Longitudinal Elastic Constants Research Articles

Volume dependence of the charge density wave phase transitions

ABSTRACT We analyse the volume dependence of the charge density wave phase transition temperature T CDW for 16 one and two dimensional materials such as the rare earth tritellurides TbTe 3 , ErTe 3 , TmTe 3 DyTe 3 , the transition metal dichalcogenide 2H-NbSe 2 , and the quasi-one dimensional conductors K 0.3 MoO 3 , NbSe 3 , ( TaSe 4 ) 2 I . The volume dependence is taken in the form of the logarithmic derivative of T CDW in function of the strain components. We point out some characteristics of this parameter. This parameter is dimensionless with an absolute value of about 10 obtained from the measurements of the thermal expansion, the longitudinal elastic constants and pressure dependence for 11 one- and two-dimensional CDW systems. In contrast a huge positive value of about 100 is found at the lower charge density wave transition in TbTe 3 , ErTe 3 , TmTe 3 and DyTe 3 .

An ultrasonic study of the effect of uniaxial green compaction pressure on the elastic anisotropy of porous copper fabricated using the pore-former route

Porous copper is potentially very attractive for various functional applications such as filters and heat exchanger materials. Within the scope of this study, porous copper samples with dual pore morphologies were fabricated following the space holder technique using a 1:2 mixture ratio of K2CO3 to NaCl as pore formers. The initial compaction pressure required for green body fabrication was systematically varied between 120 and 180 MPa, and the influence of this pressure over porosity, pore morphology, volume shrinkage, and longitudinal elastic constants was systematically studied. Three longitudinal elastic constants of the porous Cu samples were determined following the non-destructive ultrasonic phase spectroscopy method through the measurement of the phase shift vs. frequency spectra along the three orthogonal directions in each sample. When the applied pressure is increased from 120 to 160 MPa and the Cu:PF mixture ratios are 70:30 and 60:40, respectively, the elastic constant values in the green compaction direction (C11) decrease from 34.2 GPa to 7.5 GPa and 23.7 GPa–17.9 GPa. However, for Cu:PF mixture ratios of 70:30 and 60:40, under 180 MPa green compaction pressure C11 increases to 30.9 GPa and 21.2 GPa, respectively. As the applied green compaction pressure increased from 120 to 160 MPa, the samples' average elastic anisotropy ratio initially increased from 0.29 to 0.59 and then decreased to 0.55 at 180 MPa pressure. While the initial increase in anisotropy is due to increased pore flattening with increasing green compaction pressure, the decrease in anisotropy ratio in the samples fabricated under 180 MPa green compaction pressure is due to enhanced sample densification. Contour maps for different properties have been proposed to identify the optimum combination of initial powder composition and green compaction pressure for the intended end application.

Computational approach to identify structural and elastic relationship in metastable crystalline and amorphous alloy thin films: Mo1-xNix and Mo1-xSix case studies

Previously well-established experimental trends of ground-state properties of crystalline and amorphous Mo1-xSix and Mo1-xNix alloys with 0 ≤ x ≤ 1 are predicted by first-principles calculations and inter-relationship with sound velocities and elastic properties are identified. The free energy of mixing, calculated at 300 K provides accurate values of the critical Si and Ni concentrations leading to the crystalline-to-amorphous transition. Specifically, a transition from BCC to amorphous state is predicted for xSi ~ 0.14 and xNi ~ 0.32, while FCC to amorphous transition is observed for xNi ~ 0.77. These structural transitions are accompanied by modifications of the out-of-plane longitudinal and shear elastic constants. In the crystalline region, a pronounced softening of elastic moduli is predicted for both solid solution alloys. While for amorphous Mo-Ni, the elastic constants do not undergo significant changes, for amorphous Mo-Si, they exhibit two distinct behaviors depending on the electronic properties and bonding character. For 0.2 ≤ xSi ≤ 0.7, the metallic character of the amorphous alloys is maintained and the elastic properties are remarkably stable. For xSi > 0.7, a progressive increase in the atomic volume is observed and the amorphous alloys acquire a covalent character and a reduced coordination number. Surprisingly, during this transition, both the longitudinal and shear acoustic velocities continuously increase, despite a progressive softening of the elastic stiffness constants. These calculations provide deep insight at the atomic-scale and reproduce satisfactorily the earlier experimental works of magnetron co-sputtered Mo-Si films, while some disagreement on elastic properties remain for more energetic ion beam sputtered Mo-Ni films, likely partially attributed to point-defects.

