缺陷和外界压力对几种典型材料物理性质的影响
|
摘要
材料中的缺陷行为及其对宿主物理性质的影响是一个具有现实意义和广泛应用价值的重要课题,因而一直是理论和实验研究的热点。本工作采用第一性原理方法较为系统地研究了不同外界条件下的两类典型缺陷体系:金属Nb掺杂氢氦体系和B-C-N超硬多功能材料的缺陷和杂质效应。
论文主要包括:掺氢金属铌体系的晶格畸变、电子结构、光学特性和氢原子的绝热晶格动力学行为和压力效应,以及有限温度和压力下氦原子的凝聚机制;提出了一种计算金属晶体弹性性质的方法;预言了两种具有导电性质的立方相超硬B-C-N三元晶体,并且研究了相应的电子结构、基本力学特性和晶格动力学特性;提出了定体焓分析方法,并研究了BCN体系的稳定性与合成的可行性问题,研究了B-C-N体系中的杂质问题。具体的研究工作如下:
(一)在1:1,1:2和1:16的浓度下,研究了氢原子在金属铌中的电子结构、宿主晶格响应和氢原子的晶格动力学行为,提出了一种NbH的新结构,对文献报导的低位能带(lower lying band)的成因进行了进一步阐释;采用位置试探的方法,在第一性原理的框架下得到了氢原子在Nb中感受到的周期势场,通过求解氢原子的Schr(o|¨)dinger方程,得到了氢原子量子行为的较为精确表述;采用分子动力学方法在有限温度和压力下,研究了氢、氦动力学效应对宿主金属的影响及其差异性。证明了氦泡形成的局域密度和压力相关性。
(二)研究了β-C_3N_4体系的本征缺陷和杂质效应。证明在Ga间隙掺杂下,宽带隙中生成丰富的杂质能级,导致体系在可见光的广谱范围内的光学吸收和发射。
(三)研究了多种典型的B-C-N超硬材料体系的力学特性和晶格动力学稳定性,预言了B_3CN_4和B_3C_4N两种具有导电性的BCN三元立方相材料,研究了高压超硬相B_3CN_4体系中的杂质行为。
(1)提出了一种基于基本晶格振动模式下的定体焓分析方法,用以研究闪锌矿晶体的宏观稳定性及其合成的可能性,并且藉以给出材料合成压力。研究结果显示,8原子单胞描述下Zinc-blende结构的基本晶格振动模式中,呼吸模式A_1对外界压力的响应最为显著,导致该模式下体系的定体焓(constant volume enthalphy,CVE)变化剧烈。在宽广的压力范围内,金刚石、立方氮化硼晶体的CVE极小点与总能(total energy,ETOT)极小一致,表明体系是稳定的,并且其实验合成的成功具有其热动力学意义上的合理性。
(2)证明了B_3CN_4在压力为～80GPa到～120GPa的范围内ETOT和CVE极小所对应的位形一致性,表明该结构在该压力区间内是稳定的,并且能够合成;B_3C_4N稳定于25～45GPa范围内,且其切变模量过小。
(3)常压条件下两种BC_2N材料(BC_2N-1和BC_2N-2)的某些振动模式对CVE影响显著,且其极小与ETOT的极小值大幅度偏离,而且原子按照基本振动模的集体移动显示,平衡位形是总能的鞍点,这些证据表明BC_2N-1和BC_2N-2可能是不稳定结构。
(4)研究了高压条件下B_3CN_4体系的杂质模型,结果表明金属性替位掺杂将产生多个浅层受主能级,而金属间隙原子形成三条深层杂质能级(带)。三元体系及其杂质相呈现金属性低频高反射。
(四)作为材料物性研究的补充,系统地研究了晶格振动动力学和弹性力学量之间的关系,提出了利用Christoffel长波动力学矩阵,通过在倒易空间单位球内求解本征值,籍以判定材料力学稳定性的一般方法;提出了从动力学矩阵出发,计算宏观弹性常量的方法。
Booming advances of computational technology make it possible to explore physical properties of materials, even design new materials. It is of vast importance to know deep into the composition, interactions and response to environment of a material via numerical calculations, since many body problems are impossible to be solved analytically. This paper systematically studied problems in solid state matter in three aspects using first principles method: the behavior of H and He in niobium, the existence of BCN ternary compounds and elastic stability of crystals.
The problem of impurities in metals is continuous attractive, because not only the improvements on mechanical and electrical properties of a metal, but also the failures or malfunctions, especially for light elements as hydrogen and helium. Embrittlement and excessive ion implantation in metals will make the first wall of nuclear reactor shorten its mechanical lifetime. Recently, there is a trend to use hydrogen as a medium to make the full use of reproducible energy resources applicable. All these promote the researches on the behavior of hydrogen/helium in metals. On the other hand, thermonuclear reactors promote both the behavior of H and He in metals.
The typical transition metal niobium is selected as the host. Different density of hydrogen is doped into Nb till niobium monohydride is formed. The interactions between Nb and H are studied, focusing mainly on the phase of NbH, the quantium behavior of H in Nb and the thermodynamic properties of both H and He doped Nb.
The result shows that hydrogen has less effect on host lattice even for 1:1 dopant, because of the strong nd metallic bonding of transition metals. Since the mass of H is by far smaller than Nb, there exhibit considerable quantum effects. H is easier to be excited up, hovering in Nb lattices.
Four types of NbH derived fromβ-phase is studied and all structures are shown to be dynamically stable.β-phaseis the lowest in total enthalpy, next D2d-1, D2d-9 and D4h-7. The electronic structure (DOS) of any structure is not in consistent with experimental EDC data. The DOS of NbH governed not only by nearest H-H distance, but also the local geometry. This implies that NbH may be the mixture of the four structure phase.
Conventional cell of Nb_2H is used to calculate the potential experienced by H in Nb by directly evaluate the total energy at different H configurations. Schrodinger equation of H is solved numerically to obtain the energy levels and eigenstates of H, the 4T and 6T ring excited states are identified. The low density impure Nb lattice of 1/16 H dopant under pressures are studied, the lattice relaxation, electronic structure and optical absorption spectra are obtained.
