Probe Response Function Research Articles

Interval inversion as innovative well log interpretation tool for evaluating organic-rich shale formations

The identification and detailed evaluation of unconventional hydrocarbon reservoirs require the application of advanced well logging data processing techniques. Since the number of the petrophysical properties such as porosity, water and hydrocarbon saturation, kerogen content, and fractional volumes of matrix components may exceed that of the observed wireline log types, currently used quick-look methods based on few well logs provide approximate solution to a part of the above petrophysical quantities. For instance, Passey's method basically utilizes two well logs for identifying the sweet spots and estimating the total organic content (TOC). Local inversion techniques estimating the petrophysical parameters in a given depth are also limited because of low overdetermination (data-to-unknowns) ratio and hence are very sensitive to data noises. Instead of using traditional empirical methods and to avoid ambiguous solutions by local inversion evaluations, data of all wireline logs measured in a longer depth interval are simultaneously inverted to give more accurate estimate to the petrophysical parameters in a highly overdetermined inverse problem. The suggested interval inversion approach allows the determination of the fractional volumes of rock constituents with their estimation errors in a joint inversion procedure. As part of the inversion process, the forward problem is improved by using kerogen and pyrite effects corrected probe response functions. Synthetic modeling tests are made to detect the noise sensitivity and outlier resistance of the proposed inversion algorithm, while a float-encoded genetic algorithm variant of the interval inversion method is applied to invert real data measured in an organic-rich shale reservoir in Alaska, USA. The feasibility is demonstrated by a well agreement between the inversion derived TOC values and those of measured on core samples. The interval inversion method not only works reliably in the presented shale gas formations, but it can be extended to evaluating other types of unconventional reservoirs.

Indentation residual stresses in soda-lime and borosilicate glasses

Residual stress measurements by fluorescence microscopy is a well-established technique which uses the R1 and/or R2 fluorescence peaks of Cr+3 ions in Al2O3. These peaks are sensitive to the distortion of the lattice and their position changes if the crystal is stressed. Borosilicate (BS) and soda-lime (SL) composites with 10 vol% Al2O3 were produced mixing the glass and alumina powders, uniaxially compressed and sintered at high temperature. Surface morphology and microstructure were characterized by optical and scanning electron microscopies. The porosity obtained was <2%. 10 N Vickers indentations were performed and the stresses around the indentations were measured by fluorescence microscopy. Measurements of residual stresses, due to thermal expansion mismatch between the glass matrix and the Al2O3, were 163 MPa and −35 MPa for BS and SL composites samples, respectively, in agreement with Hseuh & Becher's model. The probe response function was fitted to the fluorescence data taking into account the iteraction of the laser beam within the sample and effects of light absorption, refraction and scattering by alumina particles and pores, and stresses gradients. The experimental fluorescence shift as a function of the distance from the indentations was compared with Yoffe's model and the PRF function. It was found that the experimental blister field strength is a factor of 10 smaller than that predicted by Yoffe's model, taking into account the densification of the glass underneath the indenter. Indentation residual stresses were also measured for SL glass using the modified Zeng and Rowcliffe's model. Stress profiles were measured around 50 N and 100 N Vickers indentations performed between −196 °C to 400 °C. The blister field strength increased with temperature and it could be explained by the variation of the E/H ratio with temperature. This work contributes for the understanding of the mechanisms responsible for the indentation residual stresses in glasses.

Compensating the asymmetric probe response in broad MAS NMR spectra of quadrupolar nuclei

The spinning sidebands envelope of satellite transitions often display an asymmetric shape, which is caused by an asymmetric response of the NMR probe circuit. In this work, we revisit the basic concepts of the RLC circuit at the heart of every NMR probe and present two approaches capable of minimizing this artifact. While the first one consists of deliberately mistuning the probe, the second one relies on measuring the probe's response function and deconvoluting its contribution from the spectra. Both approaches are validated with 23Na NMR spectra of a lead-free relaxor ferroelectric (BNT-1BT). This material is particularly suitable as an example of the applicability of both strategies for samples with a disordered local structure.

