The beauty of the unseen: the inner world of crystal atoms and molecules

In our imagination, crystals are clear, dazzling, and beautiful. The real thing, however, is a bit less glamorous. A crystal is in fact primarily a 3D building block of atoms and molecules. What kind of methods can be used to examine its inner world? How did crystallographic research develop in Czechoslovakia? And what can researchers today, thanks to a detailed understanding of crystal structure, discover down to the nanoscale? The story was initially published in the A / Magazine, the quarterly journal of the Czech Academy of Sciences.

The ancient Greeks used the term krystallos to refer to ice. They also called pure quartz by the same name, which was traditionally referred to as clear quartz or rock crystal – they considered it fossilised ice that had acquired great hardness through a process of prolonged freezing. The alchemists working for Holy Roman Emperor Rudolf II considered quartz to be “unripe”, early-stage diamonds, while the sages in certain parts of Asia held a similar view at the time. In many parts of the world, quartz was revered and adored, and people believed in its magical and healing powers.

The symmetry of the crystal structures of not only quartz but also many other minerals has always been a point of interest. That is why since the beginning of time, scholars, and scientists, be it during the classical era, the Renaissance, or the modern era all over the world have examined crystals, just like researchers continue to do so today.

Quartz has always attracted attention – due to its beauty and symmetry, people have even attributed magical properties to it.

Wherein lies the precision and symmetry of crystals? Are there any regularities in the arrangement of the faces and angles? What possible shapes do natural crystals come in, and what kinds of minerals are there? Such questions were asked by scholars, especially in the field of mineralogy, up until the twentieth century. Scientific research has given us the answers to most of these questions today, and we can find them in physics, mathematics, and geology textbooks. The research questions of the twentieth and twenty-first century, however, are much more sophisticated. For instance: how can we visualise the internal structure of a crystal accurately and correctly? How can we penetrate the crystal structure down to its nanoscale dimensions? Interested? Welcome to the field of crystallography.

What is inside of a crystal?
Until the early twentieth century, science was virtually able to examine only the outer structure of crystals – that is, a description of what they look like, their size and hardness, and other basic physical properties. However, scientists did not have the means to find out what exactly was inside crystals and which laws of physics applied. Ordinary optical microscopes, which make it possible to examine miniscule objects, cannot penetrate the internal structure of crystals – i.e., down to the level of the structure and distribution of individual atoms.

It is only thanks to X-rays, which were discovered by the German physicist Wilhelm Conrad Röntgen in 1895, that first allowed us to see the inner world of crystals. Initially, it was not known exactly what X-rays were – whether they were electromagnetic waves or particles. At the time of their discovery, even the very existence of atoms was still in doubt. However, it was assumed that if an X-ray was a wave, its length would roughly correspond to interatomic distance.

The discovery of the German physicist Wilhelm Conrad Röntgen (1845–1923) made it possible to examine the interior of substances.

In a revolutionary experiment in 1912, Max Theodor Felix von Laue answered both unknowns at once. When the German physicist directed a beam of X-rays at a crystal, the rays diffracted on the obstacle and formed a diffraction pattern containing information about the internal structure of the crystal (its symmetry and periodicity). Von Laue thus proved that X-rays are electromagnetic waves and at the same time that crystals are made up of symmetrically arranged atoms.

He thus laid the foundations of the so-called X-ray diffraction method, which significantly advanced materials research and development in the twentieth century. In 1914, he was awarded the Nobel Prize in Physics for his discovery of the diffraction of X-rays by crystals. To this day, the X-ray diffraction method facilitates the study of crystalline substances such as salts, metals, semiconductors, minerals, and organic and inorganic molecules. Researchers have used it to determine the structure and function of many biological molecules, including vitamins, medicinal drugs, proteins, and nucleic acids.

Although more than 110 years have passed since the discovery of X-ray diffraction analysis, it is still widely used and remains the most common crystallographic method. It is capable of imaging the structure of most crystals, with the condition that the crystals in question must be relatively large, measuring at least one hundredth of a millimetre. Other methods are therefore being developed globally and in the Czech Republic, where research teams at the Institute of Physics of the CAS are actively and successfully focusing on this.

A custom-built computer
“The basis of a crystal is a symmetrical structure. It is similar to a building made of bricks. The ordered arrangement that makes up the crystal lattice described in 3D allows one to study the internal structure of solids and various organic materials,” explains Václav Petříček from the Institute of Physics of the CAS, one of the most experienced crystallographers in the Czech Republic.

Petříček got into crystals while studying at the Faculty of Mathematics and Physics (Charles University in Prague), where he found interest in lectures given by researchers from the Institute of Physics of the CAS on subjects such as the theory of crystallographic groups. It was to this institute that his steps led him right after graduating in 1972.

