Theoretical strength and the onset of plasticity in bulk metallic glasses investigated by nanoindentation with a spherical indenter

The mechanical behavior of bulk metallic glasses (BMGs) was investigated by nanoindentation with a spherical indenter. The transition from perfectly elastic behavior to plastic deformation was clearly observed as a pop-in event (sudden displacement excursion) on the load-displacement curves. Hertzian stress analysis was used to describe fully the load-displacement behavior during elastic deformation and to determine the theoretical shear strengths of the BMGs.     

Deformation behavior of PZN–6%PT single crystal during nanoindentation

The deformation behavior of [001]^T- and [011]^T-cut single crystal solid solution of Pb(Zn_1/3Nb_2/3)O₃–6% PbTiO₃ (PZN–6%PT) in both unpoled and poled states has been investigated by nanoindentation. Nanoindentation experiments reveal that material pile-up and local damage around the indentation impressions are observed at ultra-low loads. These pile-ups and local damage cause a pop-in event (i.e. a sudden increase in displacement at an approximately constant load) in the nanoindentation load–displacement curve (P–h curve). Detailed studies of the relationships between indentation load (P), displacement (h) and harmonic contact stiffness (S) suggest that there is a surface layer, possibly due to crystal fabrication processes, which possesses different mechanical properties from the interior. The thickness of this surface layer is estimated to be approximately 300 nm. Furthermore, it is found that [011]^T-cut crystal is stiffer than [001]^T-cut crystal. On the other hand, both [001]^T- and [011]^T-cut crystals in unpoled state possess lower contact stiffness than poled crystals. This finding suggests that poling improved the mechanical property of the crystal. In summary, poled [001]^T-cut crystals have an elastic modulus of (107 ± 6) GPa and a hardness of (5.1 ± 0.4) GPa. In contrast, the modulus for [011]^T-cut crystals is not constant but increases with indentation depth.     

Dislocation structure and dynamics govern pop-in modes of nanoindentation on single-crystal metals

ABSTRACT

There are two types of pop-in mode that have been widely observed in nanoindentation experiments: the single pop-in, and the successive pop-in modes. Here we employ the molecular dynamics (MD) modelling to simulate nanoindentation for three face-centred cubic (FCC) metals, including Al, Cu and Ni, and two body-centred cubic (BCC) metals, such as Fe and Ta. We aim to examine the deformation mechanisms underlying these pop-in modes. Our simulation results indicate that the dislocation structures formed in single crystals during nanoindentation are mainly composed of half prismatic dislocation loops. These half prismatic dislocation loops in FCC metals are primarily constituted of extended dislocations. Lomer–Cottrell locks that result from the interactions between these extended dislocations can resist the slipping of half dislocation loops. These locks can build up the elastic energy that is needed to activate the nucleation of new half dislocation loops. A repetition of this sequence results in successive pop-in events in Al and other FCC metals. Conversely, the half prismatic dislocation loops that form in BCC metals after first pop-in are prone to slip into the bulk, which sustains plastic indentation process after first pop-in and prevents subsequent pop-ins. We thus conclude that pop-in modes are correlated with lattice structures during nanoindentation, regardless of their crystal orientations.     

Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.     

Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials

Nanoelectromechanics of piezoelectric indentation, including the structure of coupled electroelastic fields and stiffness relations, is analysed for flat, spherical, and conical indenter geometries. Exact solutions in elementary functions for electroelastic fields inside the material are obtained using the recently established correspondence principle between the elastic and the piezoelectric problems. The stiffness relations fully describe the indentation process and relate indentation depth, indentation force and bias to the relevant material properties and indenter parameters. This extends the results of Hertzian mechanics to piezoelectric materials. The stiffness relations are utilized for quantitative understanding of the electromechanical scanning probe microscopies (SPM) of ferroelectric and piezoelectric materials, including piezoresponse force microscopy, atomic force acoustic microscopy, scanning near-field acoustic microscopy, and heterodyne ultrasonic-electrostatic force microscopy. The structure of the electroelastic field yields a quantitative measure of signal generation volume in electromechanical SPMs and also provides a quantitative basis for the analysis of tip-induced polarisation switching and local hysteresis loop measurements.     

Effect of solid solution strengthening by iridium on the nucleation of dislocations in a molybdenum single crystal during nanoindentation

The nucleation of dislocations in single crystals of molybdenum and a Mo-1.5 at % Ir solid solution has been investigated by nanoindentation. In the curve of indentation of a Berkovich indenter into the single crystals, an abrupt transition from elastic to plastic deformation has been observed at a depth of 20–40 nm due to the nucleation of dislocations in the initially dislocation-free region under the contact. Alloying of molybdenum by iridium results in a twofold increase in shear stresses under which dislocations nucleated in the contact. Therefore, the solid solution impurity of iridium in molybdenum leads to an increase not only in the plastic strain resistance (to an increase in the hardness) but also in the elastic shear stresses under which dislocations are generated (homogeneously or heterogeneously) in the contact. The latter effect cannot be explained only by an increase in the elastic moduli because of its smallness; however, it is determined to a large extent by a higher degree of perfection of the solid solution crystal as compared to unalloyed molybdenum.     

