Index Theorems on Torsional Geometries
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欧几里得几何推理英文Euclidean Geometry ReasoningGeometry has been a fundamental branch of mathematics since ancient times, and Euclidean geometry, named after the renowned Greek mathematician Euclid, has played a pivotal role in its development. Euclid's work, compiled in his seminal text "Elements," laid the foundation for our understanding of the properties and relationships of geometric shapes and their behavior in a two-dimensional plane.At the heart of Euclidean geometry lies the concept of axioms, which are self-evident truths that serve as the starting point for logical deductions. These axioms, combined with a set of postulates, form the basis for the construction of a coherent and consistent system of geometric principles. From these fundamental building blocks, Euclid and his successors were able to derive a vast array of theorems and proofs that have stood the test of time and remain integral to our understanding of the physical world.One of the most fundamental principles in Euclidean geometry is the concept of congruence. Two geometric figures are said to becongruent if they have the same size and shape, and can be superimposed on one another without any distortion. This idea of congruence is essential in many areas of geometry, from the construction of triangles and quadrilaterals to the study of transformations and symmetry.Another key concept in Euclidean geometry is the notion of parallel lines. Parallel lines are those that never intersect, no matter how far they are extended. Euclid's fifth postulate, often referred to as the parallel postulate, states that given a line and a point not on that line, there exists a unique line passing through the point that is parallel to the original line. This seemingly simple yet profound statement has been the subject of much debate and exploration throughout the history of mathematics.The study of triangles is a fundamental aspect of Euclidean geometry, and many of the theorems and proofs within this field revolve around the properties and relationships of these three-sided figures. From the Pythagorean theorem, which relates the lengths of the sides of a right triangle, to the various congruence and similarity criteria, the study of triangles has provided a rich tapestry of geometric understanding.Quadrilaterals, too, play a crucial role in Euclidean geometry. The classification and properties of these four-sided figures, such asrectangles, squares, rhombi, and trapezoids, have led to a deeper understanding of the underlying symmetries and relationships within the geometric plane.Beyond the study of individual shapes, Euclidean geometry also explores the concept of transformations, which are the various ways in which a figure can be moved, rotated, or scaled without altering its essential properties. These transformations, such as translations, reflections, and rotations, have important applications in fields ranging from art and design to computer graphics and engineering.The elegance and logical rigor of Euclidean geometry have made it a cornerstone of mathematical education and a powerful tool for problem-solving and reasoning. Its principles have been applied in a wide range of disciplines, from architecture and engineering to physics and astronomy. Moreover, the study of Euclidean geometry has paved the way for the development of more advanced geometric systems, such as non-Euclidean geometries, which have expanded our understanding of the nature of space and the universe.In conclusion, Euclidean geometry, with its foundational axioms, theorems, and proofs, remains a vital and dynamic field of study. Its ability to provide a coherent and logical framework for understanding the properties and relationships of geometric shapes has made it an enduring and essential component of mathematicaleducation and research. As we continue to explore the depths of this ancient discipline, we uncover new insights and applications that deepen our appreciation for the beauty and power of geometric reasoning.。
Industrial Construction Vol.40,No.7,2010工业建筑2010年第40卷第7期75海港码头混凝土表面氯离子随高度变化规律*胡狄赵羽习龚奇鹤金伟良(浙江大学土木工程学院,杭州310029)摘要:海水中氯离子的侵蚀是影响钢筋混凝土结构在海洋环境中耐久性的一个重要的因素,而混凝土表面氯离子浓度是研究氯离子侵蚀的重要指标之一。
由于混凝土结构沿海拔不同高度的服役环境不同,表面氯离子浓度随高程是变化的,但其分布存在一定的规律。
根据浙江东部沿海地区某混凝土码头结构表面氯离子浓度的实测数据,通过数据统计分析,提出表面氯离子浓度随高度呈单峰高斯分布的规律;通过建立BP 神经网络预测模型,验证其高斯分布规律假设的合理性。
在对浙东沿海某混凝土码头及日本不同海域混凝土码头的表面氯离子浓度实测数据进行概率统计分析后,得到沿海混凝土结构的最严重氯离子侵蚀区域为海拔在0.4 1.6m ,其海水浸润时间比为0.285 0.478,应重点加强该区域结构的抗氯侵蚀能力。
最后,通过对实测数据的归一化处理,建立了基于高斯函数的海港码头混凝土表面氯离子浓度的高度影响系数和海水浸润时间比影响系数经验表达式。
关键词:混凝土结构;表面氯离子浓度;海拔高度CONCRETE SURFACE CHLORIDE ION CONCENTRATION VARYING WITH HEIGHT IN MARINE ENVIRONMENTHu DiZhao YuxiGong QiheJin Weiliang(Department of Civil Engineering ,Zhejiang Uinversity ,Hangzhou 310029,China )Abstract :Chloride ion is the main reason that impacts the durability of reinforced concrete structures in marine environment ,while the surface chloride concentration of concrete structures is one of the most important factor influencing the transport process of chloride into structural concrete.Because of the different local environments for concrete structures at different heights ,the surface chloride concentration varys with the heights.Based on the inspected data of surface chloride concentration from a concrete port which locates at eastern coastal area of Zhejiang Province ,a single peak Gaussian distribution is proposed to describe the surface chloride concentration along the height of structure.A model of surface chloride using BP neural network is established to predict the distribution of the surface chloride concentration along the height.To find out the most serious chloride aggression region of reinforced concrete structures ,probability based statistical analysis of inspection data from concrete ports of eastern coastal area of Zhejiang Province and Japan is carried out.The most serious chloride aggression height is from 0.4to 1.6m above the sea level ,from 0.285to 0.478of water infiltration time ratio ,where the anti-aggression capacity of chloride should be strengthened.Finally ,according to the normalized inspected data ,empirical equations are proposed to describe the influence of height and water infiltration time on surface chloride ion concentration based on a Gaussian Function.Keywords :concrete structures ;surface chloride concentration ;height*国家自然科学基金重点项目(50538070);国家自然科学基金项目(50808157);交通部西部交通建设科技项目(200631822302-06);国家科技支撑计划课题(2006BAJ03A03-03)。
应用地球化学元素丰度数据手册迟清华鄢明才编著地质出版社·北京·1内容提要本书汇编了国内外不同研究者提出的火成岩、沉积岩、变质岩、土壤、水系沉积物、泛滥平原沉积物、浅海沉积物和大陆地壳的化学组成与元素丰度,同时列出了勘查地球化学和环境地球化学研究中常用的中国主要地球化学标准物质的标准值,所提供内容均为地球化学工作者所必须了解的各种重要地质介质的地球化学基础数据。
本书供从事地球化学、岩石学、勘查地球化学、生态环境与农业地球化学、地质样品分析测试、矿产勘查、基础地质等领域的研究者阅读,也可供地球科学其它领域的研究者使用。
图书在版编目(CIP)数据应用地球化学元素丰度数据手册/迟清华,鄢明才编著. -北京:地质出版社,2007.12ISBN 978-7-116-05536-0Ⅰ. 应… Ⅱ. ①迟…②鄢…Ⅲ. 地球化学丰度-化学元素-数据-手册Ⅳ. P595-62中国版本图书馆CIP数据核字(2007)第185917号责任编辑:王永奉陈军中责任校对:李玫出版发行:地质出版社社址邮编:北京市海淀区学院路31号,100083电话:(010)82324508(邮购部)网址:电子邮箱:zbs@传真:(010)82310759印刷:北京地大彩印厂开本:889mm×1194mm 1/16印张:10.25字数:260千字印数:1-3000册版次:2007年12月北京第1版•第1次印刷定价:28.00元书号:ISBN 978-7-116-05536-0(如对本书有建议或意见,敬请致电本社;如本社有印装问题,本社负责调换)2关于应用地球化学元素丰度数据手册(代序)地球化学元素丰度数据,即地壳五个圈内多种元素在各种介质、各种尺度内含量的统计数据。
它是应用地球化学研究解决资源与环境问题上重要的资料。
将这些数据资料汇编在一起将使研究人员节省不少查找文献的劳动与时间。
这本小册子就是按照这样的想法编汇的。
测井资料常用英文代码表微梯度ML1 Microlog 1微电位ML2 Microlog 2声波时差AC Acousticlog密度DEN Density中子孔隙度CNL Compensated Dual-Spacing Neutron Log 井径CAL Caliper钻头大小BS Bit Size自然伽马GR Gamma Ray-Natural Radioactivity自然电位SP Spontaneous Potential深感应电阻率ILD Deep Investigation Induction Log中感应电阻率ILM Midium Investigation Induction Log八侧向电阻率LL8 Laterolog 8微球形聚焦电阻率MSFL Micro-Sphericlly Focused Log感应电导率COND Conductivity深侧向电阻率LLD Laterolog Deep浅侧向电阻率LLS Laterolog Shallow4米梯度电阻率RT Resistivity 4地层真电阻率RT True Formation Resistivity2.5米梯度电阻率R2.5 Resistivity 2.5中子伽马NEU Neutron中子伽马NGR Neutron Gamma Ray泥质含量SH Shale孔隙度POR Porosity渗透率PERM Permeability含水饱和度SW Water Saturation含油饱和度SO Oil Saturation of束缚水饱和度SWI Initial Water Saturation残余油饱和度SOR Residual Oil Saturation斯仑贝谢(Schlumberger)常用英文缩写数控测井系统CSU Cyber Service Units 或Computerized Logging Units 声波时差DT Delta T密度RHOB Rho Bulk中子孔隙度NPHI Neutron Phi感应电导率CILD IL-Deep Conductivity井径CALS Caliper Size自然伽马能谱NGS Natural Gamma Ray Spectrolog铀URAN Uranium钍THOR Thorium钾POTA Potassium高分辨率地层倾角仪HDT High Resolution Dipmeter Tool地层学高分辨率地层倾角仪SHDT Stratigraphy High Resolution Dipmeter Tool 地层压力RFT Repeat Formation Tester波形WF Wave Form微电阻率成像FMI Fullbore Formation Micro Imager Tool阵列感应成像AIT Array Induction Imager Tool方位侧向成像ARI Azimuthal Resistivity Imager Tool偶极声波成像DSI Dipole Shear Sonic Image Tool超声波成像USI Ultrasonic Imager Tool核磁共振CMR Combination Magnetic Resonance模块式地层动态测试仪MDT Modular Formation Dynamics Tester测井曲线名称汇总GRSL—能谱自然伽马POR 孔隙度NEWSANDPORW 含水孔隙度NEWSANDPORF 冲洗带含水孔隙度NEWSANDPORT 总孔隙度NEWSANDPORX 流体孔隙度NEWSANDPORH 油气重量NEWSANDBULK 出砂指数NEWSANDPERM 渗透率NEWSANDSW 含水饱和度NEWSANDSH 泥质含量NEWSANDCALO 井径差值NEWSANDCL 粘土含量NEWSANDDHY 残余烃密度NEWSANDSXO 冲洗带含水饱和度NEWSANDDA 第一判别向量的判别函数NEWSANDDB 第二判别向量的判别函数NEWSANDDAB 综合判别函数NEWSANDCI 煤层标志NEWSANDCARB 煤的含量NEWSANDTEMP 地层温度NEWSANDQ 评价泥质砂岩油气层产能的参数NEWSAND PI 评价泥质砂岩油气层产能的参数NEWSAND SH 泥质体积CLASSSW 总含水饱和度CLASSPOR 有效孔隙度CLASSPORG 气指数CLASSCHR 阳离子交换能力与含氢量的比值CLASS CL 粘土体积CLASSPORW 含水孔隙度CLASSPORF 冲洗带饱含泥浆孔隙度CLASSCALC 井径差值CLASSDHYC 烃密度CLASSPERM 绝对渗透率CLASSPIH 油气有效渗透率CLASSPIW 水的有效渗透率CLASSCLD 分散粘土体积CLASSCLL 层状粘土体积CLASSCLS 结构粘土体积CLASSEPOR 有效孔隙度CLASSESW 有效含水饱和度CLASSTPI 钍钾乘积指数CLASSPOTV 100%粘土中钾的体积CLASSCEC 阳离子交换能力CLASSQV 阳离子交换容量CLASSBW 粘土中的束缚水含量CLASSEPRW 含水有效孔隙度CLASSUPOR 总孔隙度,UPOR=EPOR+BW CLASSHI 干粘土骨架的含氢指数CLASSBWCL 粘土束缚水含量CLASSTMON 蒙脱石含量CLASSTILL 伊利石含量CLASSTCHK 绿泥石和高岭石含量CLASSVSH 泥质体积CLASSVSW 总含水饱和度CLASSVPOR 有效孔隙度CLASSVPOG 气指数CLASSVCHR 阳离子交换能力与含氢量的比值CLASS VCL 粘土体积CLASSVPOW 含水孔隙度CLASSVPOF 冲洗带饱含泥浆孔隙度CLASSVCAC 井径差值CLASSVDHY 烃密度CLASSVPEM 绝对渗透率CLASSVPIH 油气有效渗透率CLASSVPIW 水的有效渗透率CLASS VCLD 分散粘土体积CLASS VCLL 层状粘土体积CLASS VCLS 结构粘土体积CLASS VEPO 有效孔隙度CLASSVESW 有效含水饱和度CLASS VTPI 钍钾乘积指数CLASSVPOV 100%粘土中钾的体积CLASS VCEC 阳离子交换能力CLASS VQV 阳离子交换容量CLASS VBW 粘土中的束缚水含量CLASS VEPR 含水有效孔隙度CLASS VUPO 总孔隙度 CLASSVHI 干粘土骨架的含氢指数CLASS VBWC 粘土束缚水含量CLASS VTMO 蒙脱石含量CLASSVTIL 伊利石含量CLASSVTCH 绿泥石和高岭石含量CLASS QW井筒水流量PLIQT井筒总流量PLISK射孔井段PLIPQW单层产水量PLIPQT单层产液量PLIWEQ 相对吸水量ZRPMPEQ 相对吸水强度ZRPM POR 孔隙度PRCOPORW 含水孔隙度PRCO PORF 冲洗带含水孔隙度PRCO PORT 总孔隙度PRCOPORX 流体孔隙度PRCO PORH 油气重量PRCOBULK 出砂指数PRCOHF 累计烃米数PRCOPF 累计孔隙米数PRCO PERM 渗透率PRCOSW 含水饱和度PRCOSH 泥质含量PRCOCALO 井径差值PRCOCL 粘土含量PRCODHY 残余烃密度PRCOSXO 冲洗带含水饱和度PRCO SWIR 束缚水饱和度PRCO PERW 水的有效渗透率PRCO PERO 油的有效渗透率PRCOKRW 水的相对渗透率PRCOKRO 油的相对渗透率PRCOFW 产水率PRCOSHSI 泥质与粉砂含量PRCOSXOF 199*SXO PRCOSWCO 含水饱和度PRCOWCI 产水率PRCOWOR 水油比PRCOCCCO 经过PORT校正后的C/O值 PRCO CCSC 经过PORT校正后的SI/CA值PRCO CCCS 经过PORT校正后的CA/SI值PRCO DCO 油水层C/O差值PRCOXIW A 水线视截距PRCOCOW A 视水线值PRCOCONM 视油线值PRCOCPRW 产水率(C/O计算)PRCOCOAL 煤层CRAOTHR 重矿物的百分比含量CRASALT 盐岩的百分比含量CRASAND 砂岩的百分比含量CRALIME 石灰岩的百分比含量CRADOLM 白云岩的百分比含量CRAANHY 硬石膏的百分比含量CRA ANDE 安山岩的百分比含量CRA BASD 中性侵入岩百分比含量CRA DIAB 辉长岩的百分比含量CRA CONG 角砾岩的百分比含量CRA TUFF 凝灰岩的百分比含量CRA GRA V 中砾岩的百分比含量CRA BASA 玄武岩的百分比含量CRA常用测井曲线名称A1R1 T1R1声波幅度A1R2 T1R2声波幅度A2R1 T2R1声波幅度A2R2 T2R2声波幅度AAC 声波附加值AA VG 第一扇区平均值AC 声波时差AF10 阵列感应电阻率AF20 阵列感应电阻率AF30 阵列感应电阻率AF60 阵列感应电阻率AF90 阵列感应电阻率AFRT 阵列感应电阻率AFRX 阵列感应电阻率AIMP 声阻抗AIPD 密度孔隙度AIPN 中子孔隙度AMA V 声幅AMAX 最大声幅AMIN 最小声幅AMP1 第一扇区的声幅值AMP2 第二扇区的声幅值AMP3 第三扇区的声幅值AMP4 第四扇区的声幅值AMP5 第五扇区的声幅值AMP6 第六扇区的声幅值AMVG 平均声幅AO10 阵列感应电阻率AO20 阵列感应电阻率AO30 阵列感应电阻率AO60 阵列感应电阻率AO90 阵列感应电阻率AOFF 截止值AORT 阵列感应电阻率AORX 阵列感应电阻率APLC 补偿中子AR10 方位电阻率AR11 方位电阻率AR12 方位电阻率ARO1 方位电阻率ARO2 方位电阻率ARO3 方位电阻率ARO4 方位电阻率ARO5 方位电阻率ARO6 方位电阻率ARO7 方位电阻率ARO8 方位电阻率ARO9 方位电阻率AT10 阵列感应电阻率AT20 阵列感应电阻率AT30 阵列感应电阻率AT60 阵列感应电阻率AT90 阵列感应电阻率ATA V 平均衰减率ATC1 声波衰减率ATC2 声波衰减率ATC3 声波衰减率ATC4 声波衰减率ATC5 声波衰减率ATC6 声波衰减率ATMN 最小衰减率ATRT 阵列感应电阻率ATRX 阵列感应电阻率AZ 1号极板方位AZ1 1号极板方位AZI 1号极板方位AZIM 井斜方位BGF 远探头背景计数率BGN 近探头背景计数率BHTA 声波传播时间数据BHTT 声波幅度数据BLKC 块数BS 钻头直径BTNS 极板原始数据C1 井径C2 井径C3 井径CAL 井径CAL1 井径CAL2 井径CALI 井径CALS 井径CASI 钙硅比CBL 声波幅度CCL 磁性定位CEMC 水泥图CGR 自然伽马CI 总能谱比CMFF 核磁共振自由流体体积CMRP 核磁共振有效孔隙度CN 补偿中子CNL 补偿中子CO 碳氧比CON1 感应电导率COND 感应电导率CORR 密度校正值D2EC 200兆赫兹介电常数D4EC 47兆赫兹介电常数DAZ 井斜方位DCNT 数据计数DEN 补偿密度DEN_1 岩性密度DEPTH 测量深度DEV 井斜DEVI 井斜DFL 数字聚焦电阻率DIA1 井径DIA2 井径DIA3 井径DIFF 核磁差谱DIP1 地层倾角微电导率曲线1 DIP1_1 极板倾角曲线DIP2 地层倾角微电导率曲线2 DIP2_1 极板倾角曲线DIP3 地层倾角微电导率曲线3 DIP3_1 极板倾角曲线DIP4 地层倾角微电导率曲线4 DIP4_1 极板倾角曲线DIP5 极板倾角曲线DIP6 极板倾角曲线DRH 密度校正值DRHO 密度校正值DT 声波时差DT1 下偶极横波时差DT2 上偶极横波时差DT4P 纵横波方式单极纵波时差DT4S 纵横波方式单极横波时差DTL 声波时差DTST 斯通利波时差ECHO 回波串ECHOQM 回波串ETIMD 时间FAMP 泥浆幅度FAR 远探头地层计数率FCC 地层校正FDBI 泥浆探测器增益FDEN 流体密度FGAT 泥浆探测器门限FLOW 流量FPLC 补偿中子FTIM 泥浆传播时间GAZF Z轴加速度数据GG01 屏蔽增益GG02 屏蔽增益GG03 屏蔽增益GG04 屏蔽增益GG05 屏蔽增益GG06 屏蔽增益GR 自然伽马GR2 同位素示踪伽马HAZI 井斜方位HDRS 深感应电阻率HFK 钾HMRS 中感应电阻率HSGR 无铀伽马HTHO 钍HUD 持水率HURA 铀IDPH 深感应电阻率IMPH 中感应电阻率K 钾KCMR 核磁共振渗透率KTH 无铀伽马LCAL 井径LDL 岩性密度LLD 深侧向电阻率LLD3 深三侧向电阻率LLD7 深七侧向电阻率LLHR 高分辨率侧向电阻率LLS 浅侧向电阻率LLS3 浅三侧向电阻率LLS7 浅七侧向电阻率M1R10 高分辨率阵列感应电阻率M1R120 高分辨率阵列感应电阻率M1R20 高分辨率阵列感应电阻率M1R30 高分辨率阵列感应电阻率M1R60 高分辨率阵列感应电阻率M1R90 高分辨率阵列感应电阻率M2R10 高分辨率阵列感应电阻率M2R120 高分辨率阵列感应电阻率M2R20 高分辨率阵列感应电阻率M2R30 高分辨率阵列感应电阻率M2R60 高分辨率阵列感应电阻率M2R90 高分辨率阵列感应电阻率M4R10 高分辨率阵列感应电阻率M4R120 高分辨率阵列感应电阻率M4R20 高分辨率阵列感应电阻率M4R30 高分辨率阵列感应电阻率M4R60 高分辨率阵列感应电阻率M4R90 高分辨率阵列感应电阻率MBVI 核磁共振束缚流体体积MBVM 核磁共振自由流体体积MCBW 核磁共振粘土束缚水ML1 微电位电阻率ML2 微梯度电阻率MPHE 核磁共振有效孔隙度MPHS 核磁共振总孔隙度MPRM 核磁共振渗透率MSFL 微球型聚焦电阻率NCNT 磁北极计数NEAR 近探头地层计数率NGR 中子伽马NPHI 补偿中子P01 第1组分孔隙度P02 第2组分孔隙度P03 第3组分孔隙度P04 第4组分孔隙度P05 第5组分孔隙度P06 第6组分孔隙度P07 第7组分孔隙度P08 第8组分孔隙度P09 第9组分孔隙度P10 第10组分孔隙度P11 第11组分孔隙度P12 第12组分孔隙度P1AZ 1号极板方位P1AZ_1 2号极板方位P1BTN 极板原始数据P2BTN 极板原始数据P2HS 200兆赫兹相位角P3BTN 极板原始数据P4BTN 极板原始数据P4HS 47兆赫兹相位角P5BTN 极板原始数据P6BTN 极板原始数据PAD1 1号极板电阻率曲线PAD2 2号极板电阻率曲线PAD3 3号极板电阻率曲线PAD4 4号极板电阻率曲线PAD5 5号极板电阻率曲线PAD6 6号极板电阻率曲线PADG 极板增益PD6G 屏蔽电压PE 光电吸收截面指数PEF 光电吸收截面指数PEFL 光电吸收截面指数PERM-IND 核磁共振渗透率POTA 钾PPOR 核磁T2谱PPORB 核磁T2谱PPORC 核磁T2谱PR 泊松比PRESSURE 压力QA 加速计质量QB 磁力计质量QRTT 反射波采集质量R04 0.4米电位电阻率R045 0.45米电位电阻率R05 0.5米电位电阻率R1 1米底部梯度电阻率R25 2.5米底部梯度电阻率R4 4米底部梯度电阻率R4AT 200兆赫兹幅度比R4AT_1 47兆赫兹幅度比R4SL 200兆赫兹电阻率R4SL_1 47兆赫兹电阻率R6 6米底部梯度电阻率R8 8米底部梯度电阻率RAD1 井径(极板半径)RAD2 井径(极板半径)RAD3 井径(极板半径)RAD4 井径(极板半径)RAD5 井径(极板半径)RAD6 井径(极板半径)RADS 井径(极板半径)RATI 地层比值RB 相对方位RB_1 相对方位角RBOF 相对方位RD 深侧向电阻率RFOC 八侧向电阻率RHOB 岩性密度RHOM 岩性密度RILD 深感应电阻率RILM 中感应电阻率RLML 微梯度电阻率RM 钻井液电阻率RMLL 微侧向电阻率RMSF 微球型聚焦电阻率RNML 微电位电阻率ROT 相对方位RPRX 邻近侧向电阻率RS 浅侧向电阻率SDBI 特征值增益SFL 球型聚焦电阻率SFLU 球型聚焦电阻率SGAT 采样时间SGR 无铀伽马SICA 硅钙比SIG 井周成像特征值SIGC 俘获截面SIGC2 示踪俘获截面SMOD 横波模量SNL 井壁中子SNUM 特征值数量SP 自然电位SPER 特征值周期T2 核磁T2谱T2-BIN-A 核磁共振区间孔隙度T2-BIN-B 核磁共振区间孔隙度T2-BIN-PR 核磁共振区间孔隙度T2GM T2分布对数平均值T2LM T2分布对数平均值TEMP 井温TH 钍THOR 钍TKRA 钍钾比TPOR 核磁共振总孔隙度TRIG 模式标志TS 横波时差TT1 上发射上接受的传播时间TT2 上发射下接受的传播时间TT3 下发射上接受的传播时间TT4 下发射下接受的传播时间TURA 钍铀比U 铀UKRA 铀钾比URAN 铀V AMP 扇区水泥图VDL 声波变密度VMVM 核磁共振自由流体体积VPVS 纵横波速度比W A V1 第一扇区的波列W A V2 第二扇区的波列W A V3 第三扇区的波列W A V4 第四扇区的波列W A V5 第五扇区的波列W A V6 第六扇区的波列W A VE 变密度图WF 全波列波形ZCORR 密度校正值测井曲线代码一览表常用测井曲线名称测井符号英文名称中文名称Rt true formation resistivity. 地层真电阻率Rxo flushed zone formationresistivity 冲洗带地层电阻率Ild deep investigate induction log深探测感应测井Ilm medium investigate induction log中探测感应测井Ils shallow investigate induction log 浅探测感应测井Rd deep investigate double lateral resistivity log深双侧向电阻率测井Rs shallow investigate double 浅双侧向电阻率测井lateral resistivity logRMLL micro lateral resistivity log 微侧向电阻率测井CON induction log 感应测井AC acoustic 声波时差DEN density 密度CN neutron 中子GR natural gamma ray 自然伽马SP spontaneous potential 自然电位CAL borehole diameter 井径K potassium 钾TH thorium 钍U uranium 铀KTH gamma ray without uranium 无铀伽马NGR neutron gamma ray 中子伽马常用测井曲线名称测井符号英文名称中文名称Rt true formation resistivity. 地层真电阻率Rxo flushed zone formation resistivity 冲洗带地层电阻率Ild deep investigate induction log 深探测感应测井Ilm medium investigate induction log 中探测感应测井Ils shallow investigate induction log 浅探测感应测井Rd deep investigate double lateral resistivity log 深双侧向电阻率测井Rs shallow investigate double lateral resistivity log 浅双侧向电阻率测井RMLL micro lateral resistivity log 微侧向电阻率测井CON induction log 感应测井AC acoustic 声波时差DEN density 密度CN neutron 中子GR natural gamma ray 自然伽马SP spontaneous potential 自然电位CAL borehole diameter 井径K potassium 钾TH thorium 钍U uranium 铀KTH gamma ray without uranium 无铀伽马NGR neutron gamma ray 中子伽马5700系列的测井项目及曲线名称Star Imager 微电阻率扫描成像CBIL 井周声波成像MAC 多极阵列声波成像MRIL 核磁共振成像TBRT 薄层电阻率DAC 阵列声波DVRT 数字垂直测井HDIP 六臂倾角MPHI 核磁共振有效孔隙度MBVM 可动流体体积MBVI 束缚流体体积MPERM 核磁共振渗透率Echoes 标准回波数据T2 Dist T2分布数据TPOR 总孔隙度BHTA 声波幅度BHTT 声波返回时间Image DIP 图像的倾角COMP AMP 纵波幅度Shear AMP 横波幅度COMP ATTN 纵波衰减Shear ATTN 横波衰减RADOUTR 井眼的椭圆度Dev 井斜。
1阐述expound(explain), state引入introduce into相应的corresponding概念conception概论overview概率probability概念化conceptualize宏观的macroscopic补充complement规划plan证明demonstrate, certify, attest证实confirmation补偿compensate, make up, imburse算法algorithm判别式discriminant有限元方法 finite element method(FEM)样本单元法sample element method(SEM)赤平投影法stereographic projection method(SPM)赤平投影stereographic projection干扰位移法 interference displacement method(IDM)干扰能量法interference energy method(IEM)条分法method of slices极限平衡法limit equilibrium method界面元法boundary element method模拟simulate计算程序computer program数值分析numerical analysis计算工作量calculation load解的唯一性uniqueness of solution多层结构模型laminated model非线性nonlinear横观各向同性lateral isotropy各向同性isotropy各向异性anisotropy非均质性heterogeneity边界条件boundary condition本构方程constitutive equation初始条件initial condition初始状态rest condition岩土工程geotechnical engineering,土木工程civil engineering基础工程foundation engineering最不利滑面the most dangerous slip surface交替alternate控制论cybernetics大量现场调查mass field surveys组合式 combined type相互作用interaction稳定性评价stability evaluation均质性homogeneity介质medium层layer, stratum组构fabric1地形地貌geographic and geomorphic工程地质条件engineering geological conditions地形地貌条件geographic and geomorphic conditions 地形land form地貌geomorphology, relief微地貌microrelief地貌单元landform unit, geomorphic unit坡度grade地形图relief map河谷river valley 河道river course河床river bed(channel)冲沟gully, gulley, erosion gully, stream(brook)河漫滩floodplain(valley flat)阶地terrace冲积平原alluvial plain三角洲delta古河道fossil river course, fossil stream channel 冲积扇alluvial fan洪积扇diluvial fan坡积裙talus apron分水岭divide盆地basin岩溶地貌karst land feature, karst landform溶洞solution cave, karst cave落水洞sinkhole土洞Karstic earth cave2地层岩性地层geostrome (stratum, strata)岩性lithologic character, rock property岩体 rock mass岩层bed stratum岩层layer, rock stratum母岩matrix, parent rock相变facies change硬质岩strong rock, film软质岩weak rock硬质的competent软质的incompetent基岩bedrock岩组petrofabric覆盖层overburden交错层理cross bedding层面bedding plane片理schistosity层理bedding板理(叶理)foliation波痕ripple-mark泥痕mud crack雨痕raindrop imprints造岩矿物rock-forming minerals粘土矿物clay mineral高岭土kaolinite蒙脱石montmorillonite伊利石illite云母mica白云母muscovite黑云母biotite石英quartz长石feldspar正长石orthoclase斜长石plagioclase辉石pyroxene, picrite角闪石hornblende方解石calcite构造structure结构texture组构fabric(tissue)矿物组成mineral composition结晶质crystalline非晶质amorphous产状attitude火成岩igneous2岩浆岩magmatic rock火山岩(熔岩)lava火山volcano侵入岩intrusive(invade) rock 喷出岩effusive rock深成岩plutonic rock浅成岩pypabysal rock酸性岩acid rock中性岩inter-mediate rock基性岩basic rock超基性岩ultrabasic rock岩基rock base (batholith)岩脉(墙)dike岩株rock stock岩流rock flow岩盖rock laccolith (laccolite)岩盆rock lopolith岩墙rock dike岩床rock sill岩脉vein dyke花岗岩granite斑岩porphyry玢岩porphyrite流纹岩rhyolite正长岩syenite粗面岩trachyte闪长岩diorite安山岩andesite辉长岩gabbro玄武岩basalt细晶岩aplite伟晶岩pegmatite煌斑岩lamprophyre辉绿岩diabase橄榄岩dunite黑曜岩obsidian浮岩pumice火山角砾岩vulcanic breccia火山集块岩volcanic agglomerate凝灰岩tuff沉积岩sedimentary rock碎屑岩clastic rock粘土岩clay rock粉砂质粘土岩silty claystone化学岩chemical rock生物岩biolith砾岩conglomerate角砾岩breccia砂岩sandstone石英砂岩quartz sandstone粉砂岩siltstone钙质粉砂岩calcareous siltstone泥岩mudstone页岩shale盐岩saline石灰岩limestone白云岩dolomite泥灰岩marl泥钙岩argillo-calcareous泥砂岩argillo-arenaceous砂质arenaceous泥质argillaceous硅质的siliceous有机质organic matter 粗粒coarse grain中粒medium-grained沉积物sediment (deposit)漂石、顽石boulder卵石cobble砾石gravel砂sand粉土silt粘土clay粘粒clay grain砂质粘土sandy clay粘质砂土clayey sand壤土、亚粘土loam砂壤土、亚砂土轻亚粘土sandy loam浮土、表土regolith (topsoil)黄土loess红土laterite泥灰peat软泥ooze淤泥mire, oozed mud, sludge, warp clay 冲积物(层)alluvion冲积的alluvial洪积物(层)proluvium, diluvium, diluvion洪积的diluvial坡积物(层)deluvium残积物(层)eluvium残积的eluvial风积物(层)eolian deposits湖积物(层)lake deposits海积物(层)marine deposits冰川沉积物(层)glacier (drift)deposits崩积物(层)colluvial deposits, colluvium 残积粘土residual clay变质岩metamorphic rock板岩slate千枚岩phyllite片岩schist片麻岩gneiss石英岩quartzite大理岩marble糜棱岩mylonite混合岩migmatite碎裂岩cataclasite3地质构造地质构造geologic structure结构构造structural texture大地构造geotectonic构造运动tectogenesis造山运动orogeny升降运动vertical movement水平运动horizontal movement完整性perfection(integrity)起伏度waviness尺寸效应size effect围压效应confining pressure effect产状要素elements of attitude产状attitude, orientation走向strike倾向dip倾角dip angle, angle of dip褶皱 fold褶曲fold单斜monocline3向斜syncline背斜anticline穹隆dome挤压squeeze上盘upper section下盘bottom wall, footwall, lower wall 断距separation相交intersect断层fault正断层normal fault逆断层reversed fault平移断层parallel fault层理bedding, stratification微层理light stratification地堑graben地垒horst, fault ridge断层泥gouge, pug, selvage, fault gouge 擦痕stria, striation断裂 fracture破碎带fracture zone节理joint节理组 joint set裂隙fissure, crack微裂隙fine fissure, microscopic fissure劈理cleavage原生裂隙original joint次生裂隙epigenetic joint张裂隙tension joint剪裂隙shear joint卸荷裂隙relief crack裂隙率fracture porosity结构类型structural pattern岩体结构rock mass structure岩块block mass结构体structural element块度blockness结构面structural plane软弱结构面weak plane临空面free face碎裂结构cataclastic texture板状结构platy structure薄板状lamellose块状的lumpy, massive层状的laminated巨厚层giant thick-laminated薄层状的finely laminated软弱夹层weak intercalated layer夹层inter bedding,intercalated bed, interlayer, intermediate layer 夹泥层clayey intercalation夹泥inter-clay连通性connectivity切层insequent影响带affecting zone完整性integrity n.Integrate v. & a.degree of integrality破碎crumble胶结cement泥化argillization尖灭taper-out错动diastrophism错动层面faulted bedding plane断续的intermittent 破碎crumble共轭节理conjugated joint散状loose透镜状的lens-shaped a.