Tag: Metal-Organic Frameworks

Jun 30 2016

I have a Question: about thermal expansion

“I have a question”(ik heb een vraag). This is the name of a Belgian (Flemisch) website aimed at bringing Flemisch scientists and the general public together through scientific or science related questions. The basic idea is rather simple. Someone has a scientific question and poses it on this website, and a scientist will provide an answer. It is an excellent opportunity for the latter to hone his/her own science communication skills (and do some outreach) and for the former to get an good answer to his/her question.

All questions and answers are collected in a searchable database, which currently contains about fifteen thousand questions answered by a (growing) group of nearly one thousand scientists. This is rather impressive for a region of about 6.5 Million people. I recently joined the group of scientists providing answers.

An interesting materials-related question was posed by Denis (my translation of his question and context):

What is the relation between the density of a material and its thermal expansion?

I was wondering if there exists a relation between the density of a material and the thermal expansion (at the same temperature)? In general, gasses expand more than solids, so can I extend this to the following: Materials with a small density will expand more because the particles are separated more and thus experience a small cohesive force. If this statement is true, then this would imply that a volume of alcohol should expand more than the same volume of air, which I think is puzzling. Can you explain this to me?

Answer (a bit more expanded than the Dutch one):

Unfortunately there exists no simple relation between the density of a material and its thermal expansion coefficient.

Let us first correct something in the example given: the density of alcohol (or ethanol) is 46.07 g/mol (methanol would be 32.04 g/mol) which is significantly more than the density of air which is 28.96 g/mol. So following the suggested assumption, air should expand more. If we look at liquids, it is better to compare ethanol (0.789 g/cm3) to compare water (1 g/cm3) as liquid air (0.87 g/cm3) needs to be cooled below  -196 °C (77K). The thermal expansion coefficients of wtare and ethanol are 207×10-6/°C and 750×10-6/°C, respectively. So in this case, we see that alcohol will expand more than water (at 20°C). Supporting Denis’ statement.

Unfortunately, these are just two simple materials at a very specific temperature for which this statement is true. In reality, there are many interesting aspects complicating life. A few things to keep in mind are:

  • A gas (in contrast to a liquid or solid) has no own boundary. So if you do not put it in any type of a container, then it will just keep expanding. The change in volume observed when a gas is heated is due to an increase in pressure (the higher kinetic energy of the gas molecules makes them bounce harder of the walls of your container, which can make a piston move or a balloon grow). In a liquid or a solid on the other hand, the expansion is rather a stretching of the material itself.
  • Furthermore, the density does not play a role at all, in case of the expansion of an ideal gas, since p*V=n*R*T. From this it follows that 1 mole of H2 gas, at 20°C and a pressure of 1 atmosphere, has the exact same volume as 1 mole of O2 gas, at 20°C and a pressure of 1 atmosphere, even though the latter has a density which is 16 times higher.
  • There are quite a lot of materials which show a negative thermal expansion in a certain temperature region (i.e. they shrink when you increase the temperature). One well-known example is water. The density of liquid water at 0 °C is lower than that of water at 4 °C. This is the reason why there remains some liquid water at the bottom of a pond when it is frozen over.
  • There are also materials which show “breathing” behavior (this are reversible volume changes in solids which made the originators of the term think of human breathing: inhaling expands our lungs and chest, while exhaling contracts it again.) One specific class of these materials are breathing Metal-Organic Frameworks (MOFs). Some of these look like wine-racks (see figure here) which can open and close due to temperature variations. These volume variations can be 50% or more! 😯

The way a material expands due to temperature variations is a rather complex combination of different aspects. It depends on how thermal vibrations (or phonons) propagate through the material, but also on the possible presence of phase-transitions. In some materials there are even phase-transitions between solid phases with a different crystal structure. These, just like solid/liquid phase transitions can lead to very sudden jumps in volume during heating or cooling. These different crystal phases can also have very different physical properties. During the middle-ages, tin pest was a large source of worries for organ-builders. At a temperature below 13°C β-tin is more stable α-tin, which is what was used in organ pipes. However, the high activation energy prevents the phase-transformation from α-tin to β-tin to happen too readily. At temperatures of -30 °C and lower this barrier is more easily overcome.This phase-transition gives rise to a volume reduction of 27%. In addition, β-tin is also a brittle material, which easily disintegrates. During the middle ages this lead to the rapid deterioration and collapse of organ-pipes in church organs during strong winters. It is also said to have caused the buttons of the clothing of Napoleon’s troops to disintegrate during his Russian campaign. As a result, the troops’ clothing fell apart during the cold Russian winter, letting many of them freeze to death.

