Multi-scale and multi-component digital core construction and elastic property simulation

The conventional digital core models are usually small in size and have difficulty in representing the complex structures of heterogeneous rocks;Therefore,the parameters of simulated rock physics are difficult to be referenced.In this study,we propose a feasible simulation method for obtaining multi-scale and multi-component digital cores based on three types of sandstone samples.In the proposed method,the plug and subplug samples are scanned via micro-computed tomography at different resolutions.Furthermore,the images are precisely registered using the proposed hybrid image registration method.In case of high-resolution images,the traditional segmentation method is used to segment the cores into pores and minerals.Subsequently,we established the relations between the gray values and the porosity/mineral content in case of the low-resolution images based on the registered domains and the relation curves were applied to the segmentation of the low-resolution images.The core images constitute the multi-scale and multi-component digital core models after segmentation.Further,the elastic properties of the three samples were simulated at both fine and coarse scales based on the multi-scale and multi-component digital core models,and four component models were considered.The results show that the multi-scale and multi-component digital core models can overcome the representative limits of the conventional digital core models and accurately characterize pores and minerals at different scales.The numerical results of the elastic modulus are more representative at large scales,and considerably reliable results can be obtained by appropriately considering the minerals.

First-principles study of structural stability and elastic property of pre-perovskite PbTiO_3

The structural stability and the elastic properties of a novel structure of lead titanate, which is named pre- perovskite PbTiO3 （PP-PTO） and is constructed with TiO6 octahedral columns arranged in a one-dimensional manner, are investigated by using first-principles calculations. PP-PTO is energetically unstable compared with conventional perovskite phases, however it is mechanically stable. The equilibrium transition pressures for changing from pre- perovskite to cubic and tetragonal phases are -0.5 GPa and -1.4 GPa, respectively, with first-order characteristics. Further, the differences in elastic properties between pre-perovskite and conventional perovskite phases are discussed for the covalent bonding network, which shows a highly anisotropic character in PP-PTO. This study provides a crucial insight into the structural stabilities of PP-PTO and conventional perovskite.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Elastic Tensor and Thermodynamic Property of Magnesium Silicate Perovskite from First-principles Calculations

The thermodynamic and elastic properties of magnesium silicate （MgSiO3） perovskite at high pressure are investigated with the quasi-harmonic Debye model and the first-principles method based on the density functional theory. The obtained equation of state is consistent with the available experimental data. The heat capacity and the thermal expansion coefficient agree with the observed values and other calculations at high pressures and temperatures. The elastic constants are calculated using the finite strain method. A complete elastic tensor of MgSiO3 perovskite is determined in the wide pressure range. The geologically important quantities： Young＇s modulus, Poisson＇s ratio, Debye temperature, and crystal anisotropy, are derived from the calculated data.

Elasticity under pressure and thermal property of Mg2La from first-principles calculations

The elastic properties, thermodynamic and electronic structures of Mg_2La were investigated by using first-principles. The calculated results show that pressure affects the elastic constants of C_(11) more than that of C_(12) and C_(44). Specifically, higher pressure leads to greater bulk modulus(B), shear modulus(G), and elastic modulus(E). We predict B/G and anisotropy factor A based on the calculated elastic constants. The Debye temperature also increases with increasing pressure. Based on the quasi-harmonic Debye model, we examined the thermodynamic properties. These properties include the normalized volume(V/V_0), bulk modulus(B), heat capacity(C_v), thermal expansion coefficient(α), and Debye temperature(■). Finally, the electronic structures associated with the density of states(DOS) and Mulliken population are analyzed.

A first-principles study on electronic structure and elastic properties of Al_4Sr, Mg_2Sr and Mg_(23)Sr_6 phases

The electronic structures and mechanical properties of Al4Sr, Mg2Sr and Mg23Sr6 phases were determined by the use of first-principles calculations. The calculated heat of formation and cohesive energy indicate that Al4Sr has the strongest alloying ability as well as the highest structural stability. The elastic parameters were calculated, and then the bulk modulus, shear modulus, elastic modulus and Poisson ratio were derived. The ductility and plasticity were discussed. The results show that Al4Sr and Mg2Sr phases both are ductile, on the contrary, Mg23Sr6 is brittle, and among the three phases, Mg2Sr is a phase with the best plasticity.