岩石碎片crag岩屑cuttings, debris薄膜membrane, film层理stratification高角度high dip angle缓倾角low dip angle反倾anti-dip互层interbed v.Interbedding n.起伏的unplanar波状起伏的undulate, undulating粒径particle size构造层tectonosphere挤压compression均一的homogeneous剪切错动面shear faulted, bedding zone切割dissection切割的dissected致密close, compact构造岩tectonite糜棱岩mylonite断层角砾岩fault breccia方解石脉calcite vein碎块岩clastic rock角砾breccia岩粉rock powder岩屑debris, debry固结consolidation定向排列oriented spread构造应力tectonic stress残余应力residual stress4水文地质条件hydrogeological conditions 水文循环hydrologic cycle大气圈atmosphere水圈hydrosphere岩石圈geosphere地表径流surface runoff地下径流subsurface runoff流域valley, drainage basin流域面积drainage area, river basin area 汇水面积catchment area地下水ground water, subsurface water 地表水surface water大气水atmospheric water气态水aqueous (vapour) water液态水liquid water固态水solid water上层滞水perched water潜水phreatic water承压水confined water吸着水hygroscopic (adsorptive) water 介质medium空隙void孔隙水压力pore water pressure渗透压力osmotic pressure, seepage force 扬压力uplift pressure静水压力hydrostatic pressure外静水压力 external hydrostatic pressure动水压力hydrodynamic pressure4渗透力seepage pressure外水压力external water pressure内水压力internal water pressure水力联系hydraulic interrelation水力折减系数hydraulic reduction coefficient水头损失water head loss渗透途径filtration path, seepage path渗透系数penetration coefficient潜水位water table level水位water level, stage level水头water head含水层aquifer弱含水层(弱透水层)aquitard滞水层aquiclude透水层permeable layer, pervious layer不透水层(隔水层)aquifuge, impervious layer,impermeable layer, aquiclude潜水含水层phreatic aquifer承压含水层confined aquifer, artesian aquifer承压面bearing surface潜水面phreatic surface, water table浸润线phreatic curve不透水边界impervious boundary地下分水岭groundwater ridge粘滞性viscosity富水性abundance透水性(渗透性)permeability淋滤(溶滤作用)lixiviation, leaching反滤层inverted gravel filter水锈incrustation渗滴seep饱和saturation, saturated潜水位变化带zone of variable phreatic level气象因素meteorological factor饱水带zone of saturation包气带 aeration zone, zone of aeration包气带水aeration zone water上层滞水perched water孔隙水pore water裂隙水fissure water岩溶水karstic water结合水bound water, combined water吸着水hydroscopic water薄膜水pellicular water毛细水capillary water重力水gravitational water凝结水condensation water地下水埋藏条件condition of groundwater occurrence 地下水埋藏深度depth of groundwater occurrence压水试验packer permeability test抽水试验pumping test5物理力学性质物理力学physical mechanics n.Physico-mechanical a.屈服准则yield criteria米赛斯屈服准则Von Mises yield criteria朗肯土压力理论Ranking’s earth pressure theory剑桥模型 Cambridge model, Cam-model邓肯-张模型Duncan-chang model本构方程constitutive equation局部剪切破坏local shear failure整体剪切破坏general shear failure岩体完整性指数intactness index of rock mass 安全系数factor of safety埋深embedment depth试件coupons挠度deflection里氏震级Richter scale设计烈度design intensity基本烈度basic intensity场地烈度site intensity地震烈度seismic intensity, intensity scale卓越周期predominant period持力层sustained yield超载surcharge围岩压力surrounding rock stress附加压力superimposed stress应力松弛stress relaxation应力路迳stress path卸荷unload渗透率specific permeability饱和度degree of saturation含水量moisture content平均粒径mean diameter颗粒grain, granule, particle颗粒级配distribution of grain-size,grain composition, size distribution级配graduation,grain-size distribution, gradation, grading粒度coarseness grain size, granularity, lump不均匀系数coefficient of non-uniformity,variation coefficient, variation factor颗粒分级gradation, size grading孔隙水pore water孔隙比void ratio (ration)空隙率air voids孔隙率porosity裂隙率crackity溶隙率karstity密度density重度unit weight, bulk weight浮重度buoyant unit weight折减系数reduction factor压力消散dissipation of pressure抗力系数coefficient of resistance软化系数softening coefficient含水量water content稠度consistency塑限plastic limit液限liquid limit塑性指数plasticity index液性指数liquidity index流变rheological蠕变creep塑性plastic脆性brittleness(fragility)粘性stickness刚性rigidity弹性的elastic粘弹性viso-elasticity弹塑性elasto-plasticity压缩性compressibility均质性homogeneity非均质性nonhomogeneity (heterogeneity)各向同性isotropy各向异性anisotropy5总应力total stress有效应力effective stress超孔隙水压力excess pore pressure孔隙水压力pore water pressure抗压强度compressive strength抗拉强度tensile strength抗剪强度shear strength不排水抗剪强度undrained shear strenght峰值抗剪强度peak share strength长期抗剪强度long-term shear strength残余抗剪强度residual shear strength负摩擦力negative skin friction, dragdown摩擦角angle of friction内摩擦角angle of internal friction外摩擦角angle of external friction内聚力cohesion粘聚力cohesion假凝聚力pseudo-cohesion粘着力adhesion摩尔圆Mohr’s circle包络线envelope休止角angle of repose,angle of friction(repose, rest), repose angle 峰值peak模量modulus弹性模量modulus of elasticity,Young’s modulus, elastic modulus压缩模量modulus of compressibility变形模量modulus of deformation卸荷模量unloading modulus切线模量tangent modulus剪切模量shear modulus割线模量secant modulus旁压模量pressurmeter modulus泊松比poisson’s ration固结consolidation固结系数coefficient of consolidation固结度degree of consolidation超固结比over consolidation ration应变strain压缩比compressibility ratio压缩系数coefficient of compressibility压缩指数compression index初始曲线virgin curve正常固结土normally consolidated soil欠固结土under-consolidated soil超固结土over-consolidated soil被动土压力passive earth pressure主动土压力active earth pressure静止土压力earth pressure at rest覆盖压力overburden pressure初始应力initial stress地应力场ground(geostatic) stress field有效应力effective stress动应力dynamic stress动荷载dynamic load偏心荷载eccentric loads循环荷载inclined loads地应力ground stress, geostatic stress初始应力initial stress应力场stress field纵波longitudinal wave液化势liquefaction potential液化指数liquefaction index 交角angular岩石抗力系数coefficient of rock resistance容许承载力allowable bearing capacity临塑压力critical pressure接触压力contact pressure6工程地质问题工程地质问题engineering geological problem定性评价qualitative estimate定量评价quantitative estimate极限平衡法limit equilibrium method不良地质现象unfavorable geological condition风化weathering变形deformation位移displacement不均匀位移differential movement相对位移relative displacement沉陷settlement山崩avalanche, toppling崩塌toppling, toppling collapse滑坡、地滑creep, slide切层滑坡insequent landslide深层滑坡deep slide浅层滑坡shallow slide顺层滑坡consequent landslide滑动面sliding surface, sliding plane, slip surface滑动带sliding zone滑床slide bed滑坡体slide(sliding) mass古滑坡fossil landslide推移式滑坡slumping slide牵引式滑坡retrogressive slide管涌piping, internal erosion渗漏leakage流砂quicksand渗流seepage液化liquefaction7工程勘察engineering investigation工程地质勘察engineering geology investigation 岩土工程勘察geotechnical investigation工程地质条件engineering geological condition 工程地质评价engineering geological evaluation 勘测survey岩芯采取率core recovery, core extraction岩芯获得率RQD(岩石质量指标)rock quality designation程序(步骤)procedure勘察阶段investigational stage选点踏勘reconnaissance初步设计primary design初步规划preliminary scheme初步勘探preliminary prospecting初步踏勘ground reconnaissance可行性研究阶段feasibility stage初步设计阶段preliminary stage施工阶段construction sage踏勘reconnaissance, inspection地质测绘geological survey工程地质测绘engineering geological mapping 钻探borehole operation, boring物探geophysical exploration洞探exploratory adits6钎探rod sounding坑探exploring mining槽探trenching天然建材调查natural materials surveying (examination)岩土工程勘察报告geotechnical investigation report 鉴定identification, appraisal鉴定书expertise report鉴定人identifier, surveyor校核verification总监chief inspector比例proportion地形图geographic map地貌图geomorphological map地质图geological map工程地质图engineering geological map实测地质剖面图field-acquired geological profile(section)构造地质图geological structure map第四纪地质图quarternary geological map地质详图detail map of geology地质柱状图geologic columnar section, geologic log 钻孔柱状图logs of bore hole纵剖面图longitudinal section横剖面图cross section展示图reveal detail map节理玫瑰图rose of joints基岩等高线bed rock contour层底等高线contour of stratum bottom岩层界线strata boundary岩面高程elevation of bed rock surface坐标coordinate分层bed separation地质点geological observation point勘探点exploratory point (spot)勘探线exploratory line勘探孔exploration hole平洞adit竖井riser, shaft, vertical shaft探槽exploratory trench探井exploratory pit钻孔borehole, drill hole机钻孔ordinary drill hole套钻孔sleeve drill hole管钻孔pipe drill hole岩芯core岩芯钻探core drilling回转钻探(进)rotary drilling冲击钻探churn drilling, percussion drilling 钢砂钻探shot drilling铁砂钻进iron shot drilling跟管钻进follow-down drilling振动钻进vibro-boring, vibro-drilling泥浆钻探mud flush drilling金刚石钻进diamond drilling单动式single acting双层double layer空气钻探air flush drilling钻机drilling rig钻头drill bit, drilling bit螺旋钻头auger勺钻spoon bit冲击钻头percussion bit, chopping bit桶式钻头bucket auger 钻杆drill rod套管casing岩芯管core barrel冲洗掖flush fluid正循环冲洗direct circulation反循环冲洗reverse circulation泥浆mud, slurry泥皮mud cake护壁dado止水seal, water seal扫孔cleaning bottom of hole钻进drilling平硐adit竖井shaft钻探drilling boring8工程地质试验击实试验compaction test压缩试验compression test固结试验consolidation test单轴试验uniaxial compression test现场剪切试验in-situ shear test单剪试验simple shear test直剪试验direct shear test慢剪试验slow test单剪试验simple shear test快剪试验quick test三轴剪切试验triaxial shear test三轴压缩试验triaxial compression test动三轴试验dynamic triaxial test不固结不排水剪试验unconsolidated undrained test(quick test)固结不排水剪试验consolidated undrained test(consolidated quick test)固结排水试验consolidated drained test(slow test)原位测试in-situ test现场监测on-site(in-site) monitoring现场检测on-site (in-site) inspection观测孔observation borehole静力触探试验cone penetration test,static penetration test, static cone test标贯试验standard penetration test十字板剪切试验vane shear test, vane test检层法up-hole method, borehole method旁压试验pressuremeter test动力触探试验dynamic penetration test, dynamic sounding 点荷载试验point load test岩石试验rock test应力解除法stress relief method应力恢复法stress recovery method套孔法over-coring method9岩土体加固掌子面breast, driving face,heading face, tunnel face顶拱vault底拱invert洞室开挖excavation超挖overbreak风钻pneumatic drill开挖断面excavated section塌落slump细骨料混凝土concrete made with fine aggregate7细骨料fine aggregate, fine adjustment料场stock ground土料earth material矿渣cinder, mineral water residue, scoria, slag 性能function, performance, property, nature 凝结coagulate, congeal, congealment, coagulation 合格qualified, on test, up to standard 初凝initial set初凝时间initial setting time终凝final set配合比mix proportion塌落度slump水化热heat of hydration,hydration heat, setting heat水灰比water-cement ratio粉煤灰fly ash梅花状quincuncial pattern喷射shotcrete浇注pouring钢筋网coiremesh加固reinforce锚杆anchored bar, rock bolt锚索anchored cable锚紧端anchor station锚桩anchored peg采石场rock quarry开挖excavation清基cleanup foundation明挖open-cut爆破explosion光面爆破smooth blasting预裂法presplitting10 水工概论坝址toe of dam坝踵heel坝段monolith坝顶crest坝肩shoulders左坝肩left dam abutment副坝saddle dam三坝址the third dam site标高height mark上游水位headwater正常库水位normal reservoir level地下洞室underground opening (tunnel)压力隧洞pressure tunnel无压隧洞gravity tunnel交通洞access tunnel灌浆洞grouting tunnel明流洞free-flow tunnel孔板洞orifice tunnel排砂洞sediment tunnel尾水洞tailrace tunnel排水洞drainage tunnel导流洞diversion tunnel隧道tunnel围岩surrounding rock, ambient rock围岩应力secondary stress static应力集中stress concentrate覆盖层over burden冒顶cave in, roof fall底鼓bottom heave回弹rebound 岩爆rock burst冻结法freezing method超载over break衬砌lining围堰cofferdam堤dike近坝岸坡abutments施工(收缩)缝construction joint心墙core截水墙cutoff wall防渗墙diaphragm wall排水井drainage wells排水幕drainage curtain减压井relief wells反滤层filter zone灌浆材料grout水力劈裂hydraulic fracturing帷幔线curtain line上游围堰upstream cofferdam混凝土防渗墙concrete cutoff wall截流interim completion导水墙channel training wall正常溢洪道渠首工程service spillway headwork 消力塘lined plunge pool隔墙divider walls混凝土护坦concrete apron副厂房auxiliary power house闸门室gate chamber中闸室mid gate chamber开关站switch yard电梯井elevator shaft尾水渠tail race非常溢洪道emergency spillway11桥梁及基础工程江阴大桥Jiangyin Bridge悬索桥suspension bridge锚碇anchorage重力式嵌岩锚gravity socketed anchorage北锚碇前(后)锚面front(back) surface of northern anchorage塔墩tower墩pier散索鞍splay saddle猫道footbridge主缆main cable索股cable strand主鞍main saddle, tower saddle主跨main span边跨side span引桥approach钢箱梁steel box main girder埋深embedment depth北塔墩基础north tower base基础foundation, footing浅基础 shallow foundation深基础 deep foundation联合基础combined footing筏形基础raft(mat) foundation钢模steel form桩pile基桩 foundation pile群桩pile groups桩基础pile foundation桩承台pile cap高桩承台high-rise pile cap低桩承台buried pile cap摩擦桩friction pile端承桩end bearing pile嵌岩桩socketed pile板桩sheet pile旋喷桩jet-grouted pile灌注桩cast-in-place pile沉管灌注桩driven cast-in-place pile支护桩soldier piles, tangent piles刚性桩rigid pile柔性桩flexible pile侧向受荷桩laterally loaded pile轴向受荷桩axially loaded pile预制桩precast concrete pile振动打桩vibratory pile driving振动钻进vibratory drilling沉箱caisson沉井(沉箱)(open) caisson地下连续墙diaphragm wall, slurry wall支撑bracing超载surcharge接触应力contact pressure井点降水well-point dewatering桩极限承载力ultimate bearing capacity of pile承载力bearing capacity阻力resistance桩端阻力end resistance表面摩擦力skin friction粘着系数adhesion factor负摩擦力negative skin friction安全系数factor of safety压缩层compressed layer附加应力additional stress, superimposed stress 持力层bearing layer, sustaining layer地基土foundation soil, subsoil临塑压力critical pressure剪切破坏shear failure地基失效foundation failure冲剪破坏punching failure渐进破坏progressive failure容许荷载allowable load极限承载力ultimate bearing capacity沉降settlement沉降差differential settlement尾部倾斜angular distortion倾斜tilting坑底隆起bottom heave静止土压力earth pressure at rest稳定数stability number路堤embankment地基处理ground treatment soil improvement 垫层cushion加固stabilization注浆injection灌浆guniting帷幕curtain挡土墙retaining wall锚固anchoring喷浆guniting锚杆earth anchor盲沟French drain振冲法vibro jet 12监测仪器观测孔observation bore/hole仪器观测instrumentation读数装置readout device传感器transducer探头probe压力盒pressure cell振弦式应变计vibrating wire strain gauge伸长计、变位计extension meter板式沉降仪foundation base/pate测斜仪inclinometer测压计,渗压计piezometer垂线plumb垂直度plumbness13安全监控可靠性检查 reliability checking监控模型monitoring and prediction model监测monitoring资料datum, data可靠性reliability稳定性 stability安全 safety评估evaluation, appraise评定assessment, assess, rate评价准则criterion灾害hazard, calamity确定性方法论Deterministic methodology应急行动计划EAP(emergency action plan)事故accident紧急状态emergency紧急检查emergency inspection灾情等级hazard classification灾害评价hazard evaluation风险评估risk assessment静力(Static Analysis)动力(Dynamic Analysis)蠕变(Creep Material Model)渗流(Fluid-mechanical Interaction)热力学(Thermal Option)headward erosion溯源侵蚀scouring of levee or bank淘刷strongly weathered siliceous rock mass with quasi-lamellarweakly weathered siliceous rock mass with quasi-lamellar of continually aftershocks of 7 or 8-degree intensityEvidently 明显的Correspondingly adv.相应地; 相关地; 相同地the hanging wall of triggering seismic faultoblique~bedding bank slope专 业 外 语(为方便记忆,跟上面稍有重复)一.综合类1.geotechnical engineering 岩土工程2.foundation engineering 基础工程3.soil, earth 土4.soil mechanics 土力学cyclic loading 周期荷载unloading 卸载reloading 再加载viscoelastic found 粘弹性地基viscous damping 粘滞阻尼shear modulus 剪切模量5.soil dynamics 土动力学6.stress path 应力路径二.土的分类1.residual soil 残积土 groundwater level 地下水位2.groundwater 地下水groundwatertable 地下水位3.clay minerals 粘土矿物4.secondary minerals 次生矿物ndslides 滑坡6.bore hole columnar section 钻孔柱状图7.engineering geologic investigation 工程地质勘察8.boulder 漂石9.cobble 卵石10.gravel 砂石11.gravelly sand 砾砂12.coarse sand 粗砂13.medium sand 中砂14.fine sand 细砂15.silty sand 粉土16.clayey soil 粘性土17.clay 粘土18.silty clay 粉质粘土19.silt 粉土20.sandy silt 砂质粉土21.clayey silt 粘质粉土22.saturated soil 饱和土23.unsaturated soil 非饱和土24.fill (soil)填土三.土的基本物理力学性质1.c c Compression index2.c u undrained shear strength3.c u /p 0 ratio of undrained strength c u to effective overburden stress p 0(c u /p 0)NC ,(c u /p 0)oc subscripts NC and OC designatednormally consolidated and overconsolidated, respectively4.c vane cohesive strength from vanetest 5.e 0 natural void ratio 6.I p plasticity index 7.K 0 coefficientof “at-rest ”pressure ,for total stresses σ1 and σ28.K 0’ do main for effectivestresses σ1 ‘ and σ2’9.K 0n K 0 for normally consolidatedstate10.K 0u K 0 coefficient under rapidcontinuous loading ,simulating instantaneous loading or an undrained condition 11.K 0d K 0 coefficient under cyclic loading (frequency less than 1 Hz),as a pseudo-dynamic test for K 0 coefficient 12.k h ,k v permeability in horizontal andvertical directions, respectively 13.N blow count ,standardpenetration test 14.OCR over-consolidation ratio 15.p c preconsolidation pressure ,fromoedemeter test 16.p 0 effective overburden pressure 17.p s specific cone penetrationresistance ,from static cone test 18.q u unconfinedcompressive strengt h19.U,U m degreeof consolidation ,subscript m denotes mean value of a specimen 20.u ,u b ,u m pore pressure, subscripts b andm denote bottom of specimen and mean value, respectively 21.w 0 w L w p natural water content, liquid andplastic limits, respectively 22.σ1,σ2 principal stresses, σ1 ‘ and σ2’denote effective principal stresses四.渗透性和渗流1.Darcy’s law 达西定律2.piping 管涌3.flowing soil 流土4.sand boiling 砂沸5.flow net 流网6.seepage 渗透(流)7.leakage 渗流8.seepage (force) pressure 渗透压力9.permeability 渗透性10.hydraulic gradient 水力梯度11.coefficient of permeability 渗透系数五.地基应力和变形1.soft soil 软土2.(negative) skin friction of driven pile 打入桩(负)摩阻力3.effective stress 有效应力total stress 总应力4.field vane shear strength 十字板抗剪强度5.low activity 低活性6.sensitivity 灵敏度7.triaxial test 三轴试验8.foundation design 基础设计9.recompaction 再压缩10.bearing capacity 承载力11.soil mass 土体12.contact pressure 接触应力13.concentrated load 集中荷载14. a semi-infinite elastic solid 半无限弹性体15.homogeneous 均质16.isotropic 各向同性17.strip footing 条基18.square spread footing 方形独立基础19.underlying soil (stratum ,strata)下卧层(土)20.dead load =sustained load 恒载 持续荷载21.live load 活载22.short –term transient load 短期瞬时荷载23.long-term transient load长期荷载24.reduced load折算荷载25.settlement沉降deformation变形26.casing套管27.dike=dyke堤(防)28.clay fraction粘粒粒组29.physical properties物理性质30.subgrade路基31.well-graded soil级配良好土32.poorly-graded soil级配不良土33.sieve筛子34.Mohr-Coulomb failure condition摩尔-库仑破坏条件35.FEM=finite element method有限元法36.limit equilibrium method极限平衡法37.pore water pressure孔隙水压力38.preconsolidation pressure先期固结压力39.modulus of compressibility压缩模量40.coefficent of compressibility压缩系数pression index压缩指数42.swelling index回弹指数43.geostatic stress自重应力44.additional stress附加应力45.total stress总应力46.final settlement最终沉降47.slip line滑动线六.基坑开挖与降水1.excavation开挖(挖方)2.dewatering(基坑)降水3.failure of foundation基坑失稳4.bracing of foundation pit基坑围护5.bottom heave=basal heave (基坑)底隆起6.retaining wall挡土墙7.pore-pressure distribution孔压分布8.dewatering method降低地下水位法9.well point system井点系统(轻型)10.deep well point深井点11.vacuum well point真空井点12.braced cuts支撑围护braced excavation支撑开挖braced sheeting支撑挡板七.深基础 deep foundation1.pile foundation桩基础1)cast –in-place灌注桩diving casting cast-in-place pile沉管灌注桩bored pile钻孔桩special-shaped cast-in-place pile机控异型灌注桩piles set into rock嵌岩灌注桩rammed bulb pile夯扩桩2)belled pier foundation钻孔墩基础drilled-pier foundation钻孔扩底墩under-reamed bored pier3)precast concrete pile预制混凝土桩4)steel pile钢桩steel pipe pile钢管桩 steel sheet pile钢板桩5)prestressed concrete pile预应力混凝土桩prestressed concrete pipe pile预应力混凝土管桩2.caisson foundation沉井(箱)3.diaphragm wall地下连续墙 截水墙4.friction pile摩擦桩end-bearing pile端承桩5.(pile)shaft桩身6.wave equation analysis波动方程分析7.pile caps承台(桩帽)8.bearing capacity of single pile单桩承载力teral pile load test单桩横向载荷试验10.ultimate lateral resistance of single pile单桩横向极限承载力11.static load test of pile单桩竖向静荷载试验12.vertical allowable load capacity单桩竖向容许承载力13.low pile cap低桩承台14.high-rise pile cap高桩承台15.vertical ultimate uplift resistance of single pile单桩抗拔极限承载力16.silent piling静力压桩17.uplift pile抗拔桩18.anti-slide pile抗滑桩19.pile groups群桩20.efficiency factor of pile groups群桩效率系数(η)21.efficiency of pile groups群桩效应22.dynamic pile testing桩基动测技术23.final set最后贯入度24.dynamic load test of pile桩动荷载试验25.pile integrity test桩的完整性试验26.pile head=butt桩头27.pile tip=pile point=pile toe桩端(头)28.pile spacing桩距29.pile plan桩位布置图30.arrangement of piles =pile layout桩的布置31.group action群桩作用32.end bearing=tip resistance桩端阻33.skin(side) friction=shaft resistance桩侧阻34.pile cushion桩垫35.pile driving(by vibration) 打桩(振动)36.pile pulling test拔桩试验37.pile shoe桩靴38.pile noise打桩噪音39.pile rig打桩机八.地基处理(ground treatment)1.technical code for ground treatment of building建筑地基处理技术规范2.cushion垫层法3.preloading预压法4.dynamic compaction强夯法5.dynamic compaction replacement强夯置换法6.vibroflotation method振冲法7.sand-gravel pile砂石桩pile-stone column砂石桩8.cement-flyash-gravel pile(CFG)水泥粉煤灰碎石桩9.cement mixing method水泥土搅拌桩10.cement column水泥桩11.lime pile (lime column)石灰桩12.jet grouting高压喷射注浆法13.rammed-cement-soil pile夯实水泥土桩法14.lime-soil compaction pile 灰土挤密桩lime-soil compacted column灰土挤密桩lime soil pile灰土挤密桩15.chemical stabilization化学加固法16.surface compaction 表层压实法17.surcharge preloading超载预压法vacuum preloading真空预压法。
