Pressure and Temperature Dependence of the Elastic Moduli of Na2O-TiO2-SiO2 Glasses

Ultrasonic interferometry was used to measure elastic-wave velocities and moduli in six Na₂O-TiO₂-SiO₂ glasses; three glasses contained 20 mol% TiO₂ and three 25 mol% TiO₂. The elastic moduli and their pressure derivatives varied systematically with the SiO₂/Na₂O molar ratio of the glasses. In the group of glasses which contained 20 mol% TiO₂, dK/dP ( K =bulk modulus) decreased linearly from 4.85 to 2.59 as the SiO₂/Na₂O ratio increased; in the other group, dK/dP decreased from 4.00 to 3.05. Similarly, dμ/dP (μ=shear modulus) decreased with the SiO₂/Na₂O ratio, but somewhat non-linearly. The extrinsic and intrinsic contributions to the temperature dependencies of the elastic moduli are evaluated in light of the measured pressure dependencies of these moduli.     

A comparative study of different concentrations of (Co/Ni/Cu) effects on elastic properties of Li–Mn ferrite employing IR spectroscopy and ultrasonic measurement

Three series of divalent ions (Co²⁺/Ni²⁺/Cu²⁺) substituted into lithium-manganese ferrites were synthesized using a typical ceramic technique. Two different methods were used to investigate their elastic properties. Infrared (IR) spectroscopy showed two essential bands referring to the tetrahedral ‘υ_A’ and the octahedral ‘υ_B’ sites. The force constant, elastic wave velocity and elastic moduli of all specimens have been calculated from the results of IR spectroscopy. Using the ultrasonic pulse transmission (UPT) technique, the longitudinal and shear wave velocities were measured. Using these values; bulk modulus (B), rigidity modulus (G), Young's modulus (E), and Poisson ratio (σ) were determined. In comparison, the elastic moduli resulting from IR spectroscopy results were larger than those obtained from UPT measurements. Because the present ferrite systems are porous, the elastic moduli of the compositions from UPT have been adjusted to zero porosity by two models. The values of the adjusted elastic moduli have been shown to have the same trend as those of the uncorrected elastic moduli. Elastic parameters have generally improved dramatically for Li–Mn–Co ferrite and Li–Mn–Ni ferrite compared to Li–Mn–Cu ferrite. Higher elastic moduli values have been obtained in Li–Mn–Co spinel ferrites, suggesting that such materials are ideal for use in core shapes. Two methods were used to evaluate the Debye temperature of all compositions.     

Dynamical studies of fully oriented deuteropolyethylene by inelastic neturon scattering

Experimental parameters for interchain force fields of polyethylene are measured by neutron triple axis spectrometry and provide some of the first anisotropic information about the forces between carbon chains in simple polymers. Preparation of a bulk specimen of deuteropolyethylene with single crystal texture is reported for the first time. Near Brillouin-zone centre frequencies for both interchain optic and acoustic phonons are derived from neutron scattering studies. These measurements are combined with four frequencies obtained by Raman spectroscopy to give a total of seven experimental parameters for the interchain force field of polyethylene. These are then used to test the available force models. Overall fits of 9 and 19% are provided to these data by two Urey-Bradley force fields. Calculations of the interchain phonon dispersion curves of deuteropolyethylene based on an atom-atom potential parameter model are described. Intermolecular force constants which are derived from an analytical ‘sixexp’ form for the potential between nonbonded atoms are used. These reproduce a wide range of structural and thermodynamic data for many hydrocarbons. This rigid chain model using already fixed parameters fits the observed dynamical data within an average error of 5%. This is significantly better than the fits obtained using the Urey-Bradley force fields with adjustable parameters. The close reproduction of the experimental elastic constants gives support to the calculation of the related elastic moduli perpendicular to the chain axis. Tensile elastic moduli calculated along the two crystallographic axes perpendicular to the chain axis in the orthorhombic cell are very similar, in contrast with earlier predictions. The calculated values of 8 × 10¹⁰ and 9 × 10¹⁰ dyne cm^?2 for b and a moduli agree closely with an average interchain modulus de4rived for the crystal from bulk measurements using a two phase ‘sandwich’ model of composite polyethylene.     

