Ab Initio Thermodynamics and Kinetics for Coalescence of Two-Dimensional Nanoislands and Nanopits on Metal (100) Surfaces

Han, Yong; Stoldt, Conrad R.; Thiel, Patricia A.; Evans, James W.

doi:10.1021/acs.jpcc.6b07328

Ab Initio Thermodynamics and Kinetics for Coalescence of Two-Dimensional Nanoislands and Nanopits on Metal (100) Surfaces

Journal Article · Fri Sep 02 00:00:00 EDT 2016 · Journal of Physical Chemistry. C

DOI:https://doi.org/10.1021/acs.jpcc.6b07328· OSTI ID:1418481

Han, Yong ^[1]; Stoldt, Conrad R. ^[2]; Thiel, Patricia A. ^[3]; Evans, James W. ^[4]

Iowa State Univ., Ames, IA (United States), Dept. of Physics and Astronomy
Iowa State Univ., Ames, IA (United States). Dept. of Chemistry
Iowa State Univ., Ames, IA (United States). Dept. of Chemistry; Ames Lab., Ames, IA (United States)
Iowa State Univ., Ames, IA (United States), Dept. of Physics and Astronomy; Ames Lab., Ames, IA (United States)

Postdeposition coalescence or sintering of pairs of lowstrain two-dimensional nanoislands and nanopits on unreconstructed metal (100) surfaces is typically mediated by diffusion along step edges, and is highly sensitive to the associated kinetics. Thus, for selected systems, we provide an ab initio density functional theory (DFT) level description of both system thermodynamics and kinetics. Specifically, we assess lateral pair and trio interactions both conventionally with adatoms at 4-fold hollow adsorption sites, and unconventionally with one adatom at the bridge-site transition state for hopping. Rather than use standard cluster expansion algorithms, these interactions are determined subject to the constraint that key step-edge properties are recovered exactly. Together, both classes of interactions determine barriers for edge diffusion processes for any local step configuration, including diffusion along close-packed $$\langle$$110$$\rangle$$ edges, kink rounding, meandering processes at kinked $$\langle$$100$$\rangle$$ steps, and extraction processes at pit corners. Our formalism applies for homoepitaxial systems, and also for several lattice-matched heteroepitaxial systems. The barriers provide input for stochastic models of nanocluster evolution, which are analyzed by kinetic Monte Carlo simulation. Such modeling with DFT energetics from the PBEsol functional recovers extensive experimental observations of both the time scale and the island-size dependence for sintering of Ag islands on Ag(100). In conclusion, description of pit sintering on Ag(100) is more delicate, being sensitive to specific unconventional trio interactions.

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Ames Laboratory (AMES), Ames, IA (United States)

Sponsoring Organization:: DOE Office of Science; National Science Foundation (NSF); USDOE

DOE Contract Number:: AC02-07CH11358

OSTI ID:: 1418481

Journal Information:: Journal of Physical Chemistry. C, Journal Name: Journal of Physical Chemistry. C Journal Issue: 38 Vol. 120; ISSN 1932-7447

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

References (77)

