Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion
Abstract
We consider in detail a simple model supporting a single floppy mode that is often used to heuristically describe instances of negative thermal expansion. A key result is that the translational kinetic energy of the dilating bond network scales extensively with system size and results in dynamical properties which differ qualitatively from considerations built upon harmonic models. We develop an analogy between the dynamics of this model and a modified mechanical pendulum to elucidate the connection between the new results and the familiar harmonic limit. We then propose an appropriate Schrödinger equation for this system and study numerically the quantum mechanical solutions. Marked differences from conventional phonon dynamics and thermodynamics are seen in both classical and quantum limits, in particular a strong twofold enhancement of the (negative) coefficient of thermal expansion. We contextualize the results against real material parameters and discuss related empirical observations.
- Authors:
-
- Univ. of Connecticut, Storrs, CT (United States)
- Publication Date:
- Research Org.:
- Univ. of Connecticut, Storrs, CT (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1535865
- Alternate Identifier(s):
- OSTI ID: 1346580
- Grant/Contract Number:
- SC0016481
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 9; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Lattice dynamics; Mechanical & acoustical properties; Thermal expansion
Citation Formats
Occhialini, Connor A., Handunkanda, Sahan U., Curry, Erin B., and Hancock, Jason N. Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion. United States: N. p., 2017.
Web. doi:10.1103/physrevb.95.094106.
Occhialini, Connor A., Handunkanda, Sahan U., Curry, Erin B., & Hancock, Jason N. Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion. United States. https://doi.org/10.1103/physrevb.95.094106
Occhialini, Connor A., Handunkanda, Sahan U., Curry, Erin B., and Hancock, Jason N. Fri .
"Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion". United States. https://doi.org/10.1103/physrevb.95.094106. https://www.osti.gov/servlets/purl/1535865.
@article{osti_1535865,
title = {Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion},
author = {Occhialini, Connor A. and Handunkanda, Sahan U. and Curry, Erin B. and Hancock, Jason N.},
abstractNote = {We consider in detail a simple model supporting a single floppy mode that is often used to heuristically describe instances of negative thermal expansion. A key result is that the translational kinetic energy of the dilating bond network scales extensively with system size and results in dynamical properties which differ qualitatively from considerations built upon harmonic models. We develop an analogy between the dynamics of this model and a modified mechanical pendulum to elucidate the connection between the new results and the familiar harmonic limit. We then propose an appropriate Schrödinger equation for this system and study numerically the quantum mechanical solutions. Marked differences from conventional phonon dynamics and thermodynamics are seen in both classical and quantum limits, in particular a strong twofold enhancement of the (negative) coefficient of thermal expansion. We contextualize the results against real material parameters and discuss related empirical observations.},
doi = {10.1103/physrevb.95.094106},
journal = {Physical Review. B},
number = 9,
volume = 95,
place = {United States},
year = {Fri Mar 10 00:00:00 EST 2017},
month = {Fri Mar 10 00:00:00 EST 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 5 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Lattice coupling and Franck–Condon effects in K-edge resonant inelastic x-ray scattering
journal, March 2010
- Hancock, J. N.; Chabot-Couture, G.; Greven, M.
- New Journal of Physics, Vol. 12, Issue 3
Negative thermal expansion: a review
journal, July 2009
- Miller, W.; Smith, C. W.; Mackenzie, D. S.
- Journal of Materials Science, Vol. 44, Issue 20
YbGaGe: normal thermal expansion
journal, March 2005
- Janssen, Y.; Chang, S.; Cho, B. K.
- Journal of Alloys and Compounds, Vol. 389, Issue 1-2
Large Negative Thermal Expansion and Anomalous Behavior on Compression in Cubic ReO 3 -Type A II B IV F 6 : CaZrF 6 and CaHfF 6
journal, May 2015
- Hancock, Justin C.; Chapman, Karena W.; Halder, Gregory J.
