Abstract
We present high resolution thermal expansion measurement data obtained with high relative sensitivity of ΔL/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 α obtained using both dilatometers was evaluated using derivative of a polynomial fit. The resultant α 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−x Al x O6+δ and Bi2Sr2CaCu2O8+x along the c-axis with very good match found with published data obtained earlier using wet liquid helium based cryostats.
Highlights
Thermal expansion is an important thermodynamic technique to probe phase transitions in solids[1,2]
Length changes brought in the sample due to a temperature variation is manifested as a change in the distance between the two capacitor plates brought about efficiently through a spring (k in dilatometer#1 and K in dilatometer#2)
From the results obtained for thermal expansion measurements performed on aluminium on the two dilatometers dilatometer#1 and dilatometer#2, and two different closed cycle refrigerators CCR#1 and CCR#2 (d), we can clearly conclude that the dilatometer of choice for a thermal expansion measurement on a closed cycle cryostat is dilatometer#2 (Kuchler’s dilatometer) and either of the closed cycle refrigerators, CCR#1-Gifford–McMahon based property measurement system (PPMS)-Evercool or CCR#2-Pulse tube based PPMS Dynacool
Summary
Thermal expansion is an important thermodynamic technique to probe phase transitions in solids[1,2]. Thermal expansion measurements using capacitive dilatometry typically use wet cryostats where liquid helium is used as a cryogen The reason for this is the sub-angstrom level resolution that one needs to achieve in order to investigate low temperature phase transitions in small sized single crystals. For a dilatometer to be functional in different applied forces as well as varying spring thickness, it is necessary to ensure that the displacement of the spring on application of a force on the sample resulting in the movement of the capacitor plate, due to a change in the length of the sample, is monotonic This was studied computationally by performing a finite element method (FEM) simulation. We measure thermal expansion of two different superconducting crystals YBa2Cu3−xAlxO6+δ (Al-YBCO) and Bi2Sr2CaCu2O8+x (BSCCO-2212) along the crystallographic c-axis and find consistent data with published reports
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