地幔中石榴石的残痕元素分布——以Zabargad为例R. Vannncci 1,2, N. Shimizu 3, G.B. Piccardo 4 L. Ottolini 2, and P. Bottazzi 2t Dipartimento di Scienze della Terra, Universitfi di Pavia, via Bassi 4, 1-27100 Pavia, Italy2 CNR-Centro di Studio per la Cristallochimica e la Cristallografia, via Bassi 4, 1-27100 Pavia, Italy3 Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USADipartimento di Scienze della Terra, Universit/t di Genova, Corso Europa 26, 1-16132 Genova, Italy摘要:在Zabargad的橄榄岩体的辉石矿物形成阶段的Al-Di离子探针显示组成铁镁质层的残斑状的辉石记录了重稀土的异常,Zr,Sc的富集并没有记录在尖晶石二辉岩中。
在斜方辉石和尖晶石的晶簇中的斜方辉石在岩体的内部形成,在层状的辉石中自由生长的单斜辉石带显示出强烈的稀土元素分离模式(HREE N/LREE N>1000;Yb>100×ch)以及非常高的Zr,Sc和Y的丰度(分别高达30,672,600 ppm)。
在外部带,富单斜辉石带的残斑状辉石具有非常高的重稀土异常(HREE N/LREE N~29;Yb~269×ch),并且显示出Sc、Zr非常高的丰度(分别高达819ppm和164ppm)。
InN p-i-n Nanowire Solar Cells on Si Hieu Pham Trung Nguyen,Yi-Lu Chang,Ishiang Shih,and Zetian Mi(Invited Paper)Abstract—In this paper,we report thefirst experimental demon-stration of InN nanowire solar cells.By employing an in situ de-posited In seeding layer,we have achieved electronically pure, nearly intrinsic InN nanowires directly on Si(111)substrates by molecular beam epitaxy.The growth and characterization of Si-and Mg-doped InN nanowires is also investigated,which can ex-hibit superior structural and optical properties.We have further studied the epitaxial growth,fabrication,and characterization of InN:Si/i-InN and InN:Mg/i-InN/InN:Si axial nanowire structures on p-type and n-type Si(111)substrates,respectively.With the use of a CdS surface passivation,InN:Mg/i-InN/InN:Si nanowire homojunction solar cells exhibit a promising short-circuit cur-rent density of∼14.4mA/cm2and power-conversion efficiency of∼0.68%under simulated one-sun(AM1.5G)illumination.This work suggests thefirst successful demonstration of p-type doping in InN nanowires and also constitutes important progress for the development of InGaN-based,full-solar-spectrum photovoltaics.Index Terms—Nanotechnology,optoelectronic devices,p-i-n diodes,solar cells.I.I NTRODUCTIONS INCE the recent discovery of InN bandgap at∼0.6to0.7eV,the use of InN and related alloys for solar-cell appli-cations has been proposed and intensively investigated[1]–[9]. InN also exhibits several important attributes,including a rel-atively high absorption coefficient,high carrier mobility,and large drift velocity that are required for high-efficiency pho-tovoltaics.An energy-conversion efficiency of over20%is ex-pected for an ideal InN single-junction solar cell[10].Addition-ally,InN may be integrated with Si or other thinfilms to form heterojunction solar cells or be incorporated as a critical subcell for future InGaN-based full-solar-spectrum multijunction de-vices[11].However,InN thinfilms generally exhibit extremely poor quality,due to the lack of suitable substrates,and,to date, an InN solar cell has not been demonstrated.It is therefore imperative to explore InN nanostructures,including nanowires and quantum dots,which can exhibit drastically reduced dis-location densities,owning to the highly effective lateral stress relaxation.Additional advantages offered by the1-D nanowires for solar-cell applications include a direct path for carrier trans-port,an increased surface area for enhanced light absorption,Manuscript received July13,2010;revised August10,2010;accepted August10,2010.Date of publication November11,2010;date of current ver-sion August5,2011.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and in part by the Hydro-Quebec Nano-Engineering Scholar Program at McGill University.The authors are with the Department of Electrical and Computer Engi-neering,McGill University,Montreal,QC H3A2A7,Canada(e-mail:zetian. mi@mcgill.ca).Digital Object Identifier10.1109/JSTQE.2010.2082505and the compatibility with Si or other low-cost,large-area sub-strates[12]–[14].The growth and characterization of InN nanowires have been intensively studied.InN nanowires can be formed using the vapor–liquid–solid growth process,the spontaneous formation under nitrogen-rich conditions,or the selective-area growth on nano-patterned substrates[15]–[17].Well-spaced,vertically aligned InN nanowires have been grown on Si and other sub-strates using plasma-assisted molecular beam epitaxy(MBE) or metal–organic chemical vapor deposition.The resulting InN nanowires generally exhibit a wurtzite crystal structure,with the growth direction oriented along the c-axis.However,due to the very low dissociation temperature of InN and the very high surface migration rate of In,conventional growth techniques yield InN nanowires with tapered surface morphology and large stacking fault and dislocation densities[18]–[20],which de-crease the carrier diffusion length and severely limit the solar cell efficiency.The wires also exhibit very large size dispersion, with significant variations in the diameters and heights.Addi-tionally,due to the extremely low conduction band minimum of InN,any defects,dislocations or impurities generally form donors,thereby leading to very high electron densities,which are commonly measured in the range of∼1×1018cm−3,or higher for nominally nondoped InN[20]–[25].The resulting n-type degenerate InN nanowires exhibit poor optical properties, characterized by nearly temperature and power invariant pho-toluminescence emission spectra and photoluminescence peak energies(∼0.7to0.8eV)considerably larger than the bandgap of InN[20],[21],[26].The uncontrolled structural,electrical and optical properties have posed a significant challenge for the rational design and fabrication of InN nanowire solar cells. The realization of InN nanowire solar cells,as well as many other semiconductor devices,has been further limited by the difficulty in achieving p-type doping.In this regard,Mg-doped InNfilms and the formation of p-type carriers have been in-vestigated both theoretically and experimentally[27]–[30].A Fermi level shift toward the valence band was measured in InN:Mg layers[30],and the possibility of p-type doping is further suggested by electrolyte capacitance-voltage measure-ments[28],[31].Free-to-acceptor photoluminescence emission has also been observed in Mg-doped InN,with an activation energy of∼61meV derived for the Mg acceptor[29].In order to compensate the presence of large electron densities of nom-inally nondoped InN as well as the associated surface electron accumulation,a relatively high concentration of Mg dopant is required,which,however,may lead to the formation Mg-related, donorlike defects[29],[32],[33].Additionally,the growth and characterization of InN:Mg nanowires,to the best of our knowl-edge,has not been reported.It has been observed that the1077-260X/$26.00©2010IEEEincorporation of Mg can significantly affect the formation and structural properties of GaN nanowires[34],[35].The presence of Mg can greatly reduce the nanowire nucleation time and en-hance the growth rate on the nonpolar surfaces,thereby leading to wires with increased diameters and reduced lengths.Deterio-rated crystal structures were further observed at relatively high Mg concentrations.It is therefore of tremendous importance to develop nearly intrinsic InN nanowires as well as InN nanowire p-n junctions, in order to exploit the full potential of InN for third generation photovoltaics.In this context,we have performed a detailed in-vestigation of the MBE growth and characterization of nearly intrinsic and Si-and Mg-doped InN nanowires on Si(111) substrates without any external metal catalyst.Under optimized growth conditions,the wires exhibit nontapered surface mor-phology and excellent structural and optical properties.An ex-tremely narrow spectral linewidth of∼8meV,compared to the commonly reported values of50–100meV for n-type degener-ate InN nanowires,have been achieved for nearly intrinsic InN nanowires.Effects of Si and Mg incorporation on the structural and optical properties of InN nanowires have also been investi-gated.We have further studied the epitaxial growth,fabrication, and characterization of InN:Si/i-InN and InN:Mg/i-InN/InN:Si nanowire axial structures on p-type and n-type Si(111)sub-strates,respectively.With the use of CdS surface passivation, InN:Mg/i-InN/InN:Si nanowire homojunction solar cells exhibit a promising short-circuit current density of∼14.4mA/cm2and power-conversion efficiency of∼0.68%under simulated one-sun(AM1.5G)illumination.In Section II,the MBE growth and characterization of nearly intrinsic and Si-and Mg-doped InN nanowires isfirst presented.In Section III,we describe the design and fabrication of InN nanowire solar cells monolith-ically grown on Si.The characterization results and analysis are presented in Section IV.Finally,conclusions are made in Section V.II.MBE G ROWTH AND C HARACTERIZATIONOF I N N N ANOWIRESA.Nearly Intrinsic InN Nanowires on Si Substrates Electronically pure InN nanowires were grown on Si(111) substrates by plasma-assisted MBE under nitrogen-rich con-ditions without any external metal catalyst.To achieve high-quality InN nanowires with controllable structural properties, we investigated the self-catalytic growth of InN nanowires.In this process,a thin(∼0.5to1.6nm)In seeding layer isfirst deposited on the Si substrate surface prior to growth initia-tion[36],[37].The thin In layer forms nanoscale liquid droplets at elevated temperatures,which provides well-defined nucle-ation centers for the formation and growth of InN nanowires. Subsequently,the InN nanowire growth is carried out at a nom-inal growth rate of0.6˚A/s,nitrogenflow rate of1.0–2.0sccm, growth temperature of440–520◦C,and RF plasma forward power of∼400W.The scanning electron micrographs of InN nanowires grown on Si without and with the use of In seeding layer are shown in Fig.1(a)and(b),respectively.It is evident that significantly improved structural properties,with a nontapered surfacemor-Fig.1.Scanning electron micrographs of nondoped InN nanowires grown on Si(111)substrates by MBE(a)without and(b)with the use of an in situ deposited In seeding layer.phology and nearly identical heights,can be obtained by using an in situ deposited In seeding layer.Detailed analysis,described elsewhere[36],further confirms that the wires have a wurtzite crystal structure,orient along the c-axis and are relatively free of dislocations.Important for practical device applications is a precise control of the carrier concentration and conductivity of InN nanowires. The residual electron density of InN can be derived from a Hall-effect measurement or by analyzing the photoluminescence spectral linewidth measured at low temperatures[38],[39].For conventional n-type degenerate InN,the measured photolumi-nescence linewidths are generally in the range of50–100meV, which correspond to residual electron densities of∼1018cm−3, or higher[21].Illustrated in Fig.2are the photoluminescence spectra for the presently achieved nontapered InN nanowires measured under various laser powers at5K.An extremely narrow spectral linewidth of8meV was obtained under low excitation conditions.Detailed analysis revealed that the elec-tron density in the undoped InN nanowires is∼2×1015cm−3, or less,which is nearly a factor of500times smaller than the commonly reported values[20]–[25],suggesting,for thefirst time,the achievement of nearly intrinsic InN.The presence of an extremely low level of carrier concentration in the undoped InN nanowires is also directly reflected in the power-dependent photoluminescence emission,as shown in Fig.2.With increas-ing excitation power,there is a considerable blueshift in the photoluminescence peak energy,accompanied by a significantFig.2.Photoluminescence spectra of nondoped InN nanowires on Si(111)measured at 5K under various laserpowers.Fig.3.Photoluminescence spectra of InN nanowires on Si(111)substrates for Si doping concentrations of ∼1×1018cm −3(dashed and dotted line),2×1017cm −3(dotted line),5×1016cm −3(dashed line),nondoped (solid line),measured at 5K.broadening of the spectral linewidth.Such a clear band-filling effect has not been previously observed in the photolumines-cence emission of n-type degenerate InN.B.Si and Mg-Doped InN NanowiresWith the achievement of nearly intrinsic InN nanowires,we have subsequently investigated the growth and optical proper-ties of Si-and Mg-doped InN nanowires.These nanowires are grown by introducing the respective dopants during nanowire growth without any modifications to the previously described growth conditions.Due to the significantly enhanced In adatom surface migration and the preferred growth along the nanowire length direction,the resulting doping level is generally smaller,compared to that of planar heterostructures.It is expected that the local dopant fluctuation in the wires may also be negligible,due to the relatively large (>100nm)wire diameters.For the Si doping concentrations considered (<∼1×1018cm −3),no morphological changes to the InN nanowires were observed.However,the incorporation of Si dopant can significantly mod-ify the optical properties of InN nanowires.Illustrated in Fig.3are the photoluminescence spectra of InN:Si nanowires measured at 5K for various Si doping lev-els.It is seen that,with increasing Si doping concentration,InN nanowires exhibit a considerable blueshift in the photolumines-cence peak energy,a drastic increase in the spectral linewidth,and a significant decrease in the luminescence efficiency.SuchFig.4.Scanning electron microscopy image of InN nanowires grown on Si(111)substrates with a relatively high Mg doping concentration.The wires show deteriorated structural properties,with the presence of slightly tapered surface morphology.effects have also been observed at elevated temperatures and under various laser powers.The observed Burstein–Moss shift,i.e.,the significant increase in the photoluminescence peak en-ergy and broadening of the spectral linewidth,can be well ex-plained by the increased electron densities with increasing Si doping concentrations.However,the exact origin of the drasti-cally reduced luminescence efficiency with increasing Si doping concentration remains unclear.One possible explanation is the increasing surface electron accumulation,induced by the bulk electron density that leads to a significantly increased spatial separation of charge carriers in the wires.As a consequence,the radiative efficiency is reduced with increasing Si doping concentration.The correlation between the surface charge ac-cumulation and the bulk electron density has been suggested by recent studies [22].Detailed discussions on the surface charge properties of nearly intrinsic and Si-doped InN nanowires are described elsewhere.From photoluminescence measurements of InN:Mg films,it was determined that the Mg acceptor activation energy was about 61meV [29].However,to the best of our knowledge,the growth and properties of InN:Mg nanowires have not been reported.In this study,InN:Mg nanowires,with Mg effusion cell temperatures varying from 185◦C to 235◦C,are grown and characterized.It was observed that,for relatively low Mg concentrations,InN nanowires with excellent surface morphol-ogy and structural properties can be obtained.However,with increasing Mg flux,the wires show increasing diameter and re-ducing length,potentially due to the reduced adatom surface migration.Similar effects have also been observed for GaN:Mg nanowires [34],[35].A further increase of the Mg concentration generally leads to a tapered surface morphology,as shown in Fig.4,and the generation of dislocations.Illustrated in Fig.5are the photoluminescence spectra of InN:Mg nanowires measured at 5K for various Mg effu-sion cell temperatures.It is observed that the photolumines-cence peak intensity decreases considerably with increasing MgFig.5.5K photoluminescence spectra of InN:Mg nanowires grown at differ-ent Mg effusion cell temperatures.incorporation,which may be directly related to the formation of Mg-related defects.A detailed investigation of the underly-ing mechanism as well as the electrical transport properties and p-type conductivity of InN:Mg wires will be published in the future.III.D ESIGN AND F ABRICATION OF I N NN ANOWIRE S OLAR C ELLS ON S IThree InN nanowire solar cell designs,schematically illus-trated in Fig.6(a)–(c),have been investigated.In thefirst ap-proach,as shown in Fig.6(a),the InN nanowire solar cells consist of∼0.3μm nondoped and0.4μm Si-doped sections, which are grown directly on p-type Si(111)substrates.Such a design does not require the use of p-type InN nanowires,which had not been demonstrated prior to this study.The second and third designs employ InN p-i-n axial homojunctions,illustrated in Fig.6(b)and(c),which comprise of∼0.8μm InN:Si,0.2μm nondoped InN,and0.3μm InN:Mg sections grown on n-type Si(111)pared to thefirst design,the p-n junc-tion is formed within the wires.It may be noted that there is a small variation in the thicknesses of the device intrinsic regions, which may not have any major impact on the device efficiency. One of the primary limitations for semiconductor nanowire devices is the significant nonradiative carrier recombination as-sociated with the presence of surface states,which can be greatly minimized by using core–shell or dot/well-in-a-wire nanoscale heterostructures[40],[41].In this regard,we have further inves-tigated the use of a CdS passivation technique in the third design. Illustrated in Fig.6(c),a thin(∼10nm)CdS layer is coated on the nanowire surface using a chemical bath deposition method at∼70◦C,wherein the bath consists of CdCl2,NH4Cl,and NH4OH,with a molecular proportion of2:20:20:200[42].The resulting CdS layer is nearly intrinsic and exhibits a very high resistivity(∼106Ω·cm)[43].Such a passivation/buffer layer has been widely used in the fabrication of CuIn(Ga)Se2solar cells and has led to the most efficient(∼19.9%)thinfilm solar cells ever reported[44].Growth conditions for the various nanowire samples have been carefully controlled to achieve high-quality InN nanowires with relatively large diameters(>150nm)to effectively enhance the light absorption[45].The fabrication process for InN nanowire solar cells on Si is briefly described for the second design.A polyimide(PI)resist Fig.6.Schematic illustrations of(a)InN:Si/i-InN nanowire solar cells grown on p-type Si substrates,(b)InN:Mg/i-InN/InN:Si nanowire solar cells grown on n-type Si substrates,and(c)CdS-passivated InN:Mg/i-InN/InN:Si nanowire solar cells grown on n-type Si substrates.The top contact consists of thin (∼15nm)Ni/Au or Ti/Au layers.layer isfirst spin-coated to fully cover the InN nanowires for surface planarization.The PI layer is subsequently etched using O2:CF4(1:4)dry-etching until the top region of the wires is exposed,as shown in Fig.7(a).The sample is thenflood-exposed with UV light and hard-baked at350◦C for∼30min to cure the PI.The top exposed section of the wires is patterned,using standard photolithography,into cells of various sizes(0.09–1.00mm2)and,a thin Ni/Au(5nm/10nm)p-metal contact is deposited on the cell surface,as shown in Fig.7(b),which is followed by the deposition of thick Ni/Au metal contact layers at the periphery of the devices.Ti/Au(30nm/150nm)layers are then deposited on the backside of the n-Si substrate as the n-metal contact.The sample is annealed at300–400◦C for60s.IV.R ESULTS AND D ISCUSSSIONSThe performance characteristics of InN nanowire solar cells on Si is measured under dark and illuminated(one sun at AM 1.5G)conditions.Characteristics of thefirst design,i.e.,the InN:Si/i-InN/p-Si heterojunction nanowire solar cells isfirstFig.7.45◦scanning electron microscopy images of(a)the InN nanowire ensemble spin-coated with a PI layer,with the top region of the wires exposed by dry etching and(b)the PI immersed wire ensemble after the deposition of Ni/Au contact layers.described.The current–voltage(I–V)response of such devices measured under dark conditions is shown in Fig.8(a).It is seen that InN/Si nanowire heterojunction design exhibits very poor diode characteristics,with rectifying ratios in the range of∼2 to4measured at−0.5and0.5V.At−1V,a leakage current of more than100mA/cm2was measured.As a consequence,no significant photo response was observed.The measured short-circuit current density and energy-conversion efficiency are less than2mA/cm2and0.01%,respectively.The underlying mech-anism for the extremely poor device performance has been in-vestigated.Due to the very large electron affinity(∼5.8eV) of InN,its conduction band minimum is positioned well below the valence band maximum of Si.In addition,a thin(∼2to 3nm)amorphous layer(SiN x)is generally formed at the InN/Si misfit interface[36].The resulting energy-band diagram of the n-InN/i-InN/p-Si heterostructure under thermal equilibrium is schematically shown in Fig.8(b).The depletion occurs at both sides of the InN/Si junction.It is seen that large densities of electrons accumulate at the InN/Si junction interface,which can readily recombine with holes in the Si valence band and therefore explains the quasi-ohmic behavior observed for the n-InN/i-InN/p-Si heterojunction device under dark conditions. However,the depletion creates a significant barrier to the trans-port of photogenerated holes,leading to negligible response underillumination.Fig.8.