Tag: computational materials science

Jun 27 2016

Folding Phonons

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June 27, 2016

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).

Permanent link to this article: https://dannyvanpoucke.be/folding-phonons/

May 29 2016

One more digit of importance

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May 29, 2016

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.

Permanent link to this article: https://dannyvanpoucke.be/one-more-digit-of-importance-en/

May 22 2016

Annual Meeting of the Belgian Physical Society 2016

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May 22, 2016

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:

Permanent link to this article: https://dannyvanpoucke.be/bps2016-en/

Apr 12 2016

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

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April 12, 2016

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!

Permanent link to this article: https://dannyvanpoucke.be/cmd26-call-2016-en/

Mar 01 2016

Helium flash: the beginning of a new chapter.

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March 1, 2016

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.

Permanent link to this article: https://dannyvanpoucke.be/a-new-chapter-en/

Feb 11 2016

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

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February 11, 2016

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.

Permanent link to this article: https://dannyvanpoucke.be/paper2016_inorgchemzgodoping-en/

Feb 04 2016

Virtual Winterschool 2016: Computational Solid State Physics & Chemistry

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February 4, 2016

In just an hour, I’ll be presenting my talk at the virtual winterschool 2016. In an attempt to tempt fate as much as possible I will try to give/run real-time examples on our HPC in Gent, however at this moment no nodes are available yet to do so. Let’s keep our fingers crossed and see if it all works out.

Abstract

Modern materials research has evolved to the point where it is now common practice to manipulate materials at nanometer scale or even at the atomic scale (e.g. Intel’s skylake architecture with 14nm features, atomic layer deposition and surface structure manipulations with an STM-tip). At these scales, quantum mechanical effects become ever more relevant, making their prediction important for the field of materials science.

In this session, we will discuss how advanced quantum mechanical calculations can be performed for solids and indicate some differences with standard quantum chemical approaches. We will touch upon the relevant concepts for performing such calculations (plane-wave basis-sets, pseudo-potentials, periodic boundary conditions,…) and show how the basic calculations are performed with the VASP-code. You will familiarize yourself with the required input files and we will discuss several of the most important output-files and the data they contain.

At the end of this session you should be able to set up a single-point calculation, a structure optimization, a density of states and band structure calculation.

Additional Files/Info

Permanent link to this article: https://dannyvanpoucke.be/virtwinter2016-en/

Jan 29 2016

Winterschool on computational chemistry

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January 29, 2016

Starting next week from February 3^rd up to February 9^th the second virtual winterschool on computational chemistry will take place. This week-long winter school is packed with interesting webinars given by experts from all over the world (among others Kieron Burke and John Perdew, jep those of the DFT-functionals we are using) and me. I’ll be presenting an introductory tutorial in solid state calculations and how to use VASP for this task.

Registration for this winter school is free, and since it takes place on the world wide web, there is still room at the back :-). (In addition to a lack of worries whether or not you will be able to get your hands on a last minute plane-ticket or hotel-room and which funding agency might reimburse those tickets.) I’ll be running example-calculations real time, and hope my sidekick will perform to expectation.

Permanent link to this article: https://dannyvanpoucke.be/winterschoolcc2016-en/

Nov 28 2015

Sidekick

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November 28, 2015

This year I participated in the Robbert Dijkgraaf essay-contest 2015.
The central theme of the contest was imagination, and in my contribution
I presented the role of imagination in computational materials science,
and why it is so important for this field.

The original Dutch version of the essay can be found here.

Imagine a world where you can actually see atoms. Even more, you can use them as LEGOs and manipulate them to do your bidding. Imagine a world in which you can switch off the laws of nature, or create new ones which are more to your liking. In such a world, you are in charge. Welcome to my world: the world of “computational materials science“.

It would be a nice start for a commercial for this research field. The accompanying clip would then show images fading into one another of supercomputers and animations of chemical and biochemical processes at the atomic scale. Moving in a fast-forward pace into our future with science-fiction-like orbital labs where calculated materials are immediately transformed into new medicine, ultra-thin screens and applications for the aerospace industry. scifilab The ever faster flood of images culminates in the final slogan:”Simulate the future” with a subtext urging you to go study computational materials science. I assume that such a clip would tempt peoples imagination. It addresses our human urge to create, and holds the promise that you can do anything you want, as long as you can imagine it. In fact, your imagination becomes the only limiting factor.