The behavior of helium in niobium is simulated using Car-Parrinello molecular dynamics methods. Two types of local He concentration are considered. The result shows that He behaves vast electronic stable such that the space occupied by He is a forbidden area for near free electrons of Nb. The existence of denser He damages the metallic bonding of Nb, producing vacancy/interstitial defects. Under ambient pressure, helium bubble formation depends on the local concentration and the existence of native vacancy. In perfect host lattice, high He content results in dislocations of neighboring Nb, lattice distortion and production of vacancy/interstitial of Nb and the bubble formation at the vacancy; a helium bubble will form direct at a nearer native vacancy with no new vacancy produced and less host lattice distortion. Under high pressures, no bubbles are formed due to the strong background interactions between Nb atoms and the relatively weakened He effects.
Another type of impure systemβ-C_3N_4 is also studied. Before constructiong impure system, cubic C_3N_4 andβ-C_3N_4 are pre-studied. Cubic phase C_3N_4 is shown to be conductive, whileβ-C_3N_4 is semiconductive with a band gap of about 3.4eV(LDA). The chemical potential of cubic C_3N_4 relative to raw materials is by far larger than that ofβ-C_3N_4, resulting in the difficulty in the synthesis of cubic C_3N_4, although it may be the only one expected to be harder than diamond. The two structures ofβ-C_3N_4 suggested by Cohen's group and Hemley's Group are different in symmetry but similar in electronic structure.
Defected system ofβ-C_3N_4 including host vacancy, inter-substitution, native interstitial and group III metallic interstitial are studied. The interstitial gallium is found to have the most doping effect on the electronic structure and optical response ofβ-C_3N_4. Three deep impurity energy levels are observed in the main gap, with one of which stands on the Fermi Level. The impurity induced electronic bands enables electron transitions in almost all impurity band transition models. The doped system is active to electromagnetic field from far infrared to ultraviolet, with a reflect window of about 0.2eV at frequency 1.5eV. The doped system may be a potential optic material with high optical efficiency.
Thirdly, the existence, stability and the probability to be synthesized of zinc-blende crystal are studied using constant volume enthalpy, in addition to total energy, atomic forces and lattice vibration calculations.
Up to date, the probability to obtain a new material depends mainly on the optimized structure (atom coordination and lattice parameters), the relative enthalpy and lattice vibration properties for stability investigation. But not all materials predicted by theory are successfully synthesized, although they are confirmed to be stable and probable to be synthesized at certain conditions by the methods above mentioned. On the other hand, considerable phase synthesized experimentally are not well interpreted by theory.
In the present work we have gone further. The properties of a superhard material (B_3CN_4) are studied using ab initio pseudopotential methods within density functional framework. In addition to total energy, electronic structure and lattice dynamics, the normal vibration mode dependency of constant volume enthalpy (CVE) is systematically investigated in a wide pressure range up to about 200GPa. The new compound is shown to be conductive and comparable to BC_2N and cBN in basic mechanical properties, but dynamically stable in a narrow range from～80GPa to～120GP. The instability is confirmed by the acoustic mode softening around q-vector [0.5 0.5 0.0] and monotonic variation of CVE at normal vibration mode A_1. The lattice vibration mode dependence of CVE is expected to filter out the most stable structure of a material from the predictions based on total energy, atomic forces and lattice vibration calculations. The CVEs of kinds of zinc-blende materials such as diamond, cBN, ZnS etc. are systematically investigated and A_1 mode is found to play the dominant role in the crystallization. But for BC_2N-1 and BC_2N-2, negative results are obtained, showing that they are not stable at ambient pressures and BC_2N may not be described by 8-atom cell. This scheme is expected to clarify the most stable phase from those predicted by ab initio total energy, lattice vibration calculations.
After the stable pressure range of B_3CN_4, impurity effects on its electronic structure are studied. Vacancy of C, C substuted by N, B substituted by Ga and interstitial Ga are all calculated though. The band distortion is strongly C content dependent, reflected in the optical response spectra. While C content goes down to 1/64, almost no optical response below ~5eV is observed, while any of the other impurity systems has strong low frequency reflection/absorption just as metals. The interstitial dopant of Ga is found to produce deep impurity bands in the main gap, resulting in the blue-shift of metallic reflection edge.
Additionally, the lattice dynamics and elastic properties of typical elastic crystal are studied in order to filter the abinitio calculated elastic constants and obtain the information of lattice stability. Since more than 3 independent elastic constants are needed to describe elastic crystals except cubic ones, it is difficult to confirm if the elastic constants are reasonable, or if the calculated crystal is stable. This may be handled out by solving eigenvalue problems of Christoffel dynamics matrices in a unit reciprocal sphere. A new method of calculating elastic constants is also proposed.
