Imaging of internal stress around a mineral inclusion in a sapphire crystal: application of micro‐Raman and photoluminescence spectroscopy

We developed a micro‐Raman and photoluminescence imaging technique for visualizing the internal stress fields in a sapphire crystal. The technique was applied to an Australian sapphire gemstone with a zircon inclusion. Considering piezospectroscopic effects on Raman and photoluminescence spectra, the Raman shifts of sapphire around the zircon inclusion were converted to hydrostatic pressure and deviatoric components of stress tensor. The internal stress was highly concentrated at the tips of the zircon crystal, where the deviatoric stress and the hydrostatic pressure component reached 700 and 470 MPa, respectively. Generation of compressive stress on the crystal surface of zircon can be explained by the difference in thermal expansion coefficients and elastic constants between sapphire and zircon. In general, internal stress fields induced by mineral inclusions reflect the pressure and temperature conditions at which the host sapphire gemstones were crystallized. Thus, the present technique can be utilized to identify the origin of gemstones. Copyright © 2012 John Wiley & Sons, Ltd.     

Micro‐Raman analysis and finite‐element modeling of 3 C‐SiC microstructures

Micro‐ and nano‐electromechanical systems (MEMS and NEMS) fabricated in 3 C‐SiC are receiving particular attention thanks to the material physical properties: its wide band gap (2.3 eV), its ability to operate at high temperatures, its mechanical strength and its inertness to the exposure in corrosive environments. However, high residual stress (which is normally generated during the hetero‐epitaxial growth process) makes the use of 3 C‐SiC in Si‐based MEMS fabrication techniques very limited leading to a failure of micro‐machined/sensor structures. In this paper, micro‐Raman characterizations and finite‐element modeling (FEM) of microstructures realized on poly and single‐crystal (100) 3 C‐SiC/Si films are performed. Transverse optical (TO) Raman mode analysis reveals the stress relaxation on the free standing structure (796.5 cm⁻¹) respect to the stressed unreleased region (795.7 cm⁻¹). Also, microstructures as cantilever, bridge and planar rotating probe show an intense stress field located around the undercut region. Here, the TO Raman mode undergoes an intense shift, up to 2 cm⁻¹, ascribed to the modification of the Raman stress tensor. Indeed, the generalized axial regime, described by diagonal components of the Raman stress tensor, cannot be applied in this region. Raman maps analysis and FEM simulations show the ‘activation’ of the shear stress, i.e. non‐diagonal components of the stress tensor. The stress‐Raman modes shift correlation, in the case of fully non‐diagonal stress tensors, has been investigated. The aim of future works will be to minimize the stress field generation and the defects density within the epitaxial layer. Copyright © 2012 John Wiley & Sons, Ltd.     

Deviatoric stress and mean pressure in MgO compressed in a Kawai-type apparatus above 30 GPa: Evidence for reduction of deviatoric stress by annealing

By applying the numerical tensor analysis proposed by Yoneda and Kubo [Simultaneous determination of mean pressure and deviatoric stress based on numerical tensor analysis: a case study for polycrystalline X-ray diffraction of gold enclosed in a methanol-ethanol mixture. J. Phys.: Condens. Matter 18(2006)S979], we have determined deviatoric stress and mean pressure of polycrystalline MgO compressed in the Kawai-type apparatus. After the compression at room temperature, the mean pressure and the deviatoric stress in MgO were determined as 34.5 and 3.2 GPa, respectively. The mean pressure is significantly lower than the nominal pressure of 37.2 GPa determined by the conventional pressure determination method. By heating the sample to 1850 K with the constant press load, the deviatoric stress dramatically decreased to 0.1 GPa with a mean pressure of 34.2 GPa at room temperature after the heating. These results show both the importance of stress analysis to determine pressure more accurately and the effectiveness of annealing to reduce deviatoric stress in the sample.     

