Bulk Modulus Research Articles

Structural stability, mechanical, and thermodynamic properties under pressure of B2-type CuM (M = Be, Al, and Zn) alloys: a DFT investigation

In this work, we systematically examined the structural stability, mechanical properties, and thermodynamic behavior of B2-type CuBe alloy, and compared the results with isostructural Cu-based alloys (CuAl and CuZn) by employing first-principles calculations in the pressure range of −22 to 100 GPa. This study revealed the stable existence of CuBe alloy at low-density expansion states (e.g. ∼ −20 GPa), indicating its superior structural stability compared to CuAl and CuZn. The pressure dependence of properties such as cell parameter a (a/a 0) and density ρ (ρ/ρ 0), elastic parameters (elastic constants C ij , bulk modulus B, shear modulus G, and Young's modulus E), deduced parameters (B/G ratio, Poisson's ratio ν, Vickers hardness, sound velocity, and Debye termperature ΘD), and thermodynamic parameters (free energy F, entropy S, and heat capacity C v) were investigated. All CuM (M = Be, Al, and Zn) alloys had more difficulty undergoing uniaxial stress than shear stress. External pressure reduced the ductility of the CuBe alloy, while excess pressure (P > 50 GPa) resulted in increased ductility, which was similar to CuAl but different from CuZn. The hardness and ΘD values demonstrated consistent variation corresponding to the ductility changes. Thermodynamic parameters were minimally affected by pressure, and the stronger interactions led to greater F in the CuBe alloy. These findings offer confidence for the future design of ordered Cu-Be alloys with exceptional properties.

Mechanical properties of recycled aggregate concrete containing brick particles

To investigate the mechanical properties of recycled aggregate concrete containing brick particles(RACB), compressive strength tests were conducted on RACBs with different water cement ratios and recycled fine aggregate substitution rates. The changes in compressive strength, elastic modulus, and peak strain of RACB with recycled fine aggregate substitution rates were analyzed, and a stress–strain equation was established. A damage model was established using ultrasonic nondestructive testing technology to reveal the damage mechanism of RACB. Results show that the basic mechanical properties of RACB reach the best when the replacement rate of recycled fine aggregate (r) is 30%. The model parameter a of the stress–strain curve equation is consistent with the change rule of elastic modulus with r. The model parameter b has a quadratic function relationship with r, reflecting the brittleness of RACB. The initial damage of RACB is relatively large, and the cracks penetrate the recycled coarse aggregate, and lead to specimen failure.

Image‐based inertial impact test for viscoelastic constitutive identification: A digital replica for error quantification

AbstractPolymers find widespread use in applications where they are subjected to impact loading. Therefore, understanding the time dependence of their mechanical response is critical to the design of structures subjected to these high strain rate environments. However, characterising these materials on microsecond time scales has proven challenging. Traditional experimental techniques rely on satisfying a number of limiting assumptions and typically do not provide direct measurements of the material parameters. Here, we propose a novel implementation of the image‐based inertial impact (IBII) test to extract viscoelastic constitutive parameters on these microsecond time scales using the stress gauge implementation of the virtual fields method. We validate the experiment using a digital replica approach in which the constitutive parameters are first extracted on a finite element model of an IBII test on a viscoelastic material. The finite element data are then used to synthetically deform computer‐generated grid images, which are then polluted with grey‐level noise to simulate the images that would be captured in a real‐life experiment. These images are processed identically to a physical experiment, and the identification is repeated using the full‐field displacements extracted from the computer‐generated images to determine the ideal processing parameters. Parameter identification was found to strongly depend on the processing parameters used to extract the kinematic fields from full‐field images, emphasising the need for computational validation before attempting a physical experiment to extract constitutive parameters. The IBII experimental method was found to be capable of simultaneously identifying the bulk modulus and the shear modulus along with their associated time constant.

