Modal resonant ultrasound spectroscopy for ferroelastics

Recent experimental and theoretical improvements of resonant ultrasound spectroscopy (RUS) are summarized to investigate elastic constants of phases in shape memory alloys. The proposed inversion procedure, described in this work, is particularly suitable to reliable evaluation of the temperature dependence of elastic constants of low-symmetry ferroelastic materials which may be strongly elastically anisotropic and tend to exist in twinned forms. The method is applicable even for the evaluation of single-crystal elastic constants from RUS measurements on microtwinned crystals, since it involves a homogenization algorithm based on the macroscopic deformation response of the layered structure. This potentially allows performing meaningful acoustic studies on samples with a general submicron-size layered structure.     

Sub-gigahertz laser resonant ultrasound spectroscopy for the evaluation of elastic properties of micrometric fibers

The cross-section eigenmodes of micrometric cylinders were measured in the range of several tens of MHz to about 0.5 GHz. The vibrations were excited using subnanosecond laser pulses. The cross-section eigenmodes were simulated using finite element modeling in a 2D geometry. Using the method of resonant ultrasound spectroscopy, the vibration spectrum of an aluminum wire of diameter 33μm served to determine Young’s modulus and Poisson’s ratio with a precision of 0.7% and 0.3%, respectively. The calculated and measured frequencies of cross-section eigenmodes were fitted with a precision better than 0.5% in the 50–500 MHz range.     

On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.     

Superradiance of the system comprised of two parallel resonant thin layers

A cavity-like regime of superradiance for a double-layer medium populated by atoms with the A-scheme of transitions is considered in a semiclassical approximation under the condition that the layers are arranged symmetrically with respect to initial characteristics of the field and atomic system populating the layers. An analytical law for the linear stage of the superradiance process is found that agrees well with numerical solution of the differential equations of the model under consideration for any initial conditions nearly up to the peak of the appropriate characteristic of the field intensity module. For the case of degenerate lower doublet, the resonant character of the dependence of the superradiance pulse time delay on the distance between the layers is studied.     

Optical and magneto-optical spectroscopy of thin composite GaAs-MnAs layers

Ellipsometric and magneto-optical investigations of MnAs layers and GaAs-MnAs composites obtained by laser deposition have been performed in the energy range 1.0–4.5 eV. The spectra of the equatorial Kerr effect (EKE) and the refractive and absorption indices have been studied. Diagonal and off-diagonal components of the dielectric tensor have been calculated. It is established that the shape of the EKE spectra of MnAs layers depends on the crystallographic orientation of these layers. Features near 1.9, 3, and 4 eV are distinguished in the energy dependences of the interband density of states of the layers; these features correspond to the energies of interband d-p transitions, obtained from calculations of the MnAs band structure.     

Optical and magneto-optical spectroscopy of thin ferromagnetic InMnAs layers

Spectral dependences of the refractive n(hν) and absorption k(hν) indices (hν= 1.2–4.4 eV) and the magneto-optical constant δ(hν) (hν = 0.5–4.4 eV) of the transverse Kerr effect of the InMnAs layers produced by laser deposition have been studied. The spectra of the diagonal ?(hν) and off-diagonal ?′hν) components of the permittivity tensor of the layers have been found. A comparison of the spectral dependences δ(hν), ?′(hν) and ?′₂ × (hν)² of the InMnAs and MnAs layers have been performed. Features in the spectra of the InMnAs layers have been attributed to a competition between the contributions of the In_{1 ? x} Mn _x As matrix and MnAs inclusions.     