Poly(vinylpyrrolidone)‐stabilized silver nanoparticles for strained‐silicon surface enhanced Raman spectroscopy

Poly(vinylpyrrolidone)‐stabilized silver nanoparticles deposited onto strained‐silicon layers grown on graded Si_1−xGe_x virtual substrates are utilized for selective amplification of the Si–Si vibration mode of strained silicon via surface‐enhanced Raman scattering spectroscopy. This solution‐based technique allows rapid, highly sensitive and accurate characterization of strained silicon whose Raman signal would usually be overshadowed by the underlying bulk SiGe Raman spectra. The analysis was performed on strained silicon samples of thickness 9, 17.5 and 42 nm using a 488 nm Ar⁺ micro‐Raman excitation source. The quantitative determination of strained‐silicon enhancement factors was also made. Copyright © 2011 John Wiley & Sons, Ltd.     

Spatial anisotropy of linear electro-optic effect in crystal materials: I—Experimental determination of electro-optic tensor in LiNbO3 by means of interferometric technique

The paper presents a technique suitable for the determination of linear electro-optic effect (LEOE) tensor components in crystal materials of any symmetry. The method is based on the Michelson interferometer, where the sample being studied is set into one of its arms to measure the electro-induced changes of the optical path. We describe in detail the sample geometries that are needed to determine a complete set of the LEOE tensor components and derive the corresponding equations. The experimental technique has been tested and verified on lithium niobate crystals as well as applied to MgO-doped LiNbO₃ crystals to study their electro-optic properties. The developed method can be useful for optical engineering, which deals with new materials being used in design or production of devices, such as, e.g., modulators or deflectors.     

Reconstruction of the Green function in problems of resonance acoustic spectroscopy

A possibility for reconstruction of the Green function for a three-dimensional elastic body (resonator) is considered. The initial data are the elasticity tensor for the resonator material that is measured by the technique of resonance acoustic spectroscopy and its complex vibration response. Possibility for the response reconstruction and determination of the coordinates for a force source of vibration excitation according to the measured data is demonstrated. The difference between the measured and synthesized responses is small that provides an opportunity to perform continuous calibration of acoustic measurements and determine the distribution of stress and strain within a solid.     

Tensor field tomography of residual stresses

An approximate method is proposed for determining residual stresses in elonagted transparent articles featuring weak variation of the stress field along the axis. The proposed method is a generalization of the well-known method of determining internal stresses in optic fibers based on the integrated photoelasticity measurements. Complete determination of the stress tensor components is performed within the framework of the concept of temperature-dependent residual stresses.     

Experimental study of the Raman strain rosette based on the carbon nanotube strain sensor

This work presents a new technique named Raman strain rosette for the micro‐strain measurement of both Raman active and Raman inactive materials. The technique is based on the theoretical model of the carbon nanotube (CNT) strain sensor that applies the resonance and polarization Raman properties of CNTs and calculates the synthetic contributions of uniformly dispersed CNTs to the entire Raman spectrum. In our work, the proposed technique is applied in different experiments on the Raman inactive materials, such as step‐by‐step uniaxial tensile and Raman mapping around a circular hole. The experimental results reached by the Raman strain rosette are consistent with the actual values as a whole. This study verifies that the Raman strain rosette is applicable to quantitative measurement of all the in‐plane components of the strain tensor (including both normal and shear strains) by three polarized Raman detections for each sampling spot on a microscale. The technique is further applicable to achieving the strain fields through Raman mapping. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of the spherical tensor method for Two-Frequency pure NQR of spinI=1 nuclei

The results of a theoretical investigation of two-frequency excitation in pure nuclear quadrupole resonance (NQR) for a spinI=1 nucleus with a nonaxial elecric field gradient are presented. The multipole tensor operator technique is used for the treatment of the one- and two-frequency pulse excitations. The results are applied to the characterization of the two-frequency signal of nitrogen¹⁴N nuclei. The experiments on sodium nitrite, NaNO₂, confirm the presence of additional (two-frequency) echo in the NQR signal. The effect of resonance offsets on two-frequency NQR is also considered.     

