skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids

Abstract

Lattice mismatch - the difference in natural bond length between two species comprising a solid is a common occurrence in modern materials. Spatial patterns in certain nanocrystal heterostructures, for instance, are thought to be a result of elastic forces arising from lattice mismatch. However, the role of lattice mismatch in mediating the arrangement of atoms in such materials is incompletely understood. Here we consider a simple microscopic model for lattice mismatch, in which the difference in natural lengths between bonded atoms produces interactions mediated by elastic strain. Computer simulations reveal that the model exhibits rich phase behavior, including structures with periodic order and unusual coexistence scenarios. To explain this phase behavior, we derive an effective pairwise interaction potential between atoms, revealing preferred spatial arrangements of atoms driven by spatial variations in the interaction potential. We then develop a mean field theory based on this effective interaction which qualitatively captures observed transition to phases with modulated order. Finally, we explain the observed scenarios of coexistence between using a graphical construction, based on the realization that the free energy cost of phase separation in elastic systems grows with system size. Here, these results clarify the equilibrium effects of lattice mismatch in macroscopicmore » solids and suggest a role for lattice mismatch in creating spatially heterogeneous compositions in nanoscale materials.« less

Authors:
ORCiD logo [1];  [2];  [1]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of Vienna (Austria)
Publication Date:
Research Org.:
Univ. of California, Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1572233
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 123; Journal Issue: 13; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Lattice mismatch, strain, phase transition

Citation Formats

Frechette, Layne B., Dellago, Christoph, and Geissler, Phillip L. Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.123.135701.
Frechette, Layne B., Dellago, Christoph, & Geissler, Phillip L. Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids. United States. doi:10.1103/PhysRevLett.123.135701.
Frechette, Layne B., Dellago, Christoph, and Geissler, Phillip L. Tue . "Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids". United States. doi:10.1103/PhysRevLett.123.135701. https://www.osti.gov/servlets/purl/1572233.
@article{osti_1572233,
title = {Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids},
author = {Frechette, Layne B. and Dellago, Christoph and Geissler, Phillip L.},
abstractNote = {Lattice mismatch - the difference in natural bond length between two species comprising a solid is a common occurrence in modern materials. Spatial patterns in certain nanocrystal heterostructures, for instance, are thought to be a result of elastic forces arising from lattice mismatch. However, the role of lattice mismatch in mediating the arrangement of atoms in such materials is incompletely understood. Here we consider a simple microscopic model for lattice mismatch, in which the difference in natural lengths between bonded atoms produces interactions mediated by elastic strain. Computer simulations reveal that the model exhibits rich phase behavior, including structures with periodic order and unusual coexistence scenarios. To explain this phase behavior, we derive an effective pairwise interaction potential between atoms, revealing preferred spatial arrangements of atoms driven by spatial variations in the interaction potential. We then develop a mean field theory based on this effective interaction which qualitatively captures observed transition to phases with modulated order. Finally, we explain the observed scenarios of coexistence between using a graphical construction, based on the realization that the free energy cost of phase separation in elastic systems grows with system size. Here, these results clarify the equilibrium effects of lattice mismatch in macroscopic solids and suggest a role for lattice mismatch in creating spatially heterogeneous compositions in nanoscale materials.},
doi = {10.1103/PhysRevLett.123.135701},
journal = {Physical Review Letters},
number = 13,
volume = 123,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Tuning the optical and electronic properties of colloidal nanocrystals by lattice strain
journal, December 2008

  • Smith, Andrew M.; Mohs, Aaron M.; Nie, Shuming
  • Nature Nanotechnology, Vol. 4, Issue 1
  • DOI: 10.1038/nnano.2008.360

Effects of strain on electronic properties of graphene
journal, February 2010


Strain Engineering of Graphene’s Electronic Structure
journal, July 2009


Calculation of critical layer thickness versus lattice mismatch for Ge x Si 1− x /Si strained‐layer heterostructures
journal, August 1985

  • People, R.; Bean, J. C.
  • Applied Physics Letters, Vol. 47, Issue 3
  • DOI: 10.1063/1.96206

Spontaneous Superlattice Formation in Nanorods Through Partial Cation Exchange
journal, July 2007

