or iron‐rich minerals. Light scattering experiments, however, are commonly performed on optically transparent materials, such as oxides and silicates with lower iron contents, that may not absorb IR radiation at wavelengths around 1–3 μm efficiently enough for uniform and steady heating. CO2 gas lasers emit IR radiation with wavelengths of about 10 μm that is absorbed even by many optically transparent materials. As a consequence, CO2 lasers have been used to heat transparent mineral samples while probing their elastic properties with light scattering (Kurnosov et al., 2019; Murakami et al., 2009a; Sinogeikin et al., 2004; Zhang et al., 2015).
Requirements of uniform heating as well as stabilization and accurate assessment of temperatures impose particular challenges on laser‐heating experiments. Typical sample sizes for light scattering experiments on the order of several tens to hundred micrometers may exceed the sizes of hot spots generated by IR lasers. As a result, samples may not be heated uniformly, and the resulting thermal gradients can bias the measurements of both temperature and elastic properties. During laser‐heating experiments, temperatures are determined by analyzing the thermal emission spectrum of the hot sample. Modern optical instrumentation allows combining spectral with spatial information of the hot spot to generate temperature maps that reveal thermal gradients and facilitate more accurate temperature measurements (Campbell, 2008; Kavner & Nugent, 2008; Rainey and Kavner, 2014). Analyses of laser‐heated hot spots indicate that temperatures may vary by several hundreds of kelvins over a few tens of micrometers across the hot spot. The interaction of the sample with the IR laser often changes in the course of a laser‐heating experiment and may lead to temporal temperature fluctuations in addition to thermal gradients. As a consequence, uncertainties of temperature measurements on laser‐heated samples tend to be on the order of several hundred kelvins. The combination of sound wave velocity measurements on samples held at high pressures inside DACs with laser heating remains one of the major experimental challenges in mineral physics. The potential to determine elastic properties at pressures and temperatures that resemble those predicted to prevail throughout Earth’s mantle has motivated first efforts to combine Brillouin spectroscopy with laser heating (Kurnosov et al., 2019; Murakami et al., 2009a; Sinogeikin et al., 2004; Zhang et al., 2015) and led to successful measurements of sound wave velocities at combined high pressures and high temperatures (Murakami et al., 2012; Zhang & Bass, 2016).
When large enough crystal specimens are available, sound wave velocities can be derived by measuring the travel time of ultrasonic waves through single crystals. Initially developed for centimeter‐sized samples and using frequencies in the megahertz range (e.g., Spetzler, 1970), this technique can be adopted to micrometer‐sized samples contained in DACs by raising the frequencies of ultrasonic waves into the gigahertz range (Bassett et al., 2000; Reichmann et al., 1998; Spetzler et al., 1996). While first ultrasonic experiments in DACs were restricted to P‐wave velocity measurements, Jacobsen et al. (2004, 2002) designed P‐to‐S wave converters to generate S waves with frequencies up to about 2 GHz and to enable the measurement of S‐wave velocities on thin single crystals in DACs up to pressures of about 10 GPa (Jacobsen et al., 2004; Reichmann and Jacobsen, 2004). The relatively young techniques of picosecond acoustics and phonon imaging use ultrashort laser pulses to excite sound waves and to measure their travel times on the order of several hundred picoseconds, allowing to further reduce sample thickness. These techniques have been implemented with DACs to study elastic properties at high pressures and bear the potential to derive full elastic stiffness tensors (Decremps et al., 2014, 2010, 2008). At ambient pressure, the ultrasonic resonance frequencies of a specimen with a well‐defined shape can be measured as a function of temperature and then be inverted for the elastic properties (Schreuer & Haussühl, 2005). The technique of resonant ultrasound spectroscopy (RUS) has been used, for example, to trace the elastic stiffness tensors of olivine single crystals up to temperatures relevant for the upper mantle (Isaak, 1992; Isaak et al., 1989).