Growth and characterization of ferroelectric SrBi2Ta2O9 single crystals via high-temperature self-flux solution method

SrBi₂Ta₂O₉ (SBT) single crystals were produced by the high-temperature self-flux solution method using a Bi₂O₃ flux modified with B₂O₃. The processing conditions were optimized to obtain large and translucent SBT crystals with a layered habit and typical dimensions of approximately 7 × 5 × 0.2 mm. X-ray diffraction and x-ray topography measurements revealed that the major faces of the crystals with natural rectangular platelet morphology are perfectly (001)-oriented with edges directed along the [110] directions. The high quality of the crystals was confirmed by rocking curves (half-width of 0.04° for the (0018) reflection) and by ferroelectric measurements. The anisotropy in the dielectric and ferroelectric properties was investigated both along the [110] (ab plane) and the [001] (c axis) directions. The growth mechanism, morphology, and dielectric anisotropy of the SBT crystal platelets are discussed based on its crystallographic structure. This article was submitted by the authors in English     

Nanoindentation stress–strain curves as a method for thin-film complete mechanical characterization: application to nanometric CrN/Cr multilayer coatings

The mechanical behavior of CrN/Cr multilayer coatings deposited by rf magnetron sputtering has been investigated by nanoindentation measurements performed with indenters of different geometries. Nanoindentation stress–strain curves generated from these measurements allow us to characterize the complete mechanical behavior of these coatings in the elastic, elastoplastic, plastic and fracture deformation regimes. In particular, indentation measurements carried out with a 100-m-radius spherical indenter allowed us to study the elastic deformation regime and estimate the yield stress parameter through the initial indentation yielding point. The elastoplastic deformation regime has been studied using a 5-m-radius spherical indenter and the stationary yielding regime (fully plastic regime) has been investigated with a pyramidal indenter of Berkovich geometry. The use of a pyramidal cube-corner indenter allowed us to study coating fracture characteristics. Nanometric CrN/Cr multilayer structures as well as single CrN and Cr coatings have been characterized. The study has shown that multilayered coatings with period thicknesses less than 46 nm present values of yield stress, Youngs modulus, hardness and toughness higher than those for single-layer CrN and Cr coatings. PACS 62.20.Dc; 62.20.Qp; 68.60.Bs     

Effect of sample tilt on nanoindentation behaviour of materials

Analysis of nanoindentation is based on the elastic solution of a rigid indenter perpendicularly penetrating a flat contact surface. In reality, nanoindentation is often performed on a tilt sample surface due to sample tilt mounting or the existing roughness of a polished or raw surface. In this study, finite element simulations as well as nanoindentation experiments on a fused-quartz sample with different tilt angles were carried out to investigate the influence of sample tilt on nanoindentation behaviour of materials. It was found that sample tilt results in increases in the indentation load, contact area and contact stiffness at the same penetration depth. The contact area increase caused by sample tilt cannot be accounted for by Sneddon's equation, commonly used in nanoindentation analysis. This results in a significant underestimation of indentation projected contact area, which in turn leads to an overestimation of the mechanical properties measured by nanoindentation.     

Elastic–plastic deformation of Pb(Zn1/3Nb2/3)O3–(6–7)% PbTiO3 single crystals during nanoindentation

The elastic–plastic deformation behavior of (001)- and (011)-oriented single crystal solid solutions of Pb(Zn_1/3Nb_2/3)O₃–(6–7)% PbTiO₃ (PZN–PT) have been studied using a nanoindentation technique. A procedure is presented here to isolate the elastic, elastic–plastic and plastic contributions to the deformation using the unloading data, and a parameter, referred to as relaxation, is defined to characterize the elastic–plastic deformation during nanoindentations. This relaxation parameter increases with the maximum indentation load due to the higher indentation stress induced, and it also causes less recovery of the material upon indentation unloading compared to predicted pure elastic recovery. For a (001) surface, the relaxation value remains virtually unchanged within the range of the maximum indentation load of 10–50 mN, possibly due to a complete localized depoling of the non-180° domain switching. It is also found that the unpoled surface is more prone to stress-induced depolarization compared to the poled surfaces. Furthermore, by applying the continuous stiffness measurement (CSM) technique, the effects of multiple loading/unloading are studied for both (001)- and (011)-oriented PZN–PTs using the maximum indentation loads of 20 and 50 mN. With more loading/unloading cycles at higher CSM frequencies, stress-induced depolarization becomes prevalent and the contribution of the domain reorientation towards elastic recovery is significantly reduced. As a consequence, the relaxation value is increased, indicating more elastic–plastic deformation. This CSM effect is especially pronounced for poled (011) surfaces.     

