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Atomically informed modeling of the microstructure evolution of nanocrystalline materials

A. Mattoni. alessandro.mattoni@dsf.unica.it. Atomically informed modeling of the microstructure evolution of nanocrystalline materials. SLACS. CNR- INFM. CRS LN LR Regional Laboratories. http://www.slacs.it. Division: Material Physics

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Atomically informed modeling of the microstructure evolution of nanocrystalline materials

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  1. A. Mattoni alessandro.mattoni@dsf.unica.it Atomically informed modeling of the microstructure evolution of nanocrystalline materials

  2. SLACS CNR-INFM CRS LN LR Regional Laboratories http://www.slacs.it • Division: Material Physics • (Microstructure evolution of nanostructured materials) • (6 members, • www.dsf.unica.it/colombo) Atomistic investigation: large scale molecular dynamics simulations Large scale electronic structure calculations Continuum modeling: models for growth, interface mobilities

  3. OUTLINE The theoretical framework Molecular dynamics atomistic simulations The microstructure of interest for nanocrystalline materials Boundaries between order/disordered phase Modeling the growth of nanocrstals embedded into an amorphous matrix

  4. Molecular dynamics The material of interest is described as an assembly of molecular constituents

  5. Molecular dynamics An interatomic depending on atomic positions The interatomic forces are calculated accordingly Newton’s equations of motion are integrated numerically (“Verlet velocity”) Choose dt “judiciously” (~1fs) and iterate in time (“ad nauseam”)

  6. Interatomic potentials ”6-12” Lennard-Jones potential: repulsive core 1/r12 ; VdW attraction 1/r6 r>req Professor Sir John Lennard-Jones (FRS), one of the founding fathers of molecular orbital theory ”6-12” Lennard-Jones potential: prototypical interatomic force model for close-packed metals

  7. Interatomic potentials Stillinger-Weber potential for anysotropic covalent bonding (1985) F. Stillinger Department of Chemistry Princeton University Princeton, NJ 08540 T.A. Weber (EDIP) Environment dependent interatomic potential (1998)

  8. MD comes of age… K. Kadau et al. Int. Journal of Modern Physics C 17 1755 (2006) 320 BILLION ATOM SIMULATION ON BlueGene/L Los Alamos National Laboratory B. J. Alder and T. E. Wainwright, J. Chem. Phys.27,1208(1957) EDIP Lennard-Jones Stillinger-Weber Tersoff

  9. MD comes of age… more or less The bottleneck of standard molecular dynamics: time and length scales Compromise between accuracy and computational workload Reliability of the model potentials A. Mattoni, M. Ippolito and L. Colombo, B 76, 224103 (2007) In order to properly reproduce fracture related properties of covalent materials of group IV materials (Si, Ge, C) it is necessary to take into account interactions as long as the second nearest neighbors distance

  10. Computational Effort Typical simulation parameters number of atoms > 105 Runs as long as 6 106 iterations (6 ns) CMPTool: a set of highly efficient parallel numerical libraries for computational materials science developed in collaboration with Caspur, Rome Group of materials science (M. Rosati, S. Meloni, L. Ferraro, M. Ippolito) A. Mattoni et al. Comp. Mat. Sci. 30 143 (2004) S. Meloni et al. Comp. Phys. Comm. 169 462 (2005) 1ns annealing of 100000 atoms requires of the order of 1000 CPU hours on state-of-the-art AMD - Opteron Dual core Linux cluster

  11. Nanocrystalline materials Crystalline materials Plastically deformed materials Ion implantation Lines: Dislocations Interfaces: Grain boundaries Points: I,V, clusters, dots 0-D 1-D 2-D 3-D Amorphous materials In the amorphous phase (isotropic) the concept of dislocation is lost The microstructure evolution is controlled by: Recrystallization, normal grain growth

  12. Mixed phase nanocrystalline systems Nanocrystalline materials (nc-Si) may be prepared through the crystallization of amorphous (disordered) nc grains are embedded into a second phase matrix Experimentally it is found that the smallest grain size is obtained when the amorphous samples are annealed at a crystallization temperature that is close to half the bulk melting temperature Q. Jiang, J. Phys.: Condens. Matter 13 (2001) 5503–5506 Embedding amorphous matrix nc

  13. Nc-Si for photovoltaics Nano-crystalline silicon (nc-Si) consists in a distribution of grains embedded into an amorphous matrix Observation of domains separated by amorphous boundaries and (in some cases texturing) S. Pizzini et al.Mat. Sci. Eng. B 134 p. 118 (2006) Bright field TEM micrograph

  14. Modeling the a-/nc- evolution Mattoni and Colombo, Phys. Rev. Lett. 99, 205501 (2007) What is the equation of motion of an isolated a-c boundary (planar or curved)? Silicon as a prototype of a covalently bonded material During annealing of amorphous bulk it is difficult to deconvolve nucleation from growth (impurities, control the temperatures, grains impingement)C. Spinella et al. J. Appl. Phys. 84 5383 (1998) Atomistic simulation as a tool to perform numerical experiment under perfectly controlled conditions of temperature and purity

  15. Why does a grain grow? a-Si/c-Si is a metastable system ~ 0.1 eV/atom 1 kJ/mole=1.03 10-2 eV/atom M. G. Grimaldi et al. Phys. Rev. B 44 1546 (1991)

  16. Driving force pa-c Driving force : specific free-energy difference

  17. Interface limited growth Transition state theory Equation of motion of the a-c displacement Equation of motion a-Si c-Si

  18. Transition State Theory a-Si c-Si

  19. Curved a-c boundary The capillarity is expected to be sizeable up to R~R* and there give rise to an Accelerated -> uniform growth In silicon R*< 1 nm

  20. Planar a-c boundary A. Mattoni et al. EPL 62 862 (2003) Uniform motion: the a-c velocity is constant Exponential dependence on T with Eb=2.6eV EXP G. L. Olson Mater Sci. Rep. 3, (1988) AS N. Bernstein et al. PRB 61 6696 (2000)

  21. Curved a-c boundary nc-Si/a-Si: Crystalline fiber embedded into an amorphous phase [1 0 0] case c-Si/a-Si: Isolated Crystalline fiber embedded into the amorphous phase

  22. Characterization of the a-nc system

  23. amorphous 0.0 0.5 1.0 1.5 T/Tm Structure Factor

  24. Analysis

  25. Crystallinity Crystallinity of a mixed a-Si/nc-Si: relative number of crystalline atoms

  26. Fiber recrystallization

  27. Power law model Power law model the model describes both decreasing and increasing nonuniform growth

  28. Fiber recrystallization

  29. Fiber recrystallization Thereis a dependence of the growth exponents on temperature and there is a clear transition close to the amorphous melting

  30. Fiber recrystallization

  31. Fiber recrystallization

  32. Characterization of defects

  33. A simple explanation

  34. Conclusions • Molecular dynamics simulation are emerging as a powerfool tool to help the characterization of the microstructure evolution of nanostructured materials • An atomically informed continuum model is found to describe recrystallization in both the cases of isolated grain and distribution of grains EU-STREP “NANOPHOTO” CASPUR-ROME and CINECA-BOLOGNA computational support A. Mattoni and L. Colombo, Phys. Rev. Lett. 99, 205501 (2007) C. Spinella et al. J. Appl. Phys.84 5383 (1998) M. Fanfoni and M. Tomellini, Phys. Rev. B 54, 9828 (1996) Contact: alessandro.mattoni@dsf.unica.it www.dsf.unica.it/colombo)

  35. Recrystallization

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