Surface self-diffusion on an fcc crystal: An atomic view Ayrault, Guy; Ehrlich, Gert The Journal of Chemical Physics, Vol. 60, Issue 1 https://doi.org/10.1063/1.1680781	journal	January 1974
Growth of nanostructures by cluster deposition: Experiments and simple models Jensen, Pablo Reviews of Modern Physics, Vol. 71, Issue 5 https://doi.org/10.1103/RevModPhys.71.1695	journal	October 1999
Quantum-Well States as Fabry-Pérot Modes in a Thin-Film Electron Interferometer Paggel, J. J. Science, Vol. 283, Issue 5408 https://doi.org/10.1126/science.283.5408.1709	journal	March 1999
Core-level shifts for Au epitaxial overlayers on Ag Hsieh, T. C.; Shapiro, A. P.; Chiang, T. -C. Physical Review B, Vol. 31, Issue 4 https://doi.org/10.1103/PhysRevB.31.2541	journal	February 1985
Evolution of Far-From-Equilibrium Nanostructures Formed by Cluster-Step and Cluster-Cluster Coalescence in Metal Films Stoldt, C. R.; Cadilhe, A. M.; Jenks, C. J. Physical Review Letters, Vol. 81, Issue 14 https://doi.org/10.1103/PhysRevLett.81.2950	journal	October 1998
Free energy and stiffness of 〈110〉 and 〈010〉 steps on a (001) surface of a cubic lattice: Revival of the solid-on-solid model Zandvliet, Harold J. W.; Van Moere, Ronny; Poelsema, Bene Physical Review B, Vol. 68, Issue 7 https://doi.org/10.1103/PhysRevB.68.073404	journal	August 2003
Dynamics of vacancy island coalescence on Ag(111) Eßer, M.; Morgenstern, K.; Rosenfeld, G. Surface Science, Vol. 402-404 https://doi.org/10.1016/S0039-6028(98)00021-1	journal	May 1998
Extended lattice gas interactions of Cu on Cu(111) and Cu(001): Ab initio evaluation and implications Stasevich, T. J.; Einstein, T. L.; Stolbov, Sergey Physical Review B, Vol. 73, Issue 11 https://doi.org/10.1103/PhysRevB.73.115426	journal	March 2006
Coarsening Mechanisms in a Metal Film: From Cluster Diffusion to Vacancy Ripening Wen, J. -M.; Evans, J. W.; Bartelt, M. C. Physical Review Letters, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevLett.76.652	journal	January 1996
Diffusion of Monolayer Adatom and Vacancy Clusters: Langevin Analysis and Monte Carlo Simulations of their Brownian Motion Khare, S. V.; Bartelt, N. C.; Einstein, T. L. Physical Review Letters, Vol. 75, Issue 11 https://doi.org/10.1103/PhysRevLett.75.2148	journal	September 1995
Direct Observation of Aggregative Nanoparticle Growth: Kinetic Modeling of the Size Distribution and Growth Rate Woehl, Taylor J.; Park, Chiwoo; Evans, James E. Nano Letters, Vol. 14, Issue 1 https://doi.org/10.1021/nl4043328	journal	December 2013
Elementary Physicochemical Processes on Solid Surfaces Zhdanov, V. P. Fundamental and Applied Catalysis https://doi.org/10.1007/978-1-4899-2373-8	book	January 1991
Energetics of Si(001) Zandvliet, H. J. W. Reviews of Modern Physics, Vol. 72, Issue 2 https://doi.org/10.1103/RevModPhys.72.593	journal	April 2000
Role of codeposited impurities during growth. I. Explaining distinctive experimental morphology on Cu(0 0 1) Hamouda, Ajmi BH.; Sathiyanarayanan, Rajesh; Pimpinelli, Alberto Physical Review B, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevB.83.035423	journal	January 2011
Kinetic parameters from temperature programmed desorption spectra combined with energy relations: top and bridge CO on Rh(100) Jansen, Maarten M. M.; Hermse, Chrétien G. M.; Jansen (Tonek), A. P. J. Physical Chemistry Chemical Physics, Vol. 12, Issue 28 https://doi.org/10.1039/b926380b	journal	January 2010
