Tag: computational materials science

Nov 23 2016

VASP-tutor: Creating a primitive unit cell from a conventional unit cell…for a MOF.

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Ball-and-stick representation of diamond in two different unit cells. Left: primitive unit cell containing two atoms. All atoms at the vertices are periodic copies of the same one. Right: Conventional cubic unit cell containing eight atoms. Atoms at opposing faces are periodic copies, while all atoms at the vertices are periodic copies of the same atom.

When performing electronic structure calculations on complex systems, you prefer to do this on systems with as few atoms as possible. Such periodic cells are called unit cells. There are, however, two types of unit cells: Primitive unit cells and conventional unit cells.

A primitive unit cell is the smallest possible periodic cell of a crystalline material, making it extremely suited for calculations. Unfortunately, it is not always the nicest unit cell to work with, as it may be difficult to recognize it’s symmetry (cf. the example of diamond on the right). The conventional unit cell on the other hand shows the symmetry more clearly, but is not (always) the smallest possible unit cell. To make matters complicated and confusing, people often refer to both types as simply “unit cell”, which is not wrong, but the term unit cell is for many uniquely associated with only one of the two types.

When you are performing calculations on diamond, the conventional cell isn’t that large that standard calculations become impossible, even on a personal laptop or desktop. On the other hand, when you are studying a Metal-Organic Framework like the UiO-66(Zr) which contains 456 atoms in its conventional unit cell, you will be very happy to use the primitive unit cell with ‘merely’ 114 atoms. Also the MIL-47/53 topology which generally is studied using a conventional unit cell containing 72/76 can be reduced to a smaller primitive unit cell of only 36/38 atoms. Just as for the diamond primitive unit cell, this MIL47/53 primitive unit cell is not a nice cubic cell. Instead you end up with a lattice having lattice angles of seventy-something degrees.

Reduction of the MIL-53 conventional cell to the primitive cell. The conventional cell is shown, extending slightly into the periodic copies. The primitive lattice vectors are shown as colored arrows. The folded primitive cell shows there was some symmetry-breaking in the hydroxy groups of the metal-oxide chain. Introducing some additional symmetry fixes this in the final primitive cell.

How to reduce a conventional unit cell to a primitive unit cell?

Before you start, and if you are using VASP, make sure you have the POSCAR file giving the atomic positions as Cartesian coordinates. (Using the HIVE-4 toolbox: Option TF, suboption 2 (Dir->Cart).)

If you do not use VASP, you can still make use of the scheme below.

Open your structure using VESTA, and save it as “VASP” file: POSCAR.vasp (File → Export Data → choose “VASP” as filetype, select Cartesian Coordinates (don’t select the Convert to Niggli reduced cell as this only works for perfect crystal symmetry)).
Open the file you just saved in a text editor (e.g. notepad or notepad++). The file format is quite straight forward. The first line is a comment line while the second is a general scale-factor, which for our current purpose can be ignored. What is important to know is that the 3^rd, 4^th and 5^th lines give the lattice vectors (a, b, and c). The 6^th and 7^th line give the order, type and number of atoms for each atomic species (In VASP 5.x, the older VASP 4.x format does not have a 6^th line). The 8^th line should say “Cartesian”. From the 9^th line onward you get the atomic coordinates.
Choose 1 atom in your conventional cell which you are going to use as reference point.
Get the primitive unit cell lattice vectors by generating vectors from the reference atom. (cf. figure above) Using VESTA this can be done as follows:
1. Open your conventional cell in VESTA (if you closed it after step 1).
2. Use the distance selector (5th symbol from the top in the left-hand-side menu) and for each of the primitive lattice vectors, select the reference atom and it’s primitive copy.
3. Subtract the “fractional coordinates” of the selected atoms provided by VESTA to get a “fractional” primitive vector (the primitive a vector will be called a^prim,frac)
4. Multiply each of the conventional lattice vectors(a^conv, b^conv, and c^conv) with the corresponding component of the fractional primitive vector, and add the resulting vectors to obtain the new primitive vector:
  
