反钙钛矿锰氮化合物Mn_3（A_(1-x)B_x）N的负热膨胀性质的理论研究
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摘要
自2005年反钙钛矿锰氮化合物Mn3(Cu1-xGex)N负热膨胀性质被发现以来,该化合物以其良好的负热膨胀性质,如：各向同性的负热膨胀行为,可调的负热膨胀温区和系数,负热膨胀系数幅度较大,结构稳定且具有较好的机械性质和输运性质等,使其在诸多领域具有非常广泛的应用前景。这引起了人们对这一材料的重视。于是,人们进一步研究了不同掺杂元素以及N空位对这类体系负热膨胀性质的影响,同时也在不断地探索其负热膨胀的机理。已有的研究认为这类材料的反常热膨胀行为是来源于掺杂Ge原了引起的局域结构扭曲,另一种观点认为材料的负热膨胀性质是来源于体系中存在的磁相互作用,然而对于其反常热膨胀的起源和机理依然没有给出清楚的解释。显然对这些问题的研究无论是对于理解这类材料中出现的奇异的负热膨胀性质,还是对于开发新型的负热膨胀材料都具有重要意义。本文着重研究这类材料的反常热膨胀的机理以及Ge在体系负热膨胀性质中的作用。
本论文一共分为五章。在第一章里,我们简要介绍了负热膨胀的机理、应用前景和一些典型的负热膨胀材料。其中,重点介绍了本论文所要研究的材料Mn3(Cu1-xGex)N的负热膨胀性质、不同掺杂对其负热膨胀行为的影响以及实验上对其负热膨胀机理的研究状况。
体系中Mn离子是具有磁矩的,因此对这个材料的物理性质的研究就必然涉及到磁性方面的知识。在第二章,我们简要地介绍了本论文中用到的磁性理论以及计算磁响变温度的蒙特罗方法。最后,我们还介绍了在本文计算中采用的密度泛函理论和VASP软件包。
从第三章开始介绍我们的研究工作。
对Mn3(Cu1-xGex)N化合物,通过计算体系中不同磁构型(局域磁矩的一种排列)的能量曲线,我们发现体系的基态磁构型Γ5g具有较大的平衡晶格常数,因此当体系从基态磁构型到顺磁态的相变过程中将会伴随着体系体积的收缩。体系的电子结构性质表明,随着温度的升高,掺杂的Ge原子能够向体系费米能级附近的导带提供更多的价电子,这些导带电子一方面增强次近邻Mn离子间的吸引相互作用,同时也极化了Mn离子的局域电子,造成Mn离子局域磁矩的改变,导致体系的体积随温度的升高面减小
在第三章中,我们还讨论了Ge浓度和N空位对体系负热膨胀性质的影响。计算结果表明随着Ge含量的增大和N空位的出现,体系的基态磁构型Γ5g越来越稳定,而亚稳态磁构型的能量升高,意味着体系的相变温度随着Ge含量的增大而上升。体系在基态磁构型和顺磁态时的体积差随着Ge含量的增大而增大,说明Ge增大了体系在相变时的体积收缩量。最后,我们通过分析交换积分,发现N空位以及Ge浓度对体系的第一近邻和第二近邻交换积分产生较大的影响,从而使Γ5g磁构型更为稳定。
第四章中总结了我们关于该材料的弹性性质的研究结果。我们的计算发现体系的弹性是各向异性的,掺杂的Ge原子能够增强体系的延展性。另外,我们预测,在Ge浓度较低时(低于50%)体系杨氏模量和体积模量随着Ge浓度的增大而增大,这与实验观测的结果符合得很好。通过对体系的电子结构的分析,我们认为这个变化趋势是由于Ge原子在费米能级处贡献的价电子所造成的。
在第五章里,我们研究了不同掺杂元素对体系Mn3(A0.5B0.5)N(A=Cu、Zn、 Ag、Cd或Mg; B=Si、Ge或Sn)的负热膨胀性质的影响。计算结果表明：Si、Ge和Sn元素能够稳定体系基态磁构型Γ5g,增大基态磁构型和顺磁态时的体积差,从含Si到含Sn体系,体系的相变温度升高。对于含Cu、Zn或Mg的体系,相变时其体积收缩幅度要比含Ag或Cd的大,其中含Zn或Mg的体系最大；与含Ag或Cd的体系相比,含Mg、Cu或Zn的体系的相变温度较低,而对于这三个体系,含Zn的体系相变温度要高一些。
Since the discovery of the negative thermal expansion (NTE) in the antiperovskite manganese nitrides Mn3(Cu1-xGex)N in2005, these compounds have been paid much attention, because of their excellent NTE behaviors, such as:(1) the coefficient and working temperature of NTE can be tunable;(2) the negative coefficient can reach as large as-25x10-6K-1;(3) the negative thermal expansion is isotropic;(4) the compounds show good mechanical and metallic behaviors. Prompted by this pioneering research, many other groups have studied the doping effect on the NTE behaviors through doping Zn, Sn, Si or some other elements into the compound. At the same times, the origin of the NTE has been studied. Although many efforts have been done, the mechanism of the NTE properties is still a puzzle for the Mn3(Cu1-xGex)N compounds. Obviously, exploring the mechanism is not only important for understanding the fascinating property of such a class of compounds, but also of benefit to the synthesizing of advanced NTE materials in the future. So in this dissertation, we investigate the mechanism of the NTE behaviors and the effect of the doped Ge atoms on the NTE behaviors of the Mn3(Cu1-xxGex)N compounds.
This dissertation contains five chapters. In the first chapter, we introduce the common NTE materials as well as their applications in brief. Then, the detailed NTE properties and its possible mechanism for Mn3(Cu1-xGex)N compounds are reviewed.