Systematics of elastic and thermodynamic properties of super-hardness cubic boron nitride under high pressure

The elastic constants of cubic boron nitride (c–BN) are calculated by the first-principles method at ambient condition. The dependence of the elastic constants, the bulk modulus B, and the shear modulus G on the applied pressure are presented. The calculated results are in good agreement with the comparable experimental and theoretical values. The deviation from the Cauchy relation and the elastic anisotropy are investigated. The normalized elastic constants c_ij ′ are introduced to investigate elasticity of c–BN in more detail. Moreover, the thermodynamic properties (Debye temperature, melting temperature) and sound velocity have been investigated under high pressure for the first time.     

A comparative study of physical properties in Fe3O4 nanoparticles prepared by coprecipitation and citrate methods

Magnetite exhibits unique structural, electronic, and magnetic properties in extreme conditions that are of great research interest. In this work, the effects of preparation technique on X‐ray peak broadening, magnetic and elastic moduli properties of Fe₃O₄ nanoparticles prepared by coprecipitation (FcP‐NPs) and citrate (FC‐NPs) methods have been investigated. The structural characterization of the samples is evidence for a cubic structure with Fd‐3m space group. The Williamson‐Hall analysis was used to study crystallite sizes and lattice strain of the samples and also stress and energy density. In addition, the crystallite sizes are compared with the particle sizes and the magnetic core sizes obtained from TEM and VSM methods, respectively. In addition, the cation distribution obtained from calculated inversion parameter indicate that in the smaller particles, more amount of Fe²⁺ on the tetrahedral sites can be related to higher stress induced in the FcP‐NPs compared to the FC‐NPs. The saturation magnetization of the FcP‐NPs is almost two times bigger than the saturation magnetization of the FC‐NPs. It could be attributed to the decrease in the negative interaction on the octahedral site and also the magnetic moment on the tetrahedral site of the FcP‐NPs. The increase in force constants of the FC‐NPs determined by infrared spectra analysis compared to FcP‐NPs suggests the strengthening of their interatomic bonding. The values of shear and longitudinal wave velocities obtained from force constants have been used to determine the values of Young's modulus, rigidity modulus, bulk modulus, and Debye temperature. By comparison of the elastic results of FC‐NPs with the FcP‐NPs, we can observe that the elastic properties of the F‐NPs have been improved by synthesis method, while Poisson's ratio almost remains constant. In addition, using the values of the compliance s_ij obtained from elastic stiffness constants, the values of Young's modulus and Poisson's ratio along the oriented direction [hkl] have been calculated for the samples.     

First principles calculation of single‐crystal elastic constants of titanium tetraboride (Ti3B4) and experimental validation

The nine independent single‐crystal elastic constants of a new ceramic, titanium tetraboride (Ti₃B₄), have been determined by first principles calculations, and the data were validated experimentally through nanoindentation testing. The independent elastic constants, which are specific to the crystal structure, are important for the fundamental characterization of mechanical and physical properties of the group of hard compounds such as the transition metal borides. The elastic constants of Ti₃B₄ were determined from crystal strain energies that were calculated by applying specific deformations within WIEN2k platform utilizing full‐potential linear augmented plane wave (FLAPW) and generalized gradient approximation (GGA). The WIEN2K package is based on all‐electron calculations, and hence is considered as the most accurate for first principles calculations. It has been found that the polycrystalline elastic moduli, determined as the Voigt‐Reuss‐Hill averages of the independent elastic constants, are quite impressive (E = 492 GPa, G = 217 GPa, B = 224 GPa, ν = 0.13) placing the tetraboride very close to the well‐known titanium diboride (E = 570 GPa, G = 254 GPa, B = 249 GPa, ν = 0.12). The strong B‐B chains were found to be largely responsible for the high values of elastic stiffness constants, in particular the c₃₃ describing stiffness in the [001] direction. The electron charge densities were found to be accumulated to a higher degree along the B‐B bonds, resulting in strengthening of the B‐B chains in the lattice. The promising data motivated the first experimental synthesis of Ti₃B₄ in a bulk form, which is also described in this work. To validate the elastic constants determined from first principles, elastic moduli were determined by nanoindentations in multiple grains of a polycrystalline Ti₃B₄, synthesized by electric field‐activated reaction sintering. The range of elastic moduli determined from nanoindentation was found to agree well with the range determined by computation. The calculations and experiments demonstrate that Ti₃B₄ has the potential to be one of the leading structural ceramics.     