Imaging of electric and magnetic fields near plasmonic nanowires.

Near-field imaging is a powerful tool to investigate the complex structure of light at the nanoscale. Recent advances in near-field imaging have indicated the possibility for the complete reconstruction of both electric and magnetic components of the evanescent field. Here we study the electro-magnetic field structure of surface plasmon polariton waves propagating along subwavelength gold nanowires by performing phase- and polarization-resolved near-field microscopy in collection mode. By applying the optical reciprocity theorem, we describe the signal collected by the probe as an overlap integral of the nanowire’s evanescent field and the probe’s response function. As a result, we find that the probe’s sensitivity to the magnetic field is approximately equal to its sensitivity to the electric field. Through rigorous modeling of the nanowire mode as well as the aperture probe response function, we obtain a good agreement between experimentally measured signals and a numerical model. Our findings provide a better understanding of aperture-based near-field imaging of the nanoscopic plasmonic and photonic structures and are helpful for the interpretation of future near-field experiments.

In situ measurements of local temperature and contact stress magnitude during wear of ceramic-on-ceramic hip joints

Fluorescence microprobe spectroscopy was applied to in situ assessments of contact stress and local temperature at the contact point of dry-sliding couples during wear tests of two commercially available ceramic-on-ceramic femoral heads. The investigated ceramic hip implants consisted of either monolithic Al2O3 or Al2O3/ZrO2 composite. A specially designed pin-on-ball tribometer was employed, which enabled directly testing the femoral head components as received from the maker without further manipulation. The strong fluorescence emission from Cr3+ impurities contained in Al2O3 served as a responsive sensor for both temperature and stress. Analytical corrections for the averaging effects arising from the finite size of the laser probe were made according to a probe response formalism in which geometrical conditions of the sliding couple were incorporated as boundary conditions. The sample-probe interaction at the contact point was then experimentally calibrated by obtaining probe response functions for the two materials investigated. Based on such theoretical and experimental procedures, deconvolutive computational routines could be set up and the true variations of local temperature and stress at the contact point of the bearing surfaces retrieved from the observed time-dependent broadening and shift of a selected spectral band, respectively. The main result of the in situ investigation was that the monolithic sliding couple showed both significantly lower temperature and lower magnitude of compressive stress at the contact point as compared to the composite one, although the composite couple wore at a significantly lower specific wear rate than the monolithic one.

Studying Single Red Blood Cells Under a Tunable External Force by Combining Passive Microrheology with Raman Spectroscopy

The dynamic micromechanical and structural properties of single human red blood cells are studied using a combination of dual trap optical tweezers and confocal Raman spectroscopy. Such a combination permits us to show a direct relationship between the rheological properties and chemical structure conformation. The frequency dependence of the complex stiffness of the cells was measured using both one and two probe response functions under identical experimental conditions. Both the microrheology and Raman measurements were performed at different stretching forces applied to the cell. A detailed analysis of the auto- and cross-correlated probe motions allows exploring the local and overall viscoelastic properties of the cells over a controlled range of the deformations. The observed growth of the cell viscoelasticity with stretching was associated with structural changes in the cell membrane monitored via the Raman spectroscopy.

Interval inversion of well-logging data for automatic determination of formation boundaries by using a float-encoded genetic algorithm