Elastic properties of porous silicon nitride fabricated via a low-temperature processing route

Porous silicon nitride is a promising material for many advanced applications due to its many outstanding properties. In this work, porous silicon nitride was fabricated at 1200 °C using a mixture of silicon nitride powder and phosphoric acid. The dual role of phosphoric acid as inorganic binder and pore former has been critically analyzed through a detailed structural characterization. Elastic constants of the porous silicon nitride samples were determined using non-destructive ultrasound phase spectroscopy, and the influence of the phosphoric acid content on the elastic properties was studied at depth. Both longitudinal and shear elastic constants were determined and Young's modulus and Poisson's ratio were calculated as a function of porosity considering the actual elastic symmetry of the fabricated samples. The experimentally determined elastic constants were compared with the predictions from different analytical models to understand the influence of porosity and pore morphology on the stiffness of the fabricated samples.

Ultrasonic study of the elastic properties of functionally graded and equivalent monolithic composites

• Stiffness comparison between an FGM and equivalent monolithic composite was done. • Elastic constants were measured using ultrasound phase spectroscopy. • Despite the gradient structure, the FGM displays quasi-isotropic elastic properties. • Stiffness depends only on the ceramic content, gradient structure has no influence. • Hashin Shtrikman lower bound provides the best fit for the stiffness of the FGM. The aim of this work is to compare the stiffness of a graded composite and equivalent monolithic particulate reinforced composite experimentally. Hybrid Al-SiC-graphite composites were fabricated using spark plasma sintering. Longitudinal elastic constants were measured using non-destructive ultrasound phase spectroscopy. It is seen that for the graded composites, the stiffness depends solely on the reinforcement content, while the gradient structure has no influence. Comparison with analytical micromechanical models show that the Hashin Shtrikman lower bound predicts the elastic constants most accurately.

Development of functionally graded ZrB2–B4C composites for lightweight ultrahigh-temperature aerospace applications

In the present work, a lightweight three-layer ZrB2–B4C functionally graded composite material has been developed by spark plasma sintering route. The functionally graded material (FGM) is free from interlayer defects and displays a smooth transition between the individual layers. The composition of each layer was designed to reduce the overall density without sacrificing the functionality of the material. The density of the FGM is almost 40% lower than monolithic ZrB2 and 24% lower than ZrB2–30B4C rendering it potentially very attractive for high-temperature aerospace applications. A detailed structural characterization of the FGM was carried out to evaluate the elemental distribution in the graded composite, as well as determine the spatial distribution of the crystalline phases. Vickers hardness was measured within each layer and in the interlayer regions to further evaluate the gradient structure and interlayer transitions. Longitudinal elastic constants of the FGM along the thickness and across the layers measured using ultrasound phase spectroscopy showed that despite the gradient structure, the FGM can be treated as a quasi-isotropic solid.

Study of the elastic properties of porous copper fabricated via the lost carbonate sintering process

Porous copper has numerous potential applications due to its attractive properties such as high ductility, good corrosion resistance, high surface area, good thermal and electrical conductivity, etc. Within the scope of this work, porous copper samples with 27–67 vol% porosity were fabricated using a mixture of copper powder and potassium carbonate powder, employed as space holders. The sample fabrication process involved the steps of powder mixing, uni-axial pressing, sintering, and final washing. Detailed structural analyses of the fabricated samples were performed by density measurement following Archimedes’ principle, X-ray diffraction for phase analysis, and scanning electron microscopy for microstructural analysis. Three longitudinal elastic constants in each sample were determined in a non-destructive manner using ultrasound phase spectroscopy. Due to the applied uni-axial pressure and the resulting change in pore shape, the fabricated porous copper samples displayed transversely isotropic symmetry. A detailed analysis of the influence of pore shapes and morphologies on the experimentally determined longitudinal elastic constants has been carried out. The results have been compared with the predictions from different micromechanical models for the dependence of elastic constants on porosity.