Since the Mn ions in the compounds have the local magnetic moments, our dissertation will be relevant to the knowledge about the magnetism theory. So in the second chapter, the magnetism theory and the Monte Carlo method that is used to simulate the transition temperature are introduced. In this chapter, we also present the density functional theory and the VASP package used in our theoretical calculations.
From the third chapter, we start to report our research on Mn3(Cu1-xGex)N compounds.
In the third chapter, we report our study on the origin and the effect of the Ge atoms on the NTE behaviors in the compounds of Mn3(Cu1-xGex)N. By minimizing the energies of many different magnetic configurations (the arrangements of the local magnetic moments), we find that the antiferromagnetic (AFM) configuration Δ5g have the lowest energy and the largest lattice constant. So, when the compound transforms its magnetic state from the ground state to the paramagnetic (PM) state, the volume of the compound will be contracted. Analyzing the electronic structure of the compound indicates that the doped Ge atoms can easily donate more electrons into the conduction bands nearby the Fermi level of the compound via thermal excitation, enhancing the attractive interaction between the second neighboring Mn ions, as well as polarizing some of the local electrons to change the local magnetic moments of Mn ions, causing a gradual contraction of volume with increasing temperature.
We also study the influence of the Ge content and the N vacancies on the NTE properties of Mn3(Cu1-xGex)N compounds, which is summarized in Chapter3too. Our results indicate that, as the Ge content and the N vacancies increase, the ground state configuration Γ5g become more stable, and the energies of the matestable configurations increase, meaning that the transition temperature of the compound is elevated. The different values of the volumes between the ground state and the PM state increase as the increment of the Ge content, suggesting that the Ge atoms could enlarge the volume contraction at the magnetic transition. The exchange interactions and the influence of these interactions on the volume of the compound are also extracted, from which we find that the interactions between the first and the second neighboring Mn ions dominate the magnetic interactions and make the configuration Γ5g more stable.
In the fourth chapter, we study the elastic properties of the compounds of Mn3(Cu1-xGex)N. Through analyzing the results, we find that the compounds have high elastic anisotropy and the doped Ge atoms enhance the ductile character. Furthermore, when the Ge content increases from12.5%to50%, the bulk modulus and the Young's modulus of the compound increase. This is in agreement with the experimental results. Then, we analyze the electronic structures of the compound and propose that these elastic features are essentially attributed to the valence electrons from the doped Ge.
