Study of the Earth's interior using measurements of sound velocities in minerals by ultrasonic...

Physics of the Earth and Planetary Interiors 233 (2014) 135–153

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Physics of the Earth and Planetary Interiors

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Review

Study of the Earth’s interior using measurements of soundvelocities in minerals by ultrasonic interferometry

http://dx.doi.org/10.1016/j.pepi.2014.05.0060031-9201/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +1 631 632 9642.E-mail address: [email protected] (B. Li).

Baosheng Li a,⇑, Robert C. Liebermann a,b

a Mineral Physics Institute, Stony Brook University, United Statesb Department of Geosciences, Stony Brook University, United States

a r t i c l e i n f o

Article history:Received 20 November 2013Received in revised form 29 April 2014Accepted 2 May 2014Available online 20 May 2014

Keywords:Ultrasonic interferometryElasticityMulti-anvilMantle composition

a b s t r a c t

This paper reviews the progress of the technology of ultrasonic interferometry from the early 1950s tothe present day. During this period of more than 60 years, sound wave velocity measurements have beenincreased from at pressures less than 1 GPa and temperatures less than 800 K to conditions above 25 GPaand temperatures of 1800 K. This is complimentary to other direct methods to measure sound velocities(such as Brillouin and impulsive stimulated scattering) as well as indirect methods (e.g., resonance ultra-sound spectroscopy, static or shock compression, inelastic X-ray scattering). Newly-developed pressurecalibration methods and data analysis procedures using a finite strain approach are described and appliedto data for the major mantle minerals. The implications for the composition of the Earth’s mantle arediscussed. The state-of-the-art ultrasonic experiments performed in conjunction with synchrotronX-radiation can provide simultaneous measurements of the elastic bulk and shear moduli and their pres-sure and temperature derivatives with direct determination of pressure. The current status and outlook/challenges for future experiments are summarized.

� 2014 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1362. Early history of sound velocity measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

2.1. Resonance methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1362.2. Ultrasonics up to 10 kbar (1 GPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

2.2.1. Pulse transmission methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1372.2.2. Ultrasonic interferometric methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

3. Extension of ultrasonic experiments to pressures above 10 kbar (1 GPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
3.1. Ultrasonics at Australian National University (ANU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1393.2. Hot-pressing polycrystalline specimens at Stony Brook University (SBU) for ultrasonic experiments at the ANU . . . . . . . . . . . . . . . . . . 1393.3. Ultrasonic interferometry at Gigahertz frequencies in diamond-anvil, high-pressure cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4. Interface with multi-anvil apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.1. Measurements to high pressures at room temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.1.1. Pressure calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.1.2. Advanced ultrasonic interferometry: transfer function method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.1.3. Simultaneous P and S waves velocity measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.1.4. Data analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.1.5. Sound velocity of mantle minerals at high pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.2. Simultaneous high pressure and high temperature measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454.3. Ultrasonic Interferometry in conjunction with synchrotron X-radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

4.3.1. P-V-VP-VS-T measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454.3.2. Absolute pressure determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

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136 B. Li, R.C. Liebermann / Physics of the Earth and Planetary Interiors 233 (2014) 135–153

4.3.3. Measurements on MgSiO3 perovskite and lower mantle composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Fig. 1.mineraAK135;

4.4. Current status and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.4.1. Reconciliation of elasticity discrepancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1484.4.2. Extension of pressure and temperature range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1484.4.3. Refinement of pressure scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1494.4.4. Effect of solid-solutions and minor elements on elasticity of mantle minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1494.4.5. Measurements on melts and effect of partial melting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

1. Introduction

Laboratory studies of the sound wave velocities in minerals athigh pressure and temperatures continue to play a major role inenabling scientists to interpret seismic data for the variation ofsound velocities and density with depth in the Earth’s interior. Asseen in the global seismic models (PREM and AK135 in Fig. 1),the compressional (P) and shear wave (S) velocities exhibit discon-tinuous increases at certain depths (Dziewonski and Anderson,1981; Kennett et al., 1995); some distinct features include lowvelocity zone around 80–150 km, jumps at 410- and 670-kmdepths, and high velocity gradient in the transition zone. In addi-tion, regional seismic studies also revealed discontinuities at520 km as well as in the depths of 250–340 km (X discontinuity)(for recent example, see Y. Wang et al., in press, 2013). The corre-sponding phase transitions as possible causes of these velocityanomalies have been illustrated using a pyrolitic mantle composi-tional model. As we know, there is still debate as to whether a pyr-olite composition can reproduce the velocity profiles throughoutthe mantle, which in part results from the lack of consistent sensi-tivity to elasticity when different techniques are used. For soundvelocity measurements, these techniques employ both indirectmethods (resonance of specimens, static compression, inelasticX-ray scattering (including nuclear resonance inelastic X-ray scat-tering), shock wave compression) and direct methods (ultrasonicwave propagation, Brillouin and impulsive stimulated scattering).

Illustration of velocity structures in the mantle and the correspondinglogy and phase transitions in a pyrolitic compositional model. Solid lines:Dashed lines: PREM.

There have been many previous reviews of these techniques (e.g.,by Simmons, 1965; Anderson and Liebermann, 1968; Weidner,1987; Bass, 2007; Angel et al., 2009; and Chang et al., 2014). Thuswe shall touch only briefly on some of them in this paper. In addi-tion, the current paper focuses on laboratory ultrasonic measure-ments in the frequency range of MHz, those interested in soundvelocity measurements at low frequencies (Hz or lower) can findmore details in Jackson and Paterson (1993) and referencestherein.

The primary purpose of this paper is to review the evolution ofthe techniques of ultrasonic interferometry from their introductionafter World War II in laboratories such as the Bell Telephone Lab-oratories in Murray Hill, New Jersey to the present time (roughly60 years). This is an extension and expansion of our earlier paper(Li and Liebermann, 2007). We also discuss briefly the implicationsof such studies for interpretations of seismic models for velocityand density in the Earth’s interior (see also Li, 2009).

2. Early history of sound velocity measurements

2.1. Resonance methods

Prior to World War II, the most common method of measuringthe elasticity of solids was by exciting the natural vibrations of theextensional, flexural or torsional modes of a material and measur-ing their resonant frequencies; see Anderson and Liebermann(1968) and references therein for a review of these early laboratoryresonance methods. In the 1960s, these resonance studies wereextended to smaller specimens and, thereby, higher frequencies;Fraser and LeCraw (1964) measured the elasticity of spheres ofnon-crystalline and isotropic materials in what may be consideredthe first resonant ultrasound spectroscopic (RUS) experiments.

This technique was later exploited by Orson Anderson, NaohiroSoga and Edward Schreiber to measure the resonance of spheres oftektites and lunar samples (Soga and Anderson, 1967c; Schreiberand Anderson, 1970). Demarest (1971) extended this method tomaterials of cubic symmetry and established the theoretical frame-work for rectangular parallelepiped resonance (RPR) which havebeen used extensively in geophysics (see also Ohno, 1976). Seeexcellent reviews of RUS in the papers by Maynard (1996),Leisure and Willis (1997), and Angel et al. (2009); and for recentexamples of the application of this technique, see the studies ofthe high-temperature elasticity of wüstite by Isaak and Moser(2013) and the single-crystal elasticity of stishovite by Yonedaet al. (2012).

These laboratory resonance techniques are analogous to detect-ing the free oscillations of the Earth following large earthquakesand inverting these to infer the elastic properties of the deepinterior.

2.2. Ultrasonics up to 10 kbar (1 GPa)

Several technological developments during World War II madepossible measurements of sound velocities in solids using

Fig. 2. Schematic diagram for ultrasonic interferometric measurements.

B. Li, R.C. Liebermann / Physics of the Earth and Planetary Interiors 233 (2014) 135–153 137

high-frequency ultrasonic methods; many of these grew out ofwork at the Radiation Laboratory at the Massachusetts Instituteof Technology and comparable laboratories in England.

In particular, the wartime development of pulsed circuits inconjunction with piezoelectric transducers made pulsed ultrasonicmeasurements practical, thereby replacing the resonance meth-ods; for examples of the impact of these developments, seeHuntington (1947), Galt (1948) and Lazarus (1949).

2.2.1. Pulse transmission methodsIn the decade of the 1950s, several groups applied ultrasonic

pulse transmission techniques to study the sound velocities in nat-ural rocks. In the Department of Physics at the University of TexasAustin, Darrell Hughes and his colleagues measured both compres-sional and shear wave velocities (the latter by critical reflection ofP waves) at 5 MHz frequencies in a collection of igneous rocks pur-chased from Ward’s Scientific Establishment (Hughes and Jones,1950). Hughes and Cross (1951) extended these measurementsto 0.5 GPa at room T and to 200 �C at atmospheric pressure on asuite of rock specimens provided by Francis Birch at HarvardUniversity (including Solenhofen limestone and Twin Sistersdunite); their ultrasonic shear wave velocities agreed well withprevious measurements by resonance methods at kHz frequencieson the same rocks (Birch, 1943).

Also in the 1950s in the Hoffman Laboratory at Harvard, FrancisBirch undertook a systematic study of the compressional wavevelocities in a wide variety of natural rocks to 1 GPa at room tem-perature using the pulse transmission methods with 5 MHz X-cutquartz transducers and specimens from the Harvard MineralMuseum collection originally assembled by R. A. Daly and othersprovided by colleagues throughout the world (including the south-ern California batholith, the Bushveld complex in South Africa, andNew England). For each rock sample, modal analyses of the constit-uent minerals were obtained and three specimens oriented at rightangles were prepared for the ultrasonic measurements to deter-mine its elastic anisotropy. In all, more than 250 rocks were stud-ied and reported in two seminal papers in 1960 and 1961 (Birch,1960, 1961). Based on these data, Birch formulated a linear rela-tionship of compressional wave velocity (VP) to density (q) as afunction of mean atomic weight m, VP = a(m) + bq. This relationshipbecame known as Birch’s law and has been widely recognized as auseful tool in geophysical studies (e.g., as a formula to relate mea-sured seismic velocities to densities obtained from geodetic stud-ies). It is still used extensively for constraining the compositionof the core since direct velocity data are difficult to obtain underthese extreme conditions (e.g., Mao et al., 2012).

