Thermal Conductivity of Some Ceramic Materials at Cryogenic Temperatures

The application of ceramics in various thermal systems is rapidly expanding. Pyrex, alumina, and zirconia are among the most widely used ceramics in various thermal systems as mechanically- and chemically stable materials for insulation purposes, and more recently as material for critical components of pulse tube and Stirling cryocoolers. These ceramics have excellent mechanical properties and do not chemically react with water and other widely used refrigerants and cryogens. Importantly from the view of their application for pulse tube and Stirling cryocoolers, these ceramics have very low coefficients of thermal expansion, sizable specific heats, and low thermal conductivity. Low thermal conductivity is particularly important because heat conduction in the axial (main flow) direction of cryocoolers causes parasitic losses that can significantly deteriorate the performance of these cryocoolers.

In this study, the thermal conductivities of Pyrex 7740, 99.99% pure and dense alumina, and 8% mol yttrium-stabilized dense zirconia were experimentally measured in the 75–300 K temperature range. This temperature range covers the operating parameters of cryocoolers that can be used for the mitigation of the boiloff in liquid oxygen tanks. For 7740 Pyrex and better than 99% pure alumina, there are experimental data available from several sources. The existing data show significant differences among data from different sources, however. For dense 8% mol YSZ, there appears to be a gap in the available experimental data in the 100–300 K temperature range.

Pyrex has been among the most widely used materials in science and industry since the early 20th century for applications where exposure to corrosive and highly reactive chemicals as well as sharp temperature changes are routinely encountered [1]. The 7740 Pyrex, the standard and commonly used Pyrex type, has the following composition [2]: approximately 80.7% silica, 13% boron oxide, 4.0% sodium oxide, and 2.3% aluminum oxide. Properties of Pyrex have been measured and published in a number of publications. Antoniadis et al. [2] recently compiled the available experimental data dealing with thermal conductivities of six different materials including 7740 Pyrex and proposed a reference correlation for the prediction of the thermal conductivity of 7740 Pyrex for the temperature range of about 30–750 K range. Their correlation was based on the data of Cahill et al. [3], however. Their compiled experimental data, furthermore, show significant spread in the 70–300 K range, the temperature range that is particularly of interest to this study.

Alumina (particularly α-Al₂O₃) is another ceramic with excellent thermo-mechanical properties that has been of interest as an insulator for cryogenic applications, including the insulation of superconductors. Compared with Pyrex, however, thermophysical properties of alumina have received little attention in the past. Alumina is produced at various purities, and experimental data indicate a strong dependence of thermal conductivity on sample purity. Among the published past studies are Nemoto et al. [4] who measured the thermal conductivity of alumina with 96% purity in the 2–200 K range, and Xie et al. [5] who measured the thermal conductivity as well as the thermal expansion coefficient of 92% and 99% purity alumina (along with two other ceramics) in the 25–400 K temperature range. Data relevant to very high-purity alumina (better than 99.9%) appears not to be available.

Zirconia (ZrO₂) is a ceramic with excellent thermo-mechanical properties. Its thermal conductivity is one of the lowest among ceramics that are suitable for use as insulation material at high temperatures, as thermal barrier coating [6], as well as the material for some critical components of pulse tube and Stirling cryocoolers. Zirconia can undergo disruptive phase transitions when heated and as a result is often blended with some other stabilizing oxide. The most widely used form is yttrium-stabilized, where typically a few percent of yttrium oxide (Y₂O₃) is added to zirconia to eliminate phase transitions. Yttrium-stabilized zirconia (YSZ) can be fabricated as single-crystal, and more often by sintering powder. YSZ produced by sintering can be porous. The thermal conductivity of YSZ depends on the percentage of yttrium, porosity, and potentially the grain structure of the sintered specimens, at least when either the grains are exceedingly small or when grains are large in comparison with a specimen size. Thermal conductivity of YSZ with various yttrium percentages has been measured and reported by a number of authors [7–10]. Schlichting et al. [6] measured and analyzed the thermal conductivity of 3% porous and dense 8% YSZ, both in single crystal and sintered polycrystalline forms, as well as 3% polycrystalline form. They only considered high temperatures (0–1000 °C), however. Ackerman et al. [11] measured the thermal conductivity of 8% YSZ at temperatures below about 90 K.

