Spherical Cavity Model Research Articles

Structural and mechanical properties of Hf55Cu28Ni5Al12bulk metallic glass alloy prepared at different cooling rates

• In this report, the effect of cooling rate in Hf 55 Cu 28 Ni 5 Al 12 alloy prepared by melt spinning and suction casting methods has been studied. • Decreasing cooling rate results in formation of Hf 2 Cu quenched-in nuclei in amorphous matrix in 3 mm cast rod. • Formation of Hf 2 Cu and Al 16 Hf 6 Ni 7 in amorphous matrix is observed by varying the cooling rate in 5 mm cast rod. • Presence of quenched in nuclei in 3 mm cast rod was confirmed through by kinetic calculations using a model considering pre-existing nuclei. • Hardness of 3 mm cast rod was estimated using modified spherical cavity model which was found to be close to experimentally observed value. • Fracture toughness of 3 and 5 mm cast rods was estimated based on vein length and crack length created during indentation. • 5 mm rod showed lower fracture toughness than 3 mm cast rod due to the presence of the secondary phases.

Confinement effects on the electron transfer cross section: a study of He2+ colliding on atomic H

In this work, the role of pressure produced by the surrounding conditions of neighboring atoms on the charge transfer cross section in the interaction of ions with atoms is studied. The effect of pressure on the target is simulated by a spherical confinement cavity model with the target atom at its center. The electron transfer probability is obtained by a time-dependent solution to the Schrödinger equation by means of a finite-difference approach and the Crank–Nicolson propagation method. Results are presented for the benchmark system HeH() under different confinement conditions. Within this first-order approach to pressure effects, it is found that the radial region of the electron capture probability is affected by the cavity, meanwhile the rotational part of the interaction is only slightly modified. Furthermore, Stückelberg oscillations are preserved as a function of the impact parameter and only its intensity is reduced with a slight shift towards low impact parameters as pressure is increased. The pressure effect is larger when the electron interaction on the target is restricted to within the cavity than when it acts also outside the cavity. In addition, the larger the pressure, the smaller the electron capture cross section. The numerical results are interpreted by an analytic two-state model that supports the numerical findings.

A spherical cavity model for quadrupolar dielectrics

The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ε and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field, and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have a small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsager's theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures.

Effect of viscoplastic material parameters on polymer indentation

The effect of material parameters characterizing viscoplastic flow on the indentation response of polymers is investigated using three-dimensional finite element analyses and a one-dimensional expanding spherical cavity model. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and two indenter shapes are considered; a conical indenter and a pyramidal indenter. The ability of the simpler expanding spherical cavity model to reproduce the trends obtained from the finite element solutions is assessed for both indenter shapes. Within the range of parameter variations considered, it is found that two material stress parameters characterizing the plastic flow resistance have the largest effect on the value of the indentation hardness although variations in other material parameters can lead to significant variations.

Polymer indentation: Numerical analysis and comparison with a spherical cavity model

Three dimensional analyses of indentation of a polymer by a rigid indenter are carried out. The polymer is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out with a dynamic finite element program used to simulate quasi-static behavior. Two types of indenter are considered; a conical indenter and a pyramidal indenter. For each indenter type, different values of the sharpness of the indenter are considered and two rates of indentation are analyzed. Significant sink-in is found to occur in all cases considered. The amount of sink-in is found to be smaller for sharper indenters. The calculated values of both the nominal and true hardness do not differ significantly for the two indenter shapes. An expanding spherical cavity model is also considered and the predictions of this model are compared with the finite element results for various indenter shapes and indentation rates. The spherical cavity model is found to give fairly good agreement with the predictions of the finite element analyses for the nominal polymer hardness for both indenter shapes.

A Treatment Planning System for Pleural PDT.

Uniform light fluence distribution for patients undergoing photodynamic therapy (PDT) is critical to ensure predictable PDT outcome. However, common practice uses a point source to deliver light to the pleural cavity. To improve the uniformity of light fluence rate distribution, we have developed a treatment planning system using an infrared camera to track the movement of the point source. This study examines the light fluence (rate) delivered to chest phantom to simulate a patient undergoing pleural PDT. Fluence rate (mW/cm2) and cumulative fluence (J/cm2) was monitored at 7 different sites during the entire light treatment delivery. Isotropic detectors were used for in-vivo light dosimetry. Light fluence rate in the pleural cavity is also calculated using the diffusion approximation with a finite-element model. We have established a correlation between the light fluence rate distribution and the light fluence rate measured on the selected points based on a spherical cavity model. Integrating sphere theory is used to aid the calculation of light fluence rate on the surface of the sphere as well as inside tissue assuming uniform optical properties. The resulting treatment planning tool can be valuable as a clinical guideline for future pleural PDT treatment.