During the 1970s, crystallography was developing quite dynamically in the world, but Czechoslovakia was not experiencing the most joyous of times. The normalisation era stifled the previously budding scientific freedom, and this resulted in severely limited possibilities of contact with the West. “They already had quite good instruments for measuring crystal structures abroad, which we unfortunately did not have access to. On the other hand, it forced us to be creative and do something about it. So we set about developing our own systems and computational methods,” Petříček recalls.

He remembers calculating the data for his thesis by hand and using a calculator. “Just before my mandatory military service began, I had about a month to spare, so I created my first computer program. What used to take me half a year to calculate by hand suddenly only took a few seconds,” the researcher recalls with a smile. The computer used in the 1970s had little in common with today’s computers, but scientists and engineers from the Institute of Physics built it themselves, and today it is stored in the collection of the National Technical Museum in Prague.

Illuminating the crystal
Researchers at the Institute of Physics also worked themselves on improving and perfecting their own X-ray diffractometer. This is an instrument that sends an X-ray beam towards the object under observation (e.g., a crystal); the beam then bends (diffracts) and creates a bending pattern (a diffractogram). The structure of the observed crystal can then be calculated based on this diffractogram using certain mathematical methods.

It is helpful to clarify the difference between an X-ray diffractometer and a typical optical microscope. The use of an optical microscope is limited by the wavelength of light. However, the basic building blocks of crystals – atoms – are significantly smaller than the wavelength of light. Therefore, a microscope cannot capture them. We cannot see the individual atoms that make up a crystal by way of X-ray diffraction either – however, we can calculate their position using the pattern that emerges when X-rays are beamed through them.

The shape of the pattern varies depending on the substance – whether it is crystalline or amorphous (i.e., without a symmetrical crystal structure). If the rays pass through a crystalline substance, the result is a pattern made up of individual bright points – in practice, it looks like a night sky full of stars. However, if we shine the beam through an amorphous substance – glass, for instance – the result is a homogeneous background, which can look like a very blurry, foggy landscape with no fixed points.

In honour of his daughter
Modern diffractometers look different from those used in the 1970s. They are much more sophisticated and allow faster measurements of the substance being studied. Václav Petříček recalls that it used to take him several weeks to compile the measurements of a single crystal, and additional weeks to calculate its structure. However, it was impossible to purchase new, more powerful instruments or components for the existing ones, so he had no choice but to work on improving the calculation methods.

And in this aspect, the Czechoslovaks proved to be very capable, which Petříček came to fully appreciate during his postdoc in the USA, where he managed to go in 1983. It was certainly not something to take for granted; going beyond the Iron Curtain had strict rules during the Communist regime in Czechoslovakia. For instance, Petříček was not permitted to take his family along, as the regime was afraid he might emigrate. He had to leave his wife and five-year-old daughter Jana back home and did not see them for several months.

In the USA, he worked under Philip Coppens, a renowned figure in the world of crystallography. It was at Coppens’ incentive and with his support that the then early-career Czech researcher started working on the first version of a software program for determining crystal structures, which is nowadays used by crystallographers all over the world. The software was named JANA after Petříček’s daughter. The advantage of the Czech program JANA is that it can calculate the structure even for complicated crystal structures. Petříček and his colleagues at the Institute of Physics of the CAS are constantly updating and improving the software, and so it still remains a key crystallographic tool even 40 years after it was first developed. Lukáš Palatinus is one of the younger colleagues who is not only improving the JANA software but also developing additional programs, namely Superflip and PETS2. For the past few years, he has been focusing mainly on computational methods in nanocrystallography.

A look into nano-dimensions
It takes much more power than X-rays are able to generate to make the structure of miniature crystals visible. That’s where electron beams come into play. “Thanks to them, we are able to work with crystals around tens of nanometres in size. If we convert this into volume, we can say that we’re working with crystals up to a billion times smaller than in X-ray diffraction,” Lukáš Palatinus says about the electron diffraction method.

The very principle that electron beams falling on crystals exhibit diffraction patterns has been known for almost 100 years. However, the method was long considered impractical, as it provides more complicated outputs than X-ray diffraction. “Electrons interact more strongly than X-rays, and therefore the resulting diffraction pattern is much more complex,” Palatinus explains. For a long time, there were no computational methods available that could extract information about the crystal structure from such a complex pattern.

It was not until about 15 years ago that a method emerged that enabled the use of the electron data for a full-scale analysis of crystal structures. This represented a new chapter in crystallography, making it possible to successfully analyse the structures of a wide variety of inorganic and organic compounds, including protein structures.

It was 2007 and Lukáš Palatinus was working at the University of Lausanne, Switzerland. “Of course I noticed the groundbreaking work and immediately thought I wanted to get into that as well, but I had to finish what I had started first,” he recalls. Early in his career, he was mainly involved in structural analyses of aperiodic crystals and the development of Superflip.

