若干二元金属间化合物电子结构、弹性和热力学性质的密度泛函研究
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摘要
本论文的目标是利用密度泛函理论和准近谐德拜理论,研究具有典型代表性的二元金属间化合物的电子结构、热力学和弹塑性力学等性能,以及替位掺杂对材料性能的影响。本文计算了高温结构金属间化合物Ti-Al二元系及其Mn、Nb掺杂体系的弹塑性、弹性模量、电子结构等,分析了替位掺杂对几何结构、电子结构和键强的影响；计算了Al-Sc系四个二元相的电子结构、生成焓、德拜温度、弹性系数(含模量)和自由能,分析了AlSc和Al3Sc在高压下的弹性性质；计算了Ti-B系的电子结构和TiBx(x=1、2,常压下)及Ti1-xZrxB2(高压工况下)的力学参数和热力学参数,分析了压力变化对Ti-Zr-B金属间化合物体系的力学和热力学性质的影响,如弹性系数、各项异性、德拜温度和热熔等；设计并计算了新型超导材料Mg1-xZnxB2的电子结构和弹性系数等,并在推导得到的基于Mc-Millan公式的Tc从头算公式基础上,计算了不同Zn掺杂情况下的超导转变温度Tc,并分析了Zn掺杂对Mg-Zn-B金属间化合物体系力学性能的影响。
本文较为系统的计算了上述二元体系及其掺杂系的电子态密度、体弹模量B、弹性系数Cij、德拜温度ΘD、生成焓Ho、结合能Ecoh、热熔、自由能和Tc参量等,计算数据与已知可对比的试验数据符合良好,许多计算结果和分析结论具有独创性和良好的理论指导价值。主要的研究结果表明：
四方相TiAl中的Nb替位Ti的掺杂,在几何结构上对体系塑性性能的影响不大,但电子结构计算和布局分析表明,Nb掺杂降低了体系共价性和方向性,并提出当Nb掺杂的摩尔含量在8.33%-12.5%时有利于室温塑性的改善。Mn替Al位掺杂TiAl3后(Ti3Al8Mn)降低了由Al-Al共价键和A12p-Ti3d杂化键形成所带来的键的空间各向异性和高位错能垒,进而也改善其室温脆性。
Al-Sc系二元化合物中Al2Sc和Al3Sc结构最为稳定。OK时Al2Sc合金化形成能力最强,AlSc2最差；高温下Al2Sc结构稳定性最强,而AlSc2结构稳定性最差。研究了高压下的立方相AISc和Al3Sc的弹性系数对压力具有相似的敏感性。由于Al3Sc的各向异性弱于AISc,因此随压力的增高,Al3Sc的脆塑性转变程度不大,AISc体系的脆塑性则较大的依赖于压力的变化,随着压力的增大其塑性性能提升。
TiB2的电子成键情况较之TiB更为复杂,研究发现,TiB2的价带显示了明显的抛物线形和类sp带的特征,且非局域程度及其共价性也比TiB大。压力作用下,六方TiB2和Ti1-xZrxB2的弹性系数敏感度存在差异,掺Zr体系的剪切各向异性因子A2存在“跃变”现象,且压力对体系脆-塑转变起到了重要推动作用；另一方面,Zr的掺杂也降低了TiB2的各向异性,体系延塑性逐渐增大,但整体仍呈现出脆性性质。热力学方面,重新较为系统的估算了Ti-B和Ti-Zr-B系的热力学参量,计算表明,TiB热熔值在所有温度下都是最大的,TiB2最小,而Ti1-xZrxB2得热熔值则居于两者之间；随着压力的增大,Ti1-xZrxB2各相的德拜温度近似线性增大,并且德拜温度值随着Zr掺杂量的增大而逐步降低。
较为系统的对超导二元化合物MgB2进行了掺Zn的计算研究,结果表明,随着Zn量的增大,体系的晶格参数a和c明显拉长,且呈现出先增大后减小的情况；对于电子结构,纯态的MgB2费米面处主要是B原子的P电子共价成键,Mg2+离子降低了π带,使B原子形成近满的空穴型6带,进而增强了电声耦合作用；Zn掺杂后,影响了费密能级处的总态密度Ef等,直接影响了MgB2声子频率和电声耦合强度,研究认为Zn的替位掺杂有利于超导转变温度Tc的增大。采用自行推导得到的Tc公式计算表明,随着Zn量的增多,超导转变温度Tc先逐步升高,即当Zn掺杂量x值为0.0833和0.125时,体系的超导转变温度分别上升0.716K和0.108K,而当Zn含量继续增大时,体系的超导机制部分破坏从而Tc迅速降低。同时,随着Zn掺杂量的增大,体系的剪切各项异性A2和压缩各项异性A3整体呈现微弱的下降趋势,当Zn掺杂量x为0.14左右时,体系出现脆-塑转变现象。
The purpose of this dissertation is to demonstrate the electronic structure, thermodynamic and mechanical properties and Elemen doping performance of the typically representative binary intermetallic compounds, by using density functional theory and the quasi-harmonic Debye theory.