Real-Time TEM and Kinetic Monte Carlo Studies of the Coalescence of Decahedral Gold Nanoparticles Lim, Teck H.; McCarthy, David; Hendy, Shaun C. ACS Nano, Vol. 3, Issue 11 https://doi.org/10.1021/nn9012252	journal	October 2009
Sintering of Metal(100) Homoepitaxial Islands: Kink Rounding Barriers, Modified Size Scaling, and Experimental Behavior Liu, Da-Jiang; Stoldt, C. R.; Thiel, P. A. MRS Proceedings, Vol. 749 https://doi.org/10.1557/PROC-749-W2.8	journal	January 2002
Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory Liu, Da-Jiang; Evans, J. W. Physical Review B, Vol. 66, Issue 16 https://doi.org/10.1103/PhysRevB.66.165407	journal	October 2002
Adsorption-induced lattice relaxation and diffusion by concerted substitution Feibelman, Peter J.; Stumpf, Roland Physical Review B, Vol. 59, Issue 8 https://doi.org/10.1103/PhysRevB.59.5892	journal	February 1999
Scaling of hopping self-diffusion barriers on fcc(100) surfaces with bulk bond energies Feibelman, Peter J. Surface Science, Vol. 423, Issue 2-3 https://doi.org/10.1016/S0039-6028(98)00889-9	journal	March 1999
Evolution of far-from-equilibrium nanostructures on Ag(100) surfaces: Protrusions and indentations at extended step edges Cadilhe, A. M.; Stoldt, C. R.; Jenks, C. J. Physical Review B, Vol. 61, Issue 7 https://doi.org/10.1103/PhysRevB.61.4910	journal	February 2000
Two-dimensional equilibrium island shape and step free energies of Cu(001) Van Moere, Ronny; Zandvliet, Harold J. W.; Poelsema, Bene Physical Review B, Vol. 67, Issue 19 https://doi.org/10.1103/PhysRevB.67.193407	journal	May 2003
Shape-Controlled Synthesis of Metal Nanocrystals: Simple Chemistry Meets Complex Physics? Xia, Younan; Xiong, Yujie; Lim, Byungkwon Angewandte Chemie International Edition, Vol. 48, Issue 1, p. 60-103 https://doi.org/10.1002/anie.200802248	journal	December 2008
Platinum-based nanocages with subnanometer-thick walls and well-defined, controllable facets Zhang, L.; Roling, L. T.; Wang, X. Science, Vol. 349, Issue 6246 https://doi.org/10.1126/science.aab0801	journal	July 2015
Island Diffusion and Coarsening on Metal (100) Surfaces Pai, Woei Wu; Swan, Anna K.; Zhang, Zhenyu Physical Review Letters, Vol. 79, Issue 17 https://doi.org/10.1103/PhysRevLett.79.3210	journal	October 1997
Nanoscale “Quantum” Islands on Metal Substrates: Microscopy Studies and Electronic Structure Analyses Han, Yong; Ünal, Bariş; Jing, Dapeng Materials, Vol. 3, Issue 7 https://doi.org/10.3390/ma3073965	journal	July 2010
Adatom mobility for the solid-on-solid model Krug, J.; Dobbs, H. T.; Majaniemi, S. Zeitschrift f�r Physik B Condensed Matter, Vol. 97, Issue 2 https://doi.org/10.1007/BF01307478	journal	June 1995
Nonequilibrium kinetic study of sintering of dispersed nanoparticles Gorshkov, Vyacheslav; Kuzmenko, Vasyl; Privman, Vladimir CrystEngComm, Vol. 15, Issue 36 https://doi.org/10.1039/c3ce40498f	journal	January 2013
Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001) Stasevich, T. J.; Einstein, T. L.; Zia, R. K. P. Physical Review B, Vol. 70, Issue 24 https://doi.org/10.1103/PhysRevB.70.245404	journal	December 2004
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
What does one learn from equilibrium shapes of two-dimensional islands on surfaces? Giesen, Margret; Steimer, Christoph; Ibach, Harald Surface Science, Vol. 471, Issue 1-3 https://doi.org/10.1016/S0039-6028(00)00888-8	journal	January 2001
On the smoothing of rough surfaces Hoogeman, M. S.; Klik, M. A. J.; Gastel, R. van Journal of Physics: Condensed Matter, Vol. 11, Issue 22 https://doi.org/10.1088/0953-8984/11/22/307	journal	January 1999
