Elastic moduli and internal friction of nanocrystalline Pd and PdSi as a function of temperature

Resonant ultrasound spectroscopy was used to study the elastic constants and internal friction of two nanocrystalline palladium samples over the temperature range 3–300 K. The first material, nc-Pd, had a grain size of 80–100 nm and a density 93% of that of single-crystal bulk palladium. The second material, nc-PdSi containing 0.5 at.% Si, had a grain size of 15–22 nm and a density 97% of the single-crystal value. The bulk and shear moduli were significantly reduced in the nc-Pd material from that expected based on single-crystal data, the effect being greater for the bulk modulus. The moduli of nc-PdSi were reduced 4–5% from that based on crystalline Pd. As compared to previous reports of the elastic moduli of nanocrystalline palladium (grain size 5–15 nm) the present values for the larger-grained nc-Pd are comparable, but the present values for the smaller-grained nc-PdSi are considerably higher. An internal friction peak and a modulus defect were found in the nc-Pd material, but not in the nc-PdSi material. These effects are attributed to a relaxation process at the grain boundaries. The temperature dependence of the moduli is similar to that of crystalline palladium and is strongly influenced by electronic effects.     

Elastic properties of diamond,silicon, and germanium nanocrystals as functions of their size and shape

The dependence of elastic modulus B on the size (number of atoms (N)) and the shape of a nanocrystal of a simple monoatomic substance is studied when the nanocrystal is considered as a rectangular parallelepiped with a varied surface shape. The elastic modulus is shown to decrease during an isomorphic-isothermal decrease of the nanocrystal size. At low temperatures, the B(N) dependence is less pronounced, and the case where the B(N) function increases during an isomorphic-isothermal decrease of the nanocrystal size is possible here. The size dependences of the elastic modulus, Poisson ratio μ, Young’s modulus Y, shear modulus G, and lattice parameter compression are calculated for diamond, Si, and Ge. It is shown that B, Y, and G decrease and μ increases during an isomorphic-isothermal decrease of the nanocrystal size. The surface pressure compresses a nanocrystal at low temperatures and expands it at high temperatures. The larger the deviation of the nanocrystal shape from the most energetically favorable shape, the more pronounced the changes of these functions during an isothermal decrease of the nanocrystal size.     

Interpretation of elastic anomalies in SrTiO3 at 37K

We relate the measurements by Ming Lei and Hassel Ledbetter (1991) of elastic moduli in strontium titanate near 37K to a dynamical anharmonic mode coupling model. It is suggested that the effects are purely dynamic and not indicative of a true structural phase transition and that neither macroscopic coherence nor second sound is involved.     

Die Clausius-Mosottische Formel in der Theorie der Dielastika

Point defects in crystal lattices are specified with respect to their mechanical properties by the elastic polarisabilityα (dia-elastic case) or by the permanent elastic dipole momentp (para-elastic case) or by both together. These fundamental quantities can be obtained in macroscopic measurements of elastic moduli by applying formulae of the Clausius-Mosotti type and of the polar gas type resp. The present work gives the corresponding theory.     

Mechanical elastic constants and diffraction stress factors of macroscopically elastically anisotropic polycrystals: the effect of grain-shape (morphological) texture

The effect of the grain-shape (‘morphological’) texture of a polycrystal on the mechanical elastic constants and diffraction (X-ray) stress factors is investigated. To this end, the Eshelby–Kröner grain interaction model originally devised for polycrystals consisting of spherical grains is extended to ellipsoidal grain morphology. Results obtained for the mechanical elastic constants show that a polycrystal consisting of ellipsoidal grains with their principal axes aligned along common directions (i.e. when an ideal grain-shape texture occurs) is macroscopically elastically anisotropic. Also the diffraction (X-ray) stress factors are affected by the grain-shape texture; they reflect the macroscopic elastic anisotropy by resulting in nonlinear so-called sin²?ψ plots. In general, a grain-shape texture can have a moderate effect on the mechanical elastic constants and a pronounced effect on the diffraction elastic constants, depending on the crystal symmetry and single-crystal elastic anisotropy.     

Mechanical heterogeneities in model polymer glasses at small length scales

Molecular simulations of a model, deeply quenched polymeric glass show that the elastic moduli become strongly inhomogeneous at length scales comprising several tens of monomers; these calculations reveal a broad distribution of local moduli, with regions of negative moduli coexisting within a matrix of positive moduli. It is shown that local moduli have the same physical meaning as that traditionally ascribed to moduli obtained from direct measurements of local constitutive behaviors of macroscopic samples.     

