Phonon density of states and negative thermal expansion in ZrW2O8


Thermal expansion of solids arises from anharmonic lattice dynamics. The contrasting phenomenon of negative thermal expansion (NTE)—where expansion occurs on cooling rather than heating—was discovered1 in ZrW2O8 in 1968. Recently, this material has attracted interest in the context of NTE for several reasons: the magnitude of the effect is relatively large (−9 p.p.m. K−1); the temperature range over which NTE occurs is also large (from close to absolute zero up to the decomposition temperature of about 1,050 K); and the NTE effect is isotropic2, evidenced by the fact that ZrW2O8 remains cubic at all temperatures. These characteristics make ZrW2O8 an important system in which to study unusual lattice dynamics of this type, and potentially well suited for application in composite materials with an engineered thermal expansion coefficient3. Here we report neutron-scattering measurements of ZrW2O8 that allow us to investigate its phonon spectrum, and hence determine the energy scale for the lattice motions governing NTE. We find that NTE can be modelled by several low-energy phonon modes, suggesting that the effect arises from the unusual crystal structure of ZrW2O8, which supports highly anharmonic vibrational modes.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Generalized phonon density of states g (ω) of ZrW2O8 at T = 300 K.
Figure 2: Lattice parameter a (open circles) and Grüneisen parameter γ (crosses) of ZrW2O8 as a function of temperature.
Figure 3: Low-energy generalized density of states for T = 50 K, 100 K and 300 K as determined from inelastic neutron scattering.


  1. 1

    Martinek, C. & Hummel, F. A. Linear thermal expansion of three tungstates. J. Am. Ceram. Soc. 51, 227–228 (1968).

  2. 2

    Mary, T. A., Evans, J. S. O., Vogt, T. & Sleight, A. W. Negative thermal expansion from 0.3 to 1050 Kelvin in ZrW2O8. Science 272, 90–92 (1996).

  3. 3

    Fleming, D. A., Johnson, D. W. & Lemaire, P. J. US Patent No. 5694503 (1997).

  4. 4

    Blackman, M. On the thermal expansion of solids. Proc. Phys. Soc. B 70, 827–832 (1957).

  5. 5

    Giddy, A. P., Dove, M. T., Pawley, G. S. & Heine, V. The determination of rigid unit modes as potential soft modes for displacive phase transitions in framework crystal structures. Acta Crystallogr. A 49, 697–703 (1993).

  6. 6

    Pryde, A. K. A. et al. Origin of the negative thermal expansion in ZrW2O8and ZrV2O7. J. Phys. Condens. Matter 8, 10973–10982 (1996).

  7. 7

    Barron, T. H. K., Collins, J. G. & White, G. K. Thermal expansion of solids at low temperatures. Adv. Phys. 29, 609–730 (1980).

  8. 8

    Ramirez, A. P. & Kowach, G. R. Large low temperature specific heat in the negative thermal expansion compound ZrW2O8. Phys. Rev. Lett. 80, 4903–4906 (1998).

  9. 9

    Lovesey, S. W. Theory of Neutron Scattering from Condensed Matter Vol. 1 (Clarendon, Oxford, (1984).

  10. 10

    Squires, G. L. Introduction to the Theory of Thermal Neutron Scattering (Cambridge Univ. Press, (1978).

  11. 11

    Evans, J. S. O., Mary, T. A., Vogt, T., Subramanian, M. A. & Sleight, A. W. Negative thermal expansion in ZrW2O8and HfW2O8. Chem. Mater. 8, 2809–2823 (1996).

Download references


We thank W. Kamitakahara, P. Littlewood, D. Neuman, A. Pinczuk, T. Siegrist, C.Varma, T. Yildrim and in particular S. Simon for discussions. Work at JHU was supported by the NSF; this work used neutron research facilities supported by NIST and the NSF.

Author information

Correspondence to A. P. Ramirez.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ernst, G., Broholm, C., Kowach, G. et al. Phonon density of states and negative thermal expansion in ZrW2O8. Nature 396, 147–149 (1998).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.