高压下过渡金属硼化物与碱金属叠氮化物的理论研究
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摘要
高压下新型超硬材料和含氮高能材料的合成与设计是当前凝聚态物理和材料科学最具有吸引力和挑战性的课题之一。本文结合最新发展的晶体结构预测技术和基于密度泛函理论的第一性原理方法,系统地研究了具有潜在超硬特性的过渡金属(Mo、Sc、Ti、Y、Zr)硼化物和高能材料碱金属(Na和Li)叠氮化物的高压行为,得到了以下创新性结果:
1.澄清了实验上关于MoB_2,Mo_2B_5和MoB_4三种硼化物基态稳定结构的争议,预言了尚未合成的MoB_3的基态结构和实验合成条件,构建了Mo-B体系的零温相图。发现以上四种硼化物均具有“三明治”B-Mo-B层,都是理论维氏硬度超过20 GPa的硬质材料,其中MoB_3的硬度可以达到31.8 GPa。
2.获得了具有六角AlB_2结构的过渡金属硼化物TMB_2(TM = Zr、Sc、Ti、Y)的高压结构相变行为,发现在低于300 GPa压力下具有Zr-B强共价键的ZrB2没有结构相变,而ScB_2和YB_2分别在208和163 GPa压力下相变为单斜结构,TiB_2却在215 GPa相变为四方α-ThSi_2结构。进一步研究揭示,过渡金属原子到B原子的电荷转移是压致相变的主要诱因。
3.提出NaN3高压相变序列为:菱方→单斜I→四方→六角→单斜II,其中理论相变压力与实验符合较好。分析发现,单斜II相具有部分N-N单键,氮原子的完全聚合可能发生在200 GPa以上。预言了LiN3在34.7 GPa压力下从单斜绝缘相转变为六角金属相,在200 GPa压力以下保持分子特征。
Design and synthesis of the novel superhard and nitrogen-containing high-energy materials is one of the hot topics in condensed matter physics and material sciences. Crystal material can exhibit luxuriant structures with unique physical properties at high pressure, moreover, some materials which can not or diffcult to be synthesized at ambient pressure can also be generated under high pressure. Therefore, the high pressure techonology plays an irreplaceable role in synthesizing above new materials. Crystal structure occupies a central and often critical role in materials science. Experimentally, structural determination through x-ray diffraction technique has been developed extremely well. However, it happens frequently that experiments fail to determine structures due to the obtained low-quality x-ray diffraction data, particularly at extreme conditions (e.g., high pressure). Here, the theoretical prediction of crystal structures is greatly necessary. Exploring the crystal structure corresponding to the global minimum of the free-energy surface at high-pressure is of great importance in both study of high-pressure phase transition and design of novel materials. This is also the starting point of this work. Many methods for crystal structure prediction have been proposed so far, two newly developed“Universal Structure Predictor: Evolutionary Xtallography”(USPEX) and“Crystal structure Analysis using Particle Swarm Optimization”(CALYPSO) applied in our present work are global optimization methods for general crystal structure prediction, which are very efficient in exploring the global minimum valley competitive local minimums of the free-energy surface. These two efficient methods play an increasing important role in high-pressure phase transition and design of novel materials.
Since 2005, another family of materials consisting of heavy transition metal with high charge density and light elements (B, C, N ) have been proposed to be potential superhard by Kaner et al. Large number of experimental and theoretical work undertaken so and some potential superhard boron-rich materials such as ReB_2, OsB_2, WB_2 andWB_4 are synthesized. But so far, the synthesized borides of transition metals are hard materials without superhard, but this innovative ideal continues to inspire people to explore in this area and design new superhard materials. The first part in this work is undertaken in this context, we have systematically studied on the crystal structures of stoichiometric Mo borides by using the genetic algorithm for crystal structure prediction in order to explore possible superhard materials.
