Lattice Dynamics and Superconductivity of RuB2 A First-Principles Study

Superconductivity and its Applications 超导和超导应用超导是一种奇妙的物理现象，它是指近零电阻的材料在特定温度下，可以自发地将电流运输而不损失电能，这一现象被称为超导。

自从超导现象被发现以来，超导性质已成为物理，工程和生物等多个领域的研究热点。

本文将对超导的概念，性质和应用进行探讨。

一、超导的概念超导最早被发现是在1911年，当时在荷兰的莱顿大学，物理学家海克尔斯和卡末林发现在低温下汞的电阻突然减小并最终消失。

这一现象是有趣的，因为在当时的物理学家看来，电阻是任何材料中的必需品。

经过进一步研究，物理学家们发现这一效应是由于材料在超导状态下，电子以成对的形式移动，即库珀对，而不是独立地移动。

这一对电子之间发生了什么不尽清楚，但是这种共同运动使得电流在材料中流动时经历了相干性的运动而不会损失电能。

超导材料的主要特点是在超导状态下，所有有电荷的自由运动质量的粒子（通常是电子），即使在有外部电场的情况下也无法通过材料中传播，因此在超导状态下不能流失电能。

此外，超导体在超导状态下具有强磁场抑制效应，磁通通过超导体时，阻力为零。

二、超导的性质超导体的主要性质包括临界温度，临界电流密度和退相干距离。

1、临界温度临界温度是指在一个超导体中必须达到的温度，才能让这个超导体进入超导态。

所有的超导材料都有一个特定的临界温度，当温度降到这个温度以下时，电阻将下降到零。

对于高温超导材料（HTS），临界温度通常大于-100°C。

2、临界电流密度临界电流密度是指在一个超导状态下的电流密度水平超出了它的临界值，会导致超导材料失去超导功能。

通常，超导材料在其临界电流密度的一小部分内表现出类似于阻抗的性质，使其能够承受相对较大的电流。

但是超过这个限制，将会破坏超导和废除材料的超导性质。

3、退相干距离退相干距离是指在超导电流通过超导体时，因为磁通对超导电子对的长度进行干扰，并且当它们受到干扰时，它们的超导性的长度。

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固体物理英语固体物理基本词汇（汉英对照）一画一维晶格 One-dimensional crystal lattice一维单原子链 One-dimensional monatomic chain 一维双原子链 One-dimensional diatomic chain 一维复式格子One-dimensional compound lattice 二画二维晶格 Two-dimensional crystal lattice二度轴 Twofold axis二度对称轴 Twofold axis of symmetry几何结构因子 Geometrical structure factor三画三斜晶系 Triclinic system三方晶系 Trigonal system三斜晶系 Triclinic system刃位错 Edge dislocation小角晶界 Low angle grain boundary马德隆常数 Madelung constant四画元素晶体 Element crystal元素的电负性 Electronegativities of elements元素的电离能 Ionization energies of the elements 元素的结合能 Cohesive energies of the elements 六方密堆积 Hexagonal close-packed六方晶系 Hexagonal system反演 Inversion分子晶体 Molecular Crystal切变模量 Shear module双原子链 Diatomic linear chain介电常数 Dielectric constant化学势 Chemical potential内能 Internal energy分布函数 Distribution function夫伦克耳缺陷 Frenkel defect比热 Specific heat中子散射 Neutron scattering五画布喇菲格子 Bravais lattice布洛赫函数 Bloch function布洛赫定理 Bloch theorem布拉格反射 Bragg reflection布里渊区 Brillouin zone布里渊区边界 Brillouin zone boundary 布里渊散射 Brillouin scattering正格子 Direct lattice正交晶系 Orthorhombic crystal system正则振动 Normal vibration正则坐标 Normal coordinates立方晶系 Cubic crystal system立方密堆积 Cubic close-packed四方晶系 Tetragonal crystal system对称操作 Symmetry operation对称群 Symmetric group正交化平面波 Orthogonalized plane wave电子-晶格相互作用 Electron-lattice interaction 电子热容量 Electronic heat capacity电阻率 Electrical resistivity电导率 Conductivity电子亲合势 Electron affinity电子气的动能 Kinetic energy of electron gas 电子气的压力 Pressure of electron gas电子分布函数 Electron distribution function 电负性 Electronegativity电磁声子 Electromagnetic phonon功函数 Work function长程力 Long-range force立方晶系 Cubic system平面波方法 plane wave method平移对称性 Translation symmetry平移对称操作 Translation symmetry operator 平移不变性 Translation invariance石墨结构 Graphite structure闪锌矿结构 Blende structure六画负电性 Electronegativity共价结合 Covalent binding共价键 Covalent bond共价晶体 Covalent crystals共价键的饱和 Saturation of covalent bonds 光学模 Optical modes光学支 Optical branch光散射 Light scattering红外吸收 Infrared absorption压缩系数 Compressibility扩散系数 Diffusion coefficient扩散的激活能 Activation energy of diffusion 共价晶体 Covalent Crystal价带 Valence band导带 Conduction band自扩散 Self-diffusion有效质量 Effective mass有效电荷 Effective charges弛豫时间 Relaxation time弛豫时间近似 Relaxation-time approximation扩展能区图式 Extended zone scheme自由电子模型 Free electron model自由能 Free energy杂化轨道 Hybrid orbit七画纯金属 Ideal metal体心立方 Body-centered cubic体心四方布喇菲格子 Body-centered tetragonal Bravais lattices 卤化碱晶体 Alkali-halide crystal劳厄衍射 Laue diffraction间隙原子 Interstitial atom间隙式扩散 Interstitial diffusion肖特基缺陷 Schottky defect位错 Dislocation滑移 Slip晶界 Grain boundaries伯格斯矢量 Burgers vector杜隆-珀替定律 Dulong-Petit’s law粉末衍射 Powder diffraction里查孙-杜师曼方程 Richardson-Dushman equation 克利斯托夫方程 Christofell equation克利斯托夫模量Christofell module位移极化 Displacement polarization声子 Phonon声学支 Acoustic branch应力 Stress 应变 Strain切应力 Shear stress切应变 Shear strain八画周期性重复单元 Periodic repeated unit底心正交格子 Base-centered orthorhombic lattice 底心单斜格工 Base-centered monoclinic lattices 单斜晶系 Monoclinic crystal system金刚石结构 Diamond structure金属的结合能 Cohesive energy of metals金属晶体 Metallic Crystal转动轴 Rotation axes转动-反演轴 Rotation-inversion axes转动晶体法 Rotating crystal method空间群 Space group空位 Vacancy范德瓦耳斯相互作用 Van der Waals interaction 金属性结合 Metallic binding单斜晶系 Monoclinic system单电子近似 Single-erection approximation极化声子 Polarization phonon拉曼散射 Raman scattering态密度 Density of states铁电软模 Ferroelectrics soft mode空穴 Hole万尼尔函数 Wannier function平移矢量 Translation vector非谐效应 Anharmonic effect周期性边界条件 Periodic boundary condition九画玻尔兹曼方程 Boltzman equation点群 Point groups迪. 哈斯－范. 阿耳芬效应 De Hass－Van Alphen effect胡克定律Hooke’s law氢键 Hydrogen bond亲合势 Affinity重迭排斥能 Overlap repulsive energy结合能 Cohesive energy玻恩-卡门边界条件 Born-Karman boundary condition费密-狄喇克分布函数 Fermi-Dirac distribution function费密电子气的简并性 Degeneracy of free electron Fermi gas 费密 Fermi费密能 Fermi energy费密能级 Fermi level费密球 Fermi sphere费密面 Fermi surface费密温度 Fermi temperature费密速度 Fermi velocity费密半径 Fermi radius恢复力常数 Constant of restorable force绝热近似 Adiabatic approximation十画原胞 Primitive cell原胞基矢 Primitive vectors倒格子 Reciprocal lattice倒格子原胞 Primitive cell of the reciprocal lattice 倒格子空间 Reciprocal space倒格点 Reciprocal lattice point倒格子基矢Primitive translation vectors of the reciprocal lattice倒格矢 Reciprocal lattice vector倒逆散射 Umklapp scattering粉末法 Powder method原子散射因子 Atomic scattering factor配位数 Coordination number原子和离子半径 Atomic and ionic radii原子轨道线性组合 Linear combination of atomic orbits离子晶体的结合能 Cohesive energy of inert crystals离解能 Dissociation energy离子键 Ionic bond离子晶体 Ionic Crystal离子性导电 Ionic conduction洛伦兹比 Lorenz ratio魏德曼－佛兰兹比 Weidemann－Franz ratio 缺陷的迁移 Migration of defects缺陷的浓度 Concentrations of lattice defects 爱因斯坦 Einstein爱因斯坦频率 Einstein frequency爱因斯坦温度 Einstein temperature格波 Lattice wave格林爱森常数 Gruneisen constant索末菲理论 Sommerfeld theory热电子发射 Thermionic emission热容量 Heat capacity热导率 Thermal conductivity热膨胀 Thermal expansion能带 Energy band能隙 Energy gap能带的简约能区图式 Reduced zone scheme of energy band 能带的周期能区图式 Repeated zone scheme of energy band 能带的扩展能区图式 Extended zone scheme of energy band 配分函数 Partition function准粒子 Quasi- particle准动量 Quasi- momentum准自由电子近似 Nearly free electron approximation十一画第一布里渊区 First Brillouin zone密堆积 Close-packing密勒指数 Miller indices接触电势差 Contact potential difference基元 Basis基矢 Basis vector弹性形变 Elastic deformation排斥能Repulsive energy弹性波 Elastic wave弹性应变张量 Elastic strain tensor弹性劲度常数 Elastic stiffness constant弹性顺度常数 Elastic compliance constant 弹性模量 Elastic module弹性动力学方程 Elastic-dynamics equation 弹性散射 Elastic scattering十二画等能面 Constant energy surface晶体 Crystal晶体结构 Crystal structure晶体缺陷 Crystal defect晶体衍射 Crystal diffraction晶列 Crystal array晶面 Crystal plane晶面指数 Crystal plane indices晶带 Crystal band晶向 direction晶格 lattice晶格常数 Lattice constant晶格周期势 Lattice-periodic potential 晶格周期性 Lattice-periodicity晶胞 Cell, Unit cell晶面间距 Interplanar spacing晶系 Crystal system晶体 Crystal晶体点群 Crystallographic point groups晶格振动 Latticevibration晶格散射 Lattice scattering散射 Scattering等能面 surface of constant energy十三画隋性气体晶体的结合能 Cohesive energy of inert gas crystals 滑移 Slip滑移面 Slip plane简单立方晶格 Simple cubic lattice简单晶格 Simple lattice简单单斜格子 Simple monoclinic lattice简单四方格子 Simple tetragonal lattice简单正交格子 Simple orthorhombic lattice简谐近似 Harmonic approximation简正坐标 Normal coordinates简正振动 Normal vibration简正模 Normal modes简约波矢 Reduced wave vector简约布里渊区 Reduced Brillouin zone禁带 Forbidden band紧束缚方法 Tight－binding method零点振动能 Zero-point vibration energy 雷纳德－琼斯势 Lenard－Jones potential 满带 Filled band十四画磁致电阻 Magnetoresistance模式密度 Density of modes漂移速度 Drift velocity漂移迁移率 Drift mobility十五至十七画德拜 Debye德拜近似 Debye approximation德拜截止频率 Debye cut-off frequency 德拜温度 Debye temperature霍耳效应 Hall effect螺位错 Screw dislocation赝势 Pseudopotential。

