Gems and Geophysics
The story of how we made GHz-ultrasonic shear waves for high-pressure mineral physics
The newly faceted P-to-S elastic-wave conversion prism, pictured here between a pair of tweezers (about 6 mm apart).
A yttrium-aluminum-garnet (YAG) gem for laboratory geophysical experiments
Reference: Jacobsen, S.D., H.A. Spetzler, H.J. Reichmann, and J.R. Smyth (2004) Shear waves in the diamond-anvil cell reveal pressure-induced instability in (Mg,Fe)O, Proceedings of the National Academy of Sciences USA, 101, 5867-5871. PDF
Motivation for the general reader: Much of what we know for sure about Earth’s inaccessible interior comes from observed travel-times of seismic body waves produced during large earthquakes. Compressional waves (P-waves) are like sound waves, and travel the fastest (P is for “primary”, because they are the first direct arrivals from a distant earthquake). Shear waves (S-waves) look like water waves in that the particle motion goes “up and down” perpendicular to the direction the wave is traveling, but ironically real shear body waves don’t travel through liquids because fluids don’t support shear stresses (S is for “secondary” because the shear waves are slower and thus the second direct arrival from a distant earthquake).
Interpreting Earth’s seismic structure in terms of mutually dependent parameters such as temperature, composition, and mineralogy requires knowledge of the thermoelastic properties of the materials (minerals and melts) thought to comprise the interior. We aim to measure the elastic properties of minerals at extreme conditions relevant to Earth’s interior using ultrasonic P- and S-waves.
The great pressures required to synthesize potential mantle samples at up to 30 gigapascals (GPa) or ~900 km-depth, forces us to work with very tiny samples, usually sub-millimeter. The wavelength of our acoustic probe must be shorter than the length of the samples if we are to measure the travel time through the sample, so we have extended ultrasonic technology to the 0.5 to 2.0 GHz frequency range. These waves have 1-10 micrometer (mm) wavelengths in minerals, and travel about 5 to 10 km/s. From the velocities, we can determine the elastic parameters (moduli and elastic tensor constants) that relate stress to strain in solids.
The basic technical problem: Compressional waves are made by a piezoelectric transducer (like your stereo speaker at home, but much thinner for higher frequencies). The P-waves must be delivered to a sample through a crystal buffer rod (rather than through the air). In order to make P-waves at GHz frequencies, we sputter a thin film of ZnO (the piezoelectric material) between a sandwich of gold layers, which become the ground and lead contacts. While this works great for P, unlike ultrasonic experiments at MHz frequencies, our shear waves cannot be made by a transducer in the usual way. We borrowed the idea of using a P-to-S conversion from seismology. Here is how it works;
The idea is to produce shear by P-to-S
conversion. This occurs by reflection,
made at an angle of incidence (i)
such that the shear waves generated at the conversion facet travel
perpendicular to the incident P-wave.
This way, both waves propagate in the orthogonal  directions of the
oriented crystal (preventing polarization splitting) but also, by forcing the
conversion to occur at 90º, the shear-wave back-reflecting off the working end
of the buffer rod and sample (at right, where we do the interferometry) returns
to the conversion facet and is re-converted to P for detection at the source
transducer. This is a single-transducer
After the cubic-YAG gem was oriented on the  directions using X-rays, the various facets were cut and polished by hand with tolerances to within about ±0.2º
by H. Schulze (BGI-Bayreuth).
In this picture, the faceted gem is sitting between a piar of tweezers with the points about 6 mm apart. The conversion facet is reflecting light on the right-hand side of the crystal.
This photograph shows the transducer being sputtered onto the back side of the YAG crystal. The gold contact point is about 200 micrometers in diameter, and there’s not much geometrical spreading of the wave field through the crystal.
Sputtering GHz transducers is a form of art, mastered by Klaus Mueller (ZT-Uni Bayreuth). Thickness of the ZnO is about 1.5 mm.
Here, I have taken the side off the mount holding the crystal just after sputtering the transducer. The tip of my finger provides some scale.
At this point, we could test the crystal for a shear signal. A small sample was placed on top (at left) in order to locate the “beam” of shear waves striking the underside of the top facet.
In order to achieve a signal, we rely on the quality of the transducer and the accuracy of the gem. Sure, the conversion angle (i) must be right on (to within about 0.2 degrees), but the real challenge is to ensure the co-planarity of the vectors normal to the three most important facets shown here (the one with the transducer, the conversion facet, and the facet with a sample). If any of these facets are out of the plane, a signal only about 300 mm in diameter would not come back (after over 12 mm of travel through the crystal).
Pulse-echo train from the YAG buffer rod during the first test. The amplitude-time plot shown here is taken directly from the oscilloscope during the measurement. A single pulse of the 1.2 GHz signal measuring about 100 ns in duration is introduced into the prism.
The first large echo (labeled PSSP1) is the returning signal from one round-trip through the crystal; from P-to-S and then back S-to-P before returning to the source transducer. The pulse is 100 ns wide, and there are over 100 cycles per pulse, so I have expanded a 10 ns time-frame from the fourth echo to reveal the signal inside.
The first round-trip continues through the crystal, re-converting back to S and so on many times…the P-to-S converter rings like a bell. Here, over eight PSSP echoes are detected from the introduction of just one tone burst.
The crystal must now be coned for access into the high-pressure diamond cell.
Once we established signals in the buffer-rod crystal, we located precisely where the signal was hitting the top facet by placing a small test sample on top. The test sample is the small black circle in the middle (at left), and measures about 150 microns in diameter and about 50 microns in thickness.
By moving the sample around, I maximized the signal hitting the far-end of the sample. Once the best position was found, Hubert began coning around the sample with a rotating diamond point. The process of coning is just started here in this picture.
Coning a sharp point for access to the back of the diamond-anvil in the high-pressure cell.
The point here measured about 250 microns in diameter, and is about the size of the shear-wave signal.
The completed P-to-S conversion shear-wave buffer rod for gigahertz ultrasonic interferometry in the diamond-anvil cell!
Photo (left) of the ultrasonic diamond-anvil cell with brass alignment jig and buffer rod holder below. A transmission-line (much like a printed circuit) is fed through the holder to make contact with the delicate transducer from the side.
Schematic (right) of how it works in the DAC.
Some of the first high-pressure shear-wave data! The sample is magnesiowüstite-(Mg,Fe)O containing about 78% iron (Fe78). The complex echo returning from the culet-sample interface at about 9.1 GPa (~90 kbar) is shown inset. The shape results from interference between the diamond echo and the sample echo, arriving about 25 ns into the primary diamond echo.
By measuring the amplitude of the combined wave as a function of frequency where there is first-order interference, an acoustic “spectrum” is produced with constructive interference at frequencies where there are an integer number of wavelengths in the round-trip through the sample. The amplitude is also measured before the sample echo arrives (the smooth curve) in order to demodulate the signal from other sources, such as echoes in the cables (the broad modulation).
The travel-time data (as a function of frequency) are
calculated from the interference spectrum. We must how many wavelengths are in
the sample for each extrema, but this we can fit experimentally by guessing
several starting values and choosing the “best” integer value defined as the
one resulting in the least dispersion (variation of travel-with
frequency). The velocity should more or
less be independent of frequency in the adiabatic regime.
The people involved: Steve