Temperature dependence of elastic moduli for solid C60

The attenuation and velocity of ultrasonic waves (at a frequency of ～4 MHz) along the 〈111〉 and 〈100〉 directions in solid C₆₀ single-crystal samples are measured in the temperature range 100–300 K. The temperature dependences of the complete set of elastic constants for C₆₀ fullerite are determined from the experimental data. It is shown that the specific features in the behavior of the elastic moduli near the orientational phase transition temperature are associated with different contributions of the relaxation processes to the effective elastic moduli. The activation volume and deformation potentials for the ground and excited states of the C₆₀ low-temperature phase are evaluated from the results obtained in this work and the data available in the literature.     

High-pressure elasticity of alpha-quartz: instability and ferroelastic transition

The single-crystal elastic moduli of alpha-quartz were measured to above 20 GPa in a diamond-anvil cell by Brillouin spectroscopy. The behavior of the elastic moduli indicates that the high-pressure phase transition in quartz is ferroelastic in nature and is driven by softening of C44 through one of the Born stability criteria. The trends in elastic moduli confirm theoretical predictions, but there are important differences, particularly with respect to the magnitudes of the B(i). The quartz I-II transition occurs prior to complete softening of the mode and amorphization.     

Structural,elastic and thermodynamic properties of tetragonal and orthorhombic polymorphs of Sr2GeN2: an ab initio investigation

The structural, elastic and thermodynamic properties of the α (tetragonal) and β (orthorhombic) polymorphs of the Sr₂GeN₂ compound have been examined in detail using ab initio density functional theory pseudopotential plane-wave calculations. Apart the structural properties at the ambient conditions, all present reported results are predicted for the first time. The calculated equilibrium lattice parameters and inter-atomic bond-lengths of the considered polymorphs are in good agreement with the available experimental data. It is found that α-Sr₂GeN₂ is energetically more stable than β-Sr₂GeN₂. The two examined polymorphs are very similar in their crystal structures and have almost identical local environments. The single-crystal and polycrystalline elastic parameters and related properties – including elastic constants, bulk, shear and Young’s moduli, Poisson’s ratio, anisotropy indexes, Pugh’s criterion, elastic wave velocities and Debye temperature – have been predicted. Temperature and pressure dependence of some macroscopic properties – including the unit-cell volume, bulk modulus, volume thermal expansion coefficient, heat capacity and Debye temperature – have been evaluated using ab initio calculations combined with the quasi-harmonic Debye model.     

Computer simulation of the relation between mechanical behavior and structural evolution of oxide ceramics under dynamic loading

Computer simulation is used to investigate the deformation and damage processes taking place in brittle porous oxide ceramics under intense dynamic loading. The pore structure is shown to substantially affect the size of the fragments and the strength of the materials. In porous ceramics subjected to shock loading, deformation is localized in mesoscopic bands having characteristic orientations along, across, and at ∼45° to the direction of propagation of the shock wave front. The localized-deformation bands may be transformed into macroscopic cracks. A method is proposed for a theoretical estimation of the effective elastic moduli of ceramics with pore structure without resorting to well-known hypotheses for the relation between elastic moduli and porosity of the materials.     

Low-temperature anisotropy of the thermal conductivity of single-crystal nanofilms and nanowires

The effect of phonon focusing on the phonon transport in single-crystal nanofilms and nanowires is studied in the boundary scattering regime. The dependences of the thermal conductivity and the free path of phonons on the geometric parameters of nanostructures with various elastic energy anisotropies are analyzed for diffuse phonon scattering by boundaries. It is shown that the anisotropies of thermal conductivity for nanostructures made of cubic crystals with positive (LiF, GaAs, Ge, Si, diamond, YAG) and negative (CaF₂, NaCl, YIG) anisotropies of the second-order elastic moduli are qualitatively different for both nanofilms and nanowires. The single-crystal film plane orientations and the heat flow directions that ensure the maximum or minimum thermal conductivity in a film plane are determined for the crystals of both types. The thermal conductivity of nanowires with a square cross section mainly depends on a heat flow direction, and the thermal conductivity of sufficiently wide nanofilms is substantially determined by a film plane orientation.     

Calculation of the effect of pressurizing gases on the resonant modes of single-crystal parallelepiped

Resonant ultrasound spectroscopy provides for an experimental determination of the elastic moduli of a solid sample. The moduli are extracted by matching a theoretically computed resonant spectrum to the experimental vibrational spectrum. To determine the pressure dependence of the moduli, the vibrational spectrum can be taken with the sample in a pressurizing gas. Then the extraction of the intrinsic, pressure dependent moduli requires a theoretical treatment which permits removal of the perturbation of the spectrum due to the surface loading by the pressure and shear waves in the gas. In order to illustrate a treatment which accomplishes this removal, the theoretically computed frequency shifts and the quality factors are reported for two single-crystal parallelepiped pressurized by noble gases.     

