An Instrumented Indentation Method for Young's Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young's modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young's modulus H (n) /E (r) and the ratio of elastic work/total work W (e)/W can be derived. Consequently, a method for Young's modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.

The accuracy of Kirchhoff's approximation in describing the far field speckles produced by random self-affine fractal surfaces

Based on the rigorous formulation of integral equations for the propagations of light waves at the medium interface, we carry out the numerical solutions of the random light field scattered from self-affine fractal surface samples. The light intensities produced by the same surface samples are also calculated in Kirchhoff's approximation, and their comparisons with the corresponding rigorous results show directly the degree of the accuracy of the approximation. It is indicated that Kirchhoff's approximation is of good accuracy for random surfaces with small roughness value w and large roughness exponent alpha. For random surfaces with larger w and smaller alpha, the approximation results in considerable errors, and detailed calculations show that the inaccuracy comes from the simplification that the transmitted light field is proportional to the incident field and from the neglect of light field derivative at the interface.

A high accuracy image sensor for sinusoidal phase-modulating interferometry

We proposed a high accuracy image sensor technique for sinusoidal phase-modulating interferometer in the field of the surface profile measurements. It solved the problem of the CCD's pixel offset of the same column under two adjacent rows, eliminated the spectral leakage, and reduced the influence of external interference to the measurement accuracy. We measured the surface profile of a glass plate, and its repeatability precision was less than 8 nm and its relative error was 1.15 %. The results show that it can be used to measure surface profile with high accuracy and strong anti-interference ability. (C) 2007 Elsevier GmbH. All rights reserved.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.

A hierarchical approach coupled with coarse DEM information for improving the efficiency and accuracy of forest mapping over very rugged terrains

Forest mapping over mountainous terrains is difficult because of high relief Although digital elevation models (DEMs) are often useful to improve mapping accuracy, high quality DEMs are seldom available over large areas, especially in developing countries

High-accuracy same-beam VLBI observations using Shanghai and Urumqi telescopes

The same-beam VLBI observations of Rstar and Vstar, which were two small satellites of Japanese lunar mission, SELENE, were successfully performed by using Shanghai and Urumqi 25-m telescopes. When the separation angle between Rstar and Vstar was less than 0.1 deg, the differential phase delay of the X-band signals between Rstar and Vstar on Shanghai-Urumqi baseline was obtained with a very small error of 0.15 mm rms, which was reduced by 1-2 order compared with the former VLBI results. When the separation angle was less than 0.56 deg, the differential phase delay of the S-band signals was also obtained with a very small error of several mm rms. The orbit determination for Rstar and Vstar was performed, and the accuracy was improved to a level of several meters by using VLBI and Doppler data. The high-accuracy same-beam differential VLBI technique is very useful in orbit determination for a spacecraft, and will be used in orbit determination for Mars missions of China Yinghuo-1 and Russia Phobos-grunt.

A Numerical Method for Calculating Transmission Coefficients Across Arbitrary Potential Barriers with High Accuracy

We report a new method for calculating transmission coefficients across arbitrary potential barriers based on the Runge-Kutta method. A numerical solution of the Schrodinger equation is calculated using the Runge-Kutta method,and a new model is established to analyze the numerical results to find the transmission coefficient. This technique is applied to various cases, such as parabolic potential barrier and double-barrier structures. Transmission probability with high precision is obtained and discussed. The tunnelling current density through a MOS structure is also explored and the result coincides with the Fowler-Nordheim model,which indicates the applicability of our method.

Analysis of the practical force accuracy of electromagnet-based nanoindenters

Two important factors that influence the force accuracy of the electromagnet-based nano-indenters but have not yet attracted much attention are analyzed, and a more reasonable way to estimate the force accuracy is presented in this paper. MTS Nano Indenter (R), with the characteristics of a coil suspended in a uniform magnetic field by two sets of springs acting as an actuator and force measuring unit, is used as an example. One of the two factors is the uniformity of the magnetic field. The other is the stiffness of the supporting spring. Consequently, the practical force accuracy varies considerably from test to test because it firmly depends on the working position of the coil and the displacement stroke. A reasonable estimated accuracy value is of the order of 10 degrees mu N for typical indentation tests with a 10(2) nm indentation depth or a 10 degrees mN test force. (C) 2010 Elsevier Ltd. All rights reserved.

Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: Accuracy and uncertainty analysis

Mapping the spatial distribution of contaminants in soils is the basis of pollution evaluation and risk control. Interpolation methods are extensively applied in the mapping processes to estimate the heavy metal concentrations at unsampled sites. The performances of interpolation methods (inverse distance weighting, local polynomial, ordinary kriging and radial basis functions) were assessed and compared using the root mean square error for cross validation. The results indicated that all interpolation methods provided a high prediction accuracy of the mean concentration of soil heavy metals. However, the classic method based on percentages of polluted samples, gave a pollution area 23.54-41.92% larger than that estimated by interpolation methods. The difference in contaminated area estimation among the four methods reached 6.14%. According to the interpolation results, the spatial uncertainty of polluted areas was mainly located in three types of region: (a) the local maxima concentration region surrounded by low concentration (clean) sites, (b) the local minima concentration region surrounded with highly polluted samples; and (c) the boundaries of the contaminated areas. (C) 2010 Elsevier Ltd. All rights reserved.

ON THE SIGNIFICANCE OF WAVELENGTH POSITIONING ACCURACY IN MULTICOMPONENT ANALYSIS TECHNIQUES FOR THE CORRECTION OF LINE INTERFERENCES IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

The present paper reports some definite evidence for the significance of wavelength positioning accuracy in multicomponent analysis techniques for the correction of line interferences in inductively coupled plasma atomic emission spectrometry (ICP-AES). Using scanning spectrometers commercially available today, a large relative error, DELTA(A) may occur in the estimated analyte concentration, owing to wavelength positioning errors, unless a procedure for data processing can eliminate the problem of optical instability. The emphasis is on the effect of the positioning error (deltalambda) in a model scan, which is evaluated theoretically and determined experimentally. A quantitative relation between DELTA(A) and deltalambda, the peak distance, and the effective widths of the analysis and interfering lines is established under the assumption of Gaussian line profiles. The agreement between calculated and experimental DELTA(A) is also illustrated. The DELTA(A) originating from deltalambda is independent of the net analyte/interferent signal ratio; this contrasts with the situation for the positioning error (dlambda) in a sample scan, where DELTA(A) decreases with an increase in the ratio. Compared with dlambda, the effect of deltalambda is generally less significant.

Impact of difference accuracy on computational properties of vertical grids for a nonhydrostatic model

Starting from nonhydrostatic Boussinesq approximation equations, a general method is introduced to deduce the dispersion relationships. A comparative investigation is performed on inertia-gravity wave with horizontal lengths of 100, 10 and 1 km. These are examined using the second-order central difference scheme and the fourth-order compact difference scheme on vertical grids that are currently available from the perspectives of frequency, horizontal and vertical component of group velocity. These findings are compared to analytical solutions. The obtained results suggest that whether for the second-order central difference scheme or for the fourth-order compact difference scheme, Charny-Phillips and Lorenz ( L) grids are suitable for studying waves at the above-mentioned horizontal scales; the Lorenz time-staggered and Charny-Phillips time staggered (CPTS) grids are applicable only to the horizontal scales of less than 10 km, and N grid ( unstaggered grid) is unsuitable for simulating waves at any horizontal scale. Furthermore, by using fourth-order compact difference scheme with higher difference precision, the errors of frequency and group velocity in horizontal and vertical directions produced on all vertical grids in describing the waves with horizontal lengths of 1, 10 and 100 km cannot inevitably be decreased. So in developing a numerical model, the higher-order finite difference scheme, like fourth-order compact difference scheme, should be avoided as much as possible, typically on L and CPTS grids, since it will not only take many efforts to design program but also make the calculated group velocity in horizontal and vertical directions even worse in accuracy.

Impact of spatial resolution and spatial difference accuracy on the performance of Arakawa A-D grids

This paper alms at illustrating the impact of spatial difference scheme and spatial resolution on the performance of Arakawa A-D grids in physical space. Linear shallow water equations are discretized and forecasted on Arakawa A-D grids for 120-minute using the ordinary second-order (M and fourth-order (C4) finite difference schemes with the grid spacing being 100 km, 10 km and I km, respectively. Then the forecasted results are compared with the exact solution, the result indicates that when the grid spacing is I kin, the inertial gravity wave can be simulated on any grid with the same results from C2 scheme or C4 scheme, namely the impact of variable configuration is neglectable; while the inertial gravity wave is simulated with lengthened grid spacing, the effects of different variable configurations are different. However, whether for C2 scheme or for C4 scheme, the RMS is minimal (maximal) on C (D) grid. At the same time it is also shown that when the difference accuracy increases from C2 scheme to C4 scheme, the resulted forecasts do not uniformly decrease, which is validated by the change of the group A velocity relative error from C2 scheme to C4 scheme. Therefore, the impact of the grid spacing is more important than that of the difference accuracy on the performance of Arakawa A-D grid.