Cavity ring-down spectroscopy of molecularly thin iodine layers

Cavity ring-down spectroscopy (CRDS) has so far mostly been used for measurements in the gas phase. Only in 1999 was a first spectrum of condensed phase published. This spectrum was measured by using a coated plate between the cavity mirrors. Rather than using this method, our measurements were made using the cavity mirrors as a substrate. This way, the scattering losses could be reduced by approximately a factor of 100. In our measurements we investigated molecularly thin layers of iodine. The iodine spectra were taken in the frequency range from 16200 to 17200 cm^-1 using pulsed CRDS. Received: 14 April 2000 / Revised version: 26 July 2000 / Published online: 22 November 2000     

Boundary problems for polariton propagation in thin layers and quantum wells

Summary We show how to compute the optical functions (reflection and transmission) of a semiconductor thin slab, in the vicinity of nearly degenerate exciton states. Additional boundary conditions are not required in the coherentwave-function approach and multiple-polariton effects are included since Maxwell equations are satisfied. When the slab thickness is comparable to the exciton Bohr radius, centre of mass quantization results. When the slab thickness is smaller than the Bohr radius, we obtain, quantum well polaritons. Numerical examples appropriate to GaAs are given.     

Sensitivity of the resonant ultrasound spectroscopy to weak gradients of elastic properties

The applicability of resonant ultrasound spectroscopy on materials with weak spatial gradients in elastic coefficients and density is analyzed. It is shown that such gradients do not affect measurably the resonant spectrum but have a significant impact on the modal shapes. A numerical inverse procedure is proposed to explore the possibility of reconstructing the gradients from experimentally obtained modal shapes. This procedure is tested on synthetic data and applied to determine the gradient of the shear modulus in a continuously graded silicon nitride ceramic material. The results are in a good agreement with the gradient calculated for the examined material theoretically as well as with the results of other experimental methods.     

Account for the wedgeness and inhomogeneity of thin layers in the inverse problem of spectrophotometry on reflection

General formulas for reflectance of a weakly or moderately absorbing tapered layer and a layer with a linear dependence of the complex dielectric constant on the thickness, which are located on an absorbing substrate, are derived. Based on these formulas, a method for determining the optical constants, their dispersion, and the layer thickness from the envelopes of the extrema in the interference reflection spectrum is constructed, which generalizes the method proposed previously for homogeneous absorbing films.     

Orbital specificity in the unoccupied states of UO2 from resonant inverse photoelectron spectroscopy

One of the crucial questions of all actinide electronic structure determinations is the issue of 5f versus 6d character and the distribution of these components across the density of states. Here, a breakthough experiment is discussed, which has allowed the direct determination of the U5f and U6d contributions to the unoccupied density of states in uranium dioxide. A novel resonant inverse photoelectron and x-ray emission spectroscopy investigation of UO(2) is presented. It is shown that the U5f and U6d components are isolated and identified unambiguously.     

Determination of elastic moduli of rock samples using resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) is a method whereby the elastic tensor of a sample is extracted from a set of measured resonance frequencies. RUS has been used successfully to determine the elastic properties of single crystals and homogeneous samples. In this paper, we study the application of RUS to macroscopic samples of mesoscopically inhomogeneous materials, specifically rock. Particular attention is paid to five issues: the scale of mesoscopic inhomogeneity, imprecision in the figure of the sample, the effects of low Q, optimizing the data sets to extract the elastic tensor reliably, and sensitivity to anisotropy. Using modeling and empirical testing, we find that many of the difficulties associated with using RUS on mesoscopically inhomogeneous materials can be mitigated through the judicious choice of sample size and sample aspect ratio.     

Analytical techniques for addressing forward and inverse problems of light scattering by irregularly shaped particles

Understanding light scattering by nonspherical particles is crucial in modeling the transport of light in realistic structures such as biological tissues. We report the application of novel analytical approaches based on modified Wentzel-Kramers-Brillouin and equiphase-sphere methods that facilitate accurate characterization of light scattering by a wide range of irregularly shaped dielectric particles. We also demonstrate that these approaches have the potential to address the inverse-scattering problem by means of a spectral analysis of the total scattering cross section of arbitrarily shaped particles.     

