Thermal expansion of copper,silver, and gold below 30 K

A variable transformer technique has been used to determine the linear thermal expansion coefficients of the noble metals from 4 to 30 K. The precision of the data initially was ±0.04 Å, and this was later increased to ±0.015 Å, resulting in a sensitivity of approximately 2×10^?11 for relative length changes of a 10-cm-long sample. The results agree at all temperatures (to better than 5%) with those of White and Collins who used a differential capacitor technique. The differences are 2% or less above 20 K for Cu, above 8 K for Ag, and at all temperatures for Au. The differences between the two sets of data for the three metals are not systematic (α_WC greater for Cu, less for Ag) and may be due to differences in sample purity since much larger low-temperature anomalies were found within each set for certain samples of Cu and Ag. The resulting electronic Grüneisen parameters γ_e and theT=0 lattice Grüneisen parameters γ₀ are as follows: $$\begin{gathered} copper \gamma _{\text{e}} = 0.91 \pm 0.05 \gamma _{\text{0}} = 1.67 \pm 0.02 \hfill \\ silver \gamma _{\text{e}} = 1.18 \pm 0.15 \gamma _{\text{0}} = 2.29 \pm 0.03 \hfill \\ gold \gamma _{\text{e}} = 1.6 \pm 0.5 \gamma _{\text{0}} = 2.96 \pm 0.04 \hfill \\ \end{gathered} $$ The values of γ₀ are in reasonable (5% at worst) agreement with elastic constant values.     

Thermal expansion of Cr,Mo and W at low temperatures

Linear expansion coefficients have been measured for Cr, Mo and W from 2–30 K, 55–90 K, and near room temperature. At low temperatures, the lattice contributions for Mo and W, although small, are determined to better than 10% giving respective limiting values of the lattice Grüneisen parameter, γ₀, of 1.3 and 1.35 compared with γ(283 K) = 1.61; their electronic components are very different, giving γ_e = d In $\text{N(E}{}_{\mathrm{<mtext>F</mtext>}}\text{)}\text{d}$ In V = 1.1 (Mo) and 0.3 (W). For Cr, the ‘electronic’ term is large and negative at low temperatures, giving γ_em = ?9; anomalies occur in α (T) at 124 and 311 K.     

Thermal expansion at low temperatures of glass-ceramics and glasses

The linear thermal expansion coefficient, α, has been measured from 2 to 32 K and from 55 to 90 K for a machineable glass-ceramic, an ‘ultra-low expansion’ titanium silicate glass (Corning ULEE), and ceramic glasses (Cer-Vit and Zerodur), and for glassy carbon. α is negative for the ultra-low expansion materials below 100 K, as for pure vitreous silica. Comparative data are reported for α-quartz, α-cristobalite, common opal, and vitreous silica.     

Thermal expansion of rhodium,iridium, and palladium at low temperatures

Coefficients (α) of linear thermal expansion of Rh, Ir, and Pd are reported to be respectively 8.45, 6.65, and 11.78×10^?6 ° K^?1 at 238°K, and 3.50, 3.43, and 6.21×10^?6 °K^?1 at 75°K. At temperatures below 10°K, α may be represented by $$\begin{gathered} 10^{10} \alpha = 20{\rm T} + 0.052{\rm T}^3 (Rh) \hfill \\ 10^{10} \alpha = 9{\rm T} + 0.070{\rm T}^3 (Ir) \hfill \\ 10^{10} \alpha = 40.5{\rm T} + 0.435{\rm T}^3 (Pd) \hfill \\ \end{gathered} $$ TheT andT ³terms are identifiable with electron and lattice vibrational components, respectively. Corresponding Grüneisen parameters are γ (electron)≈2.8, 2.7, and 2.22 for Rh, Ir, and Pd, and γ ₀ (lattice)≈2.0, 2.3, and 2.25.     

