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1.
Values of the complete adiabatic elastic tensor for single-crystal chrome-diopside (a monoclinic pyroxene mineral) are presented from 298 to 1,300 K. The data were obtained using resonant ultrasound spectroscopy (RUS). They are the first published results for the temperature T dependences of the 13 individual elastic constants C
ij
of any clinopyroxene mineral. Each C
ij
is appropriately described by a linear function in T throughout the range of T. Values for each (∂C
ij
/∂T)
P
in GPa K−1 are as follows: C
11, −0.0291; C
22, −0.0248; C
33, −0.0179; C
44, −0.0103; C
55, −0.0077; C
66, −0.0152; C
12, −0.0119; C
13, −0.0064; C
23, 0.0000; C
15, 0.0025; C
25, 0.0022; C
35, −0.0046; and C
46, 0.0026. Values of (∂M/∂T)
P
in GPa K−1, where M represents an isotropic bulk property calculated from the C
ij
data, are as follows: adiabatic bulk modulus K
S
, −0.0123; isothermal bulk modulus K
T
, −0.0178; and shear modulus G, −0.00998. Some diopside derivatives, notably (∂K
S
/∂T)
P
, (∂K
T
/∂T)
P
, and (∂V
P
/∂T)
P
, where V
P
is the compressional wave velocity, have smaller magnitudes than all other minerals of importance in Earth’s mantle, thus, confirming predictions from systematics studies. We find several dimensionless quantities for this monoclinic mineral have normal values compared to other mantle minerals. Further, αK
T
(α is the volume coefficient of thermal expansion) for diopside is approximately independent of both T and volume V at elevated temperature, so its equation of state is accurately expressed in simplified form. 相似文献
2.
The full set of elastic constants for plagioclase end-member phase albite (NaAlSi3O8) is reported for the first time. Velocities of surface acoustic waves (both Rayleigh and pseudo-surface waves) were measured using impulsively stimulated light scattering on polished surfaces having six different orientations (three normal to the Cartesian axes and three lying on diagonals). Data were inverted and results tested using several non-linear optimization techniques. Compliance moduli determined under hydrostatic compression provided additional constraints and reduced covariance in the reported constants. The Cartesian coordinate system associated with the constants (using the
unit cell) has the y-axis parallel to the crystal b axis, the x-axis parallel to a* (perpendicular to b and c) and the z-axis consistent with a right-handed coordinate system. The values of the moduli C11, C12, C13, C14, C15, C16, C22, C23, C24, C25, C26, C33, C34, C35, C36, C44, C45, C46, C55, C56, C66 and their 2σ uncertainties (in parentheses) are, respectively, 69.1(0.6), 34.0(0.7), 30.8(0.5), 5.1(0.1), −2.4(0.1), −0.9(0.1), 183.5(2.7), 5.5(2.2), −3.9(0.5), −7.7(0.7), −5.8(0.7), 179.5(2.3), −8.7(0.4), 7.1(0.6), −9.8(0.6), 24.9(0.1), −2.4(0.1), −7.2(0.1), 26.8 (0.2), 0.5(0.1), 33.5(0.2). These constants differ significantly from the previously reported pseudo-monoclinic constants that were based on velocity measurements on polysynthetic twinned crystal aggregates. Differences are consistent with systematic errors in the earlier study associated with sparse data and the presence of cracks and other imperfections. 相似文献
3.
The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4
E. K. Graham J. A. Schwab S. M. Sopkin H. Takei 《Physics and Chemistry of Minerals》1988,16(2):186-198
The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe2SiO4, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: Vp = 6.67 km/s; Vs = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)T = 5.2; (?μ/?P)T=1.5;(?K/?T)P= ?0.030 GPa/K;and,(?/?T)P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg2SiO4, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C ij for which i=j) values, and generally higher for the off-diagonal (C ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former. 相似文献
4.