Revisiting thermodynamics in (LiF, NaF, KF, CrF2)–CrF3 by first-principles calculations and CALPHAD modeling

The thermodynamic description of the (LiF, NaF, KF, CrF2)–CrF3 systems has been revisited, aiming for a better understanding of the effects of Cr on the FLiNaK molten salt. First-principles calculations based on density functional theory (DFT) were performed to determine the electronic and structural properties of each compound, including the formation enthalpy, volume, and bulk modulus. DFT-based phonon calculations were carried out to determine the thermodynamic properties of compounds, for example, enthalpy, entropy, and heat capacity as functions of temperature. Phonon-based thermodynamic properties show a good agreement with experimental data of binary compounds LiF, NaF, KF, CrF3, and CrF2, establishing a solid foundation to determine thermodynamic properties of ternary compounds as well as to verify results estimated by the Neumann-Kopp rule. Additionally, DFT-based ab initio molecular dynamics (AIMD) simulations were employed to predict the mixing enthalpies of liquid salts. Using DFT-based results and experimental data in the literature, the (LiF, NaF, KF, CrF2)–CrF3 system has been remodeled in terms of the CALculation of PHAse Diagrams (CALPHAD) approach using the modified quasichemical model with quadruplet approximation (MQMQA) for liquid. Calculated phase stability in the present work shows an excellent agreement with experiments, indicating the effectiveness of combining DFT-based total energy, phonon, and AIMD calculations, and CALPHAD modeling to provide the thermodynamic description in complex molten salt systems.

Physical and mechanical characteristics deterioration and crack evolution of sandy mudstone in an open-pit mine under multiple freeze–thaw cycles

In open-pit mines located in cold regions north of the 38°N latitude, there are significant freeze–thaw phenomena in slope rocks. This study conducted freeze–thaw cycle tests, considering the number of freeze–thaw cycles and the freezing temperature, on sandy mudstone commonly found in the slopes of open-pit mines. The investigation focused on the effects of freeze–thaw cycles on the physical and mechanical properties and acoustic emission (AE) characteristics of sandy mudstone. The results show that, with an increase in the number of freeze–thaw cycles and a decrease in freezing temperature, the sandy mudstone specimens exhibit nonlinear exponential changes in mass loss rate, P-wave velocity loss rate, peak strain, uniaxial compressive strength (UCS) and elastic modulus, and the amplitude of these changes gradually decreases. The stress–strain curves of specimens shift gradually from apparently brittle to plastic. Simultaneously, the microstructure changes from dense to loose, the micro surface transitions from flat to rough, and cracks and pore defects gradually develop. The peak AE ringing counts, cumulative AE ringing counts, crack initiation stress, and crack damage stress of the specimens all decrease with an increase in the number of freeze–thaw cycles and a decrease in freezing temperature. This suggests a shift from brittle failure to ductile failure. However, the ratio of crack initiation stress and crack damage stress to peak stress does not vary significantly with the number of freeze–thaw cycles and freezing temperature.

Effect of titanium dioxide as nanomaterials on mechanical and durability properties of rubberised concrete by applying RSM modelling and optimizations

The use of rubber aggregates derived from discarded rubber tyres in concrete is a pioneering approach to replacing natural aggregate (NA) and promoting sustainable building practices. Recycled aggregate in concrete serves the dual purpose of alleviating the accumulation of discarded rubber tyres on the planet and providing a more sustainable alternative to decreasing natural aggregate. Due to fact that the crumb rubber (CR) decreases the strength when used in concrete, incorporating titanium dioxide (TiO2) as a nanomaterial to counteract the decrease in strength of crumb rubber concrete is a potential solution. Response Surface Methodology was developed to generate sixteen RUNs which contains different mix design by providing two input parameters like TiO2 at 1%, 1.5%, and 2% by cement weight and CR at 10%, 20%, and 30% as substitutions for volume of sand. These mixtures underwent testing for 28 days to evaluate their mechanical, deformation, and durability properties. Moreover, the compressive strength, tensile strength, flexural strength and elastic modulus were recorded by 51.40 MPa, 4.47 MPa, 5.91 MPa, and 40.15 GPa when 1.5% TiO2 and 10% CR were added in rubberised concrete after 28 days respectively. Furthermore, the incorporation of TiO2 led to reduced drying shrinkage and sorptivity in rubberized concrete, especially with increased TiO2 content. The study highlights that TiO2 inclusion refines pore size and densifies the interface between cement matrix and aggregate in hardened rubberized concrete. This transformative effect results in rubberized concrete demonstrating a commendable compressive strength comparable to normal concrete.

