High Pressure Elasticity of MgSiO3 Perovskite, MgO and SiO2

1997 ◽  
Vol 499 ◽  
Author(s):  
Bijaya B. Karki
Keyword(s):  
High Pressure ◽  
First Principles ◽  
Lower Mantle ◽  
Elastic Moduli ◽  
Local Density ◽  
Initial Pressure ◽  
Structural Transformations ◽  
Wave Velocities ◽  
Mgsio3 Perovskite ◽  
Shear Wave Velocities

ABSTRACTFull elastic constant tensors (cij) of three minerals namely, MgSiO3 perovskite, MgO and SiO2, are obtained as a function of pressure up to 140 GPa using first-principles computer simulations based on the local density and pseudopotential approximations. The zero pressure values and initial pressure dependence of athermal elastic constants derived from stress-strain relations are in excellent agreement with available experimental data. We find that elastic moduli, wave velocities and anisotropy of the minerals are strongly pressure dependent, particularly, in the vicinity of the structural transformations. In the view of the present experimental limitations at realistic conditions of the inner Earth, our results for high pressure elasticity are expected to be of substantial geophysical significance. Comparisons based on compressional and shear wave velocities support the prevailing hypothesis of Mg-rich silicate perovskite dominated composition for the lower mantle.

scholarly journals First Principles Calculation of the Stability of Iron Bearing Carbonates at High Pressure Conditions

Minerals ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 54
Author(s):  
Jun Tsuchiya ◽  
Risa Nishida ◽  
Taku Tsuchiya
Keyword(s):  
High Pressure ◽  
High Spin ◽  
First Principles ◽  
Lower Mantle ◽  
Local Density ◽  
First Principles Calculation ◽  
Generalized Gradient ◽  
Carbonate Minerals ◽  
Pressure Stability ◽  
The Stability

Carbonate minerals such as ferromagnesite (Mg,Fe)CO 3 are suggested to be a possible major deep-carbon host in the lower mantle, because ferromagnesite is possibly stabilized by Fe spin crossover under pressure. However, the behavior of Fe-bearing carbonates under lower mantle pressure conditions has not been suitably examined thus far. Thus, in this study, we investigate the high-pressure stability of ferromagnesite and possible high-pressure structures with the chemical composition of (Mg 0.833 Fe 0.167 )CO 3 via first principles calculation using internally consistent local density approximation with Hubbard parameter (LDA+U) method, which can more accurately account for the electronic state of Fe than the LDA and generalized gradient approximation (GGA) approaches. The enthalpy values obtained via our calculations suggest that (Mg 0.833 Fe 0.167 )CO 3 undergoes phase transition from the R 3 ¯ c structure (high spin) to the P 1 ¯ (high spin) at 50 GPa, and to C2/m (high-spin) structure above 80 GPa, under static 0 K conditions. Therefore, no spin transitions in these carbonate minerals is expected under the lower mantle pressure conditions.

ELASTIC BEHAVIOR OF SOME SUBSTITUTED Sr–Zn W-TYPE HEXAGONAL FERRITES

1999 ◽  
Vol 13 (27) ◽  
pp. 991-998 ◽  
Author(s):  
Y. PURUSHOTHAM ◽  
P. VENUGOPAL REDDY
Keyword(s):  
Linear Relationship ◽  
Room Temperature ◽  
Elastic Moduli ◽  
Dopant Concentration ◽  
Elastic Behavior ◽  
Hexagonal Ferrites ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Pulse Transmission ◽  
Transmission Technique

In the present work, we investigate the elastic behavior of monovalent and divalent doped Sr–Zn W-type hexagonal ferrites at room temperature by measuring their longitudinal and shear wave velocities using a pulse transmission technique. The values of Young (E) and rigidity (G) moduli have been corrected to the theoretical density. The zero porosity values of both the elastic moduli are found to increase with increasing dopant concentration. Further, a linear relationship between the Debye temperature and the average sound velocity has also been observed and the behavior is explained qualitatively.