a r X i v :h e p -t h /0112051v 1 6 D e c 20011Remarks on monopoles in Abelian projected continuum Yang-Mills theories ∗A.R.Fazio a S.P.Sorella baUniversit`a degli Studi di Milano and INFN,via Celoria 16,20143Milano,ItalybUERJ,Universidade do Estado do Rio de Janeiro Rua S˜a o Francisco Xavier 524,20550-013Maracan˜a ,Rio de Janeiro,BrazilA possible mechanism accounting for monopole configurations in continuum Yang-Mills theories is discussed.The presence of the gauge fixing term is taken into account.1.IntroductionThe understanding of confinement in non-abelian gauge theories is one of the major chal-lenge in theoretical physics.The idea that con-finement could be explained as a dual Meissner effect for type II superconductors is largely ac-cepted,with confirmations from lattice simula-tions.A key ingredient for the picture of dual super-conductivity is the mechanism of Abelian projec-tion introduced by ’t Hooft [1],which consists of reducing the gauge group SU (N )to an Abelian subgroup,identified with the Cartan subgroup U (1)N −1,by means of a partial gauge fixing.This is achieved by choosing any local composite oper-ator X (x )which transforms in the adjoint rep-resentation,X ′(x )=UX (x )U †.The gauge is partially fixed by requiring that X becomes di-agonal,X ′(x )=diag(λ1(x ),......,λN (x )),where λi (x )denote the gauge invariant eigenvalues.As shown in [1],monopoles configurations appear at the points x 0of the space-time where two eigen-values coincide,i.e.λi +1(x 0)=λi (x 0).Further,the gauge field is decomposed into its diagonal and off-diagonal parts.The diagonal compo-nents correspond to the generators of the Car-tan subgroup and behave as photons.The off-diagonal components are charged with respect to the Abelian residual subgroup and may become massive [2,3],being not protected by gauge invari-ance.This mass should set the confinement scale,allowing for the decoupling of the off-diagonal fields at low energy.The final Abelian projected theory turns out thus to be described by an effec-tive low-energy theory in which the relevant de-grees of freedom are identified with the diagonal components of the gauge fields and with a certain amount of monopoles,whose condensation should account for the confinement of all chromoelectric ttice simulations [4,5]have provided evidences for the Abelian dominance hypothe-sis,according to which QCD in the low-energy regime is described by an effective Abelian the-ory.This supports the realization of confinement through a dual Meissner effect,although the in-frared Abelian dominance in lattice calculations seems not to be a general feature of any Abelian gauge [6].Furthermore,many conceptual points remain to be clarified in order to achieve a satis-factory understanding of confinement in the con-tinuum.Certainly,the problem of the deriva-tion of the Abelian dominance from the QCD La-grangian is a crucial one.Also,the characteriza-tion of the effective low-energy Abelian projected theory and of its monopoles content is of great relevance.There,one usually starts by impos-ing the so called Maximal Abelian Gauge (MAG)[7],which allows for a manifest residual subgroup U (1)N −1.The presence of monopoles in the MAG follows then from Π2(SU (N )/U (1)N −1)=Z N −1.However,being the MAG a gauge-fixing condi-tion,it is manifestly noncovariant.Therefore,2monopoles here do not seem to be directly re-lated to the singularities occurring for coinciding eigenvalues in the process of diagonalization of a local covariant operator X (x ).Rather,they are associatedtosingular configurations of the fields [7].The purpose of this contribution is to discuss a possible mechanism accounting for the presence of monopoles in the MAG,for continuum gauge theories.The argument turns out to be general-ized to any renormalizable gauge,the main idea being that of showing that ’t Hooft Abelian pro-jection can be suitably carried out in the presence of gauge fixing terms.2.Monopoles in quantized Yang-Mills the-ories In what follows we present a simple way in or-der to account for monopoles in continuum quan-tized Yang-Mills theories.In particular,we point out that it is possible to introduce in the path in-tegral a covariant local quantity whose diagonal-ization is compatible with the gauge fixing,repro-ducing at the end the usual form of the Yang-Mills partition function in the presence of monopoles [7].Let us start by considering the partition func-tion for the quantized SU (N )Yang-Mills theoryZ =N[D Φ][DA ]exp − d 4x Tr14F µνF µν→Tri4B µνB µν(2)Therefore,for the partition function we getZ =N[D Φ][DA ][DB ]exp −S GF− d 4x TriF µνB µν4(3)Notice that the field B µνtransforms covariantly under a gauge transformation of SU (N )B µν−→B Uµν=UB µνU †,from which it follows that the quadratic term Tr B µνB µνis left invariantTr B µνB µν=Tr B U µνB Uµν.Also,it is worth remarking that the field B µνdoes not appear in the gauge fixing term S GF (A,b,c,¯c ).According to ’t Hooft procedure,we can now pick up any component of B µν,say B 12,and,due to its hermiticity,diagonalize it by a suitable transformation Ωof SU (N ),namelyB 12→B diag12=ΩB 12Ω†.Due to the invariance of Tr B µνB µν,we haveTr B µνB µν=Tr2B 12B 12+B jk B jk=Tr2ΩB 12Ω†ΩB 12Ω†+ΩB jk Ω†ΩB jk Ω†=Tr2B diag 12B diag12+ΩB jk Ω†ΩB jk Ω†,(4)where the sum over the indices (j,k )does not in-clude the component B 12.The partition functionZ becomesZ =N[D Φ][DA ][DB ][D Ω]exp −S GF− d 4xi4Tr2ΩB 12Ω†ΩB 12Ω†+ΩB jk Ω†ΩB jk Ω†where we have inserted the integration measure [D Ω]over the gauge transformations which diag-onalize B 12.This is always possible,thanks to eq.(4).Performing now the change of variables B µν→Ω†B µνΩ,Ω→Ω,(5)3 we obtainZ=N [DΦ][DA][DB][DΩ]exp d4x Tr −iBµνBµν −S GF4The change of variables(5)has the effect of mov-ing theΩ’s from the quadratic term BB to thefirst term F B.Recalling then that theΩ’s areprecisely those transformations which diagonalizeB12,it follows thatΩFµνΩ†=Ω ∂µAν−∂νAµ−[Aµ,Aν]+([∂µ,∂ν]Ω†)Ω Ω†,Fµν=[Dµ,Dν].Finally,we can path integrate thefield B obtain-ing the expressionZ=N [DΦ][DA][DΩ]exp d4x T r −14M.N.Chernodub, F.V.Gubarev,M.I.Po-likarpov,V.I.Zakharov,Monopoles and Con-fining Strings in QCD,hep-lat/0103033.8. F.Fucito,M.Martellini,M.Zeni,Nucl.Phys.B496(1997)259.9.K.-I.Kondo,Phys.Rev.D57(1998)7467.。