A major advance was made by Gene Simmons who utilized AC-cut quartz transducers to generate and detect the ultrasonic signalsand was, thereby, able to study the shear wave velocities in Birch’ssuite of rocks to 1 GPa (Simmons, 1964a,b). Over the next decade,protégés of Birch extended these compressional and shear wavevelocity studies to metamorphic (Christensen, 1965, 1966a), sedi-mentary (Wang, 1966), ultrabasic rocks (Christensen, 1966b;Babuska, 1972).

2.2.2. Ultrasonic interferometric methodsIn the early 1950s, Warren Mason established a physical acous-

tics group at the Bell Telephone Laboratories; he recruited a tal-ented group of young scientists to develop new techniques forconducting Megahertz-frequency ultrasonic interferometric exper-iments to measure elastic wave velocities in solids and liquids,including both the pulse superposition and phase comparisonmethods (McSkimin, 1950, 1960) Among these new experimental-ists were H. J. (Hal) McSkimin, Paul Andreatch and EmmanuelPapakakis (joining D. B. Fraser and L. C. LeCraw—see above); thegroup also included theoreticians such as R. N. Thurston and K.

Brugger who formulated new approaches to treat third-order elas-tic moduli (Thurston and Brugger, 1964). Mason also edited a bookseries on Physical Acoustics (Vols I to XVIII from 1964 to 1988)which included important experimental papers (McSkimin; Ander-son and Liebermann; Truell et al.) as well as theoretical papers(Thurston; Brugger; Alers); Vols. VI to XVIII were co-edited by R.N. Thurston. The concept of ultrasonic interferometric methodsand experimental implementations can be found easily in theabove mentioned reference. For completeness, we will briefly illus-trate here its principle with a geometry that is mostly related tothe implementation in multi-anvil apparatus to be discussed inthis paper.

Fig. 2 is a schematic diagram showing the principle of traveltime measurements using interferometric method. A megahertztone burst is transmitted via a piezoelectric transducer and a delayline (buffer rod) into the specimen. The propagating wave packet ispartially reflected at the buffer rod-specimen interface (buffer rodecho) and the acoustic energy transmitted into the specimen isreflected from the end of the specimen (specimen echo), these ech-oes are recorded by the transducer with a time delay of t corre-sponding to the waves traveling round trip inside the specimenand phase shift caused by the bonding material between the bufferrod and the specimen (h). When the phase shift caused by roundtrip travel and the bond is an integer number of p, i.e.,(xt + h) = np, the buffer rod echo and specimen echo will appearto be in-phase (n = even) or out-of-phase (n = odd). Thus, the mea-sured travel time can be expressed as t = p/f � h/2pf, with p beingan integer (in-phase) or half-integer (out-of-phase) and f is fre-quency. Applying a bond correction (see Jackson et al., 1981) tothe measured t yields the true round trip travel time in the sample.

There are a few variants of ultrasonic interferometric methodsfor the determination of t as mentioned before. The pulse echooverlap (PEO) method involves a procedure of directly movingthe specimen echo (buffer rod echo) to overlap with the bufferrod echo (specimen echo) in time axis, the time shift needed fora perfect overlap of the two echoes yields the apparent travel time(Papadakis, 1968). In contrast, the phase comparison (PC) method(McSkimin, 1950), as implemented in the Australian ScientificInstruments Ultrasonic Interferometer (ANUTECH) (see details inNiesler and Jackson, 1989; and Rigden et al., 1992), uses a pair ofphase-coherent, high frequency pulses as input signals to excitethe transducer. When the applied pulses are separated by theapparent two-way travel time of the specimen, the buffer echo


from the second source pulse will superimpose with the specimenecho from the first source pulse. As the carrier frequency is varied,the interference between the superimposed buffer rod and speci-men signals results in a series of alternating constructive (maxima)and destructive (minima) pattern in the amplitude spectrum (i.e.,x test = np, or test = p/f with p = n/2). Frequencies for the pth and(p + m)th interference extrema (m integer), fp and fp+m can be usedto estimate the apparent travel time test = m/(fp+m � fp); then the pvalue is calculated from p = fptest and the closest half or integralvalue is subsequently assigned to frequency fp; all remainingextrema can be assigned sequentially. Other interferometric imple-mentations, such as frequency sweeping (Ai and Lange, 2004) orbroadband spectroscopy (Wang et al., 2011), although with differ-ent names, are essentially the same principles as described above.In summary, for millimeter sized specimens, the precision of ultra-sonic interferometric measurements of travel time is better than10�4.

In addition to measuring solids, ultrasonic interferometry hasalso been used in the studies of sound velocity and attenuationof melts (Katahara et al., 1981; Rai et al., 1981; Manghnani et al.,1986). In his Ph.D. thesis at the University of California Berkeley,Mark Rivers (1985) developed ultrasonic velocity and absorptiontechniques to study the behavior of silicate melts a function oftemperature (1175–1925 K) and frequency (3–12 MHz) (see alsoRivers and Carmichael, 1987). Most of previous ultrasonic interfer-ometric studies on melts were conducted at room pressure inwhich the interference maxima and minima were obtained eitherusing a ‘‘varying sample length’’ approach (i.e., by changing thedepth the buffer rod dips into the melts) or a frequency sweeping(equivalent to phase comparison) approach (Ai and Lange, 2004).Recently, sound velocity measurements on water have been con-ducted under high pressure in multi-anvil apparatus to 4.2 GPa500 K using a broadband signal and phase unwrapping technique,more details about the results can be found in Z. Wang et al., (2011,2013).

Among the young Turks recruited by Mason at Bell Labs wasOrson Anderson, who had just graduated from the University ofUtah where he did his Ph.D. research under Walter Elsasser. Ander-son spent a decade in Bell Labs working with Hal McSkimin andPaul Andreatch. When he joined the staff of the Lamont GeologicalObservatory of Columbia University in the early 1960s, he broughtthe techniques of ultrasonic interferometry with him and intro-duced them to the geophysical community. He also recruited twopostdoctoral associates, Edward Schreiber from the Alfred Collegeof Ceramics and Naohiro Soga from Kyoto University. The teamwas later joined by Mineo Kumazawa, a Visiting Professor fromNagoya University, and new graduate students of Anderson (HarryDemarest, Bob Liebermann, Leon Thomsen, and Nicholas Warren).

Over the next decade, the Lamont group published more than75 papers based on experimental and theoretical studies in the dis-cipline which became known in the geophysical community asMineral Physics (for a history of that name, see Liebermann andPrewitt (2013)). The experimental studies were largely focusedon the use of physical acoustics to measure the elasticity of mate-rials, including resonance ultrasound spectroscopy (see above);however, the primary focus of the Lamont Lab was on the use ofthe pulse superposition and phase comparison methods of ultra-sonic interferometry to pressures up to 0.4 GPa and/or tempera-tures to 473 K.

Most previous sound velocity studies in geophysics had utilizednatural rock samples, which were composed of several mineralsand often suffered from the existence of cracks, pores, physicalweathering, and chemical alteration, thereby making them unsuit-able for high-frequency ultrasonic investigations. Fortunately,advances in ceramic technology and hot isostatic pressing hadmade available high-quality, low porosity, and fine-grained

polycrystalline aggregates. The Lamont team made extensive useof such ceramic specimens, which were most often obtained fromindustrial companies such as General Electric (Lucalox aluminumoxide-corundum; see Schreiber and Anderson, 1966a,b), Avco(magnesium oxide-periclase; see Anderson and Schreiber, 1965;Soga and Anderson, 1966; and Schreiber and Anderson, 1968),Ampex(alpha-ferric oxide-hematite; see Liebermann andSchreiber, 1968), Bell Telephone (zinc oxide-zincite and calciumoxide-lime; see Soga, 1968; and Soga and Anderson, 1967a), andSilk City Ceramic (magnesium orthosilicate-forsterite; seeSchreiber and Anderson, 1967 and Soga and Anderson, 1967b).

Anderson and his colleagues also used ultrasonic interferometryto study sound velocities in single crystals of minerals, includingMgO (Anderson and Andreatch, 1966), MgAl2O4-spinel (Schreiber,1967), Pyrope-almandine garnet (Soga, 1967), olivine-Fo100 andSan Carlos-Fo90 (Kumazawa and Anderson, 1969), andFe2O3-hematite (Liebermann and Banerjee, 1971).

Other laboratories in the U.S. geophysics community alsoadopted ultrasonic interferometry to study the elasticity of singlecrystals of minerals, including those of:

Gene Simmons at MIT (e.g., Wang and Simmons, 1972, 1973,1974).Gerhard Barsch (and later Earl Graham) at Penn State (e.g.,Al2O3 by Gieske and Barsch, 1968; Mg2SiO4 by Graham andBarsch, 1969; (Mg,Fe)SiO3 by Frisillo and Barsch, 1972; MgOand MgAl2O4 by Chang and Barsch, 1969a,b, 1973; SnO2 byChang and Graham, 1975).Murli Manghnani at the University of Hawaii (e.g., TiO2 byManghnani, 1969).Hartmut Spetzler and Richard O’Connell at Caltech (e.g., MgO bySpetzler, 1970; NaCl by Spetzler et al. (1972).

In most of these single-crystal experiments, sound wave veloc-ities were measured in pure mode directions to pressures up to1 GPa and/or temperatures up to 700 K.

A nice summary of ultrasonics in geology was written by GeneSimmons (1965). In 1968, the Lamont team published two paperswhich reviewed experimental techniques of physical acousticsemployed in geophysical laboratories and summarized the extantdata on single-crystals and polycrystalline aggregates of mineralsand natural rock specimens (Anderson and Liebermann, 1968;Anderson et al., 1968). See also Wang and Simmons (1971).

3. Extension of ultrasonic experiments to pressures above10 kbar (1 GPa)

For his Ph.D. research at the Rensselaer Institute of Technology,Thomas Ahrens used the ultrasonic interferometric methods ofMcSkimin (1950) in a opposed anvil, high-pressure apparatus ofthe type first developed by Bridgman (1952) and later modifiedby Griggs and Kennedy (1956). Ahrens used these techniques tomeasure the sound velocities in polycrystalline KCl to 3.6 GPa(Ahrens and Katz, 1962). In a subsequent study, Ahrens and Katz(1963), observed the calcite–aragonite transition at pressures of0.4–0.8 GPa in their ultrasonic measurements on limestone speci-mens; Chi-yuen Wang (Wang, 1966) in Birch’s laboratory con-firmed the results of Ahrens and Katz and also observed minimain the compressional wave velocities at 1.5 GPa, which were attrib-uted to the calcite transitions originally discovered by Bridgman(1939).

