碳基和类碳超硬材料的第一性原理研究
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摘要
寻找既能满足刀具和耐磨涂层等工业要求,又能弥补金刚石和立方氮化硼应用局限性的新型超硬材料一直是材料科学研究的热点。在众多新合成和潜在的超硬材料中,碳基和类碳单质或化合物占据了很大比重。其中材料的维度、尺寸、组分、密度以及键的杂化状态对碳基和类碳材料的硬度等力学性能至关重要,对它们的研究,可以加深人们对超硬材料硬度起源的理解,并为设计和预言超硬相提供可靠的理论依据。为了探讨这些参数与力学性能的关系,本论文提出从第一性原理弹性模量估算硬度的经验公式,并系统讨论从自组装碳新相,到类碳P-BN相和富硼的AlMgB14晶体,再到非晶态的玻璃碳、二元CNx和B-C-N三元体系,最后到低维度的纳米金刚石、金刚石纳米线以及碳的新层状结构等碳基和类碳基材料的结构、力学性能以及电子结构。
首先,利用密度泛函理论(DFT)输出的弹性模量或者简单的原子结构参数估算固体硬度,对于理解和从理论上预测超硬材料至关重要。论文统计了常见共价晶体化合物的弹性模量与维氏硬度的实验值,并分别拟合维氏硬度与体弹性模量、剪切模量和杨氏模量的关系。基于第一性原理计算和上述E-Hv和G-Hv关系,估算目前被普遍认为的几种超硬材料的维氏硬度。我们拟合的经验G-Hv和E-Hv线性关系建立了从第一性原理弹性常数到材料微观硬度之间的桥梁。
从二维石墨烯片层出发,我们构造了两类空隙尺寸、手性和成键比率可调的,具有较大比表面积的三维共价石墨烯聚合物,它们拥有良好的稳定性、优异的力学和电学性能。与它们的母体二维石墨烯和三维石墨相比,本文提出的三维石墨烯自组装聚合物表现出高的杨氏模量、理想强度以及可调的半导体能隙,因而在许多领域具有潜在的应用,例如半导体器件、能量存储、分子筛等。除了高密度的ZGM-12,zigzag系列的石墨烯自组装网络结构还具有负的线性压缩率,即这些材料的体积压缩时,沿某个方向的晶格常数膨胀,从而在压力敏感器件、无线电通讯以及光学材料方向有广泛的应用前景。各向异性的力学性能和特殊的洒架型通道构型是造成石墨烯聚合物表现出负的线性压缩率的主要原因。
通过第一性原理计算预言了新的正交BN相(命名为P-BN；空间群为Pmn21),它的理论硬度和体弹性模量分别为60.5GPa和403GPa,可能是位于h-BN到w-BN过渡路径上的超硬亚稳相。而对于三元硼化物AlMgB14材料,我们从理论和实验上探讨了影响其硬度的因素并解释了硬度的起源。在实验上,我们得到了AlMgB14非晶薄膜材料并关注到其硬度随着B元素含量的增加而增加。同时在理论上,通过对AlMgB14和一系列基于B12二十面体材料的电子结构分析表明共同具有的B12二十面体骨架是决定硬度的主要因素。而Al和Mg等金属元素主要通过向B12单元的电荷转移对材料硬度进行微调。这类材料在工具、模具、微机械制造及航空航天关键零部件等领域具有重要的应用价值。
受类金刚石薄膜的高硬度和良好力学性能的启发,本文研究了包含sp2和sp3杂化形式的一元无定形玻璃碳、二元的CN非晶和三元的B-C-N非晶薄膜的力学性能,它们自身或其在特定条件下可能具有较高的硬度,在许多领域有潜在应用。首先,我们提出了压力导致的玻璃碳相变的理论图像,并建立了玻璃碳的力学性能与成键类型之间的关系。在此基础上,预测了一个被命名为R3碳新的晶体相,并证实了它可以看作是非晶玻璃碳的雏形,提出了在快速冷凝熔融液体或者气体之外非晶化的另外一条路径。其次,应用第一性原理分子动力学模拟退火方法产生了四种不同化学计量比的CNx超原胞结构,进一步表征了它们的结构参数、键长和成键类型。事实上,在研究中并没有发现硬度超过6-C3N4的化合物,但是通过上述研究我们揭示出增强碳氮薄膜硬度的参数,这对实验上合成CN超硬材料有所启迪。另外,基于ta-C的结构和随机固溶体模型,本文绘出了形成能(Ef)、杨氏模量(E)以及韧性(B/G)在三元B-C-N相图中的分布图,并且预言原子百分比位于B:15-30at.%;C:50-60at.%;N:20-30at.%区间的B-C-N化合物同时拥有优异的力学性能、良好的延展性以及高的形成能力,上述理论结果为实验制备超硬非晶薄膜提供了很好的理论指导。
最后,我们考察了维度和压力(应变)对低维金刚石或石墨烯同素异形体的力学和电学性能的影响。发现纳米金刚石的杨氏模量随颗粒尺寸的增加而增加,但低于体相金刚石值。根据理论计算结果,我们进一步拟合了纳米金刚石杨氏模量与尺寸的经验函数,为实验上制备出的不同尺寸的纳米金刚石提供了估算硬度的公式。金刚石纳米线的杨氏模量和理想强度随截面积的减小而降低,并表现出很强各向异性。除此之外,金刚石纳米线的带隙强烈依赖于它的尺寸、晶体取向和拉伸应变,这也说明了金刚石纳米线具有可调的能隙。我们还构建了平面结构的(4,8)石墨烯新型二维同素异形体,并通过第一性原理总能计算和分子动力学模拟证明其室温稳定性。上述石墨烯二维同素异形体是小带隙的半导体,具有可比拟石墨烯的力学性能。
The search for superhard materials is motivated by the need of industrial applications, e.g., cutting tool and resistant coatings, which might make up for the limitations of the traditionally known superhard materials such as diamond and c-BN. Recent experimental synthesis and theoretical design have mostly focused on the carbon-based and carbon-like covalent compounds formed by light weight elements such as boron (B), carbon (C), nitrogen (N), and oxygen (O). The mechanical properties and hardness of those materials strongly depend on their dimension, size, composition, density and bonding types, which are important for investigating the origin of hardness and further providing the reasonable proof for predicting and designing superhard materials. In this thesis, we propose an empirical formula to build up a bridge between Vickers hardness and first-principles calculations, and discuss the structural parameters, mechanical, and electronical properties of carbon-related materials, including sp2and sp3mixed graphene monolith, crystalline P-BN and AlMgB14, amorphous glassy carbon, CNX and ternary B-C-N, and low-dimensional nanodiamond, nanowires, and new graphene allotrope.