The elastic response of a perfectly isotropic polycrystalline aggregate is, in principle, fully captured by the isotropic bulk and shear moduli. These moduli can be determined from the velocities of sound waves propagating in any direction through an isotropic polycrystal. Consequently, the elastic properties of many minerals have been studied on polycrystalline samples or powders, especially when single crystals of suitable size and quality were not available. Elastic moduli determined on polycrystalline samples, however, do not allow computing absolute bounds on the elastic response nor can they capture the elastic anisotropy of the individual crystals that compose the polycrystal. Polycrystalline samples need to be thoroughly characterized to exclude bias by an undetected CPO or by small amounts of secondary phases that might have segregated along grain boundaries during sample synthesis or sintering. Microcracks or vanishingly small fractions of porosity might also alter the overall elastic response of a polycrystal (Gwanmesia et al., 1990; Speziale et al., 2014).
Millimeter‐sized polycrystalline samples can be compressed and heated in multi‐anvil presses while the travel times of ultrasonic waves through the sample are being measured by an interference technique (Li et al., 2004; Li and Liebermann, 2014). When the experiment is conducted at a synchrotron X‐ray source, the sample length can be monitored by X‐ray radiography, which requires the intense X‐rays generated by the synchrotron. Otherwise the sample length can be inferred from an equation of state or solved for iteratively. Sound wave velocities can then be calculated from combinations of travel times and sample length. The stability of modern multi‐anvil presses facilitates sound wave velocity measurements on samples held at pressures and temperatures that exceed those of the transition zone in Earth’s mantle (Gréaux et al., 2019, 2016). By combining sample synthesis and ultrasonic interferometry in the same experiment, Gréaux et al. (2019) and Thomson et al. (2019) were able to determine the sound wave velocities of the unquenchable cubic polymorph of calcium silicate perovskite, CaSiO3. After synthesis at high pressure and high temperature, cubic calcium silicate perovskite cannot be recovered at ambient conditions as its crystal structure instantaneously distorts from cubic to tetragonal symmetry below a threshold temperature (Shim et al., 2002; Stixrude et al., 2007). A similar situation is encountered for stishovite, SiO2, which reversibly distorts from tetragonal to orthorhombic symmetry upon compression (Andrault et al., 1998; Karki et al., 1997b). Such displacive phase transitions can substantially change the elastic properties of materials and illustrate the need to determine elastic properties at relevant pressures and temperatures.
The wavelengths of sound waves used to derive the elastic moduli may also affect how the elastic properties of individual grains in a polycrystalline material are averaged by the measurement. At ultrasonic frequencies, sound waves travel with wavelengths between 10 μm and 10 mm that are long enough to probe the collective elastic response of fine‐grained polycrystalline samples. Sound waves probed by light scattering techniques, however, typically have wavelengths on the order of 100 nm to 10 μm (Cummins & Schoen, 1972; Fayer, 1982), which is similar to typical grain sizes in polycrystalline samples. When the wavelength is similar to or smaller than the grain size, the measured sound wave velocity may be dominated by the elastic response of individual crystals or of the assembly of only a few crystals. When light is scattered by these single‐ or oligo‐crystal sound waves, the measurement on a polycrystal takes an average over sound wave velocities within single crystals rather than averaging over the elastic properties of a sufficiently large collection of randomly oriented crystals that determine the aggregate sound wave velocities at longer wavelengths. The intensity of the scattered light also depends on the orientations of the individual crystals via the photoelastic coupling that can enhance light scattering for some orientations and emphasize their sound wave velocities over others (Marquardt et al., 2009a; Speziale et al., 2014). Nevertheless, light scattering experiments on polycrystalline samples have contributed substantially in characterizing the elastic properties of mantle minerals at high pressures (Fu et al., 2018; Murakami et al., 2009b) and at high pressures and high temperatures (Murakami et al., 2012).
Synchrotron X‐rays can be used to probe the lattice vibrations of crystalline materials. Inelastic X‐ray scattering (IXS) combines the scattering geometry of the X‐ray–lattice momentum transfer with measurements of minute energy shifts in scattered X‐rays that result from interactions