Numerical simulation on cellular structure and mechanical properties of tungsten particles/polymethyl methacrylate microcellular composites

AbstractMicrocellular composites combine the advantages of composite material and microcellular material. Introducing the inclusion phase into the polymer matrix can optimize the cellular structure and improve the mechanical properties of microcellular materials. This paper focuses on rigid W particles reinforced PMMA microcellular materials, combining compression experiments and meso FE simulations to investigate the structure–property relationship of cellular structure and compressive properties for W/PMMA microcellular composites. The results indicate that W particles promote heterogeneous nucleation, reducing the cell size to 3 μm, and reinforce the PMMA matrix. W particles (10 → 60 wt%) are linearly and exponentially related to compressive modulus and compressive strength of W/PMMA microcellular composites, increased by 49.3% and 19.8%. Void porosity (71% → 48%) is quadratic related to compressive properties of W/PMMA microcellular composites, increased by 109%. Cell sizes (5 → 1 μm, especially smaller than the W particle sizes) are exponentially related to compressive properties of W/PMMA microcellular composites, increased by 38.5%. This work provides theoretical support for the regulation of cellular structure and optimization of mechanical properties of microcellular materials.

Pressure Effects on the Structural, Electronic, Elastic, Optical, and Vibrational Properties of YMg Intermetallic Compounds:A First-Principles Study

Abstract The properties of YMg in B2 structure have been comprehensively analysed using the first-principles plane-wave pseudopotential method. Specifically, the structural, electronic, elastic, vibrational, and optical properties were investigated using the generalized gradient approximation (GGA) method in the context of density functional theory. The Vienna ab initio simulation package (VASP) was utilized for these calculations. The computed lattice parameter (3.803 Å) and bulk modulus (41.33 GPa) are consistent with the earlier data on ambient pressure. The electronic band structure and energy-dependent density of states reveal the metallic nature of the titled compounds. The Born stability requirements confirmed the mechanical stability. The analysis of Pugh's and Poisson's ratios and Cauchy's pressure reveals that YMg is ductile under the pressures in consideration. According to several anisotropy indices, the compound is noticeably anisotropic both in ambient and under pressure. Our investigation includes an analysis of several fundamental mechanical parameters of the material, including the bulk modulus, the pressure derivative of the Zener anisotropy factor, Poisson's ratio, isotropic shear modulus and Young's modulus with a particular focus on their dependence on pressure. We have determined that the elastic constants obtained remain mechanically stable, satisfying the Born Stability conditions even at high pressures of up to 60 GPa. To explore the dynamic stability of YMg, we analysed the material's phonon dispersion curves. The examined compound displays stability under dynamic conditions from 0 GPa to 30 GPa, as evidenced by its positive vibration frequencies. However, this stability is not sustained under higher pressure, as the compound becomes unstable after 30 GPa to 70 GPa. 
The electronic band structure and density of states diagrams demonstrate YMg's metallic properties. At atmospheric pressure (0 GPa), the total density of states (TDOS) near the Fermi level is approximately 1.63 states/eV, with pressure application reducing DOS. The dielectric function, refractive index, and energy loss spectra are examined within the 0–20 eV energy range. YMg exhibits its highest absorption between 4 and 11 eV. The peak optical conductivity is observed around 0.78 eV (equivalent to 1589.5409 nm), while the most significant energy loss occurs at 11.90 eV, roughly corresponding to 2.8 Hz in the ultraviolet spectrum. Moreover, we extensively analyzed the material's phonon thermodynamic and optical properties, providing insights into its behavior under various conditions. The outcomes acquired at zero pressure are generally coherent with the current theoretical values.