Surface self-diffusion barrier of Pd(100) from low-energy electron diffraction Evans, J. W.; Flynn-Sanders, D. K.; Thiel, P. A. Surface Science, Vol. 298, Issue 2-3 https://doi.org/10.1016/0039-6028(93)90051-K	journal	December 1993
Self-diffusion of adatoms on Ni(100) surfaces Chang, C. M.; Wei, C. M.; Hafner, J. Journal of Physics: Condensed Matter, Vol. 13, Issue 17 https://doi.org/10.1088/0953-8984/13/17/101	journal	April 2001
Magic Size Effects for Heteroepitaxial Island Diffusion Hamilton, J. C. Physical Review Letters, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevLett.77.885	journal	July 1996
Low-temperature shape relaxation of two-dimensional islands by edge diffusion Combe, Nicolas; Larralde, Hernán Physical Review B, Vol. 62, Issue 23 https://doi.org/10.1103/PhysRevB.62.16074	journal	December 2000
Orientation dependence of the Cu(001) surface step stiffness: Failure of solid-on-solid and Ising models to describe experimental data Dieluweit, Sabine; Ibach, Harald; Giesen, Margret Physical Review B, Vol. 67, Issue 12 https://doi.org/10.1103/PhysRevB.67.121410	journal	March 2003
Island Nucleation in Thin-Film Epitaxy: A First-Principles Investigation Fichthorn, Kristen A.; Scheffler, Matthias Physical Review Letters, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevLett.84.5371	journal	June 2000
Evolution of Two-Dimensional Wormlike Nanoclusters on Metal Surfaces Pai, Woei Wu; Wendelken, John F.; Stoldt, C. R. Physical Review Letters, Vol. 86, Issue 14 https://doi.org/10.1103/PhysRevLett.86.3088	journal	April 2001
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I. Physical Review Letters, Vol. 100, Issue 13 https://doi.org/10.1103/PhysRevLett.100.136406	journal	April 2008
Enhanced Self-Diffusion on Cu(111) by Trace Amounts of S: Chemical-Reaction-Limited Kinetics Ling, W. L.; Bartelt, N. C.; Pohl, K. Physical Review Letters, Vol. 93, Issue 16 https://doi.org/10.1103/PhysRevLett.93.166101	journal	October 2004
Coarsening of Two-Dimensional Nanoclusters on Metal Surfaces Thiel, Patricia A.; Shen, Mingmin; Liu, Da-Jiang The Journal of Physical Chemistry C, Vol. 113, Issue 13 https://doi.org/10.1021/jp8063849	journal	March 2009
Cluster expansion and the configurational theory of alloys Sanchez, J. M. Physical Review B, Vol. 81, Issue 22 https://doi.org/10.1103/PhysRevB.81.224202	journal	June 2010
Connector model for describing many-body interactions at surfaces Tiwary, Yogesh; Fichthorn, Kristen A. Physical Review B, Vol. 78, Issue 20 https://doi.org/10.1103/PhysRevB.78.205418	journal	November 2008
Step and island dynamics at solid/vacuum and solid/liquid interfaces Giesen, Margret Progress in Surface Science, Vol. 68, Issue 1-3 https://doi.org/10.1016/S0079-6816(00)00021-6	journal	September 2001
Self-learning kinetic Monte Carlo simulations of self-diffusion of small Ag islands on the Ag(111) surface Shah, Syed Islamuddin; Nandipati, Giridhar; Karim, Altaf Journal of Physics: Condensed Matter, Vol. 28, Issue 2 https://doi.org/10.1088/0953-8984/28/2/025001	journal	December 2015
Reconstruction in a thin film: Epitaxial Pt on Pd(100) Beauvais, S. L.; Behm, R. J.; Chang, S. -L. Surface Science, Vol. 189-190 https://doi.org/10.1016/S0039-6028(87)80551-4	journal	October 1987
Particle size distributions in heterogeneous catalysts: What do they tell us about the sintering mechanism? Datye, Abhaya K.; Xu, Qing; Kharas, Karl C. Catalysis Today, Vol. 111, Issue 1-2 https://doi.org/10.1016/j.cattod.2005.10.013	journal	January 2006
