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Modified Winterbottom Construction Including Boundaries

Journal Article · · Journal of Physical Chemistry. C
 [1];  [2]
  1. Northwestern Univ., Evanston, IL (United States); Northwestern University
  2. Northwestern Univ., Evanston, IL (United States)
There has been extensive work on the equilibrium shape of isolated nanoparticles with internal boundaries, and also single crystals on substrates. Surprisingly, almost shockingly, there has been very little work on the equilibrium shape of particles with internal boundaries on substrates. Here in this paper, the general solution is given for the configuration of particles which contain twin and other grain boundaries on a flat substrate, which can be applied to any polycrystalline or multiphase nanoparticle configuration. The solution is based upon combining the established modified-Wulff construction that has been extensively validated for twinned particles with the Winterbottom construction for single particles on a substrate. The solution is illustrated for the specific case of five-fold multiply twinned particles. Good agreement is observed between both existing experimental data in the literature as well as some experimental data included within this work.
Research Organization:
Northwestern Univ., Evanston, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
FG02-03ER15457
OSTI ID:
1778933
Journal Information:
Journal of Physical Chemistry. C, Journal Name: Journal of Physical Chemistry. C Journal Issue: 51 Vol. 124; ISSN 1932-7447
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (38)

Soft Matter (Nobel Lecture) journal July 1992
Shape-Controlled Synthesis of Metal Nanocrystals: Simple Chemistry Meets Complex Physics? journal December 2008
When Gold Is Not Noble: Catalysis by Nanoparticles journal April 2003
The summertop construction: Crystals in a corner journal February 1988
Epitaxial Stabilization of Face Selective Catalysts journal July 2013
Shape-controlled growth of SrTiO3 polyhedral submicro/nanocrystals journal August 2014
Equilibrium shape of a small particle in contact with a foreign substrate journal February 1967
A vector thermodlnamics for anisotropic surfaces—II. Curved and faceted surfaces journal October 1974
Modified Wulff constructions for twinned particles journal April 1983
A vector thermodynamics for anisotropic surfaces journal June 1972
Prostate cancer-specific thermo-responsive polymer-coated iron oxide nanoparticles journal May 2013
Characterization and reactivity in CO oxidation of gold nanoparticles supported on TiO2 prepared by deposition-precipitation with NaOH and urea journal March 2004
Synthesis, properties and applications of Janus nanoparticles journal June 2011
In Situ Growth of Porous Platinum Nanoparticles on Graphene Oxide for Colorimetric Detection of Cancer Cells journal February 2014
Synthesis of Gadolinium Scandate from a Hydroxide Hydrogel journal December 2017
Morphology and CO Oxidation Activity of Pd Nanoparticles on SrTiO 3 Nanopolyhedra journal April 2018
Nanoalloys:  From Theory to Applications of Alloy Clusters and Nanoparticles journal March 2008
Core/Shell Nanoparticles: Classes, Properties, Synthesis Mechanisms, Characterization, and Applications journal December 2011
Propane Oxidation over Pt/SrTiO 3 Nanocuboids journal May 2011
Facet Effect of Single-Crystalline Ag 3 PO 4 Sub-microcrystals on Photocatalytic Properties journal May 2011
Synthesis of High-Quality Brookite TiO 2 Single-Crystalline Nanosheets with Specific Facets Exposed: Tuning Catalysts from Inert to Highly Reactive journal May 2012
Bimetallic Pt−Au Clusters on TiO 2 (110):  Growth, Surface Composition, and Metal−Support Interactions journal March 2008
Elastic Strain Energy Effects in Faceted Decahedral Nanoparticles journal January 2013
Thermodynamic Analysis of Multiply Twinned Particles: Surface Stress Effects journal August 2013
Tuning of Catalytic CO Oxidation by Changing Composition of Rh−Pt Bimetallic Nanoparticles journal February 2008
Oriented Catalytic Platinum Nanoparticles on High Surface Area Strontium Titanate Nanocuboids journal March 2011
Wulff Construction for Alloy Nanoparticles journal August 2011
Electrosprayed nanoparticles and electrospun nanofibers based on natural materials: applications in tissue regeneration, drug delivery and pharmaceuticals journal January 2015
Titania nanotubes supported gelatin stabilized gold nanoparticles for medical implants journal January 2011
From formation mechanisms to synthetic methods toward shape-controlled oxide nanoparticles journal January 2013
Photocatalytic degradation of ciprofloxacin antibiotic by TiO 2 nanoparticles immobilized on a glass plate journal February 2019
Surface structure and energetics of multiply twinned particles journal July 1984
Elastic strains and the energy balance for multiply twinned particles journal July 1984
Nanoparticle shape, thermodynamics and kinetics journal January 2016
Multiply Twinned Particles at Earlier Stages of Gold Film Formation on Alkalihalide Crystals journal June 1967
Der Wulffsche Satz für die Gleichgewichtsform von Kristallen journal December 1943
Über einen geometrischen Satz von Wulff für die Gleichgewichtsform von Kristallen journal December 1943
Controlled Two-Step Formation of Faceted Perovskite Rare-Earth Scandate Nanoparticles journal April 2019

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