Aggregate Elastic Moduli Research Articles

Single‐Crystal Elasticity of Phase E at High Pressure and Temperature: Implications for the Low‐Velocity Layer Atop the 410‐km Depth

AbstractDense hydrous magnesium silicate (DHMS) phase E is a potential water carrier in subducting slabs that can transport water to the Earth's deep mantle between the bottom of the upper mantle and the uppermost transition zone. Therefore, knowledge on the high pressure‒temperature (P‒T) full elastic moduli of phase E at relevant mantle conditions is important in deciphering the existence of DHMS phases and their influences on seismic profiles in the region; however, the high P‒T elasticity data of phase E still remains lacking. In this work, we determined the combined effect of P‒T on the single‐crystal elasticity of phase E up to 24 GPa and 900 K by in situ X‐ray diffraction and Brillouin scattering measurements in externally‐heated diamond anvil cells. The aggregate elastic moduli and compressional‐wave (VP) and shear‐wave (VS) velocities of phase E are then derived by analyzing the single‐crystal elasticity and density data using the third‐order finite‐strain equations. We found that phase E exhibits much lower bulk and shear moduli and acoustic velocities than the most abundant constituent minerals in the upper mantle and transition zone, such as olivine, clinopyroxene, garnet, and wadsleyite. The modeled results using the obtained elasticity results show that the existence of phase E in a hydrated pyrolite model can result in relatively lower Vp and Vs profiles and negative velocity anomalies in seismic observations. The existence of phase E with relatively lower velocity profiles could be a possible origin of the low‐velocity layers atop the 410‐km discontinuity in some cold and highly‐hydrated regions.

Single Crystal Elastic Properties of Hemimorphite, a Novel Hydrous Silicate

Hemimorphite, with the chemical formula Zn4Si2O7(OH)2·H2O, contains two different types of structurally bound hydrogen: molecular water and hydroxyl. The elastic properties of single-crystal hemimorphite have been determined by Brillouin spectroscopy at ambient conditions, yielding tight constraints on all nine single-crystal elastic moduli (Cij). The Voigt–Reuss–Hill (VRH) averaged isotropic aggregate elastic moduli are KS (VRH) = 74(3) GPa and μ (VRH) = 27(2) GPa, for the adiabatic bulk modulus and shear modulus, respectively. The average of the Hashin–Shtrickman (HS) bounds are Ks (HS) = 74.2(7) GPa and and μ (HS) = 26.5(6) GPa. Hemimorphite displays a high degree of velocity anisotropy. As a result, differences between upper and lower bounds on aggregate properties are large and the main source of uncertainty in Ks and μ. The HS average P wave velocity is VP = 5.61(4) km/s, and the HS S-wave velocity is VS = 2.77(3) km/s. The high degree of elastic anisotropy among the on-diagonal longitudinal and pure shear moduli of hemimorphite are largely explained by its distinctive crystal structure.

The structural and elastic properties of a full-Heusler compound Cu2MnAl under pressure

First-principles calculations of the crystal structure and the elastic constants of Cu2MnAl Heusler compound have been investigated by the plane-wave pseudopotential density functional theory method. The calculated lattice and elastic constants are in agreement with the experimental and existing theoretical calculations. Based on the elastic constants, the aggregate elastic moduli (B, G), Poisson�s ratio, elastic anisotropy, melting point and Debye temperature with pressure have been investigated. It is found that the ductility, elastic anisotropy, melting point and Debye temperature increase with increasing pressure.

