There is growing interest in assessing the clinical value of ultrasound in the prediction and management of osteoporosis. However, the mechanism of ultrasound propagation in cancellous bone is not well understood. The Biot theory is one approach to modelling the interaction of sound waves with cancellous structure, and porosity is one of its input parameters. In this paper we report the relationship between broadband ultrasonic attenuation (BUA) corrected for specimen thickness (nBUA) and porosity in a porous Perspex cancellous bone mimic, a stereolithography cancellous bone mimic and in natural human and bovine tissue. nBUA and porosity have a non-linear parabolic relationship. The maximum nBUA value (nBUAmax) occurs at approximately 30% porosity in the Perspex mimic, approximately 70% in the stereolithography mimic and approximately 75% in natural cancellous bone. We discuss the effect of structure on the form of the nBUA-porosity relationship.

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There has been considerable debate on the relative dependence of broadband ultrasound attenuation (nBUA, dB MHz(-1) cm(-1)) upon the density and structure of cancellous bone. A nonlinear relationship between nBUA and porosity has recently been demonstrated using stereolithography models, indicating a high structural dependence for nBUA. We report here on the measurement of trabecular perimeter and fractal dimension on the two-dimensional images used to create the stereolithography models. Adjusted coefficients of determination (R2) with nBUA were 94.4% (p < 0.0001) and 98.4% (p < 0.0001) for trabecular perimeter and fractal dimension respectively. The feature of fractal dimension representing both the porosity and connectivity of a given structure is most exciting. Further work is required to determine the relationship between broadband ultrasound attenuation and fractal dimension in complex three-dimensional cancellous bone structures.

PACS 68.37. Hk, 78.55.Cr, 78.66.Fd Using wavelength dispersive X-ray spectrometers on an Electron Probe Micro-Analyser we have accurately quantified the elemental composition of a series of homogeneous AlInGaN epitaxial layers. The thickness of the quaternary layer (~100 nm) necessitates the combination of data measured at a number of different electron beam energies and an analytical model based on a layered structure. The samples studied have aluminium fractions in the range 0.03-0.12 and indium fractions in the region of 0.01. Photoluminescence data from the samples are used to plot the dependency of the luminescence energy, linewidth and intensity on the composition. WDX mapping was employed to investigate spatial variations in the elemental compositions and the films were found to be uniform with no evidence for clustering of In or Al on a >100 nm scale. IntroductionThe ternary nitride semiconductors InGaN and AlGaN have proved to be highly successful active layers in GaN-based devices, including light emitters and transistors. However, lattice mismatch in ternary heterostructures imposes serious limitations for the design and operation of certain devices. In addition the efficiency of InGaN light emitters is severely degraded by the incorporation of too much, or too little, indium. Use of quaternary AlInGaN layers offers potential for the fabrication of lattice matched III-N heterostructures and improvement of the quantum efficiency of light emitters [1,2], particularly in the UV region with its host of important applications. The growth of high quality AlInGaN layers requires a balance between the high temperatures suited for Al-containing layers and the low temperatures necessary for incorporation of indium. Measuring the composition of AlInGaN layers using standard X-ray diffraction is complicated by the lack of a unique solution for the quaternary system and further by overlapping diffraction peaks in the case of lattice-match to the underlying GaN. In this paper we describe the compositional analysis of a series of AlInGaN layers using an Electron Probe Micro-Analyser (EPMA) equipped with wavelength dispersive X-ray (WDX) spectrometers, allowing the elemental composition to be determined with high accuracy and sub-micron spatial resolution. The compositional data are then correlated with the light emitting properties of the layers.