On the comparison of the ballistic performance of 10% zirconia toughened alumina and 95% alumina ceramic target

Ballistic performance of different type of ceramic materials subjected to high velocity impact was investigated in many theoretical, experimental and numerical studies. In this study, a comparison of ballistic performance of 95% alumina ceramic and 10% zirconia toughened alumina (ZTA) ceramic tiles was analyzed theoretically and experimentally. Spherical cavity model based on the concepts of mechanics of compressible porous media of Galanov was used to analyze the relation of target resistance and static mechanical properties. Experimental studies were carried out on the ballistic performance of above two types of ceramic tiles based on the depth of penetration (DOP) method, when subjected to normal impact of tungsten long rod projectiles. Typical damaged targets were presented. The residual depth of penetration on after-effect target was measured in all experiments, and the ballistic efficiency factor of above two types ceramic plates were determined. Both theoretical and experimental results show that the improvement on ballistic resistance was clearly observed by increasing fracture toughness in ZTA ceramics.

The acceleration of solid particles subjected to cavitation nucleation

The cavity–particle dynamics at cavitation inception on the surface of spherical particles suspended in water and exposed to a strong tensile stress wave is experimentally studied with high-speed photography. Particles, which serve as nucleation sites for cavitation bubbles, are set into a fast translatory motion during the explosive growth of the cavity. They reach velocities of ~40 ms−1and even higher. When the volume growth of the cavity slows down, the particle detaches from the cavity through a process of neck-breaking, and the particle is shot away. The experimental observations are simulated with (i) a spherical cavity model and (ii) with an axisymmetric boundary element method (BEM). The input for both models is a pressure pulse, which is obtained from the observed radial cavity dynamics during an individual experiment. The model then allows us to calculate the resulting particle trajectory. The cavity shapes obtained from the BEM calculations compare well with the photographs until neck formation occurs. In several cases we observed inception at two or more locations on a single particle. Moreover, after collapse of the primary cavity, a second inception was often observed. Finally, an example is presented to demonstrate the potential application of the cavity–particle system as a particle cannon, e.g. in the context of drug delivery into tissue.

Measuring residual stress in glasses and ceramics using instrumented indentation

Instrumented indentation has yielded mixed results when used to measure surface residual stresses in metal films. Relative to metals, many glasses and ceramics have a low modulus-to-yield strength (E/σy) ratio. The advantage of this characteristic for measuring residual stress using instrumented indentation is demonstrated by a series of comparative spherical and conical tip finite element simulations. Two cases are considered: (i) a material with E/σy = 24—similar to glass and (ii) a material with E/σy = 120—similar to metal films. In both cases, compressive residual stress shifts the simulated load–displacement response toward increasing hardness, irrespective of tip geometry. This shift is shown to be entirely due to pile up for the “metal” case, but primarily due to the direct influence of the residual stress for the “glass” case. Hardness changes and load–displacement curve shifts are explained by using the spherical cavity model. Supporting experimental results on stressed glasses are provided.

The hardness of silicon and germanium

It is generally accepted that the hardness of silicon and germanium at low temperature is limited by a phase transformation under the indenter, as the measured hardness is equal to the transformation pressure. However, observations of the deformation under indents using transmission electron microscopy indicate that, in addition to the phase transformation, there is also plastic flow both in the transformed region and outside it. An analysis based on the spherical cavity model for indentation was developed to quantify the effect of a phase transformation on the measured hardness. This predicts that plastic deformation will extend beyond the transformed zone when the transformation pressure is greater than two-thirds of the yield stress. The analysis also predicts that the hardness can only be approximately equal to the transformation pressure if the yield strength of the transformed material is low, consistent with the experimental observations of substantial plastic deformation of the transformed phase, as well as with estimates of its lattice resistance.

Applicability of the SQM Force Field Method to the Vibrational Spectra of Sodium Acetate

The applicability of the scaled quantum mechanical force field (SQM FF) method to the prediction of the vibrational spectra of a charged molecule has been studied by the example of the acetate ion (CH3CO2-) in sodium acetate for which an efficient empirical valence force field (SVFF) based on observed IR spectra of six isotopomers of sodium acetate is available in the literature. Standard SQM FF calculations done on a free acetate ion at the B3LYP/6-31G level failed to give an acceptable estimation of even the most characteristic features of the observed spectra, which can be exemplified by the gross overestimation of the frequency separation of the nu(a)CO2- and nu(s)CO2- vibrations. In search for a better description, SQM calculations were done for three simple structural models of sodium acetate, testing different QM methods. The results indicate that in addition to taking into account the dielectric field effect of the surrounding medium, incorporation of a Na+ counterion is necessary to achieve a realistic simulation of the IR and Raman spectra. Satisfactory results were obtained with a bidentate Na-acetate complex by the SQM method coupled with a continuum model at the B3LYP/6-31+G level, whereas the use of the Onsager-type spherical cavity model and the polarizable continuum model (PCM) were found preferable over SCI-PCM.