Using the pulse transmission method of Birch (1960), NikolasChristensen (1974), then at the University of Washington,extended the rock sound velocity measurements for pyroxenites,eclogites and a dunite to 3 GPa using a Bridgman–Birch apparatus


(Birch et al., 1957) to generate the hydrostatic pressures; see alsoWang (1974) at the University of California Berkeley. H. Ito et al.(1977) measured the sound wave velocities in single crystalMgO, polycrystalline MgSiO3 and Twin Sisters dunite to 5 GPa ina wedge-type, multi-anvil apparatus (Wakatsuki and Ichinose,1982) using the pulse transmission technique. Using the sametechniques, Fukizawa and Kinoshita (1982) measured the shearwave velocities in Fe2SiO4 to 5.2 GPa and 650 C, across the oliv-ine-spinel phase boundary.

For more than two decades, Hideyuki Fujisawa and colleaguesworked on the development of techniques to perform ultrasonicmeasurements at higher pressures, using both pulse-echo overlaptechniques in piston-cylinder apparatus to 4 GPa and pulse trans-mission techniques in multi-anvil apparatus to 14 GPa (see papersby Fujisawa and Kinoshita, 1974; Kinoshita et al., 1979; Fujisawaand Ito, 1984, 1985; Sasakura et al., 1989; Suito et al., 1992;Fujisawa et al., 1994; Fujisawa, 1988, 1998).

At the U.S. Army Benet Weapons Laboratory in Watervliet, NY,Frankel et al. (1976) extended the Ahrens-Katz approach and mea-sured the sound velocities in polycrystalline NaCl between 2.5 and27 GPa (below 2.5 GPa, the authors observed some extrusion ofsample material between the opposed anvils). In a series of papersin the 1970s, F. F. Voronov at the Institute for High Pressure Physicsin Troitzk, USSR pushed the pressures to 10 GPa in belt-girdle andopposed Bridgman anvil devices; these studies are nicely summa-rized in Voronov (1981); Cook’s method (Cook, 1957) wasemployed to calculate the change in sample length from themeasured sound velocities.

3.1. Ultrasonics at Australian National University (ANU)

In the laboratory of A. E. (Ted) Ringwood at the AustralianNational University, Liebermann and his colleagues initiated a pro-gram in the 1970s to hot-press high-quality polycrystalline aggre-gates of the high-pressure phases of mantle minerals and theiranalogs and built on the advances in ceramic technology describedabove. Using starting materials synthesized by Alan Major andDouglas Mason in Ringwood’s laboratory, polycrystalline speci-mens were produced in various solid-media, high-pressure appara-tus; including piston-cylinder (to 3 GPa), girdle (to 6 GPa), belt (to9 GPa) and simple squeezer (to 12 GPa) devices. These specimenswere then studied by pulse transmission and/or pulse superposi-tion methods to pressures of 0.75 GPa at room temperature(Liebermann et al., 1974). A comparable program was conductedduring the early 1970s in the laboratory of Syun-iti Akimoto atthe University of Tokyo using pulse transmission techniques tomeasure sound velocities in polycrystalline specimens of high-pressure silicate phases hot-pressed in a tetrahedral-anvil appara-tus (see Mizutani et al., 1970, 1972; Akimoto, 1972).

Later at the ANU, Jackson and Niesler (1982; see also Jacksonet al., 1981) developed methods to conduct ultrasonic phase com-parison measurements on single crystals in a liquid-medium,hydrostatic piston-cylinder apparatus. These single crystal studieswere extended to MnO, fayalite, garnet, olivine and orthopyroxenein the Ph.D. thesis research of Sharon Webb (e.g., Webb, 1989;Webb and Jackson, 1993). Of particular interest in the latter paperwas the observation that the pressure derivative of the bulk mod-ulus Ks

0 decreased from 10.6 at low pressures to 6 at 3 GPa, con-firming the earlier work of Frisillo and Barsch (1972) andforeshadowing later experiments by Chai et al. (1997), Fleschet al. (1998) and Kung et al. (2004).

Sally Rigden utilized the 3 GPa piston-cylinder apparatus inJackson’s lab to conduct sound wave velocity experiments on thepolycrystalline specimens of high-pressure phases which had beenhot-pressed by the Liebermann (1975) team in the 1970s (Rigdenet al., 1988; Rigden and Jackson, 1991). See also the studies of

Fujisawa (1988, 1998) on polycrystalline specimens of the olivineand beta-phase polymorphs of Mg2SiO4.

3.2. Hot-pressing polycrystalline specimens at Stony Brook University(SBU) for ultrasonic experiments at the ANU

For his Ph.D. research at Stony Brook, Gabriel Gwanmesiaadapted the hot-pressing techniques developed at the ANU formulti-anvil, high-pressure apparatus, in particular the 2000-tonuniaxial split-sphere apparatus (USSA-2000) installed in the StonyBrook High Pressure Laboratory in 1985 (Remsberg et al., 1988).These hot-pressing techniques are described in Gwanmesia et al.(1990a,b, 1993) and Gwanmesia and Liebermann (1992). Subse-quently, ultrasonic interferometric techniques were used to mea-sure the sound wave velocities in polycrystalline specimens ofthe wadsleyite and ringwoodite phases of Mg2SiO4 in the piston-cylinder apparatus at the ANU in collaboration with Rigden andJackson (Gwanmesia et al., 1990a,b; Rigden et al., 1991, 1992);later these experiments were extended to pyrope-majorite garnets(Rigden et al., 1994). For his M. S. thesis research, Baosheng Li syn-thesized polycrystalline specimens of stishovite, which were stud-ied at the ANU in collaboration with Rigden (Li et al., 1996a). Thesepolycrystalline specimens of stishovite were remarkably isotropicwith velocities within 1% of the Hashin–Shtrikman and Voigt–Reuss–Hill averages of the single-crystal elastic moduli measuredby Weidner et al. (1982), which demonstrated that the intrinsicanisotropy of this rutile-structure polymorph of SiO2 was 31% forcompressional waves and 60% for shear waves (see Fig. 7 inLiebermann and Li, 1998).

3.3. Ultrasonic interferometry at Gigahertz frequencies in diamond-anvil, high-pressure cells

Building on an idea first introduced by McSkimin (1950), Hart-mut Spetzler and his colleagues at the University of Coloradodeveloped Gigahertz ultrasonic interferometry to measure theelasticity of sub-millimeter sized single crystals (Spetzler et al.,1993). By developing thin film P-wave transducers, at0.5–2.0 GHz the acoustic wavelengths in solids were reduced to5–10 lm, suitable for interface with the diamond-anvil cell(DAC). Working with Ganglin Chen at the Center for High PressureResearch (CHiPR) and scientists at the BayerischesGeoinstitüt inBayreuth, especially Hans-Josef Reichmann (now at GFZ-Potsdam),the first P-wave ultrasonic experiments in the DAC were made onsingle-crystal ice and MgO (Spetzler et al., 1996; Bassett et al.,2000). Steven Jacobsen, one of Spetzler’s graduate students, laterdeveloped a method of generating shear waves at GHz frequenciesby P-to-S conversion (Jacobsen et al., 2002a,b); Hubert Schulze, atalented sample technician in Bayreuth, played a critical role in fac-eting the P-to-S conversion buffer rod with 0.02� accuracy to pro-duce purely-polarized shear waves. GHz-ultrasonic interferometryhas since been used to study liquid-glass phase transitions up to20 GPa (Angel et al., 2007) and measure the complete elastic tensorof single crystals up to 10 GPa, including FexO (Jacobsen et al.,2004; Kantor et al., 2004), transition-metal oxide spinels(Reichmann and Jacobsen 2004; Reichmann et al., 2013), andhydrous ringwoodite (Jacobsen and Smyth, 2006). An excellentsummary of GHz-interferometry can be found in Jacobsen et al.(2005). More recent advances in Jacobsen’s laboratory atNorthwestern University are described in Chang et al. (2014); inparticular, the authors demonstrate the capability to measurenanopolycrystalline materials as well as describe the developmentof an optical contact micrometer for high-precision sample thick-ness measurements, leading to experimental uncertainty of�0.1% in the measured elastic moduli of nanopolycrystallinediamond.


4. Interface with multi-anvil apparatus

4.1. Measurements to high pressures at room temperature

The excellent capacity of multi-anvil apparatus for generationof pressures in excess of 10 GPa offered the opportunity of imple-menting ultrasonic measurements in these high-pressure devicesof the Kawai-type MA-8 and DIA-type MA-6 (see Liebermann(2011) for review of multi-anvil apparatus)). Early studies in Japaninclude those of Kinoshita (1979), Fujisawa and Ito (1984, 1985),Yoneda (1990), Yoneda and Morioka (1992) and Fujisawa (1998).The challenges these early experimental studies faced includednot only preventing specimens from plastic deformation but alsopreserving the integrity and piezoelectric performance of thetransducer at high pressures. Some studies (e.g., Yoneda, 1990)demonstrated that hydrostaticity could be achieved by using liquidpressure medium following the experience of piston cylinder appa-ratus, but achieving pressures above 10 GPa was hampered by thedegradation of the acoustic signals due to non-hydrostatic stresseson the transducer enclosed in the pressure cell. Nevertheless, thedata obtained on single-crystal MgO and MgAl2O4-spinel byYoneda (1990) and on single-crystal forsterite by Yoneda andMorioka (1992) using a Kawai-type multi-anvil apparatus wereextended to pressures more than 8 GPa, or twice that in theprevious results in piston cylinder apparatus. To achieve higherpressures, Fujisawa and Ito (1984) carried out feasibility measure-ments on pyrophyllite specimens using solid pressure medium(graphite) around the sample in a MA-8 apparatus, and reportedtravel time data up to 14 GPa. However, the measurements werelimited to the low-resolution pulse transmission method due totechnical difficulties at these high pressures. Fujisawa (1988,1998) subsequently applied these measurements to olivine andits high pressure polymorph wadsleyite.