  ⇒ a^prim= a_x^prim,frac a^conv + a_y^prim,frac b^conv+ a_z^prim,frac c^conv
  
  So imagine that the lattice vectors of the MOF above are a = ( 20, 0, 0), b = ( 0, 15, 0), and c = ( 0, 0, 5). And the primitive fractional a vector is found to be a^prim,frac = ( 0.5, -0.5, 0.5). In this case the a^prim vector will become: a^prim= ( 10, 0, 0 ) + ( 0, -7.5, 0 ) + ( 0, 0, 2.5) = (10, -7.5, 2.5).
Replace the conventional lattice vectors in the POSCAR.vasp file (cf. step 2) with the new primitive lattice vectors. Save the file.
Open the POSCAR.vasp in VESTA. If everything went well, and the conventional cell wasn’t the real primitive cell already, you should see a nice new primitive cell with the equivalent atoms perfectly overlapping one-another. This is also the reason to have your starting geometry in Cartesian coordinates. If you would have your atomic positions as fractional coordinates this first check will not work at all. Furthermore, you would need to calculate the new fractional coordinates of the atoms in the primitive unit cell. If all is well, you can close POSCAR.VASP in VESTA. (If something is wrong: either you did something wrong, and you should start again, or it wasn’t actually a super cell of a primitive cell you started to construct.)
Get the atoms of the primitive unit cell.
1. Because our atomic positions are in Cartesian coordinates in our initial geometry file, we now just need to make a list of single copies of equivalent atoms. Using VESTA (the original structure file you still have open from step 1) you can click on each atom you wish to keep and write down their index (this is the first number you find on the line with Cartesian coordinates) … For example: In case of the MIL53-MOF you can select all metal and oxygen atoms of 1 chain, and two linker molecules.
2. Remove all superfluous atoms (i.e. those of which you didn’t write down the index) from the POSCAR.vasp (using your text-editor). You may want to make a backup of this file before you start :-).
3. Update the number of atoms on the 7^th line of the POSCAR.vasp file, and check that the number is correct. The conventional cell should have had an integer multiple of the number of atoms in the primitive cell. Save the final structure as POSCAR_final.vasp .
4. The POSCAR_final.vasp should contain both the new lattice vectors and a list of atoms for a single primitive unit cell. Check this by opening the file using VESTA, and make sure you didn’t remove too many or too few atoms. If not, go back to step (a) and double check. (If you are using the HIVE4-toolbox you can first transform POSCAR_final.vasp back to direct coordinates as this may make atoms visible which nicely overlap in Cartesian coordinates: Option TF, suboption 1 (Cart->Dir) )
Congratulations you have constructed a primitive cell from a conventional cell.

As you can see, the method is quite simple and straight forward, albeit a bit tedious if you need to do this many times.

Enjoy your primitive unit cell!

PS: Small remark for those new to VESTA. You can use delete atoms in VESTA and store your structure again. This is useful if you want to play with a molecule. Unfortunately for a solid you need also to get new lattice vectors, which did not happen. As a result you end up with some atoms floating around in a periodically repeated box with the original lattice parameters. Steps 1-5 given above provide a simple way of not ending up in this situation, but require some typing on your part.

PS 2: The opposite transformation, from a primitive unit cell to a conventional unit cell, using VESTA, is shown in this youtube video.

Nov 16 2016

Modern art in research.

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Which combination to take?

Although it looks a bit like a modern piece of art, it is one more attempt at trying to find an optimum combination of parameters.

I’m currently trying to find “the best choice” for U and J for a DFT+U based project… DFT??? Density Functional Theory. This is an approximate method which is used in computational materials science to calculate the quantum mechanical behavior of electrons in matter. Instead of solving the Schrödinger equation, known from any quantum mechanic course, one solves the Hohenberg-Kohn-Sham equations. In these equations it are not the electrons which play a central role (which they do in the Schrödinger equations) but the electron density. Hohenberg, Kohn and Sham were able to show that their equations give the exact same results as the Schrödinger equations. There is, however, one small caveat: you need to have an “exact” exchange-correlation functional (a functional is just a function of a function). Unfortunately there is no known analytic form for this functional, so one needs to use approximated functionals. As you probably guessed, with these approximate functionals the solution of the Hohenberg-Kohn-Sham equations is no longer an exact solution.

For some molecules or solids the error is much larger than average due to the error in the exchange-correlation functional. These systems are therefore called “strongly-correlated” systems. Over the years, several ways have been devised to solve this problem in DFT. One of them is called DFT+U. It entails adding additional coulomb interactions (Hubbard-U-potential) between the “strongly interacting electrons”. However this additional interaction depends on the system at hand, so one always needs to fit this parameter against one of more properties one is interested in. The law of conservation of misery, however, makes sure that improving one property goes hand in hand with a deterioration of another property.