论文主要包括:掺氢金属铌体系的晶格畸变、电子结构、光学特性和氢原子的绝热晶格动力学行为和压力效应,以及有限温度和压力下氦原子的凝聚机制;提出了一种计算金属晶体弹性性质的方法;预言了两种具有导电性质的立方相超硬B-C-N三元晶体,并且研究了相应的电子结构、基本力学特性和晶格动力学特性;提出了定体焓分析方法,并研究了BCN体系的稳定性与合成的可行性问题,研究了B-C-N体系中的杂质问题。具体的研究工作如下:
(一)在1:1,1:2和1:16的浓度下,研究了氢原子在金属铌中的电子结构、宿主晶格响应和氢原子的晶格动力学行为,提出了一种NbH的新结构,对文献报导的低位能带(lower lying band)的成因进行了进一步阐释;采用位置试探的方法,在第一性原理的框架下得到了氢原子在Nb中感受到的周期势场,通过求解氢原子的Schr(o|¨)dinger方程,得到了氢原子量子行为的较为精确表述;采用分子动力学方法在有限温度和压力下,研究了氢、氦动力学效应对宿主金属的影响及其差异性。证明了氦泡形成的局域密度和压力相关性。
(二)研究了β-C_3N_4体系的本征缺陷和杂质效应。证明在Ga间隙掺杂下,宽带隙中生成丰富的杂质能级,导致体系在可见光的广谱范围内的光学吸收和发射。
(三)研究了多种典型的B-C-N超硬材料体系的力学特性和晶格动力学稳定性,预言了B_3CN_4和B_3C_4N两种具有导电性的BCN三元立方相材料,研究了高压超硬相B_3CN_4体系中的杂质行为。
(1)提出了一种基于基本晶格振动模式下的定体焓分析方法,用以研究闪锌矿晶体的宏观稳定性及其合成的可能性,并且藉以给出材料合成压力。研究结果显示,8原子单胞描述下Zinc-blende结构的基本晶格振动模式中,呼吸模式A_1对外界压力的响应最为显著,导致该模式下体系的定体焓(constant volume enthalphy,CVE)变化剧烈。在宽广的压力范围内,金刚石、立方氮化硼晶体的CVE极小点与总能(total energy,ETOT)极小一致,表明体系是稳定的,并且其实验合成的成功具有其热动力学意义上的合理性。
(2)证明了B_3CN_4在压力为～80GPa到～120GPa的范围内ETOT和CVE极小所对应的位形一致性,表明该结构在该压力区间内是稳定的,并且能够合成;B_3C_4N稳定于25～45GPa范围内,且其切变模量过小。
(3)常压条件下两种BC_2N材料(BC_2N-1和BC_2N-2)的某些振动模式对CVE影响显著,且其极小与ETOT的极小值大幅度偏离,而且原子按照基本振动模的集体移动显示,平衡位形是总能的鞍点,这些证据表明BC_2N-1和BC_2N-2可能是不稳定结构。
(4)研究了高压条件下B_3CN_4体系的杂质模型,结果表明金属性替位掺杂将产生多个浅层受主能级,而金属间隙原子形成三条深层杂质能级(带)。三元体系及其杂质相呈现金属性低频高反射。
(四)作为材料物性研究的补充,系统地研究了晶格振动动力学和弹性力学量之间的关系,提出了利用Christoffel长波动力学矩阵,通过在倒易空间单位球内求解本征值,籍以判定材料力学稳定性的一般方法;提出了从动力学矩阵出发,计算宏观弹性常量的方法。
Booming advances of computational technology make it possible to explore physical properties of materials, even design new materials. It is of vast importance to know deep into the composition, interactions and response to environment of a material via numerical calculations, since many body problems are impossible to be solved analytically. This paper systematically studied problems in solid state matter in three aspects using first principles method: the behavior of H and He in niobium, the existence of BCN ternary compounds and elastic stability of crystals.
The problem of impurities in metals is continuous attractive, because not only the improvements on mechanical and electrical properties of a metal, but also the failures or malfunctions, especially for light elements as hydrogen and helium. Embrittlement and excessive ion implantation in metals will make the first wall of nuclear reactor shorten its mechanical lifetime. Recently, there is a trend to use hydrogen as a medium to make the full use of reproducible energy resources applicable. All these promote the researches on the behavior of hydrogen/helium in metals. On the other hand, thermonuclear reactors promote both the behavior of H and He in metals.
The typical transition metal niobium is selected as the host. Different density of hydrogen is doped into Nb till niobium monohydride is formed. The interactions between Nb and H are studied, focusing mainly on the phase of NbH, the quantium behavior of H in Nb and the thermodynamic properties of both H and He doped Nb.
The result shows that hydrogen has less effect on host lattice even for 1:1 dopant, because of the strong nd metallic bonding of transition metals. Since the mass of H is by far smaller than Nb, there exhibit considerable quantum effects. H is easier to be excited up, hovering in Nb lattices.
Four types of NbH derived fromβ-phase is studied and all structures are shown to be dynamically stable.β-phaseis the lowest in total enthalpy, next D2d-1, D2d-9 and D4h-7. The electronic structure (DOS) of any structure is not in consistent with experimental EDC data. The DOS of NbH governed not only by nearest H-H distance, but also the local geometry. This implies that NbH may be the mixture of the four structure phase.
Conventional cell of Nb_2H is used to calculate the potential experienced by H in Nb by directly evaluate the total energy at different H configurations. Schrodinger equation of H is solved numerically to obtain the energy levels and eigenstates of H, the 4T and 6T ring excited states are identified. The low density impure Nb lattice of 1/16 H dopant under pressures are studied, the lattice relaxation, electronic structure and optical absorption spectra are obtained.
The behavior of helium in niobium is simulated using Car-Parrinello molecular dynamics methods. Two types of local He concentration are considered. The result shows that He behaves vast electronic stable such that the space occupied by He is a forbidden area for near free electrons of Nb. The existence of denser He damages the metallic bonding of Nb, producing vacancy/interstitial defects. Under ambient pressure, helium bubble formation depends on the local concentration and the existence of native vacancy. In perfect host lattice, high He content results in dislocations of neighboring Nb, lattice distortion and production of vacancy/interstitial of Nb and the bubble formation at the vacancy; a helium bubble will form direct at a nearer native vacancy with no new vacancy produced and less host lattice distortion. Under high pressures, no bubbles are formed due to the strong background interactions between Nb atoms and the relatively weakened He effects.
Another type of impure systemβ-C_3N_4 is also studied. Before constructiong impure system, cubic C_3N_4 andβ-C_3N_4 are pre-studied. Cubic phase C_3N_4 is shown to be conductive, whileβ-C_3N_4 is semiconductive with a band gap of about 3.4eV(LDA). The chemical potential of cubic C_3N_4 relative to raw materials is by far larger than that ofβ-C_3N_4, resulting in the difficulty in the synthesis of cubic C_3N_4, although it may be the only one expected to be harder than diamond. The two structures ofβ-C_3N_4 suggested by Cohen's group and Hemley's Group are different in symmetry but similar in electronic structure.
Defected system ofβ-C_3N_4 including host vacancy, inter-substitution, native interstitial and group III metallic interstitial are studied. The interstitial gallium is found to have the most doping effect on the electronic structure and optical response ofβ-C_3N_4. Three deep impurity energy levels are observed in the main gap, with one of which stands on the Fermi Level. The impurity induced electronic bands enables electron transitions in almost all impurity band transition models. The doped system is active to electromagnetic field from far infrared to ultraviolet, with a reflect window of about 0.2eV at frequency 1.5eV. The doped system may be a potential optic material with high optical efficiency.
Thirdly, the existence, stability and the probability to be synthesized of zinc-blende crystal are studied using constant volume enthalpy, in addition to total energy, atomic forces and lattice vibration calculations.
