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The Feminine Matrix of Sex and Gender in Classical AthensIn The Feminine Matrix of Sex and Gender in Classical Athens ,Kate Gilhuly exploresthe relationship between the prostitute,the wife,and the ritual performerin Athenian literature.She suggests that these three roles formed a symboliccontinuum that served as an alternative to a binary conception of gender inclassical Athens and provided a framework for assessing both masculine andfeminine civic behavior.Grounded in close readings of four texts,“AgainstNeaira,”Plato’s Symposium ,Xenophon’s Symposium ,and Aristophanes’Lysistrata ,this book draws on observations from gender studies and the history of sexu-ality in ancient Greece to illuminate the relevance of these representations ofwomen to civic behavior,pederasty,philosophy,and politics.In these originalreadings,Gilhuly casts a new light on the complexity of the classical Atheniansex/gender system as she demonstrates how various and even opposing strate-gies worked together to articulate different facets of the Athenian subject.Kate Gilhuly is an assistant professor in the Department of Classical Studiesat Wellesley College.Frontmatter More informationTHE FEMININE MATRIX OF SEX AND GENDER IN CLASSICAL ATHENSijKate GilhulywellesleycollegeFrontmatter More informationFrontmatterMore informationcambridge university pressCambridge,New York,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University Press32Avenue of the Americas,New York,ny10013-2473,usaInformation on this title:/9780521899987c Kate Gilhuly2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.First published2009Printed in the United States of AmericaA catalog record for this publication is available from the British Library.Library of Congress Cataloging in Publication DataGilhuly,Kate,1964–The feminine matrix of sex and gender in classical Athens/Kate Gilhuly.p.cm.Includes bibliographical references and index.isbn978-0-521-89998-7(hardback)1.Women in literature.2.Sex in literature.3.Greek literature–History and criticism.I.Title.pa3015w65g542009880.9 3522–dc222008001676isbn978-0-521-89998-7hardbackCambridge University Press has no responsibility for the persistence oraccuracy of url s for external or third-party Internet Web sites referred to inthis publication and does not guarantee that any content on such Web sites is,or will remain,accurate or rmation regarding prices,traveltimetables,and other factual information given in this work are correct atthe time offirst printing,but Cambridge University Press does not guaranteethe accuracy of such information thereafter.FrontmatterMore informationThis book is dedicated to the memory of Katherine Kilby Howard.FrontmatterMore informationContentsAcknowledgments page ixList of Abbreviations xi1Introduction1 2Collapsing Order:Typologies of Women in the Speech“AgainstNeaira”29 3Why Is Diotima a Priestess?The Feminine Continuum in Plato’sSymposium58 4Bringing the Polis Home:Private Performance and the Civic Gazein Xenophon’s Symposium98 5Sex and Sacrifice in Aristophanes’Lysistrata140Conclusion180Bibliography189Index Locorum199Subject Index205FrontmatterMore informationAcknowledgmentsThis book has been a long time in the making,and Leslie Kurke has been generous with her insight and guidance every step of the way.I owe her spe-cial thanks.Carol Dougherty has given me crucial assistance and support in thefinal stages of writing.She has read many drafts and seemed to know what I was trying to say even when I did not.Mark Griffith commented on some of these chapters in their earliest versions.The Mellon Foundation supported a year of postdoctoral work at Northwestern University.Victoria Wohl and Florence Dore have given me helpful comments and encouragement when I really needed it.Bryan Burns,Carolyn Dewald,Vincent Farenga,Tom Habinek,Amy Richlin,Greg Thalmann,and Phiroze Vasunia contributed to a lively intellectual environment at the University of Southern Califor-nia in which this bookfirst took shape.Rebecca Jamin helped prepare the manuscript.Anne Gilhuly has read and edited much of this work;all of the jargon that remains is my own.Thanks to Anabel and Aidan Bush for sharing their mother with this project.Finally,I am grateful to Mark Bush,whose love and support helped bring this book into the light of day.FrontmatterMore informationAbbreviationsABSA Annual of the British School at AthensAch.AcharniansAE Archaiologike EphemerisAes.AeschylusAeschin.AeschinesAg.AgamemnonAJAH American Journal of Ancient HistoryAJP American Journal of PhilologyAlc.AlcibiadesAp.ApologyAr.AristophanesARV J.D.Beazley,Attic Red Figure Vase-Painting(Oxford,1956)AS Ancient SocietyAth.AthenaiosAth.Deipn.Athenaios’DeipnosophistaiAth.Pol.[Aristotle]Athenaion PoliteiaAv.BirdsBibl.BibliothecaCA Classical AntiquityCJ Classical JournalCP Classical PhilologyCQ Classical QuarterlyCr.CritoCR Classical ReviewCyr.CyropaediaEkkl.Aristophanes’EkklesiazousaiEur.EuripidesFr.Aristophanes’FrogsFrGrH F.Jakoby et al.,eds.,Die Fragmente der griechischen Historiker(Berlin,1923–)GRBS Greek,Roman,and Byzantine StudiesFrontmatterMore informationxii AbbreviationsHell.HellenicaHerod.HerodotusHist.HistoriesHom.h.Aphr.Homeric Hymn to AphroditeHThR Harvard Theological ReviewIG F.H.de Gaertingen et al.,eds.,Inscriptiones Graecae,2nd ed.(Berlin,1924–)Il.Homer’s IliadInt.of Dreams Interpretation of DreamsIph.in Tauris Iphigeneia among the TauriansJHS Journal of Hellenic StudiesMem.MemorabiliaMen.MenanderNic.NiciasO.OlympianOd.OdysseyOik.OikonomikosPi.PindarPlut.PlutarchPyth.PythianRE G.Wissowa et al.,Paulys Realencyclop¨a die der classischen Altertumwis-senschaft(Munich,1903–78)Rep.RepublicRh.RhetoricaSch.Ar.Av.Scholia on Aristophanes’BirdsSymp.SymposiumTAPA Transactions of the American Philological AssociationTheog.TheogonyThesmo.ThesmophoriazousaiThuc.ThucydidesW.D.Works and DaysXen.XenophonYCS Yale Classical Studies。
