Indentation Size Effect and Microhardness Study of β-Sn Single Crystals

The load dependence of apparent microhardness of β-Sn single crystals having different growth directions is investigated. The measurements are performed on （110） planes of these crystals in the load range from 10 to 50 mN. It is found that the degree of the microhardness anisotropy decreases for higher indentation test loads. The examined materials exhibit the behaviour of indentation size effect （ISE）, i.e., the apparent hardness increases with decreasing indentation load. Neither Meyer＇s law nor the proportional specimen resistance （PSR） model can fully explain the nonlinear variation of microhardness with load. Instead, preference is given to modified the PSR model based on the consideration of the effect of machining-induced residually stressed surface on the hardness measurement.     

Dynamic characteristics of nanoindentation in Ni:A molecular dynamics simulation study

In this work,three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviour of single crystal Ni.The substrate indenter system is modelled using hybrid interatomic potentials including the manybody potential(embedded atom method) and two-body Morse potential.The spherical indenter is chosen,and the simulation is performed for different loading rates from 10 m/s to 200 m/s.Results show that the maximum indentation load and hardness of the system increase with the increase of velocity.The effect of indenter size on the nanoindentation response is also analysed.It is found that the maximum indentation load is higher for the large indenter whereas the hardness is higher for the smaller indenter.Dynamic nanoindentation is carried out to investigate the behaviour of Ni substrate to multiple loading-unloading cycles.It is observed from the results that the increase in the number of loading unloading cycles reduces the maximum load and hardness of the Ni substrate.This is attributed to the decrease in recovery force due to defects and dislocations produced after each indentation cycle.     

Pressure-induced structural transition and thermodynamic properties of RhN2 and the effect of metallic bonding on its hardness

The elastic constant, structural phase transition, and effect of metallic bonding on the hardness of RhN2 under high pressure are investigated through the first-principles calculation by means of the pseudopotential plane-wave method. Three structures are chosen to investigate for RhN2, namely, simple hexagonal P6/mmm （denoted as SH）, orthorhombic Pnnm （marcasite）, and simple tetragonal P4/mbm （denoted as ST）. Our calculations show that the SH phase is energetically more stable than the other two phases at zero pressure. On the basis of the third-order Birch Murnaghan equation of states, we find that the phase transition pressures from an SH to a marcasite structure and from a marcasite to an ST structure are 1.09 GPa and 354.57 GPa, respectively. Elastic constants, formation enthalpies, shear modulus, Young＇s modulus, and Debye temperature of RhN2 are derived. The calculated values are, generally speaking, in good agreement with the previous theoretical results. Meanwhile, it is found that the pressure has an important influence on physical properties. Moreover, the effect of metallic bonding on the hardness of RhN2 is investigated. This is a quantitative investigation on the structural properties of RhN2, and it still awaits experimental confirmation.     

Mechanical Properties of Single-Walled （5,5） Carbon Nanotubes with Vacancy Defects

First-principles simulation is used to investigate the structural and mechanical properties of vacancy defective single-walled （5,5） carbon nanotubes. The relations of the defect concentration, distribution and characteristic of defects to Young＇s modulus of nanotubes are quantitatively studied. It is found that each dangling-bond structure （per supercell） decreases Young＇s modulus of nanotube by 6.1% for symmetrical distribution cases. However the concentrative vacancy structure with saturated atoms has less influence on carbon nanotubes. It is suggested that the mechanical properties of carbon nanotubes depend strongly upon the structure and relative position of vacancies in a certain defect concentration.     

Is a nanorod (or nanotube) with a lower Young’s modulus stiffer? Is not Young’s modulus a stiffness indicator?

It has been a known fact in classical mechanics of materials that Young’s modulus is an indicator of material stiffness and materials with a higher Young’s modulus are stiffer. At the nanoscale, within the scope and under specific circumstances described in this paper, however, a nanorod (or a nanotube) with a smaller Young’s modulus (smaller stress-strain rate) is stiffer. In such a scenario, Young’s modulus is not a stiffness indicator for nanostructures. Furthermore, the nonlocal stress-strain rate is dependent on types of load, boundary conditions and location. This is likely to be one of the many possible reasons why numerous experiments in the past obtained significantly varying values of Young’s modulus for a seemingly identical nanotube, i.e. because the types of loading and/or boundary conditions in the experiments were different, as well as at which point the property was measured. Based on the nonlocal elasticity theory and within the scope of material and geometric linearity, this paper reports the strange and hitherto unrealized effect that a nanorod (or a nanotube) with a lower Young’s modulus (smaller stress-strain rate) indicates smaller extension in tensile analysis. Similarly, it is also predicted that a nanorod (or a nanotube) with a lower Young’s modulus results in smaller bending deflection, higher critical buckling load, higher free vibration frequency and higher wave propagation velocity, which are at all consequences of a stiffer nanostructure.     

