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Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

Dong J, Zhu H, Chen D - Sci Rep (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China.

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.

No MeSH data available.


Related in: MedlinePlus

Born coefficient B3 and soft acoustic mode elastic constants.(a)–(c) Born coefficient B3 and (d)–(f) soft acoustic mode elastic constant ρν2 of α-SiO2, α-GeO2, and α-AlPO4 as a function of pressure. In (a)–(c), the respective contributions of C66C44 (solid circles) and  (solid triangles) to B3 (solid squares) are shown. The open circles are  with  being the maximum value of C44. The dashed arrows represent the pressures where C44 crosses with C14. In (d)–(f), the variation of C44 and the calculated zone-edge K- and M-point soft mode frequencies with pressure are also displayed. The gray areas indicate the amorphization boundaries determined from the experiments202436.
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f2: Born coefficient B3 and soft acoustic mode elastic constants.(a)–(c) Born coefficient B3 and (d)–(f) soft acoustic mode elastic constant ρν2 of α-SiO2, α-GeO2, and α-AlPO4 as a function of pressure. In (a)–(c), the respective contributions of C66C44 (solid circles) and (solid triangles) to B3 (solid squares) are shown. The open circles are with being the maximum value of C44. The dashed arrows represent the pressures where C44 crosses with C14. In (d)–(f), the variation of C44 and the calculated zone-edge K- and M-point soft mode frequencies with pressure are also displayed. The gray areas indicate the amorphization boundaries determined from the experiments202436.

Mentions: Figure 2a,b,c and Supplementary Fig. S7 display the computed pressure dependence of these coefficients. For α-SiO2, B1 and B2 both increase with pressure, while B3 decreases rapidly beyond 18 GPa and become negative around 38 GPa. Similar behavior for the three Born criteria is observed in the reported experimental results5 and theoretical studies2223. Brillouin scattering experiment suggested B3 = 0 at 39 GPa, in comparison with about 30 GPa given by first-principles calculations. Nevertheless, there are vital differences in the determination of what triggers the mechanical instability. First-principles calculation by Binggeli et al22 predicted that neither C66 nor C44 would vanish in the pressure region of amorphization and thus vanishing of C66 or C44 is not the cause of instability. On the contrary, Brillouin scattering study by Gregoryanz el al.5 revealed that the violation of B3 is triggered by softening of C44, because they found that B3 and C44 would approach zero around the same pressure. For convenience, we show in Fig. 2a the respective contributions of C66C44 and to B3 obtained from present DFT study. They both go through a minimum near 10 GPa and then increase, but has a much greater pressure derivative than C66C44 above 18 GPa. The effect of C44 can be unveiled by constraining it to a constant (see Fig. 2a): the resulting pressure of B3 = 0 only shows a small positive shift of about 1 GPa, meaning that stiffening of C14 prevails over softening of C44. Surprisingly, it indicates that the violation of B3 is dominated by hardening of C14; the cases of α-GeO2 and α-AlPO4 are similar (see Fig. 2b,c), thereby strongly suggesting that the mechanical instability driven by stiffening of C14 may be a universal feature of quartz-like materials. Of special interest is the crossover pressures of C14 and C44 (dashed arrows in Fig. 2a,b,c), which are close to that of B3 = 0 and thus can serve as a good estimate for elastic instability. The very fact of that the reported beginning pressures of PIA in quartz and quartz-like compounds by various experiments (gray areas in Fig. 2a,b,c) generally correspond to the onset of the rapid decrease of B3 confirms that the elastic stability actually defines a homogeneous upper limit for the crystalline phase to persist.


Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

Dong J, Zhu H, Chen D - Sci Rep (2015)

Born coefficient B3 and soft acoustic mode elastic constants.(a)–(c) Born coefficient B3 and (d)–(f) soft acoustic mode elastic constant ρν2 of α-SiO2, α-GeO2, and α-AlPO4 as a function of pressure. In (a)–(c), the respective contributions of C66C44 (solid circles) and  (solid triangles) to B3 (solid squares) are shown. The open circles are  with  being the maximum value of C44. The dashed arrows represent the pressures where C44 crosses with C14. In (d)–(f), the variation of C44 and the calculated zone-edge K- and M-point soft mode frequencies with pressure are also displayed. The gray areas indicate the amorphization boundaries determined from the experiments202436.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4477368&req=5

f2: Born coefficient B3 and soft acoustic mode elastic constants.(a)–(c) Born coefficient B3 and (d)–(f) soft acoustic mode elastic constant ρν2 of α-SiO2, α-GeO2, and α-AlPO4 as a function of pressure. In (a)–(c), the respective contributions of C66C44 (solid circles) and (solid triangles) to B3 (solid squares) are shown. The open circles are with being the maximum value of C44. The dashed arrows represent the pressures where C44 crosses with C14. In (d)–(f), the variation of C44 and the calculated zone-edge K- and M-point soft mode frequencies with pressure are also displayed. The gray areas indicate the amorphization boundaries determined from the experiments202436.
Mentions: Figure 2a,b,c and Supplementary Fig. S7 display the computed pressure dependence of these coefficients. For α-SiO2, B1 and B2 both increase with pressure, while B3 decreases rapidly beyond 18 GPa and become negative around 38 GPa. Similar behavior for the three Born criteria is observed in the reported experimental results5 and theoretical studies2223. Brillouin scattering experiment suggested B3 = 0 at 39 GPa, in comparison with about 30 GPa given by first-principles calculations. Nevertheless, there are vital differences in the determination of what triggers the mechanical instability. First-principles calculation by Binggeli et al22 predicted that neither C66 nor C44 would vanish in the pressure region of amorphization and thus vanishing of C66 or C44 is not the cause of instability. On the contrary, Brillouin scattering study by Gregoryanz el al.5 revealed that the violation of B3 is triggered by softening of C44, because they found that B3 and C44 would approach zero around the same pressure. For convenience, we show in Fig. 2a the respective contributions of C66C44 and to B3 obtained from present DFT study. They both go through a minimum near 10 GPa and then increase, but has a much greater pressure derivative than C66C44 above 18 GPa. The effect of C44 can be unveiled by constraining it to a constant (see Fig. 2a): the resulting pressure of B3 = 0 only shows a small positive shift of about 1 GPa, meaning that stiffening of C14 prevails over softening of C44. Surprisingly, it indicates that the violation of B3 is dominated by hardening of C14; the cases of α-GeO2 and α-AlPO4 are similar (see Fig. 2b,c), thereby strongly suggesting that the mechanical instability driven by stiffening of C14 may be a universal feature of quartz-like materials. Of special interest is the crossover pressures of C14 and C44 (dashed arrows in Fig. 2a,b,c), which are close to that of B3 = 0 and thus can serve as a good estimate for elastic instability. The very fact of that the reported beginning pressures of PIA in quartz and quartz-like compounds by various experiments (gray areas in Fig. 2a,b,c) generally correspond to the onset of the rapid decrease of B3 confirms that the elastic stability actually defines a homogeneous upper limit for the crystalline phase to persist.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China.

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.

No MeSH data available.


Related in: MedlinePlus