Experimental and computer simulation validation of ultrasound phase interference created by lateral inhomogeneity of transit time in replica bone marrow composite models

Purpose: The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone for the assessment of osteoporosis follows a parabolic-type dependence with bone volume fraction; having minima values corresponding to both entire bone and entire marrow. Langton has recently proposed that the primary BUA mechanism may be significant phase interference due to variations in propagation transit time through the test sample as detected over the phase-sensitive surface of the receive ultrasound transducer. This fundamentally simple concept assumes that the propagation of ultrasound through a complex solid : liquid composite sample such as cancellous bone may be considered by an array of parallel ‘sonic rays’. The transit time of each ray is defined by the proportion of bone and marrow propagated, being a minimum (tmin) solely through bone and a maximum (tmax) solely through marrow. A Transit Time Spectrum (TTS), ranging from tmin to tmax, may be defined describing the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit time over the surface of the receive ultrasound transducer. Phase interference may result from interaction of ‘sonic rays’ of differing transit times. The aim of this study was to test the hypothesis that there is a dependence of phase interference upon the lateral inhomogenity of transit time by comparing experimental measurements and computer simulation predictions of ultrasound propagation through a range of relatively simplistic solid:liquid models exhibiting a range of lateral inhomogeneities. Methods: A range of test models was manufactured using acrylic and water as surrogates for bone and marrow respectively. The models varied in thickness in one dimension normal to the direction of propagation, hence exhibiting a range of transit time lateral inhomogeneities, ranging from minimal (single transit time) to maximal (wedge; ultimately the limiting case where each sonic ray has a unique transit time). For the experimental component of the study, two unfocused 1 MHz ¾” broadband diameter transducers were utilized in transmission mode; ultrasound signals were recorded for each of the models. The computer simulation was performed with Matlab, where the transit time and relative amplitude of each sonic ray was calculated. The transit time for each sonic ray was defined as the sum of transit times through acrylic and water components. The relative amplitude considered the reception area for each sonic ray along with absorption in the acrylic. To replicate phase-sensitive detection, all sonic rays were summed and the output signal plotted in comparison with the experimentally derived output signal. Results: From qualtitative and quantitative comparison of the experimental and computer simulation results, there is an extremely high degree of agreement of 94.2% to 99.0% between the two approaches, supporting the concept that propagation of an ultrasound wave, for the models considered, may be approximated by a parallel sonic ray model where the transit time of each ray is defined by the proportion of ‘bone’ and ‘marrow’. Conclusions: This combined experimental and computer simulation study has successfully demonstrated that lateral inhomogeneity of transit time has significant potential for phase interference to occur if a phase-sensitive ultrasound receive transducer is implemented as in most commercial ultrasound bone analysis devices.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

Phase-Field Simulation of Fusion Interface Events during Solidification of Dissimilar Welds: Effect of Composition Inhomogeneity

We investigate the events near the fusion interfaces of dissimilar welds using a phase-field model developed for single-phase solidification of binary alloys. The parameters used here correspond to the dissimilar welding of a Ni/Cu couple. The events at the Ni and the Cu interface are very different, which illustrate the importance of the phase diagram through the slope of the liquidus curves. In the Ni side, where the liquidus temperature decreases with increasing alloying, solutal melting of the base metal takes place; the resolidification, with continuously increasing solid composition, is very sluggish until the interface encounters a homogeneous melt composition. The growth difficulty of the base metal increases with increasing initial melt composition, which is equivalent to a steeper slope of the liquidus curve. In the Cu side, the initial conditions result in a deeply undercooled melt and contributions from both constrained and unconstrained modes of growth are observed. The simulations bring out the possibility of nucleation of a concentrated solid phase from the melt, and a secondary melting of the substrate due to the associated recalescence event. The results for the Ni and Cu interfaces can be used to understand more complex dissimilar weld interfaces involving multiphase solidification.