The determination of the elastic properties of an anisotropic polycrystalline graphite using neutron diffraction and ultrasonic measurements

The elastic properties of an extruded graphite (GR-280) used in nuclear industry have been examined. The lattice preferred orientation was determined by time-of-flight neutron diffraction that revealed weak texture with a texture index of less than 1.2. The bulk elastic properties of polycrystalline graphite with such a texture have been calculated using various averaging methods and compared with the properties obtained from the measurements of the longitudinal sound velocities, performed using special equipment at different hydrostatic pressures up to 150 MPa. The static elastic modulus of the GR-280 graphite as well as the diffraction elastic modulus was measured in situ by high resolution neutron diffraction by observing the shift of the (0 0 2) Bragg reflection under uniaxial loads up to 20 MPa. The static elastic moduli of two pyrolytic graphites have also been measured for comparison. It was shown that the anisotropy of the elastic properties of reactor graphite GR-280 is due to the crystallographic texture formed during the extrusion process, but the internal pores and microcracks are not closed even at a pressure of 150 MPa and they greatly influence the exact values of the bulk elastic moduli of graphite.     

Linear thermoelastic characterization of anisotropic poly(ethylene terephthalate) films

All nine independent elastic constants have been determined for a biaxially stretched poly(ethylene terephthalate) (PET) film using novel mechanical methods. The orthotropic directions and the in‐plane Poisson's ratios were first characterized using vibrational holographic interferometry of tensioned membrane samples. The out‐of‐plane Poisson's ratio was obtained by measuring the change in tension with the change in pressure for constant strain conditions. Pressure–volume–temperature (PVT) equipment was used to measure the bulk compressibility as well as the volumetric thermal expansion coefficient (TEC). The in‐plane Young's moduli were obtained by tensile tests, while the out‐of‐plane modulus was calculated from the compressibility and other elastic constants that describe the in‐plane behavior. The in‐plane TECs in the machine and transverse directions were determined using a thermal mechanical analyzer (TMA). The out‐of‐plane TEC was determined using these values and the volumetric TEC determined via PVT. The resulting compliance matrix satisfies all of the requirements of a positive‐definite energy criterion. The procedure of characterization utilized in this article can be applied to any orthotropic film. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2937–2947, 2002     

Elastic properties of quaternaryTeO2–ZnO–Nb2O5–Gd2O3 glasses

Tellurite glass systems in the form 75TeO₂–15ZnO–(10−x)Nb₂O₅–xGd₂O₃ (x=0.0, 0.5, 1.0, 1.5, 2.0, 2.5 mol%) have been prepared by the melt quenching technique. Both longitudinal and shear ultrasonic velocities were measured by using the pulse-echo method at 5 MHz frequency and at room temperature. Elastic moduli (longitudinal modulus, shear modulus, Young׳s modulus, Bulk modulus), Poisson׳s ratio, Debye temperature, micro-hardness and softening temperature have been calculated. Quantitative analysis of elastic moduli based on the number of bond per unit volume, average crosslink and number of vibrating atoms per unit volume has been achieved.     