Understanding the Tabletability Differences between Indomethacin Polymorphs Using Powder Brillouin Light Scattering

The unconventional tabletability of the indomethacin polymorphs - α and γ - are investigated from a topological and mechanical perspective using powder Brillouin light scattering (p-BLS) to identify the specific structure-performance relationship in these materials. Indomethacin (γ-form) was purchased and used to prepare the α polymorph. Powder X-ray diffraction was used to confirm phase identity, while p-BLS was used to obtain the mechanical properties. Energy frameworks were determined with Crystal Explorer to visualize the interaction topologies. Using a Carver press and a stress-strain analyzer, the tableting performance of each polymorph was determined. Polymorph-specific acoustic frequency distributions were observed with distinct, zero-porosity, aggregate elastic moduli determined. The p-BLS spectra for α-indomethacin display a population of low-velocity shear modes, indicating a direction of facilitated shear. This improves slip-mediated plasticity and tabletability. Our p-BLS spectra experimentally indicates that a low-energy slip system is available to α-indomethacin which supports ours and previous energy framework calculations. Despite a 2d-layered crystal motif favorable for shear deformation, the γ-form displays a higher shear modulus that is supported by our hydrogen-bonding analysis of γ-indomethacin. Our experimental, mechanical data is consistent with the predicted interaction topologies and these two inputs combined permit a comprehensive, molecular understanding of polymorph-specific tabletability.

Thermoelasticity of Iron‐ and Aluminum‐Bearing MgSiO3 Postperovskite

AbstractWe present ab initio (LDA + Usc) studies of high‐temperature and high‐pressure elastic properties of pure as well as iron‐bearing (ferrous, Fe2+, and ferric, Fe3+) and aluminum‐bearing MgSiO3 postperovskite, the likely dominant phase in the deep lower mantle of the Earth. Thermal effects are addressed within the quasiharmonic approximation by combining vibrational density of states and static elastic coefficients. Aggregate elastic moduli and sound velocities for the Mg end members are successfully compared with scarce experimental data available. Effects of iron (Fe) and aluminum (Al) substitutions on elastic properties and their pressure and temperature dependence have been thoroughly investigated. At the observed perovskite to postperovskite transition (P = 125 GPa and T = 2,500 K), compressional and shear velocities increase by 0–1% and 1.5–3.75%, respectively. This observation is consistent with some seismic studies of the D′′ discontinuity beneath the Caribbean, which suggests that our robust estimates of elastic properties of the postperovskite phase will be very helpful to understand lateral velocity variations in the deep lower mantle region and to constrain its composition and thermal structure.

Pressure effect on the mechanical and electronic properties of orthorhombic-C20

A systematic investigation of structural, mechanical, elastic anisotropy and electronic properties of a recently reported novel superhard material orthorhombic [Formula: see text] ([Formula: see text]-[Formula: see text]) under pressure is performed utilizing the density functional theory in this work. The crystal structure parameters are obtained at zero as well as at high pressure. Pressure induced elastic constants [Formula: see text], polycrystalline aggregate elastic modulus [Formula: see text], [Formula: see text] ratio, and Debye temperature changes for [Formula: see text]-[Formula: see text] have been determined. The crystal elastic anisotropies of the ultra-incompressible [Formula: see text]-[Formula: see text] are investigated in the pressure range of 0–100 GPa. The Lyakhov–Oganov model is applied to predict the hardness as functions of pressure. The calculated results reveal that [Formula: see text]-[Formula: see text] possesses high elastic anisotropy under zero pressure and high pressure, and the hardness of [Formula: see text]-[Formula: see text] decreases with pressure, while the Debye temperature behaves with the opposite trend. The results of electronic structure indicate that [Formula: see text]-[Formula: see text] exhibits insulator characteristics, and the band gap increases with pressure. This work is expected to provide a useful guide for the future synthesis and application of [Formula: see text]-[Formula: see text].

The Preference of the Ferromagnetic Ordering for the Novel Heusler Rh 2 MnTi ${\text {Rh}}_{\text {2}}\text {MnTi}$ Compound

Rh2MnTi is a novel magnetic material at potentially high speed in modern technologies. ${\text {Rh}}_{\mathrm {2}}\text {MnTi}$ is susceptible to structural distortion of the ferromagnetic tetragonal Heusler. We tried to provide additional information on the magnetic order for this material through a study by means of first-principle calculations. The numerical work on the electronic and magnetic structural parameters of ${\text {Rh}}_{\mathrm {2}}\text {MnTi}$ crystal was carried out within the density functional theory level as implemented in all-electron full-potential linearized augmented plane wave (FP-LAPW) method. The dependence of the elastic constants Cij for cubic structure, the aggregate elastic moduli B and G, and the related mechanical properties are investigated. The calculated density of states (DOS) and band structure for ${\text {Rh}}_{\mathrm {2}}\text {MnTi}$ show the absence of energy band gap in their minority-spin channel which moves away half-metallic character, the magnetic moments, and Curie temperature in both the ferromagnetic and antiferromagnetic ordering are also investigated. The dependence of Seebeck coefficient, electrical conductivity, and power factor on the Fermi level are investigated.