Today, electron diffraction and the computational methods related to it are the primary research focus of Palatinus’ team. The so-called 3D electron diffraction method is performed using a transmission electron microscope (TEM). In the diffraction (operation) mode of the microscope, data is collected from a single nanocrystal of a substance. The width of the electron beam is matched to the size of the nanocrystal. Depending on the data collection method and the sensitivity of the detector, it takes from tens of seconds to about 20 minutes to record data from a single crystal. The result of the experiment (irradiation of the crystal) is a file containing typically several thousand to tens of thousands of data points (reflections).

Palatinus’ team has gradually managed to refine and improve the method, allowing as much precise information as possible to be extracted from the complicated data sets (the diffractogram). They achieved such accuracy that they were able to experimentally determine the position of even the lightest atoms in existence – hydrogen atoms. It was this achievement that made the cover of Science in January 2017. This occurred exactly 10 years after the first published report appeared on the practical possibilities of the 3D electron diffraction method, the one that so intrigued Palatinus during his postdoc fellowship in Lausanne.

Palatinus’ team was able to experimentally determine the position of even the lightest atoms in existence – hydrogen atoms. The research results were recognised by Science Magazine and featured on its cover in January 2017.

New challenges
Since 2021, his team has been working on a project to develop a set of tools and programs that will make electron diffraction even easier to use, so that chemists, pharmacists, and materials developers, for instance, will be able to work with it on a regular basis. The project, entitled Nanocrystallography of Molecular Crystals, is financially supported by a Czech Science Foundation EXPRO grant and will take five years to complete.

“Our primary focus is on molecular crystals, which find applications in organic chemistry, the pharmaceutical industry, and wherever new molecules are being synthesised and created,” Palatinus explains. The results of irradiating a crystal comprise a huge data set of different points in three-dimensional space; essentially a long list of numbers. This is fed into a computer, which converts the jumble of numbers into a beautiful colour-schemed picture of the molecule in question.

“The goal is to map the entire crystal structure. To transform that opaque dark sky with its plethora of stars that we can see in the diffractogram into a comprehensible result. It’s a long and complicated process to get there,” adds Palatinus, who originally studied geology and was interested in large crystals and minerals rather than the nanoworld and computational models. “I don’t regret not having studied physics or mathematics – geology is a beautiful science. It’s what got me on expeditions to salt caves in Iran, for instance,” he says. “But it’s true that if I had known what I would be doing one day, I might have chosen a different major to study. I am actually a self-taught physicist,” the researcher adds with amusement.

Calculating imperfection
Palatinus’ current team includes a few people with a geoscience background and a few chemists, but “pure” physicists are in the minority and there are no mathematicians, though he says he could definitely use one. Apart from the experiments themselves, a large part of the work comprises modifying the algorithms of the crystallographic data processing software.

They are currently about halfway through the project and are making headway with some of their goals, while others are being worked on intensively. The researchers are now able to measure and obtain data relatively well from nanocrystals that are perfect or nearly perfect in their symmetry. The issue is that most crystals aren’t. The goal is thus to create a computational framework that would be capable of incorporating imperfections. One of the ways this is done is by simulating imperfect crystals and their diffraction patterns and seeing what different kinds of imperfections and defects “do” to the resulting diffraction. This is then verified or disproven by means of experiments.

“Mathematically speaking, we know how it should work, but the theory is greyscale while the tree of life is green, so there are a number of issues that crop up in practice. But we’re capable of breaking them down,” Palatinus says.

Back to quartz
For a person who isn’t immersed in the scientific world, the word crystal evokes something beautiful, something aesthetically pleasing, but not so for an experienced crystallographer. “I must admit that I am strongly professionally deformed. To me, a crystal is simply an arrangement of atoms and molecules – their structure, and the way these constituents all fit together,” the researcher says with a smile. But even he can appreciate and recognise the uniqueness of certain crystal structures, and he hasn’t forgotten his beginnings in mineralogy.

In his office stacked with papers and books, he also keeps a modest collection of interesting minerals. From time to time, he expands it with new pieces he finds on his expeditions with his children. One of the minerals in the collection is pure quartz, cut to symmetrical beauty by nature itself.

Today we know that the iridescent, clear gemstone variety of quartz is not fossilised ice, as the ancient Greeks believed. Yet the symmetry and sheer variety of crystals never ceases to fascinate us. In addition, current techniques allow us to penetrate to the level of nanoscale dimensions, revealing even the completely invisible beauty of crystals, otherwise unseen by the naked eye.

2/2023 (version for browsing)
2/2023 (version for download)

Written by: Leona Matušková, Division of External Relations, CAO of the CAS
Translated by: Tereza Novická, Division of External Relations, CAO of the CAS
Photo: Shutterstock; Wikimedia Commons; Jana Plavec, Division of External Relations, CAO of the CAS

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