The plastic, elastic modulus, electronic structure of the high-temperature Ti-Al intermetallic compounds and its Mn-doping, Nb-doping system are calculated, the affect of the doping on the geometric structure, electronic structure and the bond strength are analyzed. The electronic structure, formation enthalpy (binding energy), Debye temperature, elastic coefficient (including modulus) and the free energy of the Al-Sc binary compounds are calculated, the elastic properties of AlSc and Al3Sc in high-pressure are obtained. The electronic structure and the thermodynamic parameters of Ti-B binary compounds are calculated, the mechanical parameters and thermodynamic parameters of TiBx in atmospheric pressure and Ti1-xZrxB2 in high pressure are calculated. And the affect of the mechanical and thermodynamic properties of the Ti-Zr-B system are discussed, such as elastic coefficient, anisotropy, Debye temperature and heat capacity. The electronic structure and elastic coefficient of the Mg1-xZnxB2 s uperconducting intermetallic compounds are calculated, the ab initio formula of the Tc is derived according to the Mc-Millan's formula by BCS theory, which is used to calculate the Tc. The mechanical properties of Zn-doping on the Mg-B binary compounds are analyzed.
This calculated parameters, such as DOS, bulk modulus, elastic coefficient, Debye temperature, enthalpy of formation, binding energy, heat capacity, the free energy andμ*(λ),et al, are in good agreement with the known experimental data, many calculated results of the paper have originality and the good reference value.
It is found that:
The plastic properties of the Ti-Al-Nb are not affected by the geometric structure of the tetragonal TiAl by Nb-doping in Ti site, but the electronic structure calculations and population analysis shows that Nb doping reduced the total covalence and direction of the ternary, and the room temperature plasticity is conducive to improved with the Nb content of 8.33%-12.5%. Mn doping in Al site in TiAl3 (Ti3Al8Mn) reduced the anisotropy of the key and the dislocation energy barrier which caused by the Al-Al covalent bond and A12p-Ti3d hybrid bond, and thus improve its room temperature brittleness.
Al2Sc and Al3Sc are the most stable structure in Al-Sc binary compounds. The alloy's forming ability of Al2Sc is the strongest one at 0 K, but the AlSc2 is the worst one, as well as their structural stability at high temperatures. The elasticity coefficients of AlSc and Al3Sc with cubic phase have the similar sensitivity for the pressure. The anisotropy of Al3Sc is weaker than AlSc, thus the brittle-plastic transition of Al3Sc with the increasing pressure is not great, but the brittle-plastic transition of AlSc is larger depends on the pressure and the plastic could be upgraded as pressure increases.
The electronic structure of TiB2 is more complex than that of TiB, the valence band of TiB2 shows a clear characteristic of parabolic and like-sp band, meanwhile, the degree of non-localization and covalence of TiB2 is larger than that of TiB. The elastic coefficients of the hexagonal TiB2 and Ti1-xZrxB2 have different sensitivity for the pressure. The shear anisotropy factor A2 of the Ti-Zr-B ternary has a special phenomenon which called "jump", and the pressure plays an important role in the transition from brittle to ductile. On the other hand, Zr doping reduces the anisotropy of TiB2, the plastic of Ti-Zr-B increased gradually, the thermodynamic parameters of Ti-B and Ti-Zr-B systems are re-estimated systematically, the results show that the heat capacities of TiB are the biggest at all temperatures, on the contrary of TiB2, while the data of Ti1-xZrxB2 are located between TiB and TiB2. The Debye temperature of Ti1-xZrxB2 increases linearly as the pressure increases, and the value of Debye temperature decreased with the increase of Zr doping content.