Coherent Timescales and Mechanical Structure of Multi-Cellular Aggregates

3D cellular aggregates are a broadly studied model system for biological processes including morphogenesis, carcinogenesis, malignant invasion, wound healing, and tissue engineering. Tissue-like aggregates are well known to exhibit liquid-like behavior in the long-times (hours), particularly manifesting a “surface tension” analogous to liquids. On the other hand, the mechanical behavior in the short times (seconds to minutes) is very different and has received less attention. The current work uses shape relaxation experiments to investigate the structural characteristics of aggregates in the short times. Two coherent timescales are observed, one on the order of seconds; the other, tens of seconds. Both are found to be persistent across all examined cell types (GBM, 3T3, Rat2, L-cells) despite drastic changes in other properties such as tissue surface tension (by two orders of magnitude) and adhesion strength. A precise mathematical theory previously developed is used to extract the viscoelastic properties of aggregates from the measured timescales. The analysis suggests that aggregates are a composite of an unusually “soft” interior (weak bulk elastic modulus) enclosed by a relatively stiffer envelope. Additionally, aggregate surface tension, elastic modulus, and viscosity observe proportionality. This result suggests that the underlying cellular properties are regulated in a precise manner. The root-cause for multi-cellular aggregation to preserve such timescales requires further investigation.

Mechanical behaviour of porous lanthanide oxide microspheres: Experimental investigation and numerical simulations

Actinide oxide microspheres are considered as promising substituents to powder precursors for the production of ceramic pellets of nuclear fuel or targets. Porous microspheres of sub-millimetric size are synthesised using the Weak Acid Resin process. Controlling their microstructure and their mechanical properties is essential to predict the microstructure of green compacts and sintered pellets. Here, cerium and gadolinium are used to mimic actinides as metal cation. Single microspheres are crushed experimentally using a micropress in a Scanning Electron Microscope (SEM) to investigate their mechanical properties and visualise their fracture behaviour. The results are compared to numerical simulations based on the Discrete Element Method (DEM). In DEM, a microsphere is modelled as an assembly of bonded spheres representing aggregates. Bonds may fracture in tension or shear. A limited number of material parameters (aggregate elastic modulus, bond strength) are sufficient for the accurate simulation of the fracture behaviour of a microsphere.

Influence of the iron spin crossover in ferropericlase on the lower mantle geotherm

AbstractThe iron spin crossover in ferropericlase introduces anomalies in its thermodynamics and thermoelastic properties. Here we investigate how these anomalies can affect the lower mantle geotherm using thermodynamics properties from ab initio calculations. The anomalous effect is examined in mantle aggregates consisting of mixtures of bridgmanite, ferropericlase, and CaSiO3 perovskite, with different Mg/Si ratios varying from harzburgitic to perovskitic (Mg/Si ∼ 1.5 to 0.8). We find that the anomalies introduced by the spin crossover increase the isentropic gradient and thus the geotherm proportionally to the amount of ferropericlase. The geotherms can be as much as ∼200 K hotter than the conventional adiabatic geotherm at deep lower mantle conditions. Aggregate elastic moduli and seismic velocities are also sensitive to the spin crossover and the geotherm, which impacts analyses of lower mantle velocities and composition.

Aggregate Elasticity, Crystal Structure, and Tableting Performance for p-Aminobenzoic Acid and a Series of Its Benzoate Esters.

