Supplementary information:
The ultrasonic signals were generated by applying electric spikes of 10 ns width with an
amplitude of ≈ 300 V to a polarized PZT transducer obtained from Roditi Hamburg. The
thicknesses of the transducers were selected such that they corresponded to a nominal
resonance frequency of 5 MHz for longitudinal and 20 MHz for transverse waves. The
transducers were bonded with honey as couplant to one of the cylinder faces. A digital
oscilloscope (LeCroy LC534A) with an analog input bandwidth of 1 GHz and a digitization
rate of 2 GSa/s was used to monitor and capture the data. The time-of-flight of the ultrasonic
signals was measured using the pulse-overlap method with an absolute accuracy of a few ns
(relative accuracy of Δt/t = 0.05%) and the velocity vL,T of the ultrasonic signals was
calculated by dividing the double thickness by the time-of-flight between two consecutive
echoes or in case of multiple paths through the sample, the corresponding distance. The
thickness of the samples was measured with the Mitutoyo, digital micrometer No. 293-805
(Neuss, Germany) with an accuracy of 0.1%.This yielded a relative error ΔvL,T / vL,T for the
velocity measurements of 0.3%.
The surface acoustic waves (SAW) were excited by thermoelastic expansion and
ablation by a nitrogen laser-pulse focused to a line by a cylindrical lens on one of the sample
faces. The laser wavelength was λ = 337 nm, the pulse duration τ = 0.5 ns, and its energy
0.4 mJ. The illuminated rectangular area was approx. 8 × 0.012 mm2 resulting in an energy
density of 417 mJ/cm2 or an intensity of 838 MW/cm2. A detailed description of the set-up
(commercially available by Fraunhofer IWS, Dresden, Germany) as well as the measuring
principle and the signal analysis can be found in [1]. The excited waves were detected by a
piezoelectric PVDF foil which was pressed with a steel wedge onto the sample surface.
Amplitude and phase spectra of the pulse signals were calculated by taking the Fourier
transform of a cross correlation between the piezoelectric detector's response at the shortest
distance and with the responses at all other distances.
If the material under test is homogeneous, the generated SAW are dispersion free [2]. In
case there is a gradient of elasticity or density from the surface into the material within the
penetration length of the SAW, there is dispersion which is calculated in automated way by
the software of the apparatus based on the acquired amplitude and phase spectra of the
signals. Due to their wavelength dependent penetration depths, these waves contain
information about elastic properties from a depth of 30 to 140 µm below the surface. We
found no appreciable dispersion of the SAW in our samples.
Using the so-called Bergmann approximation [2] which is valid for a homogenous
solid with a Poisson ratio ν, the SAW phase velocity vsaw is given by:
v SAW =
0.87 + 1.12ν
× vt
1+ ν
(1)
Thus, one can compare the SAW velocity vsaw with the transverse wave velocity vt using
Eq. (1).
References:
[1] D. Schneider, Th. Wittke, Th. Schwarz, B. Schöneich, and B. Schultrich: Surf. &
Coatings Techn., 2000, vol 126, pp. 136-141
[2] I. A. Viktorov: Rayleigh and Lamb Waves, 1st ed., pp. 1-7, Plenum Press, New York,
1967