Local Elastic Properties Research Articles

Local and Effective Elastic Properties of Grain Boundaries in Silicon

When considering the mechanical behaviour of materials an important property is the tensor of elastic moduli. Recently, local elastic moduli of interfaces have been defined and studied for metallic materials [1 to 3]. In these works grain boundaries are regarded as heterogeneous continua composed of ‘phases’ associated with individual atoms which possess elastic moduli identified with the atomic-level moduli evaluated at corresponding atomic positions. From this representation it is possible to define the ‘effective’ moduli of the grain boundary region. In this paper this concept is developed for materials with covalent character of bonding, specifically silicon. Using the Tersoff's potential [4, 5], the atomic-level and effective elastic moduli of the interfacial region have been evaluated for three alternate structures of the Σ = 3 (112-)/[11-0] tilt boundary. These calculations are then compared with the continuum bounds on the effective moduli evaluated using the classical minimum-energy principles of elasticity. The effective moduli calculated in the atomistic framework are generally within the continuum bounds and thus the present study demonstrates that the heterogeneous continuum model of the interfaces is appropriate for the description of the elastic properties of grain boundaries in silicon. An important aspect addressed in this study is the uniqueness of interfacial elastic moduli since their evaluation involves the energy associated with an atom which cannot be defined uniquely. The calculations have been made for two different partitions of the total energy into energies associated with individual atoms. These two partitions lead to almost identical results for the effective moduli and continuum bounds when the tensor of the atomic-level moduli is positive definite. When some atomic-level moduli are not positive definite the results may depend on the chosen energy partition.

Frequency shift of a resonating cantilever in a.c. force microscopy: towards a realistic model

Quantifying the local elastic properties of the material requires realistic modeling of the behavior of the system. In this paper, we present a model in which the cantilever is considered as a continuous medium. The model uses the hertzian contact theory to describe the mechanical contact between the sample and the tip, represented by a spring. Moreover, this model takes into account the experimental aspect of the clamped cantilever base. The associated boundary conditions are physically justified. Experimental measurements have been performed. They show the evolution of the resonance frequency when contacting different samples. The corresponding fitted theoretical curves give reasonable agreement with experiment and allow measurement of the local elastic properties of the sample with good accuracy (better than 5%).

Elastic and Plastic Properties of Gamma + Laves Phase In-situ Composite Alloys Using Nanoindentation Techniques

ABSTRACTIn the present study, the local elastic and plastic properties of the γ- TiAl and the Laves phases have been investigated in a series of γ + Laves alloys using room-temperature compression, Vickers microhardness, and nanoindentation with an emphasis on elucidating the local property changes in γ + Laves alloys deformed at room temperature. This study shows that nanoindentation can be used to provide useful information on plastic flow in multiphase intermetallic alloys.

Effect of Random Packing on Stress Relaxation in Foam

Numerical simulations are conducted to examine the effect of randomness in the bubble packing on the local elastic properties of a foam. We find that the response to a small-amplitude strain is spatially inhomogeneous: there are regions (of several bubbles) where bubbles shift their positions in order to prevent distortion. These regions respond differently when sheared in different directions, showing that the regions are elastically anisotropic. This work verifies assumptions made in an earlier, coarse-grained model.

Elastic Microanalysis at Lower Temperatures

Acoustic microscopy is wellknown nowadays as a powerful non-destructive tool to investigate the local elastic and structural properties of compact materials, composites and films. However, the application of commercial microscopes is limited to temperatures near ambient, because aqua dest. as a quite suitable immersion fluid is usually prefered. Here we report on our recent investigations, which are governed by the aim to extend elastic microanalysis to temperatures well below room temperature. All measurements are done between 90K and 230K by use of liquid propane as acoustic bonding medium. It is shown that elastic microanalysis at lGHz can be successfully performed but is considerably affected by the strong temperature dependent properties of the coupling fluid chosen.

Dewetting dynamics and nucleation of polymers observed by elastic and friction force microscopy

Dewetting dynamics of immiscible liquid polymer bilayers were studied by atomic force microscopy. Morphological changes of the phase-separated liquids were correlated with friction and local elastic properties, and the dewetting pattern classified in terms of the relative bulk viscosities. Topographical atomic force microscopy measurements revealed that the dewetting process did not occur on the liquid–liquid interface as expected. Rather the process is three-dimensional with an apparent shear plane ‘‘deep’’ inside the low viscosity liquid film. The depth of the shear plane is immediately established in the nucleation process which was studied two and three dimensionally by friction force microscopy and compliance measurements. Since this mechanism has not been observed previously in simple liquids, the role of entanglements of these polymers is discussed together with the application of the atomic force microscopy as a three-dimensional material property specific tool capable of studying processes below the surface.