The thermal conductivities of 7740 Pyrex glass, 99.99% alumina ceramics, and 8 mol% yttria-stabilized zirconia (8 mol% YSZ) cylindrical samples at temperatures ranging from room temperature to cryogenic temperatures are measured using the standard test method for thermal conductivity of solids according to the guarded comparative-longitudinal heat flow technique (ASTM E1225-13) [12]. The schematic, a CAD model, as well as actual assembly representing the test apparatus are shown in Fig. 1. In this technique a test specimen (called sample bar) is inserted under load between two similar specimens of a material (called meter bars) of known thermal properties. A force is applied to the column to ensure good contact between specimens. A temperature gradient is established in the test stack and heat losses are minimized by evacuating the test chamber. A heater is inserted at the top of the first meter bar and a heat sink (cold tip of a cryocooler in our case) is attached to the bottom surface of the bottom meter bar. The samples and meter bars are all cylinders 19.05 mm in diameter and 38.1 mm in length, with better than $±0.1$mm tolerance.

Titanium grade 5, Ti-6Al-4V, which has a known thermal conductivity at cryogenic temperatures [12,13], was chosen for the meter bars. Ti-6Al-4V. Apiezon grade N grease was used for minimizing the interfacial resistance at each interface between the samples and the meter bars, and 44 AWG type T thermocouples (model 600-T-44-PE-71.0-SP by TE connectivity) were installed on the body of each meter bar and each sample, with an axial distance of 20 mm between each pair of thermocouples, and 9.05 mm from each end. Thermocouple heads were 0.1016 mm in diameter and they were attached to the bar surfaces by the highly conductive glue Master Bond EP21TDCS-LO. Three 50 Ohms/50 W cartridge heaters (model 3039-001 by Cryocon) were installed at the top of the upper meter bar, and the bottom of the lower meter bar was attached to the first stage of a two-stage G-M Cryocooler (Sumitomo RDK-408D2), which can provide 40 W cooling at 43 K. The cryocooler cold tip acts as a heat sink in these experiments. The components of the entire assembly are connected together via two long titanium rods, and G-10 spacers were used underneath the nuts of titanium rod to block heat conduction through the titanium rod. The entire system was insulated by a multi-layer insulator (MLI) and placed inside a vacuum chamber. The vacuum chamber is an instrumented 9 cubic feet dewar that is equipped with a vacuum pump which can provide a pressure of $10−6$ torr, and has been used in the past for experiments at cryogenic temperatures [14]. The cryocooler, vacuum dewar, and vacuum system are shown in Fig. 2.

A detailed uncertainty analysis was performed. The uncertainty of the measured thermal conductivity of sample bars was estimated using Eqs. (1)–(3), by considering random uncertainty and error propagation. Each measurement was repeated six times, and error propagation analysis considered uncertainty in $T1, T2,…,T6$⁠, which correspond to temperatures at $Z1, Z2,…, Z6$ locations, respectively (see Fig. 1(a)), as well as $D1, D2,$ and $D3$ which are the diameters of the top meter bar, the sample, and the bottom meter bar, respectively.

For the entire range of temperatures, the maximum total uncertainties were 10.1%, 16.7%, and 8.3% for zirconia, alumina, and 7740 Pyrex, respectively.

More details about the experiments can be found in Ref. [15].

Figure 3 displays our measured thermal conductivity data for 7740 Pyrex, along with data from several other sources [2]. The samples for testing were acquired from Collimated Holes, Inc. (Campbell, California).

Our measured thermal conductivity values for 7740 Pyrex are slightly higher than the data of other sources depicted in Fig. 3 for temperatures lower than about 250 K. Overall, our data are in better agreement with the data of Yang et al. [16] in comparison with data from other sources. At higher temperatures, however, the data from this study appear to merge with the data of three sources [3,17,18]. For the 75–300 K temperature range, our data as well as the data of Yang et al. [16] are consistently higher than the reported conductivities by Cahill et al. [3].