The the lattice parameters (a and c) of MgB2 is significantly elongated by Zn doped. The DOS of Fermi energy of MgB2 is mainly provided by the p electrons of B and form covalent bonds, Mg+2 ions reduce theπband and the hole-typeσband of B atoms is nearly full, thus enhancing the electron-phonon coupling; the Fermi level Ef is impacted by Zn doped, which directly affect the frequency of phonon of the MgB2 and the strength of the electron-phonon coupling. It is suggested that the Zn doping is benefit for the increasing of the superconducting transition temperature Tc. The calculation shows that with the increase of Zn content, the superconducting transition temperature Tc increases at first, and the theoretical value of Tc can increase 0.716K and 0.108K when x is equal to 0.0833 and 0.125, respectively; and then the Tc decreases rapidly with the increase of Zn content. Meanwhile, the anisotropy of shear and compression takes on a slight downward trend. When the x of Zn doping is about 0.14, the system exhibits brittle-plastic changes in behavior.
本文较为系统的计算了上述二元体系及其掺杂系的电子态密度、体弹模量B、弹性系数Cij、德拜温度ΘD、生成焓Ho、结合能Ecoh、热熔、自由能和Tc参量等,计算数据与已知可对比的试验数据符合良好,许多计算结果和分析结论具有独创性和良好的理论指导价值。主要的研究结果表明：
四方相TiAl中的Nb替位Ti的掺杂,在几何结构上对体系塑性性能的影响不大,但电子结构计算和布局分析表明,Nb掺杂降低了体系共价性和方向性,并提出当Nb掺杂的摩尔含量在8.33%-12.5%时有利于室温塑性的改善。Mn替Al位掺杂TiAl3后(Ti3Al8Mn)降低了由Al-Al共价键和A12p-Ti3d杂化键形成所带来的键的空间各向异性和高位错能垒,进而也改善其室温脆性。
Al-Sc系二元化合物中Al2Sc和Al3Sc结构最为稳定。OK时Al2Sc合金化形成能力最强,AlSc2最差；高温下Al2Sc结构稳定性最强,而AlSc2结构稳定性最差。研究了高压下的立方相AISc和Al3Sc的弹性系数对压力具有相似的敏感性。由于Al3Sc的各向异性弱于AISc,因此随压力的增高,Al3Sc的脆塑性转变程度不大,AISc体系的脆塑性则较大的依赖于压力的变化,随着压力的增大其塑性性能提升。
TiB2的电子成键情况较之TiB更为复杂,研究发现,TiB2的价带显示了明显的抛物线形和类sp带的特征,且非局域程度及其共价性也比TiB大。压力作用下,六方TiB2和Ti1-xZrxB2的弹性系数敏感度存在差异,掺Zr体系的剪切各向异性因子A2存在“跃变”现象,且压力对体系脆-塑转变起到了重要推动作用；另一方面,Zr的掺杂也降低了TiB2的各向异性,体系延塑性逐渐增大,但整体仍呈现出脆性性质。热力学方面,重新较为系统的估算了Ti-B和Ti-Zr-B系的热力学参量,计算表明,TiB热熔值在所有温度下都是最大的,TiB2最小,而Ti1-xZrxB2得热熔值则居于两者之间；随着压力的增大,Ti1-xZrxB2各相的德拜温度近似线性增大,并且德拜温度值随着Zr掺杂量的增大而逐步降低。
较为系统的对超导二元化合物MgB2进行了掺Zn的计算研究,结果表明,随着Zn量的增大,体系的晶格参数a和c明显拉长,且呈现出先增大后减小的情况；对于电子结构,纯态的MgB2费米面处主要是B原子的P电子共价成键,Mg2+离子降低了π带,使B原子形成近满的空穴型6带,进而增强了电声耦合作用；Zn掺杂后,影响了费密能级处的总态密度Ef等,直接影响了MgB2声子频率和电声耦合强度,研究认为Zn的替位掺杂有利于超导转变温度Tc的增大。采用自行推导得到的Tc公式计算表明,随着Zn量的增多,超导转变温度Tc先逐步升高,即当Zn掺杂量x值为0.0833和0.125时,体系的超导转变温度分别上升0.716K和0.108K,而当Zn含量继续增大时,体系的超导机制部分破坏从而Tc迅速降低。同时,随着Zn掺杂量的增大,体系的剪切各项异性A2和压缩各项异性A3整体呈现微弱的下降趋势,当Zn掺杂量x为0.14左右时,体系出现脆-塑转变现象。
The purpose of this dissertation is to demonstrate the electronic structure, thermodynamic and mechanical properties and Elemen doping performance of the typically representative binary intermetallic compounds, by using density functional theory and the quasi-harmonic Debye theory.