In the paper a real-valued genetic algorithm is presented for solving the non-linear well-logging inverse problem. The conventional way followed in the interpretation of well-logging data is the formulation of the inverse problem in each measuring point separately. Since barely less number of unknowns than data are estimated to one point, a set of marginally overdetermined inverse problems have to be solved, which sets a limit to the accuracy of estimation. Describing the petrophysical (reservoir) parameters in the form of series expansion, we extend the validity of probe response functions used in local forward modeling to a greater depth interval (hydrocarbon zone) and formulate the so-called interval inversion method, which inverts all data of the measured interval jointly. Assuming an interval-wise homogeneous petrophysical parameter distribution, significantly smaller number of unknowns than data have to be determined. The highly overdetermined inverse problem results in accurate and reliable estimation of petrophysical parameters given for the whole interval instead of separate measuring points. For measuring the storage capacity of the reservoir, the formation thickness is also required to be estimated. As a new feature in well logging inversion methodology, the boundary coordinates of formations are treated as new inversion unknowns and determined by the interval inversion method automatically. Instead of using traditional linear inversion techniques, global optimization is used to avoid problems of linearization related to the determination of formation thicknesses. In the paper, synthetic and field examples are shown to demonstrate the feasibility of the interval inversion method.

Spatially resolved Raman and cathodoluminescence probes in electronic materials: Basics and applications

AbstractSpatially resolved spectroscopy of both Raman and cathodoluminescence (CL) emissions represent a quite powerful characterization method in electronics. In this paper, the underlying physics that dictates the different characteristics of Raman and CL probes is revisited, deepened, and further interpreted in order to clarify how the different nature of those probes enables one bringing about different sets of complementary information. Furthermore, it is inquired into the causes for which data collected by the two different spectroscopic methods on the same material or device may, at a first glance, appear inconsistent to each other and, for some aspects, contradictory. Such differences and contradictions are then shown to disappear once the different nature of the two probes, especially with respect to their spatial response and morphology, is clarified and properly taken into account. Emphasis is finally placed on quantitatively describing the spatial response of Raman and CL probes and to apply such knowledge to elucidate the behavior of electronic materials. The two types of light emission are described according to a common formalism, which details their respective probe response functions in the three‐dimensional space. Practical applications of Raman and CL spectroscopy to resolve highly graded fields of crystal orientation and elastic stress/strain in paradigm electronic materials are finally shown and compared.

Quantitative evaluation of probe response functions for Raman and fluorescence bands of single-crystalline and polycrystalline Al2O3

The probe response functions of Raman and fluorescence bands of single-crystalline sapphire and polycrystalline Al2O3 with different grain sizes were systematically evaluated and compared. As a general issue, it was found that the probe response function strongly depended on the selected signal and, more importantly, on grain size. From a comparison between the probe characteristics of Raman and fluorescence bands, the following characteristics could be found: (i) the probe depth of the Raman bands of sapphire single-crystal (the main band at 417 cm−1 was selected as a paradigm Raman sensor) was about a half that of the Cr3+ fluorescence doublet (a direct comparison was made with the R1 band located at 14 405 cm−1); (ii) the probe depth in polycrystalline Al2O3 decreased with decreasing grain size. In this latter case, the probe depth of the R1 band could be up to >10 times larger than that of the 417 cm−1 Raman band, the difference in depth increasing with decreasing grain size. These large differences in probe geometry need to be taken into consideration when applying spectroscopy methods as, for example, piezo-spectroscopic stress assessments. Nevertheless, the results of this investigation suggest that a noticeable improvement in the in-depth spatial resolution can be obtained using Raman rather than fluorescence bands as stress probes for assessing high property gradients present in the materials.

Confocal fluorescence microscopy in alumina-based ceramics: Where does the signal come from?

Confocal Cr 3+ fluorescence microscopy is an ideal technique for investigating residual stresses in alumina-based ceramics. Due to their transparency, however, it is important to understand where the collected signal comes from by characterising the probe response function (PRF). Here, a PRF is proposed that captures all the relevant physical effects, including a newly identified consequence of scattering by pores and grain boundaries. The new PRF describes the response of a range of alumina-based ceramics to depth scanning in a high resolution confocal fluorescence microscope in a manner that balances physical significance with the accuracy of empirical fitting. The results showed that measurements could be made deep within single crystals of sapphire and ruby, although refraction degraded the depth resolution from about 3 μm at the surface to 25 μm at a depth of 500 μm. Scattering and absorption limited the depth to which polycrystalline alumina could be probed to ∼15 μm. This was further reduced to ∼4 μm for an alumina–10 vol.% SiC nanocomposite. However, the absorption increased the accuracy of near surface measurements in these materials by preventing contamination from subsurface fluorescence.

