An air-cored variable transformer can be used in connection with a mutual inductance bridge to obtain fractional Angstrom sensitivity for the study of thermal expansion of solids at liquid helium temperatures. This method has a number of attractive, though not unique, features. First, it provides a linear measurement—permitting the study of anisotropic materials. Second, it is well adapted to an absolute measurement in which only the sample changes temperature—eliminating the need for expansion estimates of other parts. Third, it allows direct mechanical calibration. Fourth, it does not require precise sample dimensions or shapes. Fifth, if cost is a consideration, the only inherently expensive part of the measurement system is a good narrow-band amplifier. This statement, however, neglects the cost of the Dewar system, the liquid helium, and a good thermometer. The major limitations appear to be an applicability solely to low temperature measurements (where the resistance of the variable transformer is low) for the highest sensitivity, and then only to samples of high thermal conductivity where thermal gradients can be minimized. The results obtained for the linear thermal expansions of copper and aluminum are comparable in precision with those obtained using different methods, and the agreement within this precision is gratifying. The anomalous (non- T 3) thermal expansion observed for sapphire is of interest, and it is unfortunate that the more routine heat capacity data do not exist in the same temperature region as our thermal expansion data. Further investigations of both the thermal expansion and heat capacities of dielectric solids in the temperature region below θ D 50 would be profitable, and are being planned.
Read full abstract