Thought Leaders

Crystallography Experiments on Complex Phenomena - Studying Charge Density Waves, MOFs and Inorganic Nanotubes

Crystallography is the study of the atomic structures of crystals, where the diffraction or reflection of x-rays through the crystal is used to determine the crystal's internal structure. Crystal structure has influence on a wide range of useful physical properties - from magnetism and conductivity to catalytic activity and chemical reactivity.

As we continue to create increasingly exotic structures, such as metal-organic frameworks and inorganic nanotubes, and probe complex phenomena such as superconductivity; crystallography is becoming an increasingly important tool.

AZoM spoke to Dr. Christos Malliakas, from Northwestern University's IMSERC, on his research into exotic systems and phenomena and the crystallographic tools he uses to complete his research.

What is a charge density wave?  Why is understanding the mechanisms behind their formation and destabilisation important?

Almost 60 years ago, R. Peierls1 and H. Frohlich2 independently suggested that the coupling of electrons and phonons in a one-dimensional metal is unstable with respect to a static lattice deformation.

A charge density wave (CDW) is a modulation of the conductive electron density in a metal and an associated modulation of the positions of atoms in the crystalline lattice (phonons, figure 1). Similar to a CDW, superconductivity is another electronically unstable state.

Interestingly, CDWs and superconductivity are often competing states where a metallic system can first undergo a transition into a CDW and then, after the CDW is destabilized, superconductivity may emerge following a reduction in temperature. The typical transition temperature of superconductors is below 100 K and tends to be around the temperature of liquid helium (4 K). On the other hand, the transition temperature of CDW systems can vary from the temperature of liquid helium to well above room temperature (>400 K).3-8

It is this relationship between CDWs and superconductivity that makes them of high interest to researchers. Developing a greater understanding of the mechanisms behind CDW modulations and their interplay with superconductivity may give rise to unusual properties in low-dimensional metals such as superconductivity at room temperature.

Figure 1. Examples of lattice modulations (phonons) upon CDW formation.

How can crystallography be used to study charge density waves?

Charge density waves (CDWs) arise from the coupling of phonons and free electrons in low -dimensional metals.

The coupling of electrons to the lattice can be either commensurate (figure 2A), incommensurate (figure 2B), or discommensurate (figure 2C) - all of which lead to the formation of a supercell, where atoms are displaced from their ideal positions in the crystal structure.9 These displacements are the result of CDW distortions, consquently observing these modulations allows the crystallographic characterization of CDWs.

Atomic structure elucidation of these complex supercells can be achieved only using advanced crystallographic techniques. Crystallography plays a very important role in solving the structure of the CDWs by combining crystallographic models with advanced theoretical calculations to gain a deeper understanding of the overall mechanism of CDWs.

In a commensurate picture, the periodicity of phonons and electrons can be expressed by an integer number, such as a 2-fold or 3-fold supercell. In this case, standard single crystal crystallographic techniques can be utilized.

When the coupling becomes incommensurate, multi-dimensional crystallographic methods (superspace) are required to describe the irrational periodicity of the supercell. This superspace approach is not trivial and it often requires a lot of work and expertise.

Finally, CDWs can be discommensurate, in which the supercell is composed of commensurate domains separated by phase slips of small incommensurate sections. In this highly complex, extreme case, total scattering crystallographic techniques, such as Pair Distribution Function analyses, are necessary to probe the periodicities at the different length scales.10

Figure 2. Illustration of a Charge-Density-Wave in a (A) commensurate, (B) Incommensurate, and (C) Discommensurate supercell.

A large portion of your research has focused on metal-organic frameworks? What do you find interesting about metal-organic frameworks?

Metal-Organic Frameworks (MOFs) are a fascinating class of compounds where basic molecular building blocks and simple precursors can be combined to create complex materials with repeating, extended structures. MOFs are built from metal ions and organic struts.

There is a huge library of combinations of different organic bridges and metals that give rise to a large number of MOFs exhibiting exciting structural topologies and physico-chemical properties. Because of the rational design of MOFs, theoretical predictions of new members and their properties is possible even before synthesizing the actual materials.

As MOFs have an incredibly high surface area which can be activated, or tailored to have a specific chemistry, they can be used for tailored catalysis, gas storage and purifications.

Figure 3. Characteristic structure of a Metal-Organic-Framework with large pores (NU-100)11

How does crystallography assist in the synthesis of MOFs?

Precise atomic models obtained using crystallographic techniques are crucial for the investigation of the different topologies and structures of MOFs.

Through structural analyses, a correlation between the size, shape, and chemistry of the organic building blocks with various metals can be made. Once these chemical and physical interactions are fully understood, strategic modification to any of the structural components can be used to synthesise specific topologies and tailor the MOF properties.