Communications and Control Engineering For other titles published in this series,go to/series/61Series EditorsA.Isidori J.H.van Schuppen E.D.Sontag M.Thoma M.Krstic Published titles include:Stability and Stabilization of Infinite Dimensional Systems with ApplicationsZheng-Hua Luo,Bao-Zhu Guo and Omer Morgul Nonsmooth Mechanics(Second edition)Bernard BrogliatoNonlinear Control Systems IIAlberto IsidoriL2-Gain and Passivity Techniques in Nonlinear Control Arjan van der SchaftControl of Linear Systems with Regulation and Input ConstraintsAli Saberi,Anton A.Stoorvogel and Peddapullaiah SannutiRobust and H∞ControlBen M.ChenComputer Controlled SystemsEfim N.Rosenwasser and Bernhard mpeControl of Complex and Uncertain SystemsStanislav V.Emelyanov and Sergey K.Korovin Robust Control Design Using H∞MethodsIan R.Petersen,Valery A.Ugrinovski andAndrey V.SavkinModel Reduction for Control System DesignGoro Obinata and Brian D.O.AndersonControl Theory for Linear SystemsHarry L.Trentelman,Anton Stoorvogel and Malo Hautus Functional Adaptive ControlSimon G.Fabri and Visakan KadirkamanathanPositive1D and2D SystemsTadeusz KaczorekIdentification and Control Using Volterra Models Francis J.Doyle III,Ronald K.Pearson and Babatunde A.OgunnaikeNon-linear Control for Underactuated Mechanical SystemsIsabelle Fantoni and Rogelio LozanoRobust Control(Second edition)Jürgen AckermannFlow Control by FeedbackOle Morten Aamo and Miroslav KrsticLearning and Generalization(Second edition) Mathukumalli VidyasagarConstrained Control and EstimationGraham C.Goodwin,Maria M.Seron andJoséA.De DonáRandomized Algorithms for Analysis and Controlof Uncertain SystemsRoberto Tempo,Giuseppe Calafiore and Fabrizio Dabbene Switched Linear SystemsZhendong Sun and Shuzhi S.GeSubspace Methods for System IdentificationTohru KatayamaDigital Control SystemsIoan ndau and Gianluca ZitoMultivariable Computer-controlled SystemsEfim N.Rosenwasser and Bernhard mpe Dissipative Systems Analysis and Control(Second edition)Bernard Brogliato,Rogelio Lozano,Bernhard Maschke and Olav EgelandAlgebraic Methods for Nonlinear Control Systems Giuseppe Conte,Claude H.Moog and Anna M.Perdon Polynomial and Rational MatricesTadeusz KaczorekSimulation-based Algorithms for Markov Decision ProcessesHyeong Soo Chang,Michael C.Fu,Jiaqiao Hu and Steven I.MarcusIterative Learning ControlHyo-Sung Ahn,Kevin L.Moore and YangQuan Chen Distributed Consensus in Multi-vehicle Cooperative ControlWei Ren and Randal W.BeardControl of Singular Systems with Random Abrupt ChangesEl-Kébir BoukasNonlinear and Adaptive Control with Applications Alessandro Astolfi,Dimitrios Karagiannis and Romeo OrtegaStabilization,Optimal and Robust ControlAziz BelmiloudiControl of Nonlinear Dynamical SystemsFelix L.Chernous’ko,Igor M.Ananievski and Sergey A.ReshminPeriodic SystemsSergio Bittanti and Patrizio ColaneriDiscontinuous SystemsYury V.OrlovConstructions of Strict Lyapunov FunctionsMichael Malisoff and Frédéric MazencControlling ChaosHuaguang Zhang,Derong Liu and Zhiliang Wang Stabilization of Navier–Stokes FlowsViorel BarbuDistributed Control of Multi-agent NetworksWei Ren and Yongcan CaoLars Grüne Jürgen Pannek Nonlinear Model Predictive Control Theory and AlgorithmsLars Grüne Mathematisches Institut Universität Bayreuth Bayreuth95440Germanylars.gruene@uni-bayreuth.de Jürgen Pannek Mathematisches Institut Universität BayreuthBayreuth95440Germanyjuergen.pannek@uni-bayreuth.deISSN0178-5354ISBN978-0-85729-500-2e-ISBN978-0-85729-501-9DOI10.1007/978-0-85729-501-9Springer London Dordrecht Heidelberg New YorkBritish Library Cataloguing in Publication DataA catalogue record for this book is available from the British LibraryLibrary of Congress Control Number:2011926502Mathematics Subject Classification(2010):93-02,92C10,93D15,49M37©Springer-Verlag London Limited2011Apart from any fair dealing for the purposes of research or private study,or criticism or review,as per-mitted under the Copyright,Designs and Patents Act1988,this publication may only be reproduced, stored or transmitted,in any form or by any means,with the prior permission in writing of the publish-ers,or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency.Enquiries concerning reproduction outside those terms should be sent to the publishers.The use of registered names,trademarks,etc.,in this publication does not imply,even in the absence of a specific statement,that such names are exempt from the relevant laws and regulations and therefore free for general use.The publisher makes no representation,express or implied,with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.Cover design:VTeX UAB,LithuaniaPrinted on acid-free paperSpringer is part of Springer Science+Business Media()For Brigitte,Florian and CarlaLGFor Sabina and AlinaJPPrefaceThe idea for this book grew out of a course given at a winter school of the In-ternational Doctoral Program“Identification,Optimization and Control with Ap-plications in Modern Technologies”in Schloss Thurnau in March2009.Initially, the main purpose of this course was to present results on stability and performance analysis of nonlinear model predictive control algorithms,which had at that time recently been obtained by ourselves and coauthors.However,we soon realized that both the course and even more the book would be inevitably incomplete without a comprehensive coverage of classical results in the area of nonlinear model pre-dictive control and without the discussion of important topics beyond stability and performance,like feasibility,robustness,and numerical methods.As a result,this book has become a mixture between a research monograph and an advanced textbook.On the one hand,the book presents original research results obtained by ourselves and coauthors during the lastfive years in a comprehensive and self contained way.On the other hand,the book also presents a number of results—both classical and more recent—of other authors.Furthermore,we have included a lot of background information from mathematical systems theory,op-timal control,numerical analysis and optimization to make the book accessible to graduate students—on PhD and Master level—from applied mathematics and con-trol engineering alike.Finally,via our web page we provide MATLAB and C++software for all examples in this book,which enables the reader to perform his or her own numerical experiments.For reading this book,we assume a basic familiarity with control systems,their state space representation as well as with concepts like feedback and stability as provided,e.g.,in undergraduate courses on control engineering or in courses on mathematical systems and control theory in an applied mathematics curriculum.However,no particular knowledge of nonlin-ear systems theory is assumed.Substantial parts of the systems theoretic chapters of the book have been used by us for a lecture on nonlinear model predictive con-trol for master students in applied mathematics and we believe that the book is well suited for this purpose.More advanced concepts