 

 

Jun 27 2016

Folding Phonons

Game-diamondsAbout a year ago, I discussed the possibility of calculating phonons (the collective vibration of atoms) in the entire Brillouin zone for Metal-Organic Frameworks. Now, one year later, I return to this topic, but this time the subject matter is diamond. In contrast to Metal-Organic Frameworks, the unit-cell of diamond is very small (only 2 atoms). Because a phonon spectrum is calculated through the gradients of forces felt by one atom due to all other atoms, it is clear that within one diamond unit-cell these forces will not be converged. As such, a supercell will be needed to make sure the contribution, due to the most distant atoms, to the experienced forces, are negligible.

Using such a supercell has the unfortunate drawback that the dynamical matrix (which is 3N \times 3N, for N atoms) explodes in size, and, more importantly, that the number of eigenvalues, or phonon-frequencies also increases (3N) where we only want to have 6 frequencies ( 3 \times 2 atoms) for diamond. For an M \times M \times M supercell we end up with 24M^3 -6  additional phonon bands which are the result of band-folding. Or put differently, 24M^3 -6 phonon bands coming from the other unit-cells in the supercell. This is not a problem when calculating the phonon density of states. It is, however, a problem when one is interested in the phonon band structure.

The phonon spectrum at a specific q-point in the first Brillouin zone is given by the square root of the eigenvalues of the dynamical matrix of the system. For simplicity, we first assume a finite system of n atoms (a molecule). In that case, the first Brillouin zone is reduced to a single point q=(0,0,0) and the dynamical matrix looks more or less like the hessian:

With \varphi (N_a,N_b) = [\varphi_{i,j}(N_a , N_b)] 3 \times 3 matrices \varphi_{i,j}(N_a,N_b)=\frac{\partial^2\varphi}{\partial x_i(N_a) \partial x_j(N_b)} = - \frac{\partial F_i (N_a)}{\partial x_j (N_b)}  with i, j = x, y, z. Or in words, \varphi_{i,j}(N_a , N_b) represents the derivative of the force felt by atom N_a due to the displacement of atom N_b. Due to Newton’s second law, the dynamical matrix is expected to be symmetric.

When the system under study is no longer a molecule or a finite cluster, but an infinite solid, things get a bit more complicated. For such a solid, we only consider the symmetry in-equivalent atoms (in practice this is often a unit-cell). Because the first Brillouin zone is no longer a single point, one needs to sample multiple different points to get the phonon density-of-states. The role of the q-point is introduced in the dynamical matrix through a factor e^{iq \cdot (r_{N_a} - r_{N_b}) }, creating a dynamical matrix for a single unit-cell containing n atoms:

Because a real solid contains more than a single unit-cell, one should also take into account the interactions of the atoms of one unit-cell with those of all other unit-cells in the system, and as such the dynamical matrix becomes a sum of matrices like the one above:

Where the sum runs over all unit-cells in the system, and Ni indicates an atom in a specific reference unit-cell, and MRi  an atom in the Rth unit-cells, for which we give index 1 to the reference unit-cell. As the forces decay with the distance between the atoms, the infinite sum can be truncated. For a Metal-Organic Framework a unit-cell will quite often suffice. For diamond, however, a larger cell is needed.

An interesting aspect to the dynamical matrix above is that all matrix-elements for a sum over n unit-cells are also present in a single dynamical matrix for a supercell containing these n unit-cells. It becomes even more interesting if one notices that due to translational symmetry one does not need to calculate all elements of the entire supercell dynamical matrix to construct the full supercell dynamical matrix.

Assume a 2D 2×2 supercell with only a single atom present, which we represent as in the figure on the right. A single periodic copy of the supercell is added in each direction. The dynamical matrix for the supercell can now be constructed as follows: Calculate the elements of the first column (i.e. the gradient of the force felt by the atom in the reference unit-cell, in black, due to the atoms in each of the unit-cells in the supercell). Due to Newton’s third law (action = reaction), this first column and row will have the same elements (middle panel).