Up to date, the probability to obtain a new material depends mainly on the optimized structure (atom coordination and lattice parameters), the relative enthalpy and lattice vibration properties for stability investigation. But not all materials predicted by theory are successfully synthesized, although they are confirmed to be stable and probable to be synthesized at certain conditions by the methods above mentioned. On the other hand, considerable phase synthesized experimentally are not well interpreted by theory.
In the present work we have gone further. The properties of a superhard material (B_3CN_4) are studied using ab initio pseudopotential methods within density functional framework. In addition to total energy, electronic structure and lattice dynamics, the normal vibration mode dependency of constant volume enthalpy (CVE) is systematically investigated in a wide pressure range up to about 200GPa. The new compound is shown to be conductive and comparable to BC_2N and cBN in basic mechanical properties, but dynamically stable in a narrow range from～80GPa to～120GP. The instability is confirmed by the acoustic mode softening around q-vector [0.5 0.5 0.0] and monotonic variation of CVE at normal vibration mode A_1. The lattice vibration mode dependence of CVE is expected to filter out the most stable structure of a material from the predictions based on total energy, atomic forces and lattice vibration calculations. The CVEs of kinds of zinc-blende materials such as diamond, cBN, ZnS etc. are systematically investigated and A_1 mode is found to play the dominant role in the crystallization. But for BC_2N-1 and BC_2N-2, negative results are obtained, showing that they are not stable at ambient pressures and BC_2N may not be described by 8-atom cell. This scheme is expected to clarify the most stable phase from those predicted by ab initio total energy, lattice vibration calculations.
After the stable pressure range of B_3CN_4, impurity effects on its electronic structure are studied. Vacancy of C, C substuted by N, B substituted by Ga and interstitial Ga are all calculated though. The band distortion is strongly C content dependent, reflected in the optical response spectra. While C content goes down to 1/64, almost no optical response below ~5eV is observed, while any of the other impurity systems has strong low frequency reflection/absorption just as metals. The interstitial dopant of Ga is found to produce deep impurity bands in the main gap, resulting in the blue-shift of metallic reflection edge.
Additionally, the lattice dynamics and elastic properties of typical elastic crystal are studied in order to filter the abinitio calculated elastic constants and obtain the information of lattice stability. Since more than 3 independent elastic constants are needed to describe elastic crystals except cubic ones, it is difficult to confirm if the elastic constants are reasonable, or if the calculated crystal is stable. This may be handled out by solving eigenvalue problems of Christoffel dynamics matrices in a unit reciprocal sphere. A new method of calculating elastic constants is also proposed.
引文
[1]Alefeld G and Volkl J. Hydrogen in Metal [M]. Berlin Heidelberg New York: Springer-Verlag, 1983.
[2] Daw M S and Baskes M I. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals [J]. Phys. Rev. Lett., 1983,50: 1285- 1288.
[3] Hillier E M K and Robinson M J. Hydrogen embrittlement of high strength steel electroplated with zinc-cobalt alloys [J]. Corrosion Science, 2004, 46 : 715-727.
[4] Lu G, Orlikowski D, Park I, Politano O and Kaxiras E. Energetics of hydrogen impurities in aluminum and their effect on mechanical properties[J]. Phys. Rev. B, 2002, 65: 064102-064109.
[5] Esaka T, Sakaguchi H and Kobayashi S. Hydrogen Storage in Proton Conductive Perovskite-type Oxides and their Application to Nickel-Hydrogen Batteries [J]. Solid State Ionics, 2004, 166: 351-357.
[6] Talyzin A V and Sundqvist B. Reversible phase transition in LiAlH4 under high-pressure conditions[J]. Phys. Rev. B, 2004, 70:180101-180103.
[7] Vajeeston P, Ravindran P, Kjekshus A and Fjellvag H. Structural stability and electronic structure for Li_3AlH_6[J]. Phys. Rev. B, 2004, 69 020104-020107.
[8] Wilson W D, Baskes M I, Bission C L. Atomistics of helium bubble formation in a face-centered-cubic metal [J]. Phys Rev B, 1976, 13: 2470-2478.
[9] Wilson W D, Bisson C L, Baskes M I. Self-trapping of helium in metals [J]. Phys Rev B, 1981, 24:616-5624.
[10] Jensen K O, Nieminen R M. Helium bubbles in metals: Molecular-dynamics simulations and positron states [J]. Phys Rev B, 1987, 35:2087-2090.
[11]Jensen K O, Nieminen R M. Noble-gas bubbles in metals: molecular-dynamics simulations and positron states [J]. Phys Rev B, 1987, 36: 8219-8232.
[12] Raajaraman R, Viswannathan B, Valsakumar M C, Gopinathan K P. Anomalous helium-bubble growth in palladium [J]. Phys Rev B, 1994-1, 50:597-600.
[13] Birtcher R, Donnelly S E, Templier C. Evolution of helium bubbles in aluminum during heavy-ion irradiation. Phys.Rrev. B, 1994-II, 50:764-769.
[14] Donnelly S E, Birtcher R C, Templier C, Vishnyakov V. Response of helium bubbles in gold to displacement-cascade damage [J]. Phys Rev B, 1995-II, 52:3970-3976.
[15] Vassen R, Trinkaus H, Jung P. Helium desorption from Fe and V by atomic diffusion and bubble migration [J]. Phys Rev B, 1991-1, 44: 4206-4213.
[16] A. Y. Liu, M. L. Cohen. Prediction of New Low Compressibility Solids. Science, 1989,245:841-842.
[17] R.H.Wentorf, Jr.Preparation of Semiconducting Cubic Boron Nitride [J]. J. Chem. Phys., 1962, 36:1990-1991.
[18] O. Mishima, K.Era, J. Tanaka, and S. Yamaoka.Ultraviolet light-emitting diode of a cubic boron nitride pn junction made at high pressure, Appl. Phys. Lett., 1988, 53: 962-964.
[19] A. Y. Liu and M. L. Cohen.Structural properties and electronic structure of low-compressibility materials: β-Si_3N_4 and hypothetical β-C_3N_4[J]. Phys. Rev. B, 1990, 41(15):10727-10734.
[20]C.M.Sung and M.Sung.Carbon nitride and other speculative superhard materials[J].Mater.Chem.Phys.,1996,43:1-18.