- Chemistry of Materials, Vol. 27, Issue 11
A system with adjustable positive or negative thermal expansion
journal, March 2007
- Grima, Joseph N.; Farrugia, Pierre S.; Gatt, Ruben
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, Issue 2082
Negative thermal expansion in beta-quartz
journal, November 1998
- Welche, P. R. L.; Heine, V.; Dove, M. T.
- Physics and Chemistry of Minerals, Vol. 26, Issue 1
Local Vibrations and Negative Thermal Expansion in
journal, January 2014
- Bridges, F.; Keiber, T.; Juhas, P.
- Physical Review Letters, Vol. 112, Issue 4
Anomalous low-temperature heat capacity in antiperovskite compounds
journal, February 2017
- Guo, Xin-Ge; Lin, Jian-Chao; Tong, Peng
- Chinese Physics B, Vol. 26, Issue 2
The Inversion of Specific Heat Curves
journal, November 1961
- Chambers, R. G.
- Proceedings of the Physical Society, Vol. 78, Issue 5
Negative Thermal Expansion in : Mechanisms, Rigid Unit Modes, and Neutron Total Scattering
journal, December 2005
- Tucker, Matthew G.; Goodwin, Andrew L.; Dove, Martin T.
- Physical Review Letters, Vol. 95, Issue 25
Soft Modes and Elasticity of Nearly Isostatic Lattices: Randomness and Dissipation
journal, February 2010
- Mao, Xiaoming; Xu, Ning; Lubensky, T. C.
- Physical Review Letters, Vol. 104, Issue 8
Evolution of Negative Thermal Expansion and Phase Transitions in Sc 1-x Ti x F 3
journal, February 2014
- Morelock, Cody R.; Gallington, Leighanne C.; Wilkinson, Angus P.
- Chemistry of Materials, Vol. 26, Issue 5
Surface phonons, elastic response, and conformal invariance in twisted kagome lattices
journal, June 2012
- Sun, K.; Souslov, A.; Mao, X.
- Proceedings of the National Academy of Sciences, Vol. 109, Issue 31
Thermodynamic functions of ZrW2O8 from its heat capacity
journal, March 2012
- Ji, FengMin; Dai, XianXi; Stevens, R.
- Science China Physics, Mechanics and Astronomy, Vol. 55, Issue 4
Colossal Positive and Negative Thermal Expansion in the Framework Material Ag3[Co(CN)6]
journal, February 2008
- Goodwin, A. L.; Calleja, M.; Conterio, M. J.
- Science, Vol. 319, Issue 5864
Elastic properties of a class of solids with negative thermal expansion
journal, July 2010
- He, Yan; Cvetkovic, Vladimir; Varma, C. M.
- Physical Review B, Vol. 82, Issue 1
Anomalous thermal conductivity and suppression of negative thermal expansion in
journal, July 2016
- van Roekeghem, Ambroise; Carrete, Jesús; Mingo, Natalio
- Physical Review B, Vol. 94, Issue 2
Frustrated Soft Modes and Negative Thermal Expansion in
journal, November 2002
- Cao, D.; Bridges, F.; Kowach, G. R.
- Physical Review Letters, Vol. 89, Issue 21
Pronounced Negative Thermal Expansion from a Simple Structure: Cubic ScF 3
journal, November 2010
- Greve, Benjamin K.; Martin, Kenneth L.; Lee, Peter L.
- Journal of the American Chemical Society, Vol. 132, Issue 44
Negative thermal expansion in cubic : Inelastic neutron scattering and lattice dynamical studies
journal, December 2004
- Mittal, R.; Chaplot, S. L.; Schober, H.
- Physical Review B, Vol. 70, Issue 21
Large Low Temperature Specific Heat in the Negative Thermal Expansion Compound
journal, June 1998
- Ramirez, A. P.; Kowach, G. R.
- Physical Review Letters, Vol. 80, Issue 22
Two-dimensional nanoscale correlations in the strong negative thermal expansion material
journal, December 2016
- Handunkanda, Sahan U.; Occhialini, Connor A.; Said, Ayman H.
