Dominant factors influencing the nanoindentation response of piezoelectric materials: a case study in relaxor ferroelectrics

The nanoindentation response of a piezoelectric material is, in general, influenced in a complex manner by its elastic, dielectric and piezoelectric properties. The present study is focused on obtaining a comprehensive understanding of the dominant material factors influencing the force–depth mechanical indentation response and the charge–depth electrical indentation response of piezoelectric materials. From a large number of three-dimensional finite element simulations of the indentation of simple and complex piezoelectric materials (such as PZT-5A and relaxor ferroelectrics), the following principal conclusions are obtained: (1) For indentations with both conducting and insulating indenters, the mechanical indentation stiffness is influenced more by the elastic properties, while the electrical indentation stiffness is influenced largely by the piezoelectric properties of the indented materials. (2) For longitudinal indentations using a conducting indenter, the elastic constants, C ₃₃ and C ₁₃, and piezoelectric constants, e₃₃ and e₁₅, are, respectively, the first and second most dominant material constants that influence the mechanical indentation stiffness and the electrical indentation stiffness. (3) For transverse indentations using a conducting indenter, the elastic constants, C ₁₁ and C ₁₂, are, respectively, the first and second most dominant material constants that influence the mechanical indentation stiffness. (4) In the indentation of relaxor ferroelectrics based on PMN-xPT and PZN-xPT, which exhibit a range of elastic, dielectric and piezoelectric properties, it is generally observed that materials with higher normal elastic and piezoelectric constants, i.e., C ₃₃ and e₃₃, respectively, exhibit higher mechanical and electrical indentation stiffnesses.     

First principles study of the temperature-dependent elastic properties of W

The temperature-dependent elastic constants of body-centred cubic (bcc) phase W are presented from first principles quasi-static approach. With the quasi-harmonic approximation model, the Hugoniot equation of state and temperature-dependence linear thermal expansion coefficient is successfully obtained. The adiabatic elastic constants show a normal behaviour with temperature: decrease with increasing temperature. Based on the obtained adiabatic elastic constants, the structural stability and polycrystalline aggregate properties including bulk modulus B, shear modulus G, and B/G ratio are analysed for bcc phase W. In addition, the sound velocities as a function of temperature for bcc phase W are predicted.     

Structural stability of W2B5 under high pressure

High-pressure structural stability studies have been carried out on tungsten boride W₂B₅ up to maximum pressure of 36 GPa using a Mao-Bell diamond-anvil cell at beamline BR-12 of the ELETTRA synchrotron facility (λ = 0.68881 Å). The hexagonal phase (S.G:P6₃/mmc) of W₂B₅ is stable up to the maximum pressure studied. The bulk modulus is estimated to be ~347 GPa using the Birch–Murnaghan equation of state. The variation of lattice parameters and bond lengths B–B and W–B have been studied and the c-axis is seen to be marginally more compressible than the a-axis.     

Pressure dependence of the electrical resistivity of natural cassiterite SnO2 and of undoped and Co-doped nanocrystalline SnO2

The pressure dependence of the electrical resistivity of three different samples of cassiterite, namely natural cassiterite SnO₂, synthetic nanocrystalline SnO₂ (with crystallite size 46?nm) and nanocrystalline Co-doped SnO₂ (with crystallite size 32?nm), has been measured up to 7?GPa at room temperature. The resistivity of natural cassiterite SnO₂ decreases from 2.5?×?10⁴?Ωm at normal pressure and temperature to 1.7?×?10⁴?Ωm at 7.0?GPa. The nanocrystalline SnO₂ has a high resistivity 6.0?×?10⁵?Ωm at normal pressure and temperature and decreases with pressure reaching a value of 2.98?×?10⁵?Ωm at 7?GPa. The activation energy of the electrical conduction of the studied samples were found to be 0.32?eV for the natural SnO₂, 0.40?eV for the nanocrystalline SnO₂ sample and 0.28?eV for the nanocrystalline Co-doped SnO₂. Measurements of the pressure dependence of the electrical resistivity of the Co-doped SnO₂ showed a decrease from 3.60?×?10⁵ to 5.4?×?10⁴?Ωm at 7.0?GPa. We did not observe any pressure-induced phase transition in SnO₂ up to 7?GPa. This study of the high-pressure phase stability of cassiterite corroborates the experimental findings of SnO₂ nanoinclusions in diamonds.     

