稀有金属 2017,41(05),505-514 DOI:10.13373/j.cnki.cjrm.XY17030044
热磁耦合马氏体相变及其物理效应
蒋成保 花慧 王敬民
北京航空航天大学材料科学与工程学院空天先进材料与服役教育部重点实验室
摘 要:
马氏体相变和磁性转变是两类典型的固态相变, 其中, 马氏体相变在钢铁等结构材料和形状记忆合金等功能材料中普遍存在, 磁性转变在磁性材料中普遍存在。此前, 这两类相变一直各自独立发生。在新型磁性形状记忆合金中发现了二者共同发生的热磁耦合马氏体相变现象, 此后基于该现象的磁场诱发相变及其引发的磁致应变、磁热、磁电阻等丰富的物理效应成为本领域的研究热点。本文综述了热磁耦合马氏体相变、磁场诱发相变及其物理效应等方面的研究进展, 并对未来发展趋势做了展望。
关键词:
磁性形状记忆合金;热磁耦合马氏体相变;磁场诱发相变;物理效应;
中图分类号: TM27
作者简介:蒋成保 (1968-) , 男, 安徽无为人, 博士, 教授, 研究方向:磁性功能材料;电话:010-82338780;E-mail:jiangcb@buaa.edu.cn;
收稿日期:2017-03-22
基金:国家自然科学基金重点项目 (51331001);国家“973”计划项目 (2012CB619404) 资助;
Thermomagnetic Coupling Martensitic Transformation and Associated Physical Effects
Jiang Chengbao Hua Hui Wang Jingmin
School of Materials Science and Engineering, Key Laboratory of Aerospace Materials and Performance of Ministry of Education, Beihang University
Abstract:
Martensitic transformation and magnetic transition are two kinds of typical solid state phase transitions. The martensitic transformation universally takes place in structural materials such as steel and functional materials such as shape memory alloys. The magnetic transition is a common physical phenomenon in magnetic materials. Previously, the two kinds of phase transitions took place independently until the co-occurrence of both, which is a thermomagnetic coupling martensitic transformation phenomenon, was observed in the advanced magnetic shape memory alloys. Based on this thermomagnetic coupling martensitic transformation, magneticfield-induced phase transformation and the associated physical effects, such as magnetostrain, magnetocaloric and magnetoresistance, have become the new research hotspots in this field. In this paper, the progress of thermomagnetic coupling martensitic transformation, magnetic-field-induced phase transformation and the associated physical effects were reviewed, and the future developments were prospected.