The transverse and longitudinal elastic constants of pulp fibers in paper sheets

Cellulose fibers are a major industrial input, but due to their irregular shape and anisotropic material response, accurate material characterization is difficult. Single fiber tensile testing is the most popular way to estimate the material properties of individual fibers. However, such tests can only be performed along the axis of the fiber and are associated with problems of enforcing restraints. Alternative indirect approaches, such as micro-mechanical modeling, can help but yield results that are not fully decoupled from the model assumptions. Here, we compare these methods with nanoindentation as a method to extract elastic material constants of the individual fibers. We show that both the longitudinal and the transverse elastic modulus can be determined, additionally enabling the measurement of fiber properties in-situ inside a sheet of paper such that the entire industrial process history is captured. The obtained longitudinal modulus is comparable to traditional methods for larger indents but with a strongly increased scatter as the size of the indentation is decreased further.

Minimum energy and iteration estimates for longitudinal Young’s modulus and Poisson’s ratio of transversely-isotropic unidirectional composites

Some formal inequalities restricting the macroscopic (effective) longitudinal elastic constants of the n-component transversely-isotropic unidirectional composites, based on the minimum energy and complementary energy principles with the help of appropriate constant strain and piece-wise constant stress trial fields and optimization techniques, have been established. Exploring further the possible longitudinal stress–strain modes, additional starting original bounds are derived leading to the new set of iteration bounds on both effective longitudinal constants, which broaden and improve upon the ones of the first set constructed earlier (Pham, 2020) for the composites with positive longitudinal Poisson’s ratio. Another new set of iteration bounds is constructed for the composites having negative longitudinal Poisson’s ratio. Illustrating numerical examples are presented for comparisons.

Phenomenological approach of the thermodynamic properties of the charge density wave systems

ABSTRACT The properties of the specific heat and elastic stiffness components at the charge density wave phase transition in several one-dimensional and two-dimensional materials are examined. Here we show that the thermodynamic properties of the rare earth tritelluride (, Er) and LuIrSi compounds can be explained in the framework of a standard mean field Landau theory. The amplitude of the experimental-specific heat jump measured at the charge density wave (CDW) phase transition increases with the transition temperature . The amplitude of the experimental discontinuity of the longitudinal elastic constants measured at the CDW phase transition scales onto a single curve. The Landau approach is discussed as well as experimental results.

Minimum energy bounds on longitudinal elastic constants of transversely isotropic unidirectional composites.

We consider the n-component transversely isotropic unidirectional elastic composites, the longitudinal axis of which is parallel to those of the transversely isotropic components as well as the generators of the cylindrical phase boundaries between them. From the minimum energy and complementary energy principles, with appropriate constant strain and piece-wise constant stress trial fields, optimization and iteration techniques, a set of bounds for the macroscopic (effective) longitudinal elastic constants of the composites (including the simple lower arithmetic average estimate for longitudinal Young modulus E eff ≥ E V ) are constructed. Numerical examples are provided to illustrate the obtained results.

Tetragonal (K, Na)NbO3 based lead-free single crystal: Growth, full tensor properties, and their orientation dependence

A Li and Ta modified (K, Na)NbO3 lead-free single crystal with a large size (13 × 10 × 20 mm3) has been grown by using the top-seeded solution growth method. The large size allows us to carry out an extensive study on this tetragonal crystal. We have measured a complete set of elastic, dielectric, and piezoelectric constants for the [001]C poled crystal with the single domain state. The crystal exhibits high shear piezoelectricity with d15 = 518 pC/N and k15 = 0.733, showing excellent potential in shear electro-sonic energy transformation devices. It is found that the high shear piezoelectricity originates from the vicinity of orthorhombic-tetragonal phase transition, which favors polarization rotation greatly. The orientation dependence of longitudinal dielectric, piezoelectric, and elastic constants and electromechanical coupling factor in the 3-dimentional space were calculated based on the single domain dataset. We believe that this work is of great importance for both fundamental studies and device designs for lead-free materials.

