Abstract
As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.
Highlights
Theoretically, with serious discrepancy[21,22,23]; experimental studies are, extremely scarce since complete measurement of the elastic moduli remains challenging
Unlike ice[9], lattice instability in quartz and quartz-like materials was predicted to be initiated by acoustic phonon softening at Brillouin zone edge[29,30], which was thereby supposed to precede elastic instability, but an improved density-functional theory (DFT) calculation exhibited that the zone-edge frequency and a combined “elastic constants” vanish almost simultaneously[23]
It has revealed a strong nonlinearity for both C44 and C66 and an elastic instability triggered by stiffening of C14, instead of by decreasing of C44
Summary
Theoretically, with serious discrepancy[21,22,23]; experimental studies are, extremely scarce since complete measurement of the elastic moduli remains challenging. Vanishing of individual elastic constant, which usually complies with phonon softening at Brillouin zone center, has been confirmed in other compounds undergoing PIA such as ice Ih9 and B4C25, and is thereafter widely interpreted as the precursor effect to lattice instability for PIA. Based on this result, attempts to explain the microstructure of the amorphous SiO2 exhibiting elastic anisotropy and memory effects have been made[11]. We are encouraged to further investigate these issues by a unified DFT simulation of the elastic and dynamical behaviors of quartz homeotype family (SiO2, GeO2, and AlPO4) under pressure, and some parallels and contrasts between our results and those previously obtained in ice are discussed
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