International Workshop on High-Volume Experimental Data, Computational Modeling and Visualization Xiangshan, October 2011 Determining the composition of surfaces and nanomaterials, by theory and experiment Michel A. Van Hove Department of Physics and Materials Science City University of Hong Kong

Optimize atomic-level structure (from theory or from experiment) at three levels  local optimization: easiest – "descend" (lowest energy, best fit)  global optimization with fixed composition: harder – "exchange pairs", "break and make bonds", "move far"  optimization of composition: both number and identities of atoms can vary adds – "exchange with external supply" or "exchange with internal supply" but must respect experimental reality Structure determination

Graphene: vacancies, added C atoms How many atoms to include for best energy? "Magic" numbers

4 60 carbon atoms are initially placed randomly a Genetic Algorithm changes their positions by:  recombining top and bottom halves each GA step is followed by a local optimization by conjugate-gradient minimization or molecular dynamics quenching  steps are needed for local optimization D.M. Deaven and K.M. Ho, Phys. Rev. Lett. 75, 288 (1995) Fullerenes: C 60, C 60  n

bimetallic alloy nanocrystals G.F. Wang, M.A. Van Hove, P.N. Ross and M.I. Baskes, Prog. Surf. Sci. 79, (2005).

Nanoparticles: pure, alloys HREM micrographs of a C-supported Pt-Ni nanoparticle catalyst U.A. Paulus et al., J. Phys. Chem. B, 106, 4181 (2002)

“Magic” cubo-octahedral nanoparticles (100) (111) 1: Vertices (6nn) 2: {111}/{111} edges (7nn) 3. {111}/{100} edges (7nn) 4. {100} facets (8nn) 5. {111} facets (9nn) Dispersion is the fraction of all atoms that are on the surface Exp.

Modified cubo-octahedral fcc nanoparticles: “non-magic” (311) geometry (110) geometry By adding atoms on the facets or removing atoms from the edges, we constructed non-perfect cubo-octahedral nanoparticles with troughs. These ridges contain new B 5 sites (5-fold coordinated adsorption sites), similar to those on fcc (110) and (311) surfaces. Remember: segregation reversal at PtNi(110) surface.

Nanoparticle structures and order-disorder transitions: size effect in PtNi nanoparticles NC1C1 C2C2 C3C3 C core Segregation profiles (C as % Pt by shell and in core) of equilibrium cubo-octahedral Pt 50 Ni 50 nanoparticles with N atoms, simulated at T=600K Surface- sandwich structure with a disordered core for smaller nanoparticles Core-shell structure with an ordered core for larger nanoparticles cross-sections G.F. Wang, M.A. Van Hove, P.N. Ross and M.I. Baskes, Prog. Surf. Sci. 79, (2005).

{100} facet reconstruction: no more "magic" initialafter 20 million MC steps Pt Re after 5 million MC steps square lattice of {100} facets hexagonal lattice on {100} facets exteriors Pt 75 Re 25

Complexity: Ni(100)+(5x5)-xLi solved by LEED H. Tochihara, S. Mizuno et al 45 structural models Ni atoms are missing (9 of 25 per 5x5 cell)

C 60 / Cu(111)

Annealing to ~340K appears to cause a reconstruction of the surface: 7 Cu atoms are expelled for each C 60, forming bare Cu islands STM imaging of Cu(111)+(4x4)-C 60 W.W. Pai, C.L. Hsu, M.C. Lin, K.C. Lin, and T.B. Tang, Phys. Rev. B 69, (2004) region B: high T (4x4)C 60 ~2.1Å lower sunk in Cu holes? regions A: low T (4x4)C 60 on simple Cu(111)? B A

C 60 on unreconstructed Cu(111) C 60 on reconstructed Cu(111) side views top views Proposed adsorption geometry of C 60 on Cu(111): C 60 over 7-Cu holes (based on STM and theory)

Cu(111)+(4x4)-C 60 : Low-Energy Electron Diffraction  Tensor LEED  allows automated optimization of 102 parameters (C 60 layer + 2 Cu layers)  42 independent beams, eV (total 7111 eV)  still fairly efficient computation because of 3-fold rotational symmetry  We tested several models:  unreconstructed: RP = (fcc on-top), (fcc hcp-site)  reconstructed: RP = (7-atom hole), (1-atom hole)  relaxations from theoretical optimum structure: ~< 0.1Å  surface, ~< 0.2Å // surface: quite good!

LEED: Cu(111)+(4x4)-C 60

LEED: Cu(111)+(4x4)-C 60 – Cu-C interface G. Xu, X.Q. Shi, R.Q. Zhang, W.W. Pai, M.A. Van Hove, in prep.

C 60 / Pt(111)

Unique case: two structures, coverages 1/13 vs 1/12 Prior XRD ( Felici et al ) for (  13x  13)R13.9°: 1 missing Pt atom / C 60 Pt(111)+(  13x  13)R13.9°-C 60 & Pt(111)+(2  3x2  3)R30°-C 60 ( =  12x  12 ) R. Felici, M. Pedio, F. Borgatti, S. Iannotta, M. Capozi, G. Ciullo and A. Stierle, Nature Mat. 4, 688 (2005) LEED pattern for (  13x  13)R13.9° LEED pattern for (2  3x2  3)R30°

Modeling "missing atoms" in DFT no hole bottom of metal slab top of metal slab 1 atom "missing" 7 atoms "missing" Moving "missing atoms" elsewhere in 3D unit cell preserves number of atoms: move to realistic step on back of slab

DFT analysis: comparing models with different numbers of atoms! where do the missing atoms go? DFT favors 1 missing atom, if vacancy atoms move to step sites Pt(111)+(  13x  13)R13.9° & (  12x  12)R30°-C 60 : DFT Adsorption energy* Adsorption energy - vacancy formation energy** no hole (hcp hollow site) 1 Pt atom missing 7 Pt atoms missing (  13x  13)R13.9° eV eV eV eV eV eV (  12x  12)R30° eV eV eV eV eV eV * = like comparing O 3 vs. O 2 vs. O (3 vs. 2 vs. 1 atom) ** = like comparing 2O 3 vs. 3O 2 vs. 6O (6 atoms each) X.Q. Shi, A.B. Pang, K.L. Man, R.Q. Zhang, C. Minot, M.S. Altman, M.A. Van Hove, submitted

LEED analysis (total E range 4860 eV for  13, 3080 eV for  12): 1 missing Pt atom for both  13 and  12 Comparison of models by Pendry R-factor fit: Pt(111)+(  13x  13)R13.9° & (  12x  12)R30°-C 60 : LEED Pendry R-factor R P (  13x  13)R13.9°(  12x  12)R30° Atop with 1 Pt atom missing Atop0.46 hcp hollow site Pt atoms missing Comparison with C 60 on other metals by LEED: Cu(111)+(4x4)-C 60 : R P = 0.38 – 7 missing Cu atoms Ag(111)+(  12x  12)R30°-C 60 : R P = 0.36 – 1 missing Ag atom

To optimize composition  both number and identities of atoms may vary  many models must be tested  from theory conserve total number of atoms among models so "exchange with external supply" or "exchange with internal supply" respect experimental reality (where can atoms go to / come from?)  from experiment XRD, LEED, PED, STM, … comparison of models does not require conserving number of atoms, if “missing” atoms do not contribute Conclusions: composition determination