First-principles study on the structural, elastic, electronic, optical and thermophysical properties of NaNO3 and K-doped NaNO3

Abstract The present work represents the structural, electronic, elastic, and thermophysical properties of pure and K-doped NaNO3 obtained using DFT calculations. The estimated structural properties of NaNO3 correspond well with the existing reported values. Electronic characteristics such as band structure and density of statesof pure and doped NaNO3 are analyzed where the calculated band gaps for pure and K-doped NaNO3 are found to be 3.05 eV and 2.90 eV, respectively. The Berry–phase calculations carried out on both systems showed the existence of ferroelectric polarization, where an enhanced spontaneous polarization value of 36 μC/cm2 for K-doped NaNO3, as compared to 20 μC/cm2 for intrinsic NaNO3. The thermophysical properties such as bulk modulus (B0), Debye temperature (θD), and specific heat capacity (Cv) were calculated over a wide temperature range from 0K to 800 K. The linear optical properties namely the dielectric constant, refractive index, absorption coefficient, extinction coefficient and electron energy loss function are calculated in wide energy range from 0 to 30 eV and discussed in detail.

An Injectable, Self-Healing, Adhesive Multifunctional Hydrogel Promotes Bacteria-Infected Wound Healing

Bacterial infections have a serious impact on public health. It is urgent to develop antibacterial hydrogels with good biocompatibility to reduce the use of antibiotics. In this study, poly(lipoic acid-co-sodium lipoate)–phytic acid (P(LA-SL)-PA) hydrogels are prepared by a simple mixture of the natural small molecules lipoic acid (LA) and phytic acid (PA) in a mild and green reaction environment. The crosslinking network is constructed through the connection of covalent disulfide bonds as well as the hydrogen bonds, which endow the injectable and self-healing properties. The P(LA-SL)-PA hydrogels exhibit an adjustable compression modulus and adhesion. The in vitro agar plates assay indicates that the antibacterial rate of hydrogels against Escherichia coli and Staphylococcus aureus is close to 95%. In the rat-infected wound model, the P(LA-SL)-PA hydrogels adhere closely to the tissue and promote epithelialization and collagen deposition with a significant effect on wound healing. These results prove that the P(LA-SL)-PA hydrogels could act as effective wound dressings for promoting the healing of infected wounds.

Properties of road subbase materials manufactured with geopolymer solidified waste drilling mud

In this study, geopolymer was adopted as an eco-friendly binding material to solidify waste drilling mud to fabricate geopolymer solidified waste drilling mud (GSWDM) as a pavement material in the subbase. Using precursor dosage, Na2SiO3 solution dosage, and slag powder (SP) dosage as parameters of mix proportion, the optimal mix proportions of GSWDM were determined through compressive strength tests. Based on a series of tests of unconfined compressive strength, splitting tensile strength, elastic modulus, and compressive resilient modulus, the effects of the SP percentage in the precursor and curing age on the mechanical properties of GSWDM were analyzed. The results indicated that all the mechanical properties of GSWDM were improved with the increasing SP percentage in the precursor. The 28-day unconfined compressive strength, splitting tensile strength, elastic modulus, and compressive resilient modulus of GSWDM were improved by 80.8%, 56.3%, 65.3%, and 76.72%, respectively, when the SP percentage in the precursor increased from 60% to 100%. A nonlinear increase in the mechanical properties of GSWDM was observed as the curing age increased, with a significant increase in the curing age from 7 days to 14 days and a slight increase in the curing age from 14 days to 28 days. Moreover, the microstructure of GSWDM was denser as the curing age and the SP percentage in the precursor grew. The results of this study verified that GSWDM can be used as construction material for road subbase.

Real and In Silico Microgels Show Comparable Bulk Moduli Below and Above the Volume Phase Transition.