Lin-gun Liu Chien-chih Chen Chung-Cherng Lin Yi-jong Yang 《Physics and Chemistry of Minerals》2005,32(2):97-102
The elastic constants of natural single-crystal aragonite (CaCO3) have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C11, C22, C33, C44, C55, C66, C12, C13 and C23 are 171.1±1.0, 110.1±0.9, 98.4±1.2, 39.3±0.6, 24.2±0.4, 40.2±0.6, 60.3±1.0, 27.8±1.6 and 41.9±2.0 GPa, respectively, for aragonite. The linear compressibilities of the a-, b- and c-axis for aragonite at ambient conditions were derived from our measured data to be 3.0±0.2, 4.2±0.2 and 7.3±0.6×10–3 GPa–1, respectively. The aggregate bulk and shear moduli for aragonite using the Voigt-Reuss-Hill (VRH) scheme are thus calculated to be 68.9±1.4 and 35.8±0.2 GPa, respectively. The value of bulk modulus is in remarkable contrast to the literature value of 46.9 GPa measured almost a century ago. Our new datum, however, is closer to that derived from recent atomistic simulation and static compression studies. 相似文献
5.
The adiabatic single-crystal elastic moduli of a natural sample of monticellite (CaMgSiO4), with the olivine crystal structure, have been measured under ambient conditions using Brillouin spectroscopy. From the single-crystal moduli the aggregate bulk and shear moduli are calculated to be K
s=106±1 and = 55.2±0.4 GPa, respectively. These results are consistent with a systematic decrease in bulk modulus with increasing molar volume among the olivine-structured silicates. The longitudinal moduli decrease in the order c
11>c
33>c22, indicating that the structure is stiffest along the a axis and most compliant along the b axis. This relationship among the longitudinal moduli holds for all silicate and germanate olivines, and is thus inferred to result from the topology of the olivine crystal structure. However, the moduli obtained in this study are at variance with previous conclusions concerning deviations from the Cauchy relations (e.g. c
12=c
44). For monticellite, off-diagonal shear moduli of the c
12-type are uniformly greater than pure shear moduli such as c
44. Similar behavior is found in pyroxenes such as diopside. The relative magnitudes of shear and off-diagonal moduli are not, therefore, a diagnostic chemical signature in minerals with complex crystal structures.Department of Applied Physics, Stanford University, Stanford CA, USA 相似文献
6.
The crystal structure of akermanite, Ca2Mg-Si2O7, consists of mixed tetrahedral sheets formed by [MgO4] tetrahedra and [Si2O7] groups interleaved along the c axis with Ca2+ ions in eight-fold coordination. Above 358 K, the structure is tetragonal
, and below it is incommensurate with modulations parallel to [110] and
. The elastic stiffness moduli, C
ij of the incommensurate phase at room temperature were measured from wave velocities in the 20–75 MHz carrier frequency range by the ultrasonic phase comparison method using optically clear synthetic single crystal plates (3×3×2 mm) oriented parallel to (100), (001), (110) and (101) planes. The C
ij values (GPa) are: C
11 159.40, C
33 149.43, C
44 30.26, C
66 58.10, C
12 76.58 and C
13 57.80. In (010) and (001) planes, the compressional modulus, V
2(L) from the longitudinal wave, L is considerably larger than the shear moduli, V
2(T1, T
2) both from the in-plane and perpendicular-to-plane shear waves, T
1 and T
2. The relatively small values of the shear moduli indicate the ease of tetrahedral rotations in response to in-plane and perpendicular-to-plane shears and may provide preconditions for structural changes involving shear-type atomic movements. 相似文献
7.
