Mechanisms of anomalous compressibility of vitreous silica

Alisha N. Clark, Charles E. Lesher, Steven D. Jacobsen, and Sabyasachi Sen

Phys. Rev. B 90, 174110 – Published 20 November 2014

Abstract

The anomalous compressibility of vitreous silica has been known for nearly a century, but the mechanisms responsible for it remain poorly understood. Using GHz-ultrasonic interferometry, we measured longitudinal and transverse acoustic wave travel times at pressures up to 5 GPa in vitreous silica with fictive temperatures $(T_{f})$ ranging between 985 °C and 1500 °C. The maximum in ultrasonic wave travel times–corresponding to a minimum in acoustic velocities–shifts to higher pressure with increasing $T_{f}$ for both acoustic waves, with complete reversibility below 5 GPa. These relationships reflect polyamorphism in the supercooled liquid, which results in a glassy state possessing different proportions of domains of high- and low-density amorphous phases (HDA and LDA, respectively). The relative proportion of HDA and LDA is set at $T_{f}$ and remains fixed on compression below the permanent densification pressure. The bulk material exhibits compression behavior systematically dependent on synthesis conditions that arise from the presence of floppy modes in a mixture of HDA and LDA domains.

Received 2 May 2014
Revised 22 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.174110

Authors & Affiliations

Alisha N. Clark^1,*, Charles E. Lesher^1,2, Steven D. Jacobsen³, and Sabyasachi Sen⁴

¹Department of Earth and Planetary Sciences, University of California, Davis, California 95616, USA
²Department of Geoscience, Aarhus University, DK-8000 Aarhus C, Denmark
³Department of Earth and Planetary Sciences, Northwestern University, Evanston, Illinois 60208, USA
⁴Department of Materials Science, University of California, Davis, California 95616, USA

^*Corresponding author: anclark@ucdavis.edu

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Issue

Vol. 90, Iss. 17 — 1 November 2014

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Images

Figure 1
Schematic diagrams of the GHz-frequency-ultrasonic interferometry experimental setup. (a) The $P$ -wave buffer rod coupled directly to a sample at 1 atm. The 100-ns GHz-frequency wave packet is produced by the GHz-frequency $P$ -wave transducer located at the base of the ${Al}_{2} O_{3}$ buffer rod. The wave packets are reflected from the buffer rod–sample interface, and the far side of the sample. Travel time is calculated from the interference of these two echoes. (b) Production of the $S$ wave from the incident $P$ wave in the high-pressure DAC assembly. Here the GHz-frequency $P$ -wave transducer is mounted on the side of the YAG buffer rod. The wave packet is converted from $P$ to $S$ waves by exploiting Snell's law at a precisely oriented face at the base of the buffer rod. The wave packet travels up the buffer rod, through the diamond, and into the sample (which is mounted flush to the diamond culet). At each interface a portion of the wave is transmitted and reflected. For high-pressure measurements the signals interfered to calculate travel time are reflected from the diamond-sample interface, and the far side of the sample. The interfered signal shown here is 100 ns with the sample signal appearing 20 ns after the diamond culet signal. Modified from [30].
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Figure 2
$P$ -wave echoes of sample $T_{f}$ = 985 °C at 0.11 ± 0.05 GPa (985_P1_61). (Top) 20-ns echoes from the diamond culet-sample boundary with two sample echoes (far side of the sample) at 854 MHz frequency. (Middle) 40-ns diamond culet signal interfered with the sample echo (at $\sim 25$ –35 ns) at 854 MHz frequency. There is positive interference with the sample and diamond echoes at this frequency corresponding to a maximum in the interferogram. (Bottom) 40-ns diamond culet signal interfered with the sample echo (at $\sim 25$ –35 ns) at 866 MHz frequency. There is negative interference with the sample and diamond echoes at this frequency corresponding to a minimum in the interferogram.
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Figure 3
(Top) Interferogram sample $T_{f}$ = 985 °C at 0.11 ± 0.05 GPa (985_P1_61) from 0.75 to 1.25 GHz. The dashed curve is the amplitude of the diamond culet signal and the solid curve is the interfered diamond culet–sample signal (see Fig. 2.) Spacing between two maxima corresponds to an integer number of wavelengths in the sample. (Bottom) Calculated travel time as a function of frequency from 0.75 to 1.25 GHz from the above interferogram. The number of wavelengths in the sample is indicated by the $m$ value. Incorrect $m$ values result in frequency-dependent travel times [e.g., $m$ (1) = 13 and 15]. Travel time is determined from the $m$ value that provides frequency-independent measurements [e.g., $m$ (1) = 14].
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Figure 4
$P$ - and $S$ -wave travel time curves normalized to the 1-atm travel time shown as circles and squares, respectively. The normalized travel time scale is offset. The intercept is $t / t_{o}$ = 1.00, with one division = 0.01. Black, gray, and white circles $(P$ wave) and squares $(S$ wave) correspond to $T_{f}$ = 985 °C, 1260 °C, and 1550 °C data sets, respectively. Decompression data are shown as triangles in contrasting colors for both $P$ - and $S$ -wave travel time curves (i.e., white and black for $T_{f}$ = 985 °C and 1550 °C, respectively). The dashed line is to guide the eye to the location of the maximum $t / t_{o}$ measurement. The gray box bounds the pressure region between the maximum travel time location, and the pressure calculated as the intersection of the extrapolated positive (anomalous) and negative (normal) limbs of the travel time curves (see text for discussion, and Appendix C in the Supplemental Material [27] for further details and data tables).
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Figure 5
Pressure associated with the maximum $t / t_{o}$ indicating the transition from anomalous to normal behavior for $P$ - and $S$ -wave data sets as a function of $T_{f}$ are shown as closed circles and squares, respectively. Linear fits to the maximum pressure associated with the maxima in $t / t_{o}$ data are also shown.
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Figure 6
Bulk $(K_{S})$ and shear $(G)$ moduli as a function of $T_{f}$ shown as closed and open circles, respectively. $K_{S}$ increases as density (and $T_{f})$ increase. $G$ is near constant over the $T_{f}$ range explored in this study. Errors shown are reported in Table 1 and for $G$ are smaller than the symbol (see Appendix B in the Supplemental Material [27]).
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