The tableting performance for p-aminobenzoic acid (PABA) and a series of its benzoate esters with increasing alkyl chain length (methyl-, ethyl-, and n-butyl) was determined over a broad range of compaction pressures. The crystalline structure of methyl benzoate (Me-PABA) exhibits no slip systems and does not form viable compacts under any compaction pressure. The ethyl (Et-PABA) and n-butyl (Bu-PABA) esters each have a similar, corrugated-layer structure that displays a prominent slip plane and improves material plasticity at low compaction pressure. The compact tensile strength for Et-PABA is superior to that for Bu-PABA; however, neither material achieved a tensile strength greater than 2 MPa over the compression range studied. Complementary studies with powder Brillouin light scattering (BLS) show the maxima of the shear wave, acoustic frequency distribution red shift in an order consistent with both the observed tabletability and attachment energy calculations. Moreover, zero-porosity aggregate elastic moduli are determined for each material using the average acoustic frequency obtained from specific characteristics of the powder BLS spectra. The Young's moduli for Et- and Bu-PABA is significantly reduced relative to PABA and Me-PABA, and this reduction is further evident in tablet compressibility plots. PABA, however, is distinct with high elastic isotropy as interpreted from the narrow and well-defined powder BLS frequency distributions for both the shear and compressional acoustic modes. The acoustic isotropy is consistent with the quasi-isotropic distribution of hydrogen bonding for PABA. At low compaction pressure, PABA tablets display the lowest tensile strength of the series; however, above a compaction pressure of ca. 70 MPa PABA tablet tensile strength continues to increase while that for Et- and Bu-PABA plateaus. PABA displays lower plasticity relative to either ester, and this is consistent with its crystalline structure and high yield pressure determined from in-die Heckel analysis. Overall the complementary approach of using both structural and the acoustic inputs uniquely provided from powder BLS is anticipated to expand our comprehension of the structure-mechanics relationship and its role in tableting performance.

Structural Stabilities and Elastic Thermodynamic Properties of SrTe Compound and SrTe1−x Ca x Alloy Under High Pressure

The effect of pressure on the structural, elastic, and thermodynamic properties of SrTe in both B1 (rocksalt) and B2 (CsCl-type) phases and the SrTe1−xCax alloys with Ca dopant concentrations at x = 0.16667, 0.20, 0.33333, 0.42857, 0.44444 and 0.50 have been investigated using the two new gradient-corrected functional developed by Perdew, J.P.; Burke, K.; Ernzerhof named Density-Gradient Expansion for Exchange in Solids (PBEsol) and generalized Wu–Cohen (WC), in a significant range of pressure from 0 GPa to 30 GPa. The structure parameters, elastic stiffness constants cij, the bulk modulus (B), Kleinman parameter (\( \xi \)), shear anisotropies Ashear are also determined. Furthermore, as reported in this study, the aggregate elastic modulus (B, G, E), Poisson’s ratio (ν) and the Lame’s coefficients (λ) are estimated. On the other hand, the ductility, brittleness, longitudinal, transverse sound velocities and the Debye temperature ΘD(T) are also obtained. Importantly, our results are in reasonable agreement with the available theoretical and experimental data. To the best of our knowledge, this is the first study of the effect of the composition on the properties of the SrTe1−xCax alloys which may encourage other works for the confirmation of the reported results.

High-pressure elastic properties of cubic Ir2P from ab initio calculations

A study of the high-pressure elastic properties of new synthetic Ir2P in the anti-fluorite structure is conducted using ab initio calculations based on density functional theory. The elastic constants C11, C12 and C44 for the cubic Ir2P are obtained by the stress-strain method and the elastic stability calculations under pressure indicate that it is stable at least 100 GPa. Additionally, the electronic density of states, the aggregate elastic moduli, that is bulk modulus, shear modulus, and Young's modulus along with the Debye temperature, Poisson's ratio, and elastic anisotropy factor are all successfully obtained. Moreover, the pressure dependence of the longitudinal and shear wave velocities in three different directions [100], [110], and [111] for Ir2P are also predicted for the first time.