Thermal boundary resistance between liquid helium and silver sinter at low temperatures

We present measurements of the thermal coupling between Ag sinter (nominal grain size 700 Å) and superfluid³He-B atp = 0.3, 10, and 20 bar as well as a phase-separated³He⁴-He mixture atp = 0.5 bar in the submillikelvin regime. In order to analyze the data of the pure³He-B sample with respect to different contributions to the thermal resistance, a one-dimensional model for the heat flow in the sinter is presented. As a result it is shown that the thermal conductivity of the liquid in the sinter has to be taken into account to extract the temperature and pressure dependence of the boundary resistance in the confining geometry of the sinter. Depending on the value of this thermal conductivity, a boundary resistance proportional toT ^–2 orT ^–3 is found. Moreover, it is shown that a pressure dependence of the boundary resistance might be explained by a pressure dependence of the thermal conductivity of the liquid in the sinter. The data on the phase-separated mixture are equally well described by aT ^–2- and aT ^–3-dependence of the boundary resistance. We point out that a common problem in most measurements of the Kapitza resistance performed so far is the small temperature interval investigated, which usually does not allow a definite conclusion concerning the temperature dependence.     

Thermal expansion of β-FeSi2 at low temperatures

We present the temperature dependence of the lattice constants (a, b, c) of β-FeSi₂ single crystals at low temperatures. a showed the largest temperature dependence of 0.14% and the relationship of a>c>b did not change at 8-300 K. The linear thermal expansion coefficients α showed remarkable anisotropy. α along the a-axis (αa) was much larger than αb and αc, and showed negative thermal expansion at temperatures below 60 K. From these results, we estimated the temperature dependence of the lattice mismatches at β-FeSi₂/Si heterojunctions.     

Thermal conductivity measurements at low temperatures

We describe briefly the experimental facilities developed for the measurement of thermal conductivity of solids in the temperature range 10K–300K. Different techniques have been used for the determination of thermal conductivity, depending on the relaxation time of the system under investigation. Measurements on stainless steel 304, using steady state and non-steady state methods are presented. Values of thermal conductivity obtained by both these methods agree to each other and are consistent with those reported earlier. Paper presented at the poster session of MRSI AGM VI, Kharagpur, 1995     

Thermal properties of Zerodur at low temperatures

The linear thermal expansion of Zerodur has been measured from 20 to 300 K and the thermal conductivity from 2 to 100 K. For each property the temperature dependence appears to reflect the composite nature of the ceramic-glass.     

Thermal conductivity of mica at low temperatures

The thermal conductivity of muscovite and phlogopite has been measured over a temperature range of 3 to 320 K, in directions parallel and perpendicular to the cleavage planes. Both materials showed anisotropic behaviour. The room temperature values for muscovite and phlogopite, respectively, were 4.05 and 3.7 W m^–1 K^–1 for conductivity parallel to the planes, and 0.46 and 0.44 W m^–1 K^–1 perpendicular to the planes. Plots of the variation of thermal conductivity with temperature for both directions in the two materials show a gradual rise in conductivity as the temperature is lowered below room temperature. All four curves reach a peak at about the same temperature of 15 K. The peak values obtained were 12.4 and 7.25 W m^–1 K^–1 parallel to the planes, and 4.7 and 2.05 W m^–1 K^–1 perpendicular to the planes.On leave from Australian Broadcasting Commission.     

Thermal conductivity of inert gases at low temperatures

An experimental and theoretical study of the thermal conductivity of helium, argon, and xenon is reported. The experimental apparatus is described, and the results are discussed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 4, pp. 671–679, April, 1976.     

Thermal conductance of metal interfaces at low temperatures

In the present work the dependence of the heat transfer coefficient between Cu and Sn, Cu and Pb, and Cu and W on the temperature and an external magnetic field has been measured. The preparation of the metal-metal junctions has been performed by melting so that a close contact at the interface was guaranteed. The heat transfer coefficient has been found by a steady-state measuring method. In the case of the Cu-Pb junction the heat transfer coefficient could be measured both in the superconducting and normal states. For all the metal—metal junctions in the normal state a linear temperature dependence of the heat transfer coefficients on the temperature has been found. In the superconducting state a strong reduction of the heat transfer coefficient has been observed. In addition, a theoretical calculation of the heat transfer coefficient on metal-metal interfaces is given. First we consider the scattering of electrons on a steplike potential barrier between two gases of free electrons. Then the thermal conductance due to scattering in an alloy layer is calculated. Such an alloy layer may arise from diffusion during the contact preparation. Comparison of these two cases with the experiments shows the thermal conductance at the interface is mainly determined by the electron scattering on lattice irregularities in the diffusion layer.     