Since actual DFT+U has two independent parameters (U and J, though for many systems they can be dependent reducing to a single parameter) I had quite some fun running calculations for a 21×21 grid of possible pairs. Afterward, collecting the data I wanted to use for fitting purposes took my script about 2h! 😯 Unfortunately the 10 properties of interest I wanted to fit give optimum (U,J)-pair all over the grid. In the picture above, you see my most recent attempt at trying to deal with them. It shows for the entire grid how many of the 10 properties are reasonably well fit.There are two regions which fit 6 properties; One around (U,J)=(5,10) and another around (U,J)=(8.5,17.5). There will be more work before this gives a satisfactory result, the show will go on.

Oct 06 2016

tUL Life Sciences Research Day 2016

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Yesterday was the tUL Life Sciences Research Day 2016. A conference event build around finding collaboration possibilities between the University of Hasselt in Belgium and the University of Maastricht (The Netherlands)…after all tUL is the “transnational University Limburg” which brings two universities together that are only separated some 26 km, but you have to cross a national border.

Although Life sciences itself is not my personal niche, I went to look for opportunities, as nano-particles which are used for drug delivery often consist of metals or oxides. These materials on the other hand are my niche. I used my current work on MOFs as a means to show what is possible from the ab-initio point of view, and presented this as a poster.

tUL Life Science Research Day 2016 Poster

Poster presented at the tUL Life Sciences Research Day, depicting my work on the unfunctionalized and the functionalized MIL-47(V) MOF.

Sep 25 2016

Mechanochemical route to the synthesis of nanostructured Aluminium nitride

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Authors:	S. A. Rounaghi, H. Eshghi, S. Scudino, A. Vyalikh, D. E. P. Vanpoucke, W. Gruner, S. Oswald, A. R. Kiani Rashid, M. Samadi Khoshkhoo, U. Scheler and J. Eckert
Journal:	Scientific Reports 6, 33375 (2016)
doi:	10.1038/srep33375
IF(2016):	4.259
export:	bibtex
pdf:	<Sci.Rep.> (open access)

Abstract

Hexagonal Aluminium nitride (h-AlN) is an important wide-bandgap semiconductor material which is conventionally fabricated by high temperature carbothermal reduction of alumina under toxic ammonia atmosphere. Here we report a simple, low cost and potentially scalable mechanochemical procedure for the green synthesis of nanostructured h-AlN from a powder mixture of Aluminium and melamine precursors. A combination of experimental and theoretical techniques has been employed to provide comprehensive mechanistic insights on the reactivity of melamine, solid state metalorganic interactions and the structural transformation of Al to h-AlN under non-equilibrium ball milling conditions. The results reveal that melamine is adsorbed through the amine groups on the Aluminium surface due to the long-range van der Waals forces. The high energy provided by milling leads to the deammoniation of melamine at the initial stages followed by the polymerization and formation of a carbon nitride network, by the decomposition of the amine groups and, finally, by the subsequent diffusion of nitrogen into the Aluminium structure to form h-AlN

Jun 27 2016

Folding Phonons

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Game-diamonds About 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 N_i indicates an atom in a specific reference unit-cell, and M^R_i an atom in the R^th 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)

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).
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 29 2016

One more digit of importance

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Over the past few weeks I have bumped into several issues each tracing back to numerical accuracy. Although I have been programming for almost two decades I never had to worry much about this, making these events seem as-if the universe is trying to tell me something.

Now, let me try to give a proper start to this story; Computational (materials) research is generally perceived as a subset of theoretical (materials) research, and it is true that such a case can be made. It is, however, also true that such thinking can trap us (i.e. the average computational physicist/chemist/mathematician/… programming his/her own code) with numerical accuracy problems. While theoretical equations use exact values for numbers, a computer program is limited by the numerical precision of the variables (e.g. single, double or quadruple precision for real numbers) used in the program. This means that actual numbers with a larger precision are truncated or rounded to the precision of the variable (e.g. 1/3 becomes 0.3333333 instead of 0.333… with an infinite series of 3’s). Most of the time, this is sufficient, and nothing strange will happen. Even more, most of the time, the additional digits would only increase the computational cost while not improving the results in a significant fashion.

