First-Principles Study of B16N16 Cluster-Assembled Porous Nanomaterials

Owing to the similar valence electron structures between the B-N bond and the C-C bond, boron nitride, similar to carbon, can form abundant polymorphs with different frameworks, which possess rich mechanical and electronic properties. Using the hollow, cage-like B₁₆N₁₆ cluster as building blocks, here, we established three new BN polymorphs with low-density porous structures, termed Cub-B₁₆N₁₆, Tet-B₁₆N₁₆, and Ort-B₁₆N₁₆, which have cubic (P4¯3m), tetragonal (P4/nbm), and orthomorphic (Imma) symmetries, respectively. Our density functional theory (DFT) calculations indicated that the existence of porous structure Cub-B₁₆N₁₆, Tet-B₁₆N₁₆, and Ort-B₁₆N₁₆ were not only energetically, dynamically, thermally and mechanically stable, they were even more stable than some known phases, such as sc-B₁₂N₁₂ and Hp-BN. The obtained Pugh's ratio showed that the Cub-B₁₆N₁₆ and Tet-B₁₆N₁₆ structures were brittle materials, but Ort-B₁₆N₁₆ was ductile. The analysis of ideal strength, Young's moduli, and shear moduli revealed that the proposed new phases all exhibited sizable mechanical anisotropy. Additionally, the calculation of electronic band structures and density of states showed that they were all semiconducting with a wide, indirect band gap (~3 eV). The results obtained in this work not only identified three stable BN polymorphs, they also highlighted a bottom-up way to obtain the desired materials with the clusters serving as building blocks.

Unexpected low thermal expansion coefficients of pentadiamond

A new carbon allotrope, pentadiamond, was recently reported in the literature. Herein, we investigate its thermal expansion and thermoelastic properties by first principles. It is observed that the bulk modulus and hardness of pentadiamond are far less than those of diamond, but the thermal expansion of pentadiamond is lower than that of diamond in the range of 0 K to 2000 K, and even negative in the temperature range of 0-190 K. The negative thermal expansion at low temperature originates from the transverse vibrations of the edge-shared atoms in the coplanar double-pentagon. The low thermal expansion at high temperature is contributed by the strong bonds in pentadiamond. Benefiting from the low thermal expansion, the elastic constants of pentadiamond decrease very slowly with respect to temperature compared with those of diamond. The low sensitivity of thermodynamic and thermoelastic properties to temperature makes pentadiamond a promising material for high anti-thermal-shock and accurate electronic device applications.

Calculation of elastic constants of embedded-atom-model potentials in the NVT ensemble

A method for the calculation of elastic constants in the NVT ensamble using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential is studied in detail. It is shown that, in such NVT MD simulations, the evaluation of elastic constants is robust and accurate because it gives the elastic tensor in a single simulation which converges using a small number of time steps and particles. These results highlight the applicability of this method in (i) the calculation of local elastic constants of nonhomogeneous crystalline materials and (ii) the calibration of interatomic potentials, as a fast and accurate alternative to the common method of explicit deformation, which requires a set of consistent simulations at different conditions. The method is demonstrated for the calculation of the elastic constants of copper in the temperature range of 0-1000 K, and results agree with the target values used for the potential calibration. The various contributions to the values of the elastic constants, namely, the Born, stress fluctuation, and ideal gas terms, are studied as a function of temperature.

Investigation of thermo-acoustoelastic guided waves by semi-analytical finite element method

Guided waves are sensitive to variations in propagation environments. Many recent studies have focused on the uniform thermal effect on Lamb waves. However, there is little research on the thermal effect in a more complex situation, such as a nonuniform thermal effect and wave propagation in an arbitrary cross-section. In this study, a thermo-acoustoelastic theory combined with the semi-analytical finite element (TAE-SAFE) method is proposed to investigate both uniform and nonuniform thermal effects on acoustoelastic guided wave propagation. In the TAE-SAFE method, effective thermo-acoustoelastic constants including third-order elastic constants are employed. Then, an acoustoelastic wave equation of the thermal effect is formulated by Hamilton's principle and computed by the semi-analytical finite element (SAFE) method. The phase velocity, group velocity, velocity thermal sensitivity, and displacement mode shape shift can be extracted by the proposed method. To validate this method, numerical results of Lamb waves in an aluminum plate subjected to a uniform thermal effect are compared with the results of a previous theoretical analysis. The results show computational veracity and validity. Two typical cases are investigated: (1) an isotropic aluminum plate under a linear temperature gradient condition; (2) a uniform temperature case in a rail track with a constant irregular cross-section. This study provides an effective numerical method to analyze thermo-acoustoelastic guided wave propagation.