Translational symmetry on the other hand will allow us to determine all other elements. The most simple are the diagonal elements, which represent the self-interaction (so all are black squares). The other you can just as easily determine by looking at the schematic representation of the supercell under periodic boundary conditions. For example, to find the derivative of the force on the second cell (=second column, green square in supercell) due to the third cell (third row, blue square in supercell), we look at the square in the same relative position of the blue square to the green square, when starting from the black square: which is the red square (If you read this a couple of times it will start to make sense). Like this, the dynamical matrix of the entire supercell can be constructed.

This final supercell dynamical matrix can, with the same ease, be folded back into the sum of unit-cell dynamical matrices (it becomes an extended lookup-table). The resulting unit-cell dynamical matrix can then be used to create a band structure, which in my case was nicely converged for a 4x4x4 supercell. The bandstructure along high symmetry lines is shown below, but remember that these are actually 3D surfaces. A nice video of the evolution of the first acoustic band (i.e. lowest band) as function of its energy can be found here.

The phonon density of states can also be obtained in two ways, which should, in contrast to the band structure, give the exact same result: (for an M \times M \times M supercell with n atoms per unit-cell)

  1. Generate the density of states for the supercell and corresponding Brillouin zone. This has the advantage that the smaller Brillouin zone can be sampled with fewer q-points, as each q-point acts as M3 q-points in a unit-cell-approach. The drawback here is the fact that for each q-point a (3nM3)x(3nM3) dynamical matrix needs to be solved. This solution scales approximately as O(N3) ~ (3nM3)3 =(3n)3M9. Using linear algebra packages such as LAPACK, this may be done slightly more efficient (but you will not get O(N2) for example).
  2. Generate the density of states for the unit-cell and corresponding Brillouin zone. In this approach, the dynamical matrix to solve is more complex to construct (due to the sum which needs to be taken) but much smaller: 3nx3n. However to get the same q-point density, you will need to calculate M3 times as many q-points as for the supercell.

In the end, the choice will be based on whether you are limited by the accessible memory (when running a 32-bit application, the number of q-point will be detrimental) or CPU-time (solving the dynamical matrix quickly becomes very expensive).

 

May 22 2016

Annual Meeting of the Belgian Physical Society 2016

ConferenceLogoWebsite_1

Wednesday May 18th was a good day for our little family. Since my girlfriend an I both are physicists by training, we attended the annual meeting of the Belgian Physical Society in Ghent, together. What made this event even more special was the fact that both of us had an oral presentation at the same conference, which never happened before. 🙂

Sylvia talked about an example of indeterminism in Newtonian mechanics, and showed how the indeterminism can be clarified by using non-standard analysis. The example considers the Norton Dome, a hill with a specifically designed shape ( y(x)=-2/3(1-(1-3/2|x|)^{2/3})^{3/2} ). When considering a point mass, experiencing only gravitational force, there are two solutions for the equation of motion: (1) the mass is there, and remains there forever (r(t)=0) and (2) the mass was rolling uphill with a non-zero speed which becomes exactly zero at the top, and continues over the top ( r(t)=\frac{1}{144} (t-T)^4 with T the time the top is reached). Here, r refers to the arc length as measured along the dome (0 at the top). In addition, there also exists a family of solutions taking the first solution at t<T, while taking the second solution at t>T. (As the first and second derivatives of these latter solutions are continuous, Newton will not complain.) This leads to indeterminism in a Newtonian system; for instance, you start with a mass on the top of the hill, and at a random point in time it starts to roll off without the presence of an external something putting it into motion. Using infinitesimals, Sylvia shows that the probability for the mass to start rolling off the dome immediately is infinitesimally close to one.

My own talk was on the use of computational materials science as a means for understanding and explaining experimental observations. I presented results on the pressure-induced breathing of the MIL-47(V) MOF, showing how the experimentally observed S-shape of the transition-pressure-curve can be explained by the spin interactions of the unpaired vanadium-d electrons: it turns out that regions with only ferromagnetic chains compress already at 85 MPa, while the addition of higher and higher percentages of anti-ferromagnetic chains increases the pressure at which the pores collapse, up to 125 MPa for the regions containing 100% anti-ferromagnetic chains. As a second topic, I showed how the electronic band structure of the linker-functionalized UiO-66(Zr) MOF changes. When one or two -OH or -SH groups are added to the benzene ring of the linker, part of the valence band is split off and moves into the band gap. In semiconductors, this would be called a gap state; however, in this case, since every linker in the material contributes

