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High Pressure Phase Equilibria

Overview

Several of the icy moons of the outer solar system probably have subsurface oceans. Particularly interesting examples are Europa (a moon of Jupiter), and Enceladus and Titan (moons of Saturn). Thermodynamic models of the interiors of icy moons can benefit from an improved understanding of how the presence of various impurities will change the temperature and pressure-dependent properties of water and ice in any such subsurface ocean.

This project focuses on phase equilibria in aqueous solutions at pressures ranging from from 0.1 to 400 MPa.

Most recent paper

"The Liquidus Temperature for Methanol-Water Mixtures at High Pressure and Low Temperature, With Application to Titan" Journal of Geophysical Research--Planets, with Lafayette co-authors Z.T. Bartholet, R.J. Chumsky, K.C. Delano, X. Huang, and D.K. Morris.

Apparatus

The apparatus consists of 3 main parts: a central high-pressure fitting containing the sample fluid, an optical system for imaging the sample, and a pressure system that includes both pressure and volume sensors

diagram

Diagrams of the pressure system (left) and imaging system (right). The imaged portion of the sample is confined to a 1~mm-wide gap between the two windows at the center of the cross. This system allows simultaneous measurements of pressure, temperature, and volume changes, along with optical images of the sample.

Pressure system

Approximately 1 mL of sample is loaded into a pressure cell that is placed in a copper container and immersed in an insulated, temperature-controlled ethanol/water bath. The pressure cell is made from a 316 stainless steel block with four ports, known as a cross (High Pressure Equipment Company #60-HF6). Two opposing ports contain replaceable plugs that have sapphire windows sealed in them with epoxy. The third port contains a plug in which a silicon diode thermometer is installed. The fourth port connects the cell to the pressure system. The sample in the pressure cell is separated from the ethylene glycol pump fluid by a vertical U-tube filled with mercury. A steel capillary tube of constant cross section forms one arm of the U-tube. A small Alnico magnet is placed in the capillary on the interface between the pump fluid and the mercury, and the height of that magnet is measured by a transducer. Changes in the transducer voltage are approximately proportional to changes in sample volume. As long as the sample is mostly liquid, this system allows simultaneous measurements of temperature, pressure, and volume of the sample. When the sample in the connecting tubing is frozen, however, the pressure inside the cross can be significantly different.
cross

Exploded view of the pressure cell. Sapphire windows in steel plugs are mounted inside a steel cross. The image shows the relative positions of the plugs with windows and the plug containing the thermometer. The window separation is approximately 1 mm.

Optical system

The imaging system consists of a lamp that shines light through an infrared filter and optical fiber that directs the beam horizontally through the sample cell. The infrared filter is used to minimize heating of the sample by the light source. After passing through the cell, the beam is reflected by 45o mirror upward through a matched pair of lenses to a long working distance optical microscope objective coupled to a Pulnix digital camera. The camera obtains images of a vertical cross-section of the sample, with 1392 \times 1040 pixels and an overall resolution of about 1.7 μm/pixel. The gap between the sapphire windows is approximately 1~mm. Although the camera's field of view does not cover the entire system, we typically observed dissolving or growing crystals corresponding to changes in temperature, pressure, and volume, indicating that the crystal images reflect the phase transitions within the sample. We have studied a variety of solutions likely to be relevant for the icy moons of the outer solar system, including aqueous mixtures of magnesium sulfate, sodium sulfate, methanol, and water.

Data

For each run, we make a movie showing the view through the windows of the growth chamber. Superimposed on the view is a graph showing Voltage (approximately proportional to Volume) vs. Temperature. Thus we can correlate changes in volume (and hence density) with the growth or dissolution of different crystal phases.
graph

Example screenshot from a run at 50 MPa. The transducer voltage (which varies linearly with volume) is plotted on the vertical scale, and the temperature is plotted on the horizontal scale. The red diamond shows the conditions corresponding to this specific image. Across the bottom are shown the date (YY/MM/DD) and time (HH:MM::SS), as well as the temperature, pressure, voltage, and rate of change of temperature. The image filename at the top of the screen includes the date, time, temperature and voltage, as well as the imaging lamp voltage, which varies from 0 to 12.0 Volts.

Preliminary Results

People

Staring in 2001, I joined Prof. Emeritus David Hogenboom, along with his long-time collaborator Jeff Kargel, of the University of Arizona, in their studies of phase equilibria at the high pressures and low temperatures relevant for icy satellites. My main initial contributions were adding image processing and much more extensive automation. I have also been fortunate to work with a wonderful array of talented Lafayette undergraduate students on this project, including:
David Hogenboom

Here is David Hogenboom on Miranda, a moon of Uranus, taking a sample for analysis in the high pressure apparatus.

Other interesting links

This page is occasionally maintained by Andrew Dougherty