Elastic moduli and thermal conductivity of injection-molded short-fiber–reinforced thermoplastics

The nine independent stiffness constants of injection-molded tensile bars of poly(phenylene sulfide) reinforced with 30 and 40% by weight of carbon or glass fibers have been measured by ultrasonic techniques. The thermal conductivities along the three principal directions of these thermoplastic composites have also been determined by the laser-flash radiometry method. The elastic moduli (tensile and shear) and thermal conductivity increase with increasing fiber volume fraction, v_f, with the tensile modulus and thermal conductivity along the mold flow direction showing the greatest change. For a composite, containing 40 weight % of carbon fibers, the Young's modulus and thermal conductivity along this direction exceed those of the polymer matrix by a factor of 8. Using the known values of v_f and the observed aspect ratio and orientation factor of the fibers, the elastic moduli and thermal conductivity have been calculated on the basis of the laminate theory. The agreement between theoretical predictions and experimental data is better than 10% on the average.     

First-principles study of structural,mechanical, and thermodynamic properties of cubic Y2O3 under high pressure

The structural, mechanical, and thermodynamic properties of cubic Y₂O₃ crystals at different hydrostatic pressures and temperatures are systematically investigated based on density functional theory within the generalized gradient approximation. The calculated ground state properties, such as equilibrium lattice parameter a₀, the bulk modulus B₀, and its pressure derivative B₀′ are in favorable agreement with the experimental and available theoretical values. The pressure dependence of a/a₀ and V/V₀ are also investigated. Furthermore, the elastic constants C_ij, bulk modulus B, shear modulus G, Young's modulus E, the ductile or brittle (B/G), Vickers hardness H_v, isotropic wave velocities and sound velocities are calculated in detail in a pressure range from 0 to 14 GPa. It was found that the Debye temperature decreases monotonically with an increase in pressure, the calculated elastic anisotropic factors indicate that Y₂O₃ has low anisotropy at zero pressure, and that its elastic anisotropy increases as the pressure increases. Finally, the thermodynamic properties of Y₂O₃, such as the dependence of the heat capacities C_V and C_P, the thermal expansion coefficient α, the isothermal bulk modulus, and the Grüneisen parameter γ on temperature and pressure, are discussed from 0 to 2000 K and from 0 to 14 GPa, respectively, applying the non-empirical Debye model in the quasi-harmonic approximation.     

Structural and Mechanical Properties of Fats Quantified by Ultrasonics

Since the velocity of an ultrasonic wave through a material depends on its density, bulk modulus (K), and shear modulus (G), a new approach to determine the shear elastic modulus and the mass fractal dimension (D) in a fat crystal network was developed. An ultrasonic chirp wave containing a range of frequencies and amplitudes, was used to estimate the structural and mechanical properties of palm oil based fats, crystallized under shear at three different temperatures (20, 25, and 30 °C). Considering the fat crystal network as a two-phase system (i.e. liquid and solid fat) the velocity of sound in both phases was obtained separately, assuming that the speed of sound in the oil phase was inversely dependent on the temperature. A constant shear modulus for the solid fraction was obtained experimentally by rheology, which was independent of the sample’s nature. These parameters were used for the determination of sample compressibility and its corresponding shear modulus by ultrasonic velocimetry. In addition fractal dimensions (D) were determined by using the relationship of the shear elastic modulus (G) to the mass fraction of the solid fat (φ) in a weak-link regime. The obtained results are comparable and consistent with previously reported fractal dimension values. This method allows online determination of the shear modulus of fats and could be potentially applied for quality control purposes in manufacturing.     