Belgian Physical Society Meeting 2016

Top left: I am presenting computational results on MOFs. Top Right: Sylvia presents the Norton Dome. Bottom: Group picture at the central garden in “Het Pand”. (Photos: courtesy of Sylvia Wenmackers (TL), Philippe Smet (TR), and Michael Tytgat (B) )

a single electron state to this gap state, it practically becomes the valence band top. As a consequence, the color of such functionalized MOF’s changes from white to yellow and orange. As a third topic, I discussed the COK-69(Ti) MOF. In this MOF the electrons in the titaniumoxide clusters are strongly correlated, just as for pure titaniumoxide. Because such systems are poorly described with standard DFT, we used the DFT+U approach, which allowed us to discern between Ti3+ and Ti4+ ions. The latter was practically done by partitioning the electron density using the Hirshfeld-I scheme.

Next to our own talks, the BPS-meeting started with two very interesting plenary lectures on the two big machines/facilities of the physics community: ITER (fusion reactor under construction) and LHC (circular collider, under constant upgrade) at CERN. Prof. Jean Jacquinot, presented the progress in fusion research (among which simulations of plasma-instabilities) and the actual building progress of the ITER facility. Prof. Sergio Bertolucci on the other hand informed us on the latest results obtained with the LHC at CERN, but also about future plans (Future Circular Collider, with a circumference of about 100 km!!). He also showed us the amount of data involved in running the CERN experiments, puting them into perspective: LHC produced in 2012 about 15 Petabyte of data per year (15.000 Terabyte) which is the same as the mount of data added to Youtube on yearly basis. At that time the ATLAS experiment had a dataset of 140 Petabyte (compare to the 100 Petabyte of google’s search index or the 180 Petabyte of facebook uploads/year). The presenters, both excellent and enthusiastic speakers, reminded us that these projects thrive on the enthusiasm of young researchers with open minds. But they also noted, something that is rather often forgotten, that it is the journey not the goal which is most important. Of course, ITER is the next step on the road to commercial fusion power, but along the way much more is learned as a result of tackling practical problems. This is even more so for the CERN experiments, where the “goal” is not as related to our daily lives (keeping the lights on) but focuses on understanding the world. This is at the core of what it means to be a physicist: the need and drive to understand the world. This is also what should drive research but becomes increasingly hampered by the funding-question: how/what profit will it make in the “real world”. Remember the transistor which makes your computer and smartphone as powerful as they are, the laser in CD/DVD-players, the internet allowing you to read this post, and so many more.

Following these plenary presentations, four young scientists competed for the young speaker award presenting their PhD research. Two presentations (1),(2) focused on vortices in superconductors, a third one discussed the use of plasmons in graphene nanoribbons to enhance telecommunication while the fourth talk introduced us into the world of string theory.

In the afternoon, there were six parallel session, of which I mainly attended the Condensed Matter and Nanostructure Physics-session (since I had my own talk there) and the Biological, Medical, Statistical and Mathematical Physics-session rooting for Sylvia. During the Condensed matter session I was mainly fascinated by the presentation of Prof. Sara Bals, on coloring atoms in 3 dimensions. She showed how, using energy-dispersive X-ray (EDX) mapping it is possible to create a 3D atomic lattice of nano-materials and clusters. This is a more direct approach than the usual X-ray diffraction (XRD) approach for identifying a crystal structure. Unfortunately, I am afraid this technique may not be well suited for the MOFs I’m working on, since they contain mainly light elements and not heavy metals(although it may be interesting to try once the technique is optimized further). It is, however, definitely a technique to remember for future projects, to suggest to experimental collaborators.

Links:

Apr 12 2016

Call for Abstracts: Condensed Matter Science in Porous Frameworks: On Zeolites, Metal- and Covalent-Organic Frameworks

Flyer for the Colloquium on Porous Frameworks at the CMD26Together with Ionut Tranca (TU Eindhoven, The Netherlands) and Bartłomiej Szyja (Wrocław University of Technology, Poland) I am organizing a colloquium “Condensed Matter Science in Porous Frameworks: On Zeolites, Metal- and Covalent-Organic Frameworks” which will take place during the 26th biannual Conference & Exhibition CMD26 – Condensed Matter in Groningen (September 4th – 9th, 2016). During our colloquium, we hope to bring together experimental and theoretical researchers working in the field of porous frameworks, providing them the opportunity to present and discuss their latest work and discoveries.