Interstellar disc

To understand the importance, or the lack thereof, of additional significant digits, let us first have a look at the precision of $\pi$ and the circumference and surface area of a disc. We will be looking at a rather large disc, one with a radius equal to the distance between the sun, and the nearest star, Alpha Centauri, which is 39 900 000 000 000 km away. The circumference of this disc is given by $2r\pi$ (or $2.5 \times 10^{14}$ km ). As a single precision variable $\pi$ will have about 7-8 significant digits. This means the calculated circumference will have an accuracy of about 1 000 000 km (or a few times the distance between the earth and the moon). Using a double precision $\pi$ variable, which has a precision of 16 decimal digits, the circumference will be accurately calculated to within a few meters. At quadrupal precision, the $\pi$ variable would have 34 significant decimal digits, and we would even be able to calculate the surface of the disc ( $r^2\pi$ or $5.0 \times 10^{33}$ m² ) to within 1 m². Even the surface of a disc the size of our milky way could be calculated with an accuracy of a few hundred square km (or ± the size of Belgium ).

Knowing this, our mind is quickly put at easy regarding possible issues regarding numerical accuracy. However, once in a while we run into one exceptional case (or three, in my case).

1. Infinitesimal finite elements

Temperature profile in the insulating layer of a cylindrical wire.

While looking into the theory behind finite elements, I had some fun implementing a simple program which calculated the temperature distribution due to heat transport in an insulating layer. The finite element approach performed rather nicely, leading to good approximate results, already for a few dozen elements. However, I wanted to push the implementation a bit (the limit of infinite elements should give the exact solution). Since the set of equations was solved by a LAPACK subroutine, using 10 000 elements instead of 10 barely impacted the required time (writing the results took most of 2-3 seconds anyway). The results on the other hand were quite funny as you can see in the picture. The initial implementation, with single precision variables, breaks down even worse already at 1000 elements. Apparently the elements had become too small leading to too small variations of the properties in the stiffness-matrix, resulting in the LAPACK subroutine returning nonsense.

So it turns out that you can have too many elements in a finite elements method.

2. Small volumes: A few more digits please

Optimized volume in Equation of State fit, as function of the range of the fitting data, and step size between data-points. green diamonds, blue triangles and black discs: 1% , 0.5% and 0.25% volume steps respectively.

Recently, I started working at the Wide Band Gap Materials group at the University of Hasselt. So in addition to MOFs I am also working on diamond based materials. While setting up a series of reference calculations, using scripts which already suited me well during my work on MOFs, I was trying to figure out for which volume range, and step size I would get a sufficient convergence in my Equation-of-States Fitting procedure. For the MOFs this is a computationally rather expensive (and tedious) exercise, which, fortunately, gives clear results. For the 2-atom diamond unit cell the calculations are ridiculously fast (in comparison), but the results were confusing. As you can see in the picture, the values I obtained from the different fits seem to oscillate. Checking my E(V) data showed nothing out of the ordinary. All energies and volumes were clearly distinguishable, with the energies given with a precision of 0.001 meV, and the volumes with a precision of 0.01 Å³. However, as you can see in the figure, the volume-oscillations are of the order of 0.001 Å³, ten times smaller than our input precision. Calculating the volumes based on the lattice parameters to get a precision of 10^-6 Å³ for the input volumes stabilizes the convergence behavior of the fits (open symbols in the figure). This problem was not present with the MOFs since these have a unit cell volume which is one hundred times larger, so a precision of 0.01 Å³makes the relative error on the volumes one hundred times smaller than was the case for diamond.

In essence, I was trying to get more accurate output than the input I provided, which will never give sensible results (even if they actually look sensible).

3. Many grains of sand really start to pile up after a while

The last one is a bit embarrassing as it lead to a bug in the HIVE-toolbox, which is fixed in the mean time.

