Paper detail

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 $Δ$L$/$L = 10$^{-9}$ and accuracy of $\pm$2$\%$ using closed cycle refrigerators employing two different dilatometers. The data quality is in excellent agreement with those obtained using wet liquid helium based systems, demonstrating great technological possibilities for future thermal expansion measurements in view of the depleting resource of liquid helium. The cryogenic environment was achieved using two different cryostats that use pulse tube and Gifford-Mcmahon coolers as the cryocoolers. Both the dilatometers employ a spring movement for achieving the parallel movement of the capacitor plates. $Dilatometer \#1$ was built in-house based on a published design while $dilatometer \#2$ was obtained commercially. Cell calibration for $dilatometer \#1$ was done using copper and minimal deviation of the cell effect from the published values were found. Linear thermal expansion coefficient $α$ obtained using both dilatometers was evaluated using two different techniques, namely, numerical differentiation and derivative of a polynomial fit. The resultant $α$ obtained for metals silver and aluminium showed excellent match with published values obtained on systems using wet cryostats. Finite element method simulations were performed for understanding the spring movement in each dilatometer using which the effect of different forces$/$pressures on the displacement of the spring was studied. Finally, we report thermal expansion measurements done on single crystals of two high temperature superconductors YBa$_2$Cu$_{3-x}$Al$_x$O$_{6+δ}$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ along the c-axis and found very good match with published data obtained using wet liquid helium based cryostats.