Zeolites, Metal-Organic Frameworks, and Covalent-Organic Frameworks are an interesting class of hybrid materials. They are situated at the boundary of research fields, with properties akin to both molecules and solids. In addition, their porosity puts them at the boundary between surfaces and bulk materials, while their modular nature provides a wealthy playground for materials design.

We invite you to submit your abstract for oral or poster contributions to our colloquium. Poster contributions participate in a Best Poster Prize competition.

The deadline for abstract submission is April 30th, 2016.

The extended deadline for abstract submission is May 14th, 2016.

 

CMD26 – Condensed Matter in Groningen is an international conference, organized by the Condensed Matter Division of the European Physical Society, covering all aspects of condensed matter physics, including soft condensed matter, biophysics, materials science, quantum physics and quantum simulators, low temperature physics, quantum fluids, strongly correlated materials, semiconductor physics, magnetism, surface and interface physics, electronic, optical and structural properties of materials. The scientific programme will consist of a series of plenary and semi-plenary talks and Mini-colloquia. Within each Mini-colloquium, there will be invited lectures, oral contributions and posters.

 

Feel free to distribute this call for abstracts and our flyer and we hope to see you in Groningen!

Feb 01 2016

Computational Materials Science: Where Theory Meets Experiments

Authors: Danny E. P. Vanpoucke,
Journal: Developments in Strategic Ceramic Materials:
Ceramic Engineering and Science Proceedings 36(8), 323-334 (2016)
(ICACC 2015 conference proceeding)
Editors: Waltraud M. Kriven, Jingyang Wang, Dongming Zhu,Thomas Fischer, Soshu Kirihara
ISBN: 978-1-119-21173-0
webpage: Wiley-VCH
export: bibtex
pdf: <preprint> 

Abstract

In contemporary materials research, we are able to create and manipulate materials at ever smaller scales: the growth of wires with nanoscale dimensions and the deposition of layers with a thickness of only a few atoms are just two examples that have become common practice. At this small scale, quantum mechanical effects become important, and this is where computational materials research comes into play. Using clever approximations, it is possible to simulate systems with a scale relevant for experiments. The resulting theoretical models provide fundamental insights in the underlying physics and chemistry, essential for advancing modern materials research. As a result, the use of computational experiments is rapidly becoming an important tool in materials research both for predictive modeling of new materials and for gaining fundamental insights in the behavior of existing materials. Computer and lab experiments have complementary limitations and strengths; only by combining them can the deepest fundamental secrets of a material be revealed.

In this paper, we discuss the application of computational materials science for nanowires on semiconductor surfaces, ceramic materials and flexible metal-organic frameworks, and how direct comparison can advance insight in the structure and properties of these materials.

Nov 16 2015

A Flexible Photoactive Titanium Metal-Organic Framework Based on a [TiIV3(µ3-O)(O)2(COO)6] Cluster

Authors: Bart Bueken, Frederik Vermoortele, Danny E. P. Vanpoucke, Helge Reinsch, Chih-Chin Tsou, Pieterjan Valvekens, Trees De Baerdemaeker, Rob Ameloot, Christine E. A. Kirschhock, Veronique Van Speybroeck, James M. Mayer and Dirk De Vos
Journal: Angew. Chem. Int. Ed. 54(47), 13912-13917 (2015)
doi: 10.1002/anie.201505512
IF(2015): 11.705
export: bibtex
pdf: <Angew.Chem.Int.Ed.> 

Abstract

The synthesis of titanium-carboxylate metal-organic frameworks (MOFs) is hampered by the high reactivity of the commonly employed alkoxide precursors. Here, we present an innovative approach to Ti-based MOFs using titanocene dichloride to synthesize COK-69, the first breathing Ti-MOF built up of trans-1,4- cyclohexanedicarboxylate linkers and an unprecedented [TiIV3(µ3-O)(O)2(COO)6] cluster. The photoactive properties of COK-69 were investigated in-depth by proton-coupled electron transfer experiments, which revealed that up to one TiIV per cluster can be photoreduced to TiIII, while preserving the structural integrity of the framework. From molecular modeling, the electronic structure of COK-69 was determined and a band gap of 3.77 eV was found.

