High Throughput Computation for Materials Discovery: The Open Quantum Materials Database (OQMD) Chris Wolverton Northwestern University

Acknowledgements Photo credit: Yongli Wang High-Throughput DFT Scott Kirklin, James Saal, Bryce Meredig, Alex Thompson, Jeff Doak

Computational Materials Science: Materials for Alternative Energies and Sustainability H  = E  Hydrogen Storage Thermoelectrics Light-Weight Materials Energy Storage / Batteries CoO Li i O Nuclear Energy Materials High- Throughput/Data Mining/Materials Discovery Catalysis / Metal Surfaces Solar Fuels: Thermochemical Production of H 2

For many energy-related problems: We need new materials H 2 Storage –High volumetric/gravimetric density of H 2, thermodynamically-reversible, fast kinetics Thermoelectrics –High figure of merit: ZT~3, earth-abundant Water Splitting Redox Cycles –Redox cycles with favorable thermodynamics (to split H 2 O or CO 2 ); fast kinetics Cheap, safe, …

Open Quantum Materials Database (OQMD) First-Principles Assisted Structure Solution (FPASS) How to discover new materials? Open Quantum Materials Database (OQMD) First-Principles Assisted Structure Solution (FPASS) Structure-independent Machine Learning model to accelerate Materials Discovery

Density Functional Theory Earned 1998 Nobel Prize in Chemistry Maps (intractable) quantum many-body problem onto system of effective one-body problems All materials properties derived from ground-state electron density Exact in principle, but in practice: no analytical form known

DFT Bottom Line PROS Reliable, efficient tool for predicting materials properties Can treat bulk, surface, and defect thermodynamics and kinetics PROS Reliable, efficient tool for predicting materials properties Can treat bulk, surface, and defect thermodynamics and kinetics CONS Limited to ~100’s of atoms per calculation Issues with certain classes of materials (f electrons, correlated oxides…) CONS Limited to ~100’s of atoms per calculation Issues with certain classes of materials (f electrons, correlated oxides…)

Atomistic Computation An atomistic method C performs the task where P is some property of interest (most commonly, a system’s total energy)

Crystal Structure Example Atomic Coordinates (r 1, r 2, … r n ) Property P: Total Energy Energy Best structure

The Inevitable Tradeoff Density functional theory Classical pair potentials Quantum Monte Carlo /

The Open Quantum Materials Database (OQMD) Open – An online (oqmd.org), freely available database… Quantum – … of self-consistently DFT-calculated properties… Materials – … for >32,000 experimentally observed and >260,000 hypothetical structures (decorations of commonly occuring crystal structures)… Database – … built on a standard and extensible database framework. Saal, Kirklin, Aykol, Meredig, and Wolverton "Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD)", JOM 65, 1501 (2013)

oqmd.org

Formation Energy  T=0K Stability Formation energy Fraction A Pure APure B AB 3 AB Prediction for A 3 B composition Currently known FE Measure of stability

oqmd.org Phase Diagrams (T=0K) binary ternary quaternary higher GCLP 1 1 R. Akbarzadeh, A., Ozoliņš, V. & Wolverton, C.. Advanced Materials 19, 3233–3239 (2007). Convex hulls: quickhull (very efficient for large number of points in small dimensions, scales poorly for high dimensional hulls)

O 506 Si 180 Al 54 Fe 15 Ca 13 K 10 Na 25 Mg 16 Example 1: What is the phase diagram of the earth? For the composition of the earth, what is the stable collection of phases? Chemical composition of the earth’s crust Source: Wikipedia

Example 1: What is the phase diagram of the earth? For the composition of the earth, what is the stable collection of phases?

Example 1: What is the phase diagram of the earth? For the composition of the earth, what is the stable collection of phases?

“More than 90% on the crust is composed of silicate minerals. Most abundant silicates are feldspars (plagioclase (39%) and alkali feldspar (12%)). Other common silicate minerals are quartz (12%) pyroxenes (11%), amphiboles (5%)... “ Source: sandatlas.com What minerals are actually in the earth’s crust? Plagioclase: NaAlSi 3 O 8 to CaAl 2 Si 2 O 8 Alkali Feldspar: KAlSi 3 O 8 Quartz: SiO 2 Pyroxene: CaMgSi 2 O 6

“More than 90% on the crust is composed of silicate minerals. Most abundant silicates are feldspars (plagioclase (39%) and alkali feldspar (12%)). Other common silicate minerals are quartz (12%) pyroxenes (11%), amphiboles (5%)... “ Source: sandatlas.com What minerals are actually in the earth’s crust? Plagioclase: NaAlSi 3 O 8 to CaAl 2 Si 2 O 8 Alkali Feldspar: KAlSi 3 O 8 Quartz: SiO 2 Pyroxene: CaMgSi 2 O 6

Example 3: The Phase Diagram of Everything What if we extend this idea to compute the ground state convex hull of the ~100-component phase diagram (for all elements in the periodic table)? There is only one such phase diagram, and all other diagrams are merely sections of this “phase diagram of everything” Using OQMD, we have computed this phase diagram. However, the question is, how to represent it? The convex hull for the 19,230 phases that are stable in the OQMD: 35,308,027 tie-lines.

Example 3: The Phase Diagram of Everything One representation: Adjacency matrix: 19230x19230 matrix of all stable phases. Each element is black if a stable tie- line exists between phases, else white. Complete adjacency matrix is available at oqmd.org

Example 3: The Phase Diagram of Everything One representation: Adjacency matrix: 19230x19230 matrix of all stable phases. Each element is black if a stable tie- line exists between phases, else white. Complete adjacency matrix is available at oqmd.org

Example 3: The Phase Diagram of Everything Graph theory representation for high-dimensional phase diagrams

Example 3: The Phase Diagram of Everything Minimum spanning tree: one of the "smallest possible connected subgraphs"

How many compounds in our database are stable? The rate of compound discovery (total and stable) within the ICSD by year. OQMD database: Total 297,099 compounds 19,757 T=0K stable 16,118 from ICSD 3487 “prototype” structures Each of these cases represents a prediction of a system where new compounds should exist! Many gaps in our current knowledge of phase stability… All ICSD Structures Stable in OQMD

Example of simplistic use of the OQMD: High-throughput search for Heusler X 2 YZ precipitate strengtheners in BCC metals More stable Dark red is best Pick a lattice parameter, and try to match it > 150,000 DFT calculations of X 2 YZ Heuslers (essentially for all possible X, Y, Z)

High-Throughput DFT Calculations: OQMD Can search through database to “screen” materials for various applications Heusler phase precipitates High strength Mg alloys Li-ion battery coatings Li-O 2 materials High-efficiency Thermoelectrics Saal, Kirklin, Aykol, Meredig, and Wolverton "Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Mechanical Database (OQMD)", JOM 65, 1501 (2013)

Open Quantum Materials Database (OQMD) First-Principles Assisted Structure Solution (FPASS) How to discover new materials? Open Quantum Materials Database (OQMD) First-Principles Assisted Structure Solution (FPASS) Structure-independent Machine Learning model to accelerate Materials Discovery

More information… OQMD (high-throughput DFT database) –oqmd.org –J. Saal et al., "Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Mechanical Database (OQMD)", JOM 65, 1501 (2013) –S. Kirklin et al., “The Open Quantum Materials Database (OQMD): Assessing the Accuracy of DFT Formation Energies” (to be submitted) –S. Kirklin and C. Wolverton, “Efficient Methods for High-Dimensional Multicomponent Ground State Equilibria” (to be submitted)