Which phonons contribute most to negative thermal expansion in ScF3?

Using calculations of the phonon distribution in ScF3 across the whole of reciprocal space, we show that the important phonons for the negative thermal expansion in this material are those associated with the rigid unit modes (RUMs) and associated quasi-RUMs. We discuss the role of the bond-bending flexibility within the ScF6 octahedra, and how this enables other phonons to make an additional but ultimately much weaker contribution to negative thermal expansion. These results inform recent discussions on the role of correlated atomic motions in giving rise to negative thermal expansion in ScF3.

[1]  V. Heine,et al.  The Rigid Unit Mode model: review of ideas and applications. , 2023, Reports on progress in physics. Physical Society.

[2]  M. Dove,et al.  Review: Pair distribution functions from neutron total scattering for the study of local structure in disordered materials , 2022, Nuclear Analysis.

[3]  X. Xing,et al.  Negative thermal expansion in framework structure materials , 2021, Coordination Chemistry Reviews.

[4]  I. da Silva,et al.  Colossal Pressure-Induced Softening in Scandium Fluoride. , 2020, Physical review letters.

[5]  Jun Chen,et al.  Anharmonicity and scissoring modes in the negative thermal expansion materials ScF3 and CaZrF6 , 2019, Physical Review B.

[6]  M. Dove Flexibility of network materials and the Rigid Unit Mode model: a personal perspective , 2019, Philosophical Transactions of the Royal Society A.

[7]  B. Fultz,et al.  Entropic elasticity and negative thermal expansion in a simple cubic crystal , 2019, Science Advances.

[8]  Juan Du,et al.  Quantitative understanding of negative thermal expansion in scandium trifluoride from neutron total scattering measurements , 2019 .

[9]  A. Kuzmin,et al.  Negative thermal expansion of ScF3: first principles vs empirical molecular dynamics , 2019, IOP Conference Series: Materials Science and Engineering.

[10]  Terumasa Tadano,et al.  First-principles study of phonon anharmonicity and negative thermal expansion in ScF3 , 2018, Physical Review Materials.

[11]  G. G. Guzmán-Verri,et al.  Negative Thermal Expansion Near the Precipice of Structural Stability in Open Perovskites , 2018, Front. Chem..

[12]  Qiang Sun,et al.  Localized Symmetry Breaking for Tuning Thermal Expansion in ScF3 Nanoscale Frameworks. , 2018, Journal of the American Chemical Society.

[13]  G. G. Guzmán-Verri,et al.  Negative thermal expansion near two structural quantum phase transitions , 2017, 1712.01446.

[14]  M. Gupta,et al.  Phonons and Anomalous Thermal Expansion Behaviour in Crystalline Solids , 2017, 1711.07267.

[15]  A. Said,et al.  Two-dimensional nanoscale correlations in the strong negative thermal expansion material ScF 3 , 2016 .

[16]  Y. Sun,et al.  Size effects on negative thermal expansion in cubic ScF3 , 2016 .

[17]  J. Deng,et al.  New Insights into the Negative Thermal Expansion: Direct Experimental Evidence for the "Guitar-String" Effect in Cubic ScF3. , 2016, Journal of the American Chemical Society.

[18]  R. Evarestov,et al.  Interpretation of unexpected behavior of infrared absorption spectra of ScF 3 beyond the quasiharmonic approximation , 2016 .

[19]  H. Fang,et al.  Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation , 2016, Reports on progress in physics. Physical Society.

[20]  Ambroise van Roekeghem,et al.  Anomalous thermal conductivity and suppression of negative thermal expansion in ScF3 , 2016, 1601.00561.

[21]  T. Bučko,et al.  Negative thermal expansion of ScF 3 : Insights from density-functional molecular dynamics in the isothermal-isobaric ensemble , 2015 .

[22]  G. G. Guzmán-Verri,et al.  Large isotropic negative thermal expansion above a structural quantum phase transition , 2015, 1712.02865.

[23]  S. Deng,et al.  First‐Principles Study of Sc1−xTixF3 (x ≤ 0.375): Negative Thermal Expansion, Phase Transition, and Compressibility , 2015 .

[24]  D. Palmer Visualization and analysis of crystal structures using CrystalMaker software , 2015 .

[25]  Qiang Sun,et al.  Negative thermal expansion in isostructural cubic ReO3 and ScF3: A comparative study , 2015 .

[26]  J. Deng,et al.  Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications. , 2015, Chemical Society reviews.

