A dynamic Young's modulus measurement system for highly compliant polymers

A new system to determine experimentally the complex Young's modulus of highly compliant elastomers at elevated hydrostatic pressures and as a function of temperature is presented. A sample cut in the shape of a bar is adhered to a piezoelectric ceramic shaker and mounted vertically inside a pressure vessel equipped with glass windows. Two independent measurement methods are then used: a resonant technique, to obtain low-frequency data, and a wave propagation technique, to obtain higher-frequency data. Both techniques are implemented utilizing laser Doppler vibrometers. One vibrometer detects sample resonances through a window located at the bottom of the pressure vessel, and a set of two separate vibrometers monitors the speed of longitudinal waves propagating in the sample, through windows located on the sides of the vessel. The apparatus is contained inside an environmental chamber for temperature control. Using this approach, Young's modulus data can be obtained at frequencies typically ranging from 100 Hz to 5 kHz, under hydrostatic pressures ranging from 0 to 2.07 MPa (300 psi), and at temperatures between -2 degrees C and 50 degrees C. Experimental results obtained on two commercial materials, Rubatex R451N and Goodrich Thorodin AQ21, are presented. The effects of lateral inertia, resulting in dispersive wave propagation, are discussed and their impacts on Young's modulus measurements are examined.     

First-principles investigations on elastic, phonon and thermodynamic properties of SrB6 under pressure

The elastic, phonon and thermodynamic properties of the divalent alkaline-earth hexaboride SrB₆ are investigated by using plane-wave pseudopotential density functional theory method. The calculated structure parameters and bulk modulus are well consistent with the available experiment and theoretical data. The pressure dependences of elastic constants C_ij, bulk modulus B₀, shear modulus G, Young's modulus E and Poisson's ratio σ are also presented. With these elastic parameters, we investigate the mechanical stability and compressibility of SrB₆. For the thermodynamic properties, both phonon and quasi-harmonic Debye model methods are adopted. Through the comparison with experimental and other theoretical results, we found the method of quasi-harmonic Debye model is a little better. Moreover, the phonon dispersion relations are also obtained. It is found that there are two LO/TO splitting around 5 THz and 26 THz, respectively.     

Numerical study of pressure relationships between sample and calibrant inside the diamond anvil cell

We present isotropic, elastic-plastic finite element calculations detailing the pressure relationship between an inclusion and its surrounding matrix, subject to an externally imposed hydrostatic strain. In general, the inclusion and the matrix have different values of hydrostatic pressure, depending on their absolute and relative values of Young's modulus and Poisson's ratio. A series of finite element models was used to explore the parameter space of the elastic and plastic properties of an inclusion within a matrix. In all cases where there is insufficient relaxation of the nonhydrostatic stress, the material with the higher bulk modulus will also have a higher pressure, regardless of the shear moduli. The complete data set was subjected to a Pareto analysis to determine the main and secondary effects which influence the final result, expressed as the ratio of the pressure of the matrix to that of the inclusion. The four most important factors which determine the pressure ratio of an inclusion and matrix are the Young's modulus of the matrix, the interaction of the Young's modulus and the yield strength of the matrix material, the Young's modulus of the inclusion, and the interaction of the Young's modulus of the inclusion with the yield strength of the matrix material. The yield strength of the inclusion has a statistically insignificant effect on the results. This information provides guidelines for designing the most effective combinations of unknowns and material standards to minimize pressure errors in equation of state measurements.     

Electronic, elastic, optical properties of rutile TiO2 under pressure: A DFT study

The electronic, elastic constants and optical properties of rutile TiO₂ have been investigated using first principle pseudopotential method within generalized gradient approximation (GGA) proposed by Perdew-Burke-Ernzerhof (PBE). The calculated volume, bulk modulus and pressure derivative of bulk modulus are in good agreement with previous experimental and computational results. An underestimated band gap (1.970 eV) along with the higher density of states and expanded energy bands around the fermi level is obtained. Calculated elastic constants satisfying the Born stability criteria suggest that rutile TiO₂ is mechanically stable under higher hydrostatic pressure. The acoustic wave speeds in [1 0 0], [0 1 0], [0 0 1], [1 1 0] and [45° to [1 0 0] and [0 0 1]] directions are predicted using the investigated elastic constants. The dielectric constant is identified with respect to electronic band structure and is utilized to derive the other optical properties like refractive index, energy loss function, reflectivity and absorption. The effect of hydrostatic pressure (0-70 GPa) is described for listed properties. Our investigated results are in good accord with the existing theoretical and experimental results.     