The Alumina sample used in the experiments was acquired from Dongguan Mingrui Ceramic Technology Co., Ltd (China). The commercial Alumina is produced by sintering at 1600 °C. Figure 4 displays a scanning electron microscope (SEM) picture representing a fractured surface that shows the grain structure in the sample. The SEM micrograph was obtained at room temperature. The average grain size is approximately 2 $μm.$

Figure 5 displays the thermal conductivity of our dense, 99.99% pure alumina. Published experimental data from several other sources are also shown in the figure. The displayed data do not all represent pure and dense Alumina, however, and show the high sensitivity of thermal conductivity to impurity. For the temperature range of interest (75–300 K) in this study, however, our data are in good agreement with the reported data of Nemoto et al. [4] and Berman [19]. For temperatures in excess of about 200 K, the data of Berman [19] and Touloukian et al. [20] also appear to converge with our data. However, the data of Touloukian is considerably higher than all other sources for temperatures lower than about 250 K. The data from various sources represented in Fig. 5 all suggest a peak in conductivity of alumina at a temperature close to or lower than 75 K. Evidently, the temperature range in our experiments did not go low enough to show this peak.

The zirconia sample used in the experiments was acquired from Dongguan Mingrui Ceramic Technology Co., Ltd (China). The commercial zirconia is produced by sintering at 1600 °C, and Fig. 6 displays a scanning electron microscope (SEM) picture representing a fractured surface that shows the grain structure of the sample. The SEM micrograph was obtained at room temperature. The average grain size is approximately 0.95 $μm.$

Figure 7 displays the thermal conductivity of the dense zirconia. Published experimental data from other sources are also shown in the figure. The displayed data confirm the sensitivity of the thermal conductivity of YSZ to its Y₂O₃ content. Furthermore, evidently, our data are filling a significant gap in the existing experimental data for 8% mol YSZ. The trends in our data are similar to the data of Ackerman et al. [11] near the lower limit of the temperature range of interest in this study, and to the data of Schlichting et al. [6] near the higher end of the aforementioned temperature range of interest. Our measured thermal conductivities appear to be slightly higher than the data of Refs. [6] and [11], although the difference between our data and the data from the aforementioned two sources is within the uncertainty limits of our data. Furthermore, our data indicate the occurrence of a peak in the thermal conductivity of 8% mol YSZ at around 140 K. We do not know the physical cause of this peak. A more detailed study in which the microstructure samples at the vicinity of the temperature where the peak occurs will be needed to elucidate the physical cause of this peak.

Thermal conductivities of 7740-type Pyrex, 99.99% pure and dense alumina, and dense 8% mol yttrium-stabilized zirconia (YSZ) were measured in the 75–300 K temperature range. These ceramics are of great interest for cryogenic applications because of their favorable thermo-mechanical properties. The ASTM E1225-13 standard method was applied for these measurements. The experimental data for Pyrex and alumina were in agreement with some previously published data. The data for alumina confirmed the sensitivity of the thermal conductivity of Alumina to its purity. Our thermal conductivity data for dense 8% YSZ filled a gap in the available data for the 100–300 K temperature range. Our data have consistent trends near the lower and higher ends of the temperature range of interest (75–300 K) with previously published data of Refs. [11] and [6], respectively. Empirical correlations were developed for the aforementioned 7740 Pyrex and 99.99%—purity dense alumina for the 75–300 K temperature range based on our experimental data. Empirical correlations were also developed for the 40 to 400 K temperature range for 8% mol YSZ, based on the experimental data generated in this work as well as the data of Ackerman et al. [11] and Schlichting et al. [6].

$k$ =

thermal conductivity (W/m·K)

$N$ =

number of repeated measurements

$q$ =

heat transfer rate (W)

$T$ =

temperature (K)

$T0$ =

reference temperature (273.15 K)

$T1, T2, …, T6$ =

temperatures measured by thermocouples 1, 2,…,6

$UA$ =

random measurement uncertainty

$UB$ =

uncertainty due to systematic error

$x$ =

generic measured property

$x¯$ =

mean value if x

$Z1, Z2, …, Z6$ =

axial location of thermocouples (m)

$ΔZ1, ΔZ2,$$ΔZ3$=

distance between pairs of thermocouples installed on the top meter bar, sample, and bottom meter ball, respectively

Greek Symbols

$θ$ =

normalized temperature

$κc$ =

coverage factor for a 95% confidence interval

$σs$ =

standard deviation

Subscripts

Alum =

alumina

bot =

bottom meter bar

Py =

Pyrex

sam =

sample

top =

top meter bar

Zirc =

zirconia