Atomistic Modeling of Materials

Atomistic modeling techniques use modern computing power to explicitly include every atom in modeling of a material. As interacting atoms are the foundation of all materials science, atomistic modeling has helped enable a new field of computational materials studies. Virtual computational experiments using atomistic modeling can greatly reduce the cost and accelerate the time scales of understanding and developing new materials.

However, modeling every atom and its interactions is extremely computationally intensive, which limits the time and length scales that can be simulated. In the early days of atomistic modeling in the 1970's, even the fastest computers could only manage full quantum mechanical calculations on a few atoms, such as might be found in a simple crystal unit cell or a molecule.

Atomistic modeling milestones at that time included such studies as the prediction of the electronic band structure of phases of Si and Ge¹. However, enormous advances in computing and computational techniques have transformed atomistic modeling over the last 40 years, making it possible today to study complex systems and geometries. For example, full quantum simulations can now be done routinely for hundreds of atoms, predicting properties ranging from defects in semiconductors² to transport mechanisms in Li batteries³.

In addition to quantum mechanics based techniques, atomistic modeling can also be done with effective interactions between atoms, called interatomic potentials. Interatomic potentials do not treat the quantum nature of electrons explicitly which allows models based on these potentials to be enormously faster to calculate than models based on quantum methods. Such interatomic potential based modeling may not be as accurate as quantum mechanical approaches but can model billions of atoms, simulating such complex materials processes as radiation damage in nanocrystalline materials⁴ and friction between surfaces⁵.

Atomistic modeling has recently become so fast and robust that it is now possible to combine high-throughput computations and data mining tools to perform the equivalent of combinatorial chemistry on the computer, scouring compositional space for new compounds with optimal properties. These high-throughput computational techniques have already been used to build valuable databases of alloy structural energies⁶, predict crystal structures^7,8 and custom design more active catalysts⁹.

As an illustration of the increasing importance of atomistic modeling, consider the publications that relate to Density Functional Theory (DFT), one of the most powerful quantum mechanical atomistic modeling methods used today. Use of DFT has grown exponentially almost since it was developed in the early sixties, and for 40 years the publication rate has been increasing approximately 10-fold every decade (Figure 1). Today, DFT makes contributions to about 10,000 papers a year.

Figure 1. Number of publications per year containing topic words "Density functional theory" or "DFT" (from ISI Web of Science).

The Computational Materials Group at University of Wisconsin - Madison, founded by Professor Dane Morgan and Professor Izabela Szlufarska, is focused on using atomistic modeling tools to understand and develop materials. Professor Dane Morgan utilizes the power of both quantum mechanical and interatomic potential based modeling to predict properties for a wide-range of materials, including fuels and cladding for nuclear reactors, battery and fuel cell and electron emittor electrodes, materials in the deep earth, aqueous mineral interfaces, and defects in semiconductors.

For example, The Computational Materials Group graduate student Edward Holby has used quantum mechanics to predict the stability of nanoparticle catalysts containing up to hundreds of atoms, demonstrating how their energetics relates to the classical Gibbs-Thomson law of particle stability (Figure 2). This understanding of nanoparticle energetics has helped us suggest how even a single nanometer change in the size of nanoparticle catalysts could greatly enhance their durability¹⁰. Driven by continued increases in computing power and improved simulation methods, atomistic modeling is sure to become a greater part of materials science in the future.

Figure 2. Energy of a Pt nanoparticle as a function of size from a macroscopic law (Gibbs-Thomson) and density function theory prediction.

References

1. J. D. Joannopoulos and M. L. Cohen, Electronic Properties of Complex Crystalline and Amorphous Phases Of Ge And Si .1. Density Of States And Band Structures, Physical Review B 7, 2644 (1973).
2. C. G. Van de Walle and J. Neugebauer, First-principles calculations for defects and impurities: Applications to III-nitrides, Journal of Applied Physics 95, 3851 (2004).
3. D. Morgan, A. Van der Ven, and G. Ceder, Li conductivity in Li_xMPO₄ (M = Mn, Fe, Co, Ni) olivine materials, Electrochemical and Solid State Letters 7, A30 (2004).
4. N. Swaminathan, P. J. Kamenski, D. Morgan, and I. Szlufarska, Effects of grain size and grain boundaries on defect production in nanocrystalline 3C-SiC, To be published in Acta Materialia (2010).
5. Y. F. Mo, K. T. Turner, and I. Szlufarska, Friction laws at the nanoscale, Nature 457, 1116 (2009).
6. S. Curtarolo, D. Morgan, and G. Ceder, Accuracy of ab-initio methods in predicting the crystal structures of metals: review of 80 binary alloys, CALPHAD 29, 163 (2005).
7. C. Fischer, K. Tibbetts, D. Morgan, and G. Ceder, Predicting Crystal Structure: Merging Data Mining with Quantum Mechanics, Nature Materials 5, 641 (2006).
8. A. R. Oganov, et al., Ionic high-pressure form of elemental boron, Nature 457, 863 (2009).
9. J. K. Norskov, T. Bligaard, J. Rossmeisl, and C. H. Christensen, Towards the computational design of solid catalysts, Nature Chemistry 1, 37 (2009).
10. E. F. Holby, W. C. Sheng, Y. Shao-Horn, and D. Morgan, Pt nanoparticle stability in PEM fuel cells: influence of particle size distribution and crossover hydrogen, Energy & Environmental Science 2, 865 (2009).