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.     

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.     

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.     

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.     

Linearized forward and inverse problems of the resonant ultrasound spectroscopy for the evaluation of thin surface layers

In this paper, linearized approximations of both the forward and the inverse problems of resonant ultrasound spectroscopy for the determination of mechanical properties of thin surface layers are presented. The linear relations between the frequency shifts induced by the deposition of the layer and the in-plane elastic coefficients of the layer are derived and inverted, the applicability range of the obtained linear model is discussed by a comparison with nonlinear models and finite element method (FEM), and an algorithm for the estimation of experimental errors in the inversely determined elastic coefficients is described. In the final part of the paper, the linearized inverse procedure is applied to evaluate elastic coefficients of a 310 nm thick diamond-like carbon layer deposited on a silicon substrate.     

Wood elastic characterization from a single sample by resonant ultrasound spectroscopy

The goal of this paper is to propose an experimental method allowing the identification of the complete elastic tensor of anisotropic biological materials such as wood using only one sample. To do so, two complementary methods are used. First, the wood eigen-directions are defined from a sample of spherical shape that is then cut into a cube in a way to perform resonant ultrasound spectroscopy (RUS). The method is successfully applied on a reference beech sample with known orthotropic directions. A comparison of the identified elastic constants with those from the literature and some inferred from ultrasonic transmission measurements is given.     

Applying nonlinear resonant ultrasound spectroscopy to improving thermal damage assessment in concrete

Nonlinear resonant ultrasound spectroscopy (NRUS) consists of evaluating one or more resonant frequency peak shifts while increasing excitation amplitude. NRUS exhibits high sensitivity to global damage in a large group of materials. Most studies conducted to date are aimed at interrogating the mechanical damage influence on the nonlinear response, applying bending, or longitudinal modes. The sensitivity of NRUS using longitudinal modes and the comparison of the results with a classical linear method to monitor progressive thermal damage (isotropic) of concrete are studied in this paper. In addition, feasibility and sensitivity of applying shear modes for the NRUS method are explored.     

Some aspects of the use of hot hollow cathodes in emission spectroscopy

Methods of introducing the sample are considered, together with the causes of instability in hollow-cathode discharges. It is found to be possible to reduce cathode sputtering.     

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone

Nonlinear resonant ultrasound spectroscopy (NRUS) is a resonance-based technique exploiting the significant nonlinear behavior of damaged materials. In NRUS, the resonant frequency(ies) of an object is studied as a function of the excitation level. As the excitation level increases, the elastic nonlinearity is manifest by a shift in the resonance frequency. This study shows the feasibility of this technique for application to damage assessment in bone. Two samples of bovine cortical bone were subjected to progressive damage induced by application of mechanical cycling. Before cycling commenced, and at each step in the cycling process, NRUS was applied for damage assessment. For independent assessment of damage, high-energy x-ray computed tomography imaging was performed but was only useful in identifying the prominent cracks. As the integral quantity of damage increased, NRUS revealed a corresponding increase in the nonlinear response. The measured change in nonlinear response is much more sensitive than the change in linear modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work must be carried out for a better understanding of the physical nature of damaged bone and for the ultimate goal of the challenging in vivo implementation of the technique.     

Two-color photoionization spectroscopy of uranium in a U–Ne hollow cathode discharge tube

A U–Ne hollow cathode discharge tube is used as a source of uranium atomic vapors as well as a photoelectron/photoion detector for carrying out two-color three-photon photoionization spectroscopy of uranium. Using the uranium excitation transition 0 cm⁻¹ (⁵L ₆ ⁰ ) → 16 900.38 cm⁻¹ (⁷M₇) at 591.5-nm laser wavelength as a first step transition and scanning the wavelength of a second laser from 558 to 568 nm, high-lying odd-parity atomic levels of uranium are studied in the energy region 34 500–34 813 cm⁻¹. All the expected 21 odd-parity atomic levels identified by various researchers in this region are observed in a single spectrum, demonstrating the high sensitivity achieved therein. In addition to this, we have identified eight autoionization resonances of uranium starting from its odd-parity atomic level at 33 801.06 cm⁻¹ pumped by two-photon excitation. Four out of these eight autoionization resonances are observed for the first time.     

