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Pure phase thermal property results: Ice Ih


To establish the accuracy of our measurement technique, we needed a well-tested granular material that could be tested in HyFI using essentially the same procedures utilized in our measurements of hydrates.  Granular ice Ih was chosen because its thermal conductivity is known near our temperature range of interest, and its thermal diffusivity and specific heat can be derived from published work.  The thermal conductivity difference between ice Ih and hydrate also made ice Ih a valuable material for calibrating our thermal diffusivity measurement.

Sample Preparation:

We form ice by boiling deionized water for 10 minutes to reduce the dissolved gas content. The water is allowed to cool under its own vapor pressure to draw out additional dissolved gases, then poured into the measurement chamber and sealed by screwing on the top endcap. To reduce sample cracking during the freezing process, the oil-filled space surrounding the teflon liner is pressurized to 2 MPa. The sample and pressure vessel, immersed in a denatured alcohol bath, are then cooled below the sample's freezing point and stabilized at a series of measurement temperatures using the bath circulator.

Measurement Results:

Thermal conductivity, λ, of ice Ih.
Thermal conductivity, λ, of ice Ih. Our measurements are in agreement with published results, a verification of our measurement technique for λ (Click for larger image).

Between approximately -25 and -5°C, five thermal property measurements are made every 2.5°C. A ninety-minute interval between measurements is sufficient for the sample to re-equilibrate with the bath temperature.

Thermal Conductivity, λ: Based on our most extreme bath temperature fluctuations of 0.03°C over our four-minute measurement, we conservatively estimate an uncertainty of ±1% in thermal conductivity. Our measurements reproduce published data for ice Ih.

Thermal Diffusivity, κ: The lack of direct thermal diffusivity measurements available for ice underscores the utility of estimating this parameter from standard needle probe thermal conductivity measurements. Comparisons for our direct measurements of k can only be obtained indirectly, using the Eq. 6 relationship between the thermal properties.  Solving Eq. 6 for k, we have:

equation  (6)

We combine published calorimeter measurements of specific heat, cp, for ice [Grant, 2000; Leaist, et al., 1982] with our thermal conductivity measurements, λ, for ice Ih.  As described below for specific heat, the density, ρ, of ice Ih is calculated from the unit cell volume of ice.  With λ, κ, cp and ρ in hand, we calculate a "published" value for κ to compare with our measurement of κ.

Measuring κ depends on measuring the thermal contact parameter, H, which in turn requires data taken just after the probe begins heating the sample. This transient-time regime, t « rp2/κ, is ~0.5 seconds for ice. The number of available data points is limited by our data acquisition rate of 18.2 readings/second (0.055 seconds/reading), and we use the first 9 points (0.495 seconds) of data to balance the transient time constraint with the need for enough points to stabilize the nonlinear fit for H.

Specific heat results for Ice Ih
Specific heat results for Ice Ih. Our measurements, (red circles) have an uncertainty of ±10%, but vary as much as 25% from the results of Leaist et al. [1982] (open diamonds) and Grant [2000] (solid line)(Click for larger image).

Data taken at t = 0.495 seconds does not satisfy the time constraint of t « 0.5 seconds for ice, and the resulting uncertainty in H produces an uncertainty of ±10% in κ . The use of fewer data points, which more realistically satisfies the transient time constraint, does not improve the scatter in H or κ because reducing the number of data points destabilizes the nonlinear fit from which H is calculated. We therefore regard κ » 10-6 - 10-5 m2/s as an upper limit to the measurement capability of a 1.6 mm diameter probe and a temperature measurement rate of 18.2 readings/second. Averaged over the measured temperature interval, our estimate of 1.45x10-6 m2/s is within 15% of the averaged published data [Grant, 2000; Leaist, et al., 1982]. Scatter in our data obscures the temperature dependence of κ in ice, however.

Thermal diffusivity results for Ice Ih
Thermal diffusivity results for Ice Ih. Our measurements, (red circles) have an uncertainty of ±10%, but vary as much as 25% from the results of Leaist et al. [1982] (open diamonds) and Grant [2000] (solid line) (Click for larger image).

Specific Heat, cp: The needle probe technique does not provide a direct measurement of specific heat. Instead, our direct measurements of thermal conductivity and diffusivity are combined with estimates of the sample density to calculate specific heat via Eq. 6. Sample densities are calculated from the molecular mass and unit cell volume for ice as demonstrated by Helgerud [2001]. Because of limitations from our uncertainty in κ , this method estimates cp in ice only to within 15-25% of published values [Grant, 2000; Leaist, et al., 1982].


These results are published in: Waite, W.F., Gilbert, L.Y., Winters, W.J., and Mason, D.H., 2006, Estimating thermal diffusivity and specific heat from needle probe thermal conductivity data, Review of Scientific Instruments, 77, 044904, doi:10.1063/1.2194481.

Measurement Data:

Our thermal property measurements for Ice Ih can be downloaded as a tab-delimited text file.


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