Keyword:
magnetic shape memory alloys; thermomagnetic coupling martensitic transformation; magnetic-field-induced phase transformation; physical effects;
Received: 2017-03-22
马氏体相变是一种典型的一级固态相变, 是一种无扩散型切变相变, 在高强钢、韧性陶瓷、形状记忆合金等重要材料中普遍存在。尤其是, 热弹性马氏体相变是形状记忆合金产生形状记忆效应、超弹性等重要功能特性的物理基础。
磁性转变是一种典型的二级固态相变, 在所有磁性材料中普遍存在。其中铁磁性到顺磁性转变, 称为居里转变。磁性转变是磁性材料设计和应用的重要物理基础之一。
长期以来, 马氏体相变和磁性转变均在各自材料结构中独立发生。1984年, Webster等[1]报道了一种Heusler合金Ni2Mn Ga, 兼具热弹性马氏体相变和磁性转变。该合金高温母相为L21结构, 低温马氏体相为四方结构。1996年, 美国麻省理工学院 (MIT) 的O'Handley等首次报道了Ni2Mn Ga磁性形状记忆合金马氏体相中, 基于磁场驱动孪晶变体再取向, 获得了0.2%的磁致应变, 其机制完全不同于以往的磁致伸缩效应, 成为本领域的研究热点[2]。之后报道了6%[3]和9.5%[4]的大磁致应变效应。Ni2Mn Ga合金中马氏体相变温度 (TM) 和居里温度 (TC) 差别很大, 分别为202和376 K, 二者在该合金中也独立发生。
在偏离平衡配比的Ni-Mn-Ga合金中, 发现了马氏体相变和居里转变共同发生的现象, 被称为热磁耦合马氏体相变, 即升温时, 从铁磁马氏体转变为顺磁奥氏体;降温时, 从顺磁奥氏体转变为铁磁马氏体[5]。在此基础上, 基于这种马氏体相变和磁性转变共同发生的现象, 后来人们实现了磁场诱发 (逆) 马氏体相变, 即在外磁场作用下, 发生 (逆) 马氏体相变, 并发现其伴随有磁致应变、磁热、磁电阻等多种物理效应[6,7,8,9,10,11], 使得磁性形状记忆合金发展成为一类新型多功能材料, 在驱动与传感、能源、信息等领域具有重要应用前景。
本文综述了热磁耦合马氏体相变、磁场诱发相变及其磁致应变、磁热、磁电阻等物理效应方面的研究进展。最后对热磁耦合马氏体相变方面的未来发展趋势进行了展望。
1 热磁耦合马氏体相变
与传统温控形状记忆合金和磁致伸缩材料、压电材料相比, 磁性形状记忆合金兼有应变大、响应快的综合优点, 被普遍认为是新一代驱动和传感材料。自1996年以后的若干年内, 人们关注的焦点一直集中在铁磁马氏体相中的磁场驱动孪晶再取向及其大磁致应变效应, 但是, 马氏体相变和磁性转变一直各自独立发生。
Jiang等[12]系统研究了不同成分Ni-Mn-Ga合金的马氏体相变温度, 揭示了电子浓度和尺寸因素对马氏体相变温度的作用规律, 发现Ni元素取代Ga元素使马氏体相变温度显著升高, 而居里温度变化很小。在此基础上, 在Ni53Mn25Ga22合金中发现了马氏体相变和居里转变共同发生的现象, 即从铁磁马氏体到顺磁奥氏体的热磁耦合马氏体相变[5]。实验中采用了差示扫描量热分析 (DSC) 和热重分析 (TG) 同步测量的方法, 分别测量马氏体相变温度和居里温度, 其中, TG是在样品腔外对称悬挂了Nd Fe B磁体, 利用因磁性变化而产生的“重量”变化来测量居里温度。测量结果如图1[5]所示, 可以看到, DSC所测的马氏体相变温度与TG所测的居里温度一致, 证明了在Ni53Mn25Ga22合金中马氏体相变与磁性转变共同发生, 是一种从铁磁马氏体到顺磁奥氏体的热磁耦合相变。