Investigation of a Solid-State Tuning Behavior in Lithium Niobate

Electric field-based frequency tuning of acoustic resonators at the material level may provide an enabling technology for building complex tunable filters. Tunable acoustic resonators were fabricated in thin plates (h/ λ  ∼  0.05 ) of X-cut lithium niobate (LiNbO₃) (90°, 90°, ψ = 170^° ). LiNbO₃ is known for its large electromechanical coupling ( K ² ) for the shear and symmetric Lamb modes (SH₀: K ² = 40 %, S₀: K ² = 30 %) in thin plates and, thus, applicability for low-insertion loss and wideband filter applications. We demonstrate the effect of a dc bias in X-cut LiNbO₃ to shift the resonant frequency by ~0.4% through direct tuning of the resonator material. A nonlinear acoustic computation predicted 0.36% tuning, which was in excellent agreement with the tuning measurement. For X-cut, we predicted electrical tuning of the S₀ mode up to 1.6% and for Y-cut the electrical tuning of the SH₀ and S₀ modes was up to 7.0% with K ² = 27.1 %. The mechanism is based on the nonlinearities that exist in the piezoelectric properties of LiNbO₃. The X-cut SH₀ mode resonators were centered near 335 MHz and achieved a frequency tuning of 6 kHz/V through the application of a dc bias.

Strain-induced dimensional phase change of graphene-like boron nitride monolayers

We investigate the coupling between the electronic bandgap and mechanical loading of graphene-like boron nitride (h-BN ) monolayers up to failure strains and beyond by means of first-principles calculations. We reveal that the kinks in the bandgap-strain curve are coincident with the ultimate tensile strains, indicating a phase change. When the armchair strain is beyond the ultimate tensile strain, h-BN fails with a phase transformation from 2D honeycomb to 1D chain structure, characterized by the 'V'-shape bandgap-strain curve. Large biaxial strains can break the 2D honeycomb structures into 0D individual atoms and the bandgap closes.

Temperature Effects on the Elastic Constants, Stacking Fault Energy and Twinnability of Ni3Si and Ni3Ge: A First-Principles Study

The volume versus temperature relations for Ni 3 Si and Ni 3 Ge are obtained by using the first principles calculations combined with the quasiharmonic approach. Based on the equilibrium volumes at temperature T, the temperature dependence of the elastic constants, generalized stacking fault energies and generalized planar fault energies of Ni 3 Si and Ni 3 Ge are investigated by first principles calculations. The elastic constants, antiphase boundary energies, complex stacking fault energies, superlattice intrinsic stacking fault energies and twinning energy decrease with increasing temperature. The twinnability of Ni 3 Si and Ni 3 Ge are examined using the twinnability criteria. It is found that their twinnability decrease with increasing temperature. Furthermore, Ni 3 Si has better twinnability than Ni 3 Ge at different temperatures.

Variation of second-order piezoelectric coefficients with respect to a finite strain measure

In this article the consequence of a change of finite strain measure is theoretically considered for nonlinear piezoelectric crystals. Analytical predictions show that second-order piezoelectric coefficients are finite strain measure dependent. Therefore, the use of any finite strain measure in constitutive modelling of piezoelectric materials requires an adequate choice of higher-order piezoelectric coefficients. This allows one to avoid unwanted corrections to the elastic and electric fields in the case of nonlinear modelling of piezoelectric materials, e.g. for piezoelectric heterostructures such as quantum wells or dots. A general transformation formula for second-order piezoelectric coefficients (elastostriction) is derived. As an example, specific transformation formulae for two common crystallographic classes, namely {\bar 4}3m and 6mm, are presented. The piezoelectric coefficients for GaN and GaAs crystals, as representative cases of these crystal classes, are recalculated and their dependence on the strain measure is demonstrated. A further implication of that effect is that a complete set of second-order piezoelectric coefficients should contain additional information about the strain measure applied during calculations or measurements.