First-Principles Calculations of Structural,Elastic and ElectronicProperties of Tetragonal HfO2under Pressure

Structural, elastic and electronic properties of tetragonal HfO₂ at applied hydrostatic pressure up to 50 GPa have been investigated using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT). The calculated ground-state properties are in good agreement with previous theoretical and experimental data. Six independent elastic constants of tetragonal HfO₂ have been calculated at zero pressure and high pressure. From the obtained elastic constants, the bulk, shear and Young's modulus, Poisson's coefficients, acoustic velocity and Debye temperature have been calculated at the applied pressure. Band structure shows that tetragonal HfO₂ is an indirect band gap. The variation of the gap versus pressure is well fitted to a quadratic function.     

Analysis of Long-Term Optical Effects in Double-Coated Optical Fibers Induced by Hydrostatic Pressure and Thermal Loading

The hydrostatic pressure and thermal loading simultaneously induced optical effects in double-coated optical fibers in the long-term are analyzed by the viscoelastic theory. Using the Laplace transformation method, close-form solutions for the microbending loss and refractive index changes are obtained. The results of the microbending loss are initially identical to those obtained by the elastic analysis, and then decrease gradually as time progresses. The microbending loss and refractive index changes of the glass fiber are functions of the material properties of the primary and secondary coatings. To minimize the microbending loss and refractive index changes in the long-term, the Young's modulus of the primary coating, and the viscosity and Poisson's ratio of the secondary coating should be increased. Nevertheless, the viscosity and Poisson's ratio of the primary coating, and the Young's modulus of the secondary coating should be decreased.     

Transverse elasticity of multi-walled carbon nanotubes

A discrete shell model is proposed to describe the radial deformation of carbon nanotubes under a hydrostatic pressure and the radial Young's modulus of (single- or multi-walled) nanotubes is obtained. It is found that the radial modulus decreases with increasing tube diameter while increases with increasing number of layers. The computational results agree well with the previous results of SWNTs and indicate that the radial modulus of carbon nanotubes is independent of the Poisson's ratio.     

Phase diagram of kaolinite from Molecular Dynamics calculations

Structural and thermal behaviors of uncharged 1:1 phyllosilicates kaolinite were investigated from molecular dynamics simulations based on the CLAYFF force field. The focus is on the variation of structural properties including bulk modulus with pressure from 0 to 20 GPa under various range of temperature. The largest bulk modulus between the pressures of 200 and 800 MPa varies from 80 GPa at 298 K to 50 GPa at 1473 K. The obtained value of C_p varies between 7.8 and 13.6 Kcal mol⁻¹ K⁻¹ in the pressure range of 0.1 MPa–20 GPa. Besides, a huge difference was noticed regarding the computed properties at the superheating point. Finally, we show the relationship between superheating point temperature and pressure leading to a phase diagram of kaolinite.     

Electronic and structural properties of zincblende AlxIn1−xN

Numerical calculations based on first-principles are applied to study the electronic and structural properties of ternary zincblende AlInN alloy. The results indicate the lattice constant has a small deviation from the Vegard’s law. The direct and indirect bowing parameters of 4.731 ± 0.794 eV and 0.462 ± 0.285 eV are obtained, respectively, and there is a direct-indirect crossover near the aluminum composition of 0.817. The bulk modulus is monotonically increased with an increase of the aluminum composition, and the deviation parameter of bulk modulus of 10.34 ± 9.37 GPa is obtained. On the contrary, the pressure derivative of bulk modulus is monotonically decreased with an increase of the aluminum composition.     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ 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 with some of the existing model calculations. The elastic constants c_ij, the aggregate elastic moduli (B, G, E), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Grüneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.     

