# Efficient Calculation of the Negative Thermal Expansion in ZrW2O8

## Abstract

We present a study of the origin of the negative thermal expansion (NTE) on ZrW _{2}O _{8} by combining an efficient approach for computing the dynamical matrix with the Lanczos algorithm for generating the phonon density of states in the quasi-harmonic approximation. The simulations show that the NTE arises primarily from the motion of the O-sublattice, and in particular, from the transverse motion of the O atoms in the W–O and W–O–Zr bonds. In the low frequency range these combine to keep the WO _{4} tetrahedra rigid and induce internal distortions in the ZrO _{6} octahedra. The force constants associated with these distortions become stronger with expansion, resulting in negative Grüneisen parameters and NTE from the low frequency modes that dominate the positive contributions from the high frequency modes. This leads us to propose an anharmonic, two-frequency Einstein model that quantitatively captures the NTE behavior.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Illinois, Urbana-Champaign, IL (United States) Stanford Univ., CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1462120

- Alternate Identifier(s):
- OSTI ID: 1510436

- Grant/Contract Number:
- CSGBD Grant No. DE-FG02-03ER15476; FG02-03ER15476; AC02-05CH11231

- Resource Type:
- Published Article

- Journal Name:
- Frontiers in Chemistry

- Additional Journal Information:
- Journal Name: Frontiers in Chemistry Journal Volume: 6; Journal ID: ISSN 2296-2646

- Publisher:
- Frontiers Media SA

- Country of Publication:
- Switzerland

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; zirconium tungstate; NTE; DFT; quasi-harmonic approximation; phonon density of states

### Citation Formats

```
Vila, Fernando D., Hayashi, Scott T., and Rehr, John J. Efficient Calculation of the Negative Thermal Expansion in ZrW2O8. Switzerland: N. p., 2018.
Web. doi:10.3389/fchem.2018.00296.
```

```
Vila, Fernando D., Hayashi, Scott T., & Rehr, John J. Efficient Calculation of the Negative Thermal Expansion in ZrW2O8. Switzerland. doi:10.3389/fchem.2018.00296.
```

```
Vila, Fernando D., Hayashi, Scott T., and Rehr, John J. Mon .
"Efficient Calculation of the Negative Thermal Expansion in ZrW2O8". Switzerland. doi:10.3389/fchem.2018.00296.
```

```
@article{osti_1462120,
```

title = {Efficient Calculation of the Negative Thermal Expansion in ZrW2O8},

author = {Vila, Fernando D. and Hayashi, Scott T. and Rehr, John J.},

abstractNote = {We present a study of the origin of the negative thermal expansion (NTE) on ZrW2O8 by combining an efficient approach for computing the dynamical matrix with the Lanczos algorithm for generating the phonon density of states in the quasi-harmonic approximation. The simulations show that the NTE arises primarily from the motion of the O-sublattice, and in particular, from the transverse motion of the O atoms in the W–O and W–O–Zr bonds. In the low frequency range these combine to keep the WO4 tetrahedra rigid and induce internal distortions in the ZrO6 octahedra. The force constants associated with these distortions become stronger with expansion, resulting in negative Grüneisen parameters and NTE from the low frequency modes that dominate the positive contributions from the high frequency modes. This leads us to propose an anharmonic, two-frequency Einstein model that quantitatively captures the NTE behavior.},

doi = {10.3389/fchem.2018.00296},

journal = {Frontiers in Chemistry},

number = ,

volume = 6,

place = {Switzerland},

year = {2018},

month = {7}

}

DOI: 10.3389/fchem.2018.00296

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

_{2}O

_{8}cell. The cell is composed of four equivalent Zr atoms (magenta), eight W atoms, of type W

_{FF}(blue) and W

_{FR}(green), and 32 O atoms of type O

_{LS}(yellow), O

_{SL}(red), O

_{FR}(orange) and O

_{FF}(black). Examples of the different types of Omore »

Works referenced in this record:

##
Rigid-unit phonon modes and structural phase transitions in framework silicates

journal, October 1996

- Hammonds, Kenton D.; Dove, Martin T.; Giddy, Andrew P.
- American Mineralogist, Vol. 81, Issue 9-10