CASTEP Scientific References - 20121.Jian Sun, Miguel Martinez-Canales, Dennis D. Klug, Chris J. Pickard, and Richard J.Needs,Persistence and Eventual Demise of Oxygen Molecules at Terapascal Pressures,Physical Review Letters108 (2012) 045503 ( abstract )2.Miguel Martinez-Canales, Chris J. Pickard, Richard J. Needs,Thermodynamically Stable Phases of Carbon at Multiterapascal Pressures,Physical Review Letters108 (2012) 045704 ( abstract )3. A. Chroneos and A. Dimoulas,Defect configurations of high-k cations in germanium,Journal of Applied Physics111 (2012) 023714 ( abstract )4.Roland Gillen and John Robertson,Hybrid functional calculations of the Al impurity in α quartz: Hole localization andelectron paramagnetic resonance parameters,Physical Review B85 (2012) 014117 ( abstract )5. A. Bhattacharya, S. Bhattacharya, and G. P. Das,Band gap engineering by functionalization of BN sheet,Physical Review B85 (2012) 035415 ( abstract )6.L. Fishwick, M. Walker, M. K. Bradley, D. P. Woodruff, and C. F. McConville,Surface structure of GaP(110): Ion scattering and density functional theory study,Physical Review B85 (2012) 045322 ( abstract )7.Takatsugu Endo, Scarlett Widgeon, Ping Yu, Sabyasachi Sen, and Keiko Nishikawa,Cation and anion dynamics in supercooled and glassy states of the ionic liquid1-butyl-3-methylimidazolium hexafluorophosphate: Results from 13C, 31P, and 19F NMRspectroscopy,Physical Review B85 (2012) 054307 ( abstract )8.James D. Aldous et al.,Cubic MnSb: Epitaxial growth of a predicted room temperature half-metal,Physical Review B85 (2012) 060403 ( abstract )9.N. D. Drummond, V. Zolyomi, and V. I. Fal'ko,Electrically tunable band gap in silicene,Physical Review B85 (2012) 075423 ( abstract )10.Philip W. Avraam, Nicholas D. M. Hine, Paul Tangney, and Peter D. Haynes,Fermi-level pinning can determine polarity in semiconductor nanorods,Physical Review B85 (2012) 115404 ( abstract )11.Naoki Imamura, Hiroshi Mizoguchi, and Hideo Hosono,Superconductivity in LaT M BN and La3T M2B2N3 (T M = Transition Metal) Synthesizedunder High Pressure,J. Am. Chem. Soc.134 (2012) 2516–2519 ( abstract )12.Jakub S. Jirkovsky, Itai Panas, Simon Romani, Elisabet Ahlberg, and David J. Schiffrin,Potential-Dependent Structural Memory Effects in Au-Pd Nanoalloys,J. Phys. Chem. Lett.3 (2012) 315–321 ( abstract )13.Martin Dracinsky, Milos Budesinsky, Beata Warzajtis, and Urszula Rychlewska,Solution and Solid-State Effects on NMR Chemical Shifts in Sesquiterpene Lactones: NMR, X-ray, and Theoretical Methods,J. Phys. Chem. A116 (2012) 680–688 ( abstract )14.Luke A. O'Dell, Christopher I. Ratcliffe, Xianqi Kong, and Gang Wu,Multinuclear Solid-State Nuclear Magnetic Resonance and Density Functional Theory Characterization of Interaction Tensors in Taurine,J. Phys. Chem. A116 (2012) 1008–1014 ( abstract )15.Yutaka Natsume et al.,Chemical-State Analysis of Organic Semiconductors Using Soft X-ray AbsorptionSpectroscopy Combined with First-Principles Calculation,J. Phys. Chem. A116 (2012) 1527–1531 ( abstract )16.Tingting Lin, Xiang-Yang Liu, and Chaobin He,Calculation of Infrared/Raman Spectra and Dielectric Properties of Various Crystalline Poly(lactic acid)s by Density Functional Perturbation Theory (DFPT) Method,J. Phys. Chem. B116 (2012) 1524–1535 ( abstract )17.Marco Delgado et al.,Evolution of Structure and of Grafting Properties of γ-Alumina with PretreatmentTemperature,J. Phys. Chem. C116 (2012) 834–843 ( abstract )ardo Cuervo Reyes, Adam Slabon-Turski, Christian Mensing, and Reinhard Nesper,Spin-Glass Behavior and Electronic Structure of LiEu2Si3,J. Phys. Chem. C116 (2012) 1158–1164 ( abstract )19.Daejin Kim et al.,Pillared Covalent Organic Frameworks with Balanced V olumetric and GravimetricHydrogen Uptake,J. Phys. Chem. C116 (2012) 1479–1484 ( abstract )ardo Cuervo Reyes and Reinhard Nesper,Electronic Structure and Properties of the Alkaline Earth Monosilicides,J. Phys. Chem. C116 (2012) 2536–2542 ( abstract )21.Jung-Il Hong et al.,Magnetism in Dopant-Free ZnO Nanoplates,Nano Letters12 (2012) 576–581 ( abstract )22.Nan Gao, Wei Tao Zheng and Qing Jiang,Density functional theory calculations for two-dimensional silicene with halogenfunctionalization,Physical Chemistry Chemical Physics14 (2012) 257–261 ( abstract )23.Marco Sacchi, Martin C. E. Galbraith and Stephen J. Jenkins,The interaction of iron pyrite with oxygen, nitrogen and nitrogen oxides: a first-principles study,Physical Chemistry Chemical Physics14 (2012) 3627–3633 ( abstract )24.Zhi Yang et al.,Density functional theory studies of Nb-benzene and Nb-borazine sandwich clusters andmolecular wires,Journal of Physics B45 (2012) 025102 ( abstract )25.P Pluengphon, T Bovornratanaraks, S V annarat and U Pinsook,The effects of Na on high pressure phases of CuIn0.5Ga0.5Se2 from ab initio calculation, Journal of Physics: Condensed Matter24 (2012) 095802 ( abstract )26.Ran He, Z S Lin, Tao Zheng, He Huang and C T Chen,Energy band gap engineering in borate ultraviolet nonlinear optical crystals: ab initiostudies,Journal of Physics: Condensed Matter24 (2012) 145503 ( abstract )27.M. G. Brik,First-principles calculations of electronic, optical and elastic properties of Ba2MgWO6 double perovskite,Journal of Physics and Chemistry of Solids73 (2012) 252–256 ( abstract )28.Y. H. Liu et al.,Study on the transformation from NaCl-type Na2TiO3 to layered titanate,Journal of Physics and Chemistry of Solids73 (2012) 402–406 ( abstract )29.Elena Bichoutskaia et al.,High-precision imaging of an encapsulated Lindqvist ion and correlation of its structure and symmetry with quantum chemical calculations,Nanoscale4 (2012) 1190–1199 ( abstract )30.Pan Li et al.,Effects of surface chemistry on the morphology transformation of ZnWO4 nanocrystals: investigated from experiment and theoretical calculations,CrystEngComm14 (2012) 920–928 ( abstract )31.Zhonghua Li et al.,Single crystal titanate-zirconate nanoleaf: Synthesis, growth mechanism and enhanced photocatalytic hydrogen evolution properties,CrystEngComm14 (2012) 1874–1880 ( abstract )32.Yonggang Wang et al.,Hydrothermal growths, optical features and first-principles calculations of sillenite-type crystals comprising discrete MO4 tetrahedra,CrystEngComm14 (2012) 1063–1068 ( abstract )33.Dajiang Mei et al.,LiGaGe2Se6: A New IR Nonlinear Optical Material with Low Melting Point,Inorganic Chemistry51 (2012) 1035–1040 ( abstract )34.Kai Feng et al.,NaGe3P3: a new ternary germanium phosphide featuring an unusual [Ge3P7] ring,Dalton Transactions41 (2012) 484–489 ( abstract )35.Su-Yun Zhang, Chun-Li Hu and Jiang-Gao Mao,New mixed metal selenites and tellurites containing Pd2+ ions in a square planar geometry, Dalton Transactions41 (2012) 2011–2017 ( abstract )36.Caixia Xu, Qian Li, Yunqing Liu, Jinping Wang, and Haoran Geng,Hierarchical Nanoporous PtFe Alloy with Multimodal Size Distributions and Its CatalyticPerformance toward Methanol Electrooxidation,Langmuir28 (2012) 1886–1892 ( abstract )37.Linjuan Zhang et al.,Lattice distortion and its role in the magnetic behavior of the Mn-doped ZnO system, New Journal of Physics14 (2012) 013033 ( abstract )38.Itziar Goikoetxea et al.,Non-adiabatic effects during the dissociative adsorption of O2 at Ag(111)? Afirst-principles divide and conquer study,New Journal of Physics14 (2012) 013050 ( abstract )39.Yongjun Zhou et al.,First-principles study on the catalytic role of Ag in the oxygen adsorption of LaMnO3(0 01) surface,Applied Surface Science258 (2012) 2602–2606 ( abstract )40.Jun Zhou et al.,Density functional theory study on oxygen adsorption in LaSrCoO4: An extended cathode material for solid oxide fuel cells,Applied Surface Science258 (2012) 3133–3138 ( abstract )41.Hui Zhao, Na Qin,The stability boundary of group-III transition metal diboride ScB2 (0 0 0 1) surfaces,Applied Surface Science258 (2012) 3328–3330 ( abstract )42.Qi-Jun Liu et al.,Structural and electronic properties of cubic SrHfO3 surface: First-principles calculations, Applied Surface Science258 (2012) 3455–3461 ( abstract )43.Baojun Wang, Luzhi Song, Riguang Zhang,The dehydrogenation of CH4 on Rh(1 1 1), Rh(1 1 0) and Rh(1 0 0) surfaces: A density functional theory study,Applied Surface Science258 (2012) 3714–3722 ( abstract )44.Li-Ming Yang, Ponniah Ravindran, Ponniah V ajeeston and Mats Tilset,Ab initio investigations on the crystal structure, formation enthalpy, electronic structure, chemical bonding, and optical properties of experimentally synthesized isoreticularmetal-organic framework-10 and its analogues: M-IRMOF-10 (M = Zn, Cd, Be, Mg, Ca, Sr and Ba),RSC Advances2 (2012) 1618–1631 ( abstract )45.Jiri Czernek, Tomasz Pawlak, Marek J. Potrzebowski,Benchmarks for the 13C NMR chemical shielding tensors in peptides in the solid state, Chemical Physics Letters527 (2012) 31–35 ( abstract )46.Min Li, Junying Zhang, Yue Zhang,First-principles calculation of compensated (2N, W) codoping impacts on band gapengineering in anatase TiO2,Chemical Physics Letters528 (2012) 63–66 ( abstract )47.X. P. Yang et al.,Preparation and XRD analyses of Na-doped ZnO nanorod arrays based on experiment and theory,Chemical Physics Letters528 (2012) 16–20 ( abstract )48.Feng Yuan et al.,Structure and hydrogen storage properties of the first rare-earth metal borohydrideammoniate: Y(BH4)3.4NH3,Journal of Materials Chemistry22 (2012) 1061–1068 ( abstract )49.Jiang Xu, Daohui Lai, ZongHan Xie, Paul Munroe and Zhong-Tao Jiang,A critical role for Al in regulating the corrosion resistance of nanocrystallineMo(Si1-x Al x)2 films,Journal of Materials Chemistry22 (2012) 2596–2606 ( abstract )50.Tae Hoon Noh et al.,Photophysical and Photocatalytic Properties of Zn3M2O8 (M = Nb, Ta),Journal of the American Ceramic Society95 (2012) 227–231 ( abstract )51.Y. H. Duan et al.,Elastic constants of AlB2-type compounds from first-principles calculations,Computational Materials Science51 (2012) 112–116 ( abstract )52.Bengt E. Tegner, Graeme J. Ackland,Pseudopotential errors in titanium,Computational Materials Science52 (2012) 2 6 ( abstract )53.D. Sen, R. Thapa, K. Bhattacharjee, K.K. Chattopadhyay,Site dependent metal adsorption on (3 ×3) h-BN monolayer: Stability, magnetic and optical properties,Computational Materials Science51 (2012) 165–171 ( abstract )54.M. G. Brik, C.-G. Ma,First-principles studies of the electronic and elastic properties of metal nitrides XN (X = Sc, Ti, V, Cr, Zr, Nb),Computational Materials Science51 (2012) 380–388 ( abstract )55.Mingjun Pang et al.,First-principles calculations on the crystal, electronic structures and elastic properties of Ag-rich γ' phase approximates in Al-Ag alloys,Computational Materials Science51 (2012) 415–421 ( abstract )56.Souraya Goumri-Said, Nawel Kanoun-Bouayed, Ali H. Reshak, Mohammed BenaliKanoun,On the electronic nature of silicon and germanium based oxynitrides and their related mechanical, optical and vibrational properties as obtained from DFT and DFPT,Computational Materials Science53 (2012) 158–168 ( abstract )57.K. Haddadi, A. Bouhemadou, S. Bin-Omran,Structural, elastic, electronic, chemical bonding and thermodynamic properties ofCaMg2N2 and SrMg2N2: First-principles calculations,Computational Materials Science53 (2012) 204–213 ( abstract )58.Huiyang Gou et al.,Origin of the rigidity in tetragonal MB (M = Cr, Mo and W) and softening of defective WB: First-principles investigations,Computational Materials Science53 (2012) 460–463 ( abstract )59.Haizhou Wang, Yongzhong Zhan, Mingjun Pang,The structure, elastic, electronic properties and Debye temperature of M2AlC (M=V, Nband Ta) under pressure from first-principles,Computational Materials Science54 (2012) 16–22 ( abstract )60.Hai-You Huang, Ming Wu,First principles calculations of hydrogen-induced decrease in the cohesive strength of α-Al2O3 single crystals,Computational Materials Science54 (2012) 81–83 ( abstract )61.Xinrui Cao, Yunsong Li, Xuan Cheng, Ying Zhang,First-principles studies of structural, electronic and optical properties of AB2 (A = Si, Ge and B = O, S) nanotubes,Computational Materials Science54 (2012) 84–90 ( abstract )62.Wei Zhou, Lijuan Liu, Mengying Yuan, Qinggong Song, Ping Wu,Electronic and optical properties of W-doped SnO2 from first-principles calculations,Computational Materials Science54 (2012) 109–114 ( abstract )63.A. Bouhemadou et al.,Theory study of structural parameters, elastic stiffness, electronic structures and lattice dynamics of RBRh3 (R = Sc, Y, La and Lu),Computational Materials Science54 (2012) 336–344 ( abstract )64.M. Romero, R. Escamilla,First-principles calculations of structural, elastic and electronic properties of Nb2SnC under pressure,Computational Materials Science55 (2012) 142–146 ( abstract )65.Benhua Luo, Xueye Wang, Y u Zhang, Yong Xia,First principle calculations for pressure induced structural phase transitions of Fe doped in SrMnO3,Computational Materials Science55 (2012) 199–204 ( abstract )66.Fanjie Kong, Yanhua Liu, Baolin Wang, Yanzong Wang, Lili Wang,Lattice dynamics of PbTe polymorphs from first principles,Computational Materials Science56 (2012) 18–24 ( abstract )67.Yong-Hui Zhang et al.,Tuning the magnetic and transport property of graphene with Ti atom and cluster,Computational Materials Science56 (2012) 95–99 ( abstract )68.Ch. Bheema Lingam, K. Ramesh Babu, Surya P. Tewari, G. Vaitheeswaran,Density functional study of electronic,bonding, and vibrational properties ofCa(NH2BH3)2,Journal of Computational Chemistry33 (2012) 987–997 ( abstract )69.Zhiwei Cui, Feng Gao, Zhihua Cui and Jianmin Qu,Developing a second nearest-neighbor modified embedded atom method interatomicpotential for lithium,Modelling and Simulation in Materials Science and Engineering20 (2012) 015014( abstract )70.Alexei Bosak et al.,New insights into the lattice dynamics of α-quartz,Zeitschrift fur Kristallographie227 (2012) 84–91 ( abstract )71.Zuocai Huang, Jing Feng, Wei Pan,Theoretical investigations of the physical properties of zircon-type YVO4,Journal of Solid State Chemistry185 (2012) 42–48 ( abstract )72.Dajiang Mei et al.,Synthesis, structure, and electronic structure of CsAgGa2Se4,Journal of Solid State Chemistry186 (2012) 54–57 ( abstract )73.Haimin Ding, Jinfeng Wang, Chunyan Li, Jinfeng Nie, Xiangfa Liu,Study of the surface segregation of carbon vacancies in TiC x,Solid State Communications152 (2012) 185–188 ( abstract )74.Mei Xia Xiao, Yong Fu Zhu, Qing Jiang,Improved electromigration reliability of Cu films by doping and interface engineering, Solid State Communications152 (2012) 210–214 ( abstract )75.R. Escamilla, M. Romero, F. Morales,Elastic properties, Debye temperature, density of states and electron-phonon coupling of ZrB12 under pressure,Solid State Communications152 (2012) 249–252 ( abstract )76.Yan Wang, Xi Zhang, Yanguang Nie, Chang Q. Sun,Under-coordinated atoms induced local strain, quantum trap depression and valencecharge polarization at W stepped surfaces,Physica B: Condensed Matter407 (2012) 49–53 ( abstract )77.Yingce Yan et al.,First-principle calculations of dilute nitride GaP1-x N x alloy in zinc-blende structures, Physica B: Condensed Matter407 (2012) 112–115 ( abstract )78.Jie Liu et al.,Influence of Ni and N on generalized stacking-fault energies in Fe-Cr-Ni alloy: A first principle study,Physica B: Condensed Matter407 (2012) 891–895 ( abstract )79.T. Chihi, M. Fatmi, B. Ghebouli,First-principles prediction of metastable niobium and tantalium nitrides M4N5 and M5N6 stoichiometry,Solid State Sciences14 (2012) 80–83 ( abstract )80.Lizhao Liu et al.,Amorphous structural models for graphene oxides,Carbon50 (2012) 1690–1698 ( abstract )81.Jingying Lu, Shang-Peng Gao, Jun Yuan,ELNES for boron, carbon, and nitrogen K-edges with