By calculating the formation enthalpy of different stoichiometry, we first build the the phase diagram of Mo-B system at zero temperature, and uncovered three intriguing ground state structures: RS_A, PS_A, and PS_B for MoB_2, Mo_2B_5, and MoB_4. In the diagram, the calculated formation enthalpies of these structures sit nearly right on the curves of convex hull which clearly show that they are all the most stable ground state structures compared to the previously proposed AlB_2-type, RS_B, and WB_4-type structures for MoB_2, Mo_2B_5, and MoB_4, respectively. The RS_A structure is in excellent agreement with the recent experimental suggestion, which strongly proves the correctness of our structure prediction and clarifies the longstanding debates on the ground state structures of these borides. Moreover, the yet synthesized MoB_3 was predicted to take the rhombohedral RSC structure and was suggested to be experimentally synthesizable by the calculation of convex hull. These four all have a similar layered of B-Mo-B sandwich structure, in which the B layer of PS_A and PS_B structure can be viewed as two/three strongly puckered networks of titled hexagons connected by the common B atoms along the b axis. The calculated phonon dispersion and formation enthalpy show the predicted structures of MoB_2, Mo_2B_5, MoB_3, and MoB_4 are all dynamical and thermodynamic stable. The mechanical properties show that these borides have high bulk (about 300 GPa ) and shear moduli ( above 200 GPa except Mo_2B andβ-MoB ). The hardness calculations suggest that these borides are all hard materials, among which MoB_3 exhibits the largest Vickers hardness of 31.8 GPa, exceeding the hardness ofα-SiO_2 (30.6 GPa) andβ-Si_3N_4 (30.3 GPa). The chemical bonding in these molybdenum borides is a complex mixture of covalent, ionic, and metallic characters. Clearly, the strong directional B-B and Mo-B covalent bonds in B-Mo-B sandwich structures are the driving force for their excellent mechanical properties.
As a typical representative of transition metal borides, AlB_2-type transition metal diborides have been concerned for their excellent mechanical properties. Experimentally, the compressibility measurements by using X-ray diffraction techniques for TiB_2 up to 65 GPa, ZrB_2 and VB_2 up to 50 GPa, and HfB_2 up to 30 GPa were performed, and some related mechanical characteristics were investigated, but no obvious phase transitions were observed in any of these compounds. Another work in this paper is to find the high-pressure phase transition of this kind of materials and seek the possible potential superhard crystal.
By using the combination of genetic evolutionary algorithm and first principles calculations, we have extensively explored the high-pressure structures of transition-metal diborides (TMB_2, TM = Sc, Ti, Y, and Zr) stabilized with the AlB_2-type structure at ambient pressure up to 300 GPa. We find that ScB_2 and YB_2 will transform into a monoclinic structure (C2/m, Z = 4) above 208 and 163 GPa, and TiB_2 will transform into the tetragonalα-ThSi_2-type phase (I41/amd, Z = 4) above 215 GPa. The formation of monoclinic phase as follows: the structural unit: six prism of AlB_2 has a strong distortion and the three B atoms of upper surface are crushed to the middle metal TM layer under pressure, forming a TM-centered hendecahedron. Therefore, the monoclinic structure can be viewed as the alternative arrangement of the TM hendecahedron upward and downward along the crystallographic c axis. For theα-ThSi_2-type phase, the B hexagons of AlB_2 phase are cut and connected with each other by twisting alternately 90o so as to form three-dimensional intersecting honeycomb stacks running along c axes. The calculated equation of states by fitting the total energy vs volume data into the third-order Birch-Murnaghan equation and the results show that AlB_2→C2/m and AlB_2→α-ThSi_2-type phase transition are first-order with clear volume drops of 4.8、3.5% and 0.13% for ScB_2,YB_2 and TiB_2, respectively. The calculated phonon dispersions show these predicted high structures are all dynamical in their pressure range. Our calculations show that the electron transfer from TM-s and TM-p to TM-d and B-p under pressure might be the main cause for the structural phase transitions which can alter the electronic bonding. Interestingly, ZrB_2 is quite stable and persists on the ambient-pressure AlB_2-type structure up to at least 300 GPa. We attribute the strong covalent hybridization between the transition-metal Zr and B to this ultrastability. Furthermore, it is found that onlyα-ThSi_2-type TiB_2 has stable phonons at ambient pressure, and it possesses large bulk and shear moduli (269 and 262 GPa) which exhibit its high resistance to compression and shear. The hardness calculations suggest that it is hard materials and its Vickers hardness is 29.8 GPa, exceeding the hardness ofα-SiO_2 (30.6 GPa) andβ-Si3N4 (30.3 GPa).