Indentation stress dependence of the temperature range of microscopic superelastic behavior of nickel-titanium thin films

The microscopic superelastic behavior of thin-film NiTi is investigated by instrumented indentation experiments conducted at different temperatures. The indentation-induced superelastic effect is found to be persistent to about 100K above the austenite transformation finish temperature (Af). In contrast, the upper temperature where superelastic effect exists is only around Af plus 40K in uniaxial tension and compression tests, beyond which the plasticity of the austenite phase overwhelms the transformation-induced superelasticity. By combining the Clausius-Clapeyron equation and spherical cavity model for indentation, we show that the high hydrostatic pressure under the indenter is capable of elevating the transformation temperatures and increase the upper temperature limit of indentation-induced superelastic behavior.

Photostimulated electron detrapping and the two-state model for electron transport in nonpolar liquids

In common nonpolar liquids, such as saturated hydrocarbons, there is a dynamic equilibrium between trapped (localized) and quasifree (extended) states of the excess electron (the two-state model). Using time-resolved dc conductivity, the effect of 1064 nm laser photoexcitation of trapped electrons on the charge transport has been observed in liquid n-hexane and methylcyclohexane. The light promotes the electron from the trap into the conduction band of the liquid. From the analysis of the two-pulse, two-color photoconductivity data, the residence time of the electrons in traps has been estimated as ca. 8.3 ps for n-hexane and ca. 13 ps for methylcyclohexane (at 295 K). The rate of detrapping decreases at lower temperature with an activation energy of ca. 200 meV (280-320 K); the lifetime-mobility product for quasifree electrons scales linearly with the temperature. We suggest that the properties of trapped electrons in hydrocarbon liquids can be well accounted for using the simple spherical cavity model. The estimated localization time of the quasifree electron is 20-50 fs; both time estimates are in agreement with the "quasiballistic" model. This localization time is significantly lower than the value of 310+/-100 fs obtained using time-domain terahertz (THz) spectroscopy for the same system [E. Knoesel, M. Bonn, J. Shan, F. Wang, and T. F. Heinz, J. Chem. Phys. 121, 394 (2004)]. We suggest that the THz signal originates from the oscillations of electron bubbles rather than the free-electron plasma; vibrations of these bubbles may be responsible for the deviations from the Drude behavior observed below 0.4 THz. Various implications of these results are discussed.

Electronic excitations of the green fluorescent protein chromophore in its protonation states: SAC/SAC-CI study.

Two ground-state protonation forms causing different absorption peaks of the green fluorescent protein chromophore were investigated by the quantum mechanical SAC/SAC-CI method with regard to the excitation energy, fluorescence energy, and ground-state stability. The environmental effect was taken into account by a continuum spherical cavity model. The first excited state, HOMO-LUMO excitation, has the largest transition moment and thus is thought to be the source of the absorption. The neutral and anionic forms were assigned to the protonation states for the experimental A- and B-forms, respectively. The present results support the previous experimental observations.

Vibrational Spectra of Lumazine in Water at pH 2−13: Ab Initio Calculation and FTIR/Raman Spectra

Harmonic vibrational frequencies and transition intensities of lumazine (2,4-(1H,3H)pteridinedione in the neutral state) have been calculated in a self-consistent reaction field of high dielectric medium (ε = 78.54) using ab initio Hartree−Fock (HF) and hybrid HF/density functional theory (DFT) methods. For the DFT method, the 4-31G basis set and the three parameter exchange functional of Becke combined with the Lee, Yang, and Parr correlational functional are used. The 6-31+G* basis set is used in the HF calculations. Both the spherical cavity model (SCM) and the self-consistent isodensity polarizable continuum model (SCIPCM) are used to simulate an aqueous environment for the N-protonated lumazines. For the N-deuterated lumazines, only the SCM is used. Simple scaling of the vibrational frequencies resulting from the DFT calculations incorporating the reaction field models of neutral lumazine, lumazine A1/N3-H monoanion, and lumazine A1,A3-dianion compare closely with Raman and Fourier transform infrared spectra of lumazine taken in aqueous media (both H2O and D2O) over a wide pH/pD range. The mean deviation between calculated and experimental vibrational frequencies is 9.10 cm-1 for neutral lumazine (9.37 cm-1 in D2O), 9.18 cm-1 for the monoanion (10.77 cm-1 in D2O), and 16.06 cm-1 for the dianion (16.00 cm-1 when prepared in D2O). Calculated vibrational energy shifts with changes in ionization exhibit many trends that are evident in the experimental data although the absolute magnitudes of many of the individual shifts do not agree exactly. The calculated H/D isotopic shifts for the neutral and monoanionic species of lumazine agree well with those seen experimentally. Correlating shifts with ionization and the H/D isotopic shifts of the vibrational modes of each species of lumazine investigated have resulted in normal mode assignments of all in-plane vibrational modes observed in the 300−1750 cm-1 range in aqueous solution.