like time varying formulations or peculiarities of sampled data systems can be easily skipped if only time invariant problems or discrete time systems shall be treated.viiviii PrefaceThe book centers around two main topics:systems theoretic properties of nonlin-ear model predictive control schemes on the one hand and numerical algorithms on the other hand;for a comprehensive description of the contents we refer to Sect.1.3.As such,the book is somewhat more theoretical than engineering or application ori-ented monographs on nonlinear model predictive control,which are furthermore often focused on linear methods.Within the nonlinear model predictive control literature,distinctive features of this book are the comprehensive treatment of schemes without stabilizing terminal constraints and the in depth discussion of performance issues via infinite horizon suboptimality estimates,both with and without stabilizing terminal constraints.The key for the analysis in the systems theoretic part of this book is a uniform way of interpreting both classes of schemes as relaxed versions of infinite horizon op-timal control problems.The relaxed dynamic programming framework developed in Chap.4is thus a cornerstone of this book,even though we do not use dynamic programming for actually solving nonlinear model predictive control problems;for this task we prefer direct optimization methods as described in the last chapter of this book,since they also allow for the numerical treatment of high dimensional systems.There are many people whom we have to thank for their help in one or the other way.For pleasant and fruitful collaboration within joint research projects and on joint papers—of which many have been used as the basis for this book—we are grateful to Frank Allgöwer,Nils Altmüller,Rolf Findeisen,Marcus von Lossow,Dragan Neši´c ,Anders Rantzer,Martin Seehafer,Paolo Varutti and Karl Worthmann.For enlightening talks,inspiring discussions,for organizing workshops and mini-symposia (and inviting us)and,last but not least,for pointing out valuable references to the literature we would like to thank David Angeli,Moritz Diehl,Knut Graichen,Peter Hokayem,Achim Ilchmann,Andreas Kugi,Daniel Limón,Jan Lunze,Lalo Magni,Manfred Morari,Davide Raimondo,Saša Rakovi´c ,Jörg Rambau,Jim Rawl-ings,Markus Reble,Oana Serea and Andy Teel,and we apologize to everyone who is missing in this list although he or she should have been mentioned.Without the proof reading of Nils Altmüller,Robert Baier,Thomas Jahn,Marcus von Lossow,Florian Müller and Karl Worthmann the book would contain even more typos and inaccuracies than it probably does—of course,the responsibility for all remaining errors lies entirely with us and we appreciate all comments on errors,typos,miss-ing references and the like.Beyond proof reading,we are grateful to Thomas Jahn for his help with writing the software supporting this book and to Karl Worthmann for his contributions to many results in Chaps.6and 7,most importantly the proof of Proposition 6.17.Finally,we would like to thank Oliver Jackson and Charlotte Cross from Springer-Verlag for their excellent rs Grüne Jürgen PannekBayreuth,Germany April 2011Contents1Introduction (1)1.1What Is Nonlinear Model Predictive Control? (1)1.2Where Did NMPC Come from? (3)1.3How Is This Book Organized? (5)1.4What Is Not Covered in This Book? (9)References (10)2Discrete Time and Sampled Data Systems (13)2.1Discrete Time Systems (13)2.2Sampled Data Systems (16)2.3Stability of Discrete Time Systems (28)2.4Stability of Sampled Data Systems (35)2.5Notes and Extensions (39)2.6Problems (39)References (41)3Nonlinear Model Predictive Control (43)3.1The Basic NMPC Algorithm (43)3.2Constraints (45)3.3Variants of the Basic NMPC Algorithms (50)3.4The Dynamic Programming Principle (56)3.5Notes and Extensions (62)3.6Problems (64)References (65)4Infinite Horizon Optimal Control (67)4.1Definition and Well Posedness of the Problem (67)4.2The Dynamic Programming Principle (70)4.3Relaxed Dynamic Programming (75)4.4Notes and Extensions (81)4.5Problems (83)References (84)ix5Stability and Suboptimality Using Stabilizing Constraints (87)5.1The Relaxed Dynamic Programming Approach (87)5.2Equilibrium Endpoint Constraint (88)5.3Lyapunov Function Terminal Cost (95)5.4Suboptimality and Inverse Optimality (101)5.5Notes and Extensions (109)5.6Problems (110)References (112)6Stability and Suboptimality Without Stabilizing Constraints (113)6.1Setting and Preliminaries (113)6.2Asymptotic Controllability with Respect to (116)6.3Implications of the Controllability Assumption (119)6.4Computation ofα (121)6.5Main Stability and Performance Results (125)6.6Design of Good Running Costs (133)6.7Semiglobal and Practical Asymptotic Stability (142)6.8Proof of Proposition6.17 (150)6.9Notes and Extensions (159)6.10Problems (161)References (162)7Variants and Extensions (165)7.1Mixed Constrained–Unconstrained Schemes (165)7.2Unconstrained NMPC with Terminal Weights (168)7.3Nonpositive Definite Running Cost (170)7.4Multistep NMPC-Feedback Laws (174)7.5Fast Sampling (176)7.6Compensation of Computation Times (180)7.7Online Measurement ofα (183)7.8Adaptive Optimization Horizon (191)7.9Nonoptimal NMPC (198)7.10Beyond Stabilization and Tracking (207)References (209)8Feasibility and Robustness (211)8.1The Feasibility Problem (211)8.2Feasibility of Unconstrained NMPC Using Exit Sets (214)8.3Feasibility of Unconstrained NMPC Using Stability (217)8.4Comparing Terminal Constrained vs.Unconstrained NMPC (222)8.5Robustness:Basic Definition and Concepts (225)8.6Robustness Without State Constraints (227)8.7Examples for Nonrobustness Under State Constraints (232)8.8Robustness with State Constraints via Robust-optimal Feasibility.2378.9Robustness with State Constraints via Continuity of V N (241)8.10Notes and Extensions (246)8.11Problems (249)References (249)9Numerical Discretization (251)9.1Basic Solution Methods (251)9.2Convergence Theory (256)9.3Adaptive Step Size Control (260)9.4Using the Methods Within the NMPC Algorithms (264)9.5Numerical Approximation Errors and Stability (266)9.6Notes and Extensions (269)9.7Problems (271)References (272)10Numerical Optimal Control of Nonlinear Systems (275)10.1Discretization of the NMPC Problem (275)10.2Unconstrained Optimization (288)10.3Constrained Optimization (292)10.4Implementation Issues in NMPC (315)10.5Warm Start of the NMPC Optimization (324)10.6Nonoptimal NMPC (331)10.7Notes and Extensions (335)10.8Problems (337)References (337)Appendix NMPC Software Supporting This Book (341)A.1The MATLAB NMPC Routine (341)A.2Additional MATLAB and MAPLE Routines (343)A.3The C++NMPC Software (345)Glossary (347)Index (353)。