In the last chapter, we study the influence of different doping elements on the NTE properties of the compound Mn3(A0.5B0.5)N(A=Cu、Zn、Ag、Cd or Mg; B=Si、Ge or Sn). Our results indicate that (1) the doped elements Si, Ge or Sn could stabilize the configuration Γ5g, and make it be the ground state configuration;(2) the doped Si, Ge or Sn enlarge the volume difference between Γ5g and the PM state, which is beneficial to the NTE of the compound;(3) compared to the compound containing Ag or Cd, the NTE behaviors of the compound containing Cu, Zn or Mg are better, among which the compound containing Zn or Mg has the better NTE behaviors than the other one; (4) the transition temperature of the compound containing Ag or Cd is higher than that containing Mg, Cu or Zn, and among Mg, Cu and Zn, the compound containing Zn has a higher transition temperature.
本论文一共分为五章。在第一章里,我们简要介绍了负热膨胀的机理、应用前景和一些典型的负热膨胀材料。其中,重点介绍了本论文所要研究的材料Mn3(Cu1-xGex)N的负热膨胀性质、不同掺杂对其负热膨胀行为的影响以及实验上对其负热膨胀机理的研究状况。
体系中Mn离子是具有磁矩的,因此对这个材料的物理性质的研究就必然涉及到磁性方面的知识。在第二章,我们简要地介绍了本论文中用到的磁性理论以及计算磁响变温度的蒙特罗方法。最后,我们还介绍了在本文计算中采用的密度泛函理论和VASP软件包。
从第三章开始介绍我们的研究工作。
对Mn3(Cu1-xGex)N化合物,通过计算体系中不同磁构型(局域磁矩的一种排列)的能量曲线,我们发现体系的基态磁构型Γ5g具有较大的平衡晶格常数,因此当体系从基态磁构型到顺磁态的相变过程中将会伴随着体系体积的收缩。体系的电子结构性质表明,随着温度的升高,掺杂的Ge原子能够向体系费米能级附近的导带提供更多的价电子,这些导带电子一方面增强次近邻Mn离子间的吸引相互作用,同时也极化了Mn离子的局域电子,造成Mn离子局域磁矩的改变,导致体系的体积随温度的升高面减小
在第三章中,我们还讨论了Ge浓度和N空位对体系负热膨胀性质的影响。计算结果表明随着Ge含量的增大和N空位的出现,体系的基态磁构型Γ5g越来越稳定,而亚稳态磁构型的能量升高,意味着体系的相变温度随着Ge含量的增大而上升。体系在基态磁构型和顺磁态时的体积差随着Ge含量的增大而增大,说明Ge增大了体系在相变时的体积收缩量。最后,我们通过分析交换积分,发现N空位以及Ge浓度对体系的第一近邻和第二近邻交换积分产生较大的影响,从而使Γ5g磁构型更为稳定。
第四章中总结了我们关于该材料的弹性性质的研究结果。我们的计算发现体系的弹性是各向异性的,掺杂的Ge原子能够增强体系的延展性。另外,我们预测,在Ge浓度较低时(低于50%)体系杨氏模量和体积模量随着Ge浓度的增大而增大,这与实验观测的结果符合得很好。通过对体系的电子结构的分析,我们认为这个变化趋势是由于Ge原子在费米能级处贡献的价电子所造成的。
在第五章里,我们研究了不同掺杂元素对体系Mn3(A0.5B0.5)N(A=Cu、Zn、 Ag、Cd或Mg; B=Si、Ge或Sn)的负热膨胀性质的影响。计算结果表明：Si、Ge和Sn元素能够稳定体系基态磁构型Γ5g,增大基态磁构型和顺磁态时的体积差,从含Si到含Sn体系,体系的相变温度升高。对于含Cu、Zn或Mg的体系,相变时其体积收缩幅度要比含Ag或Cd的大,其中含Zn或Mg的体系最大；与含Ag或Cd的体系相比,含Mg、Cu或Zn的体系的相变温度较低,而对于这三个体系,含Zn的体系相变温度要高一些。
Since the discovery of the negative thermal expansion (NTE) in the antiperovskite manganese nitrides Mn3(Cu1-xGex)N in2005, these compounds have been paid much attention, because of their excellent NTE behaviors, such as:(1) the coefficient and working temperature of NTE can be tunable;(2) the negative coefficient can reach as large as-25x10-6K-1;(3) the negative thermal expansion is isotropic;(4) the compounds show good mechanical and metallic behaviors. Prompted by this pioneering research, many other groups have studied the doping effect on the NTE behaviors through doping Zn, Sn, Si or some other elements into the compound. At the same times, the origin of the NTE has been studied. Although many efforts have been done, the mechanism of the NTE properties is still a puzzle for the Mn3(Cu1-xGex)N compounds. Obviously, exploring the mechanism is not only important for understanding the fascinating property of such a class of compounds, but also of benefit to the synthesizing of advanced NTE materials in the future. So in this dissertation, we investigate the mechanism of the NTE behaviors and the effect of the doped Ge atoms on the NTE behaviors of the Mn3(Cu1-xxGex)N compounds.