后来, 人们在其他多种非平衡成分的Ni-MnGa合金中也观察到了“铁磁马氏体-顺磁奥氏体”的热磁耦合相变[13,14,15,16,17,18,19]。研究表明, 三元Ni-Mn-Ga合金的热磁耦合马氏体相变温度高于室温, 这是由于其Ni-Mn和Mn-Mn原子间铁磁交换作用强, 居里温度较高[20,21,22]。近期有研究表明, 通过In元素取代部分Ga元素, 利用In原子的尺寸效应, 可以微调Ni-Mn-Ga合金中原子间交换作用, 从而将“铁磁马氏体-顺磁奥氏体”热磁耦合相变温度调控到了室温[23,24]。除Ni-Mn-Ga合金外, 人们在其他磁性形状记忆合金中也发现了“铁磁马氏体-顺磁奥氏体”热磁耦合相变现象。Oikawa等[25]在顺磁性Ni Al-β相中通过添加Co, 使马氏体相变温度降低, 居里温度升高, 在Ni-Co-Al合金中得到了“铁磁马氏体-顺磁奥氏体”热磁耦合相变。之后, 他们在Ni2Fe Ga合金的基础上, 通过Ni元素和Ga元素同时取代部分Fe元素, 使居里温度升高, 马氏体相变温度降低, 在300 K附近也观察到“铁磁马氏体-顺磁奥氏体”热磁耦合相变[26]。Liu等通过时效处理调控Ni52Fe17Ga27Co4合金的相变温度, 在400℃时效24 h后, 实现了“铁磁马氏体-顺磁奥氏体”热磁耦合相变[27]。Wu等在Fe2Mn Ga合金的基础上, 通过Ga元素取代部分Mn元素, 得到了体心立方结构的Fe50Mn23.5Ga27.5合金, 并实现了“铁磁马氏体-顺磁奥氏体”热磁耦合相变[28]。最近, 在不同于Heusler合金的Ni2In型六角MM'X合金中也发现了“铁磁马氏体-顺磁奥氏体”热磁耦合相变。Wang等通过V替代Mn[29]和调节Mn/Co比例[30], 在Mn-Co-Ge合金中实现了“铁磁马氏体-顺磁奥氏体”热磁耦合相变。Bruck等发现等静压力也可以调控Mn0.93Cr0.07Co Ge合金的相变温度, 并观察到了“铁磁马氏体-顺磁奥氏体”热磁耦合相变[31]。Liu等[32]在Mn Ni Ge合金中掺杂Fe, 通过结构和磁性调控, 在70~350 K的宽温度窗口内获得了相变温度连续可调的“铁磁马氏体-顺磁奥氏体”热磁耦合相变。
图1 Ni53Mn25Ga22合金的DSC和TG曲线 (插图是升温降温过程中的交流磁化率曲线) Fig.1 DSC and TG curves of Ni53Mn25Ga22alloy (insert show-ing AC susceptibility as a function of temperature during heating and cooling processes) [5]
2004年, Sutou等[33]在Ni-Mn-X (X=In, Sn, Sb) 合金中观察到另外一种热磁耦合马氏体相变, 即“顺磁马氏体-铁磁奥氏体”相变, 如图2所示。在升温过程中, 马氏体向奥氏体转变的同时, 伴随着顺磁相到铁磁相的转变。随后, Kainuma等[6]报道了掺Co的Ni Co Mn In合金, 奥氏体的铁磁性显著增强, 实现了“弱磁马氏体-强铁磁奥氏体”热磁耦合相变。此后, 人们相继报道了一系列具有“弱磁马氏体-强铁磁奥氏体”热磁耦合相变的Ni-CoMn-X (X=In, Sn, Sb) 合金[34,35,36]。对于最早发现的Ni-Mn-Ga合金, 近期有研究表明, 在富Mn的Ni-Mn-Ga合金中, 通过Co, Fe, Cu取代Ni, 也可实现“顺磁/反铁磁马氏体-铁磁奥氏体”热磁耦合相变。Wu等在富Mn的Ni-Mn-Ga三元合金中分别通过Co/Fe取代Ni, 提高奥氏体磁性的同时, 使马氏体的磁性大大降低, 实现了“顺磁马氏体-铁磁奥氏体”热磁耦合相变[37,38]。Jiang等报道了Ni-CuMn-Ga合金, Cu添加使马氏体相变温度Ms降低, 马氏体居里温度TCM降低, 而奥氏体居里温度TCA升高, 如图3所示, 从而得到了独特的相变温度关系TCM<TM<TCA, 由此实现了“顺磁马氏体-铁磁奥氏体”热磁耦合相变[39,40,41,42]。同时, Ni-Cu-Mn-Ga合金表现出优异的力学性能。Ni-Mn-Al也是一种出现较早的磁性形状记忆合金。Kainuma等[43]利用Ni-Mn-Al合金中B2结构的反铁磁特征, 采用Co部分取代Ni, 在Ni-Co-Mn-Al合金中得到了“反铁磁马氏体-铁磁奥氏体”的热磁耦合相变。最近, Wu等报道了一种完全由3d元素组成的Ni-Co-MnTi合金, 将Ti元素引入Ni-Mn合金中, 获得立方的B2型Heusler相, 并有效降低马氏体相变温度。进一步掺杂Co元素, 使奥氏体相的反铁磁性转变为铁磁性, 实现了“弱磁马氏体-铁磁奥氏体”耦合相变[44]。Wang等采用过渡金属空位[45], 或Co[46], Fe[47]元素替代Ni元素, 将MM'X型MnNi Ge合金的马氏体相变降低至母相的磁性温区, 实现了“反铁磁马氏体-铁磁奥氏体”热磁耦合相变。
