第一性原理研究几种过渡金属硼化物、氮化物及BC_5的结构、弹性及其电子性质
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摘要
超硬材料有着广泛的工业用途,它们已经被广泛应用于冶金、石油钻探、建筑工程、机械加工、仪器仪表、电子工业、以及航空航天等现代尖端科学领域。金刚石是自然界中已知硬度最高的材料,然而天然的金刚石非常稀少;立方氮化硼的硬度仅次于金刚石,可是自然界中没有天然立方氮化硼。因此寻找新型高硬度材料是实验工作者和理论工作者都非常关注的科研课题。最初,人们把硼碳氮系列化合物作为寻找超硬材料的主要对象,这使硼碳氮系列化合物的制备及理论研究取得了极大的进展。最近,实验工作者在高温高压条件下合成了硼化锇(OsB_2)(常压)、硼化铼(ReB_2)(常压)、氮化铂(PtN_2)、氮化锇(OsN_2)及氮化铱(IrN_2),这些材料的一个共同特征是,它们都有着较高的体弹模量(B≥350 GPa)和较高的剪切模量(G≥200 GPa)。众所周知,过渡金属本身尽管有着较大的体弹模量,但是它们的硬度往往很低。例如,金属锇(Os)的体弹模量达到了410 GPa (金刚石的体弹模量也不过是442 GPa),但是金属锇的硬度只有金刚石的三十分之一。因此,最近几年人们开始关注过渡金属硼化物和氮化物。
本文所用计算方法是基于密度泛函理论的投影缀加平面波法(PAW),软件为VASP。计算中使用局域密度近似(LDA)和广义梯度近似(GGA)下的PAW势。结构优化采用共轭梯度算法,所有原子位置充分优化到每个离子受力小于5 meV/A。平面波的切割能一般为500 eV。根据具体的晶格结构,计算中选用适当的Monkhorst-Pack网格,以保证相应的不可约布里渊区中有足够的k点。体弹模量及压力导数是通过使用Birch-Murnaghan三阶状态方程拟合压力和原胞体积得到的,弹性常数是使用应力应变方法来得到的。在计算所得弹性常数cij的基础上,使用Voigt-Reuss-Hill(VRH)近似进一步估算出多晶体弹模量B、剪切模量G、杨氏模量E和泊松比ν。
论文应用基于密度泛函理论的第一性原理方法,研究了几种材料的结构、弹性及其电子性质。文中首先介绍了所用的理论计算方法、密度泛函理论、弹性力学及VASP软件知识。预言了正交结构ReN_4 (Pbca)的存在,并对其结构、弹性及其电子结构性质进行了探索。最后在计算结果的基础上,预测ReN_4是一种金属性硬材料。预言了正交OsN_4 (Pbca)的存在,并详细计算了它的结构、弹性及其电子结构,计算结果表明OsN_4是一种带隙为0.7 eV的超硬半导体材料。研究了几种硼化物,其中TaB_2是实验上已经合成的一种材料。计算所得TaB_2晶格常数、剪切模量G (219 GPa)及杨氏模量E (531 GPa)与实验结果(G=228 GPa,E=551 GPa)符合很好。此外,计算结果表明几种硼化物的硬度与它们的弹性常数c44基本成正比。研究了两种结构相的Ta3N5,实验上已经合成对称群为Cmcm结构的Ta3N5,而对称群为Pnma的Ta3N5结构相尽管实验还没有合成,但是已有文献报道这种结构的Ta3N5是一种在高温高压下可以合成并能够稳定存在的物质。对两种结构相Ta3N5的结构、弹性及其电子性质进行了较为详细的研究。计算结果表明,两种相均不是超硬材料,Cmcm结构相的硬度仅有14.25 GPa,Pnma相的硬度也只是26.67 GPa。从理论上详细论证了最近合成的类金刚石BC5的晶格结构,并系统地研究了其弹性性质。从理论上证实了BC5是一种金属性超硬材料,并且分析了它具有高硬度的物理起源。计算所得BC5的体弹模量B (377-407 GPa)、剪切模量G (398-419 GPa)、弹性常数c44 (374-389 GPa)以及硬度H (84 GPa)证实BC5是一种超不可压缩超硬材料。而且BC5的弹性常数矩阵的本征值均为正值,说明它是一种具有弹性稳定性的材料。由于具有高硬度和金属性等物理性质,最近合成的的类金刚石结构的BC5是一种引人关注的先进磨料和超硬材料。电子结构分析表明,BC5中的B原子和它近邻的C原子之间仍存在sp3杂化。原来金刚石中存在的方向性很强的C-C共价键仅有部分被BC5中的B-C键取代,BC5中仍旧存在着像金刚石中那样的三维高对称性的共价键网格,这些使得BC5具有优良的力学性质和很高的硬度。
Superhard material has a wide range of industrial uses and has been widely used in metallurgy, oil drilling, construction, mechanical processing, devices, instruments, electronics, and aerospace, etc. modern cutting edge science. Diamond is the hardest material available in nature, however, natural diamond is very rare. CBN is the second hard material, just behind synthetic diamond, however, there are not natural CBN.