Homoepitaxial growth on Ni(100) and its modification by a preadsorbed oxygen adlayer Kopatzki, E.; Günther, S.; Nichtl-Pecher, W. Surface Science, Vol. 284, Issue 1-2 https://doi.org/10.1016/0039-6028(93)90533-P	journal	March 1993
Homoepitaxial growth of iron and a real space view of reflection-high-energy-electron diffraction Stroscio, Joseph A.; Pierce, D. T.; Dragoset, R. A. Physical Review Letters, Vol. 70, Issue 23 https://doi.org/10.1103/PhysRevLett.70.3615	journal	June 1993
High-Resolution EM of Colloidal Nanocrystal Growth Using Graphene Liquid Cells Yuk, Jong Min; Park, Jungwon; Ercius, Peter Science, Vol. 336, Issue 6077 https://doi.org/10.1126/science.1217654	journal	April 2012
The crossover from collective motion to periphery diffusion for two-dimensional adatom-islands on Cu(111) Karim, Altaf; Kara, Abdelkader; Trushin, Oleg Journal of Physics: Condensed Matter, Vol. 23, Issue 46 https://doi.org/10.1088/0953-8984/23/46/462201	journal	October 2011
Kinetics of shape equilibration for two dimensional islands Jensen, P.; Combe, N.; Larralde, H. The European Physical Journal B, Vol. 11, Issue 3 https://doi.org/10.1007/s100510050961	journal	October 1999
Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds Evans, J. W.; Thiel, P. A.; Bartelt, M. C. Surface Science Reports, Vol. 61, Issue 1-2 https://doi.org/10.1016/j.surfrep.2005.08.004	journal	April 2006
Thin-film cliffhanger Lagally, Max G.; Zhang, Zhenyu Nature, Vol. 417, Issue 6892 https://doi.org/10.1038/417907a	journal	June 2002
Models for adatom diffusion on fcc (001) metal surfaces Mehl, Hanoch; Biham, Ofer; Furman, Itay Physical Review B, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRevB.60.2106	journal	July 1999
Comparison of cluster expansion fitting algorithms for interactions at surfaces Herder, Laura M.; Bray, Jason M.; Schneider, William F. Surface Science, Vol. 640 https://doi.org/10.1016/j.susc.2015.02.017	journal	October 2015
Influence of adsorption-site geometry and diffusion on thin-film growth: Pt/Pd(100) Evans, J. W.; Flynn, D. K.; Thiel, P. A. Ultramicroscopy, Vol. 31, Issue 1 https://doi.org/10.1016/0304-3991(89)90037-5	journal	September 1989
Kinetic Limitations in Electronic Growth of Ag Films on Fe(100) Man, K. L.; Qiu, Z. Q.; Altman, M. S. Physical Review Letters, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevLett.93.236104	journal	December 2004
Submonolayer Ag films on Fe(100): A first-principles analysis of energetics controlling adlayer thermodynamics and kinetics Li, Wei; Huang, Li; Evans, James W. Physical Review B, Vol. 93, Issue 15 https://doi.org/10.1103/PhysRevB.93.155416	journal	April 2016
Precision Determination of Lattice Constants Jette, Eric R.; Foote, Frank The Journal of Chemical Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.1749562	journal	October 1935
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces Kellogg, G. L. Surface Science Reports, Vol. 21, Issue 1-2 https://doi.org/10.1016/0167-5729(94)90007-8	journal	December 1994
Directing Anisotropic Assembly of Metallic Nanoclusters by Exploiting Linear Trio Interactions and Quantum Size Effects: Au Chains on Ag(100) Thin Films Han, Yong; Evans, James W. The Journal of Physical Chemistry Letters, Vol. 6, Issue 12 https://doi.org/10.1021/acs.jpclett.5b00636	journal	May 2015
Single atom self-diffusion on nickel surfaces Tung, Raymond T.; Graham, William R. Surface Science, Vol. 97, Issue 1 https://doi.org/10.1016/0039-6028(80)90104-1	journal	July 1980
Dynamics and stability of nanostructures on metal surfaces Rosenfeld, G.; Morgenstern, K.; Esser, M. Applied Physics A: Materials Science & Processing, Vol. 69, Issue 5 https://doi.org/10.1007/s003390051448	journal	November 1999