As with most commercial, this one also presents reality slightly more beautiful than it actually is. As for any other scientist in any other field, your contribution to progress as a computational materials scientist is rather more limited than you would like it to be. This is a normal aspect of science. The presented divine omnipotence and omniscience, on the other had, are attainable. As a computational scientist you do have absolute control over the atomic positions and the forces at play. In contrast, an experimental scientist is forced to deal with the quirks of nature and his or her machinery. This omnipotence allows you to create any world you can imagine…inside a computer.

As a scientist, you wish to understand the world around you. This limits the freedom you gained through your omnipotence, unless you would choose to join a team of game-designers. It, however, does not mean that your creativity is curtailed in any way. On the contrary. Where the team of game-designers knows the entire story to be told, including rules and laws of nature relevant for the game world, this is not the case for computational materials science. For the latter it is often their quest to discover the story-line as they go, including relevant laws of nature. As a computational materials scientist, you become the narrator, whose task consist of thinking up new stories time and time again. The narrator, who needs to tweak existing plots, extending or confining story-lines, until the final story fits the shape of reality.

Luckily, you are not alone to bring this daunting task to a successful end. You always have the support of your loyal sidekick: your supercomputer. Using its brute force, your sidekick calculates the effects of any intrigue or plot twist you can imagine. Based on your introductory chapter, in which you describe the world and its natural laws, it will allow the story to unfold. By asking him the right questions, and comparing his answers to reality, you learn which parts of your story don’t really fit reality yet.

Ouroboros benzene. source: wikipedia How you should rewrite your introductory chapter differs every time. Sometimes it is clear what is going on: an essential character is missing (e.g. an impurity atom which is distorting the crystal lattice), or the character lives at the wrong location (not site A, then let us see about site B?). It becomes more difficult when a character refuses to play the role it was dealt (e.g. Pt atoms that remain invisible for STM, so who is going to play the role of the nanowire we observe?). The most difficult situation occurs with the need for a full rewrite of the introductory chapter. This provides too much freedom, since it is our knowledge of the limitations of reality which provides the necessary support and guidance for drafting the story-line. In such a case, you need an inspiring idea which provides you with a new point of view. Inspiration can come in many forms and at any time, often when least expected. A well-known example is this of the theoretical chemist Kekulé who, in a daydream, saw a snake bite its own tail. As a result Kekulé was able to envision the ring-shape of the benzene molecule. Such wonderful problem solving twists-of-mind are rare. They are often the consequence of long and intense study of a single problem, which drive you to the limit, since they require you to imagine something you have never thought of before. In management-circles this is called “thinking-outside-the-box”, which sound a lot easier than it actually is. It does not mean that all of the sudden everything goes, you always have to bear in mind the actual box you started from.

As a computational materials scientist you have to combine your omnipotence over your virtual world with your power to imagine new worlds, hoping to see a glimmer of reality in the reflections of your silicon chips.

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Nov 28 2015

Sidekick

Filed under blog
November 28, 2015

Met dit essay nam ik deel aan de Robbert Dijkgraaf essay-prijs 2015.
Dit jaar was het thema verbeelding, en in mijn bijdrage doe ik een
poging de rol van verbeelding naar voren te brengen binnen
computationeel materiaalonderzoek. Ik probeer eveneens uit te
leggen hoe ik computationeel onderzoek zie als onderzoeksdomein.

Een vertaling naar het Engels kan hier gevonden worden.

Stel je een wereld voor waarin je atomen kunt zien. Meer nog, je kunt ze stapelen als legoblokken en manipuleren naar eigen goeddunken. Stel je een wereld voor waarin je de natuurwetten kunt aan- of afzetten, een wereld waar je zelf nieuwe natuurwetten kunt schrijven. In zo een wereld heb jij het voor het zeggen. Welkom in mijn wereld, de wereld van het “computationele materiaalonderzoek“.

Het zou een mooi begin zijn van een reclamespot voor dit onderzoeksgebied. In de bijhorende clip krijg je in elkaar overgaande beelden te zien van supercomputers enerzijds en animaties van chemische en biochemische processen op de atomaire schaal anderzijds. Het geheel wordt dan doorgelinkt aan onze eigen toekomst met sciencefictionachtige laboratoria waar de berekende materialen direct worden omgezet tot nieuwe medicijnen, flinterdunne beeldschermen en toepassing voor de ruimtevaart. De steeds sneller elkaar opvolgende beelden scifilab culmineren dan in de slotslogan: “Simuleer de toekomst!” met als onderschrift de aansporing om computationeel materiaalonderzoek te gaan studeren. Ik stel me voor dat zo’n reclameclip wel tot de verbeelding zou spreken. Het spreekt onze menselijke drang om te creëren aan met de belofte dat je alles kunt, als je het je maar kunt voorstellen. Je verbeelding is de enige beperkende factor.