G. D. Gwanmesia J. Liu G. Chen S. Kesson S. M. Rigden R. C. Liebermann 《Physics and Chemistry of Minerals》2000,27(7):445-452
Dense isotropic polycrystalline specimens of majorite-rich garnets (Py100, Py62Mj38, Py50Mj50, Py21Mj79 and Mj100) along the pyrope (Mg3Al2Si3O12 = Py100)-majorite (MgSiO3 = Mj100) join were fabricated in a 2000-ton uniaxial split-sphere anvil apparatus (USSA-2000) at pressures from 10 to 18.5 GPa and
temperatures from 1200 to 1850 °C, within their stability fields in runs of 2–4-h duration, using hot-pressing techniques
developed by Gwanmesia et al. (1993). These specimens are single-phased, fine-grained (≤5 mm), free of microcracks, and have
bulk densities greater than 99% of the corresponding single-crystal X-ray density. Elastic compressional (P) and shear (S) wave velocities were determined at room pressure and temperature for these polycrystalline garnet specimens by phase comparison
ultrasonic interferometry. For Mj100, the P and S wave velocities are within 1% of the Hashin-Shtrikman averages calculated from the single crystal elastic moduli measured
by Brillouin spectroscopy. Both the elastic bulk modulus (K) and the shear modulus (G) decrease continuously with increasing majorite content from pyrope garnet (Py100) to pure majorite garnet (Mj100). The compositional dependence of K and G are given by K = 172.3 (40) − 0.085X, and G = 91.6 (10) − 0.038X, where X = mol% majorite), respectively, indicating that substitution of Si for Mg and Al decreases both K and G by about 5% along the solid solution series.
Received: 25 March 1999 / Accepted: 12 July 1999 相似文献
8.
The adiabatic single-crystal elastic moduli of superhydrous B, Mg10Si3O14(OH)4, have been measured at ambient conditions using Brillouin spectroscopy. This material is the first hydrous phase found to be stable at the extreme conditions of 20 GPa and 1400 °C. The single-crystal moduli, in GPa, are: C 11=280.0±1.5, C 22=307.4±1.6, C 33=293.4±1.4, C 44=90.0±1.1, C 55=99.2±0.8, C 66=89.6±0.6, C 12=66.1±2.2, C 13=105.6±2.6, C 23=81.8±2.6. With aggregate elastic properties of K VRH =154.0±4.2 and μ VRH =97.0±0.7 GPa, superhydrous B is approximately 16% suffer than forsterite and 20% softer than magnesium silicate spinel; it is also considerably more elastically isotropic than forsterite. The single-crystal moduli are compared to those of forsterite, magnesium silicate spinel and periclase, materials that are both structurally and compositionally similar to superhydrous B. The longitudinal moduli of superhydrous B and forsterite follow similar trends and appear to be dominated by the incompressibility and rotation of silicon tetrahedra. The shear and off-diagonal moduli more closely resemble those of periclase and spinel and may reflect the properties inherent to layers of magnesium octahedra. 相似文献
9.
The ambient pressure elastic properties of a natural clinopyroxene (C2/c symmetry) from Kilbourne Hole, NM have been determined.
In terms of end-members, diopside (CaMgSi2O6), hedenbergite (CaFeSi2O6), jadeite (NaAlSi2O6), cosmochlor (NaCrSi2O6), and Mg-Tschermak (MgAl(AlSi)O6), its composition is Di72He9Jd3Cr3Ts12. The analytic density, based on chemistry and cell parameters is 3.327 (0.003) g/cm3. The elastic constants [c11, c12, c13, c15, c22, c23, c25, c33, c35, c44, c46, c55, c66] are [273.8 (0.9), 83.5 (1.3), 80.0 (1.1), 9.0 (0.6), 183.6 (0.9), 59.9 (1.6), 9.5 (1.0), 229.5 (0.9), 48.1 (0.6), 76.5 (0.9),
8.4 (0.8), 73.0 (0.4), 81.6 (1.0)] GPa where uncertainties are reported at the 95% confidence level. The aggregate (mean of
Hashin-Strikman bounds) adiabatic bulk modulus is 117.2 (0.7) GPa, and the shear modulus is 72.2 (0.2) GPa. Although measured
moduli are broadly consistent with trends in elasticity versus atomic volume, deviations from the systematics would produce
significant (percent level) changes in calculated velocities for candidate mantle mineral assemblages. The compositional dependence
of elasticity for several clinopyroxenes is explored on the basis of just the Di+He and Jd+Ts mole fractions. The bulk modulus
lies within experimental uncertainties of the linear mixture of end-member properties while the shear modulus deviates by
3%.
Received: 29 September 1997 / Revised, accepted: 4 March 1998 相似文献
10.
Elastic moduli of forsterite were measured between 300 and 1,200 K (? 1.6 times the Debye temperature) by the Rectangular Parallelepiped Resonance method. All the moduli decrease regularly with temperature. A summary of the results is as follows: