Nuclear magnetic resonance analysis and activation energy spectrum of the irreversible structural relaxation of amorphous zirconium tungstate

Zirconium tungstate undergoes a sequence of phase transitions from cubic ($\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$) to orthorhombic ($\gamma -{\mathrm{ZrW}}_2{\mathrm{O}}_8$) to amorphous ($a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$) upon increasing pressure at room temperature. The amorphous phase is known to undergo anomalous endothermic recrystallization into a high-temperature $\beta -{\mathrm{ZrW}}_2{\mathrm{O}}_8$ phase above ${600}^{\circ }\mathrm{C}$ at ambient pressure (and back to $\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$ when brought to room temperature). The endothermic recrystallization of $a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$ is preceded by an irreversible exothermic structural relaxation. New W-O bonds are formed upon amorphization, continuing a tendency of increasing W coordination number in going from $\alpha$ to $\gamma -{\mathrm{ZrW}}_2{\mathrm{O}}_8$. In fact, contrarily to $\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$, in which one-quarter of the oxygen atoms are bonded only to one W (terminal oxygens), previous works found no evidence of single-bonded oxygen atoms in $a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$. It thus could be argued that the irreversible character of the structural relaxation of $a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$ is due to W-O bond breaking upon annealing of the amorphous phase. To test this hypothesis, x-ray diffraction, ${}^{17}\mathrm{O}$ magic-angle spinning NMR, Raman, and far-infrared analyses were performed on samples of amorphous zirconium tungstate previously annealed to increasingly higher temperatures, looking for any evidence of features that could be assigned to the presence of terminal oxygen atoms. No evidence of single-bonded oxygen was found before the onset of recrystallization. Furthermore, the kinetics of the structural relaxation of $a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$ is consistent with a continuous spectrum of activation energy, spanning all the range from 1 to $2.5\mathrm{eV}$. These findings suggest that the structural relaxation of amorphous zirconium tungstate, however irreversible, is not accompanied by W-O bond breaking, but most probably characterized by a succession of (mostly) irreversible local atomic rearrangements.

Figure 1

Room-temperature, x-ray diffraction patterns of (top) pristine $\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$ and, starting from the bottom, amorphous zirconium tungstate as prepared at high pressure ($a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$) and after successive heat treatments at increasingly higher temperatures.

Figure 2

Room-temperature MAS NMR ${}^{17}\mathrm{O}$ spectra of $\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$ and amorphous ${\mathrm{ZrW}}_2{\mathrm{O}}_8$ as produced and after successive treatments at increasingly higher temperatures, as indicated at right. Asterisks mark lateral bands, and the plus signs indicate rotor bands. Vertical dashed lines mark the NMR chemical shift corresponding to the oxygen bands in the NMR spectrum of $\alpha -{\mathrm{ZrW}}_2{}^{17}\mathrm{O}_8$.

Figure 3

Room-temperature, Raman spectra of $\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$ (top) and of amorphous ${\mathrm{ZrW}}_2{}^{17}\mathrm{O}_8$, as amorphized and after thermal treatments at increasingly higher temperatures. The asterisk marks the Raman peak at $40{\mathrm{cm}}^{-1}$ assigned to a vibrational mode with large-amplitude motion of terminal oxygens [20].

Figure 4

Room-temperature, Fourier-transform far-infrared spectra of $\alpha -{\mathrm{ZrW}}_2{\mathrm{O}}_8$ and $a-{\mathrm{ZrW}}_2{}^{17}\mathrm{O}_8$ as produced and after heating to $600{}^{\circ }\mathrm{C}$ and $680{}^{\circ }\mathrm{C}$.

Figure 5

(a) Nonreversible heat flux (exo down) from three consecutive TMDSC runs with the same sample of amorphous zirconium tungstate, (b) nonreversible heat flux (exo up) obtained after subtracting from nonreversible signal measured at the first TMDSC run the average nonreversible signal from the second and third runs, for each of the three samples of amorphous zirconium tungstate used in this work, and (c) progress of the structural relaxation of $a-{\mathrm{ZrW}}_2{\mathrm{O}}_8$ as a function of temperature for the three samples studied in this work, along with the fitting of Eq. (1).

Figure 6

$L$-curve plot for the determination of the regularization parameter $\lambda$.

Figure 7

Spectrum of activation energy for the irreversible structural relaxation of amorphous zirconium tungstate obtained as (a) a sub-regularized solution, (b) the optimum solution with $\lambda$ chosen from the $L$ curve, and (c) an over-regularized solution. In these panels, $q$ represents the number density of available processes for structural relaxation.

Figure 8

Progress of the isothermal structural relaxation of amorphous zirconium tungstate simulated for different annealing temperatures.