使用电容式温度计的闭合循环低温恒温器中高分辨率热膨胀测量的设置
Setup of high resolution thermal expansion measurements in closed cycle cryostats using capacitive dilatometers
摘要：
我们目前的高分辨率热膨胀测量数据获得的高相对灵敏度的$Δ$ L $/$ L = 10 $^{-9}$和准确性的$\pm$ 2 $\%$使用封闭循环制冷机采用两种不同的温度计。数据质量与使用基于湿液氦的系统获得的数据非常一致，这表明在液氦资源枯竭的情况下，未来热膨胀测量具有很大的技术可能性。使用两种不同的低温恒温器，使用脉冲管和Gifford-Mcmahon冷却器作为低温冷却器，实现了低温环境。这两种电容器都采用弹簧运动来实现电容器板的平行运动。$Dilatometer \#1$是根据已发表的设计在内部构建的，而$dilatometer \#2$是从商业渠道获得的。$dilatometer \#1$的细胞校准使用铜和最小偏差的细胞效应从公布的values.Linear热膨胀系数$α$使用两种不同的技术，即，数值微分和导数的多项式拟合得到评价。所得的$α$获得的金属银和铝显示出优异的匹配与公布的值上获得的系统使用湿低温恒温器。进行有限元方法模拟以了解每个压力计中的弹簧运动，使用该模拟研究不同力$/$压力对弹簧位移的影响。最后，我们报告热膨胀测量两个高温超导体YBa $_2$ Cu $_{3-x}$ Al $_x$ O $_{6+δ}$和Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+x}$沿c轴的单晶，发现很好的匹配使用湿液氦基低温恒温器获得的数据。
英文摘要：
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.
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