From a statistical manner, we collect and correlate experimental bulk (B), shear (G), Young's modulus (E), and ductility (G/B) with Vickers hardness (Hv) for a number of covalent materials and fit quantitative Hv-G and Hv-E relationships in Chapter2. Using these experimental formulas and first-principles calculations, we further predict the microhardness of some novel potential hard/superhard covalent compounds (BC2N, AlMgB14, TiO2, ReC, and PtN2). None of them belong to superhard materials (Hv≥40GPa) except BC2N. The present empirical formula builds up a bridge between Vickers hardness and first-principles calculations that is useful to evaluate and design promising hard/sup erhard materials.
One of great challenges in the field of graphene applications is to fabricate three dimensional graphene products which could inherit its excellent intrinsic properties and overcome its shortcomings. In Chapter3, we construct two classes of3-D graphene monoliths (GMs) with high surface area based on width-adjustable zigzag and armchair graphene nanoribbons as building blocks and sp3carbon linkers. Such design goes beyond previous widely used physical interaction and shows favorable cohesive energy and appreciable mechanical/dynamic stability. On account of their tailored motifs, wine rack pores and rigid sp3linkers, both two classes of GMs have high specific surface area, strong mechanical strengths, tunable band gap, and subtle negative or positive linear compressibility. By solving the zero band gap and dimensional problems of single layer nanosheet simultaneously, these new GM materials offer a viable strategy for realizing many promising applications, including semiconductor devices, energy storage, molecular sieves, sensitive pressure detectors, telecommunication line systems, and environment and biological field.
Using first-principles calculations, we identify a new orthorhombic BN phase (namely, P-BN; space group:Pmn21), whose theoretical hardness and bulk modulus are403GPa and60.5GPa, respectively, comparable to those of c-BN. This P-BN phase, along with Bct-BN and Z-BN, is suggested as possible intermediate phases between h-BN and w-BN. For Al-Mg-B amorphous film, we discuss and explain the origin of hardness from both the theoretical and experimental sides. For the Al-Mg-B films along the AlMg isocontent line, nanoindentation test indicates that the hardness of films increases with increasing boron contents. Meanwhile, based on the electron density of states and Mulliken population analysis, the crystal hardness is primarily determined by the B12icosahedral skeleton, whereas the contributions of metal atoms manifest as the electron donor to boron atoms. These materials may be useful in the fields of mechanical, aerospace and military.