[27]  Michel B. Johnson,et al.  The heat capacities of thermomiotic ScF3 and ScF3–YF3 solid solutions , 2015, Journal of Materials Science.

[28]  A. Wilkinson,et al.  Solid solubility, phase transitions, thermal expansion, and compressibility in Sc 1−x Al x F 3 , 2015 .

[29]  M. Dove,et al.  Simulation study of negative thermal expansion in yttrium tungstate Y2W3O12 , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[30]  A. Goodwin,et al.  Acoustic phonons and negative thermal expansion in MOF-5. , 2014, Physical chemistry chemical physics : PCCP.

[31]  H. Fang,et al.  Common origin of exotic properties in ceramic and hybrid negative thermal expansion materials , 2014, 1405.2422.

[32]  K. Refson,et al.  Framework flexibility and the negative thermal expansion mechanism of copper(I) oxide Cu 2 O , 2014, 1402.1026.

[33]  K. Chapman,et al.  Negative thermal expansion and compressibility of Sc1–xYxF3 (x≤0.25) , 2013 .

[34]  Kristin A. Persson,et al.  Commentary: The Materials Project: A materials genome approach to accelerating materials innovation , 2013 .

[35]  C. Lind,et al.  Two Decades of Negative Thermal Expansion Research: Where Do We Stand? , 2012, Materials.

[36]  B. Fultz,et al.  Structural relationship between negative thermal expansion and quartic anharmonicity of cubic ScF3. , 2011, Physical review letters.

[37]  K. Chapman,et al.  Pronounced negative thermal expansion from a simple structure: cubic ScF(3). , 2010, Journal of the American Chemical Society.

[38]  C. Smith,et al.  Negative thermal expansion: a review , 2009 .

[39]  M. Dove,et al.  Pair distribution functions calculated from interatomic potential models using the General Utility Lattice Program , 2007 .

[40]  S. Clark,et al.  Variational density-functional perturbation theory for dielectrics and lattice dynamics. , 2006 .

[41]  Matt Probert,et al.  First principles methods using CASTEP , 2005 .

[42]  N. Allan,et al.  Negative thermal expansion , 2005 .

[43]  John S. O. Evans,et al.  Negative Thermal Expansion Materials , 2004 .

[44]  Julian D. Gale,et al.  The General Utility Lattice Program (GULP) , 2003 .

[45]  K. S. Aleksandrov,et al.  Lattice dynamics and hydrostatic-pressure-induced phase transitions in ScF3 , 2002 .

[46]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[47]  Martin T. Dove,et al.  Geometrical Origin and Theory of Negative Thermal Expansion in Framework Structures , 1999 .

[48]  Arthur W. Sleight,et al.  Compounds That Contract on Heating , 1998 .

[49]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[50]  V. Heine,et al.  Rigid-unit phonon modes and structural phase transitions in framework silicates , 1996 .

[51]  V. Heine,et al.  Distortions of framework structures , 1996 .

[52]  V. Heine,et al.  Rigid unit modes in framework silicates , 1995, Mineralogical Magazine.

[53]  V. Heine,et al.  The Determination of Rigid-Unit Modes as Potential Soft Modes for Displacive Phase Transitions in Framework Crystal Structures , 1993 .

[54]  V. Heine,et al.  On the application of mean-field and landau theory to displacive phase transitions , 1992 .

[55]  R. Cowley,et al.  The continuous melting transition of a three-dimensional crystal at a planar elastic instability , 1988 .

[56]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[57]  J. G. Collins,et al.  The thermal expansion of alkali halides at low temperatures - II. Sodium, rubidium and caesium halides , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[58]  G. White The thermal expansion of alkali halides at low temperatures , 1965, Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences.

[59]  E. Grueneisen The State of a Solid Body , 1959 .

[60]  J. Maxwell,et al.  The Scientific Papers of James Clerk Maxwell: On the Calculation of the Equilibrium and Stiffness of Frames , 1864 .

[61]  Catherine A. Whitman,et al.  Negative Thermal Expansion (Thermomiotic) Materials , 2013 .

[62]  Julian D. Gale,et al.  GULP: A computer program for the symmetry-adapted simulation of solids , 1997 .

[63]  J. D. V. D. Waals,et al.  Thermische Eigenschaften der Stoffe , 1926 .

[64]  E. Grüneisen,et al.  Theorie des festen Zustandes einatomiger Elemente , 1912 .