In parallel with the efforts in MA-8 apparatus, Kinoshita et al.(1979) conducted ultrasonic experiments using MA-6 type highpressure apparatus (Yagi et al., 1975) in which a sample of NaClsandwiched between metal reflectors was enclosed in pyrophillitecubic pressure medium. Both P and S wave velocities were mea-sured using interferometry method by attaching separate trans-ducers at different anvils. A small plastic deformation of �3% wasobserved in the NaCl sample due to the nonhydrostatic stress envi-ronment. However, as the authors declared, the single crystalstructure of the sample in the entire sample was preserved as con-firmed by the X-ray diffraction, in spite of the observed small plas-tic deformation. The pressure was calibrated using (1) phasetransitions in Bi and Ba (fix points), and (2) X-ray diffractionmethod using the equation of state of NaCl of Decker (1971).Unfortunately, the X-ray diffraction and ultrasonic measurementswere only conducted in separate runs due to the different require-ments in the sample geometry and configuration in these measure-ments. The advantages of this experimental setup include thecapability of conducting simultaneous measurements of P and Swave velocities, and a stress-free location for the transducers whenthe sample is under high pressure, and the accessibility of X-raydiffraction at high pressure.

Starting in the early 1990s, under the support of Center for HighPressure Research (CHiPR), ultrasonic velocity measurements athigh pressures using interferometric methods in multi-anvil appa-ratus (1000-ton uniaxial split-cylinder apparatus: USCA-1000)were pursued in collaboration with Ian Jackson of the AustralianNational University; new protocols established in Li et al.(1996b) have become the standard reference implemented inmany successive designs for measuring elastic wave velocities ofsolids and liquids in multi-anvil apparatus. The key factorensuring a success of this implementation can be attributed to

the combination of (1) the use of well-sintered polycrystallinespecimens which yield less attenuation in MHz frequencies (e.g.,Gwanmesia et al., 1993), (2) the transducer placement in astress-free location which ensured the measurements to muchhigher pressures without degradation of ultrasonic signals (e.g.,Fig. 7 of Li et al., 1996b), and (3) a quasi-hydrostatic ‘‘samplefriendly’’ stress environment for the specimens. As shown inFig. 3, the WC anvil serves as an acoustic buffer rod to transmit/receive the high-frequency signals (20–70 MHz) into the sampleeither directly (when sample is attached to the end of the WC anvil,e.g., Li et al., 1996b,c) or by another buffer rod (fused silica glass,alumina or other material with suitable acoustic impedance)(Fig. 3). When the sample is directly attached to the end of theWC anvil, the sample is off-center and soft materials are neededto decrease the pressure gradient around the sample. As shownby Li et al. (1996b), with a stainless steel sleeve and lead insert,the pressure difference was estimated to be less than 0.5 GPa overa 2 mm thick sample. The results for P and S wave velocitiesobtained on fine-grain polycrystalline alumina (General ElectricLucalox) to 10 GPa show a reproducibility within �1% of previoussingle crystal data of Gieske and Barsch (1968) (Li et al., 1998b).When a buffer rod is enclosed in the octahedron as part of the cellassembly as shown in Fig. 3, this configuration has the advantageof placing the sample in the center of the cell to minimize the devi-atoric stress on the sample. In this case, the observed acoustic sig-nals are a series of reflections from the interfaces perpendicular tothe wave propagation path, including those from the anvil/bufferrod, buffer rod/sample, and sample/backing material interfaces,with which the ultrasonic interferometry can be performed.

From the mid-1990s, a series of measurements on mantle min-erals have been carried out in the USCA-1000 and direct velocitydata at mantle pressures were obtained for the first time, includingforsterite and it high pressure polymorphs wadsleyite and ring-woodite (Li et al., 1996c; 1998b; Li, 2003), orthoenstatite (Fleschet al., 1998); single crystal San Carlos olivine (Chen et al., 1998);pyrope-majorite solid solution of garnets (Gwanmesia et al.,1998; Chen et al., 1999). Over these years, both experimental tech-niques and data analysis have been under increased developmentsand improvements, which can be summarized as the following: (1)extended pressure range and more precise pressure calibrations;(2) advanced ultrasonic interferometry techniques and fast dataacquisition; and (3) simultaneous measurements of P and S wavesand the use of dual mode transducers; and (4) novel data analysismethods. While some of these are described in previous publica-tions, for completeness, they are also included in the currentreview.

4.1.1. Pressure calibrationAs demonstrated in these early developments, although the

multi-anvil is capable to generate higher pressures, extra consider-ation must be taken into account for successful and reliable ultra-sonic measurements. With the sample enclosed in a stainless steelsleeve and directly attached to the end of the WC anvil using a 14/8cell assembly, polycrystalline and single crystal olivine specimenswere measured up to 14 GPa (Chen et al., 1996). In these studies,similar to using manganin wires in a piston cylinder apparatus,pressure was measured by enclosing in situ pressure markerswhich exhibited phase transitions, including Bi (2.55 GPa,7.7 GPa) and/or ZnTe (9.6 GPa, 12.2 GPa) and monitoring theircharacteristic resistance change at respective phase transitions. Itis worth noting that measurement on the single crystal olivinerecovered from high pressure run indicating that there was nonoticeable increase in dislocation density and suggesting that thepressures applied on the sample in these solid-pressure mediumexperiments were nearly hydrostatic. Using this setup, many Earth


minerals have been investigated, including pyrope garnet (Chenet al., 1999), orthoenstatite (Flesch et al., 1998), wadsleyite (Liand Liebermann, 2000), MgSiO3 perovskite (Sinelnikov et al.,1998), as well as ceramic materials Al2O3 (Li et al. 1996b) andSiC (Amulele et al., 2004). In recent years, sound velocities mea-surements at room temperature have been extended to 18–20 GPa using a Kawai-type apparatus, such as the study on CaSnO3

perovskite (Schneider et al. 2008) and wadsleyite (Li et al., 2005).With the use of buffer rod in the cell assembly in a configuration

as shown in Fig. 3, it becomes possible to use the buffer rod forin situ pressure determination. In the nondestructive testingcommunity, velocities of Al2O3 are often used as temperature sen-sors in the study of molten materials (e.g., Balasubramaniam, et al.,1999). In a similar fashion, sound velocities of well-characterizedmaterials can be used as pressure markers as well. However, incontrast with using it as a temperature marker at zero pressure,the buffer rod enclosed in the high pressure cell assembly experi-ences deviatoric stresses and pressure gradients across the bufferrod; therefore, when using the velocities (or travel time) of the buf-fer rod material under hydrostatic conditions as reference valuesfor pressure determination, large uncertainties may result. Ideally,the travel time of Al2O3 is measured while it is in the buffer rodposition (i.e., off-center) while the pressure at the center of the cellassembly is determined using in situ markers based on resistivitymethod (e.g., Bi and ZnTe) or X-ray diffraction method (e.g., NaCl,MgO, Au, etc. and their pressure scales). Previously, both singlecrystal olivine (Sinelnikov et al., 2004) and polycrystalline Al2O3

(Higo et al., 2006) have been utilized as in situ pressure markersin ultrasonic measurements in multi-anvil apparatus; in the for-mer case the velocity data of Abramson et al. (1997) and Chenet al. (1996) were used as reference values while in the latter thereference values were based on a relationship between the traveltime of Al2O3 buffer rod (off-centered) and the pressure near thecenter of the cell obtained from X-ray diffraction of NaCl usingthe Decker scale (Decker, 1971). For example, the measurementson polycrystalline Al2O3 (GE Lucalox and Coors 998) reported inLi et al. (1996b) were conducted with in situ markers placed atthe center of the cell using pyrophyllite octahedron pressure med-ium and stainless steel cell assembly. The relationship of S (or P)wave travel times as a function of pressure (Fig. 4), P(GPa) = 220(1 � t/t0), where t is the measured S wave travel timeat high pressure and subscript ‘‘0’’ denotes zero pressure, can thenbe used a pressure calibration for subsequent measurements usingthe same cell assembly. A new pressure scale, with the buffer rodtravel time calibrated against NaCl scale at the center of a cell sim-ilar to Fig. 3, has been established in our lab for Al2O3 and has beenused as in situ pressure marker for the study of ringwoodite (Higoet al., 2006), coesite (Chen et al., 2013), KLB1 peridotite (X. Wanget al., 2013) and NbN (Zou et al., 2013b). The pressure determinedusing this calibration is estimated to have an error of �0.2 GPa.One great advantage of this travel-time pressure calibration is thatpressure and thus travel times can be measured under both com-pression and decompression. More details about this travel timepressure method in MgO octahedron cell assembly are describedelsewhere (Wang et al., in preparation).

4.1.2. Advanced ultrasonic interferometry: transfer function methodAs described in earlier sections, ultrasonic interferometry has

been used widely in the study of elastic properties of solid andliquid materials since the 1950s. Over the years, different methodshave been developed for the measurement of the time of wavepropagation, such as the pulse echo overlap (PEO), phase compar-ison (PC), and pulse superposition (PSP) methods (see reviews inTruell et al., 1969). In these methods, a radio-frequency (RF) pulseis transmitted and received by a piezoelectric transducer attachedto the sample or a buffer rod, and the propagation time is obtained

by measuring the delay between two consecutive echoes asdescribed above.

The development of high-performance digital oscilloscopes andfast analogue/digital acquisition cards has made it possible to usetransfer function methods based on digital signal processing (suchas Cross-Correlation Function (CCF), Hilbert Transform (HT), andContinuous Wavelet Transform (CWT) (Moreno, et al., 1999)). Wehave developed the transfer function method in the course ofdeveloping suitable techniques for ultrasonic interferometric mea-surements in multi-anvil apparatus (Li et al., 2002). Details havebeen described elsewhere and will be reviewed only briefly here.

In comparison with ultrasonic interferometry measurements atindividual frequencies or frequency sweeping, the transfer func-tion method designs a wideband signal as input that contains allthe frequency components centered at the resonance frequencyof the piezoelectric transducer, analogous to monochromaticX-ray source versus white radiation source in X-ray diffractionexperiment. Thus, the recorded signals is the response of the entirecell assembly along wave propagation path, the piezoelectric trans-ducer, buffer rod and sample, to the input pulse within frequenciesinside the passband of the designed signal. Waveforms equivalentto monochromatic frequency input signal can be reproduced byconvolving the transfer function with the desired monochromaticfrequency burst. Note that transfer function records the systemresponse to all frequencies of the passband at the same time incontrast to sweeping through frequencies in PEO and phase com-parison methods, it reduces the data collection time from morethan 30 min in conventional ultrasonic interferometry to a few sec-onds, which is especially important when travel time is used tostudy transient properties of materials. More comparisons aboutthe measured travel times using transfer function methods andother ultrasonic interferometric methods can be found in Li et al.(2002, 2004), Mueller (2013)).