(a)I–V response of InN:Si/i-InN nanowire devices on p-Si(111) measured under dark conditions.(b)Schematic of the energy band diagram of the InN:Si/i-InN/p-Si heterojunction under thermal equilibrium.The presence of a thin(∼2to3nm)amorphous SiN x layer is alsoillustrated.Fig.9.(a)I–V characteristics of InN:Mg/i-InN/InN:Si nanowire solar cells grown on n-type Si(111)substrates under dark and illumination(1-sun at AM 1.5G)conditions.(b)Illustration of the corresponding energy band diagram of the nanowire junction under thermal equilibrium.Drastically improved device performance,illustrated in Fig.9(a),has been measured for the second solar cell de-sign grown on n-type Si substrates.Under dark conditions,the InN:Si/i-InN/InN:Mg nanowire device exhibits characteristics of a diode structure,with a significantly improved rectifying ratio(∼60)measured at–1and+1V,which is attributed to the built-in electricfield in the p-i-n nanowire homojunction.Fig.10.I–V characteristics of CdS-passivated InN:Mg/i-InN/InN:Si nanowire solar cells grown on n-type Si(111)substrates under dark and light (1-sun at AM1.5G)illumination conditions.In addition,a clear photoresponse has been consistently ob-served.Under simulated AM1.5G illumination,a promising short-circuit current density of∼12.91mA/cm2is obtained for a device area of1mm2.The measured open-circuit voltage,fill factor,and power-conversion efficiency are∼0.13V,30.2%, and0.51%,respectively.The functioning of the InN p-i-n axial homojunction solar cells on n-type Si may be explained by the energy-band diagram under thermal equilibrium.Illustrated in Fig.9(b),it may be noted that the depletion region widths of the InN/Si junction are small,due to the very high doping concen-trations in InN and Si.As a consequence,electrons can readily tunnel from InN to Si.Illumination from the top of the nanowires would result in photons with energy larger than E g(InN)to be absorbed by the nanowires.The holes and electrons produced in InN can be promptly collected by the ohmic contacts at the top of the wires and the back contact of the substrate,respectively, thereby generating the observed photocurrent.While photons with energy larger than E g(Si)could also be absorbed by the substrate when light illuminates onto the Si surface through the gap between the wires,the contribution to the photocurrent is expected to be negligible,due to the presence of a significant barrier to hole transport across the InN/Si heterointerface. The performance of the afore-described InN:Si/i-InN/ InN:Mg nanowire homojunction solar cells may be severely lim-ited by the presence of surface states,which can be addressed,to a certain extent,with the use of CdS surface passivation[46].Il-lustrated in Fig.10are the measured I–V curves under dark and illuminated conditions for the third nanowire solar cell design, wherein a thin(∼10nm)CdS passivation layer is incorporated.A reduction in the reverse leakage current and an improvement in the rectifying ratio(∼150)were measured,compared to iden-tical devices fabricated without the use of any CdS passivation. The improved diode characteristics are attributed to the effec-tive carrier confinement provided by the large bandgap CdS and the suppression of carrier leakage through the wire surface.Un-der one-sun(AM1.5G)illumination,the devices exhibit further improved performance,with a short-circuit current density of ∼14.4mA/cm2,open-circuit voltage of0.14V,fill factor of 34.0%,and energy-conversion efficiency of0.68%.It may be noted that the measured short-circuit current densities are much larger than the commonly reported values for nanowire solar cells[12],[13],[47]–[49].The open-circuit voltage,however,is relatively low,which can be improved by utilizing large bandgap InGaN nanowires and by optimizing the surface passivation and fabrication processes.The performance of the presently demonstrated InN nanowire solar cells may also be severely limited by the surface electron accumulation of n-type InN and the nonideal carrier transport across the InN/Si misfit interface,due to the presence of an amorphous SiN x layer.Improved device performance is,there-fore,expected by utilizing core/shell heterostructures and by employing a planar GaN or InN buffer layer.Additionally,the energy-conversion efficiency is practically limited by the very low wire density in this experiment.Shown in Fig.7(a),the sur-face coverage of InN nanowires is less than30%.As a result,a significant portion of the solar radiation cannot be absorbed by InN,and the benefit of light trapping associated with nanowires may be absent as well.Consequently,by optimizing the wire density and diameters,the energy-conversion efficiency can be readily increased by a factor of3,or larger.More importantly, the energy-conversion efficiency is expected to improve substan-tially for InGaN nanowire solar cells with an optimized energy bandgap.The use of coalescent growth for a planar top contact layer will also greatly facilitate the device fabrication and re-duce the series resistance[50].The growth and characterization of high-performance InGaN nanowire solar cells on Si,with the use of optimized surface passivation and device fabrication processes,are being investigated.V.C ONCLUSIONIn summary,we have investigated the MBE growth and char-acterization of high quality InN nanowires on Si(111)substrates and achieved nearly intrinsic InN nanowires as well as Si-and Mg-doped InN nanowires with excellent morphological and op-tical properties.We have further demonstrated thefirst InN solar cells,consisting of InN:Si/i-InN/InN:Mg nanowire homojunc-tions on n-type Si(111)substrates,which exhibit a promising short-circuit current density of∼14.4mA/cm2and an energy-conversion efficiency of∼0.68%under one-sun(AM1.5G) illumination.Further improvement in the device performance is being investigated by optimizing the growth and fabrication processes.The present work constitutes important progress for the realization of InGaN-based third generation solar cells.It has also mitigated some of the major barriers for the future develop-ment of InN-based nanoelectronic and nanophotonic devices.A CKNOWLEDGMENTPart of the work was performed in the McGill Nanotools Microfab Laboratory.R EFERENCES[1]J.Wu,W.Walukiewicz,K.M.Yu,W.Shan,J.W.Ager,E.E.Haller,H.Lu,W.J.Schaff,W.K.Metzger,and S.Kurtz,“Superior radiation resistance of In1−x Ga x N alloys:Full-solar-spectrum photovoltaic material system,”J.Appl.Phys.,vol.94,pp.6477–6482,Nov.15,2003.[2]O.Jani,I.Ferguson,C.Honsberg,and S.Kurtz,“Design and characteri-zation of GaN/InGaN solar cells,”Appl.Phys.Lett.,vol.91,pp.132117-1–1132117-3,Sep.24,2007.[3]H.Hamzaoui,A.S.Bouazzi,and B.Rezig,“Theoretical possibilities ofIn x Ga1−x N tandem PV structures,”Sol.Energ.Mat.Sol.Cells.,vol.87, pp.595–603,May2005.[4]X.M.Cai,S.W.Zeng,and B.P.Zhang,“Fabrication and characterizationof InGaN p-i-n homojunction solar cell,”Appl.Phys.Lett.,vol.95, pp.173504-1–173504-3,Oct.26,2009.[5]L.Hsu and W.Walukiewicz,“Modeling of InGaN/Si tandem solar cells,”J.Appl.Phys.,vol.104,pp.024507-1–024507-7,Jul.15,2008.[6]J.Wu,W.Walukiewicz,W.Shan,K.Yu,J.Ager,S.Li,E.Haller,H.Lu,and W.Schaff,“Temperature dependence of the fundamental band gap of InN,”J.Appl.Phys.,vol.94,pp.4457–4460,Oct.1,2003.[7] C.Neufeld,N.Toledo,S.Cruz,M.Iza,S.DenBaars,and U.Mishra,“Highquantum efficiency InGaN/GaN solar cells with2.95eV band gap,”Appl.Phys.Lett.,vol.93,pp.143502-1–143502-3,Oct.6,2008.[8] E.Trybus,G.Namkoong,W.Henderson,S.Burnham,W.Doolittle,M.Cheung,and A.Cartwright,“InN:A material with photovoltaic promise and challenges,”J.Cryst.Growth,vol.288,pp.218–224,Mar.1,2006.[9]X.B.Zhang,X.L.Wang,H.L.Xiao,C.B.Yang,J.X.Ran,C.M.Wang,Q.F.Hou,J.M.Li,and Z.G.Wang,“Theoretical design and performance of In x Ga1−x N two-junction solar cells,”J.Phys.D:Appl.Phys.,vol.41, p.245104,Dec.21,2008.[10] C.H.Henry,“Limiting efficiencies of ideal single and multiple energygap terrestrial solar cells,”J.Appl.Phys.,vol.51,pp.4494–4500,Aug.1980.[11]H.Neff,O.Semchinova,A.Lima,A.Fillmonov,and G.Holzhueter,“Photovoltaic properties and technological aspects of In1−x Ga x N/Si,Ge (0<x<0.6)heterojunction solar cells,”Sol.Energ.Mat.Sol.Cells., vol.90,pp.982–997,May5,2006.[12]Y.Tang,Z.Chen,H.Song,C.Lee,H.Cong,H.Cheng,W.Zhang,I.Bello,and S.Lee,“Vertically aligned p-type single-crystalline GaNnanorod arrays on n-type Si for heterojunction photovoltaic cells,”Nano Lett.,vol.8,pp.4191–4195,Dec.2008.[13]Y.J.Dong,B.Z.Tian,T.J.Kempa,and C.M.Lieber,“Coaxial groupIII-nitride nanowire photovoltaics,”Nano Lett.,vol.9,pp.2183–2187, May2009.[14]K.H.Yu and J.H.Chen,“Enhancing solar cell efficiencies through1-Dnanostructures,”Nanoscale Res.Lett.,vol.4,pp.1–10,Jan.2009. [15]Z.Cai,S.Garzon,M.Chandrashekhar,R.Webb,and G.Koley,“Synthesisand properties of high-quality InN nanowires and nanonetworks,”J.Electron.Mater.,vol.37,pp.585–592,May2008.[16] C.Chao,J.Chyi,C.Hsiao,C.Kei,S.Kuo,H.Chang,and T.Hsu,“Catalyst-free growth of indium nitride nanorods by chemical-beam epitaxy,”Appl.Phys.Lett.,vol.88,pp.233111-1–233111-3,Jun.5,2006.[17] C.Liang,L.Chen,J.Hwang,K.Chen,Y.Hung,and Y.Chen,“Selective-area growth of indium nitride nanowires on gold-patterned Si(100)sub-strates,”Appl.Phys.Lett.,vol.81,pp.22–24,Jul.1,2002.[18]T.Stoica,R.Meijers,R.Calarco,T.Richter,and H.Luth,“MBE growthoptimization of InN nanowires,”J.Cryst.Growth,vol.290,pp.241–247, Apr.15,2006.[19]J.Grandal,M.Sanchez-Garcia,E.Calleja,E.Luna,and A.Trampert,“Ac-commodation mechanism of InN nanocolumns grown on Si(111)sub-strates by molecular beam epitaxy,”Appl.Phys.Lett.,vol.91,pp.021902-1–021902-3,Jul.9,2007.[20]J.Segura-Ruiz,N.Garro,A.Cantarero,C.Denker,J.Malindretos,andA.Rizzi,“Optical studies of MBE-grown InN nanocolumns:Evidence ofsurface electron accumulation,”Phys.Rev.B,vol.79,pp.115305-1–115305-9,Mar.2009.[21]T.Stoica,R.Meijers,R.Calarco,T.Richter,E.Sutter,and H.Luth,“Pho-toluminescence and intrinsic properties of MBE-grown InN nanowires,”Nano Lett.,vol.6,pp.1541–1547,Jul.12,2006.[22]V.Darakchieva,T.Hofmann,M.Schubert,B.E.Sernelius,B.Monemar,P.O.A.Persson,F.Giuliani,E.Alves,H.Lu,and W.J.Schaff,“Free electron behavior in InN:On the role of dislocations and surface electron accumulation,”Appl.Phys.Lett.,vol.94,pp.022109-1–022109-3,Jan.12,2009.[23]M.Feneberg,J.Daubler,K.Thonke,R.Sauer,P.Schley,and R.Goldhahn,“Mahan excitons in degenerate wurtzite InN:Photolumines-cence spectroscopy and reflectivity measurements,”Phys.Rev.B,vol.77, pp.245207-1–245207-6,Jun.2008.[24] A.Janotti and C.G.Van de Walle,“Sources of unintentional conductivityin InN,”Appl.Phys.Lett.,vol.92,pp.032104-1–032104-3,Jan.21,2008.[25] C.G.Van de Walle and J.Neugebauer,“Universal alignment of hydrogenlevels in semiconductors,insulators and solutions,”Nature,vol.423, pp.626–628,Jun.5,2003.[26] E.Calleja,J.Grandal,M.Sanchez-Garcia,M.Niebelschutz,V.Cimalla,and O.Ambacher,“Evidence of electron accumulation at nonpolar sur-faces of InN nanocolumns,”Appl.Phys.Lett.,vol.90,pp.262110-1–262110-3,Jun.25,2007.[27]J.H.Song,T.Akiyama,and A.J.Freeman,“Stabilization of bulk p-typeand surface n-type carriers in Mg-doped InN{0001}films,”Phys.Rev.Lett.,vol.101,pp.186801-1–186801-4,Oct.31,2008.[28]P.A.Anderson,C.H.Swartz,D.Carder,R.J.Reeves,S.M.Durbin,S.Chandril,and T.H.Myers,“Buried p-type layers in mg-doped InN,”Appl.Phys.Lett.,vol.89,pp.184104-1–184104-3,Oct.30,2006. [29]X.Q.Wang,S.B.Che,Y.Ishitani,and A.Yoshikawa,“Growth andproperties of Mg-doped in-polar InNfilms,”Appl.Phys.Lett.,vol.90, pp.201913-1–201913-3,May14,2007.[30]R.Kudrawiec,T.Suski,J.Serafinczuk,J.Misiewicz,D.Muto,andY.Nanishi,“Photoreflectance of InN and InN:Mg layers:An evidence of Fermi level shift toward the valence band upon Mg doping in InN,”Appl.Phys.Lett.,vol.93,pp.131917-1–131917-3,Sep.29,2008.[31]R.E.Jones,K.M.Yu,S.X.Li,W.Walukiewicz,J.W.Ager,E.E.Haller,H.Lu,and W.J.Schaff,“Evidence for p-type doping of InN,”Phys.Rev.Lett.,vol.96,pp.125505-1–125505-4,Mar.31,2006.[32]I.Mahboob,T.Veal,C.McConville,H.Lu,and W.Schaff,“Intrinsicelectron accumulation at clean InN surfaces,”Phys.Rev.Lett.,vol.92, pp.036804-1–036804-4,Jan.23,2004.[33] C.L.Wu,H.M.Lee,C.T.Kuo,C.H.Chen,and S.Gwo,“Absence ofFermi-level pinning at cleaved nonpolar InN surfaces,”Phys.Rev.Lett., vol.101,pp.106803-1–106803-4,Sep.5,2008.[34] B.Beaumont,S.Haffouz,and P.Gibart,“Magnesium induced changes inthe selective growth of GaN by metalorganic vapor phase epitaxy,”Appl.Phys.Lett.,vol.72,pp.921–923,Feb.23,1998.[35] F.Furtmayr,M.Vielemeyer,M.Stutzmann,J.Arbiol,S.Estrade,F.Peiro,J.R.Morante,and M.Eickhoff,“Nucleation and growth of GaN nanorods on Si(111)surfaces by plasma-assisted molecular beam epitaxy—The influence of Si-and Mg-doping,”J.Appl.Phys.,vol.104,pp.034309-1–034309-7,Aug.1,2008.[36]Y.L.Chang,F.Li,A.Fatehi,and Z.Mi,“Molecular beam epitaxialgrowth and characterization of non-tapered InN nanowires on Si(111),”Nanotechnology,vol.20,p.345203,Aug.26,2009.[37]Y.L.Chang,F.Li,and Z.Mi,“Optimization of the structural and opticalquality of InN nanowires on Si(111)by molecular beam epitaxy,”J.Vac.Sci.Technol.B,vol.28,pp.C3B7–C3B11,May2010.[38]M.Moret,S.Ruffenach,O.Briot,and B.Gil,“The determination of thebulk residual doping in indium nitridefilms using photoluminescence,”Appl.Phys.Lett.,vol.95,pp.031910-1–031910-3,Jul.20,2009. [39]S.P.Fu,T.T.Chen,and Y.F.Chen,“Photoluminescent properties of InNepifilms,”Semicond.Sci.Technol.,vol.21,pp.244–249,Mar.2006. [40]Y.L.Chang,J.L.Wang,F.Li,and Z.Mi,“High efficiency green,yellow,and amber emission from InGaN/GaN dot-in-a-wire heterostructures on Si(111),”Appl.Phys.Lett.,vol.96,pp.013106-1–013106-3,Jan.4, 2010.[41] F.Qian,Y.Li,S.Gradecak,D.Wang,C.Barrelet,and C.Lieber,“Galliumnitride-based nanowire radial heterostructures for nanophotonics,”Nano Lett.,vol.4,pp.1975–1979,Oct.2004.[42]H.Du,I.Shih,and C.Champness,“Monocrystalline CulnSe(2)photo-voltaic cell of superior performance,”J.Vac.Sci.Technol.A,vol.22, pp.1023–1026,May/Jun.2004.[43]K.S.Ramaiah,V.S.Raja,A.K.Bhatnagar,R.D.Tomlinson,R.D.Pilkington,A.E.Hill,S.J.Chang,Y.K.Su,and F.S.Juang,“Optical, structural and electrical properties of tin doped indium oxide thinfilms prepared by spray-pyrolysis technique,”Semicond.Sci.Technol.,vol.15, pp.676–683,Jul.2000.[44]M.A.Contreras,B.Egaas,K.Ramanathan,J.Hiltner,A.Swartzlander,F.Hasoon,and R.Noufi,“Progress toward20%efficiency in Cu(In,Ca)Se-2polycrystalline thin-film solar cells,”Prog.Photovolt:Res.Appl.,vol.7, pp.311–316,Jul./Aug.1999.[45]J.S.Li,H.Y.Yu,S.M.Wong,X.C.Li,G.Zhang,P.G.Q.Lo,andD.L.Kwong,“Design guidelines of periodic Si nanowire arrays for solarcell application,”Appl.Phys.Lett.,vol.95,pp.243113-1–243113-3, Dec.14,2009.[46]O.V.Galan,rramendi,I.Riech,G.Pena,A.Iribarren,J.Aguilar-Hernandez,and G.Contreras-Puente,“Characterization of the passivation of CdS thinfilms grown by chemical bath deposition on InP,”Semicond.Sci.Technol.,vol.17,pp.1193–1197,Nov.2002.。
质谱分析法:mass spectrometry质谱:mass spectrum,MS棒图:bar graph选择离子检测:selected ion monitoring ,SIM直接进样:direct probe inlet ,DPI接口:interface气相色谱-质谱联用:gas chromatography-mass spectrometry,GC-MS 高效液相色谱-质谱联用:high performance liquid chromatography-mass spectrometry,HPLC-MS电子轰击离子源:electron impact source,EI离子峰:quasi-molecular ions化学离子源:chemical ionization source,CI场电离:field ionization,FI场解析:field desorptiion,FD快速原子轰击离子源:fast stom bombardment ,FAB质量分析器:mass analyzer磁质谱仪:magnetic-sector mass spectrometer四极杆质谱仪(四极质谱仪):quadrupole mass spectrometer紫外-可见分光光度法:ultraviolet and visible spectrophotometry;UV-vis 相对丰度(相对强度):relative avundance原子质量单位:amu离子丰度:ion abundance基峰:base peak质量范围:mass range分辨率:resolution灵敏度:sensitivity信噪比:S/N分子离子:molecular ion碎片离子:fragment ion同位素离子:isotopic ion亚稳离子:metastable ion亚稳峰:metastable peak母离子:paren ion子离子:daughter含奇数个电子的离子:odd electron含偶数个电子的离子:even eletron,EE 均裂:homolytic cleavage异裂(非均裂):heterolytic cleavage 半均裂:hemi-homolysis cleavage重排:rearragement分子量:MWα-裂解:α-cleavage 电磁波谱:electromagnetic spectrum光谱:spectrum光谱分析法:spectroscopic analysis原子发射光谱法:atomic emission spectroscopy肩峰:shoulder peak末端吸收:end absorbtion生色团:chromophore助色团:auxochrome红移:red shift长移:bathochromic shift短移:hypsochromic shift蓝(紫)移:blue shift增色效应(浓色效应):hyperchromic effect 减色效应(淡色效应):hypochromic effect 强带:strong band弱带:weak band吸收带:absorption band透光率:transmitance,T吸光度:absorbance谱带宽度:band width杂散光:stray light噪声:noise暗噪声:dark noise散粒噪声:signal shot noise闪耀光栅:blazed grating全息光栅:holographic graaing光二极管阵列检测器:photodiode array detector偏最小二乘法:partial least squares method ,PLS褶合光谱法:convolution spectrometry 褶合变换:convolution transform,CT离散小波变换:wavelet transform,WT 多尺度细化分析:multiscale analysis供电子取代基:electron donating group 吸电子取代基:electron with-drawing group荧光:fluorescence荧光分析法:fluorometryX-射线荧光分析法:X-ray fulorometry 原子荧光分析法:atomic fluorometry分子荧光分析法:molecular fluorometry 振动弛豫:vibrational relexation内转换:internal conversion外转换:external conversion 体系间跨越:intersystem crossing激发光谱:excitation spectrum荧光光谱:fluorescence spectrum斯托克斯位移:Stokes shift荧光寿命:fluorescence life time荧光效率:fluorescence efficiency荧光量子产率:fluorescence quantum yield荧光熄灭法:fluorescence quemching method散射光:scattering light瑞利光:Reyleith scanttering light拉曼光:Raman scattering light红外线:infrared ray,IR中红外吸收光谱:mid-infrared absorption spectrum,Mid-IR远红外光谱:Far-IR微波谱:microwave spectrum,MV红外吸收光谱法:infrared spectroscopy 红外分光光度法:infrared spectrophotometry振动形式:mode of vibration伸缩振动:stretching vibrationdouble-focusing mass spectrograph 双聚焦质谱仪trochoidal mass spectrometer 余摆线质谱仪ion-resonance mass spectrometer 离子共振质谱仪gas chromatograph-mass spectrometer 气相色谱-质谱仪quadrupole spectrometer 四极(质)谱仪Lunar Mass Spectrometer 月球质谱仪Frequency Mass Spectrometer 频率质谱仪velocitron 电子灯;质谱仪mass-synchrometer 同步质谱仪omegatron 回旋质谱仪。