EFFECT OF Nb2O5 ON THE ELASTIC BEHAVIOR OF PZT FERROELECTRIC MATERIALS

2002 ◽  
Vol 16 (03) ◽  
pp. 79-85
Author(s):  
Y. PURUSHOTHAM ◽  
O. P. THAKUR ◽  
CHANDRA PRAKASH ◽  
P. VENUGOPAL REDDY
Keyword(s):  
Elastic Moduli ◽  
Solid State Reaction Method ◽  
Ferroelectric Materials ◽  
Ferroelectric Ceramics ◽  
Elastic Behavior ◽  
X Ray Diffraction ◽  
X Ray ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Pulse Transmission

A series of ferroelectric ceramics with the compositional formula PbZr0.52Ti0.48O3 + x wt% of Nb2O5 were prepared by the solid state reaction method. Samples were characterized by studying their X-ray diffraction and dielectric measurements. The longitudinal and shear wave velocities and corresponding elastic moduli were determined at room temperature by using the pulse transmission technique. The values of Young's modulus (E), and the rigidity (n) and bulk (k) moduli were corrected to theoretical density and were found to increase with increasing dopant concentration. The variation of elastic moduli and other elastic parameters such as Debye temperature (θ D ) with composition are explained qualitatively.

FLUID SATURATION EFFECTS ON DYNAMIC ELASTIC PROPERTIES OF SEDIMENTARY ROCKS

Geophysics ◽  
1976 ◽  
Vol 41 (5) ◽  
pp. 895-921 ◽  
Author(s):  
A. R. Gregory
Keyword(s):  
Shear Wave ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Compressional Wave ◽  
Reflection Coefficients ◽  
High Porosity ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Fluid Saturation ◽  
Saturation Effects

The influence of saturation by water, oil, gas, and mixtures of these fluids on the densities, velocities, reflection coefficients, and elastic moduli of consolidated sedimentary rocks was determined in the laboratory by ultrasonic wave propagation methods. Twenty rock samples varying in age from Pliocene to early Devonian and in porosity from 4 to 41 percent were tested under uniform pressures equivalent to subsurface depths of 0 to 18,690 ft. Fluid saturation effects on compressional‐wave velocity are much larger in low‐porosity than in high‐porosity rocks; this correlation is strengthened by elevated pressures but is absent at atmospheric pressure. At a frequency of 1 MHz, the shear‐wave velocities do not always decrease when liquid pore saturants are added to rocks as theorized by Biot; agreement with theory is dependent upon pressure, porosity, fluid‐mineral chemical interactions, and the presence of microcracks in the cementing material. Experimental results support the belief that lower compressional‐wave velocities and higher reflection coefficients are obtained in sedimentary rocks that contain gas. Replacing pore liquids with gas markedly reduces the elastic moduli of rocks, and the effect is enhanced by decreasing pressure. As a rule, the moduli decrease as the porosity increases; Poisson’s ratio is an exception to the rule. Liquid and gas saturation in consolidated rocks can also be distinguished by the ratio of compressional and shear wave velocities [Formula: see text]. The potential diagnostic value of elastic moduli in seismic exploration may stimulate interest in the use of shear‐wave reflection methods in the field.

Estimation of Dry-Rock Elastic Moduli Based on the Simulation of Mud-Filtrate Invasion Effects on Borehole Acoustic Logs

2009 ◽  
Vol 12 (06) ◽  
pp. 898-911 ◽  
Author(s):  
Tobiloluwa B. Odumosu ◽  
Carlos Torres-Verdín ◽  
Jesús M. Salazar ◽  
Jun Ma ◽  
Benjamin Voss ◽  
...  
Keyword(s):  
Bulk Modulus ◽  
Shear Wave ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Compressional Wave ◽  
Shear Rigidity ◽  
Spatial Distributions ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Mud Filtrate