Zoals bij de meeste reclamespots wordt ook in deze de werkelijkheid iets mooier voorgesteld dan ze is. Zoals voor elke andere wetenschapper geldt immers dat je bijdrage aan de vooruitgang beperkter is dan je zou willen. De gepresenteerde goddelijke almacht en alwetendheid liggen wel binnen handbereik. Als computationeel onderzoeker heb je immers absolute controle over de plaatsing van atomen en de inwerkende krachten, iets waar een experimenteel onderzoeker deels is overgelaten aan de grillen van de natuur en zijn of haar apparatuur. Deze controlevrijheid laat je toe, binnen een computer, elke wereld te creëren die je maar kunt bedenken.

Als wetenschapper wil je de wereld om je heen begrijpen, wat bovenstaande vrijheden inperkt, tenzij je ervoor kiest om in een team van computergame-designers aan de slag gaan. Dit betekent niet dat je creativiteit wordt beknot, integendeel. Waar bij het ontwerpteam het volledige verhaal bekend is, inclusief de regels en natuurwetten van de wereld waarin je speelt, is dat niet het geval bij computationeel materiaalonderzoek. Meer nog, vaak is het net je opdracht het verhaal gaandeweg te ontdekken, inclusief de natuurwetten die relevant zijn. Je wordt als het ware een verteller die telkens nieuwe verhalen moet bedenken, of bestaande plots moet aanpassen, uitbreiden of beperken, tot de verhaallijn past in de vorm van de werkelijkheid.

Je staat er gelukkig niet alleen voor om een goede afloop te regelen. Je wordt bijgestaan door je trouwe sidekick: je supercomputer. Deze is in staat met brute kracht de gekste plotwendingen door te rekenen. Op basis van jouw inleidende hoofdstuk, waarin je de wereld en haar natuurwetten schetst, zal hij het verhaal verder laten ontplooien. Door dan de juiste vragen te stellen en de antwoorden met de werkelijkheid te vergelijken kom je erachter waar je verhaal nog niet helemaal in de werkelijkheid past.

Hoe je je inleidende hoofdstuk daarop moet aanpassen verschilt per geval. Soms is het duidelijk wat er aan de hand is: er ontbreekt een cruciaal personage (bijvoorbeeld een onzuiverheidsatoom dat het kristaalrooster verstoord) of het personage woont op de foute plaats (toch niet op de plaats van atoom A, atoom B dan maar?). Moeilijker wordt het als sommige personages weigeren de hun toebedeelde rol te spelen (Die platina-atomen zijn onzichtbaar voor de rastertunnelmicroscoop, wie speelt nu de rol van de zichtbare nanodraad?). Ouroboros benzene. source: wikipedia De lastigste situatie is wanneer een volledige herschrijving van het inleidende hoofdstuk nodig is. Hierdoor krijg je te veel vrijheid in handen, terwijl het net de gekende beperkingen zijn die je houvast geven bij het opstellen van het verhaal. Je hebt dan een idee nodig dat je een link geeft met de werkelijkheid. Inspiratie kan hier velerlei vormen aannemen en op willekeurig moment komen. Een bekende anekdote is deze van de theoretische chemicus Kekulé, die in een dagdroom een slang zichzelf in de staart zag bijten en daardoor de ringvormige structuur van de benzeenmolecule uitdokterde. Zulke wonderlijk probleemoplossende gedachtenkronkels komen zelden spontaan, maar zijn veeleer het gevolg van lang en intens werk op eenzelfde vraagstuk. Dergelijke situaties drijven je tot het uiterste, je moet je immers iets voorstellen waar je nooit eerder aan gedacht hebt. In managementkringen wordt zoiets “buiten het kader denken” genoemd, wat bedrieglijk eenvoudig klinkt. Je mag immers niet vergeten dat voor onderzoek dit niet betekent dat alles plots toegelaten is (met andere woorden, je mag het kader zeker niet uit het oog verliezen bij het dagdromen).

Als computationeel materiaalonderzoeker moet je dus je almacht over je virtuele wereld combineren met je eigen vermogen nieuwe werelden in gedachten te scheppen, in de hoop zo onderweg een glimp van de buitenwereld in je siliciumchip op te vangen.

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Tag: computational materials science

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