different chemical environments in layered materials studied by density functional theory,ultramicroscopy112 (2012) 61–68 ( abstract )82.Tian Meng-kui, Shangguan Wen-feng,Photocatalytical water decomposition on visible light-driven solid-solution compounds K4Ce2Ta10-x Nb x O30 (x = 0-10),Materials Chemistry and Physics131 (2012) 569–574 ( abstract )83.M.G. Brik, A.M. Srivastava,First-principles calculations of structural, electronic, and elastic properties of MgZrSi2O7, Materials Chemistry and Physics132 (2012) 6–9 ( abstract )84.Maochang Liu, Yuanchang Du, Lijng Ma, Dengwei Jing, Liejin Guo,Manganese doped cadmium sulfide nanocrystal for hydrogen production from waterunder visible light,International Journal of Hydrogen Energy37 (2012) 730–736 ( abstract )85.Ying Lv, Zhian Zhang, Yanqing Lai, and Yexiang Liu,Electrodeposition of Porous Mg(OH)2 Thin Films Composed of Single-CrystalNanosheets,Journal of The Electrochemical Society159 (2012) D187–D189 ( abstract )86.Lu Peng-Fei et al.,Electronic Structure and Optical Properties of Antimony-Doped SnO2 from First-Principle Study,Communications in Theoretical Physics57 (2012) 145–150 ( abstract )87.Chuan-Hui Zhang, Qiong Ran, Jiang Shen,Structural stability of silicene-like nanotubes,Computer Physics Communications183 (2012) 30–33 ( abstract )88.A. Gray et al.,Mapping application performance to HPC architecture,Computer Physics Communications183 (2012) 520–529 ( abstract )89.Wei Li Cheah and Michael W. Finnis,Structure of multilayer ZrO2/SrTiO3,Journal of Materials Science47 (2012) 1631–1640 ( abstract )90.Qi-Jun Liu, Zheng-Tang Liu, Qian-Qian Gao, Li-Ping Feng and Hao Tian,The doping effect of N substituting for different atoms in orthorhombic SrHfO3,Journal of Materials Science47 (2012) 3046–3051 ( abstract )91.A. Yangthaisong,Electronic and Lattice Vibrational Properties of Cubic SrHfO3 from First-PrinciplesCalculations,Journal of Electronic Materials41 (2012) 535–539 ( abstract )92.M. J. Phasha, P. E. Ngoepe,An alternative DFT-based model for calculating structural and elastic properties ofrandom binary HCP, FCC and BCC alloys: Mg-Li system as test case,Intermetallics21 (2012) 88–96 ( abstract )93.Teruyasu Mizoguchi, Katsuyuki Matsunaga, Eita Tochigi, Yuichi Ikuhara,First principles pseudopotential calculation of electron energy loss near edge structures of lattice imperfections,Micron43 (2012) 37–42 ( abstract )94.D.G. McCulloch, D.W.M. Lau, R.J. Nicholls, J.M. Perkins,The near edge structure of cubic boron nitride,Micron43 (2012) 43–48 ( abstract )95.Masataka Hakamada, Fumi Hirashima, Kota Kajikawa and Mamoru Mabuchi,Magnetism of fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt,Applied Physics A106 (2012) 237–244 ( abstract )96.Xing Ming et al.,First-principles study of pressure-induced magnetic transition in siderite FeCO3,Journal of Alloys and Compounds510 (2012) L1–L4 ( abstract )97.Tingting Tan, Zhengtang Liu, Yanyan Li,First-principles calculations of electronic and optical properties of Ti-doped monoclinic HfO2,Journal of Alloys and Compounds510 (2012) 78–82 ( abstract )98.Yongzhong Zhan, Mingjun Pang, Haizhou Wang, Yong Du,The structural, electronic, elastic and optical properties of AlCu(Se1-x Te x)2 compounds from first-principle calculations,Current Applied Physics12 (2012) 373–379 ( abstract )99.Mingjun Pang, Yongzhong Zhan, Haizhou Wang,Ab initio investigation into the structural, electronic and elastic properties of AlCu2TM (TM = Ti, Zr and Hf) ternary compounds,Current Applied Physics12 (2012) 957–962 ( abstract )100.N. Mazumder, A. Bharati, S. Saha, D. Sen, K.K. Chattopadhyay,Effect of Mg doping on the electrical properties of SnO2 nanoparticles,Current Applied Physics12 (2012) 975–982 ( abstract )101.Hongchen Du, Guixiang Wang, Xuedong Gong, Heming Xiao,Theoretical study on the adduct of chlorine trifluoride oxide and borontrifluoride-molecular and crystal structures, vibrational spectrum, and thermodynamic properties,International Journal of Quantum Chemistry112 (2012) 1291–1298 ( abstract )102.Wenlin Zhang, Xiaoqing Wang, Guangqiu Shen, Dezhong Shen,Top-seeded growth, optical properties and theoretical studies of noncentrosymmetricTe2V2O9,Crystal Research and Technology47 (2012) 163–168 ( abstract )103.Baodan Liu et al.,Microstructure and cathodoluminescence study of GaN nanowires without/with P-doping, Crystal Research and Technology47 (2012) 207–212 ( abstract )104.Peter A. Tanner, Guohua Jia, Bing-Ming Cheng, Mikhail G. Brik,Analysis of spectra of neat and lanthanide ion-doped KPb2Cl5 excited by synchrotron radiation,physica status solidi (b)249 (2012) 581–5872 ( abstract )105.A. Trejo, A. Miranda, L. Nino de Rivera, A. Daaz-Mendez, M. Cruz-Irisson, Phonon optical modes and electronic properties in diamond nanowires,Microelectronic Engineering90 (2012) 92–95 ( abstract )106.A. Trejo, J.L. Cuevas, R. Vazquez-Medina, M. Cruz-Irisson,Phonon band structure of porous Ge from ab initio supercell calculation,Microelectronic Engineering90 (2012) 141–144 ( abstract )107.Minoru Osada and Takayoshi Sasaki,A- and B-Site Modified Perovskite Nanosheets and Their Integrations into High-kDielectric Thin Films,International Journal of Applied Ceramic Technology9 (2012) 29–36 ( abstract ) 108.D.L. Geatches, S.J. Clark, H.C. Greenwell,Iron reduction in nontronite-type clay minerals: Modelling a complex system,Geochimica et Cosmochimica Acta81 (2012) 13–27 ( abstract )109.Ting-Feng Yi et al.,Stabilities and electronic properties of lithium titanium oxide anode material for lithium ion battery,Journal of Power Sources198 (2012) 318–321 ( abstract )110.Wenjing Tang, Dechun Li, Shengzhi Zhao, Guiqiu Li and Kejian Yang, First principle study of the elastic properties of InGaAs with different dopingconcentrations of indium,Molecular Simulation38 (2012) 84–89 ( abstract )111.C. L. Zhang et al.,First principles study on mechanical properties of Mg-MgCd interface micro-zone,Molecular Simulation38 (2012) 200–203 ( abstract )112.Mengkui Tian, Wenfeng Shangguan, Wenliang Tao,The photocatalytical activities for water decomposition of K4R2M10O30 (R = Y, La, Ce, Nd, Sm; M = Ta, Nb) and their photophysical properties based on the first principlecalculation,Journal of Molecular Catalysis A: Chemical352 (2012) 95–101 ( abstract )113.Manuel Ramos, Gilles Berhault, Domingo A. Ferrer, Brenda Torres and Russell R.Chianelli,HRTEM and molecular modeling of the MoS2-Co9S8 interface: understanding thepromotion effect in bulk HDS catalysts,Catalysis Science & Technology2 (2012) 164–178 ( abstract )114.Wei Huang, Lulu Sun, Peide Han, Jinzhen Zhao,CH4 dissociation on Co(0001): A density functional theory study,Journal of Natural Gas Chemistry21 (2012) 98–103 ( abstract )115.Lu Yong-Fang, Shi Li-Qun, Ding Wei and Long Xing-Gui,First-Principles Study of Hydrogen Impact on the Formation and Migration of Helium Interstitial Defects in hcp Titanium,Chinese Physics Letters29 (2012) 013102 ( abstract )116.Sun Hong-Guo, Zhou Zhong-Xiang, Yuan Cheng-Xun, Yang Wen-Long and Wang He, Structural, Electronic and Optical Properties of KTa0.5Nb0.5O3 Surface: A First-Principles Study,Chinese Physics Letters29 (2012) 017303 ( abstract )117.Yang Ping et al.,Uniaxial stress influence on lattice, band gap and optical properties of n-type ZnO:first-principles calculations,Chinese Physics B21 (2012) 016803 ( abstract )118.Niu Wen-Xia and Zhang Hong,Ar adsorptions on Al (111) and Ir (111) surfaces: a first-principles study,Chinese Physics B21 (2012) 026802 ( abstract )119.Ye-Yu Li et al.,Synthesis, Crystal and Electronic Structures of Ba3ZnSb2O9 with the 6H-perovskite-type Structure,Chinese Journal of Structural Chemistry31 (2012) 73–78 ( abstract )120.Wang Li, Fang Li-hong, Gong Jian-hong,First-principles study of TiC(110) surface,Transactions of Nonferrous Metals Society of China22 (2012) 170–174 ( abstract )。

