### Abstract

The single-crystal elastic moduli, c_{ij} x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni_{2}SiO_{4} olivine: c_{11}=3.40(2), c_{22}=2.38(2), c_{33}=2.53(2), c_{44}=0.71(1), c_{55}=0.87(1), c_{66}=0.78(1), c_{12}=1.09(2), c_{13}=1.10(4), c_{23}=1.13(3), Ni_{2}SiO_{4} spinel: c_{11}=3.66(3), c_{44}=1.06(1), c_{12}=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c_{11}>c_{33}>c_{22}, regardless of composition. The moduli c_{55} and c_{66} are approximately equal, and greater than c_{44}. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO_{4} tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of {Mathematical expression} and {Mathematical expression}. When transition-metal cations are six-coordinated by oxygen {Mathematical expression}, and when alkaline-earth cations are six-coordinated {Mathematical expression}. The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni_{2}SiO_{4} (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni_{2}SiO_{4} are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the c_{ij}'s and shear modulus of a spinel-structure silicate to be estimated from c_{11} of the corresponding α phase and the bulk modulus of the γ phase.

Original language | English (US) |
---|---|

Pages (from-to) | 261-272 |

Number of pages | 12 |

Journal | Physics and Chemistry of Minerals |

Volume | 10 |

Issue number | 6 |

DOIs | |

State | Published - May 1 1984 |

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### ASJC Scopus subject areas

- Materials Science(all)
- Geochemistry and Petrology

### Cite this

_{2}SiO

_{4}.

*Physics and Chemistry of Minerals*,

*10*(6), 261-272. https://doi.org/10.1007/BF00311951

**Elasticity of the olivine and spinel polymorphs of Ni _{2}SiO_{4}.** / Bass, Jay D.; Weidner, Donald J.; Hamaya, N.; Ozima, M.; Akimoto, S.

Research output: Contribution to journal › Article

_{2}SiO

_{4}',

*Physics and Chemistry of Minerals*, vol. 10, no. 6, pp. 261-272. https://doi.org/10.1007/BF00311951

_{2}SiO

_{4}. Physics and Chemistry of Minerals. 1984 May 1;10(6):261-272. https://doi.org/10.1007/BF00311951

}

TY - JOUR

T1 - Elasticity of the olivine and spinel polymorphs of Ni2SiO4

AU - Bass, Jay D.

AU - Weidner, Donald J.

AU - Hamaya, N.

AU - Ozima, M.

AU - Akimoto, S.

PY - 1984/5/1

Y1 - 1984/5/1

N2 - The single-crystal elastic moduli, cij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni2SiO4 olivine: c11=3.40(2), c22=2.38(2), c33=2.53(2), c44=0.71(1), c55=0.87(1), c66=0.78(1), c12=1.09(2), c13=1.10(4), c23=1.13(3), Ni2SiO4 spinel: c11=3.66(3), c44=1.06(1), c12=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c11>c33>c22, regardless of composition. The moduli c55 and c66 are approximately equal, and greater than c44. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO4 tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of {Mathematical expression} and {Mathematical expression}. When transition-metal cations are six-coordinated by oxygen {Mathematical expression}, and when alkaline-earth cations are six-coordinated {Mathematical expression}. The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni2SiO4 (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni2SiO4 are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the cij's and shear modulus of a spinel-structure silicate to be estimated from c11 of the corresponding α phase and the bulk modulus of the γ phase.

AB - The single-crystal elastic moduli, cij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni2SiO4 olivine: c11=3.40(2), c22=2.38(2), c33=2.53(2), c44=0.71(1), c55=0.87(1), c66=0.78(1), c12=1.09(2), c13=1.10(4), c23=1.13(3), Ni2SiO4 spinel: c11=3.66(3), c44=1.06(1), c12=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c11>c33>c22, regardless of composition. The moduli c55 and c66 are approximately equal, and greater than c44. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO4 tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of {Mathematical expression} and {Mathematical expression}. When transition-metal cations are six-coordinated by oxygen {Mathematical expression}, and when alkaline-earth cations are six-coordinated {Mathematical expression}. The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni2SiO4 (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni2SiO4 are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the cij's and shear modulus of a spinel-structure silicate to be estimated from c11 of the corresponding α phase and the bulk modulus of the γ phase.

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U2 - 10.1007/BF00311951

DO - 10.1007/BF00311951

M3 - Article

AN - SCOPUS:0021364008

VL - 10

SP - 261

EP - 272

JO - Physics and Chemistry of Minerals

JF - Physics and Chemistry of Minerals

SN - 0342-1791

IS - 6

ER -