Research

Current projects (2014):

High-pressure calorimetry

We seek to develop and apply a heat-capacity probe small-enough to fit inside diamond-anvil cells. We are using high-frequency (100 kHz to 100 MHz) Joule-heating of thin metal foils to heat and cool nano-gram mass samples faster than the rate of heat-flow into the diamonds. We measure power deposited by p=IV, and infer the amplitude of temperature oscillation by measuring the third harmonic of voltage that is generated from the temperature-induced change in resistance of the thin metal foil.

Left: Photo of laser piercing glass sample obliquely. Brillouin spectroscopy measures the frequency content of the scattered light from a certain angle (40 degrees in our case) to reveal the frequency of acoustic phonons (sound).

Right: Raw data at a range of compressions from 0 to 45 GPa.

Design of high-pressure heat capacity measurement

First, we investigate a variety of experimental possibilities for high-pressure calorimetry using 1-dimensional models of heat flow in diamond-cells. Our models uncover two possibilities: qualitative measure of heat capacity using modulated laser heating with fast spectroradiometry, and quantitative heat capacity measurements using modulated Joule heating with a third-harmonic temperature measurement. In both cases, high frequencies are required (100 kHz to 100 MHz).

Second, we design and build a prototype electrical circuit including a micron-scale metal sample pressed against a diamond heat-sink. Measurements of first and third harmonics of voltage show that the 1-dimensional thermal model works well-enough to guide future high-pressure experiments (see "Current Projects" above).

Left: Design of experiment to measure heat capacity of a metal sample/heater/thermometer using high-frequency Joule heating.

Right: Prototype circuit used to confirm the validity of the thermal and electrical models, paving the way for high-pressure calorimetry experiments.

Past projects:

Amorphous CaSiO₃

High pressure-high temperature solid phases of FeSi (link to paper)

Using laser-heated diamond anvil cell experiments, we document the crystalline structures of hot dense FeSi metal up to pressures and temperatures of 47 GPa and 2800 K. First, we show that it remains solid up to at least 2350 ± 200 K at 23 GPa and 2770 ± 200 K at 47 GPa, which means that addition of silicon does not cause a large amount of melting point depression (the melting temperature of pure iron ranges from 2300 ± 100 K to 2700 ± 150 K between 20 and 50 GPa). Second, the ε (B20) to CsCl-type (B2) crystal-crystal phase transition occurs at 30 ± 2 GPa at all temperatures from 1200 K to 2300 K. It results in a 5% density increase, which may cause an increase in the miscibility of silicon in iron at P > 30 GPa, with potential implications for the cores of small rocky planets such as Mars and Mercury.

Left: The ε-B2 phase transition of FeSi occurs at 30 ± 2 GPa, with no detectable temperature dependence between 1000 and 2400 K. Data using an argon pressure medium are represented by squares. Red symbols represent ε-FeSi, blue represents B2-FeSi, and purple indicates that a mixture of the two phases is seen in the diffraction data.

Melting slope reversal of the intermetallic compound AuGa₂ (link to paper)

Using x-ray diffraction of AuGa₂ in a resistively heated diamond-cell, we document high-pressure and temperature crystal-crystal and crystal-liquid phase transitions. We find a reversal in slope of the melting curve (Clapeyron slope) at 5.5 GPa and 720 GPa that coincides with structural transitions from cubic to lower-symmetry phases, suggesting that structural rather than electronic transitions are directly responsible for the change in Clapeyron slope.

Figure: Phase diagram of AuGa2 based on evidence of melting (open triangles), freezing (solid triangles) and three crystalline phases up to 15 GPa: triangle bases show pressure uncertainty for melting and freezing, determined from scatter in pressures measured at several 10s of degrees below melting; triangle heights show the interval over which we heated or cooled between x-ray diffraction patterns. The data of Storm et al. [1966] are shown as plus symbols. The top plot shows an expanded version of the grey box in the lower plot. Crystalline phases identified in the present study are shown as polygons indicating the pressure-temperature conditions at which each phase was observed. Shaded regions indicate phase fields.

Translational model of inner core convection (link to paper)

We show that the translational model of inner core convection is more compatible with seismic data than previously recognized. If rigid translation occurs and the resulting distribution of ages of solid metal (since crystallization) are reflected in longitudinal seismic wave speeds (V_P), then seismic maps of the near surface of the inner core (to ~100 km depth) would show a sharp boundary. In fact, assuming appropriate choice of mineralogical parameters (grain growth rate, elastic constants), it would be quantitatively consistent with the seismic study of Waszek and Deuss [2011], though the real data contains more scatter than our model.

Figure: Observed traveltime residuals of Waszek and Deuss [2011] (black squares) are similar to the calculated residuals for the model proposed in this study (pink dots). Black squares and their error bars indicate the averages and standard deviations of binned traveltime residuals observed in Waszek and Deuss [2011].

Origins of plateaus in laser-heated diamond anvil cell experiments (link to paper)

By modelling heat transport in laser-heated diamond anvil cells during laser-heating, we show that latent heat due to melting or other phase transformation is unlikely to be the source of observed plateaus in any previously published studies, regardless of whether pulsed or continuous lasers were used. Rather, changes in absorption of the sample (or laser absorber) are the most likely cause. To reveal latent heat, and thus document melting directly, we recommend four new types of experiments. This study led to my current work developing high-frequency Joule-heating calorimetry experiments!

Figure: Example of a 2-D axial simulation of temperature evolution for a Gaussian laser spot with FWHM = 4.7 μm, assuming the sample’s absorption coefficient is 10 μm^-1. Top panels show distributions of temperature and of phase after 200 ns. Bottom panels show temperature evolutions along the surface of the sample, z = 2.5 μm (left), and from the surface to the center of the sample along the axis of the diamonds (right).

Hydraulic permeability change inferred from the response of a water-well in Taiwan to seismic waves from Wenchuan, China (link to paper)

We noticed that the 7-cm water-level decrease observed at Liujia well in Taiwan following the Wenchuan earthquake did not match the simplest models of hydraulic changes. Therefore, we added a single parameter (permeability healing timescale) to one of the models (a step function change in permeability) and found a much better fit that is shown below.

Figure: Water-level data at Liujia well, fitted in three ways. The red and blue curves show best fits using the Brodsky et al. (2003) model, for data ranges from 600 to 1200 and 600 to 2800 s, respectively. The green curve shows the best fit from 600 to 2800 s using the new model. The new model improves the rms misfit over this data range from 0.74 cm to 0.10 cm.