Thermoelasticity of Fe3+‐ and Al‐bearing bridgmanite: Effects of iron spin crossover

AbstractWe report ab initio (LDA + Usc) calculations of thermoelastic properties of ferric iron (Fe3+)‐ and aluminum (Al)‐bearing bridgmanite (MgSiO3 perovskite), the main Earth forming phase, at relevant pressure and temperature conditions and compositions. Three coupled substitutions, namely, [Al]Mg‐[Al]Si, [Fe3+]Mg‐[Fe3+]Si, and [Fe3+]Mg‐[Al]Si have been investigated. Aggregate elastic moduli and sound velocities are successfully compared with limited experimental data available. In the case of [Fe3+]Mg‐[Fe3+]Si substitution, the high‐spin (S = 5/2) to low‐spin (S = 1/2) crossover in [Fe3+]Si induces a volume collapse and elastic anomalies across the transition region. However, the associated anomalies should disappear in the presence of aluminum in the most favorable substitution, i.e., [Fe3+]Mg‐[Al]Si. Calculated elastic properties along a lower mantle model geotherm suggest that the elastic behavior of bridgmanite with simultaneous substitution of Fe2O3 and Al2O3 in equal proportions or with Al2O3 in excess should be similar to that of (Mg,Fe2+)SiO3 bridgmanite. However, excess of Fe2O3 should produce elastic anomalies in the crossover pressure region.

Structural and elastic stabilities of InN in both B4 and B1 phases under high pressure using density-functional perturbation theory

Structural and elastic properties of InN in both B4 (wurtzite) and B1 (rocksalt) phases are studied over a wide range of pressures from 0 to 20 GPa at T = 0 K, using the density functional perturbation theory (DFPT) for the first time. Pressure dependencies of the total energy, structure parameters, elastic stiffness constants cij, bulk modulus, Kleinman internal strain parameter, shear anisotropies and their relationship to elastic stability are also explored. In addition, the aggregate elastic modulus (B, G, E), Poisson's ratio (ν) and Lame's coefficients (λ) are estimated within the framework of Voigt–Reuss–Hill approximation for ideal polycrystalline InN aggregates, and thus the longitudinal and transverse sound velocities are obtained. We estimated the Debye temperature ΘD(T), energy E(T), entropy S(T), free energy F(T), and lattice heat capacity cv(T) as a function of temperature at null pressure for B4 (wurtzite) phase. Our results are in reasonable agreement with the available theoretical and experimental data for B4 phase. To our knowledge this is the first quantitative theoretical prediction of the B1 (rocksalt) that is still awaiting experimental confirmations.

Pressure-induced structural phase transition, elastic and thermodynamic properties of ReC under high pressure

The pressure-induced structural phase transition of rhenium monocarbon (ReC) is investigated via the projector augmented wave (PAW) method with the generalized gradient approximation (GGA). Using the first-principles calculations, the equilibrium structural parameters of ReC in rocksalt (NaCl), cesium chloride (CsCl), zinc blende (ZB), wurtzite (WZ), nickel arsenide (NiAs) and tungsten carbide (WC) types are successfully obtained, and the results are well consistent with other theoretical data. It is firstly noted that WC-ReC translates into CsCl-ReC at 510.50 GPa by analyzing the enthalpy difference versus pressure. From the calculated elastic constants, the aggregate elastic modulus (B, G, E), the Poisson's ratio (σ) and the Debye temperature ΘD of WC-type are also derived. It is observed that all the data of WC-ReC obtained increase monotonically with increasing pressure. Meanwhile, the thermodynamic properties of WC-ReC under high temperature and high pressure are investigated applying nonempirical Debye model in the quasi-harmonic approximation.