4.1.3. Simultaneous P and S waves velocity measurementsNormally, in experiments on polycrystalline samples, P and S

wave travel times are measured using pure mode P and S wavetransducers separately in different runs; one difficulty is that it isnot simple, in practice, to ensure that the P and S travel timesare measured at the same pressure in different experimental runs.Thus, it is advantageous if P and S wave are measured at the sametime in a single experiment. In the study of Kinoshita et al. (1979)(see also Ahrens and Katz, 1962, 1963), two pure mode transducerswere used on separate WC first stage anvils of the cubic type appa-ratus for P and S wave measurements, respectively. Similarly, inthe study of Knoche et al. (1997, 1998), two transducers weremounted on two second stage WC cubes in a Kawai type apparatusto accomplish simultaneous measurements of P and S wave veloc-ities. Poor signal to noise ratio was reported as one of the majorsources of uncertainties in the measured wave velocities. In thecase of Knoche et al. (1997, 1998) with sample sandwichedbetween two platinum rods, the S wave was not resolvable dueto the extremely low signal to noise ratio.

An improved design has been used in the study of Li andLiebermann (2000) in which pure mode LiNbO3 transducers of P(36�Y cut) and S (41�X cut) waves were mounted on one WC cubetogether with a tungsten buffer rod inside the high pressure cell,this ensured a reliable measurement of P and S wave velocitiesto 10 GPa at room temperature on (MgFe)2SiO4 wadsleyite withhigh signal to noise ratio (see Fig. 2 of Li and Liebermann, 2000).Recently, a dual-mode LiNbO3 transducers (10�Y-cut) has beenemployed for simultaneously generating/receiving longitudinaland transverse acoustic signals despite the fact that the transversesignal has unspecified polarization direction. The WC cube(�38 mm acoustic path length along its diagonal direction) actsas a long delay line, resulting in well separated P and S wave echo


trains in time axis (Sinelnikov et al., 2004; Kung et al., 2002). Asdemonstrated by Li et al. (2004), the travel times measured usingdual mode transducers completely agree with those measuredusing pure mode 0.1% (see Figs. 11 and 12 in Li et al., 2004).

4.1.4. Data analysisWhile ultrasonic interferometry can provide precise measure-

ments of travel times, the length of the specimen (l) is neededfor the determination of wave velocities at high pressure. Underhydrostatic compression, the length change can be obtainedthrough (l/l0)3 = (q0/q) if previous compression data are available;however, with the measurements of both P and S wave traveltimes, the length change at high pressures can be obtained by anapproach known as the Cook’s method (Cook, 1957). Starting withKT = q(@P/@q)T, and KS = q(VP

2 � (4/3)VS2), the following Eq. (1) can be

derived for the calculation of specimen length at high pressure,

l0

l¼ 1þ 1þ acT

3q0l20

ZdP

1tp2 � 4

3ts2

ð1Þ

where tp and ts denote P and S wave travel times in specimenlength l, subscript ‘‘0’’ represents values at zero pressure. The term(1 + acT) accounts for the conversion from adiabatic to isothermalvalues for the bulk modulus KS = KT (1 + acT), a is the thermalexpansion coefficient, c is the Gr}uneisen parameter, and T is tem-perature. At room temperature (T � 300 K), with a � 1–3 � 10�5

(K�1) and c � 1–2 for most mantle minerals, a value of acT � 0.01is thus often assumed. With the length from Eq. (1) and the mea-sured travel times, the velocities and the elastic bulk (K) and shear(G) moduli can be calculated at all pressures. Cook’s method hasbeen used in nearly all high pressure multi-anvil ultrasonic studieswhen direct sample length measurements were not available (e.g.,Li et al., 1996a,b,c; Rigden et al., 1988; Gwanmesia et al., 1990b).

Alternatively, we can use a finite strain approach which com-prises the following three Eqs. (2)–(4),

qV2P ¼ ð1� 2eÞ5=2ðL1 þ L2eÞ ð2Þ

qV2S ¼ ð1� 2eÞ5=2ðM1 þM2eÞ ð3Þ

P ¼ �3K0Tð1� 2eÞ5=2ð1þ 3ð4� K 00TÞe=2Þe ð4Þ

where e = (1 � (q/q0)2/3)/2, K0S = L1-4/3G0, G0 = M1, K0S0 = (5L1�L2)/

3K0S-4G00/3, G00 = (5M1�M2)/(3K0S).The adiabatic bulk modulus is converted to its isothermal value

via KS = KT(1 + acT). With a set of guessed values for K0, G0, K00S, G0

0

at zero pressure and q at each non-zero pressure, VP and VS and Pcan be calculated using Eqs. (2)–(4), then a nonlinear least squareminimization of the difference between the calculated VP, VS, and Pand those measured in the experiment results in the final valuesfor K0, G0, K0

0S, G0

0, and q at each non-zero pressure. Upon conver-gence of the least square fit, the results from the finite strainapproach should be highly consistent with those from Cook’smethod. By comparison, the finite strain method has the advantageof maintaining a self-consistency within the finite strain frame-work by searching for a set of densities that satisfies all three equa-tions of the finite strain theory. Another difference is that Cook’smethod requires travel times for P and S waves at zero pressures(either directly measured at benchtop or back extrapolated fromhigh pressure data) in order for the integration of Eq. (1) to proceedto derive the length at pressure, but the finite strain approachusing Eqs. (2)–(4) can proceed without such a requirement, as longas the density and length at ambient conditions are available.

As a demonstration, we used the raw data of Li et al. (2005) onwadsleyite and analyzed them using the two approaches describedabove. The sample lengths derived from the Cook’s method and the

finite strain approach are essentially identical, the difference is nomore than 0.01% at all pressures. As shown in Fig. 5, the densitiesderived from the finite strain analysis and those from Cook’smethod are completely indistinguishable, both of which are inremarkable agreement with the directly measured densities fromX-ray diffraction method with the pressures calculated using theobserved velocity and density data (X-ray Volume, abs P, see latersections). Moreover, the densities obtained from the above analysisof the ultrasonic data are in excellent agreement with previoushydrostatic compression data of Hazen et al. (2000). Furthermore,we plot the elastic bulk and shear moduli determined from theabove analyses together with those from single crystal Brillouinscattering measurements by Zha et al. (1998) in Fig. 5, the resultsfrom Cook’s method and finite strain approach are completelyindistinguishable, and they are in excellent agreement with thosefrom Zha et al. (1998) for both bulk and shear moduli. We note thatif the sample undergoes plastic deformation in high pressure roomtemperature experiments, additional uncertainties will be intro-duced when these approaches are used, and a more preciseapproach for determining length change is needed, such as X-rayimaging which is discussed in the next section.

4.1.5. Sound velocity of mantle minerals at high pressureThe advancements of ultrasonic measurements in multi-anvil

apparatus as described above have made elastic moduli data avail-able for many mantle and core minerals for the first time at uppermantle and transition zone pressures, especially for the shear prop-erties (Table 1). By conducting measurements at this extendedpressure regime, we are not only able to further explore the elasticbehavior of materials, but also to make more direct comparisonwith seismic data at comparable pressures. For instance, soundvelocity data of MgSiO3 enstatite to �17 GPa at room temperaturerevealed an unprecedented softening in both P and S wave veloci-ties at �10 GPa; this softening reached a minimum around 12–14 GPa followed by a recovery to its normal increase trend withpressure after 14 GPa (Kung et al., 2004). This observation hasmotivated a series of investigations at high pressure using Brillouinscattering (Zhang et al., AGU abstract, 2011), Raman spectroscopy(Zhang et al., 2013a,b), nuclear resonance inelastic X-ray scatter-ing, Mossbauer (Zhang et al., 2012), single crystal X-ray diffraction(Zhang et al., 2012, 2013a,b; Dera et al., 2013) and theoretical cal-culations (Jahn, 2008; Li et al., 2014). Recently, it has been demon-strated that orthoenstatite transforms into an unquenchable P21/cphase at �10 GPa (Zhang et al., 2012), even though a C2/c phase isenergetically more favored above �5 GPa. This Pbca- > P21/c tran-sition appears to occur in a wide range of orthopyroxene composi-tions (Dera et al., 2013; Zhang et al., 2013a,b). Our first principlescalculation (Li et al., 2014) confirmed that the Pbca enstatite struc-ture exhibits a softening C55 followed by the softening of C44 withincreasing pressure. As orthopyroxene is an important constituentphase in the upper mantle and subduction zones, further investiga-tion is required to see if such a softening and transition to P21/c inorthopyroxene also occur at temperatures relevant to the mantleunder high pressure (Zhang et al., 2013a,b). These data will be par-ticularly important for the interpretation of the ‘‘X’’ discontinuityobserved in the mantle in the depth range from 250 to 340 km(i.e., Revenaugh and Jordan, 1991; Deuss and Woodhouse, 2004),or if a phase transition induced low velocity can exist in themantle.

Another group of important mantle minerals are garnets (seeFig. 1). In the past years, velocity data for many compositions,including pyrope, majorite, pyrope-majorite solid solutions,almandine, grossular, as well as pyrolitic garnet are all availableat mantle pressure and room temperature (see Table 1 for dataand references). As pyrope-majorite garnet has the highest P and

Table 1Selected elasticity of major mantle minerals from ultrasonic interferometry measurements under high pressure.