Melting and crystallization of copper, silver, and gold droplets

The crystallization kinetics in 0.5-g droplets of melted copper, silver, and gold (special purity grade metals) cooled in vacuum at a rate of 0.01 K/s was studied. Under these experimental conditions, the physical supercooling observed in all three metals prior to crystallization was virtually zero. An analysis of the values of supercooling obtained in this study together with the data obtained previously under the same conditions showed that supercooling increases in a regular manner with the number of electrons on the outermost p level.     

Thermal conductance measurements of bolted copper to copper joints at sub-Kelvin temperatures

We have measured the thermal contact conductance of several demountable copper joints below 1 K. Joints were made by bolting together either two flat surfaces or a clamp around a rod. Surfaces were gold plated, and no intermediate materials were used. A linear dependence on temperature was seen. Most of the measured conductance values fell into a narrow range: 0.1-0.2 W K⁻¹ at 1 K. Results in the literature for similar joints consist of predictions based on electrical resistance measurements using the Wiedemann-Franz law. There is little evidence of the validity of this law in the case of joints. Nevertheless, our results are in good agreement with the literature predictions, suggesting that such predictions are a reasonable approximation.     

Thermoelectric uniformity of chromel,copel, alumel and copper wire at low temperatures

Conclusions As a result of these tests comparative data have been obtained on the thermoelectric uniformity at low temperatures of Soviet-made thermocouple wire. According to these data the ambiguity of the thermocouple calibration characteristic due only to local irregularities of electrodes may attain ±5° for chromel-alumel, ±2.5° for chromel-copel, and ±0.5° for copper-copel thermocouples, at temperatures approaching –200° C.Therefore, copper and copel are the most suitable materials for high-precision thermocouples operating at low temperatures.     

Thermal and electrical conductivities of exfoliated graphite at low temperatures

The thermal and electrical conductivities of exfoliated graphite foils have been measured along the rolling direction and across it.     

Thermal conductivity of superconducting UPt3 at low temperatures

We study the thermal conductivity within the E_1g and E_2u models for superconductivity in UPt₃ and compare the theoretical results for electronic heat transport with recently measured results reported by Lussier, Ellman and Taillefer. The existing data down to T/T_c 0.1 provides convincing evidence for the presence of both line and point nodes in the gap, but the data can be accounted for either by an E_1g or E_2u order parameter. We discuss the features of the pairing symmetry, Fermi surface, and excitation spectrum that are reflected in the thermal conductivity at very low temperatures. Significant differences between the E_1g and E_2u models are predicted to develop at excitation energies below the bandwidth of the impurity-induced Andreev bound states. The zero-temperature limit of the axis thermal conductivity, lim_T0 k_c/T, isuniversal for the E_2u model, but non-universal for the E_1g model. Thus, impurity concentration studies at very low temperatures should differentiate between the nodal structures of the E_2u and E_1g models.     

Thermal properties of small Pb spheres at low temperatures

The specific heat and thermal conductivity of 0.10-mm- and 0.34-mmdiameter spheres of Pb are reported (2–30 K). The former spheres are 99.99% Pb, the latter spheres are Pb + 5% Sb. Both types of spheres undergo a superconducting transition at 7 K, and the changes in the specific heats at the transition correlate well with the electronic coefficient determined for bulk Pb. The 5% Sb addition increases the specific heat by as much as 30%, due to an enhancement of the localized, non-Debye excitations present in pure Pb. The Debye temperatures of the spheres are 102–103 K. The thermal conductivities of packed columns of the spheres are due to lattice rather than electron transport and are about 10³ times smaller than the thermal conductivity of bulk superconducting Pb. The 0.34-mm-diameter spheres have double the thermal conductivity of the 0.10-mm-diameter spheres, in contrast to the predictions of the elastic theory of Chan and Tien. An oxide layer may be the cause of the additional thermal resistance of the smaller spheres. T ³ boundary scattering occurs below 3 K for both sphere sizes and is consistent with specific heat and elastic-constant data for bulk Pb.Supported in part by the Jet Propulsion Lab., Contract No. 955446.