Carbon nanotube bundles and thin layers probed by micro-Raman spectroscopy

Raman spectra of single-wall carbon nanotubes (CNTs) either in the form of micrometer sized bundles or thin layers prepared by dilution and sonication of powders have been compared. We have been able to collect the Raman spectrum of nanotube bundles that are not in touch with the substrate, and therefore not affected by interactions with the substrate surface. This spectrum resulted to be similar to that of the precursor nanotube powders, whereas relevant changes in the Raman spectrum are detected when the diluted powders form very thin layers on either metallic or insulating surfaces, as probed by confocal microraman imaging on well defined areas of the CNTs layers. In the case of thin layers, the intensity of the Raman D band, detected between 1 320 and 1 340 cm^-1 and ascribed to disorder effects, is strongly enhanced. This enhancement occurs independently on the kind of substrate. Received 2 September 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: sangalet@dmf.bs.unicatt.it     

Features of the surface layers of TiNi-based alloy thin ribbons

The chemical composition of the surface of TiNi-based alloys in the form of ribbons produced by rapid melt quenching in oxygen-containing environment has been investigated. It is shown that titanium oxide is formed on the Ti₅₀Ni₂₅Cu₂₅ alloy surface, while on the Ti_39.2Ni_24.8Cu₂₅Hf₁₁ alloy surface titanium and hafnium oxides are formed. Atomic-force microscope images reveal crystalline structures of titanium oxide with sizes of up to 500 × 500 nm² on the surface of the Ti₅₀Ni₂₅Cu₂₅ sample. After removing the surface oxide layer by ion etching, the ratio of elements becomes close to the stoichiometric composition.     

Measuring elastic constants of arbitrarily shaped samples using resonant ultrasound spectroscopy

One of the most important undertakings for materials is the measurement of the elastic behavior. As derivatives of the free energy with respect to atomic displacements, the elastic properties are closely connected to the thermodynamic properties of the material. Elastic behavior is a sensitive probe of the lattice environment in which all solid state phenomena occur, particularly in the vicinity of a phase transition. A useful method for measuring elastic properties is resonant ultrasound spectroscopy (RUS). Some novel materials to which RUS might be applied are often fragile or chemically reactive so that they cannot be polished into the shapes required by conventional RUS; for such cases a finite element method may be used. In this paper a discussion and test of a finite element method for RUS with arbitrarily shaped samples is provided.     

The detection of thin embedded layers using normal incidence ultrasound

A theoretical investigation of the use of normal incidence ultrasonic reflection measurements for the detection and characterization of thin layers embedded between two much thicker media has been carried out. It has been shown that the form of the relationship between the normal incidence longitudinal reflection coefficient and frequency is defined by the reflection coefficients at zero frequency and at half the resonance frequency of the layer. The reflection coefficient at zero frequency is solely a function of the impedances of the media on either side of the layer, while that at half the resonance frequency of the layer is a function of the impedances of all three media. In general, the sensitivity of the reflection coefficient to the presence of the layer increases as the product of frequency and layer thickness increases, the maximum sensitivity being at half the resonance frequency of the layer. Unfortunately, with thin layers, it is generally not practical to test at this frequency. However, the reflection coefficient curve can, in principle, be reconstructed from data measured at lower frequencies and the sensitivity of the reflection coefficient at lower frequencies to the characteristics of the layer can be predicted from the sensitivity at half the resonance frequency. The sensitivity is also critically dependent on the relative impedances of the three media and is generally greatest when the half spaces on either side of the layer have the same impedance. With favourable impedances, it is possible to detect layers whose thickness is a small fraction of the wavelength of the ultrasonic waves employed. However, with other combinations of impedances, the detection of much thicker layers is not possible.     

Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers

We present a method using attenuated total reflection (ATR) with excitation of surface plasma waves at different wavelengths and angles of incidence, which allows an accurate determination of the thickness and optical constants of absorbing surface layers from optical measurements only. This method is applied to the case of very thin Au surface layers on (111)Ag, and the results are discussed.     

X-ray photoelectron spectroscopy possibilities for analyzing the structural state of thin layers of oxide nanomaterials

A method is developed that enables us to enhance the capabilities of photoelectron spectroscopy to obtain data on the atomic structure of thin layers of oxide materials.