Evaluation of elastic modulus and hardness of thin films by nanoindentation

Simple equations are proposed for determining elastic modulus and hardness properties of thin films on substrates from nanoindentation experiments. An empirical formulation relates the modulus E and hardness H of the film/substrate bilayer to corresponding material properties of the constituent materials via a power-law relation. Geometrical dependence of E and H is wholly contained in the power-law exponents, expressed here as sigmoidal functions of indenter penetration relative to film thickness. The formulation may be inverted to enable deconvolution of film properties from data on the film/substrate bilayers. Berkovich nanoindentation data for dense oxide and nitride films on silicon substrates are used to validate the equations and to demonstrate the film property deconvolution. Additional data for less dense nitride films are used to illustrate the extent to which film properties may depend on the method of fabrication.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics

Capillary break-up rheometry of low-viscosity elastic fluids

We investigate the dynamics of the capillary thinning and break-up process for low viscosity elastic fluids such as dilute polymer solutions. Standard measurements of the evolution of the midpoint diameter of the necking fluid filament are augmented by high speed digital video images of the break up dynamics. We show that the successful operation of a capillary thinning device is governed by three important time scales (which characterize the relative importance of inertial, viscous and elastic processes), and also by two important length scales (which specify the initial sample size and the total stretch imposed on the sample). By optimizing the ranges of these geometric parameters, we are able to measure characteristic time scales for tensile stress growth as small as 1 millisecond for a number of model dilute and semi-dilute solutions of polyethylene oxide (PEO) in water and glycerol. If the final aspect ratio of the sample is too small, or the total axial stretch is too great, measurements are limited, respectively, by inertial oscillations of the liquid bridge or by the development of the well-known beads-on-a-string morphology which disrupt the formation of a uniform necking filament. By considering the magnitudes of the natural time scales associated with viscous flow, elastic stress growth and inertial oscillations it is possible to construct an operability diagram characterizing successful operation of a capillary break-up extensional rheometer. For Newtonian fluids, viscosities greater than approximately 70 mPas are required; however for dilute solutions of high molecular weight polymer, the minimum Viscosity is substantially lower due to the additional elastic stresses arising from molecular extension. For PEO of molecular weight 2.10(6) g/mol, it is possible to measure relaxation times of order 1 ms in dilute polymer solutions with zero-shear-rate viscosities on the order of 2-10 mPas.

Vascular remodelling in the internal mammary artery graft and association with elevated endothelin-1 expression

Introduction: The vasoconstricting peptide Endothelin-1 (ET-1) has been associated with atherosclerotic cardiovascular disease, AAA, hypertension and hypercholesterolemia. It is known to stimulate quiescent vascular smooth muscle cells (VSMC) into the growth cycle and has been linked to intimal thickening following endothelial injury and is associated with vessel wall remodelling in salt-sensitive hypertension models. Enhanced ET-1 expression has been reported in the internal mammary artery (IMA) and was markedly higher in patients undergoing cardiac bypass surgery who were diabetic and /or hypercholesterolemic. Aims: To firstly review the histopathology of the IMA and secondly, determine the relationship between ET-1 expression in this vessel and mitogenic activity in the medial VSMC. Methods: Vessel tissue collected at the time of CABG surgery was formalin-fixed and paraffin-embedded for histological investigation. Cross sections of the left distal IMAwere stained with Alcian Blue/Verhoeff’s van Gieson to assess medial degeneration and identify the elastic lamellae and picrosirius red to determine the collagen content (specifically type I and type III). Immunohistochemistry staining was used to assess VSMC growth (PCNA label), tissue ET-1 expression, VSMC (SMCa-actin) area and macrophage/monocyte (anti-CD68) infiltration. Quantitative analysis was performed to measure the VSMC area in relation to ET-1 staining. Results: Fifty-five IMA specimens from the CABG patients (10F; 45M; mean age 65 years) were collected for this study. Fourteen donor IMAspecimens were used as controls (7F; 7M; mean age 45 years). Significant medial hypertrophy, VSMC disorganisation and elastic lamellae destruction was detected in the CABG IMA. The amount of Alcian blue staining in the CABG IMA was almost double that of the control (31.85+/14.52% Vs 17.10+/9.96%, P= .0006). Total collagen and type I collagen content was significantly increased compared with controls (65.8+/18.3% Vs 33.7 + / 13.7%, P= .07), (14.2 + /10.0% Vs 4.8 + /2.8%, P= .01), respectively. Tissue ET-1 and PCNA labelling were also significantly elevated the CABG IMA specimens relative to the controls (69.99 + /18.74%Vs 23.33 + /20.53%, P= .0001, and 37.29 + /12.88% Vs 11.06 + /8.18, P= .0001), respectively. There was mild presence of macrophages and monocytes in both CABG and control tissue. Conclusions: The IMA from CABG patients has elevated levels of type I collagen in the extracellular matrix indicative of fibrosis and was coupled with deleterious structural remodelling. Abnormally high levels of ET-1 were measured in the medial SMC layer and was associated with VSMC growth but not related to any chronic inflammatory response within the vessel wall.