Recently, Eremets et al have been reported two experiments about the high- pressure phase transition of NaN3 and LiN3, and polymerization of nitrogen in NaN3 happened above 160 GPa. The results indicated that they are potential high energy density material. However, the new high-pressure structures reported in NaN3 experiments have not been determined. The experimental pressure range of LiN3 is lower, and wether the atom of nitrogen aggregation can be found at higher pressure? The third job in this paper is to explore the new high- pressure structures of these two alkali metal azides and their related electronic behaviors.
By means of CALYPSO package, we proposed a phase transition sequence of NaN3 up to 200 GPa as follows: rhombohedral→monoclinic I→tetragonal→hexagonal→monoclinic II, and the calculated phase transition pressure about these structures are in agreement with experiment. The azide ions of tetragonal and hexagonal structures remain their molecular characteristics in their pressure range, and the N-N single bonds appeared in C2/m-II structure above 152 GPa. Therefore, the complete polymerization of the nitrogen atom may occur in more than 200 GPa. Moreover, the phase transition from insulating tetragonal to metallic hexagonal phase which is consistent with the darken sample and resistance measurement of experiment. The simulated Raman spectra of the tetragonal phase is consistent with experiment basically, meanwhile, we believe that the new band of 1700-2010 cm-1 appeared in Raman spectra at 38 GPa should be belonged to the escaped of nitrogen impurities. However, two other high structures can not be compared with experimental results very well due to the metallization of samples and weaker Raman signal in experiment. We are looking forward to our predicted high-pressure structures can be verified by further X-ray diffraction. For LiN_3, we found a phase transition at 34.7 GPa from the ambient-pressure structure C2/m to a P6/m structure, which is similar to the P6/m-NaN_3. The phase transition pressure point 34.7 GPa is lower than that in experiment which can be attributed to the strong repulsion forces between the azides. The P6/m-LiN_3 possesses molecular characteristic and are stable up to 200 GPa. Compared to NaN_3, a higher pressure may be used to make the LiN_3 realized the polymerization of nitrogen.
1.澄清了实验上关于MoB_2,Mo_2B_5和MoB_4三种硼化物基态稳定结构的争议,预言了尚未合成的MoB_3的基态结构和实验合成条件,构建了Mo-B体系的零温相图。发现以上四种硼化物均具有“三明治”B-Mo-B层,都是理论维氏硬度超过20 GPa的硬质材料,其中MoB_3的硬度可以达到31.8 GPa。
2.获得了具有六角AlB_2结构的过渡金属硼化物TMB_2(TM = Zr、Sc、Ti、Y)的高压结构相变行为,发现在低于300 GPa压力下具有Zr-B强共价键的ZrB2没有结构相变,而ScB_2和YB_2分别在208和163 GPa压力下相变为单斜结构,TiB_2却在215 GPa相变为四方α-ThSi_2结构。进一步研究揭示,过渡金属原子到B原子的电荷转移是压致相变的主要诱因。
3.提出NaN3高压相变序列为:菱方→单斜I→四方→六角→单斜II,其中理论相变压力与实验符合较好。分析发现,单斜II相具有部分N-N单键,氮原子的完全聚合可能发生在200 GPa以上。预言了LiN3在34.7 GPa压力下从单斜绝缘相转变为六角金属相,在200 GPa压力以下保持分子特征。
Design and synthesis of the novel superhard and nitrogen-containing high-energy materials is one of the hot topics in condensed matter physics and material sciences. Crystal material can exhibit luxuriant structures with unique physical properties at high pressure, moreover, some materials which can not or diffcult to be synthesized at ambient pressure can also be generated under high pressure. Therefore, the high pressure techonology plays an irreplaceable role in synthesizing above new materials. Crystal structure occupies a central and often critical role in materials science. Experimentally, structural determination through x-ray diffraction technique has been developed extremely well. However, it happens frequently that experiments fail to determine structures due to the obtained low-quality x-ray diffraction data, particularly at extreme conditions (e.g., high pressure). Here, the theoretical prediction of crystal structures is greatly necessary. Exploring the crystal structure corresponding to the global minimum of the free-energy surface at high-pressure is of great importance in both study of high-pressure phase transition and design of novel materials. This is also the starting point of this work. Many methods for crystal structure prediction have been proposed so far, two newly developed“Universal Structure Predictor: Evolutionary Xtallography”(USPEX) and“Crystal structure Analysis using Particle Swarm Optimization”(CALYPSO) applied in our present work are global optimization methods for general crystal structure prediction, which are very efficient in exploring the global minimum valley competitive local minimums of the free-energy surface. These two efficient methods play an increasing important role in high-pressure phase transition and design of novel materials.