##
Negative thermal expansion in cubic ZrW ${}_{2}$ O ${}_{8}$ : Role of phonons in the entire Brillouin zone from *ab initio* calculations

journal, July 2013

- Gupta, M. K.; Mittal, R.; Chaplot, S. L.
- Physical Review B, Vol. 88, Issue 1

##
Density-Functional Perturbation Theory for Quasi-Harmonic Calculations

journal, January 2010

- Baroni, S.; Giannozzi, P.; Isaev, E.
- Reviews in Mineralogy and Geochemistry, Vol. 71, Issue 1

##
Zirconium Tungstate

journal, November 1995

- Auray, M.; Quarton, M.; Leblanc, M.
- Acta Crystallographica Section C Crystal Structure Communications, Vol. 51, Issue 11

##
Thermal properties of molecular crystals through dispersion-corrected quasi-harmonic ab initio calculations: the case of urea

journal, January 2016

- Erba, Alessandro; Maul, Jefferson; Civalleri, Bartolomeo
- Chemical Communications, Vol. 52, Issue 9

##
*Ab initio* single- and multiple-scattering EXAFS Debye-Waller factors: Raman and infrared data

journal, August 1998

- Dimakis, Nicholas; Bunker, Grant
- Physical Review B, Vol. 58, Issue 5

##
Phonon density of states and negative thermal expansion in ZrW2O8

journal, November 1998

- Ernst, G.; Broholm, C.; Kowach, G. R.
- Nature, Vol. 396, Issue 6707

##
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

##
Phonons and related crystal properties from density-functional perturbation theory

journal, July 2001

- Baroni, Stefano; de Gironcoli, Stefano; Dal Corso, Andrea
- Reviews of Modern Physics, Vol. 73, Issue 2

##
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

journal, July 1996

- Kresse, G.; Furthmüller, J.
- Computational Materials Science, Vol. 6, Issue 1, p. 15-50

##
Local Vibrations and Negative Thermal Expansion in ${\mathrm{ZrW}}_{2}{\mathrm{O}}_{8}$

journal, January 2014

- Bridges, F.; Keiber, T.; Juhas, P.
- Physical Review Letters, Vol. 112, Issue 4

##
First-principles computation of material properties: the ABINIT software project

journal, November 2002

- Gonze, X.; Beuken, J. -M.; Caracas, R.
- Computational Materials Science, Vol. 25, Issue 3

##
Negative Thermal Expansion in ${\mathrm{ZrW}}_{2}{\mathrm{O}}_{8}$ : 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

##
Rigid unit modes and the negative thermal expansion in ZrW _{2} O _{8}

journal, May 1997

- Pryde, Alexandra K. A.; Hammonds, Kenton D.; Dove, Martin T.
- Phase Transitions, Vol. 61, Issue 1-4

##
Efficient iterative schemes for *ab initio* total-energy calculations using a plane-wave basis set

journal, October 1996

- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186

##
From ultrasoft pseudopotentials to the projector augmented-wave method

journal, January 1999

- Kresse, G.; Joubert, D.
- Physical Review B, Vol. 59, Issue 3, p. 1758-1775

##
*Ab initio* calculation of the thermodynamic properties and atomic temperature factors of ${\mathrm{SiO}}_{2}$ α-quartz and stishovite

journal, April 1995

- Lee, Changyol; Gonze, Xavier
- Physical Review B, Vol. 51, Issue 13

##
On combining temperature and pressure effects on structural properties of crystals with standard *ab initio* techniques

journal, September 2014

- Erba, A.
- The Journal of Chemical Physics, Vol. 141, Issue 12

##
Negative Thermal Expansion in ZrW _{2} O _{8} and HfW _{2} O _{8}

journal, January 1996

- Evans, J. S. O.; Mary, T. A.; Vogt, T.
- Chemistry of Materials, Vol. 8, Issue 12

##
*Ab initio* molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium

journal, May 1994

- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 49, Issue 20, p. 14251-14269

##
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation

journal, July 2013

- Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy
- APL Materials, Vol. 1, Issue 1

##
On how differently the quasi-harmonic approximation works for two isostructural crystals: Thermal properties of periclase and lime

journal, January 2015

- Erba, A.; Shahrokhi, M.; Moradian, R.
- The Journal of Chemical Physics, Vol. 142, Issue 4