Poro-acoustoelastic constants based on Padé approximation

Stress-induced velocity variations for porous rocks are generally characterized by a strong nonlinear dependence on stress associated with complex deformations under loading. The classical theory of poro-acoustoelasticity with high-order elastic constants is based on the Taylor expansion of the strain energy function, encountering problems of divergence and limitless elastic wave velocities in describing stress-associated velocity variations, especially for high effective stresses. The extension of the theory beyond the high-order elastic constants based on the Padé approximation to the strain energy function is addressed in this article. The resultant acoustoelastic constants are characteristics of a reasonable theoretical limit in elastic wave velocities with increasing effective stresses, avoiding some of the problems associated with high-order elastic constants such as decreasing moduli with increasing effective pressure at high effective pressure, possibly implying the microstructural dependence of elastic constants. That is, the loading stress increases strain energy and wave velocity, but also induces frame-related attenuation, which in turn reduces stiffness and elastic constants. The Padé nonlinear constants can be reduced for low effective stresses to the conventional acoustoelastic constants based on the Taylor expansion. Theoretical results are compared with ultrasonic measurements for a perfectly elastic crystal, topaz (Al₂SiO₄F₂), and a porous rock, demonstrating that the Padé-approximation-based acoustoelasticity gives a more accurate description of stress-associated velocity variations, especially for higher effective stresses.

On the origins of anomalous elastic moduli and failure strains of GaP nanowires

Previous reports suggest that Raman peaks in uniaxially loaded nanowires with diamond cubic and zinc blende crystal structures shift at rates that are significantly different from bulk specimens. We have investigated the first order Raman scattering from individual, free-standing, [111] oriented GaP nanowires ranging from 75 to 180 nm in diameter at uniaxial tensile stresses up to 5 GPa. All of the phonon modes were shifted to frequencies lower than previously reported for bulk GaP, and significant splitting of the degenerate transverse optical mode was observed. A general analysis method using single and double Lorentzian fits of the Raman peaks is presented and used to report more accurate values of the phonon deformation potentials (PDPs) that relate uniaxial strains to Raman peak shifts in GaP. A new set of PDPs determined from the nanowires revealed that the they have elastic moduli and failure strains that are consistent with bulk GaP. The analysis method eliminated the anomalous, inconsistent deformation behavior commonly reported in Raman-based strain measurements of nanowires, and can be extended to other materials systems with degenerate phonons.

Charge-transfer potentials for ionic crystals: Cauchy violation, LO-TO splitting, and the necessity of an ionic reference state

In this work, we study how including charge transfer into force fields affects the predicted elastic and vibrational Γ-point properties of ionic crystals, in particular those of rock salt. In both analytical and numerical calculations, we find that charge transfer generally leads to a negative contribution to the Cauchy pressure, P(C) ≡ C12 - C66, where C12 and C66 are elements of the elastic tensor. This contribution increases in magnitude with pressure for different charge-transfer approaches in agreement with results obtained with density functional theory (DFT). However, details of the charge-transfer models determine the pressure dependence of the longitudinal optical-transverse optical splitting and that for partial charges. These last two quantities increase with density as long as the chemical hardness depends at most weakly on the environment while experiments and DFT find a decrease. In order to reflect the correct trends, the charge-transfer expansion has to be made around ions and the chemical (bond) hardness has to increase roughly exponentially with inverse density or bond lengths. Finally, the adjustable force-field parameters only turn out meaningful, when the expansion is made around ions.

Mechanical degradation of graphene by epoxidation: insights from first-principles calculations

Oxidation is a major cause for the degradation of materials including graphene, where epoxidation (forming the C-O-C bond) is very common. In addition, graphene oxide, in which the epoxy group is one of the two major functional groups (the other is hydroxy), is an important precursor material used for the bulk synthesis of graphene sheets. Information about the mechanical stabilities, non-linear elastic properties, and elastic limits under various strain components is invaluable for application of these nanomaterials. Here, we investigate the mechanical properties of the epoxidized graphene in ordered graphene oxide, namely C6O1, C6O2, and C6O3, representing the carbon : oxygen ratios of 6 : 1, 3 : 1, and 2 : 1, respectively, using first-principles calculations within the framework of density functional theory. We predict a reduction of Young's modulus of graphene by a factor of 20%, 23%, and 27% for C6O1, C6O2, and C6O3, respectively, indicating a monotonic degradation with respect to epoxidation. However, there is no clear trend for Poisson's ratio, implying that the local atomic configurations are dominant over oxygen concentrations in determining the Poisson ratio. Our computed high order elastic constants are good for the design of graphene oxide based flexible transparent electronics.

