Monocrystal Elastic Constants of the Negative-Thermal-Expansion Compound Zirconium Tungstate (${\mathrm{Z}\mathrm{r}\mathrm{W}}_2{\mathrm{O}}_8$)

We measured zirconium tungstate's elastic constants $C_{ij}$. This compound shows relatively soft, nearly isotropic elastic constants with normal Poisson ratios and no approach to Born instability. ${\mathrm{Z}\mathrm{r}\mathrm{W}}_2{\mathrm{O}}_8$ shows normal ambient-temperature elastic constants $C_{ij}$, but remarkable $d{C}_{ij}/dT$ that show dominant low-frequency acoustic-vibration modes. From the bulk modulus, we estimated the total ambient-temperature thermodynamic Grüneisen parameter as $\gamma =-1.2$. The $dB/dT$ slope gives a Grüneisen parameter $\gamma =-7$. The 300–0 K bulk-modulus increase ($40\%$) seems unprecedented and breaks Birch's law of corresponding states.

Figure 1

Blackman diagram showing points for ${\mathrm{Z}\mathrm{r}\mathrm{W}}_2{\mathrm{O}}_8$ and seventeen other oxides. We see that ${\mathrm{Z}\mathrm{r}\mathrm{W}}_2{\mathrm{O}}_8$ looks normal.

Figure 2

Zirconium tungstate's normalized low-temperature elastic constants: bulk modulus $B$, $C_{11}$, $C_{44}$. Curves represent an Einstein-oscillator function. The bulk-modulus increase may be the largest ever reported. The near linearity to such low temperatures strongly suggests a low-frequency Einstein mode.