Thermal Conductivity, Heat Capacity, and Elastic Constants of Water-Soluble Polymers and Polymer Blends

We use time-domain thermoreflectance (TDTR), and the generation and detection of longitudinal and surface acoustic waves, to study the thermal conductivity, heat capacity, and elastic properties of thin films of poly(vinyl alcohol) (PVA), poly(acrylic acid) (PAA), polyacrylamide (PAM), poly(vinylpyrrolidone) (PVP), methyl cellulose (MC), poly(4-styrenesulfonic acid) (PSS), poly(N-acryloylpiperidine) (PAP), poly(methyl methacrylate) (PMMA), and a polymer blend of PVA/PAA. The thermal conductivity of six water-soluble polymers in the dry state varies by a factor of ≈2, from 0.21 to 0.38 W m–1 K–1, where the largest values appear among polymers with a high concentration of hydrogen bonding (PAA, PAM, PSS). The longitudinal elastic constants range from 7.4 to 24.5 GPa and scale linearly with the shear elastic constants, suggesting a narrow distribution of Possion’s ratio 0.35 < ν < 0.40. The thermal conductivity increases with the average sound velocity, as expected based on the model of the minimum thermal c...

Elastic properties of lead-free (Na1/2Bi1/2)TiO3-BaTiO3 single crystals near the morphotropic phase boundary as studied by using Brillouin spectroscopy

The elastic properties of lead-free (Na1/2Bi1/2)TiO3-BaTiO3 single crystals near the morphotropic phase boundary were investigated by using Brillouin spectroscopy at room temperature. The measured longitudinal elastic constants of unpoled single crystals with a BaTiO3 content of 5% exhibited large changes depending on the scattering geometry, indicating that a substantial acoustic dispersion effect exists in this system. This was attributed to the relaxor nature due to inherent disorder in the A-site of the perovskite structure.

Flux-Grown Piezoelectric Materials: Application to α-Quartz Analogues

Using the slow-cooling method in selected MoO3-based fluxes, single-crystals of GeO2 and GaPO4 materials with an α-quartz-like structure were grown at high temperatures (T ≥ 950 °C). These piezoelectric materials were obtained in millimeter-size as well-faceted, visually colorless and transparent crystals. Compared to crystals grown by hydrothermal methods, infrared and Raman measurements revealed flux-grown samples without significant hydroxyl group contamination and thermal analyses demonstrated a total reversibility of the α-quartz ↔ β-cristobalite phase transition for GaPO4 and an absence of phase transition before melting for α-GeO2. The elastic constants CIJ (with I, J indices from 1 to 6) of these flux-grown piezoelectric crystals were experimentally determined at room and high temperatures. The ambient results for as-grown α-GaPO4 were in good agreement with those obtained from hydrothermally-grown samples and the two longitudinal elastic constants measured versus temperature up to 850 °C showed a monotonous evolution. The extraction of the ambient piezoelectric stress contribution e11 from the CD11 to CE11 difference gave for the piezoelectric strain coefficient d11 of flux-grown α-GeO2 crystal a value of 5.7(2) pC/N, which is more than twice that of α-quartz. As the α-quartz structure of GeO2 remained stable up to melting, a piezoelectric activity was observed up to 1000 °C.

Chemically Tuning Mechanics of Graphene by BN

AbstractWith finite bandgaps, g‐BNC, a boron nitride monolayer (g‐BN) phase within a graphene layer, is a promising semiconductor for next generation electronics. We report its mechanics dependence of the g‐BN concentration, including the high order elastic constants and mechanical failure, through a first‐principles study based on density functional theory. The in‐plane stiffness as well as third order elastic constants of graphene can be linearly tuned with g‐BN concentration. The longitudinal mode elastic constants are sensitive to the BN modification, in contrast to the shear mode elastic constants. This study may provide guidance in optimizing the mechanics of graphene‐based nanodevices.