##
Calculation of Thermal Expansion, Compressiblity, an Melting in Alkali Halides: NaCl and KCl

journal, February 1979

- Boyer, L. L.
- Physical Review Letters, Vol. 42, Issue 9

##
Thermal Expansion of Carbamazepine: Systematic Crystallographic Measurements Challenge Quantum Chemical Calculations

journal, August 2017

- Brandenburg, Jan Gerit; Potticary, Jason; Sparkes, Hazel A.
- The Journal of Physical Chemistry Letters, Vol. 8, Issue 17

##
Frustrated Soft Modes and Negative Thermal Expansion in ${\mathrm{Z}\mathrm{r}\mathrm{W}}_{2}{\mathrm{O}}_{8}$

journal, November 2002

- Cao, D.; Bridges, F.; Kowach, G. R.
- Physical Review Letters, Vol. 89, Issue 21

##
Negative Thermal Expansion from 0.3 to 1050 Kelvin in ZrW2O8

journal, April 1996

- Mary, T. A.; Evans, J. S. O.; Vogt, T.
- Science, Vol. 272, Issue 5258

##
Thermal expansion and x-ray-absorption fine-structure cumulants

journal, July 1993

- Frenkel, A. I.; Rehr, J. J.
- Physical Review B, Vol. 48, Issue 1

##
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces

journal, April 2008

- Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I.
- Physical Review Letters, Vol. 100, Issue 13

##
*Ab* *initio* study of the volume dependence of dynamical and thermodynamical properties of silicon

journal, February 1996

- Rignanese, G. -M.; Michenaud, J. -P.; Gonze, X.
- Physical Review B, Vol. 53, Issue 8

##
Local structure in ZrW _{2} O _{8} from neutron total scattering

journal, July 2007

- Tucker, Matthew G.; Keen, David A.; Evans, John S. O.
- Journal of Physics: Condensed Matter, Vol. 19, Issue 33

##
Recursion method for multiple-scattering XAFS Debye–Waller factors

journal, May 1999

- Poiarkova, A. V.; Rehr, J. J.
- Journal of Synchrotron Radiation, Vol. 6, Issue 3

##
Accuracy of finite-difference harmonic frequencies in density functional theory

journal, May 2017

- Liu, Kuan-Yu; Liu, Jie; Herbert, John M.
- Journal of Computational Chemistry, Vol. 38, Issue 19

##
Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory

journal, April 1997

- Gonze, Xavier; Lee, Changyol
- Physical Review B, Vol. 55, Issue 16

##
*Ab initio*molecular dynamics for liquid metals

journal, January 1993

- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 47, Issue 1, p. 558-561

##
Structural investigation of the negative-thermal-expansion material ZrW _{2} O _{8}

journal, June 1999

- Evans, John S. O.; David, W. I. F.; Sleight, A. W.
- Acta Crystallographica Section B Structural Science, Vol. 55, Issue 3

##
Calculation of Dynamical Surface Properties of Noble-Gas Crystals. I. The Quasiharmonic Approximation

journal, March 1969

- Allen, R. E.; De Wette, F. W.
- Physical Review, Vol. 179, Issue 3

##
Unusual Low-Energy Phonon Dynamics in the Negative Thermal Expansion Compound ${\mathrm{Z}\mathrm{r}\mathrm{W}}_{2}{\mathrm{O}}_{8}$

journal, November 2004

- Hancock, Jason N.; Turpen, Chandra; Schlesinger, Zack
- Physical Review Letters, Vol. 93, Issue 22

##
Bayes-Turchin approach to x-ray absorption fine structure data analysis

journal, November 2002

- Krappe, H. J.; Rossner, H. H.
- Physical Review B, Vol. 66, Issue 18

##
Multiple-scattering x-ray-absorption fine-structure Debye-Waller factor calculations

journal, January 1999

- Poiarkova, A. V.; Rehr, J. J.
- Physical Review B, Vol. 59, Issue 2

##
Theoretical x-ray absorption Debye-Waller factors

journal, July 2007

- Vila, Fernando D.; Rehr, J. J.; Rossner, H. H.
- Physical Review B, Vol. 76, Issue 1

##
Correlated atomic motions in the negative thermal expansion material ${\mathrm{ZrW}}_{2}{\mathrm{O}}_{8}:$ A local structure study

journal, July 2003

- Cao, D.; Bridges, F.; Kowach, G. R.
- Physical Review B, Vol. 68, Issue 1

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*