Ks Ks00 oKs/oT G0 G00 oG/oT Max P–T References

(GPa) (GPa/K) (GPa) (GPa/K)

OlivineMg2SiO4 128 4.44 80 1.32 12.5 GPa 300 K Li et al. (1996c)

125 4.5 �0.014 81 1.5 �0.017 9.2 GPa 1273 K Li et al. (2004)(Mg0.9Fe0.1)2SiO4 127 4.8 77 1.6 10.6 GPa 300 K Darling et al. (2004)(Mg0.9Fe0.1)2SiO4 130 4.6 �0.016 77 1.6 �0.014 8.2 GPa 1073 K Liu et al. (2005)

WadsleyiteMg2SiO4 170 4.24 108 1.49 12.5 GPa 300 K Li et al. (1996c)

172 4.2 �0.012 113 1.5 �0.017 7 GPa 873 K Li et al. (1998)163 4.8 110 1.7 3 GPa 300 K Gwanmesia et al. (1998)

(Mg0.88Fe0.12)2SiO4 172 4.6 106 1.5 12 GPa 300 K Li and Liebermann (2000)(Mg0.87Fe0.13)2SiO4 175 4.1 �0.014 106 1.6 �0.014 12 GPa 1273 K Liu et al. (2009)

RingwooditeMg2SiO4 184 4.8 120 1.8 3 GPa 300 K Rigden et al. (1992)

185 4.5 120 1.5 12 GPa 300 K Li (2003)(Mg0.91Fe0.09)2SiO4 186 4.3 �0.018 119 1.2 �0.015 19 GPa1673 K Higo et al. (2008)Fe2SiO4 205 4.3 �0.027 74 1.2 �0.017 6.5 GPa 1073 K Liu et al. (2008)

DiopsideCaMgSi2O6 116.4 4.9 �0.012 73 1.6 �0.011 8 GPa 1073 K Li and Neuville (2010)

OrthopyroxeneMgSiO3 109 7 74.9 1.6 10 GPa 300 K Flesch et al. (1998)

107 7.2 76.4 1.7 �0.011 17 GPa 1273 K Kung et al. (2004)Mg0.8Fe0.2SiO3 103.5 9.59 �0.0268 74.9 2.38 �0.012 1 GPa 623 K Frisillo and Barsch (1972)

High ClinopyroxeneMgSiO3

a 155.9a 5.4a �0.017a 98.3a 1.5a �0.015a 17 GPa 1273 K Kung et al. (2004, 2005)

Pyrope garnetMg3Al2Si3O12 175 3.9 �0.018 91 1.7 �0.01 9 GPa 1273 K Gwanmesia et al. (2006)

170.1 4.9 90.2 2.1 3 GPa 300 K Wang and Ji (2001)172 5.3 92 1.6 10 GPa 300 K Chen et al. (1999)

Majoritic garnetPyrolitic garnet 164.4 4.24 �0.0129 94.9 1.11 �0.01 18.3 GPa 1673 K Irifune et al. (2008)Py62Mj38 169 5.3 89 2 10 GPa 300 K Chen et al. (1999)Py60Mj40 172 5.34 �0.0146 91 1.53 �0.009 8 GPa 1000 K Gwanmesia et al. (2009)Py50Mj50 169 5.29 �0.0146 90.6 1.49 �0.009 8 GPa 1000 K Gwanmesia et al. (2009)

PerovskiteMgSiO3 160 4 �0.034 115 1.9 �0.029 8 GPa 573 K Sinelnikov et al. (1998)

252 4.4 �0.021 173 2 �0.028 9 GPa 873 K Li and Zhang (2005)247 4.5 176 1.6 25 GPa 1200 K Chantel et al. (2012b)

Mg0.95Fe0.05SiO3 236 4.7 174 1.56 25 GPa 1200 K Chantel et al. (2012b)

AkimotoiteMgSiO3 219.4 4.62 �0.023 132.1 1.63 �0.023 26 GPa 1500 K Zhou et al. (2013)

SpinelMgAl2O4 196.0 4.60 �0.022 109.0 0.58 �0.014 14 GPa 900 K Zou et al. (2013a)

StishoviteSiO2 305 5.3 217 1.8 3 GPa 300 K Li et al. (1996a)

Ferropericlase/Magnesiowustite 8 GPa 1600 K Chen et al. (1998)b

MgO 163.5 4.20 129.8 2.42 11 GPa 300 K Li et al. (2005)162.7 4.13 131.1 2.47 3 GPa300 K Jackson and Niesler (1982)162.7 4.24 131.1 2.41 8 GPa300 K Yoneda (1990)162.0 4.27 �0.018 128.5 2.33 �0.023 23.6 GPa 1650 K Kono et al. (2010)

(Mg0.83Fe0.17)O 165.6 4.2 112.5 1.89 9 GPa 300 K Kung et al. (2002)(Mg0.76Fe0.24)O 165 (4.2) 102 2.7 7 GPa 300 K Jacobsen et al. (2005)(Mg0.44Fe0.56)O 159 (4.2) 75 1.5 9 GPa 300 K Jacobsen et al. (2005)Fe0.94O 153 6.1 46.8 0.6 5 GPa 300 K Jacobsen et al. (2005)

Grossular garnetCa3Al2Si3O12 171.2 4.47 �0.0136 107.4 1.29 �0.013 8 GPa 1273 K Gwanmesia et al. (2014)

171.5 4.42 �0.0127 108.4 1.27 �0.011 17 GPa 1650 K Kono et al. (2010)

a Properties at 6.5 GPa.b Derived o2C11/oPoT o2C110/oPoT, and o2C44/oPoT using previous results of Cij and their pressure and temperature. Numbers in parentheses are fixed values. derivatives.


S wave velocities among all upper mantle minerals, the pressurederivatives of its bulk and shear moduli will have important effectson the velocities of the mantle mineralogical models, and thereforethe constraints on the composition of the mantle. With theadvancement of ultrasonic interferometry measurementsdescribed in this study, it is very encouraging to notice that theresults on pyrope-majorite garnets from most recent ultrasonic

interferometry measurements and those from Brillouin scatteringstudies are in good agreement (e.g., Gwanmesia et al., 2006).

Of particular importance to the study of the upper mantle andtransition zone are the measurements on olivine and its high pres-sure polymorphs, whose velocity changes across these isochemicaltransitions are believed to be responsible for the seismic disconti-nuities at 410 km and 520 km depths, respectively (Fig. 1). Over

Buffer Rod

Sample

Backing

LeadMgO or Pyrophyllite

Fig. 3. Schematic diagram of the ultrasonic measurements at room temperature in Kawai-type multi-anvil apparatus.

Fig. 4. Normalized S wave travel time of Al2O3 as a function of pressure inpyrophyllite octahedron with stainless steel cell. The pressure was determinedusing Bi, and ZnTe as pressure calibrants.

Fig. 5. (a) Comparison of densities derived from finite strain analysis (empty square) andHazen et al. (2000) (red circle) (b) Comparison of elastic bulk and shear moduli from anawith those from single crystal Brillouin scattering measurements of Zha et al. (1998) (grreader is referred to the web version of this article.)


the years, sound velocities of these phases with a varying Mg andFe contents have been measured using ultrasonic interferometryup to 20 GPa at room temperature (Li et al., 1996c, 2005; Higoet al., 2006; Li and Liebermann, 2000; Li, 2003), and the up-to-dateresults on the anhydrous Mg2SiO4 composition are shown in Fig. 6.It can be seen that the velocities for P and S waves between forste-rite and wadsleyite, as well as wadsleyite and ringwoodite, can becompared at pressures in a close proximity to those of 410- and520-km seismic discontinuities (see also Li et al. 1996b). The veloc-ity contrasts at room temperature across the forsterite-wadsleyitetransition are constrained to be �9% and �11% for P and S waves,respectively, while the subsequent wadsleyite to ringwoodite tran-sition at 520-km depth yields a velocity contrast of about 3%. Theseroom temperature measurements not only provided indispensabledata to advance our understanding about the Earth’s mantle, butalso serve as benchmark results for the investigation of water inthe mantle when compared with their hydrous counterparts (e.g.,Mao et al., 2012; Jacobsen, 2006; and references therein).

Cook’s method (solid diamond) and X-ray diffraction (solid triangle), with those oflysis using Cook’s method (orange triangle) and finite strain method (blue diamond)een square). (For interpretation of the references to colour in this figure legend, the

Fig. 6. Current status of P and S wave velocities of olivine, wadsleyite andringwoodite of Mg2SiO4 as a function of pressure from multi-anvil ultrasonicmeasurements.


4.2. Simultaneous high pressure and high temperature measurements

To conduct velocity measurements close to conditions of themantle at simultaneous pressure and temperature, feasibility stud-ies at simultaneous high pressure and temperatures above 10 GPaup to 1500 K using the Kawai type (MA-8), double-stage high-pres-sure apparatus have been performed in the labs of both StonyBrook and Bayreuth (e.g., Knoche et al., 1998; Li et al., 1998a).However, these measurements encountered a few challenges,including (1) the conventional method for determining pressure(i.e., a calibration curve fitted through a few fixed points calibratedusing known phase transformations), is not precise enough for the

Fig. 7. Schematic diagram of the ex

determination of pressure derivatives of the elastic moduli (oK/oP,oG/oP) and cross derivatives (o2K/oPoT and o2G/oPoT); and (2) thesample length at high pressure and high temperature has to relyon previous equation-of-state data which requires the sampleunder hydrostatic compression. If the sample deforms plasticallydue to the rapid decrease of yield strength with temperature orother mechanisms (e.g., phase transition, melting, etc.), estimationof sample length change using previous EOS becomes unreliable,resulting in large uncertainties in the measured velocities. Thisproblem has been addressed recently by interfacing ultrasonicmeasurements with synchrotron X-radiation in which the samplelength can be directly measured using X-radiographic imagingtechnique (Li et al., 2004; Kung et al., 2002; Higo et al., 2008;Mueller et al., 2003; Mueller, 2013).

4.3. Ultrasonic Interferometry in conjunction with synchrotronX-radiation

4.3.1. P-V-VP-VS-T measurementsUltrasonic interferometry was first adapted for use in conjunc-

tion with synchrotron X-rays at the X17B1 hutch (currently recon-structed as X17B2) at the National Synchrotron Light Source of theBrookhaven National Laboratory, where a 250-ton cubic apparatus(SAM 85) was installed to generate pressures up to 15 GPa(Weidner et al., 1992a,b). The experimental set-up features energydispersive X-ray source and a multi-elements detector for powderX-ray diffraction. In addition, a YAG crystal and a CCD camera aremounted in the direction of the X-ray beam to record the radio-graphic image of the sample enclosed in the high pressure cell(see details in Li et al., 2004). Briefly, a LiNbO3 transducer ismounted onto the back of the WC anvil (Toshiba Grade F) and con-nected to the ultrasonic interferometer by coaxial cables goingthrough a hole drilled on the supporting ring of the WC anvil

perimental setup at NSLS, BNL.

