首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
The adiabatic elastic stiffness constants of synthetic single-crystal MnO were measured in this study using pulse superposition interferometry. Data were obtained up to 1.0 GPa in pressure and over the temperature range 273 to 473 K. As a result, we were able to determine the complete set of second-order stiffness moduli (C ij s ) and their pressure and temperature derivatives, as well as higher-order properties for selected modes. Relevant results for the adiabatic bulk modulus are: K s=155.1±0.8 GPa; (Ks/P)T=4.70±0.13; and, (K s/T)P= -0.0203±0.0009 GPa/K. Our results for the second-order moduli are generally consistent with the data from previous studies. However, relative to the estimated uncertainties, small and systematic discrepancies appear to characterize the data set. The available evidence indicates that the differences result from microstructural variations (in particular, microcracks and Mn3O4 inclusions) between the synthetic MnO specimens used in different investigations. The pure shear mode C 44 exhibits anomalous soft-mode behavior with both temperature (the ambient derivative is positive) and pressure (the ambient derivative is negative). In both cases the C 44 data trends appear to primarily reflect the influence of Mn-Mn magnetoelastic interactions associated with the onset of a paramagnetic-antiferromagnetic (PM AFM) phase transition.  相似文献   

2.
Brillouin spectroscopy was used to measure the single crystal elastic properties of a pure synthetic pyrope and a natural garnet containing 89.9 mol% of the pyrope end member (Mg3Al2Si3O12). The elastic moduli, c ij , of the two samples are entirely consistent and agree with previous estimates of the elastic properties of pyrope based upon the moduli of solid solutions. Our results indicate that the elastic moduli of pyrope end-member are c 11=296.2±0.5, c 12=111.1±0.6, c 44=91.6±0.3, Ks=172.8±0.3, =92.0±0.2, all in units of GPa. These results differ by several percent from those reported previously for synthetic pyrope, but are based upon a much larger data set. Although the hydrous components of the two samples from the present study are substantially different, representing both dry and saturated samples, we find no discernable effect of structurally bound water on the elastic properties. This is due to the small absolute solubility of water in pyrope, as compared with other garnets such as grossular.  相似文献   

3.
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   

4.
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   

5.
The bulk modulus, K 0, and its pressure derivative K0, of -(Mg0.6, Fe0.4)2SiO4 have been accurately determined to 50.0 GPa under hydrostatic conditions at room temperature in a diamond cell using synchrotron radiation. Our results agree with Brillouin and ultrasonic measurements on -Mg2SiO4 at low pressure, indicating normal elastic behaviour in the metastable pressure range of this high pressure mineral. Our values of K 0 and k0 are 183.0 GPa and 5.4, respectively.  相似文献   

6.
The adiabatic elastic moduli of a single crystal of Neighborite (NaMgF 3 perovskite) have been measured at ambient conditions using Brillouin spectroscopy. The adiabatic aggregate (Voight-Reuss-Hill) bulk modulus is K = 75.6 GPa, and shear modulus is = 46.7 GPa. The experimental results show the ratio of linear compressibilities b / a = 0.80 for neighborite. These ratios reflect the different amounts of tilting freedom of the octahedral framework along each lattice axis of the perovskite structure. It is understood that the elastic compliance S ij of the crystal can directly sense the behavior of the octahedral tilting in the structural distortion of NaMgF3 perovskite. The octahedral tilting angles are considered to be the order parameters of the ferroelastic phase transition in the perovskite structure. Single crystal elasticity data provide a basis for understanding the role of octahedral tilting in the ferroelasticity of perovskite. Together with high pressure compressional data, one can thus elucidate the relationship between crystal structure and physical properties of perovskite. A detailed assessment indicates that the dominant compression mechanism for NaMgF3 perovskite is shortening of the octahedral [MgF] bond, which is also true for orthorhombically distorted MgSiO3 perovskite.  相似文献   