[21]Vladimir L.Solozhenko,Denis Andrault,Guillaume Fiquet,Mohamed Mezouar,David C.Rubie.Synthesis of superhard cubic BC_2N[J].Applied Physics Letters,2001,78:1385-1387.
[22]Vladimir L.Solozhenko,Sergey N.Dub,Nikolay V.Novikov.Mechanical properties of cubic BC_2N,a superhard phase[J].Diamond and Related materials,2001,10:2228-2231.
[23]S.N.Tkachev,V.L.Solozhenko,P.V.Zinin,M.H.Manghnani,L.C.Ming.Elastic moduli of the superhard cubic BC_2N phase by Brillouin scattering[J].Phys.Rev.B,2003,68:052104.
[24]P.V.Zinin,V.L.Solozhenko,A.J.Malkin.Atomic force microscopy studies of cubic BC_2N,a new superhard phase[J].Jounal of Materials Science,2005,40:3009-3011.
[25]H.W.Hubble,I.Kudryashov,V.L.Solozhenko,P.V.Zinin,S.K.Sharma,L.C.Ming.Raman studies of cubic BC_2N,a new superhard phase[J].Journal of Raman Spectroscopy,2004,35(10):822-825.
[26]Hong Sun,Seung Jhi,David Roundy,Marvin L.Cohen and Steven G.Louie.Structural forms of cubic BC_2N[J].Phys.Rev.B,2001,64:094108-1.
[27]Zicheng Pan,Hong Sun,Changfeng Chen.Ab initio pseudopotential studies of cubic BC2N under high pressure[J].Journal of Physics:Condensed Matter,2005,17:3211-3220.
[28]Shiyou Chen,X.G.Gong,Su-Huai Wei.Superhard Pseudocubic BC_2N Superlattices[J].Phys.Rev.Lett.,2007,98:015502(4).
[29]马文淦.计算物理学[M].合肥:中国科学技术大学出版社,2001.
[30]韩汝琦,黄昆.固体物理学[M].北京:高等教育出版社,1988.
[31]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版社,1998.
[32]阎守胜.固体物理基础[M].北京:北京大学出版社,2000.
[33]M.Born and K.Huang.Dynamical Theory of Crystal Lattices [M].Oxford:Oxford University Press,1954.
[34]E.Wigner and F.Seitz.On the Constitution of Metallic Sodium [J].Phys.Rev.,1933,43:804-810.
[35]C.C.J.Roothaan.New Developments in Molecular Orbital Theory[J].Rev.Mod.Phys.,1951,23(2):69-89.
[36]J.C.Slater.A Simplification of the Hartree-Fock Method[J].Phys.Rev.,1951,81(3):385-390.
[37]P.Hohenberg and W.Kohn.Inhomogeneous electron gas[J].Phys.Rev.,1964,136(3B):B864-B871.
[38]W.Kohn and L.J.Sham.Self-consistent equations including exchange and correlation effects[J].Phys.Rev.,1965,140(4A):A1133-A1138.
[39]D.R.Hamann,M.Schluter,and C.Chiang.Norm-Conserving Pseudopotentials[J].Phys.Rev.Lett.,1979,43(20):1494-1497.
[40]G.B.Bachelet,D.R.Hamann,and M.Schluter.Pseudopotentials that work:From H to Pu[J].Phys.Rev.B,1982,26(8):4199-4228.
[41]D.Vanderbilt.Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[J].Phys,Rev.B,1990,41(11):7892-7895.
[42]D.M.Ceperley and B.J.Alder.Ground State of the Electron Gas by a Stochastic Method[J].Phys.Rev.Lett.,1980,45(7):566-569.
[43]John P.Perdew.Accurate Density Functional for the Energy:Real-Space Cutoff of the Gradient Expansion for the Exchange Hole[J].Phys.Rev.Lett.,1985,55(16):1665-1668.
[44]John P.Perdew et al.Atoms,molecules,solids,and surfaces:Applications of the generalized gradient approximation for exchange and correlation[J].Phys.Rev.B,1992,46(11):6671-6687.
[45]John P.Perdew,Kieron Burke,and Matthias Ernzerhof.Generalized Gradient Approxinaation Made Simple[J].Phys.Rev.Lett.,1996,77(18):3865-3868.
[46]G.Makov and M.C.Payne.Periodic boundary conditions in ab initio calculations[J].Phys.Rev.B,(1994,51:4014-4022.
[47]虞福春,郑春开.电动力学[M].北京:北京大学出版社,1992.
[48]方容川.固体光谱学[M].合肥:中国科学技术大学出版社,2001.
[49]H.A.Lorentz.The Theory of Electrons[M].Teubner,1909.
[50]P.Drude.Zur Elektronentheorie der metalle[J].Annalen der Physik,1900,306(3):566.
[51]P.Drude.Zur Elektronentheorie der Metalle;Ⅱ.Teil.Galvanomagnetische und thermomagnetische Effecte[J]Annalen der Physik,1900,308(11):369.
[52]刘恩科,朱秉升,罗晋生.半导体物理学[M].北京:国防工业出版社,1994.
[53]张光寅,蓝国祥,王玉芳.晶格振动光谱学[M].北京:高等教育出版社,2001.
[54]S.Baroni,S.d.Gironcoli,S.d.Corso,A.Giannozzi.Phonons and related crystal properties from density-functional perturbation theory[J].Rev.Mod.Phys.,2001,73:515.
[55]Baroni,S.,P.Giannozzi,and A.Testa.Green's-function approach to linear response in solids[J],Phys.Rev.Lett.,1987,58(18):1861-1864.
[56]K.Kunc and R.M.Martin.Ab Initio Force Constants of GaAs:A New Approach to Calculation of Phonons and Dielectric Properties[J].Phys.Rev.Lett.,1982,48:406-409.
[57]M.T.Yin and M.L.Cohen.Theory of lattice-dynamical properties of solids:Application to Si and Ge[J].Phys.Rev.B,1982,26:3259-3272.
[58]Mikael C.Rechtsman,Frank H.Stillinger and Salvatore Torquato.Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions[J].Phys.Rev.E,2007,75:031403-031409.
[59]M.P.Allen and D.J.Tildesley.Computer Simulation of Liquids[M].Oxford:Clarendon Press,1987;reprinted 1990.