Non-destructive three-dimensional Raman analysis of domain orientation in barium titanate single-crystal

Ferroelectric domain orientation in barium titanate (BaTiO 3; BT) single-crystal has been investigated with respect to its geometrical distribution in the solid angle by using polarised Raman spectroscopy. After retrieving the angular dependence of the intensity of selected Raman modes of BT and their defocusing properties at selected laser wavelength (in-depth probe response function), both in-plane and out-of-plane domain fractions could be visualised and mapped with microscopic resolution by Raman spectroscopic assessments. It is demonstrated that polarised Raman spectroscopy is a valuable and efficient tool for fully 3D, non-destructive assessments of domain orientation in ferroelectrics.

Stress Perturbation Method for the Assessment of Cathodoluminescence Probe Response Functions

A method to determine the in-plane cathodoluminescence (CL) probe response function (PRF) (i.e., the function characterizing the in-plane luminescence intensity distribution within the electron probe volume) is proposed, which is based on "perturbing" the spectral position of a selected luminescence band using a highly graded stress field. The method is applied to the stress field developed ahead of the tip of an equilibrium crack in three different cases of CL bands, which arise from different structural phenomena: (i) the F(+) (oxygen excess) defect band in a nominally stoichiometric sapphire (alpha-Al(2)O(3)) single crystal; (ii) the chromophoric R-line in ruby lattice (alpha-Al(2-x)Cr(x)O(3)); and (iii) the near band-gap line in n-type GaN semiconductor crystal. A computer-aided data restoration procedure was applied to rationalize data retrieved from crack-tip line scans performed at different acceleration voltages. For the excitonic band-gap in GaN and for F(+) emission in sapphire the CL probe in the electron focal plane was found to be comparable, but not necessarily coincident, in size to the electron probe. On the other hand, the occurrence of self-absorption in the case of R-line photons in ruby resulted in a significantly broadened CL probe with respect to the average scattering length of electrons.

Spatially resolved Raman piezo‐spectroscopic stress analysis in CaMoO4 thin film grown on Si substrate

AbstractConfocal piezo‐spectroscopy was applied to analyze the residual stress distribution developed in a CaMoO4‐film/Si‐substrate system, based on the spectroscopic shift upon stress of the 879 cm–1 Ag Raman mode of CaMoO4. In the stress characterization, use was made of spectral line scans, as well as laser defocusing measurements. A preliminary spectroscopic calibration of the Raman band was performed with using a ball‐on‐ring flexural bending jig. As a result, a value of –1.4 cm–1/GPa was found for the biaxial piezo‐spectroscopic coefficient of the Ag Raman mode of CaMoO4. A probe deconvolution procedure was introduced in the effort to correct the convoluting effect due to the finite size of the laser probe, taking advantage of the measurement of the probe response function. A theoretical analysis of the edge‐stress effect was then carried out and, accordingly, the actual in‐depth stress distribution was deduced from the observed spectral variation. Compressive residual stresses appeared on the CaMoO4 film side, while tensile residual stress occurred in the silicon substrate, and both stress magnitudes pronouncedly decreased with increasing distance from the interface. The results indicated relief in lattice mismatch in the epilayer, and such a relaxation mechanism was discussed in the paper. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A photo-stimulated spectroscopic method for spatially resolved stress analysis in hetero-epitaxial films