For example, a simple substitution on an organic ligand can change the degree of catenation between frameworks. Subtle changes in MOF structure can be used to fine-tune catalysis so a comprehensive understanding of MOF design is a holy grail for modern chemists and solid-state physicists.

What additional information does crystallography provide for the analysis of MOFs?

Chemists can be very creative and synthesize many different organic building blocks with different functional groups and properties.

When these organic molecules are used in the synthesis of MOFs, new and exciting properties may rise, such as specific sites for catalysis, separation of gas molecules, gas storage, etc. Crystallography for example can be used to identify catalytic sites or even predict from the structure (through theoretical calculation) if pore size and internal surface are suitable for gas separation/storage applications.

Additionally, in-situ crystallographic techniques can now probe the structural changes that may be responsible for key applications, such as the expansion/contraction (breathing effect) of the framework as a function of gas pressure.

Figure 4a and 4b. An example of framework modification. Effect of single substitution of H with Br to the topology (catenated vs non-catenated framework) of a MOF12

How does the behaviour of inorganic nanotubes differ from carbon nanotubes?

Inorganic nanotubes can be more complex since more than one chemical elements are used for the formation of binary and ternary nanostructures. Therefore, the inner and/or outer surface of inorganic nanotubes can be lined with atoms different than carbon.

This makes the electronic, physical, and chemical properties of inorganic nanotubes unique. On the other hand, when structural complexity increases stability tends to decrease, e.g., a ternary nanotube system may decompose at high temperatures to its binary or elemental components.

Figure 5. Structure of the ternary inorganic nanotube system SbPS4.13

As with carbon nanotubes does the tube dimensions effect the nanotubes electronic properties?

Indeed, quantum confinement is universal and electronic properties do change with dimensions even for inorganic nanotubes.

To what extent can inorganic nanotubes be characterised using crystallography?

These days the precise structural solution of inorganic nanotubes using crystallography is possible.

Depending on the inorganic system, in-house single crystal diffractometers and standard crystallographic techniques can be good enough for solving some of the nanostructures.

Also, third-generation synchrotron facilities are easily accessible that can provide bright X-ray beams, which allow researchers to focus down to a few micron-sized crystals. Of course, both in-house and synchrotron single crystal methods require samples that are at least a few microns long in all three dimensions.

In cases where registry between individual nanotubes is not high and samples form powders instead of single crystal, total scattering crystallographic techniques may be more suitable for solving the medium range atomic structure in combination with advanced ab-initio modelling.

Figure 6. Scanning Electron Microscopy image of bundles of SbPS4 nanotubes. Typical diameter of each bundle is approximately 20 microns

What equipment do you use for your crystallographic experiments?

I have access to several diffractometers. For in-house use, I’ve been using single crystal diffractometers from STOE (IPDS2 and IPDS2T) and Bruker (Prospector, Duo, Triumph), and powder diffractometers from STOE (STADI MP), Rigaku (Miniflex600), and Inel.

I also make use of synchrotron (APS) and neutron (SNS) facilities for challenging structures.

Why did you choose instruments from STOE?

Crystallography is the backbone of our research group and part of my thesis project was related to the structural determination of incommensurate modulated structures.

I was a first year graduate student when my advisor went to Germany for Sabbatical. Apparently, a lot of institutions in Germany use STOE’s diffractometers, something that is not very common here in US. My advisor was amazed by the capabilities of STOE’s single crystal diffractometer at that time and especially the features the instrument had to offer for dealing with incommensurate structures.

Long story short, my advisor decided to buy one of these diffractometer for the group.  This is how I was first introduced to STOE’s instrumentation. For the next four years, I made extensive use of their diffractometer (the IPDS2) which was crucial for my thesis work. During that period, the group expanded and purchased one more single crystal diffractometer from STOE (the IPDS2T).

Since the summer of 2016, I’ve been managing and using STOE’s latest powder diffractometer, the STADI MP, in transmission geometry.

Several research groups in Northwestern University are interested in in-situ diffraction measurements, such as the high temperature and gas flow of corrosive gases, on a wide variety of materials ranging from oxides to chalcogenides, intermetallics, MOFs, and organic compounds.

After some research of the market, STOE was the only company, to the best of our knowledge, that could offer an in-situ furnace with a unique design which is compatible with all the different environments and materials made by the research groups.

Figure 7. STOE’s STADIMP at Northwestern University equipped with an in-situ furnace

Where can our readers find out more about your research?

Published research can be found on various scientific websites and social media. For ongoing research please visit the Integrated Molecular Structure Education and Research Center (IMSERC) website here.

About Christos Malliakas

Dr. Christos Malliakas (ORCID: 0000-0003-4416-638X) joined the IMSERC facility in January of 2016 as an X-Ray Crystallography specialist.

