Electromagnetic-resonance-ultrasound Microscopy (erum) for Quantitative Evaluation of Localized Elastic Constants of Solids

This paper presents a new acoustic-resonance microscopy, electromagneticresonanceultrasound microscopy (ERUM), to evaluate the localized elastic constant of a solid material. It is based on the resonance-frequency shift of a vibrating oriented langasite (La3Ga5SiO14) crystal contacting the specimen via a sphere tip. The vibration of langasite is excited and detected by a dynamic electric field from a sorrounding solenoid coil. Thus, the acoustic coupling between the oscillator and specimen is made only through the tip, isolating the oscillator from any other contacts. (They may otherwise obscure the effect of point contact with specimen and annihilate the quantitative evaluation.) Selection of such a vibration mode that is sensitive to Young’s modulus of the specimen is achieved by a calculation using the RayleighRitz method. On the basis of the calibration for the specimen’s contact effective stiffness, the local elastic stiffness is determined from resonance-frequency shifts of the oscillator. As an illustrative example, we measured the elastic-stiffness distribution of an Nb-Ti/Cu resin superconductive wire. We compared our measurements with both static-contact and dynamiccontact models. INTRODUCTION: Recently, multiphase composites have been widely produced as functional and intelligent materials, which often contain microscale and nanoscale components. Mechanical properties of individual components are required because they govern the composite’s macroscopic mechanical properties. Especially, elastic constants represent indispensable structural design parameters. Many small-scale components show inhomogeneous microstructure and elastic anisotropy, thus a distribution of elastic constants. For example, silicon-carbide fiber shows a multilayer microstructure, and its elastic constants vary strongly along the radial direction. Thus, measurement of elastic constants in a local area within a component assumes a central importance. One candidate measurement method is acoustic microscopy using a high-frequency surface wave. However, surface roughness and material’s anisotropy make it difficult to determine accurately wave velocities. Also, it needs a couplant such as water. Recently, ultrasonic-atomic-force microscopy has been developed to measure the elastic property in microscale and nanoscale regions. This method uses flexural vibration of a microscale cantilever. The tip attached at the free end taps the specimen surface with an applied force. The cantilever’s resonance-frequency shift is related to the specimen’s elastic properties. However, the resonance frequency depends strongly on many factors, including the contacting piezoelectric transducer and gripping condition at the fixed end, preventing one from deducing the elastic constant of the specimen quantitatively. Here, we present an alternative acoustic resonance microscopy, electromagnetic-resonantultrasound microscopy (ERUM), to evaluate a material’s local stiffness. This method uses the resonance-frequency shift of a rectangular-parallelepiped piezoelectric crystal (langasite, La3Ga5SiO14) touching the specimen only at an anti-nodal point. The piezoelectric material’s vibrations are excited and detected through dynamic electric fields using a surrounding solenoid coil. Thus, neither electrode nor mechanical contact is required for the acoustic coupling. Such noncontact excitation and detection of ultrasonic vibrations eliminates the measurement errors associated with contact coupling and ambiguous boundary conditions at the supports. Scanning the object surface with this probe and measuring the resonance frequency then provides an image of elastic-stiffness distribution. We consider the elastic-coefficient mapping of an Nb-Ti/Curesin-composite superconductive wire. ELECTROMAGNETIC-RESONANCE-ULTRASOUND MICROSCOPY: Figure 1 shows the measurement setup of ERUM. An oriented rectangular-parallelepiped langasite crystal was located within a solenoid coil, whose crystallographic X-axis (a axis) is oriented vertically. The dimensions of the crystal along the X, Y, and Z axes are 4.954, 5.769, and 4.016 mm, respectively. Langasite possessed trigonal symmetry with point group 32, showing six elastic constants Cij, two piezoelectric coefficients eij, and two dielectric coefficients εij as given in Ref.[5]. Langasite’s piezoelectric coefficients (two times larger than those of quartz) promise effective generation of vibration by applying a contactless dynamic electric filed. Furthermore, its elastic constants show weak temperature dependence (of the order of 10 K), assuring stable resonance frequencies. Received signal Tone bursts Langasite Solenoid coil