K.M.Shen for helpful discussions and communications.Experimental studies were supported by the Center for Emergent Superconductivity,an Energy Frontier Research Center,headquartered at Brookhaven National Laboratory (BNL)and funded by the U.S.Department of Energy under grant DE-2009-BNL-PM015,as well as by a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan)and the Global Centers of Excellence Program for Japan Society for the Promotion of Science.C.K.K.acknowledges support from the FlucTeam program at BNL under contractDE-AC02-98CH10886.J.L.acknowledges support from the Institute for Basic Science,Korea.I.A.F.acknowledges support from Fundação para a Ciência e a Tecnologia,Portugal,under fellowship number SFRH/BD/60952/2009.S.M.acknowledges support from NSF grant DMR-1120296to the Cornell Center for Materials Research.Theoretical studies at Cornell University were supported by NSF grant DMR-1120296to CornellCenter for Materials Research and by NSF grant DMR-0955822.The original data are archived by Davis Group,BNL,and Cornell University.Supplementary Materials/content/344/6184/612/suppl/DC1Materials and Methods Supplementary Text Figs.S1to S9References (42–45)Movies S1and S221November 2013;accepted 20March 201410.1126/science.1248783Direct,Nonoxidative Conversion of Methane to Ethylene,Aromatics,and HydrogenXiaoguang Guo,1Guangzong Fang,1Gang Li,2,3Hao Ma,1Hongjun Fan,2Liang Yu,1Chao Ma,4Xing Wu,5Dehui Deng,1Mingming Wei,1Dali Tan,1Rui Si,6Shuo Zhang,6Jianqi Li,4Litao Sun,5Zichao Tang,2Xiulian Pan,1Xinhe Bao 1*The efficient use of natural gas will require catalysts that can activate the first C –H bond ofmethane while suppressing complete dehydrogenation and avoiding overoxidation.We report that single iron sites embedded in a silica matrix enable direct,nonoxidative conversion ofmethane,exclusively to ethylene and aromatics.The reaction is initiated by catalytic generation of methyl radicals,followed by a series of gas-phase reactions.The absence of adjacent iron sites prevents catalytic C-C coupling,further oligomerization,and hence,coke deposition.At 1363kelvin,methane conversion reached a maximum at 48.1%and ethylene selectivity peaked at 48.4%,whereas the total hydrocarbon selectivity exceeded 99%,representing an atom-economical transformation process of methane.The lattice-confined single iron sites delivered stable performance,with no deactivation observed during a 60-hour test.The challenge of converting natural gas into transportable fuels and chemicals (1)has been spurred by several emerging indus-trial trends,including rapidly rising demand for H 2(for upgrading lower-quality oils)and a global shortage of aromatics caused by shifting refinery targets toward gasoline.Light olefins,which are key chemical feedstocks,are currently made from methanol,which itself is made through multistage catalytic transformations via syngas (a mixture of H 2and CO)(2,3),although there is also ongoing research to convert syngas directly to light olefins (4,5).However,in all such approaches,either CO or H 2is needed to remove oxygen from CO,result-ing in a carbon-atom utilization efficiency below 50%.Despite their low efficiency,high capital and production costs,and enormous CO 2emissions,syngas routes dominate current and near-term in-dustrial practices for natural gas conversion (6,7).Direct conversion of CH 4is potentially more economical and environmentally friendly but is challenging because CH 4exhibits high C –H bond strength (434kJ/mol),negligible electron affinity,large ionization energy,and low polarizability (8).In the pioneering work of Keller and Bhasin in the early 1980s,CH 4was activated with the assistance of oxygen (9).This finding initiated a worldwide research surge to explore the high-temperature (>1073K)oxidative coupling of methane (OCM)to C 2hydrocarbons (10,11).Hundreds of catalytic materials have since been synthesized and tested,principally during the 1990s,as well as in recent years.Unfortunately,the presence of O 2leads irreversibly to overoxidation,resulting in a large amount of the thermodynamically stable end-products CO 2and H 2O.Thus,the carbon utili-zation efficiency of OCM remains relatively low (12,13).Slow progress in discovering new cata-lysts to circumvent this problem has hindered further development,and no economically viable process has been put into practice so far.In a recent report,elemental sulfur was used as a softer oxidant than O 2(14):For a 5%CH 4/Ar mixture at 1323K,the best catalyst,PdS/ZrO 2,gave a CH 4conversion of ~16%and ethylene selectivity near 20%,albeit at the expense of the by-products CS 2and H 2S (14).In contrast,the bifunctional catalysts based on Mo/zeolites cata-lyze CH 4conversion to aromatics (benzene andnaphthalene)nonoxidatively,thereby avoiding CO 2formation (15–18).CH 4is activated on the metal sites forming CH x species,which dimerize to C 2H y .Subsequent oligomerization on the acidic sites located inside the zeolite pores yields ben-zene and naphthalene,as well as copious amounts of coke (19–21).Commercial prospects for this process are further hampered by the instability of zeolites at the very high reaction temperatures.To achieve direct conversion of CH 4efficient-ly,the challenges lie in cleaving the first C –H bond while suppressing further catalytic dehy-drogenation,avoiding both CO 2generation and coke deposition.We report that these conditions can be met using lattice-confined single iron sites embedded in a silica matrix.These sites activate CH 4in the absence of oxidants,generating methyl radicals,which desorb from the catalyst surface and then undergo a series of gas-phase reactions to yield ethylene,benzene,and naphthalene as the only products (with ethylene dominating at short space-times for a selectivity of ~52.7%at 1293K).A methane conversion as high as 48.1%is achieved at 1363K.The catalysts were obtained by fusing ferrous metasilicate with SiO 2at 1973K in air and from commercial quartz,followed by leaching with aqueous HNO 3and drying at 353K (22).The resulting catalyst was designated 0.5%Fe©SiO 2(©denotes confinement and here represents a cat-alyst characterized by the lattice-confined single iron sites embedded within a silica matrix).It con-tained 0.5weight percent (wt %)Fe and had a Brunauer –Emmett –Teller surface area of <1m 2/g.The catalyst was activated in a fixed-bed micro-reactor in the reaction atmosphere [90volume percent (vol %)CH 4/N 2]at 1173K.The efflu-ent was analyzed by online gas chromatography (GC).At 1223K,CH 4conversion was 8.1%(Fig.1A)and increased with temperature,exceeding 48.1%at 1363K (Fig.1B).Only ethylene,ben-zene,and naphthalene were produced;neither coke nor CO 2was detected,despite the relative-ly high reaction temperature.A single-pass yield of 48%hydrocarbons is achieved at 1363K and 21.4liters per gram of catalyst (gcat)per hour.Selectivities vary from 40.9to 52.1%for ethylene,21.0to 29.1for benzene,and 23.6to 38.2%for naphthalene,over the investigated temperature range (1223to 1363K).By comparison,a blank experiment (an empty reactor with no catalyst)under the same conditions showed a CH 4conversion of only 2.5%,and 95%of the product was coke (Fig.1A).A test with unmodified SiO 2as the catalyst yielded virtually1State Key Laboratory of Catalysis,Dalian Institute of Chemical Physics,Chinese Academy of Sciences,Dalian 116023,Peo-ple ’s Republic of China.2State Key Laboratory of Molecular Reaction Dynamics,Dalian Institute of Chemical Physics,Chinese Academy of Sciences,Dalian 116023,People ’s Republic of China.3State Key Laboratory of Fine Chemicals,Institute of Coal Chemical Engineering,School of Chemical Engineering,Dalian University of Technology,Dalian 116012,People ’s Republic of China.4Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,People ’s Republic of China.5Nano-Pico Center,Key Laboratory of Micro-Electro-Mechanical System (MEMS)of Ministry of Education,Southeast University,Nanjing 210096,People ’s Republic of China.6Shanghai Synchrotron Radiation Facility,Shanghai Institute of Applied Physics,Chinese Academy of Sciences,Shanghai 201204,People ’s Republic of China.