Elastic deformations of tip and sample during atomic force microscope measurements

Two established models, based on continuum mechanics, are discussed to describe the elastic deformation of the tip and the sample in the atomic force microscope. We present arguments why the elastic deformation of a surface is more rigorously described by Sneddon mechanics rather than by the habitually used Hertzian mechanics. The results presented here show that elastic deformations are an important issue for measurements with the atomic force microscope. We demonstrate how elastic deformations impose limits to the capability of the atomic force microscope to image at true atomic resolution and how elastic deformations can be used to measure local elastic properties of a sample. Against the commonly accepted assumption of a ‘‘rigid’’ tip, we show that the elastic deformation of the tip can become a significant factor, when imaging hard samples. With few exceptions, the atomic force microscope has not been operated at true atomic resolution so far and more complex contrast mechanisms, with multiple atom interaction, must be considered.

On the griffith crack in a nonhomogeneous interlayer of adjoining two different elastic materials

The effects of the interlayer thickness, local nonhomogeneous elastic property and the distribution parameter k on stress intensity factor and strain energy release rate are presented

Lipids in biological membrane fusion

The results reviewed suggest that membrane fusion in diverse biological fusion reactions involves formation of some specific intermediates: stalks and pores. Energy of these intermediates and, consequently, the rate and extent of fusion depend on the propensity of the corresponding monolayers of membranes to bend in the required directions. Proteins and peptides can control the bending energy of membrane monolayers in a number of ways. Monolayer lipid composition may be altered by different phospholipases [50, 85, 90], flipases and translocases [4, 50]. Proteins and peptides can change monolayer spontaneous curvature or hydrophobic void energy by direct interaction with membrane lipids [20, 32, 111]. Proteins may also provide some barriers for lipid diffusion in the plane of the monolayer [83, 141]. If diffusion of lipids at some specific membrane sites (e.g., in the vicinity of fusion protein) is somehow hindered, the energy of the bent fusion intermediates would reflect the elastic properties of these particular sites rather than the spontaneous curvature of the whole monolayers. Proteins may deform membranes while bringing them locally into close contact. The alteration of the geometric (external) curvature will certainly change the elastic energy of the initial state and, thus affect the energetic barriers of the formation of the intermediates [143]. In addition, the area and the energy of the stalk can be reduced by preliminary bending of the contacting membranes [111]. The possible effects of proteins and polymers on local elastic properties and local shapes of the membranes have been recently analyzed [22, 39, 45, 63]. These studies may provide a good basis for future development of theoretical models of protein-mediated fusion. Various models for biological fusion have been presented as hypothetical sequences of intermediate conformations of proteins, with membrane lipids just covering the empty spaces between the proteins. Although the results discussed above do not allow us to draw an allexplaining cartoon of the fusion mechanism, they do indicate which properties of membrane lipid bilayers (if modified by fusion proteins) would get these bilayers to fuse. In addition, these data suggest a specific geometry to bent fusion intermediates (stalks and pores) and imply a contribution by lipids to the energy of these intermediates. We think that the synthesis of rapidly developing structural information on fusion proteins with the analysis of the physics of membrane rearrangement may soon yield a real understanding of the fascinating and fundamental phenomenon of membrane fusion.

A novel finite element for treating inhomogeneous solids

AbstractThis study is concerned with the development and implementation of a novel finite element which is capable of treating the problem of interacting circular inhomogeneities in heterogeneous solids. The general form of the element, which is constructed from a cell containing a single circular inhomogeneity in a surrounding matrix, is derived explicitly using the complex potentials of Muskhelishvili and the Laurent series expansion method. The strength of the proposed eight‐noded plane element is demonstrated by its ability to treat arbitrarily and periodically located multiple inhomogeneities under general loading conditions using a limited number of elements. Assessment of the accuracy and efficiency of the devised element is obtained by comparing its performance against existing analytical and traditional finite element attempts. The current element enables the determination of the local and effective elastic properties of composite materials with relative ease.

