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Elasticity measurements at extreme conditions [Elektronische Ressource] : application to FeO and FeNi-alloy / vorgelegt von Anastasia Kantor

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213 pages
Elasticity measurements at extreme conditions: application to FeO and FeNi-alloy Von der Fakultät für Biologie, Chemie and Geowissenschaften der Universität Bayreuth zur Erlangung der Würde eines Doktors der Naturwissenschaften - Dr. rer. nat. - genehmigte Dissertation vorgelegt von Diplom-Geochemikerin Anastasia Kantor aus Moskau Bayreuth, 2008 Prüfungsausschuß: Prof. St. Peiffer, Universität Bayreuth (Vorsitzender) PD Dr. L. Dubrovinsky, Universität Bayreuth (1. Gutachter) Prof. St. KKlotz, Universität Paris (2. Gutachter) Prof. K. Bitzer, Universität Bayreuth Prof. D. Rubie, Universität Bayreuth Tag der Einreichung: 01. August 2007 Tag der wissenschaftlichen Kolloquiums: 05. Februar 2008 To the memory of my teacher Egorov-Tismenko Yu. K. Contents Abstract VII Zusammenfassung XI Chapter 1. Introduction 2 1.1. Elastic properties of solids…………………………...………...… 4 1.2. Measuring elastic properties……………………….…………….. 32 1.3. Geophysical implications………………..……………...…...…... 56 Chapter 2. Developed methods and instrumentation 2.1. Gigahertz ultrasonic interferometry laboratory at Bavarian Geoinstitut……………………………………………..……….... 72 2.2. Inelastic x-ray scattering technique ……………………………... 97 VChapter 3. Results and discussion 3.1.
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Elasticity measurements
at extreme conditions:
application to FeO and FeNi-alloy





Von der Fakultät für Biologie, Chemie and Geowissenschaften
der Universität Bayreuth




zur Erlangung der Würde eines
Doktors der Naturwissenschaften
- Dr. rer. nat. -



genehmigte Dissertation



vorgelegt von
Diplom-Geochemikerin Anastasia Kantor
aus Moskau






Bayreuth, 2008

























Prüfungsausschuß:

Prof. St. Peiffer, Universität Bayreuth (Vorsitzender)
PD Dr. L. Dubrovinsky, Universität Bayreuth (1. Gutachter)
Prof. St. KKlotz, Universität Paris (2. Gutachter)
Prof. K. Bitzer, Universität Bayreuth
Prof. D. Rubie, Universität Bayreuth


Tag der Einreichung: 01. August 2007
Tag der wissenschaftlichen Kolloquiums: 05. Februar 2008 To the memory of my teacher
Egorov-Tismenko Yu. K. Contents

Abstract VII

Zusammenfassung XI

Chapter 1. Introduction 2

1.1. Elastic properties of solids…………………………...………...… 4
1.2. Measuring elastic properties……………………….…………….. 32
1.3. Geophysical implications………………..……………...…...…... 56

Chapter 2. Developed methods and instrumentation

2.1. Gigahertz ultrasonic interferometry laboratory at Bavarian
Geoinstitut……………………………………………..……….... 72
2.2. Inelastic x-ray scattering technique ……………………………... 97


VChapter 3. Results and discussion

3.1. Elasticity and magnetization in wüstite: High- frequency
interferometry measurements, neutron diffraction study, and
inelastic x-ray scattering experiments…..………………………… 108
3.2. Anelastic behaviour of Fe O under high pressures: Evidence 0.95
from static compressibility and inelastic x-ray scattering
experiments……………………………………………...………... 135
3.3. IXS study of polycrystalline Fe Ni -alloy at high pressures 0.78 0.22
and temperature……………………….………………………...… 145

Conclusions 160

Acknowledgments 166

Bibliography 168

List of publications 198

VI

Summary




The picture of Earth’s deep interior is rapidly improving from the seismic
tomography data and indicates more complexity than previously thought. The
presence of Earth’s seismic anisotropy requires the knowledge of fully anisotropic
elasticity data for mineral phases. The single-crystal elastic constants of minerals, C , ij
are elements of the fourth-rank elasticity tensor, which relates stress to strain. The fact
that elastic strain also defines seismic wave propagation, the elastic tensor of minerals
can be applied to interpret the bulk mineralogy of the interior from seismological
observation. Knowledge of the elasticity of crystalline materials as a function of
pressures and temperature is also of primary interest for solid state physics because
elastic tensors reveal the nature of interatomic interactions.
In order to determine the full elastic tensor of minerals under high pressure
and temperature, several techniques are available, including ultrasonic interferometry
and inelastic x-ray scattering methods. One of the most accurate techniques is high-
frequency acoustic interferometry, which is capable for measuring sound wave
velocities in very small samples under high pressures. The ultrasonic interferometry
system operating at 0.5-2.0 gigahertz (GHz) frequencies was developed in the
Bavarian Geoinstitut of the University of Bayreuth for in situ high pressure and
temperature experiments. Here, GHz-ultrasonic interferometry has been used to study
VIIthe elastic properties of monoxide minerals such as FeO, liquids and nanocrystalline
samples, each with particular importance to Earth or material sciences.
Fe O, wüstite, is the end-member phase of the (Mg,Fe)O solid solution, x
thought to be the most abundant non-silicate oxide in the mantle. The full elastic
tensor of wüstite is determined by three elastic constants (C , C , C ), which have 11 12 44
been probed at high-pressures. At about 17-20 GPa, FeO is known to undergo a
displacive cubic-to-rhomobhedral phase transformation. Prior to this transformation,
we observe a pressure-induced mode softening of the C elastic constant. In addition, 44
previously undetected discontinuities in the pressure derivatives of C and C at 4.7 11 12
± 0.2 GPa were observed. This pressure is consistent with that of the magnetic
ordering commencement, as was observed by high-pressure Mössbauer spectroscopy
57in a Fe-enriched sample of FeO. The results indicate that an intermediate, partially
magnetic but still cubic phase of FeO probably exists at room temperature and in
pressure range from ~5 GPa to ~17 GPa.
In order to provide deeper knowledge of the magneto-elastic coupling in the
material, neutron diffraction experiments were performed under ambient pressure and
low temperatures. The results indicate that the magnetically ordered cubic phase of
FeO that was observed at high pressures also exists at ambient pressure at x
temperatures between 160 and 201 K.
Combined inelastic x-ray scattering and x-ray diffraction studies on a single
crystal of Fe O were performed up to 20 GPa at room temperature. The results show 0.95
strong anelastic behaviour of wüstite, which should be accounted for at high pressure.
Transition-metal oxides, non-stoichiometric compounds, and materials with complex
mesostructure have some internal degree of freedom, and could therefore experience
internal relaxation and show deviations from normal elastic behaviour.
VIIIA methodology to measure inelastic x-ray scattering in externally heated
diamond anvil cells have also been developed. This technique was used to study
polycrystalline fcc-Fe Ni alloy at high pressures (up to 72 GPa) and temperature 0.78 0.22
(up to 715 K). The bulk elasticity and its P and T derivatives were obtained for the
material. No significant deviation of the elastic properties from those of pure ε−iron
was observed and furthermore no deviation from Birch’s law. Although the bulk
elasticity of fcc Fe-Ni alloy and ε−Fe seem to be very similar, the elastic anisotropy of
hexagonal and cubic phases should be quite different. If the metal phase in the inner
core is not hexagonal, but cubic (or a mixture of the two phases exists), seismic
anisotropy may provide a better way to discriminate between them two.

IX

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