Since 2005, another family of materials consisting of heavy transition metal with high charge density and light elements (B, C, N ) have been proposed to be potential superhard by Kaner et al. Large number of experimental and theoretical work undertaken so and some potential superhard boron-rich materials such as ReB_2, OsB_2, WB_2 andWB_4 are synthesized. But so far, the synthesized borides of transition metals are hard materials without superhard, but this innovative ideal continues to inspire people to explore in this area and design new superhard materials. The first part in this work is undertaken in this context, we have systematically studied on the crystal structures of stoichiometric Mo borides by using the genetic algorithm for crystal structure prediction in order to explore possible superhard materials.
By calculating the formation enthalpy of different stoichiometry, we first build the the phase diagram of Mo-B system at zero temperature, and uncovered three intriguing ground state structures: RS_A, PS_A, and PS_B for MoB_2, Mo_2B_5, and MoB_4. In the diagram, the calculated formation enthalpies of these structures sit nearly right on the curves of convex hull which clearly show that they are all the most stable ground state structures compared to the previously proposed AlB_2-type, RS_B, and WB_4-type structures for MoB_2, Mo_2B_5, and MoB_4, respectively. The RS_A structure is in excellent agreement with the recent experimental suggestion, which strongly proves the correctness of our structure prediction and clarifies the longstanding debates on the ground state structures of these borides. Moreover, the yet synthesized MoB_3 was predicted to take the rhombohedral RSC structure and was suggested to be experimentally synthesizable by the calculation of convex hull. These four all have a similar layered of B-Mo-B sandwich structure, in which the B layer of PS_A and PS_B structure can be viewed as two/three strongly puckered networks of titled hexagons connected by the common B atoms along the b axis. The calculated phonon dispersion and formation enthalpy show the predicted structures of MoB_2, Mo_2B_5, MoB_3, and MoB_4 are all dynamical and thermodynamic stable. The mechanical properties show that these borides have high bulk (about 300 GPa ) and shear moduli ( above 200 GPa except Mo_2B andβ-MoB ). The hardness calculations suggest that these borides are all hard materials, among which MoB_3 exhibits the largest Vickers hardness of 31.8 GPa, exceeding the hardness ofα-SiO_2 (30.6 GPa) andβ-Si_3N_4 (30.3 GPa). The chemical bonding in these molybdenum borides is a complex mixture of covalent, ionic, and metallic characters. Clearly, the strong directional B-B and Mo-B covalent bonds in B-Mo-B sandwich structures are the driving force for their excellent mechanical properties.
As a typical representative of transition metal borides, AlB_2-type transition metal diborides have been concerned for their excellent mechanical properties. Experimentally, the compressibility measurements by using X-ray diffraction techniques for TiB_2 up to 65 GPa, ZrB_2 and VB_2 up to 50 GPa, and HfB_2 up to 30 GPa were performed, and some related mechanical characteristics were investigated, but no obvious phase transitions were observed in any of these compounds. Another work in this paper is to find the high-pressure phase transition of this kind of materials and seek the possible potential superhard crystal.