Nonlinear ultrafast acoustics at the nano scale

Pulsed femtosecond lasers can generate acoustic pulses propagating in solids while displaying either diffraction, attenuation, nonlinearity and/or dispersion. When acoustic attenuation and diffraction are negligible, shock waves or solitons can form during propagation. Both wave types are phonon wavepackets with characteristic length scales as short as a few nanometer. Hence, they are well suited for acoustic characterization and manipulation of materials on both ultrafast and ultrashort scales. This work presents an overview of nonlinear ultrasonics since its first experimental demonstration at the beginning of this century to the more recent developments. We start by reviewing the main properties of nonlinear ultrafast acoustic propagation based on the underlying equations. Then we show various results obtained by different groups around the world with an emphasis on recent work. Current issues and directions of future research are discussed.

Mechanical properties and stabilities of g-ZnS monolayers

Planar graphene-like ZnS monolayers are mechanically stable under various large strains.

Mechanical properties and stabilities of α-boron monolayers

α-Boron monolayers are mechanically stable under various large strains.

Elastic and ultrasonic properties of single crystalline nickel nanowires

In the present paper, we have theoretically calculated the non linear elastic constants of single crystalline Ni NWs at very broad temperature range 20-300K validating simple interaction potential model. The temperature dependent ultrasonic attenuation and other related properties are determined using their second and third order elastic constants (SOECs/TOECs). Where possible, the results are compared with experiments from literature. There is a correlation between the thermal conductivity and ultrasonic attenuation in the temperature range 100-300K. Also, a correlation between the resistivity and ultrasonic attenuation in the temperature range 40-100K has been established validating the theoretical approach.

Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p1. For liquids the second-order elastic constants are C₁₁=A+p₁, C₁₂=A-p₁, and the third-order constants are C₁₁₁=-(B+5A+3p₁), C₁₁₂=-(B+A-p₁), and C₁₂₃=A-B-p₁, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second-order constants are C₁₁=p₁γ+p₁, C₁₂=p₁γ-p₁, and the third-order constants are C₁₁₁=-p₁(γ(2)+4γ+3), C₁₁₂=-p₁(γ(2)-1), and C₁₂₃=-p₁ (γ(2)-2γ+1), where γ is the ratio of specific heats. The inequality of C₁₁ and C₁₂ results in a nonzero shear constant C₄₄=(1/2)(C₁₁-C₁₂)=p₁ for both liquids and gases. For water at standard temperature and pressure the ratio of terms p₁/A contributing to the second-order constants is approximately 4.3×10(-5). For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material 'nonlinearity parameters' associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids.

Outstanding mechanical properties of monolayer MoS2 and its application in elastic energy storage

The structural and mechanical properties of graphene-like honeycomb monolayer structures of MoS2 (g-MoS2) under various large strains are investigated using density functional theory (DFT). g-MoS2 is mechanically stable and can sustain extra large strains: the ultimate strains are 0.24, 0.37, and 0.26 for armchair, zigzag, and biaxial deformation, respectively. The in-plane stiffness is as high as 120 N m(-1) (184 GPa equivalently). The third, fourth, and fifth order elastic constants are indispensable for accurate modeling of the mechanical properties under strains larger than 0.04, 0.07, and 0.13 respectively. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson ratio monotonically decreases with increasing pressure. With the prominent mechanical properties including large ultimate strains and in-plane stiffness, g-MoS2 is a promising candidate of elastic energy storage for clean energy. It possesses a theoretical energy storage capacity as high as 8.8 MJ L(-1) and 1.7 MJ kg(-1), or 476 W h kg(-1), larger than a Li-ion battery and is environmentally friendly.

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.

Experimental determination of third-order elastic constants of diamond

To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.

Interaction of collinear and noncollinear phonons in anharmonic scattering processes and their role in ultrasound absorption of fast quasi-transverse modes in cubic crystals

The absorption of fast quasi-transverse modes during anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond and InSb) or negative (KCl and CaF(2)) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the fast quasi-transverse mode by two fast (the FFF mechanism) or two slow (the FSS) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the FFF, FSS and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the fast quasi-transverse mode is determined. The problem of the scattering of collinear and noncollinear phonons in cubic crystals and their role in the ultrasound absorption of the fast quasi-transverse modes is considered. It is shown that the FFF and FSS relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. In crystals with a considerable anisotropy of the elastic energy (InSb and KCl), the total contribution of the FFF and FSS relaxation mechanisms to the full absorption is one to two orders of magnitude larger than the contribution from the Landau-Rumer mechanism, depending on the direction. Much of the dominance of the former relaxation mechanisms over the Landau-Rumer mechanism is explained by second-order elastic moduli. The role of the Landau-Rumer mechanism in ultrasound absorption may be considerable in cubic crystals with a smaller anisotropy of the elastic energy. It is demonstrated that when anharmonic scattering processes play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the FFF or FSS mechanisms of relaxation) is insufficient for the quantitative description of the anisotropy of the full absorption of the fast quasi-transverse modes in cubic crystals.