In this paper, we have developed a laser-stimulated piezo-spectroscopic method for high-resolution stress analysis in ceramic thin films and coatings, with emphasis placed on correcting the convoluting effect arising from the finite size of the laser probe. A series of 3C–SiC/Si and Al2O3/Si3N4 samples were employed for this purpose, with various film thicknesses and substrate orientation as well. In-depth defocusing scans of selected spectral bands arising from both Raman scattering and fluorescence emission were collected. According to a quantitative measurement of the luminescence/Raman probe response function for each material investigated, a spatial probe deconvolution was carried out, from which the actual residual stress distributions could be retrieved by using a computer-aided data restoration procedure. The validity of the proposed methodology was confirmed by using different spectral stress sensors and by altering the collection configuration. The results show that with the aid of a probe deconvolution procedure, spatially resolved stress analyses can be experimentally carried out, thus greatly reducing the error involved in the averaging effect of the laser probe.

Spatially resolved crack-tip stress analysis in semiconductor by cathodoluminescence piezospectroscopy

A spatially resolved cathodoluminescence piezospectroscopic analysis is attempted for the high-resolution evaluation of the stress field developed ahead of the tip of an equilibrium crack propagating in a semiconductor. GaN was selected for this assessment as a paradigm semiconductor material. Quantitative measurements of in-plane luminescence probe response function (PRF) were preliminarily performed at different acceleration voltages upon scanning across a straight and atomically sharp interface between GaN and gold metal. Then, based on the knowledge of PRF, the convoluting effect due to the finite size of the electron probe could be corrected and an improved plot of the crack-tip stress field could be retrieved by a computer-aided data restoration procedure. The crack-tip stress intensity factor KI obtained by the cathodoluminescence piezospectroscopic method was compared with that obtained on the same crack path according to high-resolution measurements of crack-tip opening displacement. This study not only shows that a nanometer-scale spatial resolution can be experimentally achieved in a stress analysis of semiconductor materials but also that a stress data treatment based on experimental PRF is a viable approach to greatly reduce the error involved with the finite size of the electron probe.

Stress microscopy and confocal Raman imaging of load-bearing surfaces in artificial hip joints

Confocal Raman microprobe spectroscopy is a technique with considerable potential in biomedical science owing to its ability to nondestructively scan samples in 3D with high spatial resolution and to precisely characterize the chemical, physical and mechanical characteristics of biomaterials at their molecular scale. Beyond the capacity of other conventional assessments of biomaterial oxidation state, crystalline and phase fractions, Raman and luminescence techniques can be used for assessing residual stress fields in artificial hip joints. Provided that the probe response function characterizing the probe/biomaterial interaction is known, 3D residual stress fields can be determined precisely with high axial and lateral resolution.

Raman piezospectroscopic evaluation of intergrowth ferroelectric polycrystalline ceramic in biaxial bending configuration

The piezospectroscopic (PS) effect was studied in an intergrowth bismuth layer-structure ferroelectric ceramic Bi5TiNbWO15 according to a micro-Raman spectroscopic evaluation. By using a ball-on-ring flexure configuration, a biaxial stress was generated in a Bi5TiNbWO15 plate-like specimen and in situ collected Raman spectra were acquired and analyzed under several loading conditions. As the observed spectral line contained signals arising from the whole illuminated in-depth region, the laser probe information was deconvoluted (by means of an in-depth probe response function obtained according to the defocusing method) in order to deduce biaxial PS coefficients for the three Raman bands of Bi5TiNbWO15 located at 763, 857, and 886 cm−1, respectively. The biaxial PS coefficients of these bands were derived to be −1.74±0.16, −2.51±0.16, and -2.64±0.31 cm−1/GPa, respectively, and should be referred to the c axis of the Bi5TiNbWO15 crystal.

