学校代码10530学号200810020967
分类号O482密级
硕士学位论文
Mg2X(X= Si,Ge,Sn,Pb)理想强度的第 学位申请人柯江灵
指导教师唐壁玉教授
学科专业凝聚态物理
研究方向计算材料学
假如没有灰尘教学设计
二○一一年五月
Mechanical properties of Mg2X (X= Si, Ge, Sn , Pb) from the first-principles
calculations
Candidate Ke Jiangling
Supervisor Professor Tang Biyu
College Faculty of Material and Photoelectronic Physics
Program Condensed matter physics
Specialization Computational Materials
宝安中学附属小学
北大院长面试学霸
Degree Scientiae Magister
University Xiangtan University
Date May, 2011
湘潭大学
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随着传统化石能源短缺、温室效应和环境污染等问题日益严重。热电技术作
为能源危机的解决方式之一，引起人们的极大重视。热电技术是利用固体内部载
流子运动实现热能和电能直接相互转换。利用热电材料，不仅可以在一些特殊需
要的领域(如太空探测)进行发电和制冷，还可以实现对废热等废弃能量的回收利
浙江癌症村
用。目前制备热电材料的主要是碲化铋(铅)及其合金，还有一类重要材料就是硅
锗合金，其代表形式就是镁合金系列的反萤石结构化合物，由于成份中没有较为 贵重的稀土元素和对环境有剧毒的铅金属，且本身资源较为丰富，所以在热电材
料的研究中占据重要一席。然而，长期以来，镁基硅锗合金热电材料具有不高的
热转换效率和较差的力学性质，严重的影响了其在现实中的广泛运用。近年来理
论模拟研究材料力学性质的取得极大的发展，为探索具有优良的力学性能，适应
工业生产的热电材料提供了更为广泛的机遇。
本文采用基于密度泛函理论的第一性原理方法，首先研究了反萤石结构化合
物Mg2Si，Mg2Ge，Mg2Sn和Mg2Pb的弹性性能和理想强度。计算所得到的晶格常数和弹性常数很好的吻合实验数据。力学性能和理想强度的分析表明：随着
Si，Ge，Sn，Pb原子序数的升高，弹性模量，剪切模量以及杨氏模量却变小，且所有化合物呈现脆性。从理想强度计算中可以进一步得到，这类化合物的理想
拉伸强度发生在[111]方向，理想剪切强度发生在(111)[112]方向。并且它们的理
奥巴马 复旦大学想强度都随着Ⅳ族元素原子序数的上升而变小，这与小应变得到的力学性质一
塔顶吊柱
致。然后从晶胞结构演变，电荷密度等方面来说明其中力学性质的内在微观机制。
接着用相似的方法研究了纯镁在弹性限度内的力学性能和大应变情况下的
理想强度。计算得到的晶格常数和弹性常数与实验值非常吻合，力学性能分析表
明，纯镁具有一定的延展性。接着对纯镁各个方向施加大应变时的力学性能进行1210剪切方向上，得到与别的研究人员非常吻合的数据。其计算计算，在(0001)[]
结果表明：纯镁的理想拉伸强度发生在[2023]方向，其值为1.410 GPa，而在[1210]
101210方向上，其值拉伸方向有最小临界应变。纯镁理想剪切强度发生在(10)[]
为1.027 GPa。由于理想剪切强度小于理想拉伸强度，纯镁最先断裂的模式是剪
切断裂。最后分析了原胞电荷密度在应变下的演变，从而准确形象的了解纯镁在
大应变下结构变化的内在机制。
关键词：弹性性质；理想强度；结构演变；电子结构；第一性原理计算
Because of shorting of traditional fossil energy, global warming and environmental pollution become more and more serious. Thermo-electric technology as one way to solve the energy crisis attracts widespread attention. Thermo-electric technology is to achieve a direct conversion between thermal and electrical energy with solid carrier inside a material. Thermo-electric materials can be used not only in some special areas (such as space exploration area) for power generation and refrigeration, but also in recycling waste of heat. At present, thermo-electrical materials are mainly TeBi (Pb) and their alloys, the Si-Ge alloys are also an important one. The anti-fluorite structured Mg2X (X=Si, Ge, Sn and Pb) compounds are also the typical thermo-electrical materials and have attracted broadly attention due to their large abundance resources, without expensive rare earth elements and toxic Pb element. However, the low efficient thermo-electric transformation and inferior mechanical properties has severely limited its wider application for a long time. Recently tremendous development in the theoretical simulation of the materials mechanical properties provides a wider range of opportunity to explore the thermoelectric materials owning excellent mechanical properties and adaptation of industrial production.
In present study, first-principles calculations within generalized gradient approximation have been performed to investigate elastic properties and ideal strengths of anti-fluorite structured Mg2X (X=Si,
Ge, Sn and Pb) compounds. First, the optimized structural parameters and elastic constant were in good agreement with the available experimental data. The calculated mechanical properties and ideal strength showed that with increasing of atomic number of X element, the bulk modulus, shear modulus and Young’s modulus became weak, and all of Mg2X compounds exhibited brittleness. The present calculations further showed that the ideal tensile strengths of Mg2X occurred in the [111]tensile direction and ideal shear strengths occurred in the(111)[112]shear direction. Their ideal strengths become weak with the increasing of atomic number of Ⅳgroup element, which are good consistent with the mechanical properties obtained by small strain situation. Then the inherent mechanisms of mechanical properties were discussed from the structural evolution, electronic structures and so on.
Then, first-principles calculations were also used to investigate the mechanical
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