Nov 05 2015

Understanding intrinsic light absorption properties of UiO-66 frameworks: A combined theoretical and experimental study

Authors: Kevin Hendrickx, Danny E.P. Vanpoucke, Karen Leus, Kurt Lejaeghere,
Andy Van Yperen-De Deyne, Veronique Van Speybroeck, Pascal Van Der
Voort, and Karen Hemelsoet
Journal: Inorg. Chem. 54(22), 10701-10710 (2015)
doi: 10.1021/acs.inorgchem.5b01593
IF(2015): 4.820
export: bibtex
pdf:  <Inorg.Chem.>

Abstract

Linker-functionalization of UiO-66 modifies the optical band gap and thus the color of the MOF.

Linker-functionalization of UiO-66 modifies the optical band gap and thus the color of the MOF.

A combined theoretical and experimental study is performed in order to elucidate the eff ects of linker functional groups on the photoabsorption properties of UiO-66-type materials. This study, in which both mono- and di-functionalized linkers (with X= -OH, -NH2, -SH) are studied, aims to obtain a more complete picture on the choice of functionalization. Static Time-Dependent Density Functional Theory (TD-DFT) calculations combined with Molecular Dynamics simulations are performed on the linkers and compared to experimental UV/VIS spectra, in order to understand the electronic eff ects governing the absorption spectra. Di-substituted linkers show larger shifts compared to mono-substituted variants, making them promising candidates for further study as photocatalysts. Next, the interaction between the linker and the inorganic part of the framework is theoretically investigated using a cluster model. The proposed Ligand-to-Metal-Charge Transfer (LMCT) is theoretically observed and is influenced by the differences in functionalization. Finally, computed electronic properties of the periodic UiO-66 materials reveal that the band gap can be altered by linker functionalization and ranges from 4.0 down to 2.2 eV. Study of the periodic Density of States (DOS) allows to explain the band gap modulations of the framework in terms of a functionalization-induced band in the band gap of the original UiO-66 host.

Oct 16 2015

Mechanical Properties from Periodic PlaneWave Quantum Mechanical Codes: The Challenge of the Flexible Nanoporous MIL-47(V) Framework

Authors: Danny E. P. Vanpoucke, Kurt Lejaeghere, Veronique Van Speybroeck, Michel Waroquier, and An
Ghysels
Journal: J. Phys. Chem. C 119(41), 23752-23766 (2015)
doi: 10.1021/acs.jpcc.5b06809
IF(2015): 4.509
export: bibtex
pdf: <J.Phys.Chem.C> 
Graphical Abstract: Pulay stresses complicate the structure optimization of the breathing MIL-47(V) Metal-Organic Framework.
Graphical Abstract: Pulay stresses complicate the structure optimization of the breathing MIL-47(V) Metal-Organic Framework.

Abstract

Modeling the flexibility of metal–organic frameworks (MOFs) requires the computation of mechanical properties from first principles, e.g., for screening of materials in a database, for gaining insight into structural transformations, and for force field development. However, this paper shows that computations with periodic density functional theory are challenged by the flexibility of these materials: guidelines from experience with standard solid-state calculations cannot be simply transferred to flexible porous frameworks. Our test case, the MIL-47(V) material, has a large-pore and a narrow-pore shape. The effect of Pulay stress (cf. Pulay forces) leads to drastic errors for a simple structure optimization of the flexible MIL-47(V) material. Pulay stress is an artificial stress that tends to lower the volume and is caused by the finite size of the plane wave basis set. We have investigated the importance of this Pulay stress, of symmetry breaking, and of k-point sampling on (a) the structure optimization and (b) mechanical properties such as elastic constants and bulk modulus, of both the large-pore and narrow-pore structure of MIL-47(V). We found that, in the structure optimization, Pulay effects should be avoided by using a fitting procedure, in which an equation of state E(V) (EOS) is fit to a series of energy versus volume points. Manual symmetry breaking could successfully lower the energy of MIL-47(V) by distorting the vanadium–oxide distances in the vanadyl chains and by rotating the benzene linkers. For the mechanical properties, the curvature of the EOS curve was compared with the Reuss bulk modulus, derived from the elastic tensor in the harmonic approximation. Errors induced by anharmonicity, the eggbox effect, and Pulay effects propagate into the Reuss modulus. The strong coupling of the unit cell axes when the unit cell deforms expresses itself in numerical instability of the Reuss modulus. For a flexible material, it is therefore advisible to resort to the EOS fit procedure.

Sep 21 2015

Experimental truths

In statistics there exist a well known aphorism:

All models are wrong but some are useful.