Mapping the local Young's modulus by analysis of the elastic deformations occurring in atomic force microscopy

The atomic force microscope (AFM) is used to map the local elastic properties of substrates by analysis of the force versus tip motion curves. Measurements are presented, which show that gold islands on a rough polypropylene substrate can be distinguished from the surrounding polymer. Quantitative calculations of the elastic deformations of the tip and of the sample, as induced by the AFM, were performed. Surprisingly, the tip deformation is predominant over the sample deformation in a wide regime of forces and of tip radii; which are commonly used in AFM. This fact limits the capability of the AFM to measure local elastic properties. However, with our experimental set-up one can induce a total deformation dominated by the sample deformations.

Relationship between modeling of the atomic structure of grain boundaries and studies of mechanical properties

The main objective of the majority of the microscopic atomic level studies of interfaces has been investigation of the dominant atomic level structural features and their relation to geometrical and crystallography: characteristics of grain boundaries. At the same time extensive studies of mechanical properties of materials with interfaces have been made in the framwork of continuum mechanics but without taking either structure or properties of the interfaces into account. In this paper we attempt, at least partially, to bridge the gap between atomistic and continuum approaches. Since the most fundamental properties of materials entering continuum treatments are the elastic moduli, we demonstrate first that atomic-level elastic properties of interfaces can be rigorously defined and that the fourth-order tensor of effective elastic moduli of grain boundary regions can be determined in atomistic simulations. We then proceed to employ these concepts in the continuum analysis of long wavelength phonons corresponding to acoustic interface waves. It is then shown that only when the local elastic properties of interfaces are incorporated into the contiuum model, via boundary conditions derived directly from the atomic-level elastic properties of interfaces, are the interfacial waves deduced from this model in good agreement with the phonon calculations.

Measurement applications of the scanning acoustic microscope

Measurement methods using a scanning acoustic microscope are discussed. One of them, interpretation of the interference fringes, was used for measurements of the local elastic properties in an SiCSiC composite material by studying the velocity of Rayleigh waves. Separate values were obtained for the matrix and for the fibres with good reproducibility.

Analysis of local and effective elastic properties of fibre-reinforced materials

The objective of the present article is to apply the technique of asymptotic homogenization to explicitly determine both local and overall elastic properties of unidirectional (UD) metal-matrix composites (MMCs). In this approach, the complex potentials of Muskhelishvili have been used to formulate the problem in terms of an asymptotic series expansion of the doubly periodic Weierstrass elliptic functions. The analytical predictions are compared with a finite element model of a typical MMC and efforts are made to examine the effect of the elastic properties and volume fraction of the reinforcing fibres upon the resulting local stress field and overall elastic properties of the composite. Furthermore, attention is also given to the difficulties and limitations associated with the adopted techniques.

Evaluation of segmental elastic properties of the aorta in normotensive and medically treated hypertensive patients by intravascular ultrasound

Local elastic properties of the descending aorta at different levels were evaluated by means of intravascular ultrasound images and pressure measurements. For this purpose, 30 normotensive patients and 30 age-matched medically treated patients with essential hypertension, all undergoing diagnostic cardiac catheterization, were studied. Hypertension was well controlled in the essential hypertensives (137.1 +/- 6.79/74.5 +/- 2.65 mmHg). Systolic but not diastolic blood pressure in the hypertensive patients was significantly different from that of the normotensives (118.8 +/- 4.38/69.7 +/- 1.65 mmHg). The continuous loss of volume compliance with increasing distance from the heart was significantly higher in the hypertensives than in the normotensive patients [normotensives (1.45 +/- 0.19) x 10(-10) m5/N at the thoracic aorta, (0.08 +/- 0.05) x 10(-10) m5/N at the external iliac artery; hypertensives (0.81 +/- 0.09) x 10(-10) and (0.05 +/- 0.01) x 10(-10) m5/N at the corresponding sites]. Similarly, the hypertensives had an elevated elastic modulus proximal to the aortic bifurcation compared with the normotensives (244.47 +/- 44.06 versus 108.10 +/- 17.76 m/s, respectively). The decrease in buffering function of the vessel at this site is presumably caused by a turbulent flow pattern. Compared with the normotensives, the treated hypertensives had a significantly higher elastic modulus at each site where this was measured, whereas volume compliance and sectional compliance were lower. The differences in elastic modulus and compliance between hypertensive and normotensive patients seem disproportionate to the difference in systolic blood pressure (within the normal range in both the treated hypertensives and the normotensives). Therefore, normalization of high blood pressure by long-term antihypertensive treatment may not fully reverse changes, caused by arterial hypertension, in the viscoelastic properties of the arterial wall.