ACOUSTICAL CHARACTERIZATION OF NANOSTRUCTURED METAL

Ultrasonic attenuation due to phonon–phonon interaction, thermoelastic loss and dislocation damping arising from screw and edge dislocations has been evaluated in nanocrystalline copper (13 nm) in the temperature range 50–500 K, and size-dependent attenuation at a constant temperature for longitudinal and shear modes of propagation. Second and third order elastic constants have been obtained, taking the nearest neighbor distance and the hardness parameter as input data. SOEC and TOEC (obtained at different temperatures) have been used to obtain Grüneisen parameters and nonlinearity parameters, which in turn have been used to evaluate α/f2 for longitudinal and shear waves. Results have been discussed, and compared with available experimental values. It has been found that α/f2 increases with temperature and a significant contribution to the total attenuation occurs due to scattering from grain boundaries, and ultrasonic attenuation due to thermoelastic loss is negligible compared to phonon–phonon interaction, establishing that the major part of energy from the sound wave is removed owing to the interaction of acoustic phonons with thermal phonons (lattice vibrations).

A continuum description of nonlinear elasticity, slip and twinning, with application to sapphire

A model is developed for elasticity, plasticity and twinning in anisotropic single crystals subjected to large deformations. Dislocation glide and deformation twinning are dissipative, while energy storage mechanisms associated with dislocation lines and twin boundaries are described via scalar internal state variables. Concepts from continuum crystal plasticity are invoked, with shearing rates on discrete glide and twinning systems modelled explicitly. The model describes aspects of thermomechanical behaviour of single crystals of alumina over a range of loading conditions. Resolved shear stresses necessary for glide or twin nucleation at low to moderate temperatures are estimated from nonlinear elastic calculations, theoretical considerations of Peierls barriers and stacking fault energies and observations from shock physics experiments. These estimates are combined with the existing data from high-temperature experiments to provide initial yield conditions spanning a wide range of temperatures. The model reflects hardening of glide and twin systems from dislocations accumulated during basal slip. Residual elastic volume changes, predicted from nonlinear elastic considerations and approximated dislocation line energies, are positive and proportional to the dislocation line density. While the model suggests that generation of very large dislocation densities could influence the pressure–volume response, volume increases from defects are predicted to be small in crystals deformed via basal glide on a single system.

Quasi-transverse ultrasound absorption due to point defects and anharmonic scattering processes in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

The quasi-transverse ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli is analyzed. The scattering of the ultrasound by point defects and during anharmonic scattering processes is considered. The quasi-transverse ultrasound absorption is analyzed as a function of the wavevector direction in terms of the anisotropic continuum model. The Landau-Rumer mechanism is considered for anharmonic scattering processes. Known values of the second- and third-order elastic moduli are used to calculate parameters determining the ultrasound absorption. It is shown that the angular dependences of the quasi-transverse ultrasound absorption differ qualitatively if the anharmonic scattering processes dominate in cubic crystals with positive and negative anisotropies of the second-order elastic moduli. For the scattering by point defects and the anharmonic scattering processes, the angular dependences of the quasi-transverse ultrasound absorption exhibit the inverse behavior, making it possible to determine the dominating mechanism of the ultrasound relaxation in the crystals under study.

Contact phase modulation method for acoustic nonlinear parameter measurement in solid

In this work, a new method to measure in contact the nonlinearity parameter beta of solid plates is presented. A high frequency (HF) tone-burst signal of 20 MHz is inserted in the material by a contact-transducer (with a suitable coupling). A low frequency (LF) pulse (2.5 MHz) is applied to the other face, in the opposite direction, so that the nonlinear interaction of the two waves takes place during the back propagation toward the HF transducer. This collinear interaction creates a phase modulation of the HF tone-burst which is proportional to the beta coefficient and the particle velocity of the LF wave. To determine this particle velocity, in time domain, an extended self-reciprocity calibration of the contact LF transducer is used. A numeric phase demodulation is then performed, giving the beta coefficient of the sample. The proposed method is validated by nonlinearity parameter measurements in Fused Silica. The nonlinear parameter of Fused Silica measured is found to be in good agreement with the literature, and specially the negative sign of this parameter.