— George Edward Pelham Box, 1919-2013

 

"George E. P. Box" by DavidMCEddy

“George E. P. Box” by DavidMCEddy

From the point of view of the definition of the word “model” this is true in an absolute sense, since a model implicitly means approximations are made, and as such discrepancies with “the real system” exist. As a result, this real system is considered as the only “not wrong” description of itself. In the exact sciences, the real system is often nature. This may lead some scientists to believe that experimental results, and by extension conclusions based on them, are true by default. When confronted with theoretical results in disagreement with experimental conclusions, the quick response entails a failure of the theoretical model used since it is not real nature that was worked with, but only a model.

Quite often this is true, and leads to the formulation of new and better models of reality: This allowed, for example, Newton’s laws of motion to evolve to special relativity and further to general relativity. However, equally often (in materials science at least) something else may be going on: The scientist may have forgotten that the experimentalist is also using a model to create his/her experimental results. Broadly speaking, experimental results can be categorized as either being direct or indirect results. Direct results are what you could call “WYSIWYG”-results. What you measure is the quantity you are interested in: e.g. contact angles of liquids by measuring the angle between a drop of the liquid and the substrate surface, the scanning tunneling and atomic force microscopy pictures of a surface,… Indirect results on the other hand, require some post-processing of a direct result to obtain the quantity of interest. This post-processing step includes the use of a model which links the direct result to the property of interest. e.g. The atomic structure of a material. Here the direct result would be the measured X-ray diffraction (XRD) spectrum, while the model and its assumptions are nowadays neatly hidden in well-performing software. This software will try to fit known crystal models to obtain lattice parameters and atomic positions for the XRD spectrum provided. This means however that the obtained result is the best fit that can be obtained, which is not necessarily the actual atomic structure.

Graphical Abstract for paper: Fine-tuning the theoretically predicted structure of MIL-47(V) with the aid of powder X-ray diffraction.

Graphical Abstract for paper: Fine-tuning the theoretically predicted structure of MIL-47(V) with the aid of powder X-ray diffraction.

Another important aspect to remember in regard to experimental results is the fact that different samples are truly different systems. For example, a material grown as a single crystal or synthesized as a powder may give subtly different XRD-spectra. In a recent paper with Thomas Bogaerts, we investigated how well different models for the MIL-47(V) Metal Organic Framework (MOF) fitted to experimental XRD spectra of this material. We found that depending on which experimental spectrum (single crystal or powder XRD) we fitted to, a different model was preferred, showing nature to have multiple truths for the same system. The structural difference between these models is minute, since the models entail different spin configurations on the same topology. However, the effort required for the more extended fitting procedure performed by Thomas is well worth it, since it provided a new (indirect) method for determining the spin-configuration in these rather complex structure, giving access to slightly less-wrong models for the future.

 

 

Sep 12 2015

Fine-tuning the theoretically predicted structure of MIL-47(V) with the aid of powder X-ray diffraction

Authors: Thomas Bogaerts, Louis Vanduyfhuys, Danny E. P. Vanpoucke, Jelle Wieme,
Michel Waroquier, Pascal van der Voort and Veronique van Speybroeck
Journal: Cryst. Eng. Comm. 17(45), 8612-8622 (2015)
doi: 10.1039/c5ce01388g
IF(2015): 3.849
export: bibtex
pdf: <Cryst.Eng.Comm.> 
Graphical Abstract: Which model represents the experimental XRD-spectra best? Ferromagnetic or anti-ferromagnetic chains? With of without offset?
Graphical Abstract: Which model represents the experimental XRD-spectra best? Ferromagnetic or anti-ferromagnetic chains? With of without offset?

Abstract

The structural characterization of complex crystalline materials such as metal organic frameworks can prove a very difficult challenge both for experimentalists as for theoreticians. From theory, the flat potential energy surface of these highly flexible structures often leads to different geometries that are energetically very close to each other. In this work a distinction between various computationally determined structures is made by comparing experimental and theoretically derived X-ray diffractograms which are produced from the materials geometry. The presented approach allows to choose the most appropriate geometry of a MIL-47(V) MOF and even distinguish between different electronic configurations that induce small structural changes. Moreover the techniques presented here are used to verify the applicability of a newly developed force field for this material. The discussed methodology is of significant importance for modelling studies where accurate geometries are crucial, such as mechanical properties and adsorption of guest molecules.