A theoretical analysis of the effect of the hydrogenation of graphene to graphane on its mechanical properties

We investigated the effect of the hydrogenation of graphene to graphane on its mechanical properties using first-principles calculations based on density-functional theory. The hydrogenation reduces the ultimate strengths in all three tested deformation modes--armchair, zigzag, and biaxial--and the in-plane stiffness by 1/3. The Poisson ratio was reduced from 0.178 to 0.078, a 56% decrease. However, the ultimate strain in zigzag deformation was increased by 8.7%. The shear mode elastic constants are more sensitive than longitudinal ones to hydrogenation. The fourth and fifth order longitudinal mode elastic constants are inert to the hydrogenation, in contrast to a large decrease of those in second and third order. The hydrogenation does not change the monotonic decrement of the Poisson ratio with increasing pressure, but the rate is tripled. Our results indicate that graphene-graphane systems could be used for hydrogen storage with high speed of charge-discharge of hydrogen.

Ultrasonic investigations near the B-induced quantum critical point of the triangular-lattice antiferromagnet Cs2CuCl4

Measurements of the longitudinal elastic constants c11, c22 and c33 and the ultrasonic attenuation α of the quasi-two-dimensional triangular-lattice spin-1/2 Heisenberg antiferromagnet Cs2CuCl4 reveal distinct anomalies near the B-induced quantum-critical point (QCP). These anomalies are particularly strongly pronounced in the ultrasonic attenuation. In isothermal field sweeps performed at low temperatures 0.027 K ≤ T ≤ 0.3 K around the saturation field Bs, the ultrasonic attenuation of all three modes shows a pronounced double-peak structure, indicating two anomalies of different origin. Upon cooling, however, both features merge suggesting a coincidence at the QCP. While one peak, which can be attributed to the ordering temperature TN(B), becomes critically enhanced upon approaching the QCP, the other one reduces in size and narrows upon cooling. The latter effect has been tentatively assigned to the material's spin-liquid features which precede the long-range antiferromagnetic ordering.

First-principles investigation on the elastic stability and thermodynamic properties of Ti2SC

Using Vanderbilt-type plane-wave ultrasoft pseudopotentials within the generalized gradient approximation (GGA) in the frame of density functional theory (DFT), we have investigated the crystal structures, elastic, and thermodynamic properties for Ti2SC under high temperature and high pressure. The calculated pressure dependence of the lattice volume is in excellent agreement with the experimental results. The calculated structural parameter of the Ti atom experienced a subtle increase with applied pressures and the increase suspended under higher pressures. The elastic constants calculations demonstrated that the crystal lattice is still stable up to 200 GPa. Investigations on the elastic properties show that the c axis is stiffer than the a axis, which is consistent with the larger longitudinal elastic constants (C33, C11) relative to transverse ones (C44, C12, C13). Study on Poisson's ratio confirmed that the higher ionic or weaker covalent contribution in intra-atomic bonding for Ti2SC should be assumed and the nature of ionic increased with pressure. The ratio (B/G) of bulk (B) and shear (G) moduli as well as B/C44 demonstrated the brittleness of Ti2SC at ambient conditions and the brittleness decreased with pressure. Moreover, the isothermal and adiabatic bulk moduli displayed opposite temperature dependence under different pressures. Again, we observed that the Debye temperature and Grüneisen parameter show weak temperature dependence relative to the thermal expansion coefficient, entropy, and heat capacity, from which the pressure effects are clearly seen.

Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors

Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple donors while also considering possible confounding effects of the anatomic quadrant, apparent tissue density, donor age, and gender. Cortical bone specimens were sampled from the whole femora of 9 human donors at 20%, 50%, and 80% of the total femur length. Elastic constants from the main diagonal of the reduced fourth-order tensor were measured on hydrated specimens using ultrasonic wave propagation. The tissue exhibited orthotropy overall and at each location along the length of the diaphysis (p<0.0001). Elastic anisotropy increased from the mid-diaphysis toward the epiphyses (p<0.05). The increased elastic anisotropy was primarily caused by a decreased radial elastic constant (C11) from the mid-diaphysis toward the epiphyses (p<0.05), since differences in the circumferential (C22) and longitudinal (C33) elastic constants were not statistically significant (p>0.29). Anatomic variation in intracortical porosity may account for these trends, but requires further investigation. The apparent tissue density was positively correlated with the magnitude of each elastic constant (p<0.0001, R2>0.46), as expected, but was only weakly correlated with C33/C11 (p<0.05, R2=0.04) and not significantly correlated with C33/C22 and C11/C22.