Inhomogeneity of asteroid 2008 TC3 (Almahata Sitta meteorites) revealed through magnetic susceptibility measurements

Magnetic susceptibility measurements were performed on freshly fallen Almahata Sitta meteorites. Most recovered samples are polymict ureilites. Those found in the first four months since impact, before the meteorites were exposed to rain, have a magnetic susceptibility in the narrow range of 4.92 ± 0.08 log 10-9 Am2/kg close to the range of other ureilite falls 4.95 ± 0.14 log 10-9 Am2/kg reported by Rochette et al. (2009). The Almahata Sitta samples collected one year after the fall have similar values (4.90 ± 0.06 log 10-9 Am2/kg), revealing that the effect of one-year of terrestrial weathering was not severe yet. However, our reported values are higher than derived from polymict (brecciated) ureilites 4.38 ± 0.47 log 10-9 Am2/kg (Rochette et al. 2009) containing both falls and finds confirming that these are significantly weathered. Additionally other fresh-looking meteorites of non-ureilitic compositions were collected in the Almahata Sitta strewn field. Magnetic susceptibility measurements proved to be a convenient non-destructive method for identifying non-ureilitic meteorites among those collected in the Almahata Sitta strewn field, even among fully crusted. Three such meteorites, no. 16, 25, and 41, were analyzed and their composition determined as EH6, H5 and EL6 respectively (Zolensky et al., 2010). A high scatter of magnetic susceptibility values among small (< 5 g) samples revealed high inhomogeneity within the 2008 TC3 material at scales below 1-2 cm.

Inhomogeneity in sintered ZnO based non-linear resistors

Investigations have been made on the inhomogeneous characteristics of sintered ZnO based non-linear resistors caused by localized particle growth on the surface and by internal flaws. The presence of Sb2O3 was responsible for the observed particle growth. A part of the Bi2O3 on the surface was found to be in the reduced state. Two kinds of failure mode, cracking and puncturing, were observed when the samples were subjected to high-energy pulses. The puncture mode is caused by local melting around the regions of high current density, whereas the cracking mode results from thermally induced stresses.

Glasslike ordering and spatial inhomogeneity of magnetic structure in Ba3FeRu2O9: Role of Fe/Ru site disorder

Several doped 6H hexagonal ruthenates, having the general formula Ba3MRu2O9, have been studied over a significant period of time to understand the unusual magnetism of ruthenium metal. However, among them, the M = Fe compound appears different since it is observed that unlike others, the 3d Fe ions and 4d Ru ions can easily exchange their crystallographic positions, and as a result many possible magnetic interactions become realizable. The present study involving several experimental methods on this compound establishes that the magnetic structure of Ba3FeRu2O9 is indeed very different from all other 6H ruthenates. Local structural study reveals that the possible Fe/Ru site disorder further extends to create local chemical inhomogeneity, affecting the high-temperature magnetism of this material. There is a gradual decrease of Fe-57 Mossbauer spectral intensity with decreasing temperature (below 100 K), which reveals that there is a large spread in the magnetic ordering temperatures, corresponding to many spatially inhomogeneous regions. However, finally at about 25 K, the whole compound is found to take up a global glasslike magnetic ordering.

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

Effects of phase inhomogeneity and boundary conditions on the dynamic response of SMA wire actuators

This paper reports the simulation results from the dynamic analysis of a Shape Memory Alloy (SMA) actuator. The emphasis is on understanding the dynamic behavior under various loading rates and boundary conditions, resulting in complex scenarios such as thermal and stress gradients. Also, due to the polycrystalline nature of SMA wires, presence of microstructural inhomogeneity is inevitable. Probing the effect of inhomogeneity on the dynamic behavior can facilitate the prediction of life and characteristics of SMA wire actuator under varieties of boundary and loading conditions. To study the effect of these factors, an initial boundary value problem of SMA wire is formulated. This is subsequently solved using finite element method. The dynamic response of the SMA wire actuator is analyzed under mechanical loading and results are reported. Effect of loading rate, micro-structural inhomogeneity and thermal boundary conditions on the dynamic response of SMA wire actuator is investigated and the simulation results are reported.

