1.Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China 2.Center for Quantum Transport and Thermal Energy Science, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
Fund Project:Project supported by the Major Program of the National Natural Science Foundation of China (Grant No. 11890703).
Received Date:21 September 2021
Accepted Date:09 October 2021
Published Online:05 December 2021
Abstract:In the research of cryogenic physics and quantum information science, it is essential to maintain a steady low temperature of millikelvin regime continuously. Dilution refrigerator is a widely used refrigeration device to achieve extremely low temperature. It utilizes the phase separation effect of superfluid 4He and its isotope 3He mixed solution at ultra-low temperatures. The performance of heat exchanger is the key factor to determine the performance of continuous cycle refrigerating machine. At extremely low temperatures, there appears a huge interfacial thermal resistance between helium and metal (Kapitza resistance), and the problem of heat exchange can be effectively solved by using the porous sintered metal particles to increase the contact area. Therefore, it is of significance to study the heat exchange between metal particles and liquid helium at extremely low temperature and to develop the relevant high-performance sintered Ag powder heat exchanger. Keywords:dilution refrigerator/ interfacial thermal resistance/ heat exchanger
其中系数RK称为界面热阻, 也被称为卡皮查热阻, 以此纪念前苏联著名低温物理学家P. L. Kapitza, 它是单位温差下单位时间内通过单位面积的热量. 近年来, 关于界面热阻的研究取得了极大的进展[6-11]. 稀释制冷机的工作温度在1 K以下, 此时实验测量和声学不匹配模型(acoustic mismatch model, AMM)都表明RK大致正比于T–3, 也就是说随着温度的降低, 热阻会变得非常大[12], 从而导致常规换热器在极低温下无法使用. 人们通过烧结金属颗粒的方法, 将金属与液氦的接触面积提高了几个数量级, 例如百纳米直径颗粒的比表面积可以达到107 m2/m3 (或1 m2/g). 银是所有金属中导电性和导热性最好的金属之一, 银的熔点低密度大, 比其他金属更易烧结, 所以目前普遍采用的是烧结银粉换热器[13], 实物如图3所示. 用直径为数百纳米的银颗粒进行烧结, 烧结物内分布有众多的孔隙, 尺寸一般在微米或者亚微米级别, 目前尚无有效的检测方法. 考虑到3He原子必须通过狭窄的连接通道在相邻的孔隙之间运动, 多孔结构形成的孔洞和通道的大小也是需要考虑的重要因素. 为了使热交换面积较大并且流动阻力较小, 需要寻找最佳的烧结结构. 图 3 超低温稀释制冷机系统及其关键换热部件: 连续换热器和银粉烧结换热器(图片由南方科技大学量子科学与工程研究院提供) Figure3. Ultra-low temperature dilution refrigerator system and its key components: Continuous heat exchanger and sintered Ag powder heat exchanger. (Image courtesy of Institute for Quantum Science and Engineering, Southern University of Science and Technology).
从理论的角度看, 烧结银粉换热器中除了比表面积的增加以外, 还涉及传热机理的变化. 当温度降低至1 K以下, 3He会从普通液体逐渐转变成费米液体[14], 常用的声学不匹配模型并不适用, 需要考虑3He液体的量子效应, 因此必须采用朗道费米液体理论. 实验测量发现, 当温度低于10 mK时, 纯3He液体与烧结银颗粒之间的界面热阻会显著降低[15](如图4所示), 而且温度依赖关系会显著偏离T–3关系, 这对提升换热器的效能是有利的. 这一转变的主要原因是烧结后互相连接金属颗粒发生弹性形变时会产生低能振动模式, 即软声子模式, 该模式和3He准粒子的相互作用会提供额外的界面导热通道[16]. 除此以外, 银颗粒在制备过程中往往会受到污染, 表面的局域磁性杂质(如各种形式的氧原子和氧离子)会和3He的核自旋发生自旋-自旋耦合, 该耦合效应可以提供另一个导热通道. 界面热阻的磁场依赖实验已经证实了该磁性导热通道的存在[17,18]. 图 4 金属纳米颗粒与3He液体之间的界面热阻. 圆点为实验值, 虚线为单金属颗粒计算值, 实线为考虑烧结颗粒中软声子模式后的计算值, 摘自文献[16] Figure4. Interfacial thermal resistance between metal nanoparticles and liquid 3He. The dot is the experimental value, the dashed line is the calculated value of single metal particles, and the solid line is the calculated value after considering the soft phonon mode in the sintered particles, which is extracted from the Ref. [16].
图 1 3He-4He溶液相图, X为3He的浓度
图 2 稀释制冷机原理图, 箭头方向表示3He流动方向
图 3 超低温稀释制冷机系统及其关键换热部件: 连续换热器和银粉烧结换热器(图片由南方科技大学量子科学与工程研究院提供)
图 4 金属纳米颗粒与3He液体之间的界面热阻. 圆点为实验值, 虚线为单金属颗粒计算值, 实线为考虑烧结颗粒中软声子模式后的计算值, 摘自文献[16]