*Corresponding author.E-mail:xhbao@9MAY 2014VOL 344SCIENCE616REPORTSo n J u l y 12, 2016h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o mthe same result (table S1)(22).Most notably,the use of 0.5wt %Fe/SiO 2as the catalyst (prepared with wet impregnation on amorphous SiO 2with a high surface area,348m 2/g)(22)also led to high coke formation (>98%).We have varied the iron loadings,support materials,and preparation methods,which unfortunately do not preclude coke on iron nanoparticles (NPs).For example,coke remained the principal product (>50%)over 0.5%Fe/ZSM.0.8%Fe/SiO 2prepared by sol-gel method and 0.2%Fe/SiC (22)enhanced selective formation of hydrocarbons to some extent,but still with a considerable amount of coke (Fig.1A).Figure S1(22)demonstrates that the reac-tivity of 0.5%Fe©SiO 2was very reproducible.All mass balances are above 99%.At 1363K,the space-time yields for ethylene,benzene,and naphthalene were 91,18,and 9mol kgcat –1hour –1,respectively.Moreover,the process represents a new and sustainable approach to H 2production because the by-products are high –value-added hydrocarbons (ethylene and aromatics)instead of coke and CO 2(23,24).The yield of H 2varies with the reaction conditions,and the concentra-tions in the effluent range from 10.9to 51.2%(fig.1D)(22).Furthermore,the 0.5%Fe©SiO 2catalyst was very stable,and no deactivation was observedduring a 60-hour test at 1293K (Fig.1C).Meth-ane conversion remained at ~32%throughout this long run.Selectivities to ethylene (52.7%),benzene (21.5%),and naphthalene (25.8%)were constant,and the total selectivity to these pro-ducts remained >99%.The combination of atom-economy,high selectivity,and high conversion is notable,considering the rather low loading of Fe (0.5wt %)and very low surface area (<1m 2/g)of the SiO 2.Although noncatalytic pyrolysis of CH 4has been extensively studied for light hydrocarbon synthesis,the product is dominated with acetylene accompanied by high coke formation (25–27).By comparison,the catalytically initiated reaction de-scribed here compares very favorably with other reported direct-conversion processes,including pyrolysis,OCM (13),and nonoxidative aromati-zation (21).Finally,because natural gas usually contains some ethane,we added 1and 5vol %ethane to the reactant stream.The presence of ethane substantially enhanced methane conver-sion (fig.S2)(22),and ethane is almost completely converted,although a small amount of coke is formed at 1173K and a space velocity of 4.84liter gcat –1h –1.The unprecedented efficiency of the catalyt-ically initiated CH 4conversion process is attri-buted to the high activity of the coordinativelyunsaturated iron sites toward the C-H bond of CH 4(28,29).The isolated nature of these sites,as evidenced by sub-angstrom –resolution high-angle annular-dark field (HAADF)scanning transmis-sion electron microscopy (STEM)and in situ x-ray absorption near-edge spectroscopy (XANES),pre-cludes surface C-C coupling and,hence,coke formation.Transmission electron microscopy in-dicates that in the fresh 0.5%Fe©SiO 2catalyst,iron oxide NPs with a size of ~3to 4nm are distributed homogeneously throughout the SiO 2matrix (fig.S3)(22).A STEM-HAADF image of the catalyst after reaction reveals many bright dots of atomic size scattered across the SiO 2matrix,highlighted by the red circles in Fig.2A.Each dot represents an individual Fe atom,con-sidering the much lower contrast of Si and O in the HAADF image.This result suggests that the iron species are redistributed from the original oxide NPs to isolated atoms during catalyst activation.This hypothesis is validated by the in situ XANES during activation.The near-edge spec-trum of the catalyst is similar to that of Fe foil (Fig.2B).In Fig.2C,the Fourier-transformed k 3-weighted c (k )function (where k is wave number)(30)shows that,after activation,the Fe-O scattering paths apparent in the spectrum of the fresh catalyst (line 1)havedisappeared,Fig.1.Reaction performance.(A )Comparison of different catalysts at 1223K and 4.84liter gcat –1hour –1.(B )Effect of reaction temperatures and space velocities on the 0.5%Fe©SiO 2catalyst.Blue circles denote CH 4con-version,whereas bars represent product selectivities.(C )Long-term stabilitytest of 0.5%Fe©SiO 2at 1293K and 14.5liter gcat –1hour –1.(D )(Top)Hydrogen contents of the reactor effluent (open circles)and the calculated values (solid circles);(bottom)H 2peaks in GC analysis normalized by the internal standard N 2(22).a.u.,arbitrary units.SCIENCE VOL 3449MAY 2014617REPORTSo n J u l y 12, 2016h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o mwhereas new scattering paths appear (line 2).They are assigned to Fe-C and Fe-Si paths,by comparison to the spectra of reference materials such as Fe 2O 3,FeSi 2,and iron carbides (31).In the presence of CH 4above 1173K,iron oxide species in the fresh 0.5%Fe©SiO 2interact ex-tensively with the support,becoming embed-ded in the silica matrix through bonding to Si and C atoms.Thus,these otherwise extremely reactive,coordinatively unsaturated iron atoms are stabilized and persist under the very harsh reaction conditions.No aggregation was observed,even after prolonged reaction for 60hours.In contrast,the 2-to 5-nm-sized iron NPs in 0.5%Fe/SiO 2(fig.S5a)(22)after activation un-der the same conditions exhibit only a Fe –Fe bond (line 3in Fig.2,B and C).This result explains the extensive carbon deposition observed for 0.5%Fe/SiO 2,considering that iron NPs are widely used for the synthesis of carbon nanotubes (32).That process involves catalytic cleavage of C –H bonds and dissolution of carbon species into the iron lattice.Subsequent C-C coupling on an iron NP surface and crystallization from the super-saturated carbide solid solution drive the growth of nanotubes (33).However,under the harsh re-action conditions in the current reaction,0.5%Fe/SiO 2deactivates very rapidly,and iron NPs aggregated and grew to 20to 30nm after reaction (fig.S4b)(22).These results again highlight the crucial role played by the site isolation of the iron species in 0.5%Fe©SiO 2in achieving high sel-ectivity toward hydrocarbons and preventing coke formation.Furthermore,density functional theory (DFT)calculations suggest that the most stable struc-ture in the reactive atmosphere is an iron atom coordinated by one Si and two C atoms and is thus embedded within the SiO 2matrix,as de-picted in Fig.3A and fig.S5.The calculated Fe –C and Fe –Si bond lengths are 1.6and 2.4Å,respec-tively,which are consistent with those estimated from extended x-ray absorption fine structure (EXAFS)(table S2)(22).This lattice-confined single iron site initiates CH 4dehydrogenation by generating a •CH 3radical,which subsequently releases from the surface with an energy barrier of 2.32eV instead of undergoing further dehydro-genation or C-C coupling (fig.S5)(22).The Fe site is then exposed and becomes active for adsorp-tion of a second methane molecule and release of another methyl radical,with energy barriers of 3.07and 2.19eV ,respectively (Fig.3A).Migra-tion of H from C in Fe-C-Si sites to Fe involves a barrier of 0.58eV .The resulting surface H species desorbs as H 2with an energy barrier of 1.61eV .The intermediacy of methyl radicals was verified by online vacuum ultraviolet soft photoioni-zation molecular-beam mass spectrometry (VUV-SPI-MBMS)(fig.S6)(22).Molecules were ionized with a 10.6-eV VUV lamp,which has an energy lower than the CH 4ionization energy (12.6eV).This allows detection of intermediate radicals and products (34,35).Figure 3B and its inset display all species detected at 1193K.Methyl radicals,represented by the signal at mass/charge ratio (m /z )=15,are clearly observed.Additional sig-nals at m /z =28,40,42,78,92,and 128are assigned to ethylene (C 2H 4),propyne or propadiene (C 3H 4),propylene (C 3H 6),benzene (C 6H 6),toluene (C 7H 8),and naphthalene (C 10H 8),respectively.To further elucidate the mechanism,the reac-tion profile of methyl radicals at 1225K was sim-ulated with DFT (Fig.3C and fig.S7)(22).Two •CH 3radicals combine to form C 2H 6via a strongly exothermic process.C 2H 6undergoes dehydrogen-ation readily,giving C 2H 4and H atoms with an energy barrier of 1.58eV .By abstraction of H from C 2H 4,the resulting •C 2H 3radical tends to react with additional C 2H 4molecules.Further de-hydrogenation and cyclization leads to benzene,with an energy barrier of 2.85eV .C 6H 6is also readily dehydrogenated by •H and,after further chain growth and