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obsidian frontmatter 语法Obsidian frontmatter是一种在Obsidian笔记应用中使用的语法结构,用于在笔记文件的开头定义元数据或配置。
它通常被放置在Markdown文件的最前面,用三个短破折号(---)包围起来。
以下是Obsidian frontmatter的语法规则和示例:1. 使用三个短破折号将frontmatter分隔开,如下所示:```---frontmatter内容---```2. frontmatter内容是键值对的形式,使用YAML(YAMLAin't Markup Language)语法。
键和值之间使用冒号(:)分隔,键值对之间使用换行分隔。
例如:```---title: Example Notedate: 2022-01-01tags:- 个人- 笔记---```3. frontmatter可以包含任意数量和类型的键值对。
你可以自定义键名和对应的值,以满足你的需要。
4. 你可以在frontmatter中使用变量来代表一些动态信息。
例如,可以使用`{{date}}`来表示当前日期。
示例:```---title: Example Notedate: {{date}}---```5. frontmatter的内容对于Obsidian是可见的,但在渲染Markdown文件时会被忽略,不会显示在预览或导出的结果中。
通过使用Obsidian frontmatter语法,你可以在笔记文件中定义和管理一些元数据,如标题、日期、标签等,以及其他自定义信息。
这对于组织和搜索笔记非常有帮助。
毕业论文的结构1.前置部分(Front Matter):中文封面(Cover, in Chinese)英文题名页(Title Page, in English)郑重声明论文使用授权说明目录(Contents)英文摘要、关键词页(Abstract and Key Words, in English)中文摘要、关键词页(Abstract and Key Words, in Chinese)2.正文部分(Body):引言(Introduction)主体(Body)结论(Conclusion)3.文尾部分(Back Matter):参考文献(Works Cited)致谢(Acknowledgements)附录(Appendix)封底(Back Cover)论文标题1. 论文的标题应具备以下特征:1)准确。
要做到“题与文相符”,概括文章的基本内容,揭示文章的主题。
2)醒目。
要引人注目,给人留下深刻印象。
3)新颖。
要有新鲜感。
只有作者的思想新颖,论题才能富有新意。
4)简洁。
要具有高度的概括性。
字数限制在20个字以内(一般不超过10个实词)。
5)具体。
要具体地表达出论文的观点,切忌空泛而谈。
2. 英文标题四种结构1)名词性词组(包括动名词) Sister Carrie’s Broken Dream2)介词词组On the theme of Young Goodman Brown by Hawthorne3)名词词组+介词词组A comparison between a Teacher-Centered Class and aStudents-Centered Class4)疑问式How to Use a Computer in Managing an English Class (学术论文不建议使用此标题方式)有的标题由两部分组成,用冒号( :)隔开。
一般来说,冒号前面一部分是主标题,提出文章中心或主旨。
冒号后面是副标题,补充说明主标题的内容,如研究重点或研究方法。
texstudio中frontmatter用法在TexStudio中,我们可以使用frontmatter来定义文档的前言部分。
frontmatter 是一个在主文档开始前定义的区域,在其中可以包含一些与文档格式和结构有关的设置和命令。
首先,我们需要在TexStudio中创建一个新的TEX文件。
在文件的开头,我们可以使用frontmatter命令来定义frontmatter区域。
例如:```\begin{frontmatter}% 在这里插入前言内容和设置\end{frontmatter}```frontmatter区域中可以包含一些常用的设置,比如文档标题、作者、日期等。
我们可以使用相应的命令来定义这些内容。
例如:```\title{我的文档标题}\author{作者}\date{\today}```在frontmatter区域中,我们还可以定义一些特殊的设置,比如文档类型、页眉页脚样式等。
这些设置使用特定的命令进行定义。
例如,可以使用以下命令定义文档类型为book:```\documentclass{book}```使用以下命令定义页眉页脚样式为fancy:```\usepackage{fancyhdr}```除了设置和命令,frontmatter区域还可以包含一些其他的内容,比如摘要、目录等。
我们可以使用相应的命令来插入这些内容。
例如,可以使用以下命令插入摘要:```\begin{abstract}这是摘要内容。
\end{abstract}```最后,在frontmatter区域的末尾,我们需要使用\maketitle命令来生成整个前言部分的内容。
例如:```\maketitle```以上就是在TexStudio中使用frontmatter的基本用法。
通过定义frontmatter区域,我们可以方便地对文档的前言部分进行设置和格式化,从而使整个文档更具有结构性和专业性。
标题:深度解析yaml front matter语法一、引言在编写文章或博客时,我们经常会在文章的开头看到一段被称为“yaml front matter”的内容。
这段内容通常包含了一些元数据,比如文章的标题、作者、发布时间等信息。
本文将深入探讨yaml front matter的语法和使用方法。
二、yaml front matter的基本语法yaml front matter通常使用YAML(YAML Ain't Markup Language)格式来书写。
它位于文章的起始部分,用三个破折号(---)包裹起来。
以下是一个简单的yaml front matter示例:```---title: "文章标题"author: "作者名"date: 2022-01-01categories:- 技术- 编程tags:- YAML---```在上面的示例中,title、author、date、categories和tags就是yaml front matter中的元数据字段,它们的值使用冒号(:)进行键值对的表示。
另外,categories和tags字段的值是一个列表,使用短横线(-)进行表示。
三、yaml front matter的高级语法除了基本的元数据字段外,yaml front matter还可以包含一些高级的语法,比如嵌套结构、引用、复杂数据类型等。
例如:```---title: "文章标题"author: "作者名"date: 2022-01-01tags: &tags- YAML- 文章categories:- 技术references: *tags---```在上面的示例中,我们使用了引用符号(&和*)来定义和引用一个tags字段的取值,这样就可以避免重复输入同样的数值。
这种做法在管理大量文章或博客时尤其有用,可以提高编辑效率。
Microfacies of Carbonate RocksErik Fl¨ugel Microfaciesof Carbonate Rocks Analysis,Interpretationand ApplicationSecond EditionWith a contribution by Axel Munnecke 123ISBN978-3-642-03795-5e-ISBN978-3-642-03796-2DOI10.1007/10.1007/978-3-642-03796-2Springer Heidelberg Dordrecht London New YorkLibrary of Congress Control Number:2009935385c Springer-Verlag Berlin Heidelberg2010This work is subject to copyright.All rights are reserved,whether the whole or part of the material is concerned,specifically the rights of translation,reprinting,reuse of illustrations,recitation,broadcasting, reproduction on microfilm or in any other way,and storage in data banks.Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September9,1965, in its current version,and permission for use must always be obtained from Springer.Violations are liable to prosecution under the German Copyright Law.The use of general descriptive names,registered names,trademarks,etc.in this publication does not imply, even in the absence of a specific statement,that such names are exempt from the relevant protective laws and regulations and therefore free for general use.Camera-ready by Erentraud Fl¨u gel-Kahler,ErlangenCover design:WMXDesign,HeidelbergPrinted on acid-free paperSpringer is part of Springer Science+Business Media()Preface to the Second EditionA second editon of this book - yes or no - or not yet? Are changes necessary or would it be enough if minor errors in the text were corrected?So I asked for help and I got answers from friends and colleagues. I wish to thank W.Ch. Dullo (Kiel), A. Freiwald (Erlangen), H.-G. Herbig (Cologne), W. Piller (Graz), W. Schlager (Amsterdam), R. J. Stanton (Thousand Oaks, USA) for their excellent and friendly advice.They were in agreement that not enough has changed in the scientific field of ‘Microfacies of Carbonate Rocks’since 2004 when the first edition was published for a new edition to be necessary, but they all believed that an update of the references on the CD going with the volume would be useful.Therefore, the reference section has been updated to April 2009. Most of the new references are since 2002, but a few are earlier. The reference file now contains more than 16,000 references. In connection with the keywords used throughout the book these references can help the reader locate special subjects or overviews of interest.When Erik wrote this book during his last years, his primary goal was to provide students and all those interested in and working with microfacies a helpful und useful resource that contained many plates and figures.Most of the pictures in this book were collected during Erik Flügel’s scientific work, some are from papers that were published in the journal Facies, then published by the Institute of Paleontology (now Geo-zentrum Nordbayern), University Erlangen-Nürnberg, and last not least, some were graciously provided by col-leagues.The author had hoped to include an additional chapter with plates that would provide the reader with an expanded range of information about microfacies. This task has been