The plastic, elastic modulus, electronic structure of the high-temperature Ti-Al intermetallic compounds and its Mn-doping, Nb-doping system are calculated, the affect of the doping on the geometric structure, electronic structure and the bond strength are analyzed. The electronic structure, formation enthalpy (binding energy), Debye temperature, elastic coefficient (including modulus) and the free energy of the Al-Sc binary compounds are calculated, the elastic properties of AlSc and Al3Sc in high-pressure are obtained. The electronic structure and the thermodynamic parameters of Ti-B binary compounds are calculated, the mechanical parameters and thermodynamic parameters of TiBx in atmospheric pressure and Ti1-xZrxB2 in high pressure are calculated. And the affect of the mechanical and thermodynamic properties of the Ti-Zr-B system are discussed, such as elastic coefficient, anisotropy, Debye temperature and heat capacity. The electronic structure and elastic coefficient of the Mg1-xZnxB2 s uperconducting intermetallic compounds are calculated, the ab initio formula of the Tc is derived according to the Mc-Millan's formula by BCS theory, which is used to calculate the Tc. The mechanical properties of Zn-doping on the Mg-B binary compounds are analyzed.
This calculated parameters, such as DOS, bulk modulus, elastic coefficient, Debye temperature, enthalpy of formation, binding energy, heat capacity, the free energy andμ*(λ),et al, are in good agreement with the known experimental data, many calculated results of the paper have originality and the good reference value.
It is found that:
The plastic properties of the Ti-Al-Nb are not affected by the geometric structure of the tetragonal TiAl by Nb-doping in Ti site, but the electronic structure calculations and population analysis shows that Nb doping reduced the total covalence and direction of the ternary, and the room temperature plasticity is conducive to improved with the Nb content of 8.33%-12.5%. Mn doping in Al site in TiAl3 (Ti3Al8Mn) reduced the anisotropy of the key and the dislocation energy barrier which caused by the Al-Al covalent bond and A12p-Ti3d hybrid bond, and thus improve its room temperature brittleness.
Al2Sc and Al3Sc are the most stable structure in Al-Sc binary compounds. The alloy's forming ability of Al2Sc is the strongest one at 0 K, but the AlSc2 is the worst one, as well as their structural stability at high temperatures. The elasticity coefficients of AlSc and Al3Sc with cubic phase have the similar sensitivity for the pressure. The anisotropy of Al3Sc is weaker than AlSc, thus the brittle-plastic transition of Al3Sc with the increasing pressure is not great, but the brittle-plastic transition of AlSc is larger depends on the pressure and the plastic could be upgraded as pressure increases.
The electronic structure of TiB2 is more complex than that of TiB, the valence band of TiB2 shows a clear characteristic of parabolic and like-sp band, meanwhile, the degree of non-localization and covalence of TiB2 is larger than that of TiB. The elastic coefficients of the hexagonal TiB2 and Ti1-xZrxB2 have different sensitivity for the pressure. The shear anisotropy factor A2 of the Ti-Zr-B ternary has a special phenomenon which called "jump", and the pressure plays an important role in the transition from brittle to ductile. On the other hand, Zr doping reduces the anisotropy of TiB2, the plastic of Ti-Zr-B increased gradually, the thermodynamic parameters of Ti-B and Ti-Zr-B systems are re-estimated systematically, the results show that the heat capacities of TiB are the biggest at all temperatures, on the contrary of TiB2, while the data of Ti1-xZrxB2 are located between TiB and TiB2. The Debye temperature of Ti1-xZrxB2 increases linearly as the pressure increases, and the value of Debye temperature decreased with the increase of Zr doping content.
The the lattice parameters (a and c) of MgB2 is significantly elongated by Zn doped. The DOS of Fermi energy of MgB2 is mainly provided by the p electrons of B and form covalent bonds, Mg+2 ions reduce theπband and the hole-typeσband of B atoms is nearly full, thus enhancing the electron-phonon coupling; the Fermi level Ef is impacted by Zn doped, which directly affect the frequency of phonon of the MgB2 and the strength of the electron-phonon coupling. It is suggested that the Zn doping is benefit for the increasing of the superconducting transition temperature Tc. The calculation shows that with the increase of Zn content, the superconducting transition temperature Tc increases at first, and the theoretical value of Tc can increase 0.716K and 0.108K when x is equal to 0.0833 and 0.125, respectively; and then the Tc decreases rapidly with the increase of Zn content. Meanwhile, the anisotropy of shear and compression takes on a slight downward trend. When the x of Zn doping is about 0.14, the system exhibits brittle-plastic changes in behavior.
引文
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