Theoretical study of the structural phase transition and elastic properties of HfN under high pressures

The effect of hydrostatic pressure on the structures of HfN at 0 K was investigated by using the projector augmented wave (PAW) within the Perdew–Burke–Ernzerhof (PBE) form of the generalized gradient approximation (GGA). The transition pressure between NaCl (B1) and CsCl (B2) structures is predicted to be 277.3 GPa. This value is consistent with that reported by Kroll, while in contrast to the results obtained by Ojha et al. and Meenaatci et al. Moreover, the elastic properties of B1-HfN and B2-HfN under high pressures are successfully obtained. It is found that the elastic constants, bulk modulus B, shear modulus G, compressional and shear wave velocities increase monotonically with increasing pressure. The Debye temperature Θ calculated from the elastic constants of HfN is in good agreement with the experimental values. The anisotropies of B1-HfN and B2-HfN at zero pressure have also been discussed.     

Characterization of hydrogenated amorphous carbon thin films by end-Hall ion beam deposition

Pure hydrogenated amorphous carbon (α-C:H) and nitrogen doped hydrogenated amorphous carbon (α-C:H:N) thin films were prepared using end-Hall (EH) ion beam deposition with a beam energy ranging from 24 eV to 48 eV. The composition, microstructure and mechanical properties of the films were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), Raman spectroscopy, scanning probe microscopy (SPM), and nano-scratch tests. The films are uniform and smooth with root mean square roughness values of 0.5-0.8 nm for α-C:H and 0.35 nm for α-C:H:N films. When the ion energy was increased from 24 eV to 48 eV, the fraction of sp³ bonding in the α-C:H films increased from 36% to 55%, the hardness increased from 8 GPa to 12.5 GPa, and the Young's modulus increased from 100 GPa to 130 GPa. In the α-C:H:N films, N/C atomic ratio, the hardness and Young's modulus of the α-C:H:N films are, 0.087, 15 and 145 GPa, respectively. The results indicate that both higher ion energy and a small amount of N doping improve the mechanical properties of the films. The results have demonstrated that smooth and uniform α-C:H and α-C:H:N films with large area and reasonably high hardness and Young's modulus can be synthesized by EH ion source.     

Structural and elastic properties under pressure effect of the cubic antiperovskite compounds ANCa3 (A = P, As, Sb, and Bi)

Using first-principles density functional calculations, the effect of high pressures, up to 40 GPa, on the structural and elastic properties of ANCa₃, with A = P, As, Sb, and Bi, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation and the generalized gradient approximation for exchange-correlation effects. The lattice constants are in good agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline ANCa₃ aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that ANCa₃ compounds are brittle in nature. We estimated the Debye temperature of ANCa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of PNCa₃, AsNCa₃, SbNCa₃, and BiNCa₃ compounds, and it still awaits experimental confirmation.     

Regulation of the elastic modulus of polyurethane microarrays and its influence on gecko-inspired dry adhesion

We studied the influence of the elastic modulus on the gecko-inspired dry adhesion by regulating the elastic modulus of bulk polyurethane combined with changing the size of microarrays. Segmented polyurethane (PU) was utilized to fabricate micro arrays by the porous polydimethyl siloxane (PDMS) membrane molding method. The properties of the micro arrays, such as the elastic modulus and adhesion, were investigated by Triboindenter. The study demonstrates that bulk surfaces show the highest elastic modulus, with similar values at around 175 MPa and decreasing the arrays radius causes a significant decrease in E, down to 0.62 MPa. The corresponding adhesion experiments show that decrease of the elastic modulus can enhance the adhesion which is consistent with the recent theoretical models.     

