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    Optical diffraction in close proximity to plane apertures. I. Boundary-value solutions for circular apertures and slits

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    In this paper the classical Rayleigh-Sommerfeld and Kirchhoff boundary-value diffraction integrals are solved in closed form for circular apertures and slits illuminated by normally incident plane waves. The mathematical expressions obtained involve no simplifying approximations and are free of singularities, except in the aperture plane itself. Their use for numerical computations was straightforward and provided new insight into the nature of diffraction in the near zone where the Fresnel approximation does not apply. The Rayleigh-Sommerfeld integrals were found to be very similar to each other, so that polarization effects appear to be negligibly small. On the other hand, they differ substantially at sub-wavelength differences from the aperture plane and do not correctly describe the diffracted field as an analytical continuation of the incident geometrical field

    A critical evaluation of interlaboratory data on total, elemental, and isotopic carbon in the carbonaceous particle reference material, NIST SRM 1649a

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    Because of increased interest in the marine and atmospheric sciences in elemental carbon (EC), or black carbon (BC) or soot carbon (SC), and because of the difficulties in analyzing or even defining this pervasive component of particulate carbon, it has become quite important to have appropriate reference materials for intercomparison and quality control. The NIST "urban dust" Standard Reference Material(R) SRM 1649a is useful in this respect, in part because it comprises a considerable array of inorganic and organic species, and because it exhibits a large degree of (C-14) isotopic heterogeneity, with biomass carbon source contributions ranging from about 2 % (essentially fossil aliphatic fraction) to about 32 % (polar fraction). A primary purpose of this report is to provide documentation for the new isotopic and chemical particulate carbon data for the most recent (31 Jan. 2001) SRM 1649a Certificate of Analysis. Supporting this is a critical review of underlying international intercomparison data and methodologies, provided by 18 teams of analytical experts from 11 institutions. Key results of the intercomparison are: (1) a new, Certified Value for total carbon (TC) in SRM 1649a; (2) C-14 Reference Values for total carbon and a number of organic species, including for the first time 8 individual PAHs; and (3) elemental carbon (EC) Information Values derived from 13 analytical methods applied to this component. Results for elemental carbon, which comprised a special focus of the intercomparison, were quite diverse, reflecting the confounding of methodological-matrix artifacts, and methods that tended to probe more or less refractory regions of this universal, but ill-defined product of incomplete combustion. Availability of both chemical and C-14 speciation data for SRM 1649a holds great promise for improved analytical insight through comparative analysis (e. g., fossil/biomass partition in EC compared to PAH), and through application of the principle of isotopic mass balance

    Limitations to accuracy in extracting characteristic line intensities from x-ray spectra

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    The early development of quantitative electron probe microanalysis, first using crystal spectrometers, then energy dispersive x-ray spectrometers (EDXS), demonstrated that elements could be detected at 0.001 mass fraction level and major concentrations measured within 2 % relative uncertainty. However, during this period of extensive investigation and evaluation, EDXS detectors were not able to detect x rays below 1 keV and all quantitative analysis was performed using a set of reference standards measured on the instrument. Now that EDXS systems are often used without standards and are increasingly being used to analyse elements using lines well below 1 keV, accuracy can be considerably worse than is documented in standard textbooks. Spectrum processing techniques found most applicable to EDXS have now been integrated into total system solutions and can give excellent results on selected samples. However, the same techniques fail in some applications because of a variety of instrumental effects. Prediction of peak shape, width and position for every characteristic line and measurement of background intensity is complicated by variations in response from system to system and with changing count rate. However, with an understanding of the fundamental sources of error, even a total system can be tested like a "black box" in areas where it is most likely to fail and thus establish the degree of confidence that should apply in the intended application. This approach is particularly important when the microanalysis technique is applied at lower electron beam voltages where the extraction of line intensities is complicated by extreme peak overlap and higher background levels

    Transient Green's tensor for a layered solid half-space with different interface conditions

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    Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical basis for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green's tensor for such a structure is explicitly derived from the three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a "generalized ray" and each is a definite line integral along a fixed path which can be easily computed numerically. Willis' method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, along with the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code is developed for computation of the Green's tensor when both the source and the detector are located on the top surface. The Green's tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions have a great influence on the transient displacements. For example, when the interface bonding conditions vary, some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be used to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration

    Standard Reference Materials - The First Century

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    This publication describes what may be the organization's most important and certainly its most unique contribution; namely, certified reference materials. Ultimately these certified reference materials would become known at NIST as standard reference materials (SRMs). This contribution has now been mirrored around the world with reference materials being certified in at least 25 countries and routinely applied in more than twice that number. The result has been more accurate analyses of materials that impact our safety, health, and well-being

    Quantitating fluorescence intensity from fluorophore: The definition of MESF assignment

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    The quantitation of fluorescence radiance may at first suggest the need to obtain the number of fluorophore that are responsible for the measured fluorescence radiance. This goal is beset by many difficulties since the fluorescence radiance depends on three parameters 1) the probability of absorbing a photon (molar extinction), 2) the number of fluorophores, and 3) the probability of radiative decay of the excited state (quantum yield). If we use the same fluorophore in the reference solution and the analyte then, to a good approximation, the molar extinction drops out from the comparison of fluorescence radiance and we are left with the comparison of fluorescence yield which is defined as the product of fluorophore concentration and the molecular quantum yield. The equality of fluorescence yields from two solutions leads to the notion of equivalent number of fluorophores in the two solutions that is the basis for assignment of MESF (Molecules of Equivalent Soluble Fluorophore) values. We discuss how MESF values are assigned to labeled microbeads and by extension to labeled antibodies, and how these assignments can lead to the estimate of the number of bound antibodies in flow cytometer measurements

    News Briefs

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    Electron-impact cross sections for dipole- and spin-allowed excitations of hydrogen, helium, and lithium

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    Electron-impact excitation cross sections are presented for the dipole- and spin allowed transitions from the ground states to the np P-2 states for hydrogen and lithium, and to the 1snp P-1 states for helium, n = 2 through 10. Two scaling formulas developed earlier by Kim [Phys. Rev. A 64, 032713 (2001)] for plane-wave Born cross sections are used. The scaled Born cross sections are in excellent agreement with available theoretical and experimental data

    Uncertainty in quantitative electron probe microanalysis

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    Quantitative electron probe analysis is based on models based on the physics or x-ray generation, empirically adjusted to the analyses of specimens of known composition. Their accuracy can be estimated by applying them to a set of specimens of presumably well-known composition

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