Toward Improved Accuracy in Quasi-Static Elastography Using Deep Learning

Elastography is a non-invasive medical imaging technique to map the spatial variation of elastic properties of soft tissues.The quality of reconstruction results in elastography is highly sensitive to the noise induced by imaging measurements and processing.To address this issue,we propose a deep learning(DL)model based on conditional Generative Adversarial Networks(cGANs)to improve the quality of nonhomogeneous shear modulus reconstruction.To train this model,we generated a synthetic displacement field with finite element simulation under known nonhomogeneous shear modulus distribution.Both the simulated and experimental displacement fields are used to validate the proposed method.The reconstructed results demonstrate that the DL model with synthetic training data is able to improve the quality of the reconstruction compared with the well-established optimization method.Moreover,we emphasize that our DL model is only trained on synthetic data.This might provide a way to alleviate the challenge of obtaining clinical or experimental data in elastography.Overall,this work addresses several fatal issues in applying the DL technique into elastography,and the proposed method has shown great potential in improving the accuracy of the disease diagnosis in clinical medicine.

Study on structural stability,elastic and electronic properties for β-Ti under pressure based on first principles

The structural stability, elastic and electronic properties under pressure at 0 K for β-Ti have been investigated by per-forming first-principles calculations. With the increase of pressure, the structure of β-Ti becomes stabler, which is further con-firmed by the calculation for density of state （DOS）. The phase transition pressure of is about 64. 3 GPa, which is consist-ent with other theoretical predictions （63. 7 GPa） and the experimental result （50 GPa）. The pressure dependence of elastic constants shows that the low-pressure limit for a mechanically stable β-Ti is about 50 GPa with low Young？s modulus value of about 30. 01 GPa, which approaches the value of a human bone （30 GPa）. In addition, the pressure dependence of bulk modu-lus B, shear modulus G, Young’s modulus E,Poisson’s ratio σ,aggregate sound velocities,and ductility/brittleness under different pressures were also discussed. B, G and E ascend monotonously with increasing pressure, while a descends. β-Ti re-mains ductile by analysis of B/G under considered pressures.

First principles investigation of binary intermetallics in Mg-Al-Ca-Sn alloy:Stability,electronic structures,elastic properties and thermodynamic properties

The structural stability, electronic structures, elastic properties and thermodynamic properties of the main binary phases Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca in Mg-Al-Ca-Sn alloy were determined from the first-principles calculation. The calculated lattice parameters are in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies show that Al_2Ca has the strongest alloying ability and structural stability. The densities of states（DOS）, Mulliken electron occupation number, metallicity and charge density difference of these compounds are given. The elastic constants of Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca phases are calculated, and the bulk moduli, shear moduli, elastic moduli and Poisson ratio are derived. The calculations of thermodynamic properties show that the Gibbs free energies of Al_2Ca and Mg_2 Sn are lower than that of Mg_（17）Al_（12）, which indicates that Al_2Ca and Mg_2 Sn are more stable than Mg_（17）Al_（12） phase. Hence, the heat resistance of Mg-Al-based alloys can be improved by adding Ca and Sn additions.

Computation of elastic properties of 3D digital cores from the Longmaxi shale

The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element （FE） methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity （0.75） and kerogen content （ca. ≤3%） over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity （4.5%） of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties.

A first-principles study on elastic properties and stability of Ti_xV_(1-x)C multiple carbide

The structure,stability and elastic properties of di-transition-metal carbides TixV1-xC were investigated by using the first-principles with a pseudopotential plane-waves method.The results show that the equilibrium lattice constants of TixV1-xC show a nearly linear reduction with increasing addition of V.The elastic properties of TixV1-xC are varied by doping with V.The bulk modulus of Ti0.5V0.5C is larger than that of pure TiC,as well as Ti0.5V0.5C has the largest C44 among TixV1-xC（0≤x≤1）,indicating that Ti0.5V0.5C has higher hardness than pure TiC.However,Ti0.5V0.5C presents brittleness based on the analysis of ductile/brittle behavior.The Ti0.5V0.5C carbide has the lowest formation energy,indicating that Ti0.5V0.5C is more stable than all other alloys.