Motivated by the superior hardness and Young's modulus of diamond-like carbon (DLC) films, in Chapter5, we investigate the mechanical properties of sp2and sp3mixed glassy carbon, carbon nitride and ternary B-C-N films. We provide the theoretical picture of pressure-induced phase transfonnation in glassy carbon (GC) and correlation the hardness and bond types. Moreover, we predict a new crystalline carbon allotrope possessing R3symmetry (R3-carbon) using the stochastic quenching (SQ) method. The present results indicate that R3-carbon can be regarded as an allotrope similar to that of amorphous GC. A very small energy difference and the similarity of GC and the R3-carbon structures imply that small perturbations to this crystalline carbon allotrope may provide another possible pathway to amorphization of carbon besides quenching the liquid melt or gas by ultra-fast cooling. Based on ab initio molecular dynamics method, four amorphous CNX structures with different stoichiometries (CN0.47, CN0.67, CN0.92, and CN1.3) were generated within a100-atom supercell. Unfortunately, there is no superhard composition whose hardness can be comparable to those of diamond and P-C3N4. Characterizations of the pair correlation functions, bond length and the fraction of bond types of the amorphous carbon nitrides reveals that the N content in such structures plays a key role in determining the structural networks. Based on the structures of ta-C and random solution model, we present the distributions of mechanical properties and formation ability of amorphous BxCyNz solids on the ternary B-C-N phase diagram and predicted that on the phase area (B:15-30at.%; C:50-60at.%; N: 20-30at.%), B-C-N solids possess both excellent hardness and good formation ability. These theoretical results provide valuable guidance for intentionally synthesizing BxCyN7materials with desirable mechanical properties.
In Chapter6, mechanical and electronic properties of selected low dimensional carbon-based materials under different dimensionals, pressure, and strain have been investigated by means of density functional theory calculations. The computed Young's moduli of nanodiamonds are lower than the bulk value and increase with size, which can be fitted to an empirical function of diameter. For thinner diamond nanowires (area of cross section less than0.6tim2), the Young's modulus and ideal strength of these diamond nanowires decrease with decreasing cross section and show anisotropic effects. Moreover, the band gap of diamond nanowires is sensitive to the size, crystallographic orientation and tensile strain, implying the possibility of a tunable gap. Then, from first-principles calculations, we predict a planar stable graphene allotrope composed of a periodic array of tetragonal and octagonal (4,8) carbon rings. The stability of this sheet is examined by the room-temperature molecular dynamics simulation and the electronic structure is studied using state-of-the-art calculations such as the hybrid density functional and the GW approach. We find a stable planar semiconducting carbon sheet with a band gap between0.43and1.01eV with excellent mechanical properties as good as graphene's.
首先,利用密度泛函理论(DFT)输出的弹性模量或者简单的原子结构参数估算固体硬度,对于理解和从理论上预测超硬材料至关重要。论文统计了常见共价晶体化合物的弹性模量与维氏硬度的实验值,并分别拟合维氏硬度与体弹性模量、剪切模量和杨氏模量的关系。基于第一性原理计算和上述E-Hv和G-Hv关系,估算目前被普遍认为的几种超硬材料的维氏硬度。我们拟合的经验G-Hv和E-Hv线性关系建立了从第一性原理弹性常数到材料微观硬度之间的桥梁。
