# How much is left to discover? Crystal prediction in a quaternary search space

# How much is left to discover? Crystal prediction in a quaternary search space

Promotor(en):**16MAT01**/ Solid-state physics**S. Cottenier**/How many different (crystalline) solids can be made by the about 90 elements we have at our disposal? Let us simplify the situation in order to make an estimate: we consider only solids where every element in the chemical formula appears only once (e.g. NaCl or FeAsS, not TiO2) and we ignore the degree of freedom offered by crystal structure (i.e. graphite and diamond are considered to be the identical). Under these simplifications, how many different ternary solids could exist? The answer is 117 480. That’s a lot, but it is vanishingly small when compared to the number of solids with 45 different elements: 1.04 × 10^26. Nevertheless, the largest experimental crystal databases (which contain way over 100 000 entries) list tens of thousands of ternaries, but not a single crystal with 45 elements.

That’s strange… It looks like there is a driving force that prevents the existence of crystals made from too many different elements. And indeed, that driving force exists – it’s left as a little challenge for you to identify it.

How many of all possible crystals do we know already? Is there still a myriad of new solids waiting to be discovered, and can engineers therefore dream about many new materials with marvellous properties to solve current problems? Or do we know nearly all possible crystals, meaning that we are bound to solve our problems using not much more than what we have already? The saturation observed in the discovery rate of new ground state structures of crystals (see figure, from Saal et al., JOM 65, 1501 (2013)) suggests that we are reaching the boundaries of the set of discoverable crystals.

Quaternary crystals lie on the edge between the known and unknown crystals. Knowing how many of all potential quaternary crystals effectively exist will give a strong indication whether quaternary or rather quinary or senary crystals form the upper end of possible crystals. The quaternary family is huge, way too large to screen systematically in an experimental way. That’s why we have to resort to computational screening using density-functional theory (DFT). Nevertheless, even DFT calculations take too long take to explore all possible quaternary crystals. Machine learning may offer an advantage here: by starting with a systematic DFT search through a limited set of representative materials, hidden correlations between the make-up of a material and its stability may be extracted by smart computer algorithms, such as neural networks or advanced regression methods.

**Goal**You will investigate the class of quaternary crystals formed by combining an alkali or alkaline earth metal with 3 elements from groups 13 to 16. About 250 crystals of that class are experimentally known. Your goal is to find the (many or few ?) undiscovered crystals in some well-defined subclasses. First, you will perform DFT calculations using the VASP program to establish a representative data set of quaternary crystal stabilities. Based on these data, you can then apply several machine learning methods to extrapolate these results in a cheap way to the materials that remain to be investigated. Two machine learning methods of interest are neural networks and kernel ridge regression methods, but your arsenal is not limited to these two approaches. Take a look at Magpie, a platform that allows the application of many machine learning methods to your data set (http://oqmd.org/static/analytics/magpie/doc/index.html). By using this combination of DFT and machine learning, you will undoubtedly discover many new stable quaternary crystals. The number of crystals you find will contribute to answering the question whether or not the quaternaries are the last major group of crystals. Within the dataset of stable and metastable crystals that you will have produced, you will be able to search for stability hotspots and trends of properties across the set – this insight might suggest where to search for crystals with optimal values of a given property. Your calculations will be done in such a way that the results can be added to existing computational databases, where they can be retrieved and used by future researchers.

**Context for Engineering Physics students**

Physics aspect: use of quantum mechanical methods to model solids

Engineering aspect: application to the properties of crystalline materials and use of machine learning

- Study programmeMaster of Science in Engineering Physics [EMPHYS], Master of Science in Substainable Materials Engineering [EMMAEN], Master of Science in Physics and Astronomy [CMFYST]ClustersFor Engineering Physics students, this thesis is closely related to the cluster(s) MODELING, MATERIALS, NANORecommended coursesSimulations and Modeling for the Nanoscale, Computational Materials PhysicsReferences
Saal et al., JOM 65, 1501 (2013). http://dx.doi.org/10.1007/s11837-013-0755-4

Rupp et al., J. Phys. Chem. Lett. 6, 3309 (2015). http://dx.doi.org/10.1021/acs.jpclett.5b01456