Evidence on the Nature and Sources of Agglomeration EconomiesStuart S. RosenthalDepartment of Economicsand Center for Policy Research,Syracuse University,Syracuse, NY 13244-1020, USAPhone: 315-443-3809; Email: ssrosent@Web: /faculty/rosenthal/andWilliam C. StrangeRIOCAN Real Estate Investment Trust Professor of Real Estate and Urban EconomicsRotman School of Management105 St. George St.University of TorontoToronto, ON M5S 3E6, CanadaPhone: (416) 978-1949; Email: wstrange@rotman.utoronto.caWeb: www.rotman.utoronto.ca/~wstrange/Prepared for the Handbook of Urban And Regional Economics, Volume 4November 4, 2002Revised: August 24, 2003*We are grateful to Gilles Duranton, Vernon Henderson, Jacques Thisse and the participants of a presentation at the North American Regional Science Association Meetings in November, 2002. Any errors are ours alone. We are also grateful for the financial support of the National Institute of Aging, the Connaught Fund at the University of Toronto, and the Social Sciences and Humanities Research Council of Canada.AbstractThis paper considers the empirical literature on the nature and sources of urban increasing returns, also known as agglomeration economies. An important aspect of these externalities that has not been previously emphasized is that the effects of agglomeration extend over at least three different dimensions. These are the industrial, geographic, and temporal scope of economic agglomeration economies. In each case, the literature suggests that agglomeration economies attenuate with distance.Recently, the literature has also begun to provide evidence on the microfoundations of external economies of scale. The best known of these sources are those attributed to Marshall (1920): labor market pooling, input sharing, and knowledge spillovers. Evidence to date supports the presence of all three of these forces. In addition, there is also evidence that natural advantage, home market effects, consumption opportunities, and rent-seeking all contribute to agglomeration.JEL Codes: R0 (Urban, Rural, and Regional Economics: General), O4 (Economic Growth and Aggregate Productivity), D2 (Production and Organizations), C1 (Econometric and Statistical Methods: General)Keywords: agglomeration economies, productivity, external economies, microfoundations, urban growth1. IntroductionThe degree of concentration of economic activity is striking. Roughly 75% of Americans live in cities as defined by the Census Department, and yet cities occupy only 2% of the land area of the lower 48 states. A similar story could be told for any other developed county: labor and capital are both heavily concentrated in cities.It is not just aggregate activity that is agglomerated. Individual industries are concentrated too. Figure 1, for instance, presents the density of employment in the furniture industry (SIC). Most of the country has almost no employment in the industry, as the map shows. The map also shows that the counties that do have employment are not randomly scattered across the U.S. They are disproportionately located in the western part of North Carolina and in other nearby locations. Clearly, furniture is an industry that makes use of particular raw materials, especially wood. Forestry is an important industry in North Carolina and elsewhere in the Southeast, so the location is sensible because of the access it offers to raw materials. But there are a lot of other equally sensible locations elsewhere in the county, from Maine to Oregon. Clearly, something beyond locating near raw materials sources is taking place.The macro pattern of Figure 1 repeats itself in Figure 2, a map of the location of software producers (SIC 7371-7373 and 7375) in the vicinity of San Francisco. The map reports both the locations of existing establishments and the locations where new establishments are created (births). As can readily be seen, both are concentrated. In this case, there is no material input that is analogous to trees. Despite this, activity is highly concentrated in what is known as the Silicon Valley north of San Jose and in San Jose itself. Again, something is going on that is leading to this kind of geographic concentration.This chapter will survey empirical work on the forces that lead to concentration, both of industries in clusters and of aggregate activity in cities. These forces are known variously as agglomeration economies or external economies of scale. In surveying the empirical work, the chapter will be concerned with two related questions: what is the nature and what are the sources of the increasing returns that produce agglomeration? In considering the nature of agglomeration economies we will be concerned with a number of smaller questions. Are they local, as seems to be the case in software, or do they operate at a regional scale, as seems to be the case for furniture? Are they restricted to individual industries like software and furniture, or are their effects comprehensive, extending across all activities? What is the dynamic nature of agglomeration economies? Are the effects of proximity felt immediately or does agglomeration have its positive effect on productivity only with a lag? Finally, are the effects dependent simply on the amount of activity that takes place somewhere, or is the nature of local interactionsimportant to the process of agglomeration? All of these questions relate to what we will define as the scope of agglomeration economies. The empirical answers to these questions will be discussed together in Section 2.The second broad question concerns the sources of agglomeration economies. Marshall (1920) suggests three. The first of these is the sharing of inputs whose production involves internal increasing returns to scale. The second is labor market pooling, where agglomeration allows a better match between an employer's needs and a worker's skills and reduces risk for both. The third source is spillovers in knowledge that take place when an industry is localized, allowing workers to learn from each other.1 Other sources have been suggested more recently. These include home market effects, where the concentration of demand encourages agglomeration, and economies in consumption, where cities exist because people like the bright lights. On the negative side, it has also been suggested that agglomeration is related to rent-seeking, with inefficient mega-cities arising more frequently in undemocratic countries. This so-called urban primacy has many effects, with one being to redistribute the government's expropriated resources among the urban mob. Section 3 considers the empirical work that has addressed these issues.Sections 2 and 3 review an econometric literature that is only about thirty years old. This literature has made substantial progress, especially in recent years as more refined data have become available. This has allowed researchers to ask questions that could not have been asked with more aggregate data. For example, evaluating the geographic extent of agglomeration economies is not possible without geographically refined data. Access to better data has also enabled researchers to answer old questions with greater precision, such as whether agglomeration economies are industry-specific or extend to the entire city. Despite the impressive record of progress of this program of formal econometric work, we believe there is much to be learned from less formal research. In Section 4, we consider some representative case studies. This is obviously a much older way to understand the facts that bear on agglomeration than through regression analysis. Even so, we believe it is an important part of the entire empirical story, both confirming and placing in context the formal empirical work and identifying important details in the big picture of agglomeration that the formal work misses.We now turn to the scope of agglomeration economies.1 In another chapter in this volume, Duranton and Puga (2004) propose a different taxonomy: matching, sharing, and learning.2. The scope of urban increasing returns2.1 IntroductionExternal economies exist when the scale of the urban environment adds to productivity. There are at least three dimensions over which these externalities may extend. We refer to the extent of the externality as its scope. The first and most familiar is the industrial scope. This is the degree to which agglomeration economies extend across industries, possibly even across all industries in a city, rather than being confined within industry boundaries. This distinction is well known, with the economies of scale that arise from spatial concentration of activity within a given industry being known as localization economies. The externalities that arise from the concentration of all economic activity, or from city size itself, are known as urbanization economies. As will become apparent, empirical evidence in the literature suggests that as agents become closer in industrial space (i.e., their production processes become more similar), then there is greater potential for interaction.The second kind of scope is geographic. Nearly every textbook in urban economics begins by explaining why cities exist. The answer is that proximity is advantageous. Thus, the discussion of agglomeration begins with the idea that geographic distance is crucial to understanding cites. The aspect of geographic distance that will matter most here is the attenuation of agglomeration economies with distance: if agents are physically closer, then there is more potential for interaction.The third kind of scope is temporal. It is possible that one agent's interaction with another agent at a point in the past continues to have an effect on productivity in the present. For example, learning may take place only gradually, and awareness of a location's supply chain possibilities may take time to develop. Of course, such knowledge can decay over time. This means that in addition to the fairly well-known static agglomeration economies, there may also be dynamic agglomeration economies. That two agents who are separated temporally continue to affect each other is logically similar to the way that agents who are separated in physical or industrial space interact. The degree to which these time-separated interactions continue to be potent defines the temporal scope of agglomeration economies.This section will examine recent empirical studies that shed light on each of these three aspects of the scope of external economies of scale. Table 1 provides a selective overview of the literature. We will begin by characterizing how one might proceed given a hypothetical “perfect” data set, free of measurement error, with no omitted variables, and including instruments that resolve all issues related to endogenous regressors. Against the backdrop of this ideal, we will discuss estimation strategies have been pursued in the presence of the imperfect data sets that actually are available. We then examine the evidence on the industrial, geographic,and temporal scope of agglomeration. Finally, we conclude the section by discussing empirical literature that sheds light on the manner in which the industrial organization and business "culture” of the local economy affects the generation and reception of external economies of scale.2.2 Strategies for evaluating the scope of agglomeration economies2.2.1 ContextExternal economies are by definition shifters of an establishment's production function. The first issue that must be confronted is whether the effect is Hicks neutral, or whether it augments labor or some other input in the production function. We will suppose the change to be neutral, consistent with empirical evidence from Henderson (1986). Given the Hicks neutrality assumption, an establishment's production function may be written as g(A)f(x), where x is a vector of the usual inputs (land, labor, capital, and materials) and A characterizes the establishment's environment. The latter allows for the influence of agglomeration.A general specification of agglomeration economies is that the aggregate urban external effect arises as the sum of a large number of individual externalities. We will treat the externalities as being between establishments, although they could instead be between individuals. Consider two establishments, j and k. The effect of establishment k on establishment j depends on the scale of activity at both establishments. In addition, the impact of k on j also depends on the distance between the two establishments, where distance is measured over three different dimensions. First, the influence of j on k depends on the geographic distance between the two establishments, d G jk. Second, it also depends on the type of industrial activity that takes place at the two establishments. It is natural to refer to this as the industrial distance between j and k, denoted here as d I jk. Two establishments carrying out the same kind of production would have d I jk, = 0, and d I jk would increase as the production processes become more dissimilar. Third, the impact of the interaction may extend temporally. At any point in time, establishment j may currently benefit from interaction with establishment k at some point in the past. This temporal dimension of distance is denoted d T jk. For example, for an interaction two years ago, d T jk would equal two.An increase in any of these kinds of distance --spatial, industrial, or temporal-- presumably leads to the attenuation of the agglomerative effect of establishment k on establishment j's production function. Formally, let the set of establishments with which establishment j might possibly benefit from interacting with be defined as K. Assume that all benefits to j from interaction with establishment k∈K equal q(x j, x k)a(d G jk, d I jk, d T jk). The first expression, q(x j, x k), reflects benefits from interaction that depend on the scales of j's and k's activities, denoted by their input vectors x j and x k. For example, it is common to suppose that thestrength of the interaction is captured by the size of establishment k's workforce, with othercharacteristics of establishment k having no effect. The second expression captures theattenuation of the interaction as establishments become more distant from each other.Specifically, holding the scale of the interaction constant, the benefit of an interaction withestablishment k ∈ K at geographic distance d G jk, industrial distance d I jk, and temporal distanced T jk is defined as a(d G jk, d I jk, d T jk). The total benefit of agglomeration enjoyed by establishment jis then equal to the sum over interaction partners of the agglomerative effect as a function ofgeographic, industrial, and temporal distance:A j = ∑k ∈ K q(x j, x k)a(d G jk, d I jk, d T jk). (2.1)The construction of (2.1) immediately suggests some issues that bear on the estimation ofagglomeration economies. The first is that A varies across establishments because each belongsto a given industry and is situated at a unique location over a particular period of time. Thesecond issue is that each dimension of agglomeration economies could in principle be measuredcontinuously. This would require some attempt to capture the attenuation of agglomerationeconomies as establishments move farther apart, both in the standard sense of physical space butalso in the more novel sense of industrial and temporal space.It is fair to say that relatively little of the empirical work on the scope of agglomerationeconomies has addressed the issues of establishment uniqueness and continuity. Instead, withregard to geography, most studies have grouped industries and plants into politically definedregions such as Metropolitan Statistical Areas (MSAs) or counties. Activity in neighboringregions is then typically assumed, usually implicitly, to have no effect on the region in question,and all activity within the specified region is treated as being situated at exactly the same spot.With regard to the type of industrial activity, most studies have collapsed industrial activity intojust two broad categories: activity within an establishment's industry (i.e., SIC code) and activityoutside of the establishment's industry. This, of course, does not capture the possibility thatsome industries belonging to different industry categories are close cousins, while others arehardly related at all.2 With regard to temporal dimensions of agglomeration, several studies haveconsidered the influence of time, but most have not.Assuming that A j could be fully specified and measured without error, the equation to beestimated is2Ellison and Glaeser (1997) examine exactly this issue when they construct measures of co-agglomeration.y j = g(A j)f(x j). (2.2)y j is establishment j's output, x j represents j's traditional inputs and A j is given in (2.1). Inprinciple, estimates of equation (2.2) would provide measures of the productivity effects of theindustrial, spatial, and temporal dimensions of agglomeration. In practice, attempts to estimate(2.2) face many challenges. We will now set out the challenges in detail.2.2.2 Measuring the scope of agglomerationIn order to estimate an approximation to equation (2.2), measures of A must first beconstructed that correspond to the three dimensions of the scope of agglomeration economies.Thus, for a given geographic distance from establishment j, measures of A should ideally includethe amount of economic activity present in a variety of different industries at different distancesin industrial space from j. This would allow one to determine the industries that benefit fromproximity. Including measures of physical distance would allow one to determine how closeestablishments need to be in order to benefit from their agglomeration. Finally, it would also bedesirable to allow for dynamic externalities and consider the impacts of historic activity.Obtaining all these controls is a daunting challenge. Thus, most models of agglomeration bearon one or perhaps two of the key aspects of scope, but never all three.2.2.3 Estimating the production function: omitted variables and simultaneityThe most natural way to understand agglomeration economies is to directly estimate theproduction function, (2.2). In carrying out this estimation, it is necessary to have measures of thevarious elements of x j, including employment, land, capital, and materials. Labor inputs areperhaps the easiest to measure, since many data sets provide counts of workers, hours worked,and on occasion, proxies for skill level (e.g. education). Data on purchased materials areavailable in some data sets, but data on materials produced internally typically are not. SeeCiccone and Hall (1996) and Henderson (2003a) for discussions of this issue. Few data setsmake available measures of land use and information on the stock of capital, informationessential to estimating (2.2). Thus, a fundamental challenge that must be faced in estimating aproduction function is in finding data on inputs.The issue of measurement error has been central to the literature since the outset.Because this is an old issue and one that has already been surveyed with considerable care(Eberts and McMillen (1999)), our treatment will be relatively brief. First, it is clear that theabsence of data on capital can affect the estimates. For instance, Sveikauskas (1975) lacks dataon capital. As Moomaw (1983) points out, however, if capital is used more intensively in largecities, then the error terms will be positively correlated with the city size terms, leading toupward bias in coefficient estimates. In fact, Moomaw shows that this can inflate estimates by a factor of four.3 Second, land is also an important input, and its contribution to production is also difficult to measure. Land will be used less intensively in large cities, so presumably this omission would lead to downward bias in the estimates.A more recent effort to estimate (2.2) directly is Henderson (2003a). We believe that this paper is a model of a productivity-based study of agglomeration, coming closest to the ideal that we discussed at the beginning of the section. In this paper, Henderson constructs a panel of plant-level data from the Longitudinal Research Database (LRD) including measures of the capital stock, materials and labor. Using the LRD's micro-data, Henderson controls for industrial scope in the usual way by dividing activities into those that take place within a given industry and those that do not. Henderson also draws on the panel structure of the data to address issues related to the temporal scope of agglomeration. For the most part, Henderson considers county and MSA-level indicators, rather than using variables that directly reflect proximity. An exception to this is some analysis of neighboring counties. While Henderson’s work is also noteworthy for the careful treatment of the data, the strength of the empirical work rests primarily with the use of plant-level information and detail on purchased factor inputs available from the confidential LRD files. While these data appear to offer some of the best opportunities for making contributions to the understanding of agglomeration, access to them is tightly guarded. This means that many researchers choose to work with other less ideal data.4 Even when plant-level data are available, direct estimation of equations such as (2.2) requires that the analyst address challenging endogeneity problems. Agglomeration economies enhance plant productivity, but successful entrepreneurs also seek out productive locations. If overachieving entrepreneurs were disproportionately found in agglomerated areas, this would cause one to overestimate the relationship between agglomeration and output. Henderson initially attempts to address this problem through two-stage least squares (2SLS) using local environment measures as instruments. The instrument list includes cross-sectional MSA attributes such as the market potential of the MSA, county air quality attainment status and other variables thought to be strictly exogenous. However, Henderson notes that these regressors make weak instruments, rendering the 2SLS approach ineffective.53A related literature considers the impact of public infrastructure (i.e., roads and bridges) on productivity. See Holtz-Eakin (1994). These studies also wrestle with measuring private capital.4In order to gain access to the LRD data researchers must become sworn “employees” of the