Thermal Expansion

Thermal expansion refers to the change in size (length or volume) that a material undergoes as its temperature changes. In cryogenic systems this effect can be quite large and must be allowed for in the design. In isotropic materials, which include most engineering materials, the thermal expansion is the same in each direction and so we talk about linear thermal expansion. There are important exceptions, such as composite materials and some polymers, which aren’t isotropic and expand differently in different directions.

In cryogenics, we are concerned with the reduction of temperature from 300K down to cryogenic temperatures and in these circumstances most materials of interest contract in length rather than expand with the temperature reduction. Thus, we see a negative thermal expansion in cryogenics. The physical mechanism for this effect is an anharmonic component in the potential of the lattice vibration. Simply put, as the temperature of the material is reduced, not only are the vibrations of the atoms in the lattice reduced but the mean spacing of the atoms within the lattice also is reduced and thus the material contracts. There are some amorphous materials that remain constant or even expand upon cooling and, as in all cases with cryogenic material properties, the properties of the specific material to be used must be found.

Thermal expansion is given in terms of thermal expansivity (a = 1/L (dL/dT), or more usefully for most applications, in terms of the integrated expansion (or contraction) between two temperatures. The effect in cryogenic systems is significant; a typical value for austenitic stainless steel is 3 mm of contraction per meter between 300K and 4K. In general, the bulk of thermal contraction in materials occurs between 300K and 77K, but depending on the application contraction between 77K and 4K may be significant.

Thermal contraction can have significant impact in cryogenic systems, particularly as different materials experience different amounts of contraction. Systems that are properly aligned when warm may go out of alignment when cooled; gaps or interferences between components may occur upon cooling, resulting in higher than expected heat leaks and thermal shorts. Over-constrained systems may experience high stress and even fail upon cooldown. This last problem can be a significant issue in wiring that is installed without allowing for shrinkage during cooling. Design solutions to such issues include the use of bellows, flexible hose or sliding supports to compensate for contraction. The use of loops in wiring systems to avoid over stressing of the wires upon cooldown is common. Supports in cryogenic systems must be designed to allow for changes in length during cooldown while maintaining the alignment within tolerances. Thermal radiation shields and MLI systems (Cold Facts, Fall 2013 and Summer 2010) are typically designed with overlaps so that gaps do not open up upon cooldown. The starting point of all these solutions is to be aware of the problem and know the impact of thermal contraction on the design. Testing of prototypes may be required. Figure 1 shows some recent and reference measurements of the integrated thermal expansion of aluminium and stainless steel alloys between 300K and 77K.

A good description of the physical mechanism behind thermal expansion and many other cryogenic material properties is given in Low Temperature Solid State Physics, H. M. Rosenberg, Oxford (1963). Good sources of thermal expansion data include Experimental Techniques for Low Temperature Measurements, J.W. Elkin, Oxford (2006), Helium Cryogenics, S.W. Van Sciver, Springer (2012) and Cryogenic Engineering, T.M. Flynn, Dekker (1997). A recent example of a direct measurement of the thermal expansion of specific materials at cryogenic temperatures is given in “Cryogenic Coefficient of Thermal Expansion Measurements of Type 440 and 630 Stainless Steels”, H. Cease et al., Adv. Cryo. Engr., Vol. 60 (2014). Examples of the impact on thermal expansion on the alignment of complex cryogenic systems and the level of analysis and prototyping required to manage this effect include “Capture Cavity Cryomodule for Quantum Beam Experiment at KEK Superconducting RF Test Facility,” K. Tsuchiya et al., Adv. Cryo Engr. Vol . 59A (2014) and “Design Methodology of Long Complex Helium Cryogenic Transfer Lines,” J. Fydrych et al., Adv. Cryo. Engr., Vol. 55A (2012).