High-resolution shallow water 3-D survey and inversion for geophysical parameters

In the shallow water environment even in subsurface depths less than 30 m, 3-D structures can affect wave propagation. A high-resolution (500–3500 Hz) 3-D survey (53 lines; 5-km length, 10-m line spacing, 5-m shot spacing) using a Huntec deep-towed boomer source and STARFIX navigation was carried out offshore New Jersey in 1989. Additional 3-D acquisition along with vibra coring will be conducted in the same region in the summer of 1993. Processing and 3-D interpretation of the data record geologic features hundreds of meters across but only several meters in total depth, i.e., glacial meltwater channels prior to the most recent Wisconsin glaciation. Reducing spatial sampling even to 100-m line spacing results in severe spatial aliasing of these features, making geologic interpretation erroneous. In addition to 3-D structure, local subsurface elastic properties need to be estimated quantitatively by inverse methods. The global optimization methods can be employed to derive earth models and their uncertainties. A major challenge is to combine 3-D acquisition, imaging, interpretation, and core data with the requirements of material property estimation such that a complete understanding of propagation in shallow water environment can be achieved.

Elastography: Elasticity Imaging Using Ultrasound with Application to Muscle and Breast In Vivo

Changes in tissue elasticity are generally correlated with its pathological state. In many cases, despite the difference in elasticity, the small size of a lesion or its location deep in the body preclude its detection by palpation. In general, such a lesion may or may not posses echogenic properties that would make it ultrasonically detectable. Elastography is an ultrasonic method for imaging the elasticity of compliant tissues. The method estimates the local longitudinal strain of tissue elements by ultrasonically assessing the one dimensional local displacements. This information can be combined with first order theoretical estimates of the local stress to yield a quantitative measure of the local elastic properties of tissue. The elasticity information is displayed in the form of a gray scale image called an elastogram. An experimental system for elastography in phantoms based on a single element transducer has been described previously [1]. Here we introduce a new elastography system based on a linear array transducer that is suitable for in vivo scanning. We describe tissue mimicking phantom experiments and preliminary in vivo breast and muscle elastograms confirming the feasibility of performing elastography in vivo. An elastogram of a breast containing an 8 mm palpable cancer nodule clearly shows the lesion. Elastograms and their corresponding sonograms show some similarities and differences in the depiction of tissue structures.

Elastography: Elasticity Imaging Using Ultrasound with Application to Muscle and Breast in Vivo

Changes in tissue elasticity are generally correlated with its pathological state. In many cases, despite the difference in elasticity, the small size of a lesion or its location deep in the body preclude its detection by palpation. In general, such a lesion may or may not possess echogenic properties that would make it ultrasonically detectable. Elastography is an ultrasonic method for imaging the elasticity of compliant tissues. The method estimates the local longitudinal strain of tissue elements by ultrasonically assessing the one dimensional local displacements. This information can be combined with first order theoretical estimates of the local stress to yield a quantitative measure of the local elastic properties of tissue. The elasticity information is displayed in the form of a gray scale image called an elastogram. An experimental system for elastography in phantoms based on a single element transducer has been described previously [1]. Here we introduce a new elastography system based on a linear array transducer that is suitable for in vivo scanning. We describe tissue mimicking phantom experiments and preliminary in vivo breast and muscle elastograms confirming the feasibility of performing elastography in vivo. An elastogram of a breast containing an 8 mm palpable cancer nodule clearly shows the lesion. Elastograms and their corresponding sonograms show some similarities and differences in the depiction of tissue structures.

Atomic force and scanning tunneling microscopies of organic surfaces

Recent progress in scanned probe microscopies (SPM) such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) on organic surfaces is reviewed. Topics include imaging of individual chemisorbed molecules, supported physisorbed molecular assemblies, biopolymers and (bulk) synthetic polymeric materials investigated under various environmental conditions such as vacuum, fluids and air. The effects of tip/ surface interactions that result in local surface modifications and image alterations are discussed. The potential of the AFM to measure the local elastic and tribological properties of organic surfaces is demonstrated.

Phonons and Local Elastic Properties of Grain Boundaries

Phonons and Local Elastic Properties of Grain Boundaries