Nanoadhesion of a Power-Law Graded Elastic Material

The Dugdale—Barenblatt model is used to analyze the adhesion of graded elastic materials at the nanoscale with Young＇s modulus E varying with depth z according to a power law E = E0（z/c0）k （0 〈 k 〈 1） while Poisson＇s ratio v remains a constant, where E0 is a referenced Young＇s modulus, k is the gradient exponent and c0 is a characteristic length describing the variation rate of Young＇s modulus. We show that, when the size of a rigid punch becomes smaller than a critical length, the adhesive interface between the punch and the graded material detaches due to rupture with uniform stresses, rather than by crack propagation with stress concentration. The critical length can be reduced to the one for isotropic elastic materials only if the gradient exponent k vanishes.     

Stability and elastic properties of Nb_xC_y compounds

Density functional theory(DFT) is applied to investigate the stability and mechanical properties of NbxCy compounds.The structures of NbxCy compounds are optimized, and the results are in good agreement with previous work. The calculated results of the cohesive energy and the formation enthalpy of NbxCy show that they are thermodynamically stable structures, except for Pmc21-Nb2 C. The mechanical properties such as the bulk modulus, Young’s modulus, the shear modulus, and Poisson’s ratio are obtained by Voigt–Reuss–Hill approximation. The results show that the Young’s modulus and shear modulus of NbC are larger than other NbxCy compounds. The mechanical anisotropy is characterized by calculating several different anisotropic indexes and factors, such as universal anisotropic index(AU), shear anisotropic factors(A1, A2,A3), and percent anisotropy(ABand AG). The surface constructions of bulk and Young’s moduli are illustrated to indicate the mechanical anisotropy. The hardness of NbxCy compounds is also discussed in this paper. The estimated hardness for all NbxCy compounds is less than 20 GPa.     

Mechanical Properties of Ni-Coated Single Graphene Sheet and Their Embedded Aluminum Matrix Composites

The effects of Ni coating on the mechanical behaviors of single graphene sheet and their embedded Al matrix composites under axial tension are investigated using molecular dynamics （MD） simulation method. The results show that the Young＇s moduli and tensile strength of graphene obviously decrease after Ni coating. The results also show that the mechanical properties of Al matrix can be obviously increased by embedding a single graphene sheet. From the simulation, we also find that the Young＇s modulus and tensile strength of the Ni-coated graphene/Al composite is obviously larger than those of the uncoated graphene/Al composite. The increased magnitude of the Young＇s modulus and tensile strength of graphene/Al composite are 52.27% and 32.32% at 0.01 K, respectively, due to Ni coating. By exploring the effects of temperature on the mechanical properties of single graphene sheet and their embedded Al matrix composites, it is found that the higher temperature leads to the lower critical strain and tensile strength.     

Shell Model for Elastic and Thermodynamic Properties of Gallium Nitride with Hexagonal Wurtzite Structure

Shell model molecular dynamic simulation with interatomic pair potential is utilized to investigate the elastic and thermodynamic properties of gallium nitride with hexagonal wurtzite structure （w-GaN） at high pressure. The calculated elastic constants Cij at zero pressure and 300 K agree well with the experimental data and other calculated values. Meanwhile, the dependences of the relative volume V/Vo, elastic constants Cij, entropy S, enthalpy H, and heat capacities Cv and Up on pressure are successfully obtained. From the elastic constants obtained, we also calculate the shear modulus G, bulk modulus B, Young＇s modulus E, Poisson＇s ratio v, Debye temperature ΘD, and shear anisotropic factor Ashear on pressures.     

First-principles study of the structural,elastic, and optical properties for Sr0.5Ca0.5TiO3

A detailed theoretical study of the structural, elastic, and optical properties for Sr0.5Ca0.5TiO3 is carried out by first- principles calculations. The band structure exhibits a direct bandgap of 2.08 eV at the F point in the Brillouin zone. The bulk modulus, shear modulus, Young＇s modulus, and Poisson＇s ratio are derived based on the calculated elastic constants. The bulk modulus B = 153 GPa and shear modulus G = 81GPa are in good agreement with available experimental data. Poisson＇s ratio v = 0.275 suggests that Sr0.sCa0.sTiO3 should be classified as being a ductile material. Using the electronic band structure and density of states, we analyze the interband contribution to the optical properties. The real and imaginary parts of the dielectric function, as well as the optical properties such as the optical absorption coefficient, refractive index, extinction coefficient, and energy-loss spectrum are calculated. The static dielectric constant ε1 （0） and the refractive index n（0） are also investigated.     