Structural,elastic, electronic,phonon and thermal properties of Ir3Ta and Rh3Ta alloys

We have studied the structural, elastic, electronic, phonon and thermodynamic properties of Ir₃Ta and Rh₃Ta alloys, using ab initio calculations. For the L1₂ phase, we report the calculated lattice constants, bulk modulus and elastic constants, and these values are compared with previously published values. We also derive the elastic constants from the values of the slopes of the acoustic branches in the phonon dispersion curves. The band structures show that both materials are metallic. The phonon dispersion curves, and their corresponding total and projected densities of states, are obtained using a linear response in the framework of the density functional perturbation theory. The specific heat capacity at constant volume and different temperatures is calculated, and this aspect is discussed using the quasi-harmonic approximation.     

Ab-initio study of the structural,electronic, elastic and vibrational properties of HfX (X = Rh,Ru and Tc)

The structural, elastic, electronic and phonon properties of HfX (X = Rh, Ru and Tc) in the caesium-chloride phase have been investigated using the density functional theory within the generalized gradient approximation. The optimized lattice constant (a₀), bulk modulus (B) and the elastic constants (C_ij) are evaluated. The results are in a good agreement with the available experimental and theoretical data in the literature. Electronic band structures and densities of states have been derived for these compounds. The present band structure calculations indicate that the phases of caesium-chloride HfX (X = Rh, Ru and Tc) compounds are metals. Phonon dispersion curves and their corresponding total and projected density of states have been obtained using the direct method. The phonon spectra suggest that these compounds are dynamically stable in the caesium-chloride phase.     

Pressure-induced structural transition in UGa2

High-pressure X-ray diffraction has been performed on UGa₂ up to 20?GPa using a diamond anvil cell. UGa₂ exhibits the AlB₂-type structure with space group P6/mmm at room temperature and atmospheric pressure. At about 16?GPa a reversible structural transformation to a tetragonal phase was observed. The bulk modulus of the AlB₂-type phase has been determined to be ～100?GPa, which is comparable to rare earth digallides like TmGa₂ and HoGa₂.     

High-pressure phase transition and lattice dynamics of rock-salt and FeSi-type phases of MgS

A phase transition of MgS under high pressure is investigated using a first-principles method. It is found from energy-volume calculations that the rock-salt (B1) phase of MgS transforms into a FeSi-type (B28) phase at 143?GPa. The calculated ground-state parameters in the B1 phase are in excellent agreement with available experimental and theoretical data. Ab initio phonon calculations are also performed to investigate the structural behaviour of MgS under high pressure. An unstable transverse acoustic mode and a phase transition from B1 to B28 phase at ~143.7?GPa driven by this soft mode are predicted. The B28 structure of MgS is stable up to 350?GPa according to lattice dynamics calculations.     

Analytical derivation of the effective temperature for field-dependent hopping conductivity

The electric-field enhancement of hopping conductivity in amorphous solids can be described in terms of an effective temperature T _eff given by for hopping, at a temperature T and field F, within a uniform distribution of electronic states with localization length γ^?1. We have derived this expression analytically and find at low fields a value for C of 1/2^1/2, which is consistent with the F-independent value C = 0.67 previously obtained numerically for band-tail hopping. With increasing electric field, the decrease in C(F) matches the hopping transport characteristics in amorphous semiconductors (hydrogenated amorphous silicon and hydrogenated amorphous carbon nitride) better than previous numerical simulations.     

Elastic and phonon properties of quaternary Heusler alloys CoFeCrZ (Z = Al,Si, Ga and Ge) from density functional theory

The structural, elastic and phonon properties of the quaternary CoFeCrZ (Z = Al, Si, Ga and Ge) Heusler alloys have been investigated using the generalized gradient approximation method within density functional theory. The ground-state properties, including, lattice constant and bulk modulus are in good agreement with the available theoretical and experimental data. The elastic constants C_ij are computed using the stress–strain technique. The calculated results indicate that CoFeCrZ (Z = Al, Si, Ga and Ge) alloys are ductile materials. Debye temperatures are predicted from calculated elastic constants. The phonon dispersion relations of CoFeCrZ (Z = Al, Si, Ga and Ge) alloys are calculated for the first time using the density functional theory and the direct method with 2 × 2 × 2 supercell.     