  • Robinson, R. D.; Sadtler, B.; Demchenko, D. O.
  • Science, Vol. 317, Issue 5836, p. 355-358
  • DOI: 10.1126/science.1142593

Cation Exchange Reactions in Ionic Nanocrystals
journal, November 2004

  • Son, Dong Hee; Hughes, Steven M.; Yin, Yadong
  • Science, Vol. 306, Issue 5698, p. 1009-1012
  • DOI: 10.1126/science.1103755

Sequential Cation Exchange in Nanocrystals: Preservation of Crystal Phase and Formation of Metastable Phases
journal, November 2011

  • Li, Hongbo; Zanella, Marco; Genovese, Alessandro
  • Nano Letters, Vol. 11, Issue 11
  • DOI: 10.1021/nl202927a

Cation exchange on the nanoscale: an emerging technique for new material synthesis, device fabrication, and chemical sensing
journal, January 2013

  • Rivest, Jessy B.; Jain, Prashant K.
  • Chem. Soc. Rev., Vol. 42, Issue 1
  • DOI: 10.1039/C2CS35241A

Forging Colloidal Nanostructures via Cation Exchange Reactions
journal, February 2016


Formation Mechanism and Properties of CdS-Ag 2 S Nanorod Superlattices
journal, April 2008

  • Demchenko, Denis O.; Robinson, Richard D.; Sadtler, Bryce
  • ACS Nano, Vol. 2, Issue 4
  • DOI: 10.1021/nn700381y

Ising model for phase separation in alloys with anisotropic elastic interaction—I. Theory
journal, August 1995


Some developments in the theory of modulated order. II. Deformable-lattice models and the axial next-nearest-neighbor Ising model as a random magnet
journal, August 1985


Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
journal, February 1977


THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method
journal, October 1992

  • Kumar, Shankar; Rosenberg, John M.; Bouzida, Djamal
  • Journal of Computational Chemistry, Vol. 13, Issue 8
  • DOI: 10.1002/jcc.540130812

Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
journal, January 1998

  • Matsumoto, Makoto; Nishimura, Takuji
  • ACM Transactions on Modeling and Computer Simulation, Vol. 8, Issue 1
  • DOI: 10.1145/272991.272995

Diffusion Constants near the Critical Point for Time-Dependent Ising Models. I
journal, May 1966


Elastic properties of central-force networks with bond-length mismatch
journal, November 1990


Statistical Mechanics of a Compressible Ising Model with Application to β Brass
journal, July 1971

  • Baker, George A.; Essam, John W.
  • The Journal of Chemical Physics, Vol. 55, Issue 2
  • DOI: 10.1063/1.1676156

Lattice gas transition of He on Grafoil. A continuous transition with cubic terms
journal, October 1975


Phase Boundary and Universality of the Triangular Lattice Antiferromagnetic Ising Model
journal, September 1992


Critical Properties from Monte Carlo Coarse Graining and Renormalization
journal, August 1981


Suppression of Capillary Wave Broadening of Interfaces in Binary Alloys due to Elastic Interactions
journal, August 2005


Critical Exponents for Long-Range Interactions
journal, October 1972


Solid State Intercalation, Deintercalation, and Cation Exchange in Colloidal 2D Bi 2 Se 3 and Bi 2 Te 3 Nanocrystals
journal, January 2017


Tailoring ZnSe–CdSe Colloidal Quantum Dots via Cation Exchange: From Core/Shell to Alloy Nanocrystals
journal, August 2013

  • Groeneveld, Esther; Witteman, Leon; Lefferts, Merel
  • ACS Nano, Vol. 7, Issue 9
  • DOI: 10.1021/nn402931y

Lattice Mismatch in Crystalline Nanoparticle Thin Films
journal, December 2017


Shape effects on the cluster spreading process of spin-crossover compounds analyzed within an elastic model with Eden and Kawasaki dynamics
journal, March 2015


Critical temperature and correlation length of an elastic interaction model for spin-crossover materials
journal, February 2012


Simple Two-Dimensional Model for the Elastic Origin of Cooperativity among Spin States of Spin-Crossover Complexes
journal, June 2007


Elastic interaction of high-spin and low-spin complex molecules in spin-crossover compounds. II
journal, December 1989