Fig. 8. Difference between absolute pressure and the pressure inferred from theNaCl placed next to the sample using Decker Scale. The gray region represents theuncertainties of Decker NaCl scale.


(Fig. 7). The high pressure cell consists of cubic pressure mediummade of boron-epoxy mixture (4:1 wt%); the sample (polycrystal-line or single-crystal) is placed near the center of the cell assemblyand surrounded by a boron nitride sleeve. An amorphous carbonsleeve is used as the heating element. A double side polished bufferrod (for instance, Al2O3) is in contact with the sample for transmit-ting acoustic energy into and out of the sample. The rear surface ofthe sample is backed by NaCl + BN mixture (10:1 wt%) whichserves two purposes: (1) providing a pseudo-hydrostatic pressureenvironment; and (2) serving as an in situ pressure marker. Inthe course of an experiment at any P and T conditions, X-ray dif-fraction spectrum from the sample or the NaCl pressure standardcan be collected at the same time as the ultrasonic waveform dataare recorded, followed by a collection of X-ray image for the deter-mination of sample length (Fig. 7).

In a typical experiment with polycrystalline sample, three typesof data are collected: (1) X-ray diffraction from the sample and thepressure standard, (2) ultrasonic waveforms using transfer func-tion method, and (3) X-ray radiographic image of the sample. Dataprocessing of these raw data results in the determination of pres-sure (P), unit cell volume (V), compressional (VP) and shear (VS)wave velocities at all pressure and temperature (T). In practice,data collections are usually performed along cooling after anneal-ing the sample at T > 673 K to relax the deviatoric stress accumu-lated in the cell assembly during compression/decompression atroom temperature (Li et al., 2004; Wang et al., 1994). Such mea-surements have also been adapted to a double stage Kawai-typeapparatus installed at Advanced Photon Source, Chicago. Moreabout the technical details can be found in Li et al. (2004, 2005)and Kung et al. (2004, 2005); in the following, we will focus onthe new advancements since our previous publications.

4.3.2. Absolute pressure determinationIn high pressure X-ray experiments, NaCl, MgO, Au, and Pt are

the most commonly used pressure calibration materials to beenclosed in the sample chamber (e.g., Fei et al., 2007); by using apreviously established equation of state, such as the pressure scaleestablished by Decker (1971) for NaCl, the pressure exerted on thesample can thus be obtained by assuming a pressure continuity inthe high pressure cell. The accuracy of pressure determination hasa critical influence on the study of equation of states for mantle andcore mineral phase. According to Decker et al. (1972), the DeckerNaCl scale is accurate within 2% at 5 GPa, 4% at 10 GPa, and �5%within 20–30 GPa. In an attempt to improve the NaCl pressurescale, Brown (1999) proposed an updated version which has anuncertainty of less than 1% in pressure up to 5 GPa, approximately1.5% at 10 GPa and 3% at 25 GPa. At the same volume compression,the Brown scale claims that pressures determined using the Deckercalibration are lower by 3% in the pressure range of 10–20 GPa at300 K. At higher temperatures, pressures determined using thetwo scales are similar (at 1100 K and 20 GPa the difference is0.2 GPa). It has been suggested that the largest contribution tothe uncertainty at high pressures is the lack of knowledge of thevolume dependence of the Grüneisen parameter when aMie–Grünesen–Debye approach is used to construct the scale.

Simultaneous determination of P and S wave velocities and den-sity allows for precise determination of elastic bulk and shear mod-uli and their pressure and temperature derivatives without using apressure standard; in addition, the pressure exerted on the sample(absolute pressure) can be calculated directly using the density andthe elastic modulus derived from the measured velocity measure-ments (Li et al., 2005; Matsui et al., 2012; Ruoff et al., 1973; Zhaet al., 1998). Details of using such experimental data for pres-sure-standard-free data analysis have been described in Li andZhang (2005) (see also Li et al., 2005; Liu et al., 2008; Kono et al.,2010; Mueller et al., 2003). In essence, finite strain Eqs. (2) and

(3) are used to fit the entire high pressure and high temperaturedataset to derive the pressure and temperature dependences forthe bulk and shear moduli, after which the bulk properties are usedin Eq. (4) to calculate (absolute) pressure. Since sound velocitymeasurements using ultrasonic interferometry as described aboveyield adiabatic values but the pressure generation and data collec-tion using large volume apparatus are along isothermal conditions(Wang et al., 1994), the acoustically determined bulk modulus KS

has to be converted to isothermal KT when calculating pressureon the sample (absolute pressure) using Eq. (4).

By comparing the pressures calculated using the data obtainedon wadsleyite and (Mg0.83Fe0.17)O with those derived from NaCl(placed next to the sample in the cell assembly) using Decker scale,a difference of �2 GPa was found at �20 GPa (Li et al., 2005), whichis 5–6% higher than the claimed uncertainty of Decker scale (Fig. 8).However, the elastic moduli as well as the compression curve at300 K of wadsleyite, when plotted as a function of the calculatedpressure, show excellent agreement with those obtained from sin-gle crystal Brillouin scattering measurements of Zha et al.(1998)and the compression data of Hazen et al. (2000), both of whichwere obtained under hydrostatic conditions (Fig. 5). By contrast,Matsui et al. (2012) reported that the newly obtained NaCl equa-tion of state (Matsui Scale hereafter) shows an agreement withthose of Decker (1971) within 0.34 GPa in the pressure range of19–21 GPa (�1.7%), and �1 GPa at pressure around 30 GPa(�3.2%); this scale was obtained by combining data at zero pres-sure (estimated P and S wave velocities based on those ofSpetzler et al. (1972); V0 taken from JCPDS card 05-0628; KS0 fromChang (1965)) with new measurements within the pressure rangefrom 6.66 to 12.04 GPa on NaCl using the above simultaneousultrasonic interferometry and X-ray diffraction techniques. In com-parison to Brown scale which yields pressure higher than Deckerscale, the pressures determined using Matsui scale are lower thanDecker scale. In other words, the pressures determined using Mat-sui scale and Brown scales may differ by 5–6% in the pressureregime of 10–20 GPa. Although the lack of self-consistencybetween zero pressure data (V0, K0) and high pressure data inMatsui et al. (2012) may potentially result in uncertainties largerthan those claimed, the new data within 6.6–12 GPa appear to bein good agreement with those from previous studies.

Ultrasonic interferometry measurements in conjunction withX-ray diffraction and X-radiography have also been conducted onMgO (Li et al., 2006), which yielded elastic bulk and shear moduli

Fig. 9. P and S wave velocities of MgSiO3 perovskite as a function of pressure. Thedashed linear line is a guide to the eye.


in excellent agreement with previously reported data measuredusing ultrasonic and Brillouin scattering techniques under hydro-static pressures (see comparison in Fig. 4 of Li et al., 2006); how-ever, the pressures calculated from the NaCl placed next to theMgO sample differ from the calculated absolute pressure by �6%at 10–12 GPa, which is in good agreement with the findings fromexperiments on wadsleyite shown in Fig. 8. It should be noted thatin this experiment, the data were collected after annealing thesample at �1073 K, thus, the deviatoric stress on the MgO samplewas believed to be negligible. Based on all these observations, weconclude that, even though the pressure derived from NaCl placednext to the sample is different from Decker scale, the elastic prop-erties and their pressure derivatives can be accurately derived andgood agreement with previous studies can be achieved if the soundvelocities and density are measured simultaneously and analyzedusing a pressure-standard-free approach. This is evident in thestudies of wadsleyite, MgO and NaCl mentioned above (Li et al.,2006; Matsui et al., 2012) as well as many others (Liu et al.,2005; Gwanmesia et al., 2014; Higo et al., 2008). The apparentpressure difference between absolute pressure and those derivedfrom NaCl shown in Fig. 8 might be related to a combined effectof uncertainty in pressure scale, the difference in yield strengthsbetween the sample and NaCl, and quasihydrostatic conditionsdue to the use of solid pressure medium. It is likely that whenthe existence of these non-ideal configurations is registered inthe measured X-ray diffraction (hence the density) and velocitiesof the sample, the finite strain fit converges to an effective pressureequivalent to a hydrostatic pressure with these non-ideal configu-rations accounted for, as evidenced in the example of wadsleyite.

4.3.3. Measurements on MgSiO3 perovskite and lower mantlecomposition

Using these combined X-radiation and ultrasonic measure-ments, many important mantle minerals have been investigatedat simultaneous high pressure and high temperature. For instance,the temperature derivative of the shear modulus of wadsleyite, akey parameter for the mineral physics modeling of the velocitycontrast at 410 km depth, was experimentally determined for thefirst time (Li et al., 1998). In subsequent years, the measurementshave also extended to olivine, wadsleyite and ringwoodite for the(Mg1�xFex)2SiO4 with x = 0 and 0.1 (Liu et al., 2005; Liu et al.,2009; Higo et al., 2008). As shown in Table 1, for olivine and itshigh pressure polymorphs with iron content around 10 mol%, theirpressure derivatives appear to be very similar in bulk and shearmoduli although the temperature derivatives seem to vary slightly.Using these data, Liu et al. (2009) investigated the nature of410 km discontinuities with various iron content to match themagnitude of the 410 km discontinuity based on the iron partition-ing data of Irifune and Isshiki (1998). The olivine in the upper man-tle dissociates into magnesium rich silicate perovskite plusferropericlase in the lower mantle.

