Citation
Murphy, Caitlin Anne (2012) Thermoelasticity of Hexagonal ClosePacked Iron from the Phonon Density of States. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GQ17GV90. https://resolver.caltech.edu/CaltechTHESIS:02162012075245736
Abstract
Iron is the main constituent in Earth’s core, along with ~5 to 10 wt% Ni and some light elements (e.g., H, C, O, Si, S). This thesis explores the vibrational thermodynamic and thermoelastic properties of pure hexagonal closepacked iron (εFe), in an effort to improve our understanding of the properties of a significant fraction of this remote region of the deep Earth and in turn, better constrain its composition.
In order to access the vibrational properties of pure εFe, we directly probed its total phonon density of states (DOS) by performing nuclear resonant inelastic xray scattering (NRIXS) and in situ xray diffraction (XRD) experiments at Sector 3IDB of the Advanced Photon Source (APS) at Argonne National Laboratory. NRIXS and in situ XRD were collected over the course of ~14 days at eleven compression points between 30 and 171 GPa, and at 300 K. Our in situ XRD measurements probed the sample volume at each compression point, and our long NRIXS datacollection times and highenergy resolution resulted in the highest statistical quality dataset of this type for εFe to outer core pressures. Hydrostatic conditions were achieved in the sample chamber for our experiments at smaller compressions (P ≤ 69 GPa) via the loading of a neon pressure transmitting medium at the GeoSoilEnviroCARS (GSECARS) sector of the APS. For measurements made at P > 69 GPa, the sample was fully embedded in boron epoxy, which served as the pressure transmitting medium.
From each measured phonon DOS and thermodynamic definitions, we determined a wide range of vibrational thermodynamic and thermoelastic parameters, including the LambMössbauer factor; vibrational components of the specific heat capacity, free energy, entropy, internal energy, and kinetic energy; and the Debye sound velocity. Together with our in situ measured volumes, the shape of the total phonon DOS and these parameters gave rise to a number of important properties for εFe at Earth’s core conditions.
For example, we determined the Debye sound velocity (vD) at each of our compression points from the lowenergy region of the phonon DOS and our in situ measured volumes. In turn, vD is related to the compressional and shear sound velocities via our determined densities and the adiabatic bulk modulus. Our highstatistical quality dataset places a new tight constraint on the density dependence of εFe’s sound velocities to outer core pressures. Via comparison with existing data for iron alloys, we investigate how nickel and candidate light elements for the core affect the thermoelastic properties of iron. In addition, we explore the effects of temperature on εFe’s sound velocities by applying pressure and temperaturedependent elastic moduli from theoretical calculations to a finitestrain model. Such models allow for direct comparisons with onedimensional seismic models of Earth’s solid inner core (e.g., the Preliminary Reference Earth Model).
Next, the volume dependence of the vibrational free energy is directly related to the vibrational thermal pressure, which we combine with previously reported theoretical values for the electronic and anharmonic thermal pressures to find the total thermal pressure of εFe. In addition, we found a steady increase in the LambMössbauer factor with compression, which suggests restricted thermal atomic motions at outer core pressures. This behavior is related to the highpressure melting behavior of εFe via Gilvarry’s reformulation of Lindemann’s melting criterion, which we used to obtain the shape of εFe’s melting curve up to 171 GPa. By anchoring our melting curve shape with experimentally determined melting points and considering thermal pressure and anharmonic effects, we investigated εFe’s melting temperature at the pressure of the inner–core boundary (ICB, P = 330 GPa), where Earth’s solid inner core and liquid outer core are in contact. Then, combining this temperature constraint with our thermal pressure, we determined the density of εFe under ICB conditions, which offers information about the composition of Earth’s core via the seismically inferred density at the ICB.
In addition, the shape of the phonon DOS remained similar at all compression points, while the maximum (cutoff) energy increased regularly with decreasing volume. As a result, we were able to describe the volume dependence of εFe’s total phonon DOS with a generalized scaling law and, in turn, constrain the ambient temperature vibrational Grüneisen parameter. We also used the volume dependence of our previously mentioned vD to determine the commonly discussed Debye Grüneisen parameter (γD), which we found to be ~10% smaller than our vibrational Grüneisen parameter at any given volume. Finally, applying our determined vibrational Grüneisen parameter to a MieGrüneisen type relationship and an approximate form of the empirical Lindemann melting criterion, we predict the vibrational thermal pressure and estimate the highpressure melting behavior of εFe at Earth’s core pressures, which can be directly compared with our previous results.
Finally, we use our measured vibrational kinetic energy and entropy to approximate εFe’s vibrational thermodynamic properties to outer core pressures. In particular, the vibrational kinetic energy is related to the pressure and temperaturedependent reduced isotopic partition function ratios (βfactors) of εFe and in turn, provide information about the partitioning behavior of solid iron in equilibrium processes. In addition, the volume dependence of vibrational entropy is directly related to the product of εFe’s vibrational component of the thermal expansion coefficient and the isothermal bulk modulus, which we find to be independent of pressure (volume) at 300 K. In turn, this product gives rise to the volumedependent thermal expansion coefficient of εFe at 300 K via established EOS parameters, and the vibrational Grüneisen parameter and temperature dependence of the vibrational thermal pressure via thermodynamic definition.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Earth's core; Nuclear resonant scattering; High pressure; Phonon density of states; Melting of iron; Thermal pressure; Gruneisen parameter; Diamondanvil cell; Sound velocities; Coredensity deficit; Thermal expansion  
Degree Grantor:  California Institute of Technology  
Division:  Geological and Planetary Sciences  
Major Option:  Geophysics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  18 May 2012  
Record Number:  CaltechTHESIS:02162012075245736  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:02162012075245736  
DOI:  10.7907/GQ17GV90  
Related URLs: 
 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  6825  
Collection:  CaltechTHESIS  
Deposited By:  Caitlin Murphy  
Deposited On:  23 Aug 2012 22:35  
Last Modified:  03 Oct 2019 23:54 
Thesis Files

PDF (Complete thesis, typos corrected)
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PDF (Chapters 56, typos corrected)
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PDF (Introduction, Chapters 14, Appendix A, Bibliography)
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