Values and signs of the third order susceptibility coefficients in an isotropic transparent solid

We describe a method which enables, for the first time through a single measurements, the determination of the values and relative signs of the individual nonzero elements of the third order susceptibility tensor. It makes use of a three pulse transient phase grating technique operating in the Raman Nath regime. This technique is applied to a standard transparent optical glass; the adequacy of the Kleinman symmetry relation confirms the nonresonant character of the electronic nonlinear process involved.     

X‐ray nanotomography and focused‐ion‐beam sectioning for quantitative three‐dimensional analysis of nanocomposites

Knowing the relationship between three‐dimensional structure and properties is paramount for complete understanding of material behavior. In this work, the internal nanostructure of micrometer‐size (～10 µm) composite Ni/Al particles was analyzed using two different approaches. The first technique, synchrotron‐based X‐ray nanotomography, is a nondestructive method that can attain resolutions of tens of nanometers. The second is a destructive technique with sub‐nanometer resolution utilizing scanning electron microscopy combined with an ion beam and `slice and view' analysis, where the sample is repeatedly milled and imaged. The obtained results suggest that both techniques allow for an accurate characterization of the larger‐scale structures, while differences exist in the characterization of the smallest features. Using the Monte Carlo method, the effective resolution of the X‐ray nanotomography technique was determined to be ～48 nm, while focused‐ion‐beam sectioning with `slice and view' analysis was ～5 nm.     

The Casimir effect of Reissner-NordstrSm black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.     

Raman scattering characterization of vertical aligned 1D IrO2 nanocrystals grown on single crystal oxide substrates

Raman scattering (RS) has been used as a technique for characterization of IrO₂ one dimensional (1D) nanocrystals (NCs) deposited on sapphire(100) and LiNbO₃(100) substrates under various conditions. The IrO₂ NCs were grown via metalorganic chemical vapor deposition method using (MeCp)(COD)Ir as the precursor and reactive magnetron sputtering using Ir metal target. The red-shifts and asymmetric broadening of the Raman lineshape for the NCs were analyzed by a modified spatial correlation (MSC) model, which includes the factor of stress induced shift. The proposed MSC model showed that the effects of stress and nanometric size can be separated in analyzing the observed Raman features. The usefulness of the experimental RS together with the MSC model analysis as a residual stress and structural characterization technique for 1D NCs has been demonstrated.     

Thickness determination of gold layer on pre‐Columbian objects and a gilding frame,combining pXRF and PLS regression

In conservation, restoration and characterization studies of art and archaeological objects, the improvement of analytical techniques is a tendency. X‐ray fluorescence (XRF) is a versatile technique, and it has been widely used in the last decades for characterization of a great variety of materials (metals, glass, paints, inks, ceramics, etc.) applied to cultural heritage studies. Besides the chemical composition, it is possible to infer the layer thickness through XRF, enabling a general knowledge of the manufacturing techniques implemented by the culture of origin, as well as the association with the technological level reached for the production of each kind of artefact. The aim of this study is to introduce an alternative way for gold thickness determination of coatings in cultural heritage objects, combining portable XRF data and partial least square regression. As a case of study, we present the use of this methodology in portable XRF measurements performed in situ on a gilding frame in Brazil and in two pre‐Columbian artefacts from Chavin culture in Peru. Gold layers with thicknesses determined by Rutherford backscattering spectrometry (RBS) were used as standards to perform a calibration model and to check the methodology before its application to unknown artefacts. Copyright © 2016 John Wiley & Sons, Ltd.     

