists have re-defined a crystal as “any solid having an essentially discrete diffraction diagram. This is divided into two subcategories: crystallographic (those falling into the historical definition of a crystal) and non-crystallographic (aperiodic quasicrystals). So in present day, both crystals falling under the traditional definition and the new quasicrystal structures fall under the definition of a "crystal" [1].

This revised definition impacts scientists and crystallographers research because it expands the “tolerance,” of the crystal community. The previous definition of crystals was as rigid as the crystals themselves, allowing no room for changes in order or symmetry – in other words, no room for growth.

The expansion of the definition of crystals does not mean that quasicrystals have completely broken the mold. According to UMass Dartmouth researcher Siva Rasapalli, quasicrystals are still crystalline structures with some similarities to the old definition of crystals. For example, quasicrystal structure repeats inward rather than outward. So, while quasicrystals have opened up a whole new field of research for crystal science, they have only altered the landscape rather than completely changing it.

Aside from opening the crystal community for new ideas, the revised crystal definition encouraged scientists to take action. After Shechtman’s findings, scientists increased their quasicrystal research – finding new types with decagonal, pentagonal, and octagonal symmetries [3][4].

New or expanded scientific definition invites questions, debate, and further research. Shechtman's discovery inspired scientific quasicrystal experimentation for the past 25 years and prompted some to even take their research outside of the lab resulting in a the identification of a natural quasicrystal form.

Icosahedrite - The Natural Quasicrystal

The original sample of Icosahedrite (Al63Cu24Fe13) that showed natural formation

In 2009, Daniel Shechtman’s findings resurfaced with the discovery of a naturally occurring quasicrystal called Icosahedrite. This newly approved mineral consists of the elements Al (Aluminum,) Cu (Copper,) and Fe (Iron).
Icosahedrite crystals have the following characteristics [5]:

The discovery of Icosahedrite along the Khatyrka River in Chukhotka, Russia was no accident. Research teams had searched for a natural quasicrystal for over a decade.

The Icosahedrate find changed how chemists classify minerals and the way we look at the field altogether. Eventually the teams found what they were looking for, but the results that the rock yielded were disappointing because it's still not known exactly how Icosahedrite naturally formed [5].

In the laboratory, chemists can create the temperature and pressure needed to create Icosahedrite but can't explain how this natural quasicrystal forms, especially in a remote location uninterrupted by humans. Eventually, the Icosahedrite finding could lead to a new definition of minerals, the discovery of new compositions of quasicrystals, and more for you to consider in your future as chemists.

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