Investigation of the local mechanical properties of potassium chloride single crystals by atomic force microscopy

Using an atomic force microscope (AFM), the of hardness H and Young’s modulus E are measured in near-surface layers of KCl single crystals to a depth of 300 nm at loads of 5–100 µN. The values of H and E are estimated indirectly by analyzing P(h) curves (load vs. indentation depth curves). The value of H is also estimated directly by measuring the area of an indentation with the help of an AFM with a nanoscale resolution. The effect of structural features of the surface around an indentation on the accuracy of the H and E estimates is revealed. The sharp dependence of H on the load (the nanoscale effect) is revealed. The experimental results agree qualitatively with the predictions of the geometrically necessary dislocation model developed by Nix and Gao. However, in order to quantitatively estimate mass transfer from a nanoindenter, a structural analysis is required with allowance for plastic deformation in crystals.     

Electronic Structure and Elastic Properties of Ti3AlC from First-Principles Calculations

We perform a first-principles study on the electronic structure and elastic properties of TiaA1C with an antiperovskite structure. The absence of band gap at the Fermi level and the finite value of the density of states at the Fermi energy reveal the metallic behavior of this compound. The elastic constants of Ti3AlC are derived yielding c11 = 356 GPa, c12 = 55 GPa, c44 = 157 GPa. The bulk modulus B, shear modulus G and Young＇s modulus E are determined to be 156, 151 and 342 GPa, respectively. These properties are compared with those of Ti3AlC2 and Ti2AlC with a layered structure in the Ti-Al-C system and FeaAlC with the same antiperovskite structure.     

Mechanical Properties and Electronic Structures of Cotunnite TiO2

Based on the first-principles plane-wave basis pseudopotential calculations, we investigate mechanical properties and electronic structures of the hardest known oxide, cotunnite TiO2. The calculated results show that cotunnite TiO2 has the highest bulk modulus （348 GPa） and hardness （32 GPa） among the high-pressure phases of TiO2, but its mechanical properties are not superior to those of c-BN. Moreover, the high hardness of cotunnite TiO2 can be understood from both the dense crystal structure （high valence electron density and short bond lengths） and the unusual mixtures of covalent and ionic bonding of Ti-O.     

A displacement sensing nanoindentation study of tribo-mechanical properties of the Ni-Co system

An analysis of the tribo-mechanical properties of the Ni-Co system, at the submicrometric contact scale, is conducted using displacement sensing nanoindentation. In particular, the influence of contact depth and surface finishing methods on the hardness, H, and Young's modulus, E, of the materials is analysed. Mechanically and electrolitically polished samples were tested with a conospherical indenter using a range of loads between 0.05 and 10 mN. It is shown that the hardness of these materials depends on the surface finishing method and increases with decreasing contact depth, while the Young's modulus is relatively insensitive to contact depth. Furthermore, sample polycrystallinity leads to a large scattering of hardness values in Co-rich samples and of Young's modulus values in Ni-rich ones. The combined parametric ratio H/E, which can be related to the tribological behaviour of the material, was found to be higher in samples with Co content larger than 80 wt.%.     

Berkovich nanoindentation and deformation mechanisms in GaN thin films

The deformation mechanisms of GaN thin films obtained by metal-organic chemical vapor deposition (MOCVD) method were studied using nanoindentation with a Berkovich diamond indenter, micro-Raman spectroscopy and the cross-sectional transmission electron microscopy (XTEM) techniques. Due to the sharpness of the tip of Berkovich indenter, the nanoindentation-induced deformation behaviors can be investigated at relatively lower load and, hence, may cover wider range of deformation-related phenomena over the same loading range. The load-displacement curves show the multiple “pop-ins” during nanoindentation loading. No evidence of nanoindentation-induced phase transformation and cracking patterns were found up to the maximum load of 300 mN, as revealed from the micro-Raman spectra and the scanning electron microscopy (SEM) observations within the mechanically deformed regions. In addition, XTEM observation performed near the cross-section of the indented area revealed that the primary deformation mechanism in GaN thin film is via propagation of dislocations on both basal and pyramidal planes. The continuous stiffness measurement (CSM) technique was used to determine the hardness and Young's modulus of GaN thin films. In addition, analysis of the load-displacement data reveals that the values of hardness and Young's modulus of GaN thin films are 19 ± 1 and 286 ± 25 GPa, respectively.     