- Physical Review B, Vol. 94, Issue 21
Negative thermal expansion of : Insights from density-functional molecular dynamics in the isothermal-isobaric ensemble
journal, December 2015
- Lazar, Petr; Bučko, Tomáš; Hafner, Jürgen
- Physical Review B, Vol. 92, Issue 22
Soft Manifold Dynamics behind Negative Thermal Expansion
journal, June 2008
- Schlesinger, Z.; Rosen, J. A.; Hancock, J. N.
- Physical Review Letters, Vol. 101, Issue 1
Negative thermal expansion materials
journal, April 1998
- Sleight, Arthur W.
- Current Opinion in Solid State and Materials Science, Vol. 3, Issue 2
Negative thermal expansion and low-frequency modes in cyanide-bridged framework materials
journal, April 2005
- Goodwin, Andrew L.; Kepert, Cameron J.
- Physical Review B, Vol. 71, Issue 14
Colossal negative thermal expansion in BiNiO3 induced by intermetallic charge transfer
journal, June 2011
- Azuma, Masaki; Chen, Wei-tin; Seki, Hayato
- Nature Communications, Vol. 2, Issue 1
Zero thermal expansion in YbGaGe due to an electronic valence transition
journal, October 2003
- Salvador, James R.; Guo, Fu; Hogan, Tim
- Nature, Vol. 425, Issue 6959
Two Decades of Negative Thermal Expansion Research: Where Do We Stand?
journal, June 2012
- Lind, Cora
- Materials, Vol. 5, Issue 12
Ab initio molecular dynamics simulations of the Sc K-edge EXAFS of scandium trifluoride
journal, May 2016
- Bocharov, Dmitry; Krack, Matthias; Kalinko, Aleksandr
- Journal of Physics: Conference Series, Vol. 712
The heat capacities of thermomiotic ScF3 and ScF3–YF3 solid solutions
journal, February 2015
- Romao, Carl P.; Morelock, Cody R.; Johnson, Michel B.
- Journal of Materials Science, Vol. 50, Issue 9
Toward an Understanding of the Local Origin of Negative Thermal Expansion in ZrW 2 O 8 : Limits and Inconsistencies of the Tent and Rigid Unit Mode Models
journal, June 2014
- Sanson, Andrea
- Chemistry of Materials, Vol. 26, Issue 12
Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation
journal, May 2016
- Dove, Martin T.; Fang, Hong
- Reports on Progress in Physics, Vol. 79, Issue 6
Elasticity and Response in Nearly Isostatic Periodic Lattices
journal, November 2009
- Souslov, Anton; Liu, Andrea J.; Lubensky, T. C.
- Physical Review Letters, Vol. 103, Issue 20
The Theory of an Electron on a Loxodrome
journal, March 2012
- Tourigny, David S.
- Modern Physics Letters B, Vol. 26, Issue 08
The role of rigid unit modes in negative thermal expansion
journal, July 2003
- Tao, J. Z.; Sleight, A. W.
- Journal of Solid State Chemistry, Vol. 173, Issue 2
Large Negative Magnetic Contribution to the Thermal Expansion in Iron-Platinum Alloys: Quantitative Theory of the Invar Effect
journal, July 2003
- Khmelevskyi, S.; Turek, I.; Mohn, P.
- Physical Review Letters, Vol. 91, Issue 3
Dynamics of Some Constrained Lattices
journal, February 2001
- Simon, M. E.; Varma, C. M.
- Physical Review Letters, Vol. 86, Issue 9
Invar alloys
journal, June 1996
- Shiga, Masayuki
- Current Opinion in Solid State and Materials Science, Vol. 1, Issue 3
Buckminster Fuller's “Tensegrity” structures and Clerk Maxwell's rules for the construction of stiff frames
journal, January 1978
- Calladine, C. R.
- International Journal of Solids and Structures, Vol. 14, Issue 2
Heat-capacity analysis of a large number of -type compounds
journal, February 1983
- Junod, A.; Jarlborg, T.; Muller, J.