Relation of Single-Crystal Elastic Constants to Polycrystalline Isotropic Elastic Moduli of MgO: II, Temperature Dependence

The technical adiabatic elastic moduli E_[hkl] and G_hkl of single crystals of magnesium oxide were measured over the temperature range 298° to about 1600°K by a Förster-type resonance method. These data were compared with the low-temperature values (80° to 560°K) of the principal elastic constants c_ij and coefficients Sy reported by Durand. Combining Durand's data and the present data, the elastic moduli for single-crystal magnesium oxide were evaluated for the temperature range 80° to 1600°K. Young's modulus and the shear modulus of densely formed isotropic polycrystalline magnesium oxide were measured over the temperature range 298° to 1600°K. The data on the elastic constants of the single crystals were compared with the measured elastic moduli of the isotropic polycrystalline magnesium oxide on the basis of the Voigt-Reuss-Hill approximation. The temperature dependence of the elastic moduli was fitted into the expression M = M_c— BT exp (—T_c/T) suggested by Wachtman et al. ; mean deviations were less than 0.4% for the temperature range considered. The significance of the present data is discussed with particular emphasis on the following points: (1) the temperature variation of the elastic modulus is a function of thermal expansion, (2) the temperature dependence of the elastic modulus can be well described by the foregoing expression for a wide range of temperature, (3) the expression gives a value of the elastic modulus at 0°K, and (4) it may be possible to make use of measurements on the elastic properties of a densely sintered polycrystalline material to obtain information heretofore obtainable only from the corresponding single-crystal data.     

Elastic Properties of Polycrystalline Yttrium Oxide, Holmium Oxide, and Erbium Oxide: High-Temperature Measurements

The Young's and shear moduli of polycrystalline yttrium oxide, holmium oxide, and erbium oxide were determined from room temperature to 1000°C using the sonic resonance technique. The bulk modulus and Poisson's ratio were computed as functions of temperature for each oxide. The Young's, shear, and bulk moduli decreased linearly with increasing temperature, whereas Poisson's ratio remained constant. The first and second Grüneisen constants, γ and δ, were calculated from the bulk modulus data and shown to be virtually independent of temperature. The Soga-Anderson equation adequately described the bulk modulus data for each oxide.     

Pressure and temperature dependence of second-order elastic constants from third-order elastic constants in TMC (TM=Nb,Ti, V,Zr)

In this paper, we present an efficient and effective method to predict the pressure dependence and temperature dependence of second-order elastic constants (SOECs) by introducing third-order elastic constants (TOECs) in the monocarbide ultrahigh temperature ceramics. The method is validated by comparing with experiments and previous calculations in four TMCs (TM = Nb, Ti, V, Zr). Using this method, we investigate the derivatives of SOECs against pressure and temperature as well as the anisotropic properties of polycrystalline modulus. In addition, we fit the SOECs with pressure and temperature under the framework of CALPHAD for practice usage.     

High-Temperature Elasticity and Expansivity of Forsterite and Steatite

The elastic constants and coefficients of thermal expansion of polycrystalline forsterite (Mg₂SiO₄) and steatite (MgSiO₃) were determined from room temperature to 1000°K. Two elastic moduli, the adiabatic bulk modulus, B_s , and the shear modulus, G, decrease linearly with temperature above 500°K. The Grüneisen constant γ and a parameter δ, defined as — (dB_s/dT)/αB_s, calculated from the present data were virtually independent of temperature at the high-temperature range. Poisson's ratio, δ, rises linearly with temperature over the range of measurement; the slope is highest for materials with the lowest room-temperature value of σ.     

First‐Principles Study of Elastic,Structural, Electronic,Thermodynamical, and Optical Properties of Yttria (Y2O3) Ceramic in Cubic Phase