Thus, the research projects of looking for new materials with high hardness are very concerned by the experimental and theoretical workers. In the initial process of search for superhard material, people pin high hopes on the B-C-N compounds. This promoted the remarkable headway of the preparation and theoretical research of the B-C-N compounds. Recently, under high pressure and temperature, OsB_2, ReB_2, PtN_2, OsN_2 and IrN_2 have been synthesized experimentally, the common features of which are that they all have large bulk modulus (B≥350 GPa) and shear modulus (G≥200 GPa). It is well known that the transition metal’s hardness is relatively low despite the large bulk modulus. For example, the bulk modulus of pure Os is 410 GPa (the bulk modulus of diamond is just 442 GPa), but the hardness of pure Os is only one thirtieth of that of diamond. Thus, people started to pay attention to the transition metal borides and nitrides in recent years.
The calculations presented in this study were performed within the density functional theory, using the project-augmented wave (PAW) method as implemented in Vienna Ab initio simulation package (VASP). Both the local density approximation (LDA) and the generalized gradient approximation (GGA) were used with the PAW potential. The structure was optimized with the conjugate-gradient algorithm method. A plane wave cutoff energy of 500 eV was employed throughout. According to the specific lattice structure, appropriate Monkhorst-Pack mesh was chosen to guarantee the sufficient k-points in the irreducible Brillouin zone. The bulk modulus and its pressure derivative are obtained by fitting pressures and cell volumes with the third-order Birch-Murnaghan equation of state. The strain-stress method was used to obtain the elastic constant. From the calculated cij, the polycrystalline bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratioνwere further estimated using the Voigt-Reuss-Hill approximation.
Using first-principles method, this paper has investigated the structural, mechanical and electronic properties of several materials. This paper first introduces the theoretical calculation method used here and, the density functional theory, elastic mechanics and the knowledge of VASP. We predict the existence of orthorhombic structure ReN_4 (Pbca) and investigate its structural, elastic and electronic properties systematically. On the basis of the calculated results, we show that ReN_4 (Pbca) is a metallic hard material. This paper predicts the existence of orthorhombic structure OsN_4 (Pbca). And we have systematically studied the structural, elastic and electronic properties of OsN_4. The calculated results show that the orthorhombic structure OsN_4 is semiconducting superhard material with a band gap of 0.7 eV. Several transition metal borides, among which TaB_2 has been synthesized experimentally, have been investigated. For TaB_2, the calculated lattice parameters, shear modulus 219 GPa as well as Young’s modulus 531 GPa are in good agreement with the available experiment data (G=228 GPa, E=551 GPa). Moreover, the calculated results show that the hardness of the several transition metal borides is essentially proportional to their respective constant c44. Two phases of Ta3N5 have been investigated in this paper. The Cmcm phase i.e. the most stable modification of Ta3N5 up to 9 GPa has been synthesized. The Pnma phase has not been synthesized but is predicted to be the new high pressure modification at about 9 GPa. This paper systematically studied the structural, elastic and electronic properties of the two phases of Ta3N5. The calculated results show that both phases of Ta3N5 are not superhard materials, the hardness of Cmcm phase is only 14.25 GPa, and the hardness of Pnma one is 26.67 GPa. This paper has theoretically studied the crystal structure of the recently synthesized diamondlike BC5, and systematically investigated its elastic properties, our calculations confirm that BC5 is a metallic superhard material, and we systematically analyzed the origin of it high hardness. Our calculated bulk modulus B (377-407 GPa), shear modulus G (398-419 GPa), elastic constant c44 (374-389 GPa), and theoretical hardness H (84 GPa) confirm that BC5 is an ultraincompressible and superhard material. Also, it exhibits mechanical stability and metallic feature. With these physical properties, such as high hardness and metallic behavior, the recently synthesized diamondlike BC5 is attractive for advanced abrasive and superhard materials. Electronic structure analysis shows that the sp3 hybridization still exists in BC5 between B and its neighboring C atoms. The strong directional covalent C-C bonds in diamond are only partly substituted by the B-C bond in BC5. There are still three dimensional covalent network of high symmetry in BC5, which result in excellent mechanical properties and high hardness.