U.S. Census and conduct their research in a secure room at one of the Census research stations set up for such purposes. Census research stations are currently found in Washington D.C., Boston, Pittsburgh, and San Francisco. In addition, access to the confidential Census files is costly and requires a level of funding typically only available from a major grant.5 See Hanson (2001) for more on the endogeneity issue.Next, Henderson (2003a) estimates a version of (2.2) drawing on the panel structure of his data and imposing constant slope coefficients over time. Time-differencing the data, he estimates this system by generalized method of moments (GMM) using predetermined industry environment variables as instruments (e.g. lagged levels of different types of local employment). Once more, however, Henderson finds that the instruments are weak, though not as weak as the cross-sectional instruments for the 2SLS model. In addition, by using predetermined data for instruments in conjunction to differencing the data over time, he is forced to dramatically reduce the sample over which the estimation is conducted.After experimenting with both 2SLS and GMM, Henderson concludes that controlling for endogeneity through the use of fixed effects is superior. Specifically, he estimates his productivity equation including MSA-time specific fixed effects in addition to plant fixed effects. By adding the MSA-time fixed effects the hope is that this will capture the influence of unobserved attributes that might have drawn a given entrepreneur to the area and that might otherwise be correlated with the error term in the estimating equation. Including MSA-time specific fixed effects is appealing and may well be one of the most effective ways to address the endogenous nature of the local industrial environment. Nevertheless, even this approach may still be exposed to endogeneity problems because the presence of a plant in a given MSA and time period represents the outcome of a profit-maximizing choice.2.2.4 Indirect strategies for measuring the influence of agglomeration on productivityEstimating the production function directly is not the only way to look for evidence of the scope of agglomeration economies. Because of the challenges associated with that approach, many recent studies have begun to favor one of four indirect approaches.The first of these is to consider growth. Glaeser et al (1992) and Henderson et al (1995), for example, examine the impact of MSA-level agglomeration on employment growth. In the case of Glaeser et al (1992), growth is measured using data from the County Business Patterns while Henderson et al (1995) rely on the Census of Manufactures. The idea here is that agglomeration economies enhance productivity and productive regions (e.g. MSAs) grow more rapidly as a result.Studying the growth of total employment presents different challenges than estimating productivity directly. Data on total employment are often readily available and the analysis lends itself to linear regressions. However, existing employers are constrained by prior choices, most importantly the level and kind of capital previously installed. Those fixed factors affect how the employer values the marginal worker, and consequently how it changes its employment level in response to a change in its environment. In principle, this difficulty can be overcome by looking at changes in total employment over a sufficiently long time frame so that there are nofixed factors and all establishments are effectively new. Even then, one still has to address endogeneity problems: not only is the growth of total employment in a given area sensitive to the composition of employment in the area (an agglomeration effect), but growth affects the level and composition of employment. Implementing this approach, therefore, ideally requires a long panel and effective instruments to control for endogenous variables. The primary approach used to address this problem in the Glaeser et al (1992) and Henderson et al (1995) papers, is to use deeply lagged levels of past conditions of the MSAs as regressors.6A different approach to studying the scope and effect of agglomeration on productivity has been to focus on births of new establishments and their employment. This approach was taken by Carlton (1983) and by Rosenthal and Strange (2003). The idea here is that entrepreneurs seek out profit-maximizing locations and are disproportionately drawn to the most productive regions. As with the other approaches, focusing on births has both advantages and disadvantages. On the positive side, data on purchased factor inputs (e.g. capital stock, labor, materials, and land) are not required, new establishments are largely unconstrained by previous decisions, and new establishments make their location and employment decisions taking the existing economic environment as exogenously given.Studying plant births also presents difficulties. The principal drawback is that many locations do not receive any births in a given period which can lead to technical challenges on the econometric side. In addition, births are more likely to occur in areas where there is already an existing concentration of industrial activity as spinoffs. Rosenthal and Strange (2003) control the zeros problem by using Tobit models and comparing results to those from probit models that look for positive versus zero births. In addition, Rosenthal and Strange (2003) control for “churning” effects by studying zipcode level employment data and including MSA fixed effects as control variables. Even if an entrepreneur is tied to the local MSA because of past employment and other factors, the entrepreneur will still seek out the profit maximizing location within the MSA.The third approach used to examine the scope and influence of agglomeration is to study wages. This approach rests on the assumption that in competitive markets labor is paid the value of its marginal product. Even without perfect competition, in more productive locations, wages will therefore be higher. Recent examples of this approach include Glaeser and Mare (2001) and Wheaton and Lewis (2002). An advantage of this approach is that wage data are readily available. Moreover, by focusing on wages this makes feasible the use of a variety of widely available datasets, such as the public access version of the Census, the Consumer Population6Glaeser et al (1992) use 1956 employment levels to help explain growth over the 1956 to 1987 period. Henderson et al (1995) use 1970 employment levels to help explain growth over the 1970 to 1987 period.。
Journal of Molecular Catalysis A:Chemical264(2007)153–161Preparation of mesoporous silica/polymer sulfonate composite materials Masahiro Fujiwara a,∗,Kumi Shiokawa a,Yingchun Zhu ba Kansai Center,National Institute of Advanced Industrial Science and Technology(AIST),1-8-31Midorigaoka,Ikeda,Osaka563-8577,Japanb Shanghai Institute of Ceramics,Chinese Academy of Sciences,Shanghai200050,People’s Republic of ChinaReceived21June2006;received in revised form22August2006;accepted9September2006Available online15September2006AbstractMesoporous silica/polymer sulfonate composite materials were prepared by simply mixing hexadecyltrimethylammonium bromide,polymer sulfonates and TEOS(tetraethoxysilane)in alkaline aqueous solution.Nafion and poly(sodium4-styrenesulfonate)were employed as polymer sulfonates.XRD patterns and nitrogen adsorption–desorption isotherms showed that the precipitates obtained had mesostructure similar to MCM-41.Especially,the crystallinity of hexagonal structure of composite materials synthesized with Nafion was high.From all the results obtained here, it is concluded that the polymer sulfonate resins might be incorporated in the wall framework of mesoporous silica matrix.However,when the excess amount of Nafion was mixed,the acid sites of Nafion were significantly lost in the obtained materials.These composite materials present new classes of organically modified mesoporous silicas,where organic polymers are incorporated in the framework of mesoporous silica.They were used as catalysts for␣-methylstyrene dimerization and Friedel–Crafts alkylation reaction of aromatics.©2006Elsevier B.V.All rights reserved.Keywords:Mesoporous silica;Nafion;Poly(styrenesulfonate);Nano-composite;Solid acid;␣-Methylstyrene dimerization1.IntroductionResearches on mesoporous silicas and related materials are importantfields of recent material science[1,2].Especially MCM-41and its analogues[2]are actively studied because of their high potentials for various applications.The function-alization of mesoporous silica with organic compounds began with the surface modification using silane compounds such as R-Si(OR )3[1,3].After this kind of approach,the framework modification using disilane compounds followed.These materi-als are often called periodic mesoporous organosilicas(PMOs) [4–6].For example,Inagaki and co-workers notified that ben-zene ring and analogues are completely incorporated into the framework of mesoporous silica materials,and that these mate-rials are effective acid catalysts after sulphonation[7].Another trend is the polymerizations in the pore voids of mesoporous materials:many researchers produced composite materials with the corresponding polymers by this method[8].Mesoporous composite materials,where an organic polymer is introduced into their“framework”,are also investigated.In2000,we briefly ∗Corresponding author.Tel.:+81727519253.E-mail address:m-fujiwara@aist.go.jp(M.Fujiwara).reported that Nafion resin,whose structure is illustrated inFig.1,was incorporated in the framework of M41S type ofmesoporous silica[9].This material was a unique catalyst for ␣-methylstyrene dimerization.Recently,another group devel-oped the composite materials with polyacrylate[10].In Fig.2,a classification of these composite materials of mesoporous sil-ica with organic components is proposed.Type(A)is surfacemodification using R-Si(OR )3compounds[1,3],and Type(B)isframework modification such as periodic mesoporous organosil-icas(PMOs)[4–7].Type(C)shows composite materials withpolymeric compounds in the pore voids[8].Composite meso-porous materials with polymers in the framework are namedType(D)here[9,10].In this paper,we wish to report further examination of thecomposite materials of mesoporous silica with Nafion resin.Thematrices of mesoporous materials are expected to offer orderednanostructures useful as solid support[11].Nafion resin is alsoa functional perfluorinated sulfonic acid polymer to be usedas acid catalyst[12]and as polymer electrolyte for fuel cellapplication[13].Composite materials of Nafion resin with amor-phous silica have been utilized in these technologies[14,15].The ordered nanostructures of Nafion and analogous resins withmesoporous silica matrix are expected to be useful for variousapplications.1381-1169/$–see front matter©2006Elsevier B.V.All rights reserved. doi:10.1016/j.molcata.2006.09.016154M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical264(2007)153–161Fig.1.Structure of Nafion resin.2.Experimental2.1.Preparation of mesoporous silica/Nafion composite materialThe preparation procedure is considerably simplified from our previously reported method[9].Nafion solution commer-cial available was directly used and no hydrothermal treatment was performed.A typical synthesis of mesoporous silica/Nafion composite is following:5.0g of5%Nafion alcohol solution (from Aldrich)was added to200mL of the aqueous solution of NaOH(1.73g;43.25mmol)and hexadecyltrimethylammo-nium bromide(3.48g;9.55mmol),and this mixed solution was stirred for a few minutes.To this solution,16.69g(80mmol) of tetraethoxysilane(TEOS)was added dropwise for5min, and the resulting solution was further stirred for12h at room temperature.An as-synthesized sample thus obtained wasfil-tered,washed with sufficient amount of H2O and dried at80◦C for12h.Template was removed by refluxing with1M H2SO4 solution of EtOH(solid sample/EtOH solution=1g/150mL)for 12h.Thefiltered solid was refluxed again with pure EtOH(sam-ple/EtOH=1g/150mL)for12h,filtered,washed with H2O at room temperature and dried at80◦C for12h.2.2.Preparation of mesoporous silica/Nafion composite material from amorphous silica/Nafion compositeThe general preparation method of MCM-41type of meso-porous silica from porous amorphous silica is described in elsewhere[16].This procedure was applied to amorphous sil-ica/Nafion composite.The amorphous silica/Nafion composite used here was SAC-13purchased from Aldrich.To the aqueous solution of NaOH(0.15g;3.80mmol)with hexadecyltrimethy-lammonium bromide(0.37g;1.00mmol)in4mL of H2O,0.61g of SAC-13was added.After stirred for1h,the resulting mixture was placed in a stainless autoclave,sealed tightly and heated at 110◦C for24h under autogenous pressure.The following pro-cedures were similar to the above-mentioned process.2.3.Preparation of mesoporoussilica/poly(4-styrenesulfonate)composite materialTo the solution of NaOH(0.799g;19.98mmol)and hex-adecyltrimethylammonium bromide(1.582g;4.341mmol)in 90mL of H2O,0.412g of poly(sodium4-styrenesulfonate)dis-solved in10mL of H2O was added,and to this homogeneous solution8.403g(40.34mmol)of TEOS was mixed.The result-ing solution was stirred for2days at ambient temperature. The precipitate thus formed wasfiltered,washed with sufficient amount of H2O and air-dried.The following procedures were similar to the above-mentioned process.2.4.Preparation of mixture of Nafion with hexadecyltrimethylammonium bromideA5%alcohol solution of Nafion(7.656g;Nafion content: 0.353g;sulfonic acid equivalent:0.341mmol)was mixed with NaOH(0.038g:0.95mmol)in5mL of H2O.After removing solvent under reduced pressure,the residue was dissolved in a mixed solution of H2O(10mL)and EtOH(10mL).Finally hexadecyltrimethylammonium bromide(0.125g;0.343mmol) was added.After about1day,white precipitate obtained was filtered and air-dried.2.5.Preparation of mixture of poly(4-styrenesulfonate)with hexadecyltrimethylammonium bromideThe solution of0.412g of poly(sodium4-styrenesulfonate) in6mL of H2O was mixed with the aqueous solution(50mL)of hexadecyltrimethylammonium bromide(0.728g;2.00mmol). The white precipitate was formed in a few minutes.After stirring for1h,the white precipitate wasfiltered and dried at60◦C. 2.6.Product characterizationsXRD patterns were recorded with a MAC Science MXP3V diffraction apparatus with Nifiltered Cu K␣radiation (λ=0.15406nm).N2adsorption-desorption isotherms were obtained at−196◦C(in liquid N2)using a Bellsorp Mini instru-ment(BEL JAPAN Inc.).BJH calculation was performed toesti-Fig.2.Conceptual schemes of composite materials of mesoporous silica with organic components.M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical264(2007)153–161155mate the mesopore size using adsorption branches of isotherms. Elemental analyses of silicon were performed by the alkali fusion-gravimetric method according to JIS G1212(Japanese industrial standard).Elemental analyses offluorine were car-ried out with the lanthanum-alizarin complexone method using a Shimadzu UV-1600photometry apparatus after the extraction of alkali fusion method.Elemental analyses of carbon were per-formed by the common combustion gas quantification method. Thermogravimetric analyses(TGA)were performed on a Shi-madzu TGA-50apparatus.All samples were held in a platinum sample holder and were heated under air from room temperature to800◦C at the rate of5◦C/min.FT-IR spectra were mea-sured on a Perkin-Elmer Spectrum One spectrometer.Transmit-tance electron microscope(TEM)images were obtained using a JEM-2100F(JEOL)high-resolution transmissionfield emis-sion electron microscope(HRTEM)operated at300kV.The acid capacities of composite materials were estimated by the titra-tion method.The composite materials were immersed in0.1M of aqueous solution of NaCl,and the acid amounts of the ion-exchanged solutions thus obtained were analyzed by titrating with0.01M NaOH using phenolphthalein as indicator.2.7.Catalytic reactionsThe experimental procedure of␣-methylstyrene(AMS) dimerization was described in our previous paper[9].A com-petitive Friedel–Crafts reaction of toluene and p-xylene with benzyl alcohol was performed by the mixed solution of toluene (0.92g,10mmol),p-xylene(1.05g,10mmol)and benzyl alco-hol(0.22g,2mmol)in the presence of a catalyst(0.05g)at 90◦C for7h with vigorous stirring.Afterfiltering the catalyst, thefiltrate was analyzed by a capillary GC.3.Results and discussion3.1.Synthesis of mesoporous silica/Nafion composite materialComposite materials made of mesoporous silica and Nafion resin were prepared by a procedure modified formesoporous Fig.3.XRD patterns of as-synthesized and template-free(solvent extracted) mesoporous silica/Nafion composite materials.(A)As-synthesized MCM/ Nafion-1.(B)As-synthesized MCM/Nafion-2.(C)Template-free MCM/Nafion-1.(D)Template-free MCM/Nafion-2.silica synthesis.TEOS was added to a homogeneous alkaline solution of hexadecyltrimethylammonium bromide with Nafion resin.After stirring at room temperature,as-synthesized com-posite materials of mesoporous silica and Nafion resin were obtained as a white precipitate.Although hydrothermal treat-ment in an autoclave was given in our previous paper[9],we found that this hydrothermal treatment is not essential for the synthesis after the publication of the paper.The surfactant as template was removed by refluxing in H2SO4–EtOH solution (1M of H2SO4).H2SO4is expected to contribute to both the regeneration of sulfonic acid sites in Nafion polymer resin and the surfactant removal.The sample names and the profiles of composite materials are summarized in Table1.The data of a composite material prepared under hydrothermal conditions[9] are also included in Table1as MCM/Nafion-H.Fig.3shows XRD patterns of two composite materials(MCM/Nafion-1andTable1Properties of various mesoporous silica/polymer composites materialsSample Starting ratio d100a SSA b(m2/g)PV c(cm3/g)PPD d(nm) g/mol e wt%f2θnmMCM/Nafion-1 3.13 5.21 2.32(2.34) 3.81(3.77)1239 1.12 2.52 MCM/Nafion-2 6.7211.18 2.20(2.22) 4.01(3.98)1211 1.26 2.75 MCM/Nafion-314.8724.76 2.20(2.28) 4.01(3.87)3330.26 2.52 MCM/Nafion-H g 6.5810.96 2.25(2.35) 3.92(3.76)918 1.00 2.75 MCM/PSS8.8815.19 2.14(2.24) 4.13(3.94)8380.66 2.75a d100:X-ray diffraction(100)interplanar spacing.In parentheses,as-synthesized sample.b BET specific surface area.c Primary mesopore volume calculated from adsorption branch of BJH pore size distribution curve.d Peak pore diameter from adsorption branch of BJH pore size distribution curve.e Starting ratio of polymer(as acid type)and TEOS;gram of polymer/molar of TEOS.f Estimated weight percentage when polymer is completely incorporated in solid material and all TEOS converts into silica(SiO2).g MCM/Nafion composite material we reported[9].156M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical264(2007)153–161Fig.4.Infrared spectra of as-synthesized(A)and template-free(B)MCM/ Nafion-1composite material.MCM/Nafion-2)in as-synthesized and template-free forms. XRD patterns indicated the formation of the hexagonal structure characteristically observed in the MCM-41type of mesoporous silica[2].The peaks assigned to d110,d200and d210interpla-nar spacings were found besides those from d100interplanar ones in all four samples.The surfactants were removed success-fully by the extraction using H2SO4in EtOH with the hexagonal structure maintained.Template removal by calcination was not performed to avoid thermal decomposition of Nafion resin.The peaks derived from the hexagonally ordered structure became stronger after the template removal in both cases(MCM/Nafion-1and MCM/Nafion-2).Infrared spectra of as-synthesized and template-free (extracted)samples are shown in Fig.4.In the as-synthesized sample,strong absorptions of the surfactant were observed approximately at2929and2850cm−1(Fig.4A).These absorp-tions disappeared after the treatment with H2SO4(Fig.4B), indicating the complete removal of the surfactant.On the other hand,the absorptions of C–F stretching modes of Nafion resin at1210and1160cm−1were not found in either spectra,while they are detected in amorphous silica/Nafion composite[14a]. It seems that in the case of amorphous silica/Nafion compos-ite,the contact time of Nafion resin with alkaline solution is comparatively short(the preparation solution gels immediately), preventing the serious decomposition of C–F bonds[14a].In our case,Nafion resin was dissolved in the high alkaline solution for a long time,resulting in critical degradation.The TEM images of MCM/Nafion-1are shown in Fig.5.The ordered structure(hexagonally arranged)was confirmed from the layered lines in the solid.The distance between layers is estimated to be3.0–3.8nm,approximately according with that from XRD patterns.The nitrogen adsorption–desorption isotherms of the template-free samples are shown in Fig.6.Both samples, MCM/Nafion-1and MCM/Nafion-2,indicated the typical type IV isotherms(IUPAC)of ordered mesoporous silica materi-als.The pore size of MCM/Nafion-2was larger than that of MCM/Nafion-1.These results were consistent with the d100 interplanar spacings from XRD patterns(Fig.3).Specific sur-face areas(BET surface area)and pore volumes of both samples were over1000m2/g and1cm3/g,respectively.These data were at the level similar to the MCM-41type of mesoporous sil-icas[1,2],and considerably higher than those of amorphous silica/Nafion composite materials[15].These properties are similar to those of the sample prepared under hydrothermal con-ditions(MCM/Nafion-H)in our previous paper[9].Therefore, a simpler preparation method using the direct use of commer-cial reagent under ambient conditions proved to be applicable. However,when more than20wt%of Nafion resin was added to the starting solution,the ordered structure of the corresponding composite material was considerably collapsed(MCM/Nafion-3).The peak at2.28in2θobserved in the as-synthesized sample (Fig.7A)indicated its moderately ordered structure.However, this peak almost disappeared after the removal of template (Fig.7A),showing the destruction of the ordered structure. In Fig.7B,the nitrogen adsorption–desorption isotherm and the pore size distribution estimated from the BJH method of template-free MCM/Nafion-3are presented.The porosity of this sample was poor and the peak of the pore diameterwas Fig.5.TEM images of MCM/Nafion-1(template-free).M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical264(2007)153–161157Fig.6.