cyclization,yields the thermody-namically more stable naphthalene.The low bar-rier for transformation of C 2H 6to C 2H 4explains the absence of C 2H 6among the experimentally observed products under steady-state reaction con-ditions,whereas the thermodynamically more stable hydrocarbons C 2H 4,C 6H 6,and C 10H 8ac-cumulated and were detected.At equilibrium at 1225K and atmospheric pressure,the yields of C 2H 4,C 6H 6,and C 10H 8from CH 4were estimated to be 9.0,34.0,and 57.0%(22),respectively.The relative ratios of these products could be manipulated by changing the reaction conditions.For example,increasing the CH 4flow rate in the VUV-SPI-MBMS re-actor favors formation of C 2H 4(Fig.3D),whereas lower flow rates (corresponding to longer resi-dence times)promote cyclization of intermediates leading to aromatics,which are consistent with the GC analysis obtained in the microreactor.These results lend further support to the hypothesis that the reaction is initiated by the catalytic generation of methyl radicals,which subsequently undergo a series of gas-phase reactions.Thus,the conversion efficiency is high,despite the very limited number of surface iron sites and the extremely low surface area of the catalyst.Heterogeneous systems for CH 4activation gen-erally still suffer from poor carbon utilization,caused in part by low selectivity.Here,we dem-onstrate an atom-economical direct CH 4conver-sion process,enabled by the lattice-confined single iron sites embedded within a silica matrix,which activate CH 4and generate methyl radicals.A conversion as high as 48.1%was obtained at 1363K and a space velocity of 21.4liter gcat –1hour –1,with a selectivity to C 2H 4of >48.4%(the re-mainder being aromatics).No deactivation was observed even after reaction for 60hours,and the total carbon selectivity to the three products re-mained >99%.Although the dehydrogenation itself is endothermic,high selectivity to ethylene in this process substantially reduces the heat input (estimated to be about half that of a typical thermal pyrolysis process with dominating acet-ylene in product),as shown in table S3(22).These findings open up new possibilities for fundamental studies of direct,nonoxidative activation of CH 4.Fig.2.Structural features of 0.5%Fe©SiO 2.(A )STEM-HAADF image of the catalyst after reaction,with the inset showing the computational model of the single iron atom bonded to two C atoms and one Si atom within silica matrix.(B )In situ XANES upon activation and (C )Fourier transformed (FT)k 3-weighted c (k )-function of the EXAFS spectra.Solid lines denote reference samples of Fe foil,FeSi 2,and Fe 2O 3.Line 1denotes the fresh 0.5%Fe©SiO 2.Line 2stands for 0.5%Fe©SiO 2and line 3for 0.5%Fe/SiO 2upon activation in 10%CH 4/N 2at 1173K for 2hours,respectively.R(Å),distance in angstroms.9MAY 2014VOL 344SCIENCE618REPORTSo n J u l y 12, 2016h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o mIt is anticipated that combining a catalyst such as this one with an efficient reactor technology may enable the development of non –syngas-based routes to transform light hydrocarbons into high –value-added chemicals.References and Notes/lab/ACC-US-chemical-investment-linked-to-shale-gas-reaches-$100-billion_58946.html.2.J.Li et al .,J.Am.Chem.Soc.134,836–839(2012).3.F.Diederich,Angew.Chem.Int.Ed.52,6–7(2013).4.H.M.T.Galvis et al .,J.Am.Chem.Soc.134,16207–16215(2012).5.H.M.Torres Galvis et al .,Science 335,835–838(2012).6.Note that the construction of two megascale methanol plants in the U.S.Pacific Northwest was recentlyannounced to supply olefin feedstocks to Dalian,/lab/Chinese-group-plans-two-mega-methanol-plants-in-USPacific-Northwest-to-supply-olefins-feedstock_58289.html.rkins,A.Z.Khan,Aust.J.Chem.42,1655–1670(1989).9.G.E.Keller,M.M.Bhasin,J.Catal.73,9–19(1982).10.H.Arakawa et al .,Chem.Rev.101,953–996(2001).11.J.H.Lunsford,Angew.Chem.Int.Ed.Engl.34,970–980(1995).12.S.Arndt et al .,Catal.Rev.Sci.Eng.53,424–514(2011).13.U.Zavyalova,M.Holena,R.Schlögl,M.Baerns,ChemCatChem 3,1935–1947(2011).14.Q.Zhu et al .,Nat.Chem.5,104–109(2013).15.L.S.Wang et al .,Catal.Lett.21,35–41(1993).16.B.M.Weckhuysen,D.J.Wang,M.P.Rosynek,J.H.Lunsford,J.Catal.175,338–346(1998).17.R.W.Borry,Y.H.Kim,A.Huffsmith,J.A.Reimer,E.Iglesia,J.Phys.Chem.B 103,5787–5796(1999).18.D.J.Wang,J.H.Lunsford,M.P.Rosynek,J.Catal.169,347–358(1997).19.D.Ma et al .,J.Catal.208,260–269(2002).20.R.Ohnishi,S.T.Liu,Q.Dong,L.Wang,M.Ichikawa,J.Catal.182,92–103(1999).21.S.Ma,X.Guo,L.Zhao,S.Scott,X.Bao,J.Energy Chem.22,1–20(2013).22.Supplementary materials are available on Science Online.23.T.V.Choudhary,C.Sivadinarayana,C.C.Chusuei,A.Klinghoffer,D.W.Goodman,J.Catal.199,9–18(2001).24.M.A.Ermakova,D.Y.Ermakov,A.L.Chuvilin,G.G.Kuvshinov,J.Catal.201,183–197(2001).25.A.Beloqui Redondo,E.Troussard,J.A.van Bokhoven,Fuel Process.Technol.104,265–270(2012).26.A.Holmen,O.Olsvik,O.A.Rokstad,Fuel Process.Technol.42,249–267(1995).27.G.P.Van Der Zwet,P.A.J.M.Hendriks,R.A.Van Santen,Catal.Today 4,365–369(1989).28.H.Schwarz,Angew.Chem.Int.Ed.50,10096–10115(2011).29.E.W.McFarland,H.Metiu,Chem.Rev.113,4391–4427(2013).30.B.Qiao et al .,Nat.Chem.3,634–641(2011).31.E.de Smit,A.M.Beale,S.Nikitenko,B.M.Weckhuysen,J.Catal.262,244–256(2009).32.R.C.Che,L.M.Peng,X.F.Duan,Q.Chen,X.L.Liang,Adv.Mater.16,401–405(2004).33.X.Pan et al .,Nat.Mater.6,507–511(2007).34.Z.Zhou,H.Guo,F.Qi,Trends Analyt.Chem.30,1400–1409(2011).35.L.Luo et al .,Sci.Rep.3,1625(2013).Acknowledgments:This work was financially supported by the “Strategic Priority Research Program ”of the Chinese Academy of Sciences (grant XDA09030101),the National Natural Science Foundation of China (grants 21321002,11079005,21033009,and 21103181),and the Ministry of Science and Technology of China (grants 2011CBA00503and 2013CB933100).We thank S.L.Scott and H.Metiu for fruitful discussion.An international patent application under the Patent Cooperation Treaty is pending (PCT/CN2013/079977).Supplementary Materials/content/344/6184/616/suppl/DC1Materials and Methods Figs.S1to S7Tables S1to S3References (36–66)10March 2014;accepted 15April 201410.1126/science.1253150Fig.3.Investigation of the reaction mechanism over 0.5%Fe©SiO 2.(A )DFT calculations on catalytic generation of methyl radicals at 1223K.(B )Species in the reactor effluent at 1193K,detected by VUV-SPI-MBMS.amu,atomic mass units.(C )DFT simulated reaction profile of methyl radicals in the gas phase at 1225K.D G,Gibbs free energy.(D )Relative intensity of VUV-SPI-MBMS signals of major products as a function of CH 4flow rate at 1223K. SCIENCE VOL 3449MAY 2014619REPORTSo n J u l y 12, 2016h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o m(6184), 616-619. [doi: 10.1126/science.1253150]344Science Pan and Xinhe Bao (May 8, 2014)Tan, Rui Si, Shuo Zhang, Jianqi Li, Litao Sun, Zichao Tang, Xiulian Liang Yu, Chao Ma, Xing Wu, Dehui Deng, Mingming Wei, Dali Xiaoguang Guo, Guangzong Fang, Gang Li, Hao Ma, Hongjun Fan,Aromatics, and HydrogenDirect, Nonoxidative Conversion of Methane to Ethylene,Editor's Summaryavoided surface reactions between the radicals that would deposit solid carbon.in the gas phase to form ethylene and aromatics along with hydrogen. The isolation of the active sites exposes methane to isolated iron sites on a silica catalyst. Methyl radicals were generated and coupled (p. 616) report a high-temperature nonoxidative route that et al.Guo tend to overoxidize the products. provide chemical feedstocks. However, the reaction conditions needed to activate the strong C-H bond Direct routes to converting methane to higher hydrocarbons can allow natural gas to be used to Upgrading Methane Sans OxygenThis copy is for your personal, non-commercial use only.Article Tools/content/344/6184/616article tools:Visit the online version of this article to access the personalization and Permissions/about/permissions.dtlObtain information about reproducing this article: is a registered trademark of AAAS.Science Advancement of Science; all rights reserved. The title Avenue NW, Washington, DC 20005. Copyright 2016 by the American Association for thein December, by the American Association for the Advancement of Science, 1200 New York (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week Science o n J u l y 12, 2016h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o m。