Resonant ultrasound spectroscopy

Abstract

Resonant ultrasound spectroscopy (RUS) involves the study of the mechanical resonances of solids. The resonant response of a particular object depends on its shape, elastic constants, crystallographic orientation, density, and dissipation. It is possible to obtain the complete elastic constant matrix of relatively low-symmetry materials from a RUS spectrum on a single small sample (<1 mm 3 ). The measurement and the computation of the RUS spectra of solids are reviewed. Several examples of the use of the technique are discussed. Contents 1 Introduction 6001 2 Ultrasonic waves in condensed matter 6002 2.1 Crystalline elasticity 6002 2.2 Plane-wave propagation methods 6003 3 Resonant ultrasound spectroscopy 6005 4 Theoretical basis of RUS 6008 4.1 Computation of the eigenfrequencies 6008 4.1.1 The general computational method. 6009 4.1.2 Use of symmetry to speed the calculations. 6011 4.2 Determination of the sample parameters 6017 4.2.1 Minimization of the error function. 6017 4.2.2 Calculation of the derivatives of the error function. 6017 4.3 Effects of dissipation 6019 5 Applications of RUS 6020 5.1 Phase transitions 6020 5.2 Hydrogen-metal systems 6024 5.3 Other uses 6025 5.4 Outlook 6025 6 Conclusions 6027

Resonant ultrasound spectroscopy for measurement of mechanical damping: Comparison with broadband viscoelastic spectroscopy

“…RUS allows one to obtain the elements of the elastic modulus tensor from a single specimen. In principle, 3 one can also determine the full anisotropy of mechanical damping, however the method has not been developed. One difficulty is the identification of the vibration mode in question.…”

“…[1][2][3] In a typical embodiment of the method, a rectangular parallelpiped or cubic sample is supported by transducers at opposite corners. Corners are used since they always move during vibration ͑they are never nodes͒ and they provide elastically weak coupling to the transducers.…”

“…Mechanical damping is important in applications of vibration abatement and as a probe of phase transitions, defects in crystals, and dislocation mobility. In principle, 3 one can determine the full anisotropy of mechanical Q, however the method has not been developed. One difficulty is the identification of the vibration mode in question.…”

“…Damping, tan ␦, can be determined but interpretation depends on identification of the vibration mode. Most resonant frequencies in RUS depend on combinations of elastic constants, 3 and the width of resonant peaks depends on combinations of complex moduli. 10 Broadband viscoelastic spectroscopy ͑BVS͒ 11 covers a wider range of frequency, a͒ Author to whom correspondence should be addressed; electronic mail: lakes@engr.wisc.edu 11 decades ͑a factor of 10 11 ͒ of time and frequency at subresonant frequencies and at pure resonant modes.…”

Anisotropic Elastic and Acoustic Properties of Bulk Graphene Nanoplatelets Consolidated by Spark Plasma Sintering

“…Hereafter, the samples from these two sets will be denoted as T 1−4 and T ⊥ 1−3 , respectively, where the symbol in the superscript denotes the orientation of the sample with respect to the GNPs and the number in the subscript is the number of the sample. Additionally, two samples in forms of thin rectangular plates were prepared for the resonant ultrasound spectroscopy (RUS, [13,14]) measurements. One of these plates (thickness 0.21 mm, lateral dimensions 2.27 mm Ö3.40 mm) was oriented parallel to the preferential orientation of the GNPs, the second one (thickness 0.40 mm, lateral dimensions 1.87 mm Ö2.81 mm) was oriented perpendicularly to this plane.…”