图2 Ni50Mn50-yIny, Ni50Mn50-ySny和Ni50M50-ySby合金马氏体相变和磁性转变与成分关系Fig.2 Martensitic transformation and magnetic transition in Ni50Mn50-yIny (a) , Ni50Mn50-ySny (b) 和Ni50M50-ySby (c) alloys[33]
图3 Ni50Mn25+xGa25-x合金和Ni46Cu4Mn25+xGa25-x合金的相图 (其中PM, FM, PA和FA分别表示顺磁马氏体、铁磁马氏体、顺磁奥氏体和铁磁奥氏体) Fig.3Phase diagrams of Ni Mn Ga (a) and Ni Cu Mn Ga (b) alloys (PM, FM, PA and FA representing paramagnet-ic martensite, ferromagnetic martensite, paramagnetic austenite, and ferromagnetic austenite, respective-ly) [39]
2 磁场诱发 (逆) 马氏体相变
热磁耦合马氏体相变现象的发现, 使马氏体相变由原来的温度、应力驱动, 拓展到外加磁场也可以驱动相变。热磁耦合马氏体相变不仅伴随着晶体结构的转变, 还伴随磁化强度的突变。因为铁磁相在磁场状态下更加稳定, 能量更低, 所以弱磁相在磁场作用下会转变为铁磁相, 即磁场诱发相变。与温度驱动相变有正、逆相变一样, 磁场诱发相变也有正、逆相变, 本文分别称之为磁场诱发马氏体相变和磁场诱发逆马氏体相变。
磁场诱发 (逆) 马氏体相变的发生与马氏体相和奥氏体相之间的Zeeman能差有关, 即ΔEzeeman=ΔM·μ0H, 其中, ΔM指马氏体相和奥氏体相之间的磁化强度之差, μ0H为外加磁场[48]。以磁场诱发马氏体相变为例, 无外磁场时, 在马氏体相变开始温度Ms以上, 两相之间的吉布斯自由能之差不足以驱动马氏体相变。此时, 施加外磁场, 磁场将在原来吉布斯自由能差值的基础上, 补偿相变所需的驱动力, 从而在Ms以上的温度, 由磁场驱动马氏体相变。
ΔM值是决定在特定温度下驱动相变所需磁场大小的关键因素。这可以通过Clausius-Clapeyron方程来理解, 即:
式中μ0ΔH是外加的磁场, ΔT为在μ0ΔH磁场下马氏体相变温度的变化, ΔM和ΔS分别是马氏体相变前后的磁化强度变化和熵变。比值ΔT/ (μ0ΔH) 表示单位磁场下相变温度的变化程度, 反映了相变对外磁场的相应灵敏度。可以看出, ΔM越大, ΔS越小, ΔT/ (μ0ΔH) 越大, 相变对磁场响应越灵敏, 从而诱发相变所需要的磁场越小。从已有文献来看, 不同成分磁性形状记忆合金的相变熵变ΔS差别很小, 而ΔM对成分变化极为敏感。“铁磁马氏体-顺磁奥氏体”和“顺磁/反铁磁马氏体-铁磁奥氏体”这两种热磁耦合相变的ΔM较大, 因而基于这两种耦合相变的磁场诱发相变是本领域的研究热点。
对于“铁磁马氏体-顺磁奥氏体”热磁耦合相变, 铁磁马氏体在磁场下更加稳定, 施加磁场使马氏体相变温度升高。在高于马氏体相变开始温度的温区, 即奥氏体状态, 能够实现磁场诱发从顺磁奥氏体向铁磁马氏体的转变, 即磁场诱发马氏体相变。从图4可以看出, Ni52Mn26Ga22合金马氏体为铁磁性相, 奥氏体为顺磁性相, 在5 T的磁场下相变温度降低了3 K, ΔT/ (μ0ΔH) =0.6K·T-1[18]。从降温过程中M-H曲线可以看出, 样品的磁化强度随着外磁场升高不断增加, 并伴有明显的磁滞。这归因于磁场诱发了顺磁奥氏体到铁磁马氏体的转变。Inoue等[49]通过原位中子衍射实验直接证明了Ni-Mn-Ga合金中磁场诱发马氏体相变。