accomplished by A. Munnecke (Erlangen). Chapter 20 contains plates and figures that have been used successfully in the Course on Micro-facies held every year or two at the University in Erlangen.I wish to thank all of my colleagues at the institute in Erlangen, and especially A. Munnecke for the compilation of Chapter 20.Ch. Schulbert was most helpful in solving software problems with the text and CD.I thank Ch. Bendall (Springer Verlag Heidelberg) for overseeing the printing of this new edition. Erlangen, June 2009Erentraud Flügel-KahlerPrefaceThe objective of this book is to provide a synthesis of the methods used in microfacies studies of carbonate rocks and to show how the application of microfacies studies has contributed to new developments in car-bonate geology. In contrast with other textbooks on car-bonate sedimentology this book focuses on those com-positional and textural constituents of carbonates that reflect the depositional and diagenetic history and de-termine the practical usefulness of carbonate rocks.The chapters are written in such a way, that each one can be used as text in upper level undergraduate and graduate courses. The topics of the book also ap-ply to research workers and exploration geologists, looking for current information on developments in the use of microfacies analysis.Since microfacies studies are based on thin sections, instructive plates showing thin-section photographs ac-companied by thorough and detailed explanations form a central part of this book. All plates in the book con-tain a short summary of the topic. An –> sign leads the reader to the figures on the plate. The description of the microphotographs are printed in a smaller type. Care has been taken to add arrows and/or letters (usually the initials of the subject) so that the maximum informa-tion can be extracted from the figures.Rather than being a revised version of ‘Microfacies Analysis of Limestones’ (Flügel 1982) ‘Microfacies of Carbonate Rocks’ is a new book, based on a new con-cept and offering practical advice on the description and interpretation of microfacies data as well as the application of these data to basin analysis. Microfacies analysis has the advantages over traditional sedimen-tological approaches of being interdisciplinary, and in-tegrating sedimentological, paleontological and geo-chemical aspects.‘Microfacies of Carbonate Rocks’:•analyses both the depositional and the diagenetic his-tory of carbonate rocks,•describes carbonate sedimentation in various ma-rine and non-marine environments, and considers both tropical warm-water carbonates and non-tropi-cal cool-water carbonates,•presents diagnostic features and highlights the sig-nificance of microfacies criteria,•stresses the biological controls of carbonate sedi-mentation and provides an overview on the most common fossils found in thin sections of limestones,• discusses the relationships between diagenetic pro-cesses, porosity and dolomitization,•demonstrates the importance of microfacies for es-tablishing and evaluating sequence stratigraphic frameworks and depositional models,•underlines the potential of microfacies in differenti-ating paleoclimate changes and tracing platform-ba-sin relationships, and•demonstrates the value of microfacies analysis in evaluating reservoir rocks and limestone resources, as well as its usefulness in archaeological prov-enance studies.Structure of the BookMicrofacies of Carbonate Rocks starts with and in-troductory chaper (Chap.1) and an overview of mod-ern carbonate deposition (Chap. 2) followed by 17 chap-ters that have been grouped into 3 major parts. Microfacies Analysis (Chap. 3 to Chap. 10) summa-rizes the methods used in microfacies studies followed by discussions on descriptive modes and the implica-tions of qualitative and quantitative thin-section crite-ria.Microfacies Interpretation (Chap. 11 to Chap. 16) demonstrates the significance of microfacies studies in evaluating paleoenvironment and depositional sys-tems and, finally,Practical Use of Microfacies (Chap. 17 to Chap. 19) demonstrates the importance of applied microfacies studies in geological exploration for hydrocarbons and ores, provides examples of the relationships between carbonate rock resources and their facies and physical properties, and also illustrates the value of microfacies studies to archaeologists.Important references are listed at the end of chap-ters or sections under the heading ‘Basics’. The codeV I I Inumbers K... are keywords leading to references on specific fields of interest (see CD), e.g. K021 (cold-water carbonates), K078 (micrite), or K200 (hydrocar-bon reservoir rocks).The book is also accompanied by a CD containing •an alphabetical list of about 16,000 references (updated in this version up to April 2009) on carbonate rocks (see also Appendix) as word document,and•visual comparison charts for percentage estimation.Synopsis of the Book‘s ContentsChapter 1: New Perspectives in Microfacies. Micro-facies studies, which were originally restricted to the scale of thin sections, provide an invaluable source of information on the depositional constraints and envi-ronmental controls of carbonates, as well as on the prop-erties of carbonate rocks. Microfacies studies assist in understanding sequence stratigraphic patterns and are of economic importance both in reservoir studies and in the evaluation of limestone resources.Chapter 2: Modern Depositional Environments. Knowl-edge of modern carbonates is a prerequisite for under-standing ancient carbonate rocks. Modern carbonates are formed both on land and in the sea, in shallow- and in deep marine settings, and in tropical and non-tropi-cal regions, but the present is only part a key to the Past.Microfacies AnalysisChapter 3: Methodology. Which methods can be used in the field? Which sampling strategy should be ap-plied and how many samples are required? Which labo-ratory techniques are useful in microfacies analysis? Which other techniques should be combined with microfacies studies?Chapter 4: Microfacies Data: Matrix and Grains. This chapter offers practical advice on how to handle micro-facies data, and deals with how to describe and inter-pret thin-section characteristics. Matrix types and grain categories are discussed with regard to their diagnostic criteria, origin and significance.Chapter 5: Microfacies Data: Fabrics. Typical deposi-tional and diagenetic fabrics in limestones reflect the history of the rock. Microfacies