Sound velocity determination in gel-based emulsions

Sound velocity is a main parameter in non destructive characterization, closely related to the elastic properties and to the microstructure of heterogeneous materials.The accurate determination of the sound velocity using pulse-echo technique relies on the ability to reduce pulse distortion and to measure specimen dimensions with a high precision. In the field of bio-mimetic materials and biological tissues, the nature of the specimen makes this last requirement highly difficult or inappropriate.The present work, using a through-transmission configuration, allows, in a stress free environment, to access the sound velocity in soft, low acoustic contrast materials without requiring the specimen dimensions. The specimen sound velocity is obtained from the echo time-of-flights through a Z-scan process providing the absolute medium sound velocity as reference.The technique uses an excitation burst at a frequency below the transducer resonance to ensure a significantly reduction in pulse distortions and improve signal-to-noise ratio. The accurate determination of the echo time-of-flight relies on a highly efficient cross-correlation/Hilbert transform signal processing.The method has been applied to gel-based emulsions of different microstructures considered as biomimetic phantoms, as well as to their constituents: pure gelatin and vegetable oil.     

A Harmonic Map of Space-Time

In this paper, we study an n-dimensional space-time (M,g) with Einstein field equation and nondegenerate Ricci tensor. It is shown that taking the Ricci tensor \(\mathit{Ric}=\bar{g}\) as another semi-Riemannian metric on M, the identity map \(i:(M,g)\rightarrow ( M,\bar{g}) \) is a harmonic map. We also obtain a characterization of a vacuum using a differential equation satisfied by the electromagnetic stress tensor on space-time. In addition, we also show that if the Ricci tensor of (M,g) is parallel and the signatures of g and \(\bar{g}\) are same, then the semi-Riemannian manifold \(( M,\bar{g}) \) is an Einstein manifold.     

On the calculation of forces and total energy changes via the quantum mechanical stress field

Many-electron systems are within density functional theory described in terms of an appropriately defined local stress tensor. The differential equation for its exchange and correlation part is solved also for the case of density gradient dependent exchange and correlation energy. Formulae are given (i) for the direct calculation of the global stress tensor of a homogeneously strained crystal via surface integrals of the local stress tensor along intercell boundaries, and (ii) similarly for the energy change of inhomogeneously strained crystals.     

Second and fourth order stark shifts in the 6snd 1 D 2 barium rydberg series

Stark splittings of⁶ snd ¹ D ₂ Rydberg states were measured betweenn=10 and 24 by quantum beat spectroscopy at very low electric field strengths, allowing the determination of tensor polarizabilities and atn=14, 19, and 24 the determination of tensor hyperpolarizabilities. The irregular behaviour of the tensor polarizabilities was explained by Coulomb approximation calculations. The fourth order contributions to the Stark Hamiltonian were written as effective operators. Representation in spherical tensor form gives tensors of rank zero, two, and four. The associated scalar and tensor hyperpolarizabilities were derived. Using these formulae, theoretical values for the hyperpolarizabilities were calculated.     

Raman spectroscopy and polarization: Selected case studies

We show, through several selected case studies, the potential benefits that can be obtained by controlling the polarization states of the exciting and scattered radiations in a Raman scattering experiment. When coupled with polarization control, Raman spectroscopy is thus capable of providing extra information on the structural properties of the materials under investigation. The experimental examples presented in this work are taken from the area of both conventional, i.e., far-field, as well as from near-field Raman spectroscopy. They cover topics such as the stress tensor measurement in strained semiconductor structures, the vibration mode assignment in pentacene thin films and the Raman scattering tensor determination from near-field measurements on azobenzene monolayers. The basic theory necessary for modelling the far- and near-field polarized Raman responses is also given and the model efficiency is illustrated on the experimental data.     

Micro‐beam Laue alignment of multi‐reflection Bragg coherent diffraction imaging measurements

Multi‐reflection Bragg coherent diffraction imaging has the potential to allow three‐dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro‐crystals. Until now such measurements were hampered by the need for laborious, time‐intensive alignment procedures. Here a different approach is demonstrated, using micro‐beam Laue X‐ray diffraction to first determine the lattice orientation of the micro‐crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focused ion beam milled micro‐crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro‐crystals are now feasible and can be successfully carried out even in heavily distorted samples.