从二维石墨烯片层出发,我们构造了两类空隙尺寸、手性和成键比率可调的,具有较大比表面积的三维共价石墨烯聚合物,它们拥有良好的稳定性、优异的力学和电学性能。与它们的母体二维石墨烯和三维石墨相比,本文提出的三维石墨烯自组装聚合物表现出高的杨氏模量、理想强度以及可调的半导体能隙,因而在许多领域具有潜在的应用,例如半导体器件、能量存储、分子筛等。除了高密度的ZGM-12,zigzag系列的石墨烯自组装网络结构还具有负的线性压缩率,即这些材料的体积压缩时,沿某个方向的晶格常数膨胀,从而在压力敏感器件、无线电通讯以及光学材料方向有广泛的应用前景。各向异性的力学性能和特殊的洒架型通道构型是造成石墨烯聚合物表现出负的线性压缩率的主要原因。
通过第一性原理计算预言了新的正交BN相(命名为P-BN；空间群为Pmn21),它的理论硬度和体弹性模量分别为60.5GPa和403GPa,可能是位于h-BN到w-BN过渡路径上的超硬亚稳相。而对于三元硼化物AlMgB14材料,我们从理论和实验上探讨了影响其硬度的因素并解释了硬度的起源。在实验上,我们得到了AlMgB14非晶薄膜材料并关注到其硬度随着B元素含量的增加而增加。同时在理论上,通过对AlMgB14和一系列基于B12二十面体材料的电子结构分析表明共同具有的B12二十面体骨架是决定硬度的主要因素。而Al和Mg等金属元素主要通过向B12单元的电荷转移对材料硬度进行微调。这类材料在工具、模具、微机械制造及航空航天关键零部件等领域具有重要的应用价值。
受类金刚石薄膜的高硬度和良好力学性能的启发,本文研究了包含sp2和sp3杂化形式的一元无定形玻璃碳、二元的CN非晶和三元的B-C-N非晶薄膜的力学性能,它们自身或其在特定条件下可能具有较高的硬度,在许多领域有潜在应用。首先,我们提出了压力导致的玻璃碳相变的理论图像,并建立了玻璃碳的力学性能与成键类型之间的关系。在此基础上,预测了一个被命名为R3碳新的晶体相,并证实了它可以看作是非晶玻璃碳的雏形,提出了在快速冷凝熔融液体或者气体之外非晶化的另外一条路径。其次,应用第一性原理分子动力学模拟退火方法产生了四种不同化学计量比的CNx超原胞结构,进一步表征了它们的结构参数、键长和成键类型。事实上,在研究中并没有发现硬度超过6-C3N4的化合物,但是通过上述研究我们揭示出增强碳氮薄膜硬度的参数,这对实验上合成CN超硬材料有所启迪。另外,基于ta-C的结构和随机固溶体模型,本文绘出了形成能(Ef)、杨氏模量(E)以及韧性(B/G)在三元B-C-N相图中的分布图,并且预言原子百分比位于B:15-30at.%;C:50-60at.%;N:20-30at.%区间的B-C-N化合物同时拥有优异的力学性能、良好的延展性以及高的形成能力,上述理论结果为实验制备超硬非晶薄膜提供了很好的理论指导。
最后,我们考察了维度和压力(应变)对低维金刚石或石墨烯同素异形体的力学和电学性能的影响。发现纳米金刚石的杨氏模量随颗粒尺寸的增加而增加,但低于体相金刚石值。根据理论计算结果,我们进一步拟合了纳米金刚石杨氏模量与尺寸的经验函数,为实验上制备出的不同尺寸的纳米金刚石提供了估算硬度的公式。金刚石纳米线的杨氏模量和理想强度随截面积的减小而降低,并表现出很强各向异性。除此之外,金刚石纳米线的带隙强烈依赖于它的尺寸、晶体取向和拉伸应变,这也说明了金刚石纳米线具有可调的能隙。我们还构建了平面结构的(4,8)石墨烯新型二维同素异形体,并通过第一性原理总能计算和分子动力学模拟证明其室温稳定性。上述石墨烯二维同素异形体是小带隙的半导体,具有可比拟石墨烯的力学性能。
The search for superhard materials is motivated by the need of industrial applications, e.g., cutting tool and resistant coatings, which might make up for the limitations of the traditionally known superhard materials such as diamond and c-BN. Recent experimental synthesis and theoretical design have mostly focused on the carbon-based and carbon-like covalent compounds formed by light weight elements such as boron (B), carbon (C), nitrogen (N), and oxygen (O). The mechanical properties and hardness of those materials strongly depend on their dimension, size, composition, density and bonding types, which are important for investigating the origin of hardness and further providing the reasonable proof for predicting and designing superhard materials. In this thesis, we propose an empirical formula to build up a bridge between Vickers hardness and first-principles calculations, and discuss the structural parameters, mechanical, and electronical properties of carbon-related materials, including sp2and sp3mixed graphene monolith, crystalline P-BN and AlMgB14, amorphous glassy carbon, CNX and ternary B-C-N, and low-dimensional nanodiamond, nanowires, and new graphene allotrope.
From a statistical manner, we collect and correlate experimental bulk (B), shear (G), Young's modulus (E), and ductility (G/B) with Vickers hardness (Hv) for a number of covalent materials and fit quantitative Hv-G and Hv-E relationships in Chapter2. Using these experimental formulas and first-principles calculations, we further predict the microhardness of some novel potential hard/superhard covalent compounds (BC2N, AlMgB14, TiO2, ReC, and PtN2). None of them belong to superhard materials (Hv≥40GPa) except BC2N. The present empirical formula builds up a bridge between Vickers hardness and first-principles calculations that is useful to evaluate and design promising hard/sup erhard materials.