criteria indicating breaks and changes in sedimentation (discontinuity sur-faces) are of specific interest in refining sequence strati-graphic boundaries. Variously sized fissures, micro-cracks and breccias can be used in deciphering syn-and post-depositional destructive processes.Chapter 6: Quantitative Microfacies Analysis. Whilst previous chapters focused on qualitative criteria this chapter deals with quantitative data including grain size analysis, frequency analysis and multivariate studies. Constituent analysis and the distribution patterns of spe-cific grain types are valuable tools in the reconstruc-tion of paleoenvironmental controls and depositional settings.Chapter 7: Diagenesis, Porosity and Dolomitization. Understanding diagenetic processes and their products is of high economic importance. The diagenetic micro-facies of a rock reflects changes in the course of its lithification history. The main topics discussed in this chapter are porosity types, carbonate cements, diage-netic textures including compaction and pressure solu-tion, and dolomitization/dedolomitization and dolomite textures. The last part of the chapter deals with thin-section criteria for metamorphic carbonates and marbles.Chapter 8: Classification – chosing a name for your sample. A classification is simply a tool for organizing information, and should not be the only source of con-clusions. Whilst a name based on texture and compo-sition can not replace a well-defined microfacies type, rock names are essential for the categorization of samples. Textural classifications proposed by Dunham and by Folk have proven to be the most practical. Spe-cific concepts must be adhered to in the naming of reef limestones, non-marine carbonates, recrystallized car-bonates rocks and mixed siliciclastic-carbonate rocks. Chapter 9: Limestones are Biological Sediments. In contrast to siliciclastic rocks, both the formation and the destruction of most limestones is directly or indi-rectly influenced and controlled by biological pro-cesses. This chapter stresses the biological controls on carbonate sedimentation. Microbes, encrusting organ-isms, and macro- and microborers can yield useful in-formation on paleoenvironment, depositional con-straints and carbonate production.Chapter 10: Fossils in Thin Sections. It Is Not That Difficult. The recognition of fossils in thin sections is not so difficult once the diagnostic criteria for the main groups have been understood, particularly for algae and foraminifera, sessile invertebrates, and organisms with shells. This chapter provides an overview of the most common fossils found in thin sections of limestones. The text concentrates on identification criteria, envi-ronmental and temporal distribution, and on the sig-nificance of the fossils. Numerous instructive plates are included to aid in the recognition and differentia-tion skeletal grains in thin sections.PrefaceMicrofacies InterpretationChapter 11: Summarizing Microfacies Criteria: Micro-facies Types. How can microfacies data be combined in sensitive and practicable microfacies types? Which criteria should be used, which grain types are of par-ticular importance and, how many microfacies types are reliable? The creation of microfacies types is illus-trated by means of examples.Chapter 12: Recognizing Paleoenvironmental Condi-tions. Carbonate sediments are particularly sensitive to environmental changes. Microfacies and organisms are excellent paleoenvironmental proxies as they re-flect hydrodynamic conditions, the impact of storms, substrate conditions, light, oxygenation, seawater tem-perature and salinity. Significant differences between the compositions of skeletal grain associations for warm-water and cold-water carbonates provide a use-ful tool for estimating paleoclimatic changes. How deep was the sea? Microfacies studies provide an answer. Chapter 13: Integrated Facies Analysis. Understand-ing the formation and diagenesis of carbonate rocks requires the combination of microfacies with mineral-ogical and geochemical data. The chapter deals with acid-insoluble residues and authigenic minerals in car-bonate rocks, discusses the value of minor elements and stable isotopes in tracing the depositional and di-agenetic history of limestones, and deals with the po-tential of organic matter in carbonate rocks for facies analysis.Chapter 14: Depositional Models, Facies Zones and Standard Microfacies. Microfacies are essential for de-fining depositional models and recognizing facies zones. Facies models assist in understanding deposi-tional history. Changes in sedimentological and bio-logical criteria across shelf-slope-basin transects form the basis of generalized models for carbonate platforms, ramps and shelves. Facies belts are reflected by their biotic zonation patterns and the distribution of Stan-dard Microfacies Types (SMF Types). The latter are virtual categories that summarize microfacies with iden-tical criteria. Which criteria are used in differentiating the SMF Types of platform and ramp carbonates? What are the problems involved in the SMF concept? Re-vised and refined SMF types are a meaningful tool in tracing facies belts, but must be used with care. Com-mon microfacies of carbonate ramps (Ramp Micro-facies Types) show only partial correspondence to the SMF Types of rimmed platforms.Chapter 15: Basin Analysis: Recognizing Depositional Settings. Which diagnostic criteria characterize lime-stones of different carbonate systems? Case studies for non-marine and marine carbonate rocks demonstrate how to translate microfacies into ancient depositional settings. Non-marine settings can be successfully re-constructed for pedogenic carbonates, paleokarst de-posits and ancient speleothems, travertine deposits, and lacustrine carbonates, these can be characterized by spe-cific microfacies types. Marine settings can be differ-entiated into peritidal carbonates, platforms and ramps, platform-slope-basin transects, and pelagic deep-ma-rine carbonates. Grain Composition Logs are particu-larly effective in tracing platform-basin relations. Chapter 16: Recognizing Depositional Constraints and Processes. Selected case studies are used to demon-strate the value of microfacies data in interpreting depo-sitional controls.•How can microfacies be used in sequence stratigra-phy? Cyclic depositional patterns and sequence strati-graphic constraints are documented by microfacies data that assist in recognizing sequence boundaries, para-sequences, high-frequency sea-level changes, and sys-tems tracts.