Nanoindentation analysis of the pop-in events on SiGe single layer

The growth of metastable silicon germanium (Si_0.8Ge_0.2) thin film on Si(1 0 0) by ultrahigh-vacuum chemical vapor deposition has been subjected to residual indentation studies. A nanoindentation system has been applied to analyze SiGe film after different annealing treatments. A number of phenomena have been found for the heteroepitaxial growth of SiGe film at the critical thickness of 350 nm, including single discontinuity (the so-called “pop-in” event) as well as the elastic/plastic contact translation. Atomic force microscopy is employed to investigate the surface impression. Pop-in events in the load-indentation depth curves of 400 and 500 °C and no nano-cracks in the vicinity regions are found. The values of H ranging from 13.13±0.9, 21.66±1.3, 18.52±1.1, 14.47±0.7 GPa and the values of E ranging from 221.8±5.3, 230.7±6.4, 223.5±4.6, 156.7±3.8 GPa, are obtained. The elastic/plastic contact translation of the SiGe film occurs at different annealing conditions, with h_f/h_max values in the range of 0.501, 0.392, 0.424, and 0.535 for samples are treated at RT, 400, 500, and 600 °C, respectively. The mechanism responsible for the pop-in event in such crystal structure is due to the interaction of the indenter tip with the pre-existing threading dislocations, since the release of the indentation load is bound to be reflected in the directly compressed volume.     

考虑相界效应的Ni基单晶合金纳米压痕模拟

利用分子动力学方法分别模拟金刚石压头压入Ni模型和Ni基单晶合金γ/γ′模型的纳米压痕过程,通过计算得到两种模型[001]晶向的弹性模量及硬度.采用中心对称参数分析不同压入深度时两种模型内部位错形核、长大过程以及Ni基单晶合金γ/γ′(001)相界面错配位错对纳米压痕过程的影响.结果显示:压入深度0.641 nm之前,两种模型的压入载荷-压入深度曲线相似,说明此时相界面处的错配位错对纳米压痕过程的影响很小;压入深度0.995 nm时,在错配位错处发生位错形核,晶体在γ相中沿着{111}面滑移,随即导致Ni基单晶合金γ/γ′模型压入载荷的下降,并在压入深度达到1.487 nm之前低于Ni模型相同压入深度时的压入载荷;压入深度从1.307 nm开始,由于相界面错配位错的阻碍作用,Ni基单晶合金γ/γ′模型压入载荷上升速度较快.     

Molecular dynamics study of the mechanical characteristics of Ni/Cu bilayer using nanoindentation

<正>In the present work,a three-dimensional molecular dynamics simulation is carried out to perform the nanoindentation experiment on Ni single crystal.The substrate indenter system is modeled using hybrid interatomic potentials including the many-body potential embedded atom method(EAM),and two-body morse potential.To simulate the indentation process,a spherical indenter(diameter = 80 A,1 A=0.1 nm) is chosen.The results show that the mechanical behaviour of a monolithic Ni is not affected by crystalline orientation.To elucidate the effect of a heterogeneous interface, three bilayer interface systems are constructed,namely Ni(100)/Cu(111),Ni(110)/Cu(111),and Ni(111)/Cu(111).The simulations along these systems clearly describe that mechanical behaviour directly depends on the lattice mismatch. The interface with the smaller mismatch between the specified crystal planes is proved to be harder and vice versa.To describe the relationship between film thickness and interface effect,we choose various values of film thickness ranging from 20 A to 50 A to perform the nanoindentation experiment.It is observed that the interface is significant only for the relatively small thickness of film and the separation between interface and the indenter tip.It is shown that with the increase in film thickness,the mechanical behaviour of the film shifts more toward that of monolithic material.     

Experimental investigations of the normal loading of elastic spherical and conical indenters on to elastic flats