Anisotropy of Young's modulus,shear modulus,and Poisson's ratio for the B2-phase of a Ti50Ni48Fe2 single crystal under hydrostatic compression conditions up to 0.6 GPa

We present calculations of Young's modulus, the shear modulus, and Poisson's ratio as a function of direction in the (100) and (110) planes of the B2 phase of a Ti₅₀Ni₄₈Fe₂ single crystal. The calculations were done on the basis of our measurements of the velocities of transverse and longitudinal ultrasonic waves propagating in the indicated alloy at atmospheric pressure and for a hydrostatic pressure of 0.6 GPa at a temperature of 298 K. We have shown that in contrast to the effect of temperature, as the pressure is reduced along the pathway to the martensitic transformation B2 R, application of pressure to the alloy found in the same pretransitional state increases the anisotropy of the crystal lattice.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–49, March, 1995.     

Structural and elastic properties of TiN under high pressure

We have investigated the structural and elastic properties of TiN at high pressures by the first-principles plane wave pseudopotential density functional theory method at applied pressures up to 45.4 GPa. The obtained normalized volume dependence of the resulting pressure is in excellent agreement with the experimental data investigated using synchrotron radial x-ray diffraction (RXRD) under nonhydrostatic compression up to 45.4 GPa in a diamond-anvil cell. Three independent elastic constants at zero pressure and high pressure are calculated. From the obtained elastic constants, the bulk modulus, Young's modulus, shear modulus, acoustic velocity and Debye temperature as a function of the applied pressure are also successfully obtained.     

Ab initio calculation of elastic properties of rock-salt and zinc-blend MgS under pressure

The elastic properties of zinc-blend (ZB) and rock-salt (RS) MgS are calculated by ab initio method. The calculation shows that the enthalpy for RS structure and for ZB structure essentially is the same at ambient pressure. The ZB structure becomes unstable above 5 GPa. For these two structures, the pressure dependences of typical elastic properties, i.e. the bulk modulus, the shear modulus, the Young's modulus, the Poisson's ratio, and the anisotropy factor, are presented. The Debye temperature and sound velocity under high pressure have also been calculated. Debye approximation is used to estimate the zero-point vibrational energy.     

Compression behavior of nanocrystalline anatase TiO2

We present a synchrotron X-ray diffraction study of pressure-induced changes in nanocrystalline anatase (with a crystallite size of 30-40 nm) to 35 GPa. The nanoanatase was observed to a pressure above 20 GPa. Direct transformation to the baddeleyite-TiO₂ polymorph was seen at 18 GPa. A fit of the pressure versus volume data to a Birch-Murnaghan equation yielded the following parameters: zero-pressure volume, V₀=136.15 Å³, bulk modulus, K_T=243(3) GPa, and the pressure derivative of bulk modulus, K′=4 (fixed). The bulk modulus value obtained for the nanocrystalline anatase is about 35% larger than that of the macrocrystalline counterpart.     

The structural, elastic and thermodynamical properties of zinc-blend structure InN from first principles

A theoretical study of the structural, elastic and thermodynamic properties of the cubic zinc-blende (ZB) structure InN are presented in this paper by performing first principles calculations within local density approximation. The values of lattice constant, bulk modulus and its pressure derivatives and elastic constants are in excellent agreement with the available experimental data and other theoretical results. It is found that the ZB structure InN should be unstable above 20 GPa mechanically. The pressure and temperature dependencies of the bulk modulus, the heat capacity and the thermal expansion coefficient and the entropy S, as well as the Grüneisen parameter are obtained by the quasi-harmonic Debye model in the ranges of 0-1500 K and 0-25 GPa.     

Phase transition, elastic, thermodynamic properties of zinc-blend BeSe from first-principles

The structural phase transition, elastic, thermodynamics properties of BeSe in zinc-blende were investigated by performing first-principles calculations within generalized gradient approximation. The phase transition pressure P_t between the B3 phase and the B8 phase of BeSe was determined. The pressure dependencies of elastic constants, shear modulus, Young's modulus, and Poisson's ratio of BeSe are calculated. The thermodynamic properties of the zinc-blende structure BeSe are calculated by using the quasi-harmonic Debye model. The pressure and temperature dependencies of the heat capacity and the thermal expansion coefficient, as well as the Grüneisen parameter are investigated systematically in the ranges of 0–50 GPa and 0–1200 K.