[60]R.Car and M.Parrinello.Unified Approach for Molecular Dynamics and Density-Functional Theory[J].Phys.Rev.Lett.,1985,55:2471-2474.
[61]陈纲,廖理几.晶体物理学基础[M].北京:科学出版社,1992.
[62]Charles kittel,项金钟吴兴惠译.Introduction to solid state physics[M].北京:化学工业出版社,2005.
[63]Hauck J.Ordering of hydrogen in Niobium hydride phases[J].Acta Cryst,1977,A33:208-211.
[64]Ho,K.-M.et al.First-Principles Investigation of Metal-Hydrogen Interactions in NbH[J].Phys.Rev.Lett.,1984,53:1586-1589.
[65]Tao,H.-J.et al.Investigation of the Electronic Structure and Phonon Anharmonicity in β-and γ-NbH[J].Phys.Rev.B,1986,34:8394-8400.
[66]Segall M D,Lindan P L D,Probert M J,Pickard C J,Hasnip P J,Clark S J,Payne M C.Firstprinciples simulation:ideas,illustrations and the CASTEP code[J].J.Phys.Condens.Matter,2002,14:2717-2744.
[67]Baroni S,Dal Corso A,de Gironcoli S,and Giannozzi P,http://www.pwscf.org.
[68]Christodoulos F and Gillan M J.A theoretical study of the quantum states of hydrogen in niobium[J].J.Phys.Condens.Matt.,1991,3:9429-9445.
[69]Ritcher D,Shapiro S M.Study of the temperature dependence of the localized vibrations of H and D in niobium[J].Phys.Rev.B,1980,22:599-605.
[70]Echert J,Goldstone J A,Tonks D,Richter D.Inelastic neutron scattering studies of vibrational excitations of hydrogen in Nb and Ta[J].Phys.Rev.B,1983,27:1980-1990.
[71] Ikeda S, Furusaka M, Fukunaga T, Taylor A D. Hydrogen wave functions in metal hydrides ZrH2 and NbH0.3[J]. J. Phys.: Condens. Matter,1990, 2: 4675.
[72] CPMD, Copyright IBM Corp 1990-2005, Copyright MPI fur Festko rperforschung Stuttgart 1997-2001
[73] Goedecker S, Teter M, Hutter J. Separable dual-space Gaussian pseudopotentials [J]. Phys Rev B , 1996, 54:1703-1710.
[74] Goedecker S. Integral representation of the Fermi distribution and its applications in electronic-structure calculations [J]. Phys Rev B, 1993, 48: 17573-17575.
[75] M. L. Cohen. Calculation of bulk moduli of diamond and zinc-blende solids [J].Phys. Rev. B, 1985,32: 7988-7991.
[76]A. Y. Liu and M. L. Cohen. Prediction of new low compressibility solids[J]. Science, 1989,245:841-842.
[77]A. Y. Liu and M. L. Cohen. Structural properties and electronic structure of low-compressibility materials: β-Si_3N_4 and hypothetical β-C_3N_4[J]. Phys. Rev. B, 1990,41:10727-10734.
[78] G. P. Srivastava and D. L. Weaire. for a review of LDA applications to cohesive properties of solids[J].Adv. Phys.,1987, 36: 463.
[79]A. Y. Liu and R. M. Wentzcovitch. Stability of carbon nitride solids[J]. Phys. Rev. B ,1994,50, 10362-10365.
[80] D. M. Teter and R. J. Hemley, Low-compressibility carbon nitrides[J].Science, 1996,271:53-55.
[81] M. Cote and M. L. Cohen. Carbon nitride compounds with 1:1 stoichiometry[J]. Phys. Rev. B,1997, 55:5684-5688.
[82]J. E. Lowther. Defective and amorphous structure of carbon nitride[M]. Phys. Rev. B,1998, 57:5724-5727.
[83] C. Niu, Y. Z. Lu, and C. M. Leiber. Experimental realization of the covalent solid carbon nitride[J]. Science,1993, 261: 334-337.
[84] D. Marton, K. J. Boyd, A. H. Al-Bayati, S. S. Todorov, and J. W. Rabalais. Carbon Nitride Deposited Using Energetic Species: A Two-Phase System[J].Phys. Rev. Lett., 1994,73:118-121.
[85] K. M. Yu, M. L. Cohen, E. E. Haller, W. L. Hansen, A. Y. Liu, and I. C. Wu. Observation of crystalline C_3N_4[J].Phys. Rev. B, 1994,49: 5034-5037.
[2] Daw M S and Baskes M I. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals [J]. Phys. Rev. Lett., 1983,50: 1285- 1288.
[3] Hillier E M K and Robinson M J. Hydrogen embrittlement of high strength steel electroplated with zinc-cobalt alloys [J]. Corrosion Science, 2004, 46 : 715-727.
[4] Lu G, Orlikowski D, Park I, Politano O and Kaxiras E. Energetics of hydrogen impurities in aluminum and their effect on mechanical properties[J]. Phys. Rev. B, 2002, 65: 064102-064109.
[5] Esaka T, Sakaguchi H and Kobayashi S. Hydrogen Storage in Proton Conductive Perovskite-type Oxides and their Application to Nickel-Hydrogen Batteries [J]. Solid State Ionics, 2004, 166: 351-357.
[6] Talyzin A V and Sundqvist B. Reversible phase transition in LiAlH4 under high-pressure conditions[J]. Phys. Rev. B, 2004, 70:180101-180103.
[7] Vajeeston P, Ravindran P, Kjekshus A and Fjellvag H. Structural stability and electronic structure for Li_3AlH_6[J]. Phys. Rev. B, 2004, 69 020104-020107.
[8] Wilson W D, Baskes M I, Bission C L. Atomistics of helium bubble formation in a face-centered-cubic metal [J]. Phys Rev B, 1976, 13: 2470-2478.
[9] Wilson W D, Bisson C L, Baskes M I. Self-trapping of helium in metals [J]. Phys Rev B, 1981, 24:616-5624.
[10] Jensen K O, Nieminen R M. Helium bubbles in metals: Molecular-dynamics simulations and positron states [J]. Phys Rev B, 1987, 35:2087-2090.
[11]Jensen K O, Nieminen R M. Noble-gas bubbles in metals: molecular-dynamics simulations and positron states [J]. Phys Rev B, 1987, 36: 8219-8232.
