Properties of sintered submicron copper and silver powders and their relation to low temperature heat exchangers

Abstract

Measurements of surface area, porosity, electrical resistivity, and Young's modulus of sintered copper and silver submicron powders with packing fractions in the range 32–54% are reported. These parameters are of value in the design and understanding of sintered heat exchangers for the cooling of liquid helium into the millikelvin temperature range. The surface area and porosity measurements support a model in which the open pores are represented by orthogonal cylinders. This model is particularly well suited to describing heat flow in liquid helium in the pores of the sinter. From the residual electrical resistivity, the thermal conductivity κ of the sinter was calculated to vary between κ/T ~ 0.2 and 2 W∙m⁻¹∙K⁻² over the range of packing fractions from 32 to 50%. These conductivities are comparable to the conductivity of either pure ³He or dilute ⁴He – ³He mixtures in the open pores of the sinter. The elastic constant of the sinter varied from ~ 1 to 12% of that of the bulk metal over the range of packing fractions. By treating the sinter as an effective or composite medium for phonons with wavelengths larger than the pore or particle size, the elastic constant measurements support the possibility of there being a very large density of phonon states in the frequency range that would be excited at millikelvin temperatures. These modes could be important in the heat exchange between liquid helium in the pores of the sinter and the electrons in the metal powder.