One of the HIVE-toolbox users informed me that the dosgrabber routine had crashed because it could not find the Fermi-level in the output of a VASP calculation. Although VASP itself gives a value for the Fermi-level, I do not use it in the above sub-program, since this value tend to be incorrect for spin-polarized systems with different minority and majority spins. However, in an attempt to be smart (and efficient) I ended up in trouble. The basic idea behind my Fermi-level search is just running through the entire Density of States-spectrum until you have counted for all the electrons in the system. Because the VASP estimate for the Fermi-level is not that far of, you do not need to run through the entire list of several thousand entries, but you could just take a subset-centered around the estimated Fermi-level and check in that subset, speeding this up by a factor of 10 to 100. Unfortunately I calculated the energy step size between density of states entries as the difference between the first two entries, which are given to with an accuracy of 0.001 eV. I guess you already have a feeling what will be the problem. When the index of the estimated Fermi-level is 1000, the error will be of the order of 1 eV, which is much larger than the range I took into account. Fortunately, the problem is easily solved by calculating the energy step size as the difference between the first and last index, and divide by the number of steps, making the error in the particular case more than a thousand times smaller.

So, trying to be smart, you always need to make sure you really are being smart, and remember that small number can become very big when there are a lot of them.

May 22 2016

Annual Meeting of the Belgian Physical Society 2016

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ConferenceLogoWebsite_1

Wednesday May 18^th 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

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

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Together 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 26^th biannual Conference & Exhibition CMD26 – Condensed Matter in Groningen (September 4^th – 9^th, 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 30^th, 2016.

The extended deadline for abstract submission is May 14^th, 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!

Mar 01 2016

Helium flash: the beginning of a new chapter.

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During the past two and a half years, part of being a delocalized physicist has meant for me that I had to work at one end of the country while my girlfriend and son lived at the other. Today this situation drastically changed, as I moved with my FWO-postdoctoral project from my alma mater to the University of Hasselt, where I started in the Wide Band Gap Materials group of Prof. Ken Haenen.

My delocalization will now take the form of Metal-Organic Frameworks on the one side and Diamond based materials on the other. As the sole computational solid state physicist in an otherwise entirely experimental group (and even institute) I seem to have returned to a well known configuration (At Ghent university I was initially the house-theoretician of the SCRiPTS group). Also the idea of performing calculations on diamond brings back memories, since this allotrope of carbon lives two levels above the germanium on which Pt nanowires grow. All-in-all I look forward to an exciting time. But first things first: getting my HPC credentials and data safely transported from the one end of the country to the other.

Feb 11 2016

First-Principles Study of Antisite Defect Configurations in ZnGa₂O₄:Cr Persistent Phosphors

Filed under 2016, publications

Authors:	Arthur De Vos, Kurt Lejaeghere, Danny E. P. Vanpoucke, Jonas J. Joos, Philippe F. Smet, and Karen Hemelsoet
Journal:	Inorg. Chem. 55(5), 2402-2412 (2016)
doi:	10.1021/acs.inorgchem.5b02805
IF(2016):	4.857
export:	bibtex
pdf:	<Inorg.Chem>

Graphical Abstract: First-principles simulations on zinc gallate solid phosphors (ZGO) containing a chromium dopant and antisite defects (left) rationalize the attractive interactions between the various elements. A large number of antisite pair configurations is investigated and compared with isolated antisite defects. Defect energies point out the stability of the antisite defects in ZGO. Local structural distortions are reported, and charge transfer mechanisms are analyzed based on theoretical density of states (right) and Hirshfeld-I charges.

Abstract

Zinc gallate doped with chromium is a recently developed near-infrared emitting persistent phosphor, which is now extensively studied for in vivo bioimaging and security applications. The precise mechanism of this persistent luminescence relies on defects, in particular, on antisite defects and antisite pairs. A theoretical model combining the solid host, the dopant, and/or antisite defects is constructed to elucidate the mutual interactions in these complex materials. Energies of formation as well as dopant, and defect energies are calculated through density-functional theory simulations of large periodic supercells. The calculations support the chromium substitution on the slightly distorted octahedrally coordinated gallium site, and additional energy levels are introduced in the band gap of the host. Antisite pairs are found to be energetically favored over isolated antisites due to significant charge compensation as shown by calculated Hirshfeld-I charges. Significant structural distortions are found around all antisite defects. The local Cr surrounding is mainly distorted due to a ZnGa antisite. The stability analysis reveals that the distance between both antisites dominates the overall stability picture of the material containing the Cr dopant and an antisite pair. The findings are further rationalized using calculated densities of states and Hirshfeld-I charges.

Tag: computational materials science

VASP-tutor: Creating a primitive unit cell from a conventional unit cell…for a MOF.