- Physical Review B, Vol. 27, Issue 3
Structural Relationship between Negative Thermal Expansion and Quartic Anharmonicity of Cubic
journal, November 2011
- Li, Chen W.; Tang, Xiaoli; Muñoz, J. A.
- Physical Review Letters, Vol. 107, Issue 19
Intermetallic charge-transfer transition in Bi La NiO as the origin of the colossal negative thermal expansion
journal, July 2013
- Oka, Kengo; Mizumaki, Masaichiro; Sakaguchi, Chika
- Physical Review B, Vol. 88, Issue 1
The Ginzburg interval in soft-mode phase transitions: consequences of the rigid unit mode picture
journal, April 1994
- Sollich, P.; Heine, V.; Dove, M. T.
- Journal of Physics: Condensed Matter, Vol. 6, Issue 17
Classical model of negative thermal expansion in solids with expanding bonds
journal, June 2016
- Schick, Joseph T.; Rappe, Andrew M.
- Physical Review B, Vol. 93, Issue 21
Colossal negative thermal expansion in reduced layered ruthenate
journal, January 2017
- Takenaka, Koshi; Okamoto, Yoshihiko; Shinoda, Tsubasa
- Nature Communications, Vol. 8, Issue 1
Origin of Negative Thermal Expansion in Cubic Revealed by High Pressure Inelastic Neutron Scattering
journal, May 2001
- Mittal, R.; Chaplot, S. L.; Schober, H.
- Physical Review Letters, Vol. 86, Issue 20
Interpretation of unexpected behavior of infrared absorption spectra of beyond the quasiharmonic approximation
journal, June 2016
- Piskunov, Sergei; Žguns, Pjotrs A.; Bocharov, Dmitry
- Physical Review B, Vol. 93, Issue 21
Negative thermal expansion materials: technological key for control of thermal expansion
journal, February 2012
- Takenaka, Koshi
- Science and Technology of Advanced Materials, Vol. 13, Issue 1
Topological boundary modes in isostatic lattices
journal, December 2013
- Kane, C. L.; Lubensky, T. C.
- Nature Physics, Vol. 10, Issue 1
Unusual Low-Energy Phonon Dynamics in the Negative Thermal Expansion Compound
journal, November 2004
- Hancock, Jason N.; Turpen, Chandra; Schlesinger, Zack
- Physical Review Letters, Vol. 93, Issue 22
The role of static disorder in negative thermal expansion in ReO3
journal, June 2009
- Rodriguez, Efrain E.; Llobet, Anna; Proffen, Thomas
- Journal of Applied Physics, Vol. 105, Issue 11
Size effects on negative thermal expansion in cubic ScF 3
journal, July 2016
- Yang, C.; Tong, P.; Lin, J. C.
- Applied Physics Letters, Vol. 109, Issue 2
Large isotropic negative thermal expansion above a structural quantum phase transition
journal, October 2015
- Handunkanda, Sahan U.; Curry, Erin B.; Voronov, Vladimir
- Physical Review B, Vol. 92, Issue 13
Works referencing / citing this record:
Molecular dynamics simulation of zirconium tungstate amorphization and the amorphous-crystalline interface
journal, November 2019
- Greathouse, Jeffery A.; Weck, Philippe F.; Gordon, Margaret E.
- Journal of Physics: Condensed Matter, Vol. 32, Issue 8
Negative thermal expansion near two structural quantum phase transitions
journal, December 2017
- Occhialini, Connor A.; Handunkanda, Sahan U.; Said, Ayman
- Physical Review Materials, Vol. 1, Issue 7
Entropic elasticity and negative thermal expansion in a simple cubic crystal
journal, November 2019
- Wendt, David; Bozin, Emil; Neuefeind, Joerg
- Science Advances, Vol. 5, Issue 11
Entropic elasticity and negative thermal expansion in a simple cubic crystal
text, January 2019
- Wendt, David; Bozin, Emil; Neuefeind, Joerg
- arXiv