•Which criteria characterize reef limestones? Major reef types differ in biota, matrix, sediment, and cements. Which methods should be employed in reconstructing former platforms and reefs that are only recorded by eroded relicts deposited on slopes and in basins? Clast analysis can solve this puzzle.•Which criteria define ancient cold-water carbonates? Ancient cool-water shelf and reef carbonates are typi-fied by specific biotic, compositional and diagenetic features.•Which facies criteria are diagnostic of ancient vent-and seep carbonates? Case studies provide answers.•How to handle mixed carbonate-siliciclastic sedi-ments and interpret limestone-marl successions?•Constraints on carbonate deposition exhibit secular variations, which are discussed in the last section. Practical Use of MicrofaciesChapter 17: Reservoir Rocks and Host Rocks. Carbon-ates are the most important reservoir rocks for hydro-carbons as well as forming important host rocks for ores. Limestones and dolomites contain more than 50% of the world’s oil and gas reserves. Reservoir potential differs for carbonates formed in different depositional settings and depends on the interplay of depositional processes and diagenetic history. The microfacies of cores and cuttings assist in the translation of lithological data into petrophysical information. Facies-based out-crop-analogue studies indicate the scale of porosity andpermeability variations within carbonate bodies. Micro-facies analysis also assists in the genetic interpretation of carbonate-hosted base metal deposits controlled by specific facies patterns.Chapter 18: Carbonate Resources, Facies Control and Rock Properties. Carbonate rocks are important raw materials for chemical and construction industries and are high on the list of extracted mineral resources, both in terms of quantity and of value. Both exploration and exploitation can be enhanced by taking into account the relationships between depositional and diagenetic facies that control technologically relevant chemical and physical parameters, as well as the weathering and decay properties of carbonate rocks. Conservation and preservation of works of art and building stones should start with thin-section studies of the textural and di-agenetic criteria that describe the porosity and perme-ability of the material.Chapter 19: Archaeometry. Microfacies analysis, com-bined with geochemical data has considerable poten-tial in provenance analysis of archaeological materi-als. Thin sections reveal the source of building stones and of material used for mosaics and works of arts. The microfacies of temper grains in ancient pottery helps in understanding the source and production ar-eas for ceramics. Last but not least, microfacies stud-ies can throw new light at the love affair between Antony and Cleopatra....AcknowledgmentsThanks are due to many people who have provided photographs, information and advice:Gernot Arp (Göttingen), Martina Bachmann (Bre-men), Benoit Beauchamp (Calgary), Thilo Bechstädt (Heidelberg), Michaela Bernecker (Erlangen), Joachim Blau (Giessen), Florian Böhm (Kiel), Thomas Brachert (Mainz), Ioan Bucur (Cluj-Napoca), Werner Buggisch (Erlangen),Thomas Clausing (Halle), Wolf-Christian Dullo (Kiel), Paul Enos (Lawrence, Kansas), Gerd Flajs (Aachen), Christof Flügel (München), Helmut Flügel (Graz), Beate Fohrer (Erlangen), Holger Forke (Ber-lin), André Freiwald (Erlangen), Robert van Geldern (Erlangen), Markus Geiger (Bremen), Gisela Gerdes (Oldenburg), Eberhard Gischler (Frankfurt), Dirk von Gosen (Erlangen), Jürgen Grötsch (Damascus). Hans-Georg Herbig (Köln), Richard Höfling (Erlangen), B ernhard Hubmann (Graz), Andi Imran (Makassar), Michael Joachimski (Erlangen), Josef Kazmierczak (Warszawa), Martin Keller (Erlangen), Stephan Kempe (Darmstadt), Helmut Keupp (B erlin), Wolfgang Kiessling (B erlin), Roman Koch (Erlangen), Karl Krainer (Innsbruck), Jochen Kuss (Bremen), Michael Link (Erlangen), Heinz Lorenz (Erlangen), Ulrich Michel (Nürnberg), Axel Munnecke (Erlangen), Fritz Neuweiler (Göttingen), Alexander Nützel (Erlangen), Joachim Reitner (Göttingen), Jürgen Remane (Neuchâtel), Elias Samankassou (Genéve), Diethard Sanders (Innsbruck), Chris Schulbert (Erlangen), Baba Senowbari-Daryan (Erlangen), Robert J. Stanton (Thousand Oaks, California), Torsten Steiger (B ad B lankenburg), Thomas Steuber (B ochum), Harald Tragelehn (Köln), Jörg Trappe (Bonn), Dragica Turnsek (Ljubljana), Andreas Wetzel (Tübingen).I am indebted to Birgit Leipner-Mata and Marieluise Neufert (Institute of Paleontology Erlangen) for labo-ratory work and photography.Chris Schulbert (Institute of Paleontology) was a valuable help with all computer problems.I am sincerely grateful to my friend Johann Georg Haditsch (Graz) for critical reading the text of the book. Special thanks go to Karen Christenson (Nürnberg-Kraftshof) who took care of linguistic problems and pitfalls.Editing, layout, drawings and the preparation of plates and figures have been carried out by my wife Erentraud Flügel-Kahler. I am most grateful for her en-couragement and constant help.Finally, I am obliged to all institutions who gave permission to use published material and to the staff of Springer Verlag, especially to Dr. Wolfgang Engel for his constant encouragement and to Dr. J. Witschel for assistance with the book.X IContents1New Perspectives in Microfacies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1The Microfacies Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2New Perspectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2Carbonate Depositional Environments. . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1Carbonates are Born not Made. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2The ‘Sorby Principle’: Limestones are Predominantly BiogenicSediments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3Modern Carbonates: Obligatory Reading. . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2Carbonate Sediments Originate on Land and in the Sea. . . . . . . . . . . . . . . 8 2.3Classification of Marine Environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.1Boundary Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.2Vertical and Horizontal Zonations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2.1Vertical Zonations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2.2Horizontal Zonations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4Review of Modern Carbonate Depositional Environments. . . . . . . . . . . . . 