对于“弱磁马氏体-铁磁奥氏体”热磁耦合相变, 铁磁奥氏体在磁场下更加稳定, 磁场可使马氏体相变温度降低, 在马氏体状态能够实现磁场诱发从弱磁马氏体向铁磁奥氏体的转变。2006年, Kainuma等[6]报道的Ni45Co5Mn36.6In13.4, 马氏体相和奥氏体相之间的饱和磁化强度之差△M=100A·m2·kg-1, 在单位磁场下相变温度的变化程度为ΔT/ (μ0ΔH) =4.3 K·T-1。在270 K马氏体状态下, 施加7 T的磁场诱发了逆马氏体相变, 如图5所示。2008年, Wang等[50]利用磁场下的原位高能X射线, 观察到了Ni45Co5Mn36.6In13.4合金在磁场强度增加过程中从马氏体转变为奥氏体的结构变化, 从实验上直接证明了磁场诱发逆马氏体相变。
图4 Ni52Mn26Ga22合金的M-T和M-H曲线Fig.4 Thermomagnetizaiton (a) and isothermal magnetization (b) curves of Ni52Mn26Ga22alloy[18]
3 基于热磁耦合马氏体相变的多功能物理效应
由于马氏体相和奥氏体相之间的晶体结构不同, 在热磁耦合马氏体相变的过程中, 会伴随有应变、热、电阻等物理性质的变化, 从而产生磁致应变、巨磁热和巨磁阻等多功能物理效应, 使磁性形状记忆合金在驱动与传感、能源、信息等领域有广泛应用前景。
图5 Ni45Co5Mn36.6In13.4合金M-T和M-H曲线Fig.5 Thermomagnetizaiton (a) and isothermal magnetization (b) curves of Ni45Co5Mn36.6In13.4alloy[6]
3.1 磁致应变效应
在磁性形状记忆合金中产生磁致应变效应的机制主要有两种: (1) 磁场驱动孪晶变体再取向; (2) 磁场诱发相变。通过磁场驱动孪晶变体再取向, 已获得了超过6%的大磁致应变, 但是其输出应力较小 (<5 MPa) [3,4]。发现热磁耦合马氏体相变以后, 由于其输出力超过100 MPa, 基于该现象的磁场诱发相变所引发的磁致应变效应成为新的关注焦点。
2006年, Kainuma等[6]报道了在预应变的Ni45Co5Mn36.6In13.4单晶中高达3%的磁致应变效应, 且估算出7 T磁场下的输出应力为108 MPa, 如图6所示。同年Kainuma等[35]在预变形的铸态多晶Ni43Co7Mn39Sn11合金中也获得了约1%的大磁致应变。这种磁致应变效应是单程的, 撤去磁场后, 其应变不能回复。2012年, Monroe等[7]在Ni45Co5Mn36.5In13.5单晶在加压约束下获得3%的可回复大磁致应变。他们认为随着压应力的增大, 相变过程中择优取向马氏体组织不断增多, 从而产生可回复大磁致应变值。
人们在一些自由状态的Ni-Co-Mn-Sn[51,52], Ni-Mn-In[53], Ni-Mn-Fe-In[54]合金中也发现了磁致应变效应 (~0.2%) 。2009年, Liu等[55]在Ni45.2Mn36.7In13Co5.1取向多晶中获得了0.25%的可回复磁致应变。Li等[56]在Ni45Co5Mn37In13中获得0.40%的可回复磁致应变。最近, Jiang等在NiCu Mn Ga合金中通过调控马氏体变体组织, 使马氏体组织择优取向并且在反复相变过程可回复, 得到了0.47%的可回复磁致应变[57]。
3.2 磁热效应
磁热效应是磁性材料受磁场作用, 磁矩有序发生改变, 磁熵发生变化, 并伴随着样品温度上升或下降的现象。对于具有热磁耦合相变的合金, 在磁场作用下, 不仅发生磁有序/无序变化, 还伴随着一级结构相变, 从而产生巨磁热效应。磁性形状记忆合金基于其成分改变可以实现相变温度的连续调节 (涵盖室温) , 以及低成本、易制备、大磁熵变等特性, 成为广受关注的一类重要的磁制冷材料。
2001年, Hu等[58]首先报道了Ni52.6Mn23.1Ga24.3单晶中“铁磁马氏体-铁磁奥氏体”相变的磁热效应, 在5 T的磁场下获得了18.0 J·kg-1·K-1的磁熵变。Long等[17]报道了具有“铁磁马氏体-顺磁奥氏体”热磁耦合相变特征的Ni55.5Mn20Ga24.5合金中磁热效应, 在325 K, 2 T的磁场下获得了15.1J·kg-1·K-1的磁熵变。Jiang等通过In取代Ga, 使Ni57Mn18Ga21.6In3.4合金的“顺磁奥氏体-铁磁马氏体”热磁耦合马氏体相变温度调节到室温附近[23]。通过5 T的磁场诱发马氏体相变获得了室温巨磁热效应。Wu等采用等结构合金化方法开发出Mn-Ni Ge Fe合金系, 其“铁磁马氏体相-顺磁奥氏体”的热磁耦合马氏体相变发生在70~350 K宽温度窗口内。在5 T磁场下, 表现出稳定的磁熵变[32]。
