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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

Structural changes commensurate with the soft K-point wave vector.Structural changes of (a) SiO2, (b) GeO2, and (c) AlPO4 from the initial α phase to the modulated phases at respectively 40, 12, and 36 GPa commensurate with the reciprocal lattice vector (1/3, 1/3, 0).
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f4: Structural changes commensurate with the soft K-point wave vector.Structural changes of (a) SiO2, (b) GeO2, and (c) AlPO4 from the initial α phase to the modulated phases at respectively 40, 12, and 36 GPa commensurate with the reciprocal lattice vector (1/3, 1/3, 0).

Mentions: To understand the transformation mechanism, the deformation behaviors of the three compounds before and after the instability were analyzed. Just before the vanishing of K-point mode, the six closing intertetrahedral angles and the two cross opening intratetrahedral angles intersect with each other (see Supplementary Fig. S3), indicating that cooperative rotations of tetrahedral units result in flattening of themselves due to nearest-neighbor intertetrahedral anion-anion repulsions20, which just creates low-energy passageways for cations to move from tetrahedral to octahedral bonding. Inspection of the topology of the opening intratetrahedral angles reveals a spiral order parallel to the c direction (see Supplementary Fig. S3), which may play an important role in originating the stiffening of most of the elastic moduli and the elastic instability. It appears like that the spiral order is strongly correlated with the emergence of a high-symmetry anion packing, as evidenced by the converging x, y, and z fractional coordinates (see Supplementary Fig. S2). The nature of the interatomic arrangement resulting from the instability was investigated by structural optimizations on a 3 × 3 × 1 supercell (commensurate with the K-point wave vector) where atoms were displaced from equilibrium along a pattern corresponding to the soft K-point mode as the starting configuration. It is shown that when the cations are shifted to the edges of the tetrahedral units under further compression, a shear instability in xy plane occurs, leading to the lateral movement of the anions with respect to each other until a denser packing containing octahedrally coordinated cations forms (see Fig. 4). Particularly, α-SiO2 transforms to quartz II phase (space group C2) with alternating layers of tetrahedral and octahedral configurations, whereas α-GeO2 to a monoclinic phase (space group C2/m) containing only GeO6 octahedra. The resulting structure for AlPO4 consists in AlO6 octahedra, PO4 tetrahedra, and PO6 octahedra, which can be artifact as PO6 octahedra was not observed until above near 80 GPa34. Those obtained post-quartz phases qualitatively reproduce the experimental observations. The transformation pathways share the same eutaxic ordering conjectured by O’Keeffe et al35, which emphasizes the balance between attractive and repulsive forces among ions, while simultaneously maximizing the density. However, consistent with the dynamical instability revealed for both cations and anions by partial phonon density of states (see Supplementary Fig. S9), the cations and anions are found to respond to pressure cooperatively rather than moving in a sequential fashion as proposed by Huang et al19. The resulting structures show different coordination environment, indicating that the transformation pathway should depend crucially on the strength of the covalent bonding, which might explain the mixed coordination configurations observed in SiO2 and AlPO4, instead of in GeO2. On releasing pressure, only the low-symmetry phase in AlPO4 reverts to the quartz-like phase, similar to the experimental observation of “memory effect” in α-AlPO4 rather than in α-SiO2 and α-GeO234.


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

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

Structural changes commensurate with the soft K-point wave vector.Structural changes of (a) SiO2, (b) GeO2, and (c) AlPO4 from the initial α phase to the modulated phases at respectively 40, 12, and 36 GPa commensurate with the reciprocal lattice vector (1/3, 1/3, 0).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4477368&req=5

f4: Structural changes commensurate with the soft K-point wave vector.Structural changes of (a) SiO2, (b) GeO2, and (c) AlPO4 from the initial α phase to the modulated phases at respectively 40, 12, and 36 GPa commensurate with the reciprocal lattice vector (1/3, 1/3, 0).
Mentions: To understand the transformation mechanism, the deformation behaviors of the three compounds before and after the instability were analyzed. Just before the vanishing of K-point mode, the six closing intertetrahedral angles and the two cross opening intratetrahedral angles intersect with each other (see Supplementary Fig. S3), indicating that cooperative rotations of tetrahedral units result in flattening of themselves due to nearest-neighbor intertetrahedral anion-anion repulsions20, which just creates low-energy passageways for cations to move from tetrahedral to octahedral bonding. Inspection of the topology of the opening intratetrahedral angles reveals a spiral order parallel to the c direction (see Supplementary Fig. S3), which may play an important role in originating the stiffening of most of the elastic moduli and the elastic instability. It appears like that the spiral order is strongly correlated with the emergence of a high-symmetry anion packing, as evidenced by the converging x, y, and z fractional coordinates (see Supplementary Fig. S2). The nature of the interatomic arrangement resulting from the instability was investigated by structural optimizations on a 3 × 3 × 1 supercell (commensurate with the K-point wave vector) where atoms were displaced from equilibrium along a pattern corresponding to the soft K-point mode as the starting configuration. It is shown that when the cations are shifted to the edges of the tetrahedral units under further compression, a shear instability in xy plane occurs, leading to the lateral movement of the anions with respect to each other until a denser packing containing octahedrally coordinated cations forms (see Fig. 4). Particularly, α-SiO2 transforms to quartz II phase (space group C2) with alternating layers of tetrahedral and octahedral configurations, whereas α-GeO2 to a monoclinic phase (space group C2/m) containing only GeO6 octahedra. The resulting structure for AlPO4 consists in AlO6 octahedra, PO4 tetrahedra, and PO6 octahedra, which can be artifact as PO6 octahedra was not observed until above near 80 GPa34. Those obtained post-quartz phases qualitatively reproduce the experimental observations. The transformation pathways share the same eutaxic ordering conjectured by O’Keeffe et al35, which emphasizes the balance between attractive and repulsive forces among ions, while simultaneously maximizing the density. However, consistent with the dynamical instability revealed for both cations and anions by partial phonon density of states (see Supplementary Fig. S9), the cations and anions are found to respond to pressure cooperatively rather than moving in a sequential fashion as proposed by Huang et al19. The resulting structures show different coordination environment, indicating that the transformation pathway should depend crucially on the strength of the covalent bonding, which might explain the mixed coordination configurations observed in SiO2 and AlPO4, instead of in GeO2. On releasing pressure, only the low-symmetry phase in AlPO4 reverts to the quartz-like phase, similar to the experimental observation of “memory effect” in α-AlPO4 rather than in α-SiO2 and α-GeO234.

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