Summary Reliable estimates of dry-rock elastic properties are critical to the accurate interpretation of the seismic response of hydrocarbon reservoirs. We describe a new method for estimating elastic moduli of rocks in-situ based on the simulation of mud-filtrate invasion effects on resistivity and acoustic logs. Simulations of mud-filtrate invasion account for the dynamic process of fluid displacement and mixing between mud-filtrate and hydrocarbons. The calculated spatial distributions of electrical resistivity are matched against resistivity logs by adjusting the underlying petrophysical properties. We then perform Biot-Gassmann fluid substitution on the 2D spatial distributions of fluid saturation with initial estimates of dry-bulk (kdry) modulus and shear rigidity (µdry) and a constraint of Poisson's ratio (?d) typical of the formation. This process generates 2D spatial distributions of compressional and shear-wave velocities and density. Subsequently, sonic waveforms are simulated to calculate shear-wave slowness. Initial estimates of the dry-bulk modulus are progressively adjusted using a modified Gregory-Pickett (1963) solution of Biot's (1956) equation to estimate a shear rigidity that converges to the well-log value of shear-wave slowness. The constraint on dynamic Poisson's ratio is then removed and a refined estimate of the dry-bulk modulus is obtained by both simulating the acoustic log (monopole) and matching the log-derived compressional-wave slowness. This technique leads to reliable estimates of dry-bulk moduli and shear rigidity that compare well to laboratory core measurements. Resulting dry-rock elastic properties can be used to calculate seismic compressional-wave and shear-wave velocities devoid of mud-filtrate invasion effects for further seismic-driven reservoir-characterization studies.

scholarly journals Relationships between Dynamic Elastic Moduli in Shale Reservoirs

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6001
Author(s):  
Sheyore John Omovie ◽  
John P. Castagna
Keyword(s):  
Organic Carbon ◽  
Shear Modulus ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
P Wave ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Average Formation ◽  
Dynamic Elastic Moduli ◽  
Shale Reservoirs

Sonic log compressional and shear-wave velocities combined with logged bulk density can be used to calculate dynamic elastic moduli in organic shale reservoirs. We use linear multivariate regression to investigate modulus prediction when shear-wave velocities are not available in seven unconventional shale reservoirs. Using only P-wave modulus derived from logged compressional-wave velocity and density as a predictor of dynamic shear modulus in a single bivariate regression equation for all seven shale reservoirs results in prediction standard error of less than 1 GPa. By incorporating compositional variables in addition to P-wave modulus in the regression, the prediction standard error is reduced to less than 0.8 GPa with a single equation for all formations. Relationships between formation bulk and shear moduli are less well defined. Regressing against formation composition only, we find the two most important variables in predicting average formation moduli to be fractional volume of organic matter and volume of clay in that order. While average formation bulk modulus is found to be linearly related to volume fraction of total organic carbon, shear modulus is better predicted using the square of the volume fraction of total organic carbon. Both Young’s modulus and Poisson’s ratio decrease with increasing TOC while increasing clay volume decreases Young’s modulus and increases Poisson’s ratio.

Ultrasonic Measurement of Elastic Properties of Nanostructured Alumina

2006 ◽  
Vol 321-323 ◽  
pp. 1711-1714 ◽  
Author(s):  
Noh Yu Kim ◽  
Hee Joon Kim ◽  
Se Woong Oh ◽  
N. Hozumi ◽  
Cheol Kyou Lee ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Ultrasonic Measurement ◽  
Nano Particles ◽  
Acoustic Microscope ◽  
Al2o3 Powder ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Longitudinal And Shear Waves ◽  
Scanning Acoustic Microscope ◽  
Mechanical Modulus

In this paper, elastic moduli of nanostructured alumina are evaluated by simultaneous measurement of longitudinal and shear wave velocities using mode-converted ultrasound in scanning acoustic microscope (SAM). Mode-converted longitudinal and shear waves inside alumina sample are captured to calculate acoustic wave velocities and determine elastic constants such as Young’s modulus and Bulk modulus. Al2O3 nanostructured alumina samples are formed by compacting micro-sized Al2O3 powder with nano-sized Al2O3 powder from 10wt% to 50wt%, and tested by SAM to investigate elastic moduli. A correlation is found from experiment that the more percentage of nano-particles are added, the higher elastic moduli are obtained. It is also shown that the mode-converted ultrasound is sensitive enough to characterize mechanical modulus of nanostructured alumina quantitatively.

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