The compressibility of soft colloids influences their phase behavior and flow properties, especially in concentrated suspensions. Particle compressibility, which is proportional to the reciprocal of the bulk modulus K, is a key parameter for soft polymer-based particles that can be compressed in crowded environments. Here, microgels with different degrees of cross-linking, i.e.,softness, are investigated below and above their volume phase transition temperature (VPTT). By combining molecular dynamics simulations with small-angle neutron scattering with contrast variation, a change in the particle bulk moduli of two orders of magnitude is observed. The degree of cross-linking has a significant impact on the bulk modulus of the swollen microgel, while above the VPTT the values of K are almost independent of the cross-linking density. The excellent agreement between experimental results and simulations also highlight that the model microgels from computer simulationspossess both the internal architecture and the elastic properties of real polymeric networks. This paves the way to a systematic use of simulations to investigate the behavior of dense microgelsuspensions below and above their VPTT.

Investigation of the Influence of Alloy Atomic Doping on the Properties of Cu-Sn Alloys Based on First Principles

In order to design Cu-Sn alloys with excellent overall performance, the structural stability, mechanical properties, and electronic structure of X-doped Cu-Sn alloys were systematically calculated using first-principles calculations. The calculation results of the cohesive energy indicate that the Cu-Sn-X structures formed by X atoms (X = Ag, Ca, Cd, Mg, Ni, Zr) doping into Cu-Sn can stably exist. The Cu-Sn-Ni structure is the most stable, with a cohesive energy value of −3.84 eV. Doping of X atoms leads to a decrease in the bulk modulus, Possion’s ratio and B/G ratio. However, doping Ag and Ni atoms can improve the shear modulus, Young’s modulus, and strain energy of the dislocation. The doping of Ni has the highest enhancement on shear modulus, Young’s modulus, and strain energy of the dislocation, with respective values as follows: 63.085 GPa, 163.593 GPa, and 1.689 W/J·m−1. The analysis of electronic structure results shows that the covalent bond between Cu and X is the reason for the performance differences in Cu-Sn-X structures.

Thermal decomposition of oxygen‐containing Ta3N5${\rm {Ta}}_3{\rm {N}}_5$

AbstractTransition metal nitrides, especially tantalum nitrides, are pivotal for applications in extreme environments demanding excellent mechanical properties and thermodynamic stability. Among them, ‐TaN, a high‐pressure polymorph of tantalum nitride with its exceptional bulk modulus (362 GPa) and hardness (31.7 GPa) promises to have many technological uses. Another nitride, , has gained importance as a photocatalyst for water splitting using visible light. The Ta–N phase diagram indicates that the thermal decomposition of pure leads to the formation of ‐TaN. However, usually has some amount of oxygen as an impurity mainly due to its synthesis route. We found that the ‐TaN phase, which is usually observed at high pressures, is formed during the thermal decomposition of oxygen containing . The presence of ‐TaN is verified using several experimental techniques such as X‐ray diffraction, Raman spectra, high‐angle annular dark field scanning transmission electron microscopy (STEM‐HAADF), and electron energy loss spectroscopy (EELS). Elemental distribution analyzed through energy dispersion X‐ray spectroscopy (XEDS) in STEM reveals about 7 at.% of oxygen in ‐TaN. First‐principle calculations are performed to examine the thermodynamic stability of oxygen substituted ‐TaN and pure ‐TaN via formation enthalpies, elastic constants, and phonon dispersion calculations. The computational studies confirm that oxygen in ‐TaN enhances its thermodynamic stability. The calculated electron localization functions establish the bonding characteristics between Ta, N, and O, confirming the same.

Tunable Chemochromism and Elastic Properties in Intercalated MoO3: Au-, Cr-, Fe-, Ge-, Mn-, and Ni-MoO3.

Chemical tunability of the elastic constants of α-MoO3, a two-dimensional layered oxide, is demonstrated with mutability on the order of tens of GPa, simply by choice of a metal intercalant including Au, Cr, Fe, Ge, Mn, and Ni. Using Brillouin laser light scattering from confined acoustic phonons in nanometer-thick materials, the in-plane angular dispersion of the quantized acoustic phonon branches of 2D layered, intercalated MoO3 is measured and used to determine the bulk modulus (K), Young's moduli (E11, E22, and E33), each of the nine independent elastic tensor elements (cij), and the thickness. Intercalation of metals generally reduces the anisotropy in MoO3 except in Ge-MoO3, for which the in-plane longitudinal elastic anisotropy is unaffected. Chemochromism from transparent white (MoO3 and Fe-MoO3) to near black (Ni-MoO3) to brilliant dark blue (Ge-MoO3) is demonstrated and is associated with a reduction in electronic band gap with intercalation and an increase in absorption >600 nm for some intercalants (Cr-, Ge-, and Mn-MoO3).