Nanoindentation-induced elastic–plastic transition and size effect in α-Al2O3(0001)

The mechanical properties of α-Al₂O₃(0001) have been investigated using the technique of nanoindentation with a Berkovich indenter. Coupled with the Hertzian contact theory, a theoretical shear strength of 28?±?2?GPa was determined from the onset of pop-in events on load–displacement curves during loading, and the intrinsic hardness 30?±?3?GPa was obtained by analysis of the so-called indentation size effect, based on the concept of geometrically necessary dislocations. The predicted values of the shear strength, hardness and elastic modulus are in good agreement with available experimental data. The importance of experimentally calibrating the area function over the contact depth range prior to nanoindentation tests is emphasized.     

Thermal behaviour of poly(methyl methacrylate)/fullerene composite films

ABSTRACT

Poly(methyl methacrylate) films and poly(methyl methacrylate)/fullerene composite films were fabricated by casting from toluene solutions. The mass fraction of fullerene (C₆₀) was varied from 0.05–3?wt. %. The effect of the fullerene (C₆₀) content on the thermal degradation parameters of the composite films was evaluated by thermogravimetric (TG) analysis. It was found that the incorporation of C₆₀ improved the thermal stability of the polymers. The films eventually decomposed in three stages. Incorporation of fullerene caused a change in the distribution of mass loss over the stages of degradation in comparison with the pristine polymer. Using differential scanning calorimetry (DSC), the phase transitions from the glassy state to the elastic one was studied for the examined polymeric materials. New data relating to the effect of C₆₀ on the glass transition temperature of composites with low weight fractions of filler were obtained. Specifically, for films containing up to 0.1 wt. % of C₆₀, a single glass transition temperature was found, whereas for composites with a higher concentration of filler, two glass transition temperatures were recorded.     

Ab initio study of Heusler alloys Co2XY (X = Cr,Mn, Fe; Y = Al,Ga) under high pressure

The structural, electronic, and magnetic properties of ferromagnetic Heusler alloys Co₂XY (X?=?Cr, Mn, Fe; Y?=?Al, Ga) have been investigated by means of the all-electron full-potential linearized augmented plane wave method within the generalized gradient approximation for the exchange and correlation potential. The main focus of this study is to elaborate the changes brought about in the electronic and the magnetic properties by applied pressure. The calculated total spin magnetic moments of all the compounds are found to be in good agreement with experiments. Out of these compounds, Co₂CrAl is found to be perfectly half-metallic (HM) and the other compounds are found to be nearly HM. Thus the HM to metal transition was observed at 75?GPa pressure for Co₂CrAl and the nearly half-metal to half-metal transition was observed at 40?GPa and 18?GPa for Co₂CrGa and Co₂MnAl, respectively, while no transition is observed in other compounds under investigation. It can be clearly seen that pressure affects the minority spin states rather than the majority states, leading to a slight reconstruction of the minority spin states with a shift in the Fermi level driving the above-mentioned transition.     

Mechanical recrystallization of ultra-strength tungsten nanoneedles

We present field-ion microscopy observation and crystallographic analysis which shows that plastic deformation mode in the tungsten nanotip in the field of high mechanical stresses occur by combining formations of strain localization bands and crystal lattice reorientations. Nanomechanical tensile tests in situ at about 15?GPa have revealed the large-angle reorientations of grains corresponding to the coincident site lattice with Σ?=?33, which can be regarded as a result of reactions between lattice dislocations.     

Thermal behaviour of polystyrene/silica composites

The particle-size distribution in silica powder prepared by the sol–gel method has been determined by dynamic light scattering analysis. The average diameter of the particles was found to be 250?nm. Using a low-temperature nitrogen adsorption–desorption technique, it was found that the synthesised powder may be referred to as mesoporous materials. Polystyrene/silica composite films were fabricated by casting from o-xylene solutions. It was found, using thermogravimetry, that incorporation of silica leads to an increase in both the onset temperature of polymer degradation and in the temperature at which the maximum rate of weight loss occurs. Using differential scanning calorimetry, the phase transitions from the glassy state to the elastic one were studied for the polymeric materials. New data relating to the effect of silica on the glass-transition temperature, T_g, of composites with a low weight fraction of SiO₂ were found. Specifically, we found a non-monotonic concentration dependence of the value of T_g. The present results advocate for employing silica as an effective filler for producing polymer composites with enhanced thermal properties.     