Analysis of elastic anisotropy of tight sandstone and the influential factors

Tight sandstone has a certain anisotropy. Using ultrasonic measurements of samples in three different directions and related matched experiments, this study systematically analyzes the pore structure and anisotropy of tight sandstone samples obtained from oil fields and compares results with those of shale. Results firstly show that the anisotropy of tight sandstone is mainly related to the compositional layering and thin interbedding which occur in different sedimentary environments. Tight sandstone has typical transverse isotropic medium characteristics, Young’s modulus increases in different directions with increasing confining pressure, Poisson’s ratio change is not obvious, anisotropic coefficients decrease with increasing effective pressure, and a certain linear relationship exists between ε, γ, and δ. This article finally summarizes anisotropy in different areas, thereby providing a foundation for the use of suitable appraisal models in different regions. This research can be used as an experimental reference for logging evaluation, seismic data interpretation, and fracturing develop of tight sandstones.

Elastic and thermodynamic properties of Re_2N at high pressure and high temperature

First principles calculations are preformed to systematically investigate the elastic and thermodynamic properties of Re2N at high pressure and high temperature. The Re2N exhibits a clear elastic anisotropy and the elastic constants C11 and C33 vary rapidly in comparison with the variations in C12, C13 and C44 at high pressure. In addition, bulk modulus B, elastic modulus E, and shear modulus Gas a function of crystal orientations for Re2N are also investigated for the first time. The tensile directional dependences of the elastic modulus obey the following trend： [0001] [1211] [1010] [1011]EEEE〉〉〉 . The shear moduli of Re2N within the （0001） basal plane are the smallest and greatly reduce the resistance of against large shear deformations. Based on the quasi-harmonic Debye model, the dependences of Debye temperature, Grüneisen parameter, heat capacity and thermal expansion coefficient on the temperature and pressure are explored in the whole pressure range from 0 to 50 GPa and temperature range from 0 to 1600 K.

First-principles calculations of structural,elastic and electronic properties of AB_(2)type intermetallics in Mg–Zn–Ca–Cu alloy

Electronic structure and elastic properties of MgCu_(2),Mg_(2)Ca and MgZn_(2)phases were investigated by means of first-principles calculations from CASTEP program based on density functional theory(DFT).The calculated lattice parameters were in good agreement with the experimental and literature values.The calculated heats of formation and cohesive energies shown that MgCu_(2)has the strongest alloying ability and structural stability.The elastic constants of MgCu_(2),Mg_(2)Ca and MgZn_(2)phases were calculated,the bulk moduli,shear moduli,Young's moduli and Poisson's ratio were derived.The calculated results shown that MgCu_(2),Mg_(2)Ca and MgZn_(2)are all ductile phases.Among the three phases,MgCu_(2)has the strongest stiffness and the plasticity of MgZn_(2)phase is the best.The density of states(DOS),Mulliken electron occupation number and charge density difference of MgCu_(2),Mg_(2)Ca and MgZn_(2)phases were discussed to analyze the mechanism of structural stability and mechanical properties.

First-principles calculations of structural,elastic and electronic properties of(TaNb)0.67(HfZrTi)0.33 high-entropy alloy under high pressure

To clarify the effect of pressure on a(TaNb)0.67(HfZrTi)0.33 alloy composed of a solid solution with a single body-centered-cubic crystal structure,we used first-principles calculations to theoretically investigate the structural,elastic,and electronic properties of this alloy at different pressures.The results show that the calculated equilibrium lattice parameters are consistent with the experimental results,and that the normalized structural parameters of lattice constants and volume decrease whereas the total enthalpy differenceΔE and elastic constants increase with increasing pressure.The(TaNb)0.67(HfZrTi)0.33 alloy exhibits mechanical stability at high pressures lower than 400 GPa.At high pressure,the bulk modulus B shows larger values than the shear modulus G,and the alloy exhibits an obvious anisotropic feature at pressures ranging from 30 to 70 GPa.Our analysis of the electronic structures reveals that the atomic orbitals are occupied by the electrons change due to the compression of the crystal lattices under the effect of high pressure,which results in a decrease in the total density of states and a wider electron energy level.This factor is favorable for zero resistance.

First-principles investigation of the electronic,elastic and thermodynamic properties of VC under high pressure

An investigation of the electronic, elastic and thermodynamic properties of VC under high pressure has been conducted using first-principles calculations based on density functional theory （DFT） with the plane-wave basis set, as implemented in the CASTEP code. At elevated pressures, VC is predicted to undergo a structural transition from a relatively open NaCl-type structure to a more dense CsCl,type one. The predicted transition pressure is 520 GPa. The elastic constant, Debye temperature and heat capacity each as a function of pressure and/or temperature of VC are presented for the first time.