7.
The second-order elastic constants up to 30 GPa, which encompass the stability field of the spinel forms, their pressure derivatives and the third-order elastic constants of both hydrous and anhydrous -Mg2SiO4 have been obtained theoretically. A combination of deformation theory and finite strain elasticity theory has been employed to arrive at the expressions for second-order and third-order elastic constants from the strain energy of the lattice. The strain energy is calculated by taking into account the interactions up to second nearest neighbours in the -Mg2SiO4 lattice. This is then compared with the strain-dependent lattice energy from continuum model approximation to obtain the expression of elastic constants. The second-order elastic constants Cij compare favourably with the measurements in the case of anhydrous as well as hydrous -Mg2SiO4 and with other calculations on the anhydrous phase. All the third-order elastic constants of both the compounds are negative. The third-order elastic constant C144(–52.41 and –45.07 GPa for anhydrous and hydrous -Mg2SiO4, respectively) representing the anisotropy of shear mode has a smaller value than C111 (–2443.94 and –2101.25 GPa for anhydrous and hydrous phases, respectively), which corresponds to the longitudinal mode. The pressure-induced variations in the longitudinal elastic constants (i.e.,dC11/dp) are relatively large (4.08 and 4.09 for dry and hydrous ringwoodite, respectively) compared with those for the shear (0.22 and 0.32 for dry and hydrous ringwoodite, respectively) and off-diagonal constants (1.40 and 1.41 for dry and hydrous ringwoodite, respectively). The variation of the shear moduli Cs and anisotropy factor A with pressure have also been studied. The average value of elastic anisotropy is 0.835 in the case of anhydrous -Mg2SiO4 and 0.830 in the hydrous phase. The reversal of sign of the Cauchy pressure C12 – C44, which describes the angular character of atomic bonding in metals and other compounds, at around 21 GPa for both the compounds may be a precursor to the phase transition from ringwoodite to periclase and perovskite at an elevated temperature. The aggregate elastic properties like the adiabatic bulk modulus K (175.4 and 150.2 GPa for anhydrous and hydrous phases, respectively), and the isotropic compressional (P) and shear (S) wave velocities were calculated and the mode Grüneisen Parameters (GPs) of the acoustic waves were determined based on the quasi-harmonic approximation. The low temperature limit of both hydrous and anhydrous phases of -Mg2SiO4 are positive (1.69 and 1.78, respectively, for hydrous and anhydrous phases) and hence we expect the thermal expansion to be positive down to absolute zero. The Anderson–Grüneisen parameter obtained for hydrous as well as anhydrous phases of -Mg2SiO4 from the second-order and third-order elastic constants are 2.30 and 2.29, respectively.  相似文献   

8.
Twenty-one energy-dispersive X-ray diffraction spectra for fayalite at 400° C constitute the basis for an elevated-temperature static compression isotherm for this important silicate mineral. A Murnaghan regression of the resulting molar volumes yields 103.8 GPa and 7.1 for the 400° C, room-pressure values of the isothermal bulk modulus (K 0) and its first pressure derivative (K0), respectively. When compared to the room-temperature static compression isotherm of Yagi et al. (1975), our 400° C value for K 0 yields 5.4 ×10–2 GPa/deg for (K/T)00. When combined with literature volume data, our measurements indicate that the fayalite isochores are strongly concave toward the pressure axis [( 2 T/P 2 ) v <>This is publication number 1125 of the School of Earth Sciences, Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455, USA  相似文献   

9.
The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, , consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log10 units of time above . In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; S = S/G (where S is the shear relaxation time, G is the shear modulus at infinite frequency and S is the zero frequency shear viscosity). The value of G known for SiO2 and several other silicate glasses. The shear modulus, G , and the bulk modulus, K , are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to S, G may be considered a constant (independent of composition and temperature) and the value of S, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.For silicate melts, the relaxation times calculated from the Maxwell relationship agree well with available data for the onset of the frequency-dependence (dispersion) of acoustic velocities, the onset of non-Newtonian viscosities, the scan-rate dependence of the calorimetric glass transition, with the timescale of an oxygen diffusive jump and with the Si-O bond exchange frequency obtained from 29Si NMR studies.  相似文献   

10.
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   

11.
 Physical properties including the equation of state, elasticity, and shear strength of pyrite have been measured by a series of X-ray diffraction in diamond-anvil cells at pressures up to 50 GPa. A Birch–Murnaghan equation of state fit to the quasihydrostatic pressure–volume data obtained from laboratory X-ray source/film techniques yields a quasihydrostatic bulk modulus K 0T =133.5 (±5.2) GPa and bulk modulus first pressure derivative K ′ 0T =5.73 (±0.58). The apparent equation of state is found to be strongly dependent on the stress conditions in the sample. The stress dependency of the high-pressure properties is examined with anisotropic elasticity theory from subsequent measurements of energy-dispersive radial diffraction experiments in the diamond-anvil cell. The calculated values of K 0T depend largely upon the angle ψ between the diffracting plane normal and the maximum stress axis. The uniaxial stress component in the sample, t=σ3−σ1, varies with pressure as t=−3.11+0.43P between 10 and 30 GPa. The pressure derivatives of the elastic moduli dC 11/dP=5.76 (±0.15), dC 12/dP=1.41 (±0.11) and dC 44/dP=1.92 (±0.06) are obtained from the diffraction data assuming previously reported zero-pressure ultrasonic data (C 11=382 GPa, C 12=31 GPa, and C 44=109 GPa). Received: 21 December 2000 / Accepted: 11 July 2001  相似文献   