Direct Measurement of the Nanoscale Mechanical Properties of NiTi Shape Memory Alloy

ABSTRACTThe mechanical properties of sputter-deposited NiTi shape memory alloy thin films ranging in thickness from 35 nm to 10 μm were examined using nanoindentation and atomic force microscopy (AFM). Indents made in films as thin as 150 nm showed partial shape recovery upon heating, although film thickness was found to have a marked effect on the results. A modified spherical cavity model is used to describe the findings, which suggest that the substrate tends block the shape memory effect as film thickness decreases below a threshold level which is specific to applied load. This has the net effect of decreasing the indent recovery below the critical film thickness. The fact that the spherical cavity model predicts the critical film thickness at which the shape memory effect is blocked indicates that the increased recovery of nanoscale indentations is due to a suppression of plastic processes rather than an enhancement of shape memory processes.

Mechanisms controlling the hardness of Si and Ge

ABSTRACTIt is generally accepted that the hardness of silicon and germanium is limited by a phase transformation. Observations of the deformation under indents using transmission electron microscopy indicate that, in addition to the phase transformation, there is also plastic flow both in the transformed and in the untransformed material. These observations are consistent with those made elsewhere and with predictions based on the spherical cavity model for indentation, modified to quantify the effect of a phase transformation on the measured hardness. The analysis predicts that the hardness can only be approximately equal to the transformation pressure provided the yield strength of the transformed material is low, and that there is a region where plastic deformation in the untransformed material can occur in addition to the phase transformation. These predictions are consistent with the experimental observations of substantial plastic deformation of the transformed phase, as well as with estimates of its Peierls stress.

A CIS study of solvent effects on the electronic absorption spectrum of Reichardt's dye

A configuration interaction singles wavefunction, in conjunction with a self-consistent reaction field and a simple Onsager spherical cavity model, has been used to calculate the solvent induced shifts in Reichardt's dye (RD). The results from this simple method are in good agreement with experiment for aprotic solvents, but large discrepancies exist for protic solvents. This discrepancy can be partially compensated for by including one explicit solvent molecule H-bonded to RD. Geometry optimization of the S1 state in RD predicts a pyramidal sp3 hybridized N atom and an overall structure that differs significantly from that in the S0 state. Analysis of the calculated dipole moments and selected molecular orbitals are in accord with previous analyses of the S0→S1 charge transfer transition in RD. However, the nature of the S0→S2 transition appears to change with solvent dielectric strength (ϵ). At low ϵ this transition seems to have significant charge transfer character that decreases as ϵ increases.

Study of Elastic Modulus and Yield Strength of Polymer Thin Films Using Atomic Force Microscopy

Nanometer-scale elastic moduli and yield strengths of polycarbonate (PC) and polystyrene (PS) thin films were measured with atomic force microscopy (AFM) indentation measurements. By analysis of the AFM indentation force curves with the method by Oliver and Pharr, Young's moduli of PC and PS thin films could be obtained as 2.2 ± 0.1 and 2.6 ± 0.1 GPa, respectively, which agree well with the literature values. By fitting Johnson's conical spherical cavity model to the measured plastic zone sizes, we obtained yield strengths of 141.2 MPa for PC thin films and 178.7 MPa for PS thin films, which are ∼2 times the values expected from the literature. We propose that it is due to the AFM indentation being asymmetric, which was not accounted for in Johnson's model. A correction factor, ε, of ∼0.72 was introduced to rescale the plastic zone size, whereupon good agreement between theory and experiment was achieved.

Deep penetration micro-indentation testing of high density polyethylene

The deep penetration micro-indentation test of high density polyethylene has been analyzed in terms of the opening of a cavity in front of the indenter. The expansion of a cylindrical cavity opening under an internal pressure, as previously considered by Wright et al., has been compared to the opening of a spherical cavity. These model predictions have been tested experimentally using a small diameter (36 μm), flat cylindrical indenter. The micro-indenter was driven by a piezo-electric transducer under displacement control. The test data could be fitted more closely to a spherical cavity model, taking into account varying crystallinity in the sample and varying strain rate in the test. The plastic properties of the sample could thus be measured accurately from point to point, with a spatial resolution dependent on the indenter diameter. Microstructural examination of the spherulitic distortions under a large diameter (1 mm) tip showed a conical zone of little plastic deformation moving ahead of the tip.