Structural, elastic, optical, thermodynamical, and electronic properties of yttrium oxide compound in cubic phase have been studied using the full‐potential augmented plane waves (FP‐LAPW) within density functional theory (DFT) framework. Four different approximations were used for exchange‐correlation potentials terms, comprised Perdew–Burke–Ernzerhof generalized parameterization of gradient approximation (GGA‐PBE), Wu–Cohen (WC‐GGA), local‐density approximation (LDA), and new approximation modified Becke and Johnson (mBJ‐GGA). The structural properties such as equilibrium lattice parameter, bulk modulus and its pressure derivative have been obtained using optimization method. Moreover, Elastic constants, Young's modulus, shear modulus, Poisson's ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature, and Grüneisen parameters have been calculated. Obtained structural, elastic and other parameters are consistent with experimental data. Moreover pressure dependence of the elastic moduli was studied. From electronic calculations, it has been found that the band gap was 5.7 eV at Г point in the Brillouin zone using mBJ‐GGA approximation. Optical properties, such as the dielectric function, refractive index, extinction index, and optical band gap, were calculated for radiation up to 14 eV. In addition, the unique type of bonding in Y₂O₃ was discussed by three method including effective charge, B/G ratio, and charge density distribution.     

THE LINEAR ELASTIC BEHAVIOR OF A BIDISPERSE WEAIRE-PHELAN SOAP FOAM

The linear elastic constants for a dry Weaire-Phelan foam with bidisperse cell-size distribution are computed. This highly ordered structure has eight polyhedral bubbles in the unit cell: two pentagonal dodecahedra and six tetrakaidecahedra with twelve pentagonal faces and two hexagonal faces. Both dodecahedra have equal volume and all of the tetrakaidecahedra have equal volume, but these volumes are different for the bidisperse structures considered here. These volume constraints preserve the cubic symmetry of the Weaire-Phelan structure so that the elastic response is completely characterized by a bulk modulus k for volume compression and two shear moduli μ₁ and μ ₂. The shear moduli can be combined to obtain an effective isotropic shear modulus μ¯, which represents the shear response averaged over all orientations of the foam. For the monodisperse case, μ¯ = 0.8684 TV¯,^-1/3 where TT is surface tension and V is the average bubble volume. For bidisperse structures, p. never differs from the monodisperse case by more than 0.5% and the at always lie within 4% of ft. The pressure inside the dodecahedra is always greater than the pressure inside the tetrakaidecahedra even when the dodecahedra are larger.     

The Influence of Crysnanoclay Addition on Mechanical and Thermal Properties of Thermoplastic Polyurethane Elastomeric with Polycarbonate Nanocomposites

A series of crysnanoclay-loaded thermoplastic polyurethane (TPU) elastomer/polycarbonate (PC) nanocomposites have been prepared using twin screw extruders. The physicomechanical properties such as tensile behaviors, flexural properties and impact strength of the composites have been reported. Significant improvement in tensile modulus and flexural modulus were noticed for nanocomposites. The thermal characteristics of nanocomposites have been determined by thermogravimetric analysis (TGA) techniques. Thermal degradation kinetic parameters such as energy of activation (E_a) have been calculated from TGA thermograms for the nanocomposites using three mathematical models namely; Coats–Redfern, Horowitz – Metzger and Broido's methods and the results are compared. The effect of crysnanoclay on the storage modulus (E′), loss modulus (E″), and damping factor (tan δ) as a function of temperature have been measured by dynamic mechanical analysis (DMA). The storage moduli of nanocomposites have been increased after incorporating crysnanoclay in polymer matrix.     

Evolution of a metastable thin film with high-hardness wear resistance for advanced cutting tool application

The structure and elastic properties of rocksalt and wurtzite Ti–Al–N ternary solid solutions were investigated using first principles calculations. We also performed an experimental evaluation using the sputtering method to obtain the reliability. The phase transition of (Ti_1−xAl_x)N solid solutions was occurred at x = 0.5–0.75 for both calculations and experimental results. The bulk modulus of rocksalt and wurtzite solid solutions decreases with increasing Al content. On the other hand, shear moduli and Young's moduli gradually increase with Al content only in rocksalt solid solutions. The theoretical and experimental results indicate that the overall mechanical properties of rocksalt solid solutions are superior to those of wurtzite solid solutions. Therefore, controlling the crystal structure of the Ti–Al–N ternary metastable system was crucial for optimizing the material properties.