Lightweight, mechanically robust and scalable cellulose-based foam enabled by organic-inorganic network and air drying

Lightweight and high-strength cellulose-based foams have gained increasing momentum due to their combination of sustainability and high performance. However, complex modification to cellulose fibers can sacrifice the environmental friendliness and further limit productional scalability. Here, we engineer lightweight yet strong cellulose-based foams made from mechanically treated microfibrillated cellulose (MFC), reinforced by organic-inorganic network, and scaled by surfactant foaming combined with air drying. Consisting of strong coordination and extensive secondary interaction within the organic-inorganic network, the resulting cellulose composite foams achieve both a high compressive modulus of 451.3 kPa and a yield strength of 25.1 kPa at a low density of 32.9 mg cm−3, which exceed other MFC-based foams based on surfactant foaming. In addition, the incorporation of the organic-inorganic network has no negative effect on the scalability, recyclability, or biodegradability of cellulose composites foam, making closed-loop material recycling possible. The life-cycle assessment reveals that replacing petroleum-based foams with our cellulose composite foams result in substantial reductions in carbon emissions. The structural design and manufacturing of our cellulose-based foam can stimulate market interest for cellulose foam and the development of the bioeconomy.

Theoretical Investigation of Mechanical and Electronic Properties of Hexagonal BaB2

A comprehensive investigation of the electronic and mechanical properties in the hexagonal BaB2 binary system using state of the art first-principles computational techniques is critical for an in-depth understanding of the fundamental properties unique to this binary system. In this context, we derived elastic constants using the metric-tensor formulation, which allowed us to find important mechanical properties such as Bulk Modulus, Shear Modulus, and Vickers's hardness which are fundamental mechanical quantities. Also, this research includes a detailed analysis of the electronic band structures and a study comparison of Fermi surface topologies. The charge density at the Fermi level (N(EF)), which is very important in superconductivity theories, was found to be 1.43 states/eV.uc. Furthermore, we have explored whether there exists a close relationship between these properties and the superconducting behavior of the BaB2 material. Nevertheless, our calculations unequivocally demonstrate that the information derived from electronic band structures and Fermi surfaces alone is insufficient for a comprehensive explanation of the superconductivity phenomenon observed in such materials.

Experimental study on I/II/III mixed mode fracture characteristics of a combined rock mass under creep loading

I/II/III mixed mode fractures of intersecting joint fissures often occur in natural rock masses, and jointed rock masses are prone to rockbursts in deep underground engineering when subjected to long-term crustal stresses. However, most studies of the mechanical mechanisms of these intersected joints have been conducted by simplifying two-dimensional joint model tests. Furthermore, the fracture mechanisms of two-dimensional intersected joints under tension and compression are completely different from those of three-dimensional joints. This paper presents a novel prefabricated specimen with combinations of intersecting joints capable of detecting the failure behaviours of rock I/II/III mixed mode fractures under creep loading. Uniaxial compression and multistage creep tests are performed on prefabricated sandstone specimens with intersecting joints of 0°/0°, 0°/30°, 0°/60°, and 0°/90°. The experimental results show that with the increase in the number of prefabricated intersecting joints, the uniaxial compressive strength and elastic modulus values of the sandstone specimens gradually decrease. In addition, the sandstone specimens experience relatively few AE events and minor axial strain variations in the first creep stage and the second creep stage of the multistage creep test. The axial strain increases sharply due to the sharp increase in the number of AE events in the third creep stage. The 0°/60° sandstone specimen undergoes accelerated creep failure, resulting in mixed X-shaped tensile‒shear rupture. The RA value is high based on the quantification of the creeping cracks using the acoustic emission parameters of the rise angle (RA) and average frequency (AF). The AF values of the 0°/0°, 0°/30°, and 0°/90° sandstone specimens are high. The experimental results show that a larger joint intersection angle leads to greater mutual restraints and greater effects of prefabricated crack propagation in the rock specimens, thus increasing the final failure strength. Finally, based on the acoustic emission count, a characteristic variable D suitable for characterizing the creep damage evolution of a joint rock mass is established. The findings of this paper can facilitate an effective understanding of the creep effect of I/II/III mixed mode fracture and its micromechanism. The research results will have a certain reference value for the detection and risk mitigation of instantaneous and time-delayed rockbursts.