Barrier Inhomogeneity and Electrical Properties of InN Nanodots/Si Heterojunction Diodes

The electrical transport behavior of n-n indium nitride nanodot-silicon (InN ND-Si) heterostructure Schottky diodes is reported here, which have been fabricated by plasma-assisted molecular beam epitaxy. InN ND structures were grown on a 20 nm InN buffer layer on Si substrates. These dots were found to be single crystalline and grown along [0 0 0 1] direction. Temperature-dependent current density-voltage plots (J-V-T) reveal that the ideality factor (eta) and Schottky barrier height (SBH) (Phi(B)) are temperature dependent. The incorrect values of the Richardson constant (A**) produced suggest an inhomogeneous barrier. Descriptions of the experimental results were explained by using two models. First one is barrier height inhomogeneities (BHIs) model, in which considering an effective area of the inhomogeneous contact provided a procedure for a correct determination of A**. The Richardson constant is extracted similar to 110 A cm(-2) K(-2) using the BHI model and that is in very good agreement with the theoretical value of 112 A cm(-2) K(-2). The second model uses Gaussian statistics and by this, mean barrier height Phi(0) and A** were found to be 0.69 eV and 113 A cm(-2) K(-2), respectively.

The inhomogeneity of plastic-deformation in ductile single-crystals

A discrete slip model which characterizes the inhomogeneity of material properties in ductile single crystals is proposed in this paper. Based on this model rate-dependent finite element investigations are carried out which consider the finite deformation, finite rotation, latent hardening effect and elastic anisotropy. The calculation clearly exhibits the process from microscopic inhomogeneous and localized deformation to necking and the formation of LSBS and reveals several important features of shear localization. For example, the inhomogeneous deformation is influenced by the imperfections and initial non-uniformities of material properties. The inhomogeneous deformation may either induce necking which results in the lattice rotation and leads to geometrical softening, which in turn promotes the formation of CSBS, or induces heavily localized deformation. The microscopic localized deformation eventually develops into the LSBS and results in a failure. These results are in close agreement with experiment. Our calculations also find that the slip lines on the specimen's surface at necking become curved and also find that if the necking occurs before the formation of LSBS, this band must be misoriented from the operative slip systems. In this case, the formation of LSBS must involve non-crystallographic effects. These can also be indirectly confirmed by experiment. All these suggest that our present discrete slip model offers a correct description of the inhomogeneous deformation characterization in ductile crystals.

Cathodoluminescence study on in composition inhomogeneity of thick InGaN layer

We have investigated the optical properties of thick InGaN film grown on GaN by cathodeluminescence (CL) spectroscopy. It is found that there is obvious In composition variation in both growth and lateral direction of InGaN film. The depth distribution of In composition is closely related to the strain relaxation process of InGaN film. Accompanied with the relaxation of compressive strain, the In composition of InGaN layer increases and the CL peak energy shifts towards red. Moreover, a rather apparent In composition fluctuation is found in the relaxed upper part of InGaN layer as confirmed by CL imaging.

Al compositional inhomogeneity of AlGaN epilayer with a high Al composition grown by metal-organic chemical vapour deposition

The A1 compositional distribution of A1GaN is investigated by cathodoluminescence (CL). Monochromatic CL images and CL spectra reveal a lateral A1 compositional inhomogeneity, which corresponds to surface hexagonal patterns. Cross-sectional CL images show a relatively uniform Al compositional distribution in the growth direction, indicating columnar growth mode of A1GaN films. In addition, a thin A1GaN layer with lower Al composition is grown on top of the buffer A1N layer near the bottom of the A1GaN epilayer because of the larger lateral mobility of Ga adatoms on the growth surface and their accumulation at the grain boundaries.

The effects of LT AlN buffer thickness on the optical properties of AlGaN grown by MOCVD and Al composition inhomogeneity analysis

We have investigated the growth of AlGaN epilayers on a sapphire substrate by metalorganic chemical vapour deposition using various low-temperature ( LT) AlN buffer thicknesses. Combined scanning electron microscopy and cathodoluminescence investigations reveal the correlation between the surface morphology and optical properties of AlGaN films in a microscopic scale. It is found that the suitable thickness of the LT AlN buffer for high quality AlGaN growth is around 20 nm. The Al compositional inhomogeneity of the AlGaN epilayer is attributed to the low lateral mobility of Al adatoms on the growing surface.