10 2.4.1Non-Marine Carbonate Environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1.1Pedogenic Carbonates, Paleosols, and Caliche/Calcretes. . . . . . . . . . . . . . 10 2.4.1.2Palustrine Carbonates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1.3Cave Carbonates, Speleothems and Karst. . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1.5Glacial Carbonates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.1.6Travertine, Calcareous Tufa and Calcareous Sinter. . . . . . . . . . . . . . . . . . . 14 2.4.1.7Lacustrine Carbonates: Lakes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.1.8Fluvial Carbonates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4.2Transitional Marginal-Marine Environments: Shorelines andPeritidal Sediments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.2.1Beach (Foreshore), Barriers and Coastal Lagoons. . . . . . . . . . . . . . . . . . . . 24 2.4.2.2Peritidal Environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.3Shallow-Marine Sedimentary Environments: ‘Shallow’ and ‘Deep’. . . . . . 25 2.4.3.1Pericontinental vs Epicontinental Shallow Seas. . . . . . . . . . . . . . . . . . . . . 26 2.4.3.2Carbonate Shelves, Ramps and Platforms. . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4.3.3Shelf Margins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.3.4Reefs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.4Tropical and Non-Tropical Carbonates: Different in Composition,Controls and Significance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.4.1Latitudinal Zonation and Diagnostic Criteria of Tropical and Non-TropicalCarbonates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4.4.2Tropical and Subtropical Shallow-Marine Carbonates. . . . . . . . . . . . . . . . 34 2.4.4.3Non-Tropical Shelf and Reef Carbonates. . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4.5Deep-Marine Environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.5.1Settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.5.2Sedimentation Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.5.3Pelagic Sedimentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.5.4Resedimentation (‘Allochthonous Carbonates’). . . . . . . . . . . . . . . . . . . . . 49XIIContents 2.4.5.5Carbonate Plankton and Carbonate Oozes. . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4.5.6Preservation Potential and Dissolution Levels. . . . . . . . . . . . . . . . . . . . . . . 49 2.4.5.7Carbonate Slopes, Periplatform Carbonates and Caronate Aprons. . . . . . . 50 2.4.6Seep and Vent Carbonates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Microfacies Analysis3Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1Field Work and Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.1Field Observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.1.1Lithology, Texture and Rock Colors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.1.2Bedding and Stratification, Sedimentary Structures andDiagenetic Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.1.1.3Fossils and Biogenic Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1.1.4Field Logs and Compositional Logs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.1.2Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1.2.1Search Sampling and Statistical Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1.2.2How Many Samples?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1.2.3Practical Advice for Microfacies Sampling. . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2Laboratory Work: Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.1Slices, Peels and Thin Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.2Casts, Etching and Staining. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2.3Microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.3.1Petrographic Microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.3.2Stereoscan Microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.3.3Fluorescence, Cathodoluminescence and Fluid Inclusion Microscopy. . . . 67 3.2.4Mineralogy and Geochemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.2.5Trace Elements and Stable Isotope Analysis. . . . . . . . . . . . . . . . . . . . . . . . 704Microfacies Data: Matrix and Grains. . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.1Fine-Grained Carbonate Matrix: Micrite, Microspar, Calcisiltite. . . . . . . . 73 4.1.1Micrite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.1.2Modes of Formation of Micrite and Other Fine-Grained Matrix Types. . . 80 4.1.3Microspar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.1.4Calcisiltite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.1.5Practical Aids in Describing and Interpreting Fine-Grained Limestones. . 98 4.1.6Significance of Fine-Grained Carbonates. . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.2Carbonate Grains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.2.1Bioclasts (Skeletal Grains). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2.2Peloids: Just a Term of Ignorance?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.2.3Cortoids – Carbonate Grains Characterized by Micrite Envelope. . . . . . . . 118 4.2.4Oncoids and Rhodoids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.2.4.1Oncoids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.2.4.2Rhodoids and Macroids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.2.5Ooids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.2.6Pisoids and Vadoids – Simply ‘Larger Ooids’ or Carbonate Grainson their Own?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 4.2.7Aggregate Grains: Grapestones, Lumps and Other Composite Grains. . . . 163 4.2.8Resediments: Intra-, Extra- and Lithoclasts – Insiders and Foreigners. . . . 166 4.2.8.1Intraclasts: Origin and Facies-Diagnostic Types. . . . . . . . . . . . . . . . . . . . . 167 4.2.8.2Extraclasts: Strange Foreigners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 4.3Morphometry of Carbonate Grains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 4.3.1Intentions and Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.3.2Significance of Morphometric Data for Carbonate Grains. . . . . . . . . . . . . 175。
手册使用前的准备(简单说明):参考AIPC---FRONT MATTER:在使用中,要使用最新的更新日期的版本:飞机的尾号,如:B2939. 中国的注册号以B开头如:美国则以N开头。
这些都是国际组织给定的:表示构形。
如表示为B2932为B737-300飞机,3K9中的3表