Introducing the area under stress–velocity curve: Theory, measurement and association with rock properties

AbstractSince many years ago, ultrasonic velocity has been used to investigate the physical and mechanical behaviour of rocks, thereby playing an important role in reservoir characterization and seismic interpretation. In order to develop the knowledge of ultrasonic tools, we performed a noble analysis on the ultrasonic behaviour of rocks under confining stress and evaluated a distinctive property of porous media that is measured as the area under the stress–velocity curve (here defined as S*). We further investigated its relationship with elastic and mechanical behaviours of rock. To validate the theoretical framework developed in this work, 20 core plugs from various rock units with complex microstructures were subjected to triaxial compressional tests to calculate their area under the curve. Calculations were made for crack‐closing, elastic and post‐elastic stages (e.g. pore collapse) along the ultrasonic velocity–stress curve. Moreover, the selected samples had their microstructure investigated by thin‐section studies to quantify their porosity and pore type. The results were analysed to check for the effect of pore type on S* in different stages of the stress–velocity curve. Based on the outputs of the analysis of variance and Pearson's correlation coefficient analysis, the curve had its shape and underlying area closely related to the porosity and pore geometry. Indeed, the results showed that the shale and sandstone with micro cracks and carbonate with stiff pores correspond to smaller and larger areas under the curve in crack‐closing and inelastic stages, respectively. Cross‐correlating the results to compressibility (inverse of bulk modulus), it was figured out that the calculated area under curve was well consistent with the compressibility. In addition, S* represents both static and dynamic behaviours of the rock, and the results revealed that the shape and curvature of the stress–velocity curve give valuable information about the rock microstructure. Another finding was the fact that the type of fluid and wave velocity seemingly affect the S*. Our findings can help interpret wave velocity behaviour in reservoir rocks and other stressful porous media.

First-principles study of binary and ternary phases in Mg-Gd-Ni alloys

Given the high demand for magnesium alloys across industries, it's crucial to enhance their performance by developing alloys with superior characteristics. The performance of magnesium alloys is closely related to the properties of the precipitated phase. However, there has been insufficient exploration of the mechanical properties of precipitated phases in Mg-Gd-Ni alloys. Hence, this paper calculates the formation energy, electronic structure, elastic modulus, and elastic anisotropy of the precipitated phase in Mg-Gd-Ni alloys using first principles. Calculations of formation energies and elastic constants demonstrate that MgGdNi4, Mg2Ni, 18R-LPSO, Mg2Gd, and 14H-LPSO possess commendable thermodynamic and mechanical stability. Elastic modulus calculations reveal a significant increase in the elastic modulus of magnesium, especially the bulk modulus, upon the addition of Gd and Ni elements, increasing from 34.5 GPa to a peak of 84.9 GPa. Furthermore, the strength increments of the corresponding precipitated alloys, calculated based on the elastic modulus, underscore MgGdNi4 as exhibiting the most significant strength increment. The elastic anisotropy of each second phase is evaluated using the elastic anisotropy factor, the three-dimensional surface, and the projection onto each two-dimensional plane. The order of elastic modulus anisotropy for shear and Young's modulus is MgGdNi4 > Mg2Ni > 18R-LPSO > Mg2Gd > 14H-LPSO. This study provides valuable data for regulating properties in magnesium alloys.