Christos has extensive experience in non-classical crystallographic techniques such as incommensurate modulated structures and total scattering diffraction methods.

Dr. Malliakas received his Ph.D. at Michigan State University under the direction of Prof. Mercouri Kanatzidis. Christos performed his post-doctoral work in the Emerging Materials group at the Materials Science Division at Argonne National Laboratory under John Mitchell’s group leadership.

Christos’ research interests include solid state chemistry and theory of solids, synthesis, crystal growth, in-situ and advanced characterization of materials. Dr. Malliakas has published more than 150 articles in peer-review journals.

About the Northwestern University Integrated Molecular Structure Education and Research Center

The mission of the Northwestern University Integrated Molecular Structure Education and Research Center (IMSERC) is to further research at Northwestern by providing access to and educating students on the proper use of instrumentation needed for molecular structure characterization.

IMSERC has been established to educate Northwestern students to be scientific leaders of the 21st century, and to support world-class research. The synthesis of small molecules fuels research of numerous core disciplines and interdisciplinary activities, including chemistry, molecular/cellular biology, drug discovery, chemical biology, translational medical research, materials, catalysis, nanotechnology and energy storage/conversion.

All research at Northwestern utilizing novel compounds relies on IMSERC to characterize these molecules before application testing can begin. The equipment in IMSERC is made available to class instructors so that NU students learn how groups conduct cutting-edge research projects.

Under this model, IMSERC acts as a “one-stop shop” where research groups and educators can expect to bring questions about their samples and expect to find solutions that further their research projects.


  1. Peierls, R. E., Quantum Theory of Solids. The Clarendon Press, Oxford: 1955.
  2. Frohlich, H., On the Theory of Superconductivity: The One-Dimensional Case. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1954, 223 (1154), 296-305.
  3. Kim, H. J.; Malliakas, C. D.; Tomić, A. T.; Tessmer, S. H.; Kanatzidis, M. G.; Billinge, S. J. L., Local Atomic Structure and Discommensurations in the Charge Density Wave of CeTe3. Physical review letters 2006, 96 (22), 226401.
  4. Malliakas, C.; Billinge, S. J. L.; Kim, H. J.; Kanatzidis, M. G., Square nets of tellurium: Rare-earth dependent variation in the charge-density wave of RETe3 (RE = rare-earth element). Journal of the American Chemical Society 2005, 127 (18), 6510-6511.
  5. Malliakas, C. D.; Iavarone, M.; Fedor, J.; Kanatzidis, M. G., Coexistence and coupling of two distinct charge density waves in Sm2Te5. Journal of the American Chemical Society 2008, 130 (11), 3310-3312.
  6. Malliakas, C. D.; Kanatzidis, M. G., Divergence in the behavior of the charge density wave in RETe3 (RE = rare-earth element) with temperature and RE element. Journal of the American Chemical Society 2006, 128 (39), 12612-12613.
  7. Malliakas, C. D.; Kanatzidis, M. G., Charge density waves in the square nets of tellurium of AMRETe4 (A = K, Na; M = Cu, Ag; RE = La, Ce). Journal of the American Chemical Society 2007, 129 (35), 10675-10677.
  8. Malliakas, C. D.; Kanatzidis, M. G., A Double Charge Density Wave in the Single Tellurium Square Net in Cu0.63EuTe2? Journal of the American Chemical Society 2009, 131 (20), 6896-6897.
  9. Malliakas, C. D. Charge Density Waves and Structural Modulations in polytelluride componds. Michigan State University, 2007.
  10. Bozin, E. S.; Malliakas, C. D.; Souvatzis, P.; Proffen, T.; Spaldin, N. A.; Kanatzidis, M. G.; Billinge, S. J. L., Entropically Stabilized Local Dipole Formation in Lead Chalcogenides. Science 2010, 330 (6011), 1660-1663.
  11. Farha, O. K.; Yazaydin, A. O.; Eryazici, I.; Malliakas, C. D.; Hauser, B. G.; Kanatzidis, M. G.; Nguyen, S. T.; Snurr, R. Q.; Hupp, J. T., De novo synthesis of a metal-organic framework material featuring ultrahigh surface area and gas storage capacities. Nat Chem 2010, 2 (11), 944-8.
  12. Farha, O. K.; Malliakas, C. D.; Kanatzidis, M. G.; Hupp, J. T., Control over Catenation in Metal-Organic Frameworks via Rational Design of the Organic Building Block. Journal of the American Chemical Society 2010, 132 (3), 950-952.
  13. Malliakas, C. D.; Kanatzidis, M. G., Inorganic single wall nanotubes of SbPS4-xSex (0 ≤ x ≤ 3) with tunable band gap. Journal of the American Chemical Society 2006, 128 (20), 6538-6539.

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