In-depth analysis of residual stress in an alumina coating on silicon nitride substrate using confocal Raman piezo-spectroscopy

Confocal Raman piezo-spectroscopy was applied to the non-destructive evaluation of residual stresses as they develop in a chemical-vapor-deposited Al 2O 3 coating on a Si 3N 4 ceramic substrate. According to a selected confocal configuration of the optical probe, with its focal plane set to in-depth scan the sample, the residual stress could be measured at various depths along the thickness of both coating and substrate. The residual stresses stored in the Al 2O 3 coating layer were measured using both the Cr 3+ fluorescence band, located at 14,400 cm −1 (R 1), and the Al 2O 3 Raman band at 417 cm −1. When the R 1 fluorescence band was used, no variation could be resolved for the residual stress along the coating depth direction; in contrast, a clear in-depth stress distribution was observed when the 417 cm −1 Raman band was used. The minimum stress magnitude was located at the coating external surface and the maximum at the coating/substrate interface. Given the high transparency of the Al 2O 3 coating, the residual stress field stored within the Si 3N 4 substrate could also be measured as a function of depth (according to the piezo-spectroscopic shift of the 206 cm −1 Raman band of Si 3N 4). A deconvolution procedure of confocal spectra was proposed, which is based on the knowledge of the probe response functions of both coating and substrate materials. Laser probe deconvolution enabled us to retrieve the actual in-depth stress distribution from the stress distribution experimentally observed by defocusing experiments.

Confocal Raman spectroscopic analysis of cross-linked ultra-high molecular weight polyethylene for application in artificial hip joints

Confocal spectroscopic techniques are applied to selected Raman bands to study the microscopic features of acetabular cups made of ultra-high molecular weight polyethylene (UHMWPE) before and after implantation in vivo. The micrometric lateral resolution of a laser beam focused on the polymeric surface (or subsurface) enables a highly resolved visualization of 2-D conformational population patterns, including crystalline, amorphous, orthorhombic phase fractions, and oxidation index. An optimized confocal probe configuration, aided by a computational deconvolution of the optical probe, allows minimization of the probe size along the in-depth direction and a nondestructive evaluation of microstructural properties along the material subsurface. Computational deconvolution is also attempted, based on an experimental assessment of the probe response function of the polyethylene Raman spectrum, according to a defocusing technique. A statistical set of high-resolution microstructural data are collected on a fully 3-D level on gamma-ray irradiated UHMWPE acetabular cups both as-received from the maker and after retrieval from a human body. Microstructural properties reveal significant gradients along the immediate material subsurface and distinct differences are found due to the loading history in vivo, which cannot be revealed by conventional optical spectroscopy. The applicability of the confocal spectroscopic technique is valid beyond the particular retrieval cases examined in this study, and can be easily extended to evaluate in-vitro tested components or to quality control of new polyethylene brands. Confocal Raman spectroscopy may also contribute to rationalize the complex effects of gamma-ray irradiation on the surface of medical grade UHMWPE for total joint replacement and, ultimately, to predict their actual lifetime in vivo.

Electron probe response function and piezo-spectroscopic behaviour of semiconductor materials in presence of highly graded stress fields

The response function of the electron probe and the stress dependence of cathodoluminescence spectra emitted by selected semiconductor materials have been evaluated by scanning across sharp bi-material interfaces and along highly graded residual stress fields generated at the tip of an equilibrium crack, respectively. These microscopic procedures can be made fully quantitative provided that the crack opening displacement of the investigated crack is preliminarily measured in a scanning electron microscope for an in situ estimate of the crack-tip stress intensity factor. Taking advantage of the high scanning flexibility of the electron probe, capable of nanometric lateral displacements, spectral shifts typical of the K-dominated zone along the axis of crack propagation were recorded as a function of distance from the crack-tip. A plot of equi-biaxial stress versus spectral band shift was then obtained whose slope represents the piezo-spectroscopic coefficient of the selected material band. A theoretical analysis was attempted to analyse the in-plane interaction between sample and electron probe and to put forward suitable conditions for a reliable assessment of highly graded stress fields. Conditions were worked out into generalized plots as a function of spectroscopic and mechanical parameters for GaN, 3C–SiC and GaAs, as paradigm semiconductor materials.