(A)Nitrogen adsorption–desorption isotherms of mesoporous silica/Nafion composite materials.( )Adsorption branch of MCM/Nafion-1;( )desorption branch of MCM/Nafion-1;( )adsorption branch of MCM/Nafion-2;(᭹)desorption branch of MCM/Nafion-2.(B)Pore size distributions estimated from the adsorption branches of the isotherms by BJH method.( )MCM/Nafion-1;( )MCM/Nafion-2.broad.The specific surface area and the pore volume decreased to333m2/g and0.259cm3/g,respectively.Thus,the addition of excess amount of Nafion resin inhibited the formation of ordered structure.Another approach to the preparation of the composite mate-rial was attempted by using an amorphous silica/Nafion com-posite.It is well known that porous amorphous silica can be transformed into mesoporous MCM-41type material in the pres-ence of surfactant in alkaline solution[2,16].An amorphous silica/Nafion composite material commercially available(SAC-13;Nafion content:approximately13wt%)was immersed in an alkaline solution dissolving hexadecyltrimethylammonium bromide.This solution system was placed in an autoclave to be hydrothermally treated by reacted at115◦C for24h[16]. The XRD patterns of as-synthesized and template-free samples thus obtained are shown in Fig.8.The crystallinity of the as-synthesized sample was poor,and after the removal of template the hexagonal structure nearly collapsed.Even in this case,a comparatively high content of Nafion resin(13wt%)is thought to prevent the formation of ordered structure in the case of MCM/Nafion-3.3.2.Analyses of composition of mesoporous silica/Nafion composite materialThe contents of Nafion resin in these composite materials were analyzed by various methods.The results of TGA measure-ment of these composite materials are listed in Table2.Nafion resin is thermally decomposed from150to600◦C[17],and the weight decrease of pure mesoporous silica(without Nafion resin)we prepared was measured4.78%due to the thermal dehydration of silanols in this temperature range.The corrected values of the weight decreases by this blank measurement are shown in the parentheses.Although there are no direct propor-tional relationships between the starting contents of Nafion and the weight decreases,combustible Nafion contents increased from MCM/Nafion-1to MCM/Nafion-3.A similar tendency was observed in the elemental analysis shown in Table2.The Fig.7.(A)XRD patterns of as-synthesized and template-free(solvent extracted)MCM/Nafion-3.(B)Nitrogen adsorption–desorption isotherm and the pore size distribution by BJH method from adsorption branch(in inset)of MCM/Nafion-3.158M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical264(2007)153–161Fig.8.XRD patterns of as-synthesized(A)and template-free(B)mesoporous silica/Nafion composite material obtained from an amorphous silica/Nafion composite(SAC-13).carbon andfluorine contents increased with the starting Nafion resin contents.It should be noted that thefluorine contents were low in these composite materials,although the weight ratios of fluorine to carbon must be approximately3.2according to the chemical formula of Nafion(Fig.2)[14a].These lower con-tents offluorine indicated that carbon–fluorine bonds in Nafion resin were significantly cleaved during the preparation process, because aliphatic perfluoro group is known to be unstable under basic conditions(although aromatic C–F bond is reported to be tolerant in alkaline solution)[11a].No observation of C–F bonds in infrared spectra(Fig.4),which can be observed in amorphous silica/Nafion composite[14a],was likely to result from the decrease in thefluorine content in the resin.The acid capacities of these composite materials were estimated by the cation exchange method with NaCl[14].The acid equivalents are also summarized in Table2.The acid content of pure Si-MCM-41(with Nafion resin)was under 0.001mequiv.H+/g.Pure Nafion resin(NR-50)and its compos-ite material with amorphous silica(SAC-13;Nafion content: 13wt%)is reported to have0.89or0.14mequiv.H+/g of acid capacities,respectively[14].In the parentheses of Table2, the weight percentages of Nafion in the composite materials calculated from the measured acid capacities are listed on the assumption that all sulfonic acid sites of Nafion resin are active. The calculated Nafion content of MCM/Nafion-1(5.92wt%) from acid capacity was reasonably consistent with the estimated values from both starting ratio and TGA measurement.On the other hand,in the case of MCM/Nafion-2,the Nafion content estimated from the acid capacity(17.02wt%)was in discord with other results.Furthermore,the acid capacity of MCM/Nafion-3was approximately0.003mequiv.H+/g.From these results,it was concluded that high contents of Nafion in the composite materials led to the some decomposition of Nafion resin,while no significant changes were observed in the case of low Nafion contents.3.3.Synthesis of mesoporous silica/poly-sulfonate composite materialThe formation of composite materials of mesoporous silica with polyacrylate was recently claimed in a report[10],where a procedure analogous to ours was used.We also studied the prepa-ration of a composite material made of mesoporous silica and another poly-sulfonate.Poly(4-styrenesulfonic acid)sodium salt was employed for the synthesis.In a similar manner to Nafion, TEOS was added to the mixed alkaline solution of poly(sodium 4-styrenesulfonate)(PSS)and hexadecyltrimethylammonium bromide,forming a composite material(MCM/PSS)after stir-ring.The XRD patterns of the as-synthesized and template-free samples are shown in Fig.9A.Although the peak intensities of these two patterns were lower than those of composite materials with Nafion,an ordered structure in the nano-level was observed. In the as-synthesized MCM/PSS,peaks assigned to d110,d200 and d210interplanar spacings were found as well as d100inter-planar one.Those peaks are not so clear in the template-free MCM/PSS,and its pore structure might be a wormhole like one[18].The nitrogen adsorption–desorption isotherms of this MCM/PSS composite material presented in Fig.9B are basi-cally type IV.The peak pore diameter was found at2.75nm (in inset).Thus,a poly(styrenesulfonate)polymer can be suc-cessfully introduced into mesoporous silica material as well as Nafion resin.Table2Results of elemental analysis,TGA and acid capacity of mesoporous silica/polymer composite materialsSample Stating ratio(wt%)a Elemental analysis(wt%)b TGA(%)c Acid capacity(mequiv.H+/g)dC Si FMCM/Nafion-1 5.21 2.7539.1 1.659.06(4.27)0.0527(5.92)MCM/Nafion-211.18 2.8939.3 1.7110.75(5.97)0.1515(17.02)MCM/Nafion-324.76 3.9236.8 5.8713.99(9.21)0.003(0.3)a Starting weight composition of Nafion calculated from carbon in Nafion and silicon in TEOS,regarding as Nafion formula are n=7and m=1in Fig.1.b Elemental analyses of C,Si and F were performed by common combustion gas quantification method,alkali fusion-gravimetric method or lanthanum-alizarin complexone method,respectively.c Percentage of weight loss from150to600◦C.In parentheses,the corrected value by deducting the weight decrease(4.78%)by the dehydration of mesoporous silica prepared without Nafion is noted.d Acid capacity estimated from the titration of ion-exchanged solution from NaCl using NaOH solution.In parentheses,the weight percent of Nafion calculated from this acid capacity using the pure Nafion resin acid capacity[14a],0.89mequiv.H+/g(on the supposition that all sulfonic acid sites are active).M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical 264(2007)153–161159Fig.9.(A)XRD patterns of as-synthesized and template-free (solvent extracted)mesoporous silica/poly(sodium 4-styrenesulfonate)composite material (MCM/PSS).(B)Nitrogen adsorption–desorption isotherm and the pore size distribution by BJH method from adsorption branch (in inset)of MCM/PSS.3.4.Mechanistic discussion on the formation ofmesoporous silica/poly-sulfonate composite materials It is well known that the polymer electrolyte such as ion-exchange resin and surfactant readily form their complex by their ionic interaction [19].When sodium polyacrylate or poly(4-styrenesulfonate)was mixed with hexadecyltrimethy-lammonium bromide in aqueous solution,their complexes were instantly produced as precipitates.On the other hand,sodium salt of Nafion resin obtained by neutralization with sodium hydroxide scarcely afforded the precipitate with the surfactant in aqueous solution.Only after the considerable evaporation of solvent,a white viscous solid was obtained.Fig.10shows XRD patterns of the complexes obtained from sodium salt of Nafion or sodium poly(4-styrenesulfonate)withhexadecyltrimethylam-Fig.10.XRD patterns of precipitated solids from Nafion resin (A)or sodium poly(4-styrenesulfonate)(B)with hexadecyltrimethylammonium bromide.monium bromide.In the XRD pattern of the complex from sodium poly(4-styrenesulfonate)and the surfactant,a sharp peak at 2.11in 2θ(interplanar space:4.18nm)was found (B in Fig.10).These kinds of XRD pattern often observed in the com-plexes of polyelectrolytes and surfactants indicate the formation of lamellar structure complexes of polymer electrolytes with sur-factants [19d].On the other hand,in the case of the complex from Nafion resin and surfactant,no clear peak was observed in the XRD pattern (A in Fig.10),indicating that Nafion forms no ordered complex with cationic surfactant.A broad peak found at 2.22in 2θ(interplanar space:3.98nm)is likely to be derived from the cluster structure of sulfonic acid parts of Nafion resin [20].This cluster structure might restrict the formation of the complex with surfactant.In Fig.11,a possible formation mechanism of composite material consisting of mesoporous silica and polymer sulfonate is displayed.Two routes of composite materials formation are assumed.In the case of MCM/PSS synthesis,some layered phases of poly(styrenesulfonate)and surfactant are formed at first.The hydrolysis of TEOS to silica occurs in this solu-tion.With the progress of the condensation of silanols (Si–OH)to siloxane bonds (Si–O–Si),the hexagonal structure by the influences of surfactant is formed gradually.However,the lay-ered structure of poly(styrenesulfonate)and surfactant is com-paratively strong so as to restrict the transformation of the layered structure to the hexagonal one (route A).The lower crystallinity of MCM/PSS is thought to be caused from this effect.On the other hand,complex compounds are scarcely formed from Nafion resin and surfactant,not suppressing the above-mentioned transformation and the fabrication of hexag-onal structure (route B).It is thought that the electrostatic interaction between the sulfonate group of Nafion and cationic surfactant compels the mixing of Nafion resin in aqueous phase as shown in route B of Fig.11,when the amount of Nafion is not overabound.It is not sure that Nafion resin bearing highly hydrophobic perfluoro main chain is incorporated into the aque-ous phase of the mixed solution.However,the low fluorine contents in MCM/Nafion composite materials confirmed by the160M.Fujiwara et al./Journal of Molecular Catalysis A:Chemical 264(2007)153–161Fig.11.Expected mechanisms of mesoporous silica/polymer sulfonate composite materials.elemental analysis suggested that the reaction of carbon–fluorine bond proceeds to eliminate fluorine in high alkaline solution.The main chains of Nafion resin become more hydrophilic by this reaction,increasing the affinity for silica matrix.Finally,the well-defined hexagonal structure of MCM/Nafion compos-ite materials is obtained in the case of low loading of Nafion resin.3.5.Catalytic Friedel–Crafts reaction by mesoporous silica/Nafion composite materialsWe have previously shown the unique behavior of meso-porous silica/Nafion composite materials for ␣-methylstyrene (AMS)dimerization.Representative results are listed in ing this catalyst,intermediate products (products 1and 2)are predominantly obtained and the further reaction (intramolecular Friedel–Crafts reaction)to form an indan deriva-tive (product 3)is inhibited,while the product 3was yielded effectively by amorphous silica/Nafion composite (SAC-13)[9].A competitive Friedel–Crafts type reaction of toluene and p -xylene with benzyl alcohol was examined using MCM/Nafion-1and SAC-13(Fig.12B).While no selectivity for the benzy-lation of toluene or p -xylene was observed in the reaction by SAC-13,the reaction of p -xylene occurred preferably in the case of MCM/Nafion-1catalyst.These results indicated that Friedel–Crafts reaction catalyzed by MCM/Nafion-1is more influenced by the substituents on the benzene ring than that by SAC-13.p -Xylene with two electron-donating groupsisFig.12.Results of ␣-methylstyrene (AMS)dimerization (A)and competitive Friedel–Crafts type reaction of toluene and p -xylene with benzyl alcohol (B).。
a r X i v :0704.2111v 4 [h e p -t h ] 14 A u g 2007YITP-07-20arXiv:0704.2111[hep-th]April 2007Index Theorems on Torsional GeometriesTetsuji K IMURA Yukawa Institute for Theoretical Physics,Kyoto University Sakyo-ku,Kyoto 606-8502,Japan tetsuji@yukawa.kyoto-u.ac.jp Abstract We study various topological invariants on a torsional geometry in the presence of a totally anti-symmetric torsion H under the closed condition d H =0,which appears in string theory compactification scenarios.By using the identification between the Clifford algebra on the geom-etry and the canonical quantization condition of fermions in quantum mechanics,we constructN =1quantum mechanical sigma model in the Hamiltonian formalism.We extend this modelto N =2system,equipped with the totally anti-symmetric tensor associated with the torsion onthe target space geometry.Next we construct transition elements in the Lagrangian path integralformalism and apply them to the analyses of the Witten indices in supersymmetric systems.Weexplicitly show the formulation of the Dirac index on the torsional manifold which has alreadybeen studied.We also formulate the Euler characteristic and the Hirzebruch signature on thetorsional manifold.1IntroductionFlux compactification scenarios have become one of the most significant issues in the study of low energy effective theories from string theories(for instance,see[1,2,3]and references therein).Non-trivialfluxes induce a superpotential,which stabilizes moduli of a compactified geometry and de-creases the number of“redundant”massless modes in the low energy effective theory in four di-mensional spacetime.This mechanism,called the moduli stabilization,also gives a new insight into cosmology as well as string phenomenology([4]and a huge number of related works).Flux compactification provides another interesting issue to the compactified geometry itself:In a specific situation,for instance,the NS-NS three-formflux H mnp behaves as a torsion on the com-pactified geometry and gives rise to a significant modification[5],i.e.,the K¨a hler form is no longer closed.This phenomenon indicates that thefluxes modify the background geometry in supergravity in a crucial way.Of course,the Calabi-Yau condition[6]should be influenced by the back reactions from thefluxes onto the geometry.If a certain n-dimensional manifold has a non-trivial structure group G on its tangent bundle, this manifold,called the G-structure manifold,admits the existence of nowhere vanishing tensors; for example,the metric(G⊆O(n)),the Levi-Civita anti-symmetric tensor(G⊆SO(n)),the almost complex structure(G⊆U(m)where n=2m),and the holomorphic m-form(G⊆SU(m)).This classification does not exclude the existence of torsion.(In this sense,a Calabi-Yau n-fold is one of the SU(n)-structure manifolds.)This classification is also studied in terms of Killing spinors on the manifold.In particular,the six-dimensional SU(3)-structure manifold has been investigated in terms of intrinsic torsion[7]and has been applied to the string theory compactification scenarios [8].Since we mainly study supergravity theories as low energy effective theories of string theories, we always assume the existence of the metric g mn and dilatonfieldΦon the compactified manifold. In a generic case of the string compactification,we can also introduce non-trivial NS-NS three-form flux H mnp with its Bianchi identity.In type II theories appropriate R-Rfluxes are also incorporated. All of these are strongly related via the preserved condition of supersymmetry.In the heterotic case, supersymmetry variations of the gravitinoψm,the dilatinoλand the gauginoχgive rise to the Killing spinor equations0=δψm= ∂m+14 Γm∇mΦ−1F mnΓmnη+,(1.1c)4whereη+is the Weyl spinor on the six-dimensional manifold whose normalization is given asη†+η+= 1,andω−mab=ωmab−H mab[5].Then the NS-NS three-formflux H mnp is interpreted as a totallyanti-symmetric contorsion(or equivalently,a totally anti-symmetric torsion)on the manifold with negative sign:H m np=−T m np=−Γm[np].The analysis of the manifold becomes much clear when we introduce a set of mathematical definitions such asAlmost complex structure:J m n≡iη†+Γm nη+,J m p J p n=−δn m,(1.2a)3Lee-form:θ≡J d J=J m q J n r J p s∇[s J qr]=−32forms.These invariants are described in terms of polynomials of Riemann curvature two-form(see, for example,[17,18,19]).So far the index of the Dirac operator in the presence of torsion has been studied[20,21,22,23].Unfortunately,however,the other indices on a torsional manifold have not been analyzed so much.In particular,it is quite worth studying the Euler characteristic on a complex manifold in the presence of torsion,which will give a new insight on the number of generation in the flux compactification scenarios.The main discussion of this paper is to analyze such kinds of topological invariants derived from the Dirac operator,which appears in the following equations of motion for fermionicfields in the supergravity[24]:0=/D(ω)λ−13H)λ,(1.4a)0=/D(ω,A)χ−13H,A)χ.(1.4b)First,we define the index of the Dirac operator on the torsional manifold in the infinity limit ofβ:index/D≡limβ→∞Tr Γ(5)e−βR =limβ→0Tr Γ(5)e−βR ,(1.5) where R is an appropriate regulator,given by the square of the Dirac operator(or,equivalently, the Laplacian)in a usual case.Notice that since a topological value is definitely independent of the continuous parameterβ,we can take the zero limitβ→0.This topological invariant can be represented as an appropriate quantum number in supersymmetric quantum mechanics[14]via the identification of the cohomology on the manifold with the supersymmetric states in the quantum mechanics.To investigate this,we define the Witten index in the quantum mechanicslimβ→0Tr (−1)F e−β H|X .