This dissertation contains five chapters. In the first chapter, we introduce the common NTE materials as well as their applications in brief. Then, the detailed NTE properties and its possible mechanism for Mn3(Cu1-xGex)N compounds are reviewed.
Since the Mn ions in the compounds have the local magnetic moments, our dissertation will be relevant to the knowledge about the magnetism theory. So in the second chapter, the magnetism theory and the Monte Carlo method that is used to simulate the transition temperature are introduced. In this chapter, we also present the density functional theory and the VASP package used in our theoretical calculations.
From the third chapter, we start to report our research on Mn3(Cu1-xGex)N compounds.
In the third chapter, we report our study on the origin and the effect of the Ge atoms on the NTE behaviors in the compounds of Mn3(Cu1-xGex)N. By minimizing the energies of many different magnetic configurations (the arrangements of the local magnetic moments), we find that the antiferromagnetic (AFM) configuration Δ5g have the lowest energy and the largest lattice constant. So, when the compound transforms its magnetic state from the ground state to the paramagnetic (PM) state, the volume of the compound will be contracted. Analyzing the electronic structure of the compound indicates that the doped Ge atoms can easily donate more electrons into the conduction bands nearby the Fermi level of the compound via thermal excitation, enhancing the attractive interaction between the second neighboring Mn ions, as well as polarizing some of the local electrons to change the local magnetic moments of Mn ions, causing a gradual contraction of volume with increasing temperature.
We also study the influence of the Ge content and the N vacancies on the NTE properties of Mn3(Cu1-xGex)N compounds, which is summarized in Chapter3too. Our results indicate that, as the Ge content and the N vacancies increase, the ground state configuration Γ5g become more stable, and the energies of the matestable configurations increase, meaning that the transition temperature of the compound is elevated. The different values of the volumes between the ground state and the PM state increase as the increment of the Ge content, suggesting that the Ge atoms could enlarge the volume contraction at the magnetic transition. The exchange interactions and the influence of these interactions on the volume of the compound are also extracted, from which we find that the interactions between the first and the second neighboring Mn ions dominate the magnetic interactions and make the configuration Γ5g more stable.
In the fourth chapter, we study the elastic properties of the compounds of Mn3(Cu1-xGex)N. Through analyzing the results, we find that the compounds have high elastic anisotropy and the doped Ge atoms enhance the ductile character. Furthermore, when the Ge content increases from12.5%to50%, the bulk modulus and the Young's modulus of the compound increase. This is in agreement with the experimental results. Then, we analyze the electronic structures of the compound and propose that these elastic features are essentially attributed to the valence electrons from the doped Ge.
In the last chapter, we study the influence of different doping elements on the NTE properties of the compound Mn3(A0.5B0.5)N(A=Cu、Zn、Ag、Cd or Mg; B=Si、Ge or Sn). Our results indicate that (1) the doped elements Si, Ge or Sn could stabilize the configuration Γ5g, and make it be the ground state configuration;(2) the doped Si, Ge or Sn enlarge the volume difference between Γ5g and the PM state, which is beneficial to the NTE of the compound;(3) compared to the compound containing Ag or Cd, the NTE behaviors of the compound containing Cu, Zn or Mg are better, among which the compound containing Zn or Mg has the better NTE behaviors than the other one; (4) the transition temperature of the compound containing Ag or Cd is higher than that containing Mg, Cu or Zn, and among Mg, Cu and Zn, the compound containing Zn has a higher transition temperature.
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