Measurement of local internal friction in metallic glasses

Abstract

Atomic force acoustic microscopy (AFAM), an advanced scanning probe microscopy technique, has been used to measure local elastic properties with a spatial resolution given by the tip-sample contact radius. AFAM is based on inducing out-of-plane vibrations in the specimen. The vibrations are sensed by the AFM cantilever from by the photodiode signal when its tip is in contact with the material under test. To measure local damping, the inverse quality factor Q−1 of the resonance curve is usually evaluated. Here, from the contact-resonance spectra obtained, we determine the real and imaginary part of the contact stiffness k* and from these two quantities the local damping factor Qloc−1 is obtained which is proportional to the imaginary part γ of the contact stiffness. The evaluation of the data is based on the cantilever's mass distribution with damped flexural modes and not on an effective point-mass approximation for the cantilever’s motion. The given equation is simple to use and has been employed to study the local Qloc−1 of amorphous PdCuSi metallic glass and its crystalline counterpart as a function of position of the AFM tip on the surface. The width of the distribution changes dramatically from the amorphous to the crystalline state as expected from the consequences of the potential-energy landscape picture. The center value of the distribution curve for Qloc−1 coincides very well with published data, based on global ultrasonic or internal friction measurements. This is compared to Qloc−1 measured in crystalline SrTiO3, which exhibits a narrow distribution, as expected.

Measurement of the Indentation Modulus and the Local Internal Friction in Amorphous SiO2 Using Atomic Force Acoustic Microscopy

“…In comparison to the metallic glass PdCuSi [2], the distribution in M' M' ∆ and in Q loc -1 [6] is significantly smaller than expected. Since we deal here with a so-called oxide network glass, the distribution of local configurations is limited compared to the metallic glass.…”

“…In other words, there exists a spatially varying relative local modulus M' M' ∆ and a locally varying internal friction. These effects have been found in the metallic glass PdCuSi as well [2,6], however, not in the polycrystalline counterpart PdCuSi or the single crystal SrTiO 3 which served as materials for comparison [2,6].…”

“…Therefore a corresponding variation must be seen in the internal friction as well. Based on the evaluation procedure discussed in [6], Fig. 1b shows …”

“…To what extent Q loc -1 contributes to Q res -1 is determined by the local velocity ∂y/∂t of the cantilever at the tip position. How to evaluate the local indentation modulus and the local internal friction Q loc -1 has been discussed in a number of recent papers, see for example [5,6].…”

“…and a commercial ultrasonic transducer (Panametrics v133-SM) with a center frequency of 2.25 MHz to excite the modes using the AFAM technique [2,6]. In order to convert the measured contact stiffnesses into indentation moduli, calibration of the AFAM technique has to be undertaken [2].…”