12.
The elastic moduli of single crystals of pyrope-rich garnet and San Carlos olivine have been measured over a 3 GPa pressure range at room temperature. The combination of improved ultrasonic techniques and this large pressure range provide for more reliable characterization of the pressure dependence of acoustic wave velocities than has previously been possible. First and second pressure derivatives of the velocities have been determined within 1 percent and 10 percent respectively. The Hashin-Shtrikman bounds for the pressure dependences of the bulk and shear moduli of the garnet used in this study are; K = 173.6 GPa, K = 4.93, K = –0.28 GPa–1, G= 94.9 GPa, G = 1.56, G = –0.08 GPa–1 and the Hashin-Shtrikman least-upper bounds and greatestlower bounds for the pressure dependences of the bulk and shear moduli of the San Carlos olivine are K=129.8 GPa, K = 4.66, K= –0.15 GPa–1, G = 77.8 GPa, G = 1.93, G = –0.11 GPa–1 and K = 129.2 GPa, K = 4.63, K= –0.15 GPa–1 G = 77.3 GPa, G=1.96, G = –0.11 GPa–1 respectively. The determination of the room-pressure elastic moduli of this pyrope-almandine garnet removes the previously observed anomaly in the predictions of systematic treatments of variations of the elastic moduli of garnets with composition. The determination of the second pressure derivatives of the moduli of garnet and olivine illustrates the importance of these terms in extrapolations to higher pressures — with K/P for these crystals being reduced by 17 percent and 9 percent respectively over the 3 GPa pressure range.  相似文献   

13.
The thirteen single-crystal elastic moduli for diopside as determined by the acoustic technique based on Brillouin scattering are: c11=2.23, c22=1.71, c33=2.35, c44=0.74, c55=0.67, c66=0.66, c12=0.77, c13=0.81, c15=0.17, c23=0.57, c25=0.07, c35=0.43, c46=0.073. The Reuss bound of the adiabatic bulk and shear moduli calculated from these data are K s=1.08 Mbar and G=0.651 Mbar. The room-pressure isothermal bulk modulus, K T , and the pressure derivative of the bulk modulus, K′ T have also been determined on a four-circle diffractometer, from a single crystal mounted in a gasketed opposed-anvil diamond cell, giving values of K T =1.13 Mbar and K′ T =4.8. The principal axes of the strain ellipsoid, calculated from the elastic moduli and observed in the static compression data, are identical, and the linear compressibilities are in reasonable agreement. The single-crystal elastic moduli can be correlated with the structural features of diopside.  相似文献   

14.
The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, C v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C v and other previously measured thermodynamic parameters, the thermal expansion coefficient, , at room temperature was calculated from = K S (T/P) S C V/TVK T, which yields a constant value of ( ln / ln V)T= 6.1(5) for forsterite to 10% compression. This value is in agreement with ( ln / ln V)T for a large variety of materials.At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.  相似文献   

15.
The elastic properties of two types of aluminosilicate (basaltic and rhyolitic) glasses have been studied using both Brillouin and Raman spectroscopy at ambient conditions. It has been found that the elastic moduli of the basaltic glasses decrease with increasing SiO2 concentration. The shear moduli displayed the least dependence on SiO2 content. The bulk moduli of the basaltic glasses strongly depend on the sum of the Q 3 and Q 4 anionic units. Among the modifiers, iron cations showed the strongest effect on the elastic properties of the rhyolitic glasses. For the elastic moduli of rhyolitic glasses, the major effect of alkaline earth cations is on shear modulus; however, both iron and alkali cations showed stronger effects on bulk modulus and similar relative contribution between bulk and shear moduli (based on the equivalent M+ cation). The dependences of elastic moduli on bulk NBO/T observed in both types of glasses suggest that the elastic modulus of an aluminosilicate glass depends on the concentration of effective modifying cations rather than the apparent concentration of all non-network-forming cations. An analysis of data also indicated that the ideal molar mixing model is failed in prediction of the elastic properties of the present multicomponent glasses by using the known parameters.  相似文献   

16.
The single crystal elastic constants of nonmetamict zircons have been measured as a function of pressure to 12 kb at room temperature and also as a function of temperature between 25 and 300° C at atmospheric pressure. The pressure derivatives of the elastic constants are: C 11=10.78, C 33=5.88, C 44=0.99, C 66=?0.31, C 12=3.24, C 13=6.20. The anomalous negative behaviour of C 66 versus pressure could be associated with a high pressure phase transition. The pressure and temperature derivatives of the isotropic elastic wave velocities and elastic moduli for nonmetamict zircon are calculated from the present single crystal data by the Voigt, Ruess, and Hill approximations and compared with the values of some other oxides and silicates. The pressure derivative of the isotropic adiabatic bulk modulus is relatively high (dK S/dP=6.50), and the pressure derivative of the shear modulus is relatively low, (dG/dP=0.78), compared to the corresponding values for some other oxides and silicates. The Debye temperature, ?D, and the high temperature limit of the Grüneisen parameter, γHt, calculated from the elastic constants and their pressure derivatives, agrees well with the Debye temperature and the thermal Grüneisen parameter, γth, calculated from the thermal expansion, heat capacity, and compressibility data.  相似文献   

