Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids

Abstract

The mechanical resonant response of a solid depends on its shape, density, elastic moduli and dissipation. We describe here instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm 3 ) samples as a function of temperature, and provide examples to demonstrate the power of the technique. The information acquired is in some cases comparable to that obtained from other more conventional ultrasonic measurement techniques, but one unique feature of resonant ultrasound spectroscopy (RUS) is that all moduli are determined simultaneously to very high accuracy. Thus in circumstances where high relative or absolute accuracy is required for very small crystalline or other anisotropic samples RUS can provide unique information. RUS is also sensitive to the fundamental symmetry of the object under test so that certain symmetry breaking effects are uniquely observable, and because transducers require neither couplant nor a flat surface, broken fragments of a material can be quickly screened for phase transitions and other temperature-dependent responses.

Effect of disorder on the thermal transport and elastic properties in thermoelectricZn4Sb3

“…The elastic moduli are measured using resonant ultrasound spectroscopy ͑RUS͒. [14][15][16] In the RUS experiment, the mechanical resonances of a freely vibrating solid of known shape are measured, and an iteration procedure is used to "match" the measured lines with the calculated spectrum. This allows determination of all elastic constants of the solid from a single frequency scan, which clearly indicates a main advantage of RUS: there is no need for separate measurements to probe different moduli, and multiple sample remounts and temperature sweeps are avoided.…”

Temperature dependence of elastic moduli of polycrystalline β plutonium

“…Resonant ultrasound spectroscopy (RUS) [71][72][73] measurements of the adiabatic bulk and shear moduli of pure polycrystal β-Pu are reported here. The Pu measured had the highest available purity, and measurements were completed without thermal cycling.…”

Instrumentação para espectroscopia de ressonância de ultrassom

“…Quando a amostra entra em ressonância com o primeiro transdutor piezoelétrico, o sinal no segundo transdutor (receptor) apresenta um máximo. Para amostras com dimensões típicas, uma varredura de freqüência de 0,4 a 3 MHz é suficiente para detectar as freqüências de ressonância necessárias para calcular todo o tensor de elasticidade do material que compõe a amostra [10].…”

“…A simplicidade da técnica, no entanto, tem como contraponto a complexidade do processo do cálculo do tensor de elasticidade da amostra a partir do seu espectro RUS. A solução para este problema, no entanto, tem sido implementada em programas de computador que permitem a análise de monocristais de materiais com classe de simetria cúbica a ortorrômbica, além de amostras policristalinas isotrópicas [10].…”