Quantitative characterizations of anisotropic dynamic properties in organic-rich shale with different kerogen content

Understanding the quantitative responses of anisotropic dynamic properties in organic-rich shale with different kerogen content(KC)is of great significance in hydrocarbon exploration and development.Conducting controlled experiments with a single variable is challenging for natural shales due to their high variations in components,diagenesis conditions,or pore fluid.We employed the hot-pressing technique to construct 11 well-controlled artificial shale with varying KC.These artificial shale samples were successive machined into prismatic shape for ultrasonic measurements along different directions.Observations revealed bedding perpendicular P-wave velocities are more sensitive to the increasing KC than bedding paralleling velocities due to the preferential alignments of kerogen.All elastic stiffnesses except C_(13)are generally decreasing with the increasing KC,the variation of C_(1) and C_(33)on kerogen content are more sensitive than those of C_(44)and C_(66).Apparent dynamic mechanical parameters(v and E)were found to have linear correlation with the true ones from complete anisotropic equations independent of KC,which hold value towards the interpretation of well logs consistently across formations,Anisotropic mechanical parameters(ΔE and brittlenessΔB)tend to decrease with the reducing KC,withΔB showing great sensitivity to KC variations.In the range of low KC(<10%),the V_(P)/V_(S) ratio demonstrated a linearly negative correlation with KC,and the V_(P)/V_(S) ratio magnitude of less than 1.75may serve as a significant characterization for highly organic-rich(>10%)shale,compilation of data from natural organic rich-shales globally verified the similar systematic relationships that can be empirically used to predict the fraction of KC in shales.

First principles study of electronic structure, chemical bonding and elastic properties of BiOCuS

The electronic structures, chemical bonding and elastic properties of the tetragonal phase BiOCuS were investigated by using density-functional theory （DFT） within generalized gradient approximation （GGA）. The calculated energy band structures show that the tetragonal phase BiOCuS is an indirect semiconductor with the calculated band gap of about 0.503 eV. The density of states （DOS） and the partial density of states （PDOS） calculations show that the DOS near the Fermi level is mainly from the Cu-3d state. Population analysis suggests that the chemical bonding in BiOCuS has predominantly ionic character with mixed covalent-ionic character. Basic physical properties, such as lattice constant, bulk modulus, shear modulus, elastic constants, were calculated. The elastic modulus and Poisson ratio were also predicted. The results show that tetragonal phase BiOCuS is mechanically stable and behaves in a ductile manner.

First principles calculation of electronic structure, chemical bonding and elastic properties of ultra-incompressible Re_2P

The electronic structures, chemical bonding and elastic properties of the Co2P-type structure phase ultra-incompressible Re2P （orthorhombic phase） were investigated by density-functional theory （DFT） within generalized gradient approximation （GGA）. The calculated energy band structures show that the orthorhombic structure phase Re2P is metallic material. The density of state （DOS） and the partial density of state （PDOS） calculations show that the DOS near the Fermi level is mainly from the Re-5d state. Population analysis suggests that the chemical bonding in Re2P has predominantly covalent character with mixed covalent-ionic character. Basic physical properties, such as lattice constant, bulk modulus, shear modulus, and elastic constants Cij, were calculated. The elastic modulus and Poisson ratio were also predicted. The results show that the Co2P-type structure phase Re2P is mechanically stable and behaves in a brittle manner.

Chemical bonding and elastic properties of quaternary arsenide oxides YZnAsO and LaZnAsO investigated by first principles

The structural parameters, chemical bonding and elastic properties of the tetragonal phase quaternary arsenide oxides YZnAsO and LaZnAsO were investigated by using density-functional theory （DFT） within generalized gradient approximation （GGA）. The GGA calculated structural parameters are in agreement with the experimental results. Population analysis suggests that the chemical bonding in YZnAsO and LaZnAsO can be classified as a mixture of ionic and covalent characteristic. Single-crystal elastic constants were calculated and the polycrystalline elastic modules were estimated according to Voigt, Reuss and Hill＇s approximations （VRH）. The result shows that both YZnAsO and LaZnAsO are relatively soft materials exhibiting ductile behavior. The calculated polycrystalline elastic anisotropy result shows that LaZnAsO is more anisotropy in compressibility and YZnAsO is more anisotropy in shear.