Constrained grain-boundary sliding and inelasticity of polycrystals

A model of inelastic behavior of polycrystals that is based on the idea of constrained grain-boundary sliding is developed. This model assumes that grain-boundary sliding is accommodated only through grain elastic deformation, which is valid under low stresses. By way of examples, the dynamic inelastic behavior and a decrease in the elastic moduli of polycrystals subjected to a small-amplitude ultrasonic field are investigated. It is shown that some of the available experimental data obtained on ultra-fine-grained materials can be explained in terms of the model. The theory predicts that the decrease in the elastic moduli is a size effect that is bound to be observed when the grain size is small. These predictions are supported experimentally.     

Elastic waves in carbon 2D supracrystals

The elastic moduli and propagation velocities of elastic waves in 2D supracrystalline nanoallotropes of carbon have been calculated. It has been shown that these velocities in sp ² nanoallotropes are close to those in graphene and exceed the propagation velocities of elastic waves in single-crystal diamond by a factor of 2. The propagation velocities of both longitudinal and transverse elastic waves in carbon 2D supracrystalline sp ³ nanoallotropes are several times lower than those in sp ² nanoallotropes.     

Principles of Pyrex® glass chemistry: structure–property relationships

Pyrex^® glass was one of the first commercial boroaluminosilicate glass compositions, selected in 1915 from thousands of compositions due to its ability to sustain mechanical and thermal shock. While the microscopic structure of Pyrex^® glass has recently been investigated, the microscopic origins of its macroscopic properties are not well understood, i.e., the atomic scale foundation of the original empirical invention of Pyrex^® glass has yet to be established. In this work, we have tackled this problem by investigating the effects of varying Si/Al and Na/B ratios on the boron and aluminum speciation and a range of physical and rheological properties in the Pyrex^® glass family. We show that the canonical Pyrex^® boroaluminosilicate composition is indeed optimal for attaining relatively high values of glass transition temperature and elastic moduli and a low coefficient of thermal expansion, while simultaneously maintaining a high glass-forming ability.     

The temperature dependences of the elastic moduli of solid C60

This paper reports on the determination of the temperature dependences of the complete set of the elastic moduli of solid C₆₀ from sound-velocity measurements made along different crystallographic directions in single-crystal samples within the 100-to 300-K range. Substantial differences in their behavior were revealed, which are accounted for by different relative contributions from relaxation processes to various elastic moduli.     

Relaxing local modes and the theory of low-frequency Raman scattering in glasses

Raman scattering in glasses is investigated theoretically. The experimental Raman spectra of glasses exhibit a low-frequency peak (at ～10 cm^?1) that, as a rule, is attributed to vibrational modes of nanometer-sized structural units (nanocrystallites). It is established that the elastic moduli of nanocrystallites must necessarily be dependent on their sizes due to the Laplace pressure effect. A theory of the low-frequency peak is constructed using a realistic size distribution function of nanocrystallites with allowance made for the Laplace pressure effect and the dissipation of vibrational energy. Within this theory, the shape of the low-frequency peak and its evolution with temperature can be analyzed quantitatively. The proposed approach offers a physical interpretation of the experimental data and provides insight into the relation of the characteristic nanocrystallite sizes to the elastic moduli and surface tension coefficients of materials.     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

First-principles predictions of anisotropies in elasticity and sound velocities of CsCl-type refractory intermetallics: TiTM,ZrTM and HfTM (TM = Fe,Ru, Os)

ABSTRACT

Structural properties, elastic properties, sound velocities and Debye temperatures of CsCl-type refractory TiTM, ZrTM and HfTM (TM?=?Fe, Ru, Os) intermetallics were investigated using first-principles calculations. The calculated equilibrium lattice parameters are coincided with the reported experimental and theoretical data. Based on single-crystal elastic constants, polycrystalline elastic moduli, Poisson’s ratios, sound velocities and Debye temperatures were evaluated. Anisotropies in elastic moduli of these CsCl-type intermetallics were discussed by elastic anisotropy indexes, three-dimensional surface constructions and their projections, and directional elastic modulus. The results showed that ZrFe has the highest elastic anisotropy and ZrOs presents the lowest one. Finally, sound velocities, Debye temperatures and their anisotropies were also calculated and discussed.     

Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.