Quantum size effects in metal nanofilms: Comparison of an electron-gas model and density functional theory calculations Han, Yong; Liu, Da-Jiang Physical Review B, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevB.80.155404	journal	October 2009
Cu 2 S 3 complex on Cu(111) as a candidate for mass transport enhancement Walen, Holly; Liu, Da-Jiang; Oh, Junepyo Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.045426	journal	January 2015
Ab initio study of step formation and self-diffusion on Ag(100) Yu, Byung Deok; Scheffler, Matthias Physical Review B, Vol. 55, Issue 20 https://doi.org/10.1103/PhysRevB.55.13916	journal	May 1997
Far-from-equilibrium film growth on alloy surfaces: Ni and Al on NiAl(110) Han, Yong; Jing, Dapeng; Ünal, Barış Physical Review B, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevB.84.113414	journal	September 2011
Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points Henkelman, Graeme; Jónsson, Hannes The Journal of Chemical Physics, Vol. 113, Issue 22 https://doi.org/10.1063/1.1323224	journal	December 2000
Real-Time Ab Initio KMC Simulation of the Self-Assembly and Sintering of Bimetallic Epitaxial Nanoclusters: Au + Ag on Ag(100) Han, Yong; Liu, Da-Jiang; Evans, James W. Nano Letters, Vol. 14, Issue 8 https://doi.org/10.1021/nl5017128	journal	June 2014
Mechanisms of atomic diffusion on the flat, stepped, and faceted surfaces of Al(110) Tiwary, Yogesh; Fichthorn, Kristen A. Physical Review B, Vol. 81, Issue 19 https://doi.org/10.1103/PhysRevB.81.195421	journal	May 2010
Energies of steps, kinks, and defects on Ag{100} and Ag{111} using the embedded atom method, and some consequences Nelson, R. C.; Einstein, T. L.; Khare, S. V. Surface Science, Vol. 295, Issue 3 https://doi.org/10.1016/0039-6028(93)90293-S	journal	October 1993
Fast scanning tunnelling microscopy as a tool to understand changes on metal surfaces: from nanostructures to single atoms Morgenstern, Karina physica status solidi (b), Vol. 242, Issue 4 https://doi.org/10.1002/pssb.200440002	journal	March 2005
Formation of a Novel Ordered Ni 3 Al Surface Structure by Codeposition on NiAl(110) Han, Yong; Ünal, Barış; Evans, J. W. Physical Review Letters, Vol. 108, Issue 21 https://doi.org/10.1103/PhysRevLett.108.216102	journal	May 2012
Sensitivity of short-range trio interactions to lateral relaxation of adatoms: Challenges for detailed lattice-gas modeling Sathiyanarayanan, Rajesh; Stasevich, T. J.; Einstein, T. L. Surface Science, Vol. 602, Issue 6 https://doi.org/10.1016/j.susc.2008.01.022	journal	March 2008

Similar Records

Modeling of Diffusivity for 2D Vacancy Nanopits and Comparison with 2D Adatom Nanoislands on Metal(100) Surfaces Including Analysis for Ag(100)

Journal Article · Wed Feb 21 23:00:00 EST 2018 · Journal of Physical Chemistry. C · OSTI ID:1422773

Destabilization of Ag nanoislands on Ag(100) by adsorbed sulfur

Journal Article · Mon Oct 17 00:00:00 EDT 2011 · Journal of Chemical Physics · OSTI ID:1037985

Submonolayer Ag films on Fe(100): A first-principles analysis of energetics controlling adlayer thermodynamics and kinetics

Journal Article · Mon Apr 11 00:00:00 EDT 2016 · Physical Review B · OSTI ID:1337667

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Ab Initio Thermodynamics and Kinetics for Coalescence of Two-Dimensional Nanoislands and Nanopits on Metal (100) Surfaces

Citation Formats

References (77)

Similar Records

Related Subjects