Results obtained from a series of experimental investigations are described in which an elastic polyisoprene hemisphere and elastic rubber cones of included angles 60°, 90°, 120° and 150° were loaded normally on to smooth blocks of soda–lime glass and polydimethylsiloxane (PDMS) containing 10% and 20% by volume of the curing agent. The load versus displacement data were continuously recorded with an instrumented indentation machine. It is shown that, whereas the loading behaviour of the hemisphere on to the blocks of the soda–lime glass and PDMS closely follows the theory of Hertz (see equation (1)), the load versus displacement behaviour of the rubber cones of included angles 60°, 90° and 120° could not be fitted by the Sneddon equation (see equation (5)) for rigid conical indenters loading on to an elastic half-space or by the modified Sneddon equation (see equation (6)) employing the combined moduli of the indenter and the half-space. The discrepancy between the predictions of the modified Sneddon equation and the experimental measurements is very significant, thus confirming our recent concern about the validity of using the modified Sneddon equation for analysing the experimental data obtained from nanoindentation experiments. Estimates of the errors caused by the use of the modified Sneddon equation have been made to further illustrate our contention. On the other hand, the behaviour of the 150° included angle cone loading on to the blocks of rubber, PDMS (1?:?10) and PDMS (1?:?20), has been shown to be particularly striking, as the rubber cone behaved as if it were rigid; moreover, the experimental data are well fitted by the Sneddon equation corresponding to a 150° rigid cone loading on to an elastic half-space. Finally, it has been proposed that, in order to determine the elastic modulus of a very stiff solid (i.e. Young's modulus close to that of the indenter) correctly using the technique of instrumented indentation, including nanoindentation, the included angle of the indenter, made of diamond, should be 150° and the measured load versus displacement data should be analysed using the Sneddon equation corresponding to a rigid cone of an included angle of 150°.     

Orientation-dependent deformation mechanisms of bcc niobium nanoparticles

Nanoparticles usually exhibit pronounced anisotropic properties, and a close insight into the atomic-scale deformation mechanisms is of great interest. In present study, atomic simulations are conducted to analyse the compression of bcc nanoparticles, and orientation-dependent features are addressed. It is revealed that surface morphology under indenter predominantly governs the initial elastic response. The loading curve follows the flat punch contact model in [1 1 0] compression, while it obeys the Hertzian contact model in [1 1 1] and [0 0 1] compressions. In plastic deformation regime, full dislocation gliding is dominated in [1 1 0] compression, while deformation twinning is prominent in [1 1 1] compression, and these two mechanisms coexist in [0 0 1] compression. Such deformation mechanisms are distinct from those in bulk crystals under nanoindentation and nanopillars under compression, and the major differences are also illuminated. Our results provide an atomic perspective on the mechanical behaviours of bcc nanoparticles and are helpful for the design of nanoparticle-based components and systems.     

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.     

Young’s modulus and fracture during Knoop indentation of potassium, rubidium, cesium, and ammonium acid phthalate single crystals on the (010) plane

The correlation of the anisotropy of the Young??s modulus of organic single crystals of potassium, rubidium, cesium, and ammonium acid phthalates with strain and fracture patterns during Knoop indentation on the (010) cleavage plane in the [001] and [100] directions has been studied. The data on the maximum anisotropy of the strain and fracture patterns of the ammonium acid phthalate single crystal have been discussed in view of the published data on the structure, mechanical, elastic, and X-ray spectral properties of these crystals.     

Growth and characteristics of Mn-doped PMN–PT single crystals

Large sized 0.71PMN–0.29PT single crystals with different Mn-doping content (pure, 1 at.%, 3 at.%) have been grown by a modified Bridgman method. The piezoelectric and dielectric properties of the as-grown crystals are measured. The phase transitions of the poled 0.71PMN–0.29PT with the orientation along 〈001〉 and 〈110〉 directions take place during the heating process. The phase transition of the pure crystals is more complicated than that of the Mn-doped crystals. Both the pure 〈001〉- and 〈110〉-oriented crystals have two dielectric abnormal peaks besides the Curie peak. With Mn-doping, the temperature for the first dielectric abnormal peak shifts to a higher value. The Mn-doping content affects the piezoelectric and dielectric properties of the crystal greatly. 1 at.% Mn-doped crystals possesses a larger coercive field and mechanical quality factor at the expense of a little lower piezoelectric response. The growth and characteristics of pure and Mn-doped 0.71PMN–0.29PT single crystals are reported and discussed in this paper.     

Formation of a new dynamical mode in -uranium observed by inelastic x-ray and neutron scattering

Phonon dispersion curves were obtained from inelastic x-ray and neutron scattering measurements on alpha-uranium single crystals at temperatures from 298 to 573 K. Both measurements showed a softening and an abrupt loss of intensity in the longitudinal optic branch along [00zeta] above 450 K. Above the same temperature a new dynamical mode of comparable intensity emerges along the [01zeta] zone boundary with energy near the top of the phonon spectrum. The new mode forms without a structural transition but coincides with an anomaly in the mechanical deformation behavior. We argue that the mode is an intrinsically localized vibration and formed as a result of a strong electron-phonon interaction.     

Normal modes of vibrations in CuBr

Phonon dispersion curves of CuBr have been measured at room temperature in the [001], [110] and [111] directions using inelastic neutron scattering. The results are interpreted in terms of a rigid ion model. Estimations are given for elastic constants.