本文所用计算方法是基于密度泛函理论的投影缀加平面波法(PAW),软件为VASP。计算中使用局域密度近似(LDA)和广义梯度近似(GGA)下的PAW势。结构优化采用共轭梯度算法,所有原子位置充分优化到每个离子受力小于5 meV/A。平面波的切割能一般为500 eV。根据具体的晶格结构,计算中选用适当的Monkhorst-Pack网格,以保证相应的不可约布里渊区中有足够的k点。体弹模量及压力导数是通过使用Birch-Murnaghan三阶状态方程拟合压力和原胞体积得到的,弹性常数是使用应力应变方法来得到的。在计算所得弹性常数cij的基础上,使用Voigt-Reuss-Hill(VRH)近似进一步估算出多晶体弹模量B、剪切模量G、杨氏模量E和泊松比ν。
论文应用基于密度泛函理论的第一性原理方法,研究了几种材料的结构、弹性及其电子性质。文中首先介绍了所用的理论计算方法、密度泛函理论、弹性力学及VASP软件知识。预言了正交结构ReN_4 (Pbca)的存在,并对其结构、弹性及其电子结构性质进行了探索。最后在计算结果的基础上,预测ReN_4是一种金属性硬材料。预言了正交OsN_4 (Pbca)的存在,并详细计算了它的结构、弹性及其电子结构,计算结果表明OsN_4是一种带隙为0.7 eV的超硬半导体材料。研究了几种硼化物,其中TaB_2是实验上已经合成的一种材料。计算所得TaB_2晶格常数、剪切模量G (219 GPa)及杨氏模量E (531 GPa)与实验结果(G=228 GPa,E=551 GPa)符合很好。此外,计算结果表明几种硼化物的硬度与它们的弹性常数c44基本成正比。研究了两种结构相的Ta3N5,实验上已经合成对称群为Cmcm结构的Ta3N5,而对称群为Pnma的Ta3N5结构相尽管实验还没有合成,但是已有文献报道这种结构的Ta3N5是一种在高温高压下可以合成并能够稳定存在的物质。对两种结构相Ta3N5的结构、弹性及其电子性质进行了较为详细的研究。计算结果表明,两种相均不是超硬材料,Cmcm结构相的硬度仅有14.25 GPa,Pnma相的硬度也只是26.67 GPa。从理论上详细论证了最近合成的类金刚石BC5的晶格结构,并系统地研究了其弹性性质。从理论上证实了BC5是一种金属性超硬材料,并且分析了它具有高硬度的物理起源。计算所得BC5的体弹模量B (377-407 GPa)、剪切模量G (398-419 GPa)、弹性常数c44 (374-389 GPa)以及硬度H (84 GPa)证实BC5是一种超不可压缩超硬材料。而且BC5的弹性常数矩阵的本征值均为正值,说明它是一种具有弹性稳定性的材料。由于具有高硬度和金属性等物理性质,最近合成的的类金刚石结构的BC5是一种引人关注的先进磨料和超硬材料。电子结构分析表明,BC5中的B原子和它近邻的C原子之间仍存在sp3杂化。原来金刚石中存在的方向性很强的C-C共价键仅有部分被BC5中的B-C键取代,BC5中仍旧存在着像金刚石中那样的三维高对称性的共价键网格,这些使得BC5具有优良的力学性质和很高的硬度。
Superhard material has a wide range of industrial uses and has been widely used in metallurgy, oil drilling, construction, mechanical processing, devices, instruments, electronics, and aerospace, etc. modern cutting edge science. Diamond is the hardest material available in nature, however, natural diamond is very rare. CBN is the second hard material, just behind synthetic diamond, however, there are not natural CBN.
Thus, the research projects of looking for new materials with high hardness are very concerned by the experimental and theoretical workers. In the initial process of search for superhard material, people pin high hopes on the B-C-N compounds. This promoted the remarkable headway of the preparation and theoretical research of the B-C-N compounds. Recently, under high pressure and temperature, OsB_2, ReB_2, PtN_2, OsN_2 and IrN_2 have been synthesized experimentally, the common features of which are that they all have large bulk modulus (B≥350 GPa) and shear modulus (G≥200 GPa). It is well known that the transition metal’s hardness is relatively low despite the large bulk modulus. For example, the bulk modulus of pure Os is 410 GPa (the bulk modulus of diamond is just 442 GPa), but the hardness of pure Os is only one thirtieth of that of diamond. Thus, people started to pay attention to the transition metal borides and nitrides in recent years.