Elasticity of single-crystal quartz to 10 GPa

The second-order elastic constants of quartz were determined by Brillouin spectroscopy to 10 GPa in a diamond anvil cell. All elastic constants exhibit smooth pres- sure trends. A decrease in the magnitudes of C14 and C66 with pressure is observed, while C 44 shows a weak pressure dependence. Our measured elastic constants are more con- sistent with previous density functional theory calculations than with earlier experimental results. Aggregate elastic moduli were calculated and fit to a finite-strain equation of state, yielding values for the pressure derivatives of the adia- batic bulk modulus, K 0S ʹ, and shear modulus, G 0 ʹ, of α-quartz of 6.2(2) and 0.9(1), respectively. The equation of state obtained from our data is consistent with static X-ray diffrac- tion data. A finite-strain extrapolation of our data predicts a violation of a Born stability criterion, indicating a mechani- cal instability in the structure, at ~26 GPa which is broadly consistent with the pressure range at which a phase transition and pressure-induced amorphization in quartz are observed.

Elasticity and Thermodynamic Properties of EuS Related to Phase Transition

First-principles calculations of the crystal structures, phase transition, and elastic properties of EuS have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as some of the existing model calculations. The dependence of the elastic constants, the aggregate elastic modulus, and the elastic anisotropy on pressure have been investigated. Moreover, the variation of the Poisson’s ratio, Debye temperature, and the compressional and shear elastic wave velocities with pressure have been investigated for the first time. Through the quasi-harmonic Debye model, the thermal expansions, heat capacities, Grneisen parameters and Debye temperatures dependence on the temperature and pressure are obtained in the pressure range from 0 GPa to 60 GPa and temperature range from 0 K to 800 K.

First-principles calculations of elastic and thermodynamic properties of the four main intermetallic phases in Al–Zn–Mg–Cu alloys

First-principles calculations are performed to investigate the structural, elastic, and thermodynamic properties of the four main intermetallic phases, namely, MgZn2, Al2CuMg, Al2Cu, and Al3Zr, in Al–Zn–Mg–Cu alloys. The calculated lattice parameters agree with experimental and theoretical values. The formation enthalpy (ΔH) decreases in the order Al3Zr>MgZn2>Al2CuMg>Al2Cu, whereas the binding energy (Eb) decreases in the order Al3Zr>Al2Cu>Al2CuMg>MgZn2. The calculated result is in accordance with the experimental phenomena. The elastic constants Cij, aggregate elastic modulus (B, G, E), Poisson’s ratio, elastic anisotropy, and Debye temperature have been calculated. The calculated intermetallic phases exhibit elastic anisotropy on the basis of the universal elastic anisotropy index AU. According to the critical values for B/G and Poisson’s ratio, MgZn2 is a ductile phase, whereas Al2CuMg, Al2Cu, and Al3Zr are brittle phases. The Debye temperature decreases in the order Al3Zr>Al2CuMg>Al2Cu>MgZn2. The electronic structures have been investigated based on band structures and density of states. Metallic bonding mode coexists with a fractional ionic interaction in MgZn2, Al2CuMg, and Al2Cu. In Al3Zr, metallic bond coexists with covalent interaction. The temperature and pressure dependencies of volume, heat capacity, and thermal expansion coefficient are investigated systematically in pressures ranging from 0GPa to 20GPa and at temperatures ranging from 0K to 900K.

Non-linear elastic behavior of hexagonal silicon carbide

The full sets of non-vanishing second- and third-order elastic constants (SOEC and TOEC) in 2H-SiC have been determined by the method of homogeneous deformation with interactions extending upto fourth neighbors using the sublattice displacement to the first degree in strains. The effective SOEC are obtained in terms of SOEC and TOEC. The aggregate elastic moduli and its pressure dependence have been studied. In 2H-SiC, the value of , showing the compressibility along the ab-plane to be larger, reducing the system more anisotropic, which is corroborated in the pressure derivatives of SOEC. TOEC of the shear modes, like and have smaller values than their longitudinal counterparts like and , uantifying the effect of pressure on the longitudinal wave velocity to be greater. Absolute value of , predicting anisotropy along ab-plane to be more pronounced than c-axis. The pressure derivatives for the longitudinal moduli ( and ) are positive while the shear moduli ( and ) are negative, consistent with the pressure derivatives of the bulk modulus () and shear modulus () of polycrystalline 2H-SiC. The elastic shear softening predicts the B4 -to-B1 structural phase transformation in 2H-SiC.