[12] Raajaraman R, Viswannathan B, Valsakumar M C, Gopinathan K P. Anomalous helium-bubble growth in palladium [J]. Phys Rev B, 1994-1, 50:597-600.
[13] Birtcher R, Donnelly S E, Templier C. Evolution of helium bubbles in aluminum during heavy-ion irradiation. Phys.Rrev. B, 1994-II, 50:764-769.
[14] Donnelly S E, Birtcher R C, Templier C, Vishnyakov V. Response of helium bubbles in gold to displacement-cascade damage [J]. Phys Rev B, 1995-II, 52:3970-3976.
[15] Vassen R, Trinkaus H, Jung P. Helium desorption from Fe and V by atomic diffusion and bubble migration [J]. Phys Rev B, 1991-1, 44: 4206-4213.
[16] A. Y. Liu, M. L. Cohen. Prediction of New Low Compressibility Solids. Science, 1989,245:841-842.
[17] R.H.Wentorf, Jr.Preparation of Semiconducting Cubic Boron Nitride [J]. J. Chem. Phys., 1962, 36:1990-1991.
[18] O. Mishima, K.Era, J. Tanaka, and S. Yamaoka.Ultraviolet light-emitting diode of a cubic boron nitride pn junction made at high pressure, Appl. Phys. Lett., 1988, 53: 962-964.
[19] A. Y. Liu and M. L. Cohen.Structural properties and electronic structure of low-compressibility materials: β-Si_3N_4 and hypothetical β-C_3N_4[J]. Phys. Rev. B, 1990, 41(15):10727-10734.
[20]C.M.Sung and M.Sung.Carbon nitride and other speculative superhard materials[J].Mater.Chem.Phys.,1996,43:1-18.
[21]Vladimir L.Solozhenko,Denis Andrault,Guillaume Fiquet,Mohamed Mezouar,David C.Rubie.Synthesis of superhard cubic BC_2N[J].Applied Physics Letters,2001,78:1385-1387.
[22]Vladimir L.Solozhenko,Sergey N.Dub,Nikolay V.Novikov.Mechanical properties of cubic BC_2N,a superhard phase[J].Diamond and Related materials,2001,10:2228-2231.
[23]S.N.Tkachev,V.L.Solozhenko,P.V.Zinin,M.H.Manghnani,L.C.Ming.Elastic moduli of the superhard cubic BC_2N phase by Brillouin scattering[J].Phys.Rev.B,2003,68:052104.
[24]P.V.Zinin,V.L.Solozhenko,A.J.Malkin.Atomic force microscopy studies of cubic BC_2N,a new superhard phase[J].Jounal of Materials Science,2005,40:3009-3011.
[25]H.W.Hubble,I.Kudryashov,V.L.Solozhenko,P.V.Zinin,S.K.Sharma,L.C.Ming.Raman studies of cubic BC_2N,a new superhard phase[J].Journal of Raman Spectroscopy,2004,35(10):822-825.
[26]Hong Sun,Seung Jhi,David Roundy,Marvin L.Cohen and Steven G.Louie.Structural forms of cubic BC_2N[J].Phys.Rev.B,2001,64:094108-1.
[27]Zicheng Pan,Hong Sun,Changfeng Chen.Ab initio pseudopotential studies of cubic BC2N under high pressure[J].Journal of Physics:Condensed Matter,2005,17:3211-3220.
[28]Shiyou Chen,X.G.Gong,Su-Huai Wei.Superhard Pseudocubic BC_2N Superlattices[J].Phys.Rev.Lett.,2007,98:015502(4).
[29]马文淦.计算物理学[M].合肥:中国科学技术大学出版社,2001.
[30]韩汝琦,黄昆.固体物理学[M].北京:高等教育出版社,1988.
[31]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版社,1998.
[32]阎守胜.固体物理基础[M].北京:北京大学出版社,2000.
[33]M.Born and K.Huang.Dynamical Theory of Crystal Lattices [M].Oxford:Oxford University Press,1954.
[34]E.Wigner and F.Seitz.On the Constitution of Metallic Sodium [J].Phys.Rev.,1933,43:804-810.
[35]C.C.J.Roothaan.New Developments in Molecular Orbital Theory[J].Rev.Mod.Phys.,1951,23(2):69-89.
[36]J.C.Slater.A Simplification of the Hartree-Fock Method[J].Phys.Rev.,1951,81(3):385-390.
[37]P.Hohenberg and W.Kohn.Inhomogeneous electron gas[J].Phys.Rev.,1964,136(3B):B864-B871.
[38]W.Kohn and L.J.Sham.Self-consistent equations including exchange and correlation effects[J].Phys.Rev.,1965,140(4A):A1133-A1138.
[39]D.R.Hamann,M.Schluter,and C.Chiang.Norm-Conserving Pseudopotentials[J].Phys.Rev.Lett.,1979,43(20):1494-1497.
[40]G.B.Bachelet,D.R.Hamann,and M.Schluter.Pseudopotentials that work:From H to Pu[J].Phys.Rev.B,1982,26(8):4199-4228.
[41]D.Vanderbilt.Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[J].Phys,Rev.B,1990,41(11):7892-7895.
[42]D.M.Ceperley and B.J.Alder.Ground State of the Electron Gas by a Stochastic Method[J].Phys.Rev.Lett.,1980,45(7):566-569.
[43]John P.Perdew.Accurate Density Functional for the Energy:Real-Space Cutoff of the Gradient Expansion for the Exchange Hole[J].Phys.Rev.Lett.,1985,55(16):1665-1668.
[44]John P.Perdew et al.Atoms,molecules,solids,and surfaces:Applications of the generalized gradient approximation for exchange and correlation[J].Phys.Rev.B,1992,46(11):6671-6687.
[45]John P.Perdew,Kieron Burke,and Matthias Ernzerhof.Generalized Gradient Approxinaation Made Simple[J].Phys.Rev.Lett.,1996,77(18):3865-3868.
[46]G.Makov and M.C.Payne.Periodic boundary conditions in ab initio calculations[J].Phys.Rev.B,(1994,51:4014-4022.
[47]虞福春,郑春开.电动力学[M].北京:北京大学出版社,1992.