Longitudinal resonant spectrophone for CO-laser photoacoustic spectroscopy

A photoacoustic (PA) system for monitoring gaseous air pollutants absorbing in the CO-laser range is presented. The characteristics of the CO laser and the interference caused by water-vapor absorption demand a special design of the PA cell and experimental setup. The optimum cell design was found by numerical simulation of the acoustic properties of various cell geometries. For this purpose a model using infinitesimal analogue acoustic impedances was developed. Based on a matrix formalism for fourterminals, a computer program was applied that permits the calculation of the frequency response of the PA signal amplitude at any position within a one-dimensional PA cell. Excellent agreement with experimental data is obtained. As a result, a new design for an acoustically resonant spectrophone with improved properties is presented. The response of the cell with aQ-factor of 52, operated at 555 Hz, is 2000 Pa cm/W.     

Bone micro-damage assessment using non-linear resonant ultrasound spectroscopy (NRUS) techniques: a feasibility study

Non-linear resonant ultrasound spectroscopy (NRUS) is a technique exploiting the significant non-linear behavior of damaged materials, related to the presence of damage. This study shows for the first time the feasibility of this technique for damage assessment in bone. Two samples of bovine cortical bone were subjected to a progressive damage experiment. Damage accumulation was progressively induced in the samples by mechanical testing. For independent assessment of damage, X-ray CT imaging was performed at each damage step, but only helped in the detection of the prominent cracks. Synchrotron micro-CT imaging and histology using epifluorescence microscopy were performed in one of the two samples at the last damage step and allowed detection of micro-cracks for this step. As the quantity of damage accumulation increased, NRUS revealed a corresponding increase in the non-linear response. The measured change in non-linear response is much more sensitive than the change in elastic modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique where bone access will be a challenging problem.     

Nonlinear spectroscopy of resonant levels by the photon-echo technique

A new method to measure the relaxation times of population, orientation and alignment of the resonant level is proposed.     

In-source spectroscopy on astatine and radium for resonant laser ionization

At on-line isotope separator facilities, rare isotopes of radioactive elements such as astatine, radium or polonium are demanded for fundamental research on nuclear structure. These elements are generally suitable for a resonance ionization laser ion source, but more data on the atomic structure is necessary to develop efficient laser ionization schemes. Due to the missing stable reference isotopes spectroscopic investigation of the atomic structure can only be performed during on-line operation. At the Isotope Separator and ACcelerator (ISAC) facility at TRIUMF, the elements astatine and radium were investigated by in-source laser spectroscopy to optimize the laser ionization efficiency. For astatine, laser spectroscopy was performed to search for high lying bound states as well as for auto-ionizing resonances. This led to the identification of four new high lying bound states of odd parity, while no auto-ionizing resonances were observed in the investigated region. Furthermore, the feasibility and the impact of laser ionization on the yield of radium isotopes was investigated using an activated target after proton irradiation.     

Mode propagation of ultrasound in hollow waveguides

It has previously been shown that there is close agreement between theoretical and experimental behaviour of pulses of ultrasound propagating in solid cylindrical waveguides. Waveguides are used in a number of areas of medical ultrasonics and it is therefore important to be able to model sound propagation in them accurately. This paper extends the analysis of guided wave propagation to hollow waveguides. In particular, frequency spectra of modes of progagation are given and theoretical group velocity curves are compared with experimental results. Signal strengths of modes propagating in both solid and hollow stainless steel waveguides of similar cross-sectional area are also compared.     

Complete mode identification for resonance ultrasound spectroscopy

This study is devoted to deducing exact elastic constants of an anisotropic solid material without using any advance information on the elastic constants by incorporating a displacement-distribution measurement into resonant ultrasound spectroscopy (RUS). The usual RUS method measures free-vibration resonance frequencies of a solid and compares them with calculations to find the most suitable set of elastic constants by an inverse calculation. This comparison requires mode identification for the measured resonance frequencies, which has been difficult and never been free from ambiguity. This study then adopts a laser-Doppler interferometer to measure the displacement-distribution patterns on a surface of the vibrating specimen mounted on pinducers; comparison of the measured displacement distributions with those computed permits us to correctly identify the measured resonance frequencies, leading to unmistakable determination of elastic constants. Because the displacement patterns are hardly affected by the elastic constants, an exact answer is surely obtained even when unreasonable elastic constants are used as initial guesses at the beginning of the inverse calculation. The usefulness of the present technique is demonstrated with an aluminum alloy and a langasite crystal.     

On the mean value of the energy for resonant states

In this work we discuss possible definitions of the mean value of the energy for a resonant (Gamow) state. The mathematical and physical aspects of the formalism are reviewed. The concept of rigged Hilbert space is used as a supportive tool in dealing with Gamow-resonances.     

On the resonant diffraction of X-rays

Il Nuovo Cimento D - Data on the absorption by a crystalline powder of Ge and on the intensities diffracted by the (111) planes of a perfect Ge crystal were collected in the laboratory at...