In the lower mantle, magnesium-rich perovskite is believed totake �80% in volume in a pyrolitic composition. The bulk modu-lus and its pressure derivative for MgSiO3 perovskite have beeninvestigated by many studies using static compression as wellas Brillouin scattering and their values have been constrained tobe within a range of 246–272 GPa (Yeganeh-Haeri et al., 1989;Fiquet et al., 1998; Funamori et al., 1996; Wang et al., 1994).Recent Brillouin scattering and ultrasonic interferometry mea-surements show a consistent result of 253 ± 2 GPa (Sinogeikenet al.,2003; Li and Zhang, 2005) for the bulk modulus; however,its pressure derivative is still not very well constrained at lowermantle pressures despite that many static compression studieshave been conducted to the pressure of the lower mantle.Moreover, the shear modulus at high pressures has only beenmeasured using ultrasonic techniques described above

(e.g., Sinelnikov, et al., 1998; Li and Zhang, 2005) and by Brillouinscattering (Murakami et al., 2012, using a polycrystalline sample).Results from previous ultrasonic interferometry measurements upto �9 GPa of pressure yielded oK/oP = 4.3–4.4 and oG/oP = 1.8–2.0,and our unpublished measurements at an extended pressure to�20 GPa appear to support these results (Fig. 9). Recently, newultrasonic interferometry measurements have also obtained byChantel et al. (2012b) and Zhou et al. (2013); the velocities fromthese studies are compared with those from Li and Zhang (2005)in Fig. 9. Although there is only one datum in Zhou et al. (2013),the results of both P and S waves are in excellent agreement withour unpublished data as well as the extrapolation of Li and Zhang(2005). The P wave velocities from Chantel et al. (2012b) are ingood agreement with our measurements and that of Zhou et al.(2013), while the S wave data agree within 2%. However, whencompared with Brillouin scattering measurements on polycrystal-line samples at 8 and 24 GPa, all of the ultrasonic measurementsshow higher velocities. As a result, Murakami et al. (2012) reporta lower value for the pressure derivative of the shear modulus ofperovskite and infer that the mineralogy of the lower mantle isperovskitic. As a consequence, the oG/oP of MgSiO3-perovskitemerits further investigations by ultrasonic and/or single crystalBrillouin spectroscopic techniques at pressures relevant to thelower mantle.

While many measurements on mantle minerals were con-ducted on polycrystalline specimens, measurements on singlecrystal have also been conducted for some materials, such as ZnOand MgO (Decremps, et al., 2001; Chen et al., 1998). Technicallyspeaking, when working on single crystals, the experimental setupand data collection procedures are essentially the same as workingwith polycrystalline except for that the samples have to be pre-pared along selected crystallographic orientations in order toobtain the full elastic tensor (hence the VRH averaged bulk andshear moduli) (see Liebermann and Li, 1998). In this case, the finite


strain data analysis can be made based on the expression for theindividual elastic constant, for instance, the travel time equationof state approach proposed by Spetzler and Yoneda (1993). Theresults on MgO to 8 GPa and 1600 K demonstrated that the anisot-ropy of MgO decreases with pressure and then increases withincreasing temperature at high pressures. A direct implication isthat (Mg,Fe)O, the second most abundant lower mantle mineral,can also contribute to the lower mantle anisotropy, even thoughit remains in cubic crystal structure throughout the lower mantleconditions.

4.4. Current status and outlook

Currently, simultaneous ultrasonic interferometry and X-radia-tion measurements techniques have been implemented at manymajor synchrotron sources in the world, including SPring8 in Japan,the NSLS and the APS in the U.S., and DESY in Germany, and anincreased number of studies have been reported in the last fewyears (e.g., Chantel et al., 2012b; Kono et al., 2010; Irifune et al.,2008; Higo et al., 2008; Gwanmesia et al., 2009; Mueller et al.,2006, 2007) (see also Table 1). As shown in Fig. 10, the currentsimultaneous P–T conditions of ultrasonic interferometry havereached more than 25 GPa and 1800 K, which covers the depthrange throughout the upper mantle and transition zone and intothe uppermost lower mantle. With the intrinsic high precision ofultrasonic interferometry (coupled with precise temperature mea-surement, the capabilities of a pressure-standard-free data analysisand absolute pressure determination in multi-anvil apparatus),this technique is serving as the most self-consistent and approachfor studying the elasticity of mantle minerals and comparison withseismic results. In the following, some remarks about the currentstatus and future challenges in ultrasonic interferometric measure-ments for an improved understanding of the elasticity of theEarth’s interior are highlighted.

Fig. 10. Current status of sound velocity measurements in multi-anvil apparatus at highultrasonic, and resonance ultrasonic spectroscopy investigations. For Brillouin scattering

4.4.1. Reconciliation of elasticity discrepanciesInconsistent conclusions about the mantle mineralogical mod-

els, in many cases, are due to the discrepancies in the elasticitydata selected from previous published results of bulk modulusand shear modulus and their pressure and temperature deriva-tives. As demonstrated in the current study on wadsleyite, wefound that the apparent discrepancies in oK/oP and oG/oP can bereconciled when consistent data analysis is used, at least for thosefrom single crystal Brillouin scattering and ultrasonic interferome-try measurements at comparable pressures. If the Brillouin scatter-ing data of KS, G, VP and VS from Duffy et al. (1995) on forsterite arefit to finite strain Eqs. (2) and (3), the derived oK/oP (�4.5) is inexcellent agreement with the value of 4.44 previously reportedin Li et al. (1996c) from ultrasonic measurements. This appearsto be also true for many major mantle minerals listed in Table 1,including ringwoodite, pyrope-majorite garnet, and MgO (see thereferences in Table 1 for detailed comparisons). At higher temper-ature data, good agreement can be found in the temperature deriv-atives of MgO, as well as those from single crystal resonancespectroscopy at high temperature and zero pressure (e.g., diopside,MgO). Additional work in this direction is still needed to reachcomplete agreement for all mantle minerals.

4.4.2. Extension of pressure and temperature rangeAs shown in Fig. 10, multi-anvil ultrasonic interferometry has

been extended to a P–T range that overlaps with resonance ultra-sonic spectroscopy at high temperature and zero pressure(�1800 K), single-crystal Brillouin scattering at high pressure-room temperature (>80 GPa) and high temperature-room pressure(�1800 K) (for the development of laser heating Brillouin scatter-ing measurements on polycrystalline samples, see Murakamiet al., 2009 and a recent review by Speziale et al., 2014), as wellas other optical spectroscopic methods, such as nuclear resonanceinelastic X-ray scattering and inelastic X-ray scattering in diamond

pressure and temperature in comparison to single crystal Brillouin scattering, GHzmeasurements on polycrystalline samples, see Speziale et al. (2014).


anvil cells. The apparent discrepancies mentioned above in somecases are caused by the pressure ranges; for example, the differ-ences seen in the high-pressure polymorphs of olivine betweenthose measured to 3 GPa and to those >10 GPa. An important targetin this respect is magnesium silicate perovskite as shown in Fig. 9;it is especially important to resolve the discrepancy between theultrasonic interferometry data and the polycrystalline Brillouinscattering data, so that more reliable inferences on the mineralog-ical composition of lower mantle can be obtained. Although X-raydiffraction experiments using multi-anvil apparatus have beenconducted above 100 GPa (e.g., Yamazaki et al., 2014), adaptingthese developments to sample sizes suitable for ultrasonic mea-surements remains challenging.

4.4.3. Refinement of pressure scalesAs shown above, the ultrasonic interferometry interfaced with

synchrotron offers a unique opportunity for absolute pressuredetermination. Applying these techniques to the study of pressurecalibrant materials, such as those on MgO (Kono et al., 2010) andNaCl (Matsui et al., 2012) as well as Au and Pt at extended pressureand temperature range will greatly reduce the inconsistency (seeFei et al., 2007) among different calibrants, which in turn will facil-itate the comparison between equation of state studies and thosefrom direct sound velocity measurements.

4.4.4. Effect of solid-solutions and minor elements on elasticity ofmantle minerals

The data listed in Table 1 are mostly on the end members ofmantle phases, such as magnesium end member for olivine andits high-pressure polymorphs, although the effect of iron has beenstudied so far in these minerals and Gwanmesia and others haveinvestigated solid solutions in garnets (e.g., Gwanmesia et al.,2009). In some minerals, the effect of hydrogen (water) (e.g.,Jacobsen et al., 2006; Mao et al., 2012; Jiang et al., 2006; Chantelet al., 2012a) and aluminum (e.g., Lakshtanov et al., 2007;Jackson et al., 2005) have also been investigated by Brillouin scat-tering measurements. A systematic study on the effect of minorelements such as Al, Na, Ca, and H in these mineral phases usingultrasonic interferometric methods is still under investigation inmany laboratories. Of particular importance is the effect of water,which will help to delineate the cause of the low velocities justabove the transition zone and provide insight into the water bud-get in the mantle.

4.4.5. Measurements on melts and effect of partial meltingUltrasonic interferometry has been successfully used for the

study of elastic moduli of liquid at ambient pressures (e.g.,Katahara et al., 1981; Rai et al., 1981; Manghnani et al., 1986;Rivers and Carmichael, 1987; Ai and Lange, 2004) using eitherthe varying sample length method or a frequency sweep method.Previous attempts for conducting such measurements at high pres-sures have been plagued by the difficulty of precisely measuringsample length, a necessary parameter to obtain sound velocityafter measuring the travel time from ultrasonic interferometry.As described above, this has been resolved by using X-ray imagingtogether with ultrasonic measurements. Recently, sound velocitymeasurements have been applied to melt phases at NSLS in aMA-6 apparatus (Li and Liu, 2010), at SPring8 (Nishida et al.,2013) in MA-8 apparatus, and at APS in Paris-Edinburgh press(Kono et al., 2013). These techniques can be also applied to thestudy of effect of partial melting on sound velocities to interpretthe anomalously low velocity zones in the upper mantle, just abovethe 410-km discontinuity and at the bottom of the lower mantle.

Acknowledgements

We thank the editors of PEPI, Timothy Horscroft and Kei Hirosefor their invitation to write this review.We thank Hideyuki Fujisa-wa, Steven Jacobsen and Akira Yoneda for constructive feedback onthe original submitted version of this review. The experimentaldata used in this paper are from research funded by the NSF(EAR 06-35651, EAR10-45630) and DOE/NNSA (DEFG5209NA29456, DE-NA0001815). Use of the X17B2 beamline was sup-ported by COMPRES, the Consortium for Materials PropertiesResearch in Earth Sciences under NSF Cooperative AgreementEAR 11-57758 and by the Mineral Physics Institute, Stony BrookUniversity. Use of the National Synchrotron Light Source, Brookha-ven National Laboratory, was supported by the U.S. Department ofEnergy, Office of Science, Office of Basic Energy Sciences, underContract No. DE-AC02-98CH10886.Portions of this work were per-formed at GeoSoilEnviroCARS (Sector 13), Advanced Photon Source(APS), Argonne National Laboratory. GeoSoilEnviroCARS is sup-ported by the National Science Foundation – Earth Sciences(EAR-1128799) and Department of Energy- GeoSciences(DE-FG02-94ER14466). Use of the Advanced Photon Source wassupported by the U.S. Department of Energy, Office of Science,Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.MPI#500.

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