By using the combination of genetic evolutionary algorithm and first principles calculations, we have extensively explored the high-pressure structures of transition-metal diborides (TMB_2, TM = Sc, Ti, Y, and Zr) stabilized with the AlB_2-type structure at ambient pressure up to 300 GPa. We find that ScB_2 and YB_2 will transform into a monoclinic structure (C2/m, Z = 4) above 208 and 163 GPa, and TiB_2 will transform into the tetragonalα-ThSi_2-type phase (I41/amd, Z = 4) above 215 GPa. The formation of monoclinic phase as follows: the structural unit: six prism of AlB_2 has a strong distortion and the three B atoms of upper surface are crushed to the middle metal TM layer under pressure, forming a TM-centered hendecahedron. Therefore, the monoclinic structure can be viewed as the alternative arrangement of the TM hendecahedron upward and downward along the crystallographic c axis. For theα-ThSi_2-type phase, the B hexagons of AlB_2 phase are cut and connected with each other by twisting alternately 90o so as to form three-dimensional intersecting honeycomb stacks running along c axes. The calculated equation of states by fitting the total energy vs volume data into the third-order Birch-Murnaghan equation and the results show that AlB_2→C2/m and AlB_2→α-ThSi_2-type phase transition are first-order with clear volume drops of 4.8、3.5% and 0.13% for ScB_2,YB_2 and TiB_2, respectively. The calculated phonon dispersions show these predicted high structures are all dynamical in their pressure range. Our calculations show that the electron transfer from TM-s and TM-p to TM-d and B-p under pressure might be the main cause for the structural phase transitions which can alter the electronic bonding. Interestingly, ZrB_2 is quite stable and persists on the ambient-pressure AlB_2-type structure up to at least 300 GPa. We attribute the strong covalent hybridization between the transition-metal Zr and B to this ultrastability. Furthermore, it is found that onlyα-ThSi_2-type TiB_2 has stable phonons at ambient pressure, and it possesses large bulk and shear moduli (269 and 262 GPa) which exhibit its high resistance to compression and shear. The hardness calculations suggest that it is hard materials and its Vickers hardness is 29.8 GPa, exceeding the hardness ofα-SiO_2 (30.6 GPa) andβ-Si3N4 (30.3 GPa).
Recently, Eremets et al have been reported two experiments about the high- pressure phase transition of NaN3 and LiN3, and polymerization of nitrogen in NaN3 happened above 160 GPa. The results indicated that they are potential high energy density material. However, the new high-pressure structures reported in NaN3 experiments have not been determined. The experimental pressure range of LiN3 is lower, and wether the atom of nitrogen aggregation can be found at higher pressure? The third job in this paper is to explore the new high- pressure structures of these two alkali metal azides and their related electronic behaviors.
By means of CALYPSO package, we proposed a phase transition sequence of NaN3 up to 200 GPa as follows: rhombohedral→monoclinic I→tetragonal→hexagonal→monoclinic II, and the calculated phase transition pressure about these structures are in agreement with experiment. The azide ions of tetragonal and hexagonal structures remain their molecular characteristics in their pressure range, and the N-N single bonds appeared in C2/m-II structure above 152 GPa. Therefore, the complete polymerization of the nitrogen atom may occur in more than 200 GPa. Moreover, the phase transition from insulating tetragonal to metallic hexagonal phase which is consistent with the darken sample and resistance measurement of experiment. The simulated Raman spectra of the tetragonal phase is consistent with experiment basically, meanwhile, we believe that the new band of 1700-2010 cm-1 appeared in Raman spectra at 38 GPa should be belonged to the escaped of nitrogen impurities. However, two other high structures can not be compared with experimental results very well due to the metallization of samples and weaker Raman signal in experiment. We are looking forward to our predicted high-pressure structures can be verified by further X-ray diffraction. For LiN_3, we found a phase transition at 34.7 GPa from the ambient-pressure structure C2/m to a P6/m structure, which is similar to the P6/m-NaN_3. The phase transition pressure point 34.7 GPa is lower than that in experiment which can be attributed to the strong repulsion forces between the azides. The P6/m-LiN_3 possesses molecular characteristic and are stable up to 200 GPa. Compared to NaN_3, a higher pressure may be used to make the LiN_3 realized the polymerization of nitrogen.
引文
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