17.
Titania, TiO2, precipitation in natural blue sapphire (Fe, Ti: -Al2O3) has been investigated using high resolution and analytical transmission electron microscopy. The structure and habit of the TiO2 precipitate depends on both the Ti4+ concentration and the temperature at which the precipitate formed. Tetragonal TiO2 (Rutile) grows at 1350° C but at 1150° C an orthorhombic non-equilibrium TiO2 polymorph precipitates. Both TiO2 polymorphs nucleate in the (0001)s plane as lens shaped discs twinned along their diameter. The crystallographic alignment of each type of TiO2 precipitate with respect to the -Al2O3 host matrix provides a high degree of structural coherency with minimal lattice mismatch. Electron diffraction analysis established the following precipitate/host orientation relationships: tetragonal TiO2: {011}r {11 07B;100}r(0001)s and 01 r10 0s twinned along the (011)r planeand orthorhombic TiO2: {021}{11 0}s, {100}(0001)s and 0 2 10 0s twinned along the (021) plane.  相似文献   

18.
New high-pressure orthorhombic (GdFeO3-type) perovskite polymorphs of MnSnO3 and FeTiO3 have been observed using in situ powder X-ray diffraction in a diamond-anvil cell with synchrotron radiation. The materials are produced by the compression of the lithium niobate polymorphs of MnSnO3 and FeTiO3 at room temperature. The lithium niobate to perovskite transition occurs reversibly at 7 GPa in MnSnO3, with a volume change of -1.5%, and at 16 GPa in FeTiO3, with a volume change of -2.8%. Both transitions show hysteresis at room temperature. For MnSnO3 perovskite at 7.35 (8) GPa, the orthorhombic cell parameters are a=5.301 (2) A, b=5.445 (2) Å, c=7.690 (8) Å and V= 221.99 (15) Å3. Volume compression data were collected between 7 and 20 GPa. The bulk modulus calculated from the compression data is 257 (18) GPa in this pressure region. For FeTiO3 perovskite at 18.0 (5) GPa, cell parameters are a=5.022 (6) Å, b=5.169 (5) Å, c=7.239 (9) Å and V= 187.94 (36) Å3. Based on published data on the quench phases, the FeTiO3 perovskite breaks down to a rocksalt + baddelyite mixture of FeO and TiO2 at 23 GPa. This is the first experimental verification of the pressure-induced breakdown of a perovskite to simple oxides.  相似文献   

19.
Thirteen energy-dispersive x-ray diffraction spectra for -Fe2SiO4 (spinel) collected in situ at 400° C and pressures to 24 GPa constitute the basis for an elevated-temperature static compression isotherm for this important high-pressure phase. A Murnaghan regression of these molar volume measurements yields 177.3 (±17.4) GPa and 5.4(±2.5) for the 400° C, room pressure values of the isothermal bulk modulus (K P 0) and its first pressure derivative (K P 0), respectively. When compared to the room-Tdeterminations of K P 0 available in the literature, our 400° C K P 0 yields -4.1 (±6.2)×10-2 GPa/degree for the average value of (K/T) P 0 over the temperature interval 25° C<><400°>A five-parameter V(P, T) equation for -Fe2SiO4 based on simultaneous regression of our data combined with the elevated P-Tdata of Yagi et al. (1987) and the extrapolated thermal expansion values from Suzuki et al. (1979) yields isochores which have very little curvature [(2 T/P 2) v 0], in marked contrast to the isochores for fayalite (Plymate and Stout 1990) which exhibit pronounced negative curvature [(T/P 2) v <0]. along=" the=">-Fe2SiO4 reaction boundary VRvaries from a minimum of approximately 8.3% at approximately 450° C to approximately 8.9% at 1200° C. Extrapolation of the fayalite and -Fe2SiO4 V(P, T) relationships to the temperature and pressure of the 400 km discontinuity suggests a V R of approximately 8.4% at that depth, approximately 10% less than the 9.3% V R at ambient conditions.  相似文献   

20.
The torsional mode frequency t in Cs1–xRbx-Vermiculite has been determined using an angular force constant model and a virtual crystal approximation. The sensitivity of t has been examined with respect to the force constants between the Kagome' oxygen frame and the interlayer cations. These force constants were used to calculate the longitudinal elastic constants, C11 and C33 and are consistent with the observed elastic anisotropy in related layer silicates. The observed nonlinear x-dependence of the torsional mode frequency in ternary systems can be related to the polarizability of the interlayer cations (Cs+,Rb+).  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号