Differential Priors for Elastic Nets

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.

Determination of mechanical properties of PECVD silicon nitride thin films for tunable MEMS Fabry-Pérot optical filters

This paper reports an investigation on techniques for determining elastic modulus and intrinsic stress gradient in plasma-enhanced chemical vapor deposition (PECVD) silicon nitride thin films. The elastic property of the silicon nitride thin films was determined using the nanoindentation method on silicon nitride/silicon bilayer systems. A simple empirical formula was developed to deconvolute the film elastic modulus. The intrinsic stress gradient in the films was determined by using micrometric cantilever beams, cross-membrane structures and mechanical simulation. The deflections of the silicon nitride thin film cantilever beams and cross-membranes caused by in-thickness stress gradients were measured using optical interference microscopy. Finite-element beam models were built to compute the deflection induced by the stress gradient. Matching the deflection computed under a given gradient with that measured experimentally on fabricated samples allows the stress gradient of the PECVD silicon nitride thin films introduced from the fabrication process to be evaluated.

Characterization of mechanical properties of silicon nitride thin films for MEMS devices by nanoindentation

An experimental investigation of mechanical properties of thin films using nanoindentation was reported. Silicon nitride thin films with different thicknesses were deposited using plasma enhanced chemical vapor deposition (PECVD) on Si substrate. Nanoindentation was used to measure their elastic modulus and hardness. The results indicated that for a film/substrate bilayer system, the measured mechanical properties are significantly affected by the substrate properties. Empirical formulas were proposed for deconvoluting the film properties from the measured bilayer properties.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Neural compensation for compliant loads during rhythmic movement

An experiment was performed to characterise the movement kinematics and the electromyogram (EMG) during rhythmic voluntary flexion and extension of the wrist against different compliant (elastic-viscous-inertial) loads. Three levels of each type of load, and an unloaded condition, were employed. The movements were paced at a frequency of I Hz by an auditory metronome, and visual feedback of wrist displacement in relation to a target amplitude of 100degrees was provided. Electro-myographic recordings were obtained from flexor carpi radialis (FCR) and extensor carpi radialis brevis (ECR). The movement profiles generated in the ten experimental conditions were indistinguishable, indicating that the CNS was able to compensate completely for the imposed changes in the task dynamics. When the level of viscous load was elevated, this compensation took the form of an increase in the rate of initial rise of the flexor and the extensor EMG burst. In response to increases in inertial load, the flexor and extensor EMG bursts commenced and terminated earlier in the movement cycle, and tended to be of greater duration. When the movements were performed in opposition to an elastic load, both the onset and offset of EMG activity occurred later than in the unloaded condition. There was also a net reduction in extensor burst duration with increases in elastic load, and an increase in the rate of initial rise of the extensor burst. Less pronounced alterations in the rate of initial rise of the flexor EMG burst were also observed. In all instances, increases in the magnitude of the external load led to elevations in the overall level of muscle activation. These data reveal that the elements of the central command that are modified in response to the imposition of a compliant load are contingent, not only upon the magnitude, but also upon the character of the load.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Effect of deposition conditions on mechanical properties of low-temperature PECVD silicon nitride films

The effect of deposition conditions on characteristic mechanical properties - elastic modulus and hardness - of low-temperature PECVD silicon nitrides is investigated using nanoindentation. lt is found that increase in substrate temperature, increase in plasma power and decrease in chamber gas pressure all result in increases in elastic modulus and hardness. Strong correlations between the mechanical properties and film density are demonstrated. The silicon nitride density in turn is shown to be related to the chemical composition of the films, particularly the silicon/nitrogen ratio. (c) 2006 Elsevier B.V. All rights reserved.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.

A numerical study of effect of grain boundaries on elastic and plastic properties in nanocomposite materials

Nanocomposite materials have received considerable attention in recent years due to their novel properties. Grain boundaries are considered to play an important role in nanostructured materials. This work focuses on the finite element analysis of the effect of grain boundaries on the overall mechanical properties of aluminium/alumina composites. A grain boundary is incorporated into the commonly used unit cell model to investigate its effect on material properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the ''effective'' plastic property of the grain boundary is estimated. In addition, the strengthening mechanism is also discussed based on the Estrin-Mecking model.