The calculations presented in this study were performed within the density functional theory, using the project-augmented wave (PAW) method as implemented in Vienna Ab initio simulation package (VASP). Both the local density approximation (LDA) and the generalized gradient approximation (GGA) were used with the PAW potential. The structure was optimized with the conjugate-gradient algorithm method. A plane wave cutoff energy of 500 eV was employed throughout. According to the specific lattice structure, appropriate Monkhorst-Pack mesh was chosen to guarantee the sufficient k-points in the irreducible Brillouin zone. The bulk modulus and its pressure derivative are obtained by fitting pressures and cell volumes with the third-order Birch-Murnaghan equation of state. The strain-stress method was used to obtain the elastic constant. From the calculated cij, the polycrystalline bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratioνwere further estimated using the Voigt-Reuss-Hill approximation.
Using first-principles method, this paper has investigated the structural, mechanical and electronic properties of several materials. This paper first introduces the theoretical calculation method used here and, the density functional theory, elastic mechanics and the knowledge of VASP. We predict the existence of orthorhombic structure ReN_4 (Pbca) and investigate its structural, elastic and electronic properties systematically. On the basis of the calculated results, we show that ReN_4 (Pbca) is a metallic hard material. This paper predicts the existence of orthorhombic structure OsN_4 (Pbca). And we have systematically studied the structural, elastic and electronic properties of OsN_4. The calculated results show that the orthorhombic structure OsN_4 is semiconducting superhard material with a band gap of 0.7 eV. Several transition metal borides, among which TaB_2 has been synthesized experimentally, have been investigated. For TaB_2, the calculated lattice parameters, shear modulus 219 GPa as well as Young’s modulus 531 GPa are in good agreement with the available experiment data (G=228 GPa, E=551 GPa). Moreover, the calculated results show that the hardness of the several transition metal borides is essentially proportional to their respective constant c44. Two phases of Ta3N5 have been investigated in this paper. The Cmcm phase i.e. the most stable modification of Ta3N5 up to 9 GPa has been synthesized. The Pnma phase has not been synthesized but is predicted to be the new high pressure modification at about 9 GPa. This paper systematically studied the structural, elastic and electronic properties of the two phases of Ta3N5. The calculated results show that both phases of Ta3N5 are not superhard materials, the hardness of Cmcm phase is only 14.25 GPa, and the hardness of Pnma one is 26.67 GPa. This paper has theoretically studied the crystal structure of the recently synthesized diamondlike BC5, and systematically investigated its elastic properties, our calculations confirm that BC5 is a metallic superhard material, and we systematically analyzed the origin of it high hardness. Our calculated bulk modulus B (377-407 GPa), shear modulus G (398-419 GPa), elastic constant c44 (374-389 GPa), and theoretical hardness H (84 GPa) confirm that BC5 is an ultraincompressible and superhard material. Also, it exhibits mechanical stability and metallic feature. With these physical properties, such as high hardness and metallic behavior, the recently synthesized diamondlike BC5 is attractive for advanced abrasive and superhard materials. Electronic structure analysis shows that the sp3 hybridization still exists in BC5 between B and its neighboring C atoms. The strong directional covalent C-C bonds in diamond are only partly substituted by the B-C bond in BC5. There are still three dimensional covalent network of high symmetry in BC5, which result in excellent mechanical properties and high hardness.
引文
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[1] D. M. Teter,R. J. Hemley,Low-Compressibility Carbon Nitrides,Science 1996,271,5245,53.
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[22] Q. F. Gu,G. Krauss,W. Steurer,Transition Metal Borides: Superhard versus Ultra-incompressible,Adv. Mater. 2008,20,3620.
[23] H. Y. Chung,M. B. Weinberger,J. B. Levine,A. Kavner,J. M. Yang,S. H. Tolbert,R. B. Kaner,Synthesis of Ultra-Incompressible Superhard Rhenium Diboride at Ambient Pressure,Science 2007,316,5823,436.
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[1] X. F. Hao,Y. H. Xu,Z. J. Wu,D. F. Zhou,X. J. Liu,X. Q. Cao,J. Meng,Low-compressibility and hard materials ReB2 and WB2:Prediction from first-principles study,Phys. Rev. B 2006,74,22,224112.
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