(1.6) We identify(1.5)with(1.6)via the identification of the the regulator R and the chirality operatorΓ(5) on the manifold with the Hamiltonian H and the fermion number operator(−1)F in the quantum mechanics,respectively.The trace Tr denotes the sum of all transition elements whosefinal states X|correspond to the initial states|X .Second,we rewrite the Witten index from the Hamiltonian formalism,as described above,to the Lagrangian path integral formalism.During this process,we introduce discretized transition elements and adopt the Weyl-ordered form in order to avoid any ambiguous ordering of quantum operators.Then we integrate out momentum variables and ob-tain the transition elements described in the configuration space path integral.Third,we discuss the Feynman rule which defines free propagators and interaction terms in the supersymmetric systems. Finally,we evaluate the Witten indices in the quantum mechanical nonlinear sigma models in appro-priate ways.This procedure is summarized in a clear way by de Boer,Peeters,Skenderis and van Nieuwenhuizen[25],and Bastianelli and van Nieuwenhuizen[26].We will apply this technique tothe analysis of index theorems on the torsional manifold.To simplify the discussion,we impose the closed condition d H=0on the NS-NS three-form in the same way as[21,20].This indicates that we only focus on the index theorems on the strong K¨a hler with torsion(1.3d).Although this condition is too strong tofind the suitable solution in the heterotic string compactification with non-trivialfluxes [27,24],it is still of importance to analyze the manifold with such condition,which also appears in type II string theory compactifications.This paper is organized as follows:In section2we construct N=1and N=2quantum super-symmetric Hamiltonians equipped with a non-vanishing totally anti-symmetricfield H mnp,which can be regarded as the torsion on the manifold considered.In section3we describe the transition ele-ments in the Hamiltonian formalism and rewrite them to functional path integrals in the Lagrangian formalism.We also prepare bosonic and fermionic propagators in the quantum mechanics.This transition elements play significant roles in the evaluation of the Witten indices in next sections.In section4and5the Witten index in N=1supersymmetric quantum mechanical nonlinear sigma model is analyzed.First we review the Witten index associated with the Dirac index on a usual Rie-mannian manifold without boundary.Next we generalize the index on the manifold in the presence of non-trivial torsion H.We obtain an explicit expression of the Pontrjagin class and of the Chern character on the torsional manifold.The Euler characteristic corresponding to the Witten index in N=2supersymmetric system is discussed in section6.This topological invariant is also discussedon the torsional manifold.In section7we also analyze the derivation of the Hirzebruch signature on the manifold with and without torsion from the N=2supersymmetric quantum mechanics.We summarize this paper and discuss open problems and future works in section8.We attach some ap-pendices in the last few pages.In appendix A we list the convention of differential geometry which we adopt in this paper.In appendix B a number of useful formulae,which play important roles in the computation of Feynman graphs,are listed.2Supersymmetric quantum HamiltoniansFirst of all,we prepare a bosonic operator x m and its canonical conjugate momentum p m in quantum mechanics,whose canonical quantization condition is defined as a commutation relation between them in such a way as[x m,p n]=i δm n.Since we consider a quantum mechanical nonlinear sigma model,we regard x m as a coordinate on the target space of the sigma model,where its index runs m= 1,...,D.Since the target space is curved,the differential representation of the canonical momentum operator is given as g14=−i ∂m equipped with the determinant of the target space metric g=det g mn.We also introduce a real fermionic operatorψa in the quantum mechanics,equipped with the local Lorentz index a=1,...,D.In the quantum mechanics of real fermions,we definethe canonical quantization condition as an anti-commutation relation {ψa ,ψb }= δab .Since,under the identification ψa ≡ 2Γa ,the structure of this quantization condition can be interpreted as the SO (D )Clifford algebra given by the anti-commutation relation between the Dirac gamma matrices {Γa ,Γb }=2δab on the target geometry,we will investigate the Dirac index on this curved geometry in terms of the Witten index in the quantum mechanics.First let us discuss N =1supersymmetry,and extend this to N =2supersymmetry under a certain condition.We should choose N =1or N =2in the case when we want to study the index density for the Pontrjagin classes,or for the Euler characteristics,respectively [14]1.2.1N =1real supersymmetryNow let us introduce the N =1supersymmetry algebra with respect to a real fermionic charge Q 1:{Q 1,Q 1}=2 H 1.(2.1)Note that H 1is the quantum Hamiltonian in N =1system,where the superscript “1”indicates N =1.We will realize this algebra in terms of quantum operators x m ,p m and ψa .It is useful to introduce a covariant momentum operator associated with a covariant derivative D m (ω−12ωmab −13H mab .Since the Dirac operator acts onspinors on the geometry,the Lorentz generator Σab is given in the spinor representation,which can be described in terms of the real fermions via the identification Γa = ψa such asΣab =i2 ψa ψb −ψb ψa ≡i 4[π(−1/3)m ,ψa ]g −14[π(−1/3)m ,ψn ]g −13H n pm ψp ,(2.4)where Γn 0pm is the Levi-Civita connection defined in appendix A.Actually,the above commutator is associated with the covariant derivative of the Dirac gamma matrix on the target geometry.By using the covariant momentum π(−1/3)m ,let us represent the supercharge Q 1H and the Hamilto-nian H 1H (where the subscript H denotes that the operator contains the torsion H )as follows:Q 1H ≡ψm g 14=ψm g 12 ωmab −14,(2.5a)H1H =14π(−1)mg mn√4+ 224H mnp H mnp.(2.5b)Note that we used the closed condition d H=0.Since we used the complete square in H1H,the magnitude of the torsion in the covariant momentum is changed toπ(−1)m.This is consistent with the analysis of the Killing spinor equation in the heterotic theory[24].We can also formulate the N=1 supersymmetric charges with introducing a(non-abelian)gaugefields on the target space:Q1H=ψm g14,{Q1H,Q1H}=2 H1H,(2.6a)H1H =14 π(−1)m g mn√4+ 23H mnp H mnp−12 ωmab+αH mab ψab−iAαm(ˆc†Tαˆc),(2.6c)where we used the anti-hermitian matrix Tαas a generator of the gauge symmetry group.We also introduced a complex ghostfieldˆc i living in the quantum mechanics.2.2N=2complex supersymmetryNow we introduce two sets of real fermionic operatorsψaα(α=1,2)and perform the complexification of fermionic operators via linear combinationϕa≡12(ψa1+iψa2),√ϕa=(ϕa)†.Then the canonical quantization condition is extended in such a way as{ϕa,ϕb}=0,{ϕb}=0,{ϕa,4[πm,ϕn]g−14[πm,ϕn]g−1ϕaϕa ,(2.9a)g14=i 2ϕb.(2.9b)Next,let us express N=2supercharge Q and extend it as the supercharge equipped with the torsion given by three-formflux H.In the same way as the N=1supercharge,we will identify the de Rham cohomology on the manifold with the N=2supersymmetry algebra.In the case on the Riemannian manifold,we identify the exterior derivative d on the geometry with the N= 2supercharge Q≡ϕm g14,whereπm is the covariant momentum in the N=2quantum mechanics defined asπm=p m− ϕb.(2.10) Let us introduce the torsion on the geometry.Following the discussions[28,29,20,30,31],we extend the exterior derivative d to d H in such a way asd H≡d+H∧,(d H)2=(d H)∧.(2.11) This means that d H is nilpotent up to the derivative d H,i.e.,this yields the equivariant cohomology. In this paper we always impose the vanishing condition d H=0.In addition,by using the Darboux theorem,we can identify the one-form with the holomorphic variable,while the adjoint of the one-form can be identified with the anti-holomorphic variable.Thus,we identify the exterior derivative d H and its adjoint d†H with appropriate operators in terms of complex fermionsϕm and14πm g−Q H≡4πm g−1αiH mnpϕnQ H associated with d†H,i.e.,the adjoint of the derivative d H.Here we also introduced the scale factorα,which should befixed compared with the N=1supercharge.In order tofix the coefficient α,let us truncate the supercharge Q H to the supercharge Q1H in the N=1supersymmetry(2.5)via the restrictionψa2=0andψa1≡ψa:Q H→12ψm g14−i√=3(d H)dcab=0,wefind that the4supersymmetry algebra is given by{Q H,Q H}= Q H,6(d H)abcd{Q H,2 [4p m g−1ϕb+i4πm g−13H mabϕab ,(2.16a)H H=14 πm+iϕab g mn√2H ncd ϕcd+4−1ϕnϕa6∂m(H npq) ϕnpq−3 2g mn 8H mnr H pq r ϕmnpq+ϕpq − ϕn+ 2H|y whichappears in(1.6).We will introduce a number of useful tools to investigate the quantum mechanical path integral,i.e.,the complete sets of eigenstates,and the Weyl-ordered form.Next we will move to the concrete constructions of the transition elements in the N=1and in the N=2systems.In this paper we omit many technical details which can be seen in the works[25,26].We mainly follow the convention defined in[26].Before going to the main discussion,for later convenience,let us take a rescaling on the fermionic operators which we introduced in the previous section:N=2system:ϕa→√ψa,ghostfields:ϕgh→√eigenvalues2.According to[25,26],let us introduce the complete set of the x-eigenfunctions and the complete set of the p-eigenfunctionsd D x|xexp i4,(3.3b)(2π )D/2where the plane wave is normalized tod D p exp iϕb}=δab,and a complex Grassmann odd variableη:|η ≡e bη|≡ 0|eϕa=0, ϕa= ηa.(3.4b) The inner product of these coherent state is given by ηaζa.In the same analogy as(3.2),we introduce a complete set of the Dirac fermion coherent states:1= D a=1dηaηa η|,(3.5a) Da=1dηD dη1,D a=1dηa≡dη1dη2···dηD.(3.5b) Generically we define the following matrix element M(z,y)in the quantum mechanics:M(z,y)= z| O( x, p)|y ,(3.6) where|y and z|are the initial andfinal state,respectively.Now we are quite interested in the transition element with respect to the quantum Hamiltonian H and a parameterβ:T(z,η|exp −β2The symbol“b”on an operator is omitted if there are no confusions.Next we introduce N −1complete sets of position eigenstates x k and of the fermion coherent states λk into the above transition elements.At the same time let us also insert N complete sets of momentum eigenstates p k and of another fermion coherent states ξk to yield z,H |y,ζ=N −1i =1d D x iN −1 i ′=1dλi ′λi ′Nj =1d D p jN −1 j ′=0dξj ′ξj ′×N −1 k =0x k +1,H W (x k +1ξk ,1ξk |x k ,λk=g (z )g (y )−1(2π )D N −1 i =1d Dx iN −1 j ′=0dη·ξN −1+ǫǫ−ǫ−H W (x k +1ξk ,ξk −1η=2=12=1g (x k )compen-sate exactly the g1λk to yield a useful equationd λk ·(λk −ξk −1)f (λk )=f (ξk −1),(3.9)where f (λ)is an arbitrary function of the fermionic variable λ.Notice that His the quantum Hamil-tonian in terms of quantum operators,while H W is its Weyl-ordered form.The translation from theoperator to the Weyl-ordered form is given in terms of the symmetrized form HS by H= H S +further terms =H W .(3.10)Integrating out the (discretized)momenta and taking the continuum limit N →∞,ǫ/β→d τwithN −1k =0ǫ/β→ 0−1d τ,we obtain the continuum path integral description in a following form:T (z,g (y )1(2πβ )D/2eS (int)−1g (z )appears due to the expanding the metric in S (int)at the point z and due to the integrating out the free kinetic terms of fields (see,for detail,section 2.1in [26]).The symbol ··· 0denotes the contraction of interaction terms in terms of propagatorsand setting the external source to zero.From now on we simply abbreviate e −1S (source) 0asexp(−1∂αmk m ∂ϕb )n bS≡a,b∂∂βbn bαa ϕa +βb N !i∂2g mn π(−1)m π(−1)n S+22R pqmn (Γ0)(ϕmϕq)S +26∂m (H npq )(ϕnpq)S+2ϕmnpq )S −2(ϕmn2H mabϕab +ϕb +iϕab ,(3.15b)and of the N =1HamiltonianH 1;W H=18g mn Γp 0mq Γq 0np+124H mnp H mnp − 22ω−mab ψab −i A αm (ˆc †T αˆc ).(3.16b)To proceed computations in path integral formalism in the N =1system,we would like to add a second set of “free”Majorana fermions in order to simplify the path integral in the N =1systemin the same way as the one in the N =2system.Denoting the original Majorana fermions ψa by ψa 1,and the new ones by ψa 2,and combining them,we again construct Dirac fermions χa and √χa =12ψa 1−iψa2 .(3.17)Notice that,in this context,ψa 2differs from the second component of the previously defined Dirac fermions ϕa because now ψa 2is introduced as a “free”fermion in the N =1Hamiltonian.3.3Explicit form of the transition element in N =2systemWe are ready to discuss the explicit form of the transition element in the N =2system in the framework of the Lagrangian formalism.Let us first decompose the bosonic and fermionic vari-ables into two parts,i.e.,the background fields and quantum fluctuations in such a way as x m (τ)=x m bg (τ)+q m (τ)and ξa (τ)=ξa bg (τ)+ξa qu (τ),respectively.These background fields follow the freeequations of motion whose solutions arex m bg (τ)=z m +τ(z m −y m),ξabg(τ)=ζa ,ηa ,(3.18)with constraints (via the mean-value theorem)q m(−1)=q m(0)=0,0−1d τq m (τ)=0,(3.19a)ξaqu (−1)=η|exp−βg (y )1(2πβ )D/2eS (int)H,(3.20a)S (int)H=−1S H =−12g mn (x ) d x md τ+b m c n +a m a n+ξa qudd τωmab (x )2H mab (x )(ξab +2 0−1d τR cdab (ω(x ))ξa ξd −β ξabcd −2ξab60−1d τ∂m (H npq (x ))ξnpq−β3H mnp (x )H mnp (x ),(3.20d)−1β−1d τ1d τd q nξa qudξb qu(τ)=δab θ(σ−τ),(3.21d) ξa qu (σ)ξbqu (τ) =0=ξb qu (τ) ,(3.21e)where the δ(σ−τ)is the “Kronecker delta”,and −1≤τ,σ≤0.The definitions of various functions are defined as ∆(σ,τ)=σ(τ+1)θ(σ−τ)+τ(σ+1)θ(τ−σ)=∆(τ,σ),θ(τ−τ)=1η,H 1H|y,ζ,ζgh = g (z )41ηa ζaeS (int)1,H,(3.22a)ηgh ·ζgh −1S 1,H −S (0)1,(3.22b)−1ηa ζa +β 0−1d τ1d τd x nξa qudd τˆc i qu−1d τω−mab (x )ψa 1ψb1−−1d τd x mξgh T αξgh+βξgh T αξgh−β2ω−mab(x)ω−n ab(x) −1S(0)1=− 0−1dτ 1dτd q nξa qu d dτˆc i qu .(3.22e)In the same way as(3.18),the dynamicalfields are decomposed into the backgroundfields and the quantumfieldsψa1(τ)=ψa1,bg(τ)+ψa1,qu(τ),ψa1,bg(τ)=12 ζa+ξi,gh(τ)=2δab θ(σ−τ)−θ(τ−σ) .(3.24) The propagator of ghostfieldˆc i gh is also given asˆc i qu(σ)ˆc†j,qu(τ) =δi jθ(σ−τ).(3.25) 4Witten index in N=1quantum mechanicsIn this section we will discuss the Witten index in the N=1quantum mechanical system derived from the path integral formalism.To obtain this,we will analyze Feynman path integral in terms of Feynman(dis)connected graphs.Since the form of the Witten index(or equivalently,the Dirac index) is same as the one of the chiral anomaly,we refer to the derivation of the chiral anomaly given in section6.1and6.2of[26].4.1FormulationAs mentioned before,by using the identification between the Clifford algebra on the target geometry and the anti-commutation relations of fermions in the quantum mechanics,we can describe the Dirac index equipped with the regulator R in terms of the transition element of N =1quantum mechanicsindex /D (ˆω)≡lim β→0TrΓ(5)e−βR=lim β→0Tr (−1)F e −β2D/2TrD a =1ϕa +c H 1H.(4.1)Note that the chirality operator Γ(5)on the target geometry can be identified with the fermion number operator (−1)F in the N =1quantum mechanics,i.e.,the chirality operator is defined as Γ(5)=(−i )D/2Γ1Γ2···ΓD ,the number operator (−1)F is replaced in terms of the fermion operatorsΓa ≡√ϕa,Γ(5)≡(−i )D/2D a =1ϕa +ϕa )by hand.(See the explanation in section 6.1in [26]and we will find that thisfactor is canceled out via the fermionic measure computation.)The symbol Tr in the above expression of the index is defined asTr O ≡d Dx 0ζaeζ|O|x 0,ζ .(4.3)Then,inserting the complete set of the fermion coherent states (3.5),we obtain the explicit form of the Dirac index,i.e.,the Witten index with respect to the N =1quantum mechanical path integral:index /D (ˆω)=limβ→0(−i )D/2g (x 0)Da =1d ζaeζ|D b =1ϕb +ηη× x 0,H 1H |x 0,ζ .(4.4a)Here the appearing transition element has already described in the previous section such asx 0,H 1H|x 0,ζ =1ηa ζaexp−1S (int)1,H =−12−1d τ˙q m ω−mab (x )ψab1−βwhere x=x0+q,ω−mab(x)=ωmab(x)−H mab(x)andψa1=ψa1,bg+ψa1,qu(τ).The functional G1(x)is defined in(3.22d).The fermionic terms are summarized asD a=1 dζa eηη ϕb |η = D a=1 dζa eηη+ζb= D a=1 dζa eηηD b=1 ηb+ζ),hence ζηcan be replaced by unity.For the same reason,we rewrite other exponential factor in such a way asηη=−1ζ)(ζ−ηa dηa dζa dηa dζa·2D d(ζ+η)1d(η−ζ)D.(4.5b)Thus,combining the above two equations,we showa dζ+η)D···d(ζ)1···d(η−2(η−η)b ηb+ηa dζa b ζb−ηζfrom the Weyl-ordered Hamiltonian.We perform this fermionic delta function to the transition element.Generically we consider the following equation in the N=1system:a dηb eη2 =2D/2 a dψa1,bg F(ψa1,bg).(4.5d)The factor2D/2cancels the factor2−D/2in(4.4),which we introduced caused by the free fermionψa2. Next,rescaling the fermionsψa1by a factor(β )−12ψa1,we remove theβ dependence in the path integral measure.Here we show the Witten index in the path integral formalism:index/D(ˆω)=limβ→0(−i)D/2g(x0)Da=1dψa1,bg exp −1S(int)1,H=−12 g mn(x)−g mn(x0) ˙q m˙q n+b m c n+a m a n−18 0−1dτG1(x),(4.6b)where x=x0+q.In addition,all the bosonic and fermionic propagators are proportional toβ :q m(σ)q n(τ) =−β g mn(x0)∆(σ,τ),(4.7a)q m(σ)˙q n(τ) =−β g mn(x0) σ+θ(τ−σ) ,(4.7b)˙q m(σ)˙q n(τ) =−β g mn(x0) 1−δ(τ−σ) ,(4.7c)a m(σ)a n(τ) =β g mn(x0)δ(σ−τ),(4.7d)b m(σ)c n(τ) =−2β g mn(x0)δ(σ−τ),(4.7e)ψa1,qu(σ)ψb1,qu(τ) =1ξa qu(0)=0.•We could,for convenience,choose a frame with∂m g pq(x0)=0,called the Riemann normal coordinate frame.Due to this wefind∂m e n a=∂m E a n=0,Γp0nq(x0)=0andωmab(x0)=0.Notice,however that∂p∂q e m a(x0)=0,∂mωnab(x0)=0and so forth.•The torsion given by the NS-NSflux H mnp(or,in mathematically equivalent form,the Bismut torsion T(B))is also expanded in the Riemann normal coordinate frame around x0.•The Feynman amplitudes should be independent of the target space metric,at least invariant under the rescale of the metric.The torsion is given by the NS-NS three-formflux H mnp,which is represented in terms of the Bismut torsion T(B)in the supergravity[24]:H mnp(x)=32J m q J n r J p s∂[q J rs](x).(4.8)As mentioned in the above comment,we will take the Riemann normal coordinate frame at the point x0.At this point we can set theflat metric at the lowest order approximation in the following way:g mn(x0)=δmn,∂p g mn(x0)=0,∂p∂q g mn(x0)=0.(4.9)Due to(4.8),and since the complex structure is proportional to the metric,theflux(or the torsion) should be also expanded around the point x0with the valuesH mnp(x0)=32 ∂mω−nab(x0)−∂nω−mab(x0) 0−1dτ˙q m q n=12R mnab(ω+(x0)) 0−1dτq m˙q n,(4.11) where we used the symmetricity on a Riemann tensor with torsion R pqmn(ω−)=R mnpq(ω+)−(d H)pqmn and the periodicity of the bosonic quantumfields q m(0)=q m(−1).Furthermore we also generalized the derivative to the covariant derivative because now we analyze on a point x0on which the torsion free connections vanish:Γp0mn(x0)=ωmab(x0)=H mab(x0)=0.Let us evaluate the functional integral in terms of the bosonic propagators(4.7)at the point x0. The exponent exp(−1W H= exp(−1W H=∞k=11 S(int)1,H k ,(4.12)where ··· indicates the value given only by the connected Feynman graphs.For later discussions,it is also worth mentioning that the volume form and the Riemann curvature two-form are given in terms of the vielbein one-form e a=e m a d x m in the following way:d2n x04.2Pontrjagin classes4.2.1Riemannian manifoldIn this case S (int)1becomes much simpler than (4.6a)because there are no terms from H -flux.The spinconnection ω−is also reduced to ω.We also easily find that the terms equipped with higher deriva-tives carrying more than three bosonic quantum fields q m always generate higher-loops Feynman graphs because of the absence of the tadpole graphs.Furthermore,the terms of order in β do not contribute to the final result.Then we truncate S (int)1in the following way:−12β R mn (ω(x 0)) 0−1d τq m ˙q n ,R mn ≡1(2π)D/2d Dx 02βR mn0−1d τq m ˙q n.(4.16)Let us first evaluate the sum of connected graphs:−12β R mn0−1d τq m ˙q n=∞ k =112β k R m 1n 1···R m k n k 0−1d τ1···d τk q m 1˙q n 1 (τ1)··· q m k˙q n k (τk ) .(4.17)Since the two indices in the Riemann tensors are anti-symmetric whereas the propagators are sym-metric with respect to the exchanging of bosonic quantum fields,we easily find that the contraction at the same “time”τi yields a vanishing amplitude.We also know that the partial integration is al-lowed since q m (τi )=0at the end points.Then,there are (k −1)!ways to contract k vertices and the symmetry of each vertex in both q yields a factor 2k −1.Then we find that the effective action (4.17)is described as−1k ! −12∞ k =21kI k =logy/23!y。