图6 预应变Ni45Co5Mn36.6In13.4合金磁致应变效应Fig.6 Magnetostrain effect of predeformed Ni-Co-Mn-In alloy[6]
与“铁磁马氏体-顺磁奥氏体”热磁耦合相变不同, “弱磁马氏体-铁磁奥氏体”热磁耦合马氏体相变在外磁作用下呈现出反磁热效应。2005年, Krenke等[8]报道了Ni50Mn37Sn13合金的反磁热效应, 在5 T磁场下磁熵变达到19 J·kg-1·K-1, 与著名的磁制冷材料Gd-Si-Ge合金相当[8]。Liu等[9]直接测量出Ni45.2Mn36.7In13Co5.1合金在2 T的磁场下高达6.2 K的绝热温变。最近, Wang等报道的Ni40Co10Mn40Sn10合金在室温附近获得了大的磁熵变14.9 J·kg-1·K-1, 如图7所示[59]。其相变过程中ΔM/ΔS=7.3 K·T-1, 工作温度窗口高达33 K, 最终获得了Ni-Mn基合金中最大的有效磁制冷能力值251 J·kg-1。
3.3 磁电阻效应
由于相变过程中奥氏体和马氏体的电阻率显著不同, 因此在磁场诱发相变过程中, 电阻率发生变化, 产生了巨磁电阻效应。
图7 Ni40Co10Mn40Sn10合金的等温磁化曲线和不同磁场下磁熵变随温度的变化曲线Fig.7 Isothermal magnetic curves near reverse matensite (a) and magneto-entropy change curves (b) under different magnetic field in Ni40Co10Mn40Sn10alloy[59]
2006年, Yu等[60]报道了Ni50Mn50-xInx单晶中基于磁场诱发逆马氏体相变而产生的巨磁电阻效应。对具有“弱磁马氏体-铁磁奥氏体”热磁耦合相变的Ni50Mn34In16合金, 在低于转变温度100 K温度范围内施加9 T磁场, 由于磁场诱发逆马氏体相变, 产生了60%~80%的巨磁电阻效应, 如图8[60]所示。Koyama等[61]在Ni50Mn36Sn14合金多晶中也发现了巨磁阻效应, 在马氏体相变温度附近施加18 T的磁场伴随着磁场诱发逆马氏体相变, 产生了50%的磁电阻突变。Sharma等[62]在Ni50Mn34In16合金中通过Cu取代Ni, 使马氏体相变温度升高, 在290 K获得了50%室温附近的巨磁阻效应。随后, 有大量关于Ni (Co) Mn Z (Z=In, Sn, Sb) 合金基于磁场诱发相变获得巨磁电阻效应的报道[52,63,64,65,66,67,68]。作为一种潜在应用于磁阻记录头等装置的材料, 其使用温度可以由成分改变来连续调节 (涵盖室温) , 并具有低成本、易制备等特性, 受到人们关注。
图8 Ni50Mn34In16在磁电阻随磁场变化曲线Fig.8 Variation of magnetoresistance vs field strength at vari-ous temperatures for Ni50Mn34In16alloy[60]
4 展望
经过人们不懈地努力, 已经对热磁耦合马氏体相变现象有了深刻的认识。这种耦合相变展现出的多种物理效应, 使磁性形状记忆合金有望发展成为一类重要的多功能材料, 在驱动与传感、能源、信息等领域有广阔应用前景。未来需从以下几个方面进一步开展研究工作。首先, 热磁耦合相变的微观机制, 尤其是晶体结构与磁结构是怎样耦合作用的, 需要更深入地研究和理解, 这对于耦合相变调控、新材料设计和优异功能特性的实现都有重要意义。其次, 诱发相变所需的磁场过高, 尚难以实际应用, 降低驱动场应是本领域未来重点关注的课题。再次, 热磁耦合马氏体相变的滞后较大, 导致功能输出时能量耗散大、且输出灵敏度低, 怎样调控微结构, 从而获得窄滞后热磁耦合相变也是该领域一项具有挑战性的课题。
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