Setup of high resolution thermal expansion measurements in closed cycle cryostats using capacitive dilatometers

We present high resolution thermal expansion measurement data obtained with high relative sensitivity of Delta L/L = 10(-9) and accuracy of +/- 2 % using closed cycle refrigerators employing two different dilatometers. Experimental details of the set-up utilizing the multi-function probe integrated with the cold head of two kinds of closed cycle refrigerators, namely, pulse tube and Gifford-McMahon cryocoolers, has been described in detail. The design consists of decoupling the bottom sample puck and taking connections from the top of the multi-function probe to mitigate the vibrational noise arising from the cold heads, using which smooth and high quality thermal expansion data could be obtained. It was found that dilatometer#2 performs a better noise mitigation than dilatometer# 1 due to the constrained movement of the spring in dilatometer#2. This was confirmed by finite element method simulations that were performed for understanding the spring movement in each dilatometer using which the effect of different forces/pressures and vibrations on the displacement of the spring was studied. Linear thermal expansion coefficient a obtained using both dilatometers was evaluated using derivative of a polynomial fit. The resultant a obtained using dilatometer#2 and either of the closed cycle cryostats on standard metals silver and aluminium showed excellent match with published values obtained using wet cryostats. Finally, thermal expansion measurements is reported on single crystals of two high temperature superconductors YBa2Cu3-xAlxO6+delta and Bi2Sr2CaCu2O8+x along the c-axis with very good match found with published data obtained earlier using wet liquid helium based cryostats.