Mechanical properties of InAs/InP semiconductor alloys

The microindentation studies have been reported for undoped and doped InAs/InP semiconductor alloys grown by metal organic vapor phase epitaxy (MOVPE). It was found that the microhardness value increases with increase of applied load and attains a constant value for further increase in the load. The mechanical properties like, fracture toughness, brittleness index, fracture surface energy and indentation size effect coefficient were determined using the microhardness value. The indented samples were etched in H₂SO₄:H₂O₂:H₂O of the ratio of (1:1:1) for 30 s. This reveals the dislocation rosette patterns generated around the edges of the indentation on subsequent etching process.     

Tunable optical limiting of gold nanorod thin films

Permalloy (Py) films were deposited on Si(111) or Corning 0211 glass substrates. There were two deposition temperatures: T _s=room temperature (RT) and T _s=270°C. The film thickness (t _f) ranges from 10 to 130 nm. The crystal structure properties of the films were studied by X-ray diffraction and transmission electron microscopy. Mechanical properties (including Young’s modulus E _f and hardness H _f) of each film were measured by the nanoindentation (NI) technique. E _f of the Py/Si(111) films was checked again by the laser induced surface acoustic wave (LA-SAW) technique. It was found that the NI technique is best suited for the measurements of E _f and H _f, but only when the sample belongs to the (soft film)/(soft substrate) system, such as the Py/glass film. For the (soft film)/(hard substrate) system, such as the Py/Si(111) film, the NI technique often provides higher values of E _f and H _f than expected. The anomalous phenomenon, associated with the NI technique may be related to the anisotropic crystal structures in the Py films on different kinds of substrates. From this study, we conclude that [E _f of Py/Si(111)]>[E _f of Py/glass] and [H _f of Py/Si(111)]>[H _f of Py/glass]. The good mechanical properties of the Py/Si(111) film make it a better candidate for recording head applications.     

First-Principles Calculations of Elastic Properties of LaNi4.75Sn0.25 Alloys under Pressure

The equilibrium lattice constants, bulk modulus, shear modulus, elastic constants and Debye temperature of LaNi4.75 Sn0.25 under pressure are calculated using the full-potential linearized augmented plane wave （FP-LAPW） method as well as the quasi-harmonic Debye model. The results at zero pressure are in excellent agreement with the experimental data. The Sn atom is found to occupy the equivalent 3g site （0.5a, 0.75b, 0.5c） in the quadruple cell. The Debye temperature of LaNi4.75Sn0.25 is lower than that of LaNi5. The dependences of bulk modulus on finite temperature and on finite pressure are also investigated. The results show that the bulk modulus B increases monotonously as pressure increases.     

Determination of silicone coating Young's modulus using atomic force microscopy

The polymerisation degree of thin polymer coatings was checked by following the variation of their local mechanical properties. Atomic force microscope (AFM) was used in an indentation mode to investigate the mechanical characteristics of silicone coatings on polycarbonate substrates. The evolution of Young's modulus of the silicone coatings was determined as a function of the polymer annealing time. We have used a relative method to measure Young's moduli, which involves a calibration step with a set of reference polymers. No variation was observed for the modulus of silicone coatings annealed during more than 40 min at 130 °C. This result indicates that over-heating does not modify the mechanical properties of the coating.     

Correlation between structural and mechanical properties of PbTiO3 thin films grown by pulsed-laser deposition

Tetragonal lead titanate (PbTiO₃, PT) thin films are grown on (1 0 0) MgO substrate by pulsed-laser deposition (PLD) for expected applications in integrated optics. The realisation of outstanding and reliable devices into integrated circuits requires sufficient mechanical resistance despite that the obtained PT films display interesting waveguiding properties associated with low optical losses. Two mechanical properties characteristic of elasticity and hardness of PT films are studied. The elastic modulus (E or Young's modulus) and the hardness (H) are measured by the nanoindentation technique. These mechanical properties are correlated to the crystalline quality of PT/MgO thin films. The films show epitaxial relationship with the MgO substrate and the orientation of crystallites perpendicularly to the surface substrate may be the consequence of a growth process along c-axis, a-axis or both. Differences on curves plotting hardness and elastic modulus as a function of indentation depth are observed as the curves are less dispersed for the films mainly c-axis oriented.