Approximant phases,phason planes and domain-boundary networks in Al−Ni−Rh alloys

Structurally complicated ξ′- and ξ-phases have been found, for the first time, in as-cast Al₇₃Ni₅Rh₂₂ and Al₇₅Ni₁₅Rh₁₀ alloys. The lattice parameters of these two phases were determined by means of electron diffraction and high-resolution transmission electron microscopy (HREM). These two phases have similar orthorhombic structures but with different lattice parameters of a?=?23.2?Å, b?=?16.4?Å, c?=?12.0?Å for the ξ′-phase and a?=?20.3?Å, b?=?16.4?Å, c?=?14.8?Å for the ξ-phase. A new two-dimensional domain-boundary network has also been observed in these two phases. Domain boundaries with normals closely parallel to the [001] direction are actually phason planes represented by a translation vector of r?=(1/2)a?+(1/2τ)c in the ξ′-phase and r=±(1/2τ²) a?+(τ/2)c in the ξ-phase, whereas the newly-found wide and zigzag boundaries perpendicular to the above set were attributed from the step-like boundary structures of domains related by a translation vector of r?=(1/τ)((1/2)a?+(1/2τ)c). The structural difference between the two types of planar faults is discussed.     

Dislocation configurations in twin-free melt-textured YBa2Cu3O7 processed at high pressure and temperature

Melt-textured YBa₂Cu₃O₇ samples were deformed under high pressure–high temperature (HP–HT) conditions (P?=?2?GPa, T?=?900 and 800°C, t?=?15?min). During the HP–HT treatment, samples were in contact with annealed zirconia, preventing oxygen loss, in such a way that the orthorhombic superconductor phase was preserved at the end of the experiment. The deformed microstructure, investigated by transmitted electron microscopy, exhibited original features characterized by a very low twin density, a memory effect on the dislocations shape and a non-classical faulted loops distribution in the matrix. A mechanism, based on the interaction between twin and gliding dislocations, is proposed to explain the nucleation of these aligned loops.     

Effect of heterogeneous solute distribution on the anomalous thermomechanical response of Cu–Ni alloy single crystals below 50 K

The anomalous temperature dependence of the critical resolved shear stress (CRSS) of Cu–Ni alloys observed below a certain temperature, T _o?=?50?K, has been accounted for by introducing a stress-concentration factor f(T)?=?[(T?′?+?T _o)/(T?′?+?T)] in the monotonic CRSS–T formulation of the kink-pair nucleation model of solid-solution hardening. The empirical constant T?′ is found to depend not only on the solute concentration, c, but also on the nature of the solute distribution in the host lattice. It is found that the solute distribution is random for c?≤?14 at.% Ni in the Cu lattice and for c?≤?20 at.% Cu in the Ni lattice, whereas some sort of local ordering occurs for all other values of solute concentration.     

A study of the spin-Hamiltonian parameters for Cr5+ at the rhombically-distorted tetrahedral P5+ site of Ca2PO4Cl crystal using a two-mechanism model

The complete high-order perturbation formulae of spin-Hamiltonian (SH) parameters (g factors g_i and hyperfine structure constants A_i , where i = x, y, z) containing contributions from both the crystal-field (CF) and charge-transfer (CT) mechanisms (the latter mechanism is neglected in the widely-used CF theory) are established for d¹ ions in rhombic tetrahedra. From these formulae, the SH parameters of Cr⁵⁺ ion at the rhombically-distorted tetrahedral P⁵⁺ site of Ca₂PO₄Cl crystal are calculated. The CF and CT energy levels used in the calculation are obtained from the optical spectra of the studied Ca₂PO₄Cl : Cr⁵⁺ crystal. The calculated results showed reasonable agreement with the experimental values. The signs of the hyperfine structure constants A_i and the relative importance of the CT mechanism to SH parameters are acquired from the calculations.     

Unusual room-temperature compressive plasticity in nanocrystal-toughened bulk copper-zirconium glass

Cast Cu₅₀Zr₅₀ alloy rods with a diameter of 1?mm have been found to consist of a glassy phase containing fine crystalline particles with a size of about 5?nm. They have a glass transition temperature T _g of 675?K, and a large supercooled-liquid region extending 57?K above T _g. The rods exhibit a high yield strength of 1860?MPa and a Young's modulus of 104?GPa. Because they contain a dispersion of embedded nanocrystals, the as-cast bulk metallic glass rods can sustain a compressive plastic strain at room temperature of more than 50%, an exceptional value which is explicable by compensation of any shear softening by nanocrystal coalescence and pinning of shear bands.