[48]方容川.固体光谱学[M].合肥:中国科学技术大学出版社,2001.
[49]H.A.Lorentz.The Theory of Electrons[M].Teubner,1909.
[50]P.Drude.Zur Elektronentheorie der metalle[J].Annalen der Physik,1900,306(3):566.
[51]P.Drude.Zur Elektronentheorie der Metalle;Ⅱ.Teil.Galvanomagnetische und thermomagnetische Effecte[J]Annalen der Physik,1900,308(11):369.
[52]刘恩科,朱秉升,罗晋生.半导体物理学[M].北京:国防工业出版社,1994.
[53]张光寅,蓝国祥,王玉芳.晶格振动光谱学[M].北京:高等教育出版社,2001.
[54]S.Baroni,S.d.Gironcoli,S.d.Corso,A.Giannozzi.Phonons and related crystal properties from density-functional perturbation theory[J].Rev.Mod.Phys.,2001,73:515.
[55]Baroni,S.,P.Giannozzi,and A.Testa.Green's-function approach to linear response in solids[J],Phys.Rev.Lett.,1987,58(18):1861-1864.
[56]K.Kunc and R.M.Martin.Ab Initio Force Constants of GaAs:A New Approach to Calculation of Phonons and Dielectric Properties[J].Phys.Rev.Lett.,1982,48:406-409.
[57]M.T.Yin and M.L.Cohen.Theory of lattice-dynamical properties of solids:Application to Si and Ge[J].Phys.Rev.B,1982,26:3259-3272.
[58]Mikael C.Rechtsman,Frank H.Stillinger and Salvatore Torquato.Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions[J].Phys.Rev.E,2007,75:031403-031409.
[59]M.P.Allen and D.J.Tildesley.Computer Simulation of Liquids[M].Oxford:Clarendon Press,1987;reprinted 1990.
[60]R.Car and M.Parrinello.Unified Approach for Molecular Dynamics and Density-Functional Theory[J].Phys.Rev.Lett.,1985,55:2471-2474.
[61]陈纲,廖理几.晶体物理学基础[M].北京:科学出版社,1992.
[62]Charles kittel,项金钟吴兴惠译.Introduction to solid state physics[M].北京:化学工业出版社,2005.
[63]Hauck J.Ordering of hydrogen in Niobium hydride phases[J].Acta Cryst,1977,A33:208-211.
[64]Ho,K.-M.et al.First-Principles Investigation of Metal-Hydrogen Interactions in NbH[J].Phys.Rev.Lett.,1984,53:1586-1589.
[65]Tao,H.-J.et al.Investigation of the Electronic Structure and Phonon Anharmonicity in β-and γ-NbH[J].Phys.Rev.B,1986,34:8394-8400.
[66]Segall M D,Lindan P L D,Probert M J,Pickard C J,Hasnip P J,Clark S J,Payne M C.Firstprinciples simulation:ideas,illustrations and the CASTEP code[J].J.Phys.Condens.Matter,2002,14:2717-2744.
[67]Baroni S,Dal Corso A,de Gironcoli S,and Giannozzi P,http://www.pwscf.org.
[68]Christodoulos F and Gillan M J.A theoretical study of the quantum states of hydrogen in niobium[J].J.Phys.Condens.Matt.,1991,3:9429-9445.
[69]Ritcher D,Shapiro S M.Study of the temperature dependence of the localized vibrations of H and D in niobium[J].Phys.Rev.B,1980,22:599-605.
[70]Echert J,Goldstone J A,Tonks D,Richter D.Inelastic neutron scattering studies of vibrational excitations of hydrogen in Nb and Ta[J].Phys.Rev.B,1983,27:1980-1990.
[71] Ikeda S, Furusaka M, Fukunaga T, Taylor A D. Hydrogen wave functions in metal hydrides ZrH2 and NbH0.3[J]. J. Phys.: Condens. Matter,1990, 2: 4675.
[72] CPMD, Copyright IBM Corp 1990-2005, Copyright MPI fur Festko rperforschung Stuttgart 1997-2001
[73] Goedecker S, Teter M, Hutter J. Separable dual-space Gaussian pseudopotentials [J]. Phys Rev B , 1996, 54:1703-1710.
[74] Goedecker S. Integral representation of the Fermi distribution and its applications in electronic-structure calculations [J]. Phys Rev B, 1993, 48: 17573-17575.
[75] M. L. Cohen. Calculation of bulk moduli of diamond and zinc-blende solids [J].Phys. Rev. B, 1985,32: 7988-7991.
[76]A. Y. Liu and M. L. Cohen. Prediction of new low compressibility solids[J]. Science, 1989,245:841-842.
[77]A. Y. Liu and M. L. Cohen. Structural properties and electronic structure of low-compressibility materials: β-Si_3N_4 and hypothetical β-C_3N_4[J]. Phys. Rev. B, 1990,41:10727-10734.
[78] G. P. Srivastava and D. L. Weaire. for a review of LDA applications to cohesive properties of solids[J].Adv. Phys.,1987, 36: 463.
[79]A. Y. Liu and R. M. Wentzcovitch. Stability of carbon nitride solids[J]. Phys. Rev. B ,1994,50, 10362-10365.
[80] D. M. Teter and R. J. Hemley, Low-compressibility carbon nitrides[J].Science, 1996,271:53-55.
[81] M. Cote and M. L. Cohen. Carbon nitride compounds with 1:1 stoichiometry[J]. Phys. Rev. B,1997, 55:5684-5688.
[82]J. E. Lowther. Defective and amorphous structure of carbon nitride[M]. Phys. Rev. B,1998, 57:5724-5727.
[83] C. Niu, Y. Z. Lu, and C. M. Leiber. Experimental realization of the covalent solid carbon nitride[J]. Science,1993, 261: 334-337.
[84] D. Marton, K. J. Boyd, A. H. Al-Bayati, S. S. Todorov, and J. W. Rabalais. Carbon Nitride Deposited Using Energetic Species: A Two-Phase System[J].Phys. Rev. Lett., 1994,73:118-121.
[85] K. M. Yu, M. L. Cohen, E. E. Haller, W. L. Hansen, A. Y. Liu, and I. C. Wu. Observation of crystalline C_3N_4[J].Phys. Rev. B, 1994,49: 5034-5037.