One of great challenges in the field of graphene applications is to fabricate three dimensional graphene products which could inherit its excellent intrinsic properties and overcome its shortcomings. In Chapter3, we construct two classes of3-D graphene monoliths (GMs) with high surface area based on width-adjustable zigzag and armchair graphene nanoribbons as building blocks and sp3carbon linkers. Such design goes beyond previous widely used physical interaction and shows favorable cohesive energy and appreciable mechanical/dynamic stability. On account of their tailored motifs, wine rack pores and rigid sp3linkers, both two classes of GMs have high specific surface area, strong mechanical strengths, tunable band gap, and subtle negative or positive linear compressibility. By solving the zero band gap and dimensional problems of single layer nanosheet simultaneously, these new GM materials offer a viable strategy for realizing many promising applications, including semiconductor devices, energy storage, molecular sieves, sensitive pressure detectors, telecommunication line systems, and environment and biological field.
Using first-principles calculations, we identify a new orthorhombic BN phase (namely, P-BN; space group:Pmn21), whose theoretical hardness and bulk modulus are403GPa and60.5GPa, respectively, comparable to those of c-BN. This P-BN phase, along with Bct-BN and Z-BN, is suggested as possible intermediate phases between h-BN and w-BN. For Al-Mg-B amorphous film, we discuss and explain the origin of hardness from both the theoretical and experimental sides. For the Al-Mg-B films along the AlMg isocontent line, nanoindentation test indicates that the hardness of films increases with increasing boron contents. Meanwhile, based on the electron density of states and Mulliken population analysis, the crystal hardness is primarily determined by the B12icosahedral skeleton, whereas the contributions of metal atoms manifest as the electron donor to boron atoms. These materials may be useful in the fields of mechanical, aerospace and military.
Motivated by the superior hardness and Young's modulus of diamond-like carbon (DLC) films, in Chapter5, we investigate the mechanical properties of sp2and sp3mixed glassy carbon, carbon nitride and ternary B-C-N films. We provide the theoretical picture of pressure-induced phase transfonnation in glassy carbon (GC) and correlation the hardness and bond types. Moreover, we predict a new crystalline carbon allotrope possessing R3symmetry (R3-carbon) using the stochastic quenching (SQ) method. The present results indicate that R3-carbon can be regarded as an allotrope similar to that of amorphous GC. A very small energy difference and the similarity of GC and the R3-carbon structures imply that small perturbations to this crystalline carbon allotrope may provide another possible pathway to amorphization of carbon besides quenching the liquid melt or gas by ultra-fast cooling. Based on ab initio molecular dynamics method, four amorphous CNX structures with different stoichiometries (CN0.47, CN0.67, CN0.92, and CN1.3) were generated within a100-atom supercell. Unfortunately, there is no superhard composition whose hardness can be comparable to those of diamond and P-C3N4. Characterizations of the pair correlation functions, bond length and the fraction of bond types of the amorphous carbon nitrides reveals that the N content in such structures plays a key role in determining the structural networks. Based on the structures of ta-C and random solution model, we present the distributions of mechanical properties and formation ability of amorphous BxCyNz solids on the ternary B-C-N phase diagram and predicted that on the phase area (B:15-30at.%; C:50-60at.%; N: 20-30at.%), B-C-N solids possess both excellent hardness and good formation ability. These theoretical results provide valuable guidance for intentionally synthesizing BxCyN7materials with desirable mechanical properties.
In Chapter6, mechanical and electronic properties of selected low dimensional carbon-based materials under different dimensionals, pressure, and strain have been investigated by means of density functional theory calculations. The computed Young's moduli of nanodiamonds are lower than the bulk value and increase with size, which can be fitted to an empirical function of diameter. For thinner diamond nanowires (area of cross section less than0.6tim2), the Young's modulus and ideal strength of these diamond nanowires decrease with decreasing cross section and show anisotropic effects. Moreover, the band gap of diamond nanowires is sensitive to the size, crystallographic orientation and tensile strain, implying the possibility of a tunable gap. Then, from first-principles calculations, we predict a planar stable graphene allotrope composed of a periodic array of tetragonal and octagonal (4,8) carbon rings. The stability of this sheet is examined by the room-temperature molecular dynamics simulation and the electronic structure is studied using state-of-the-art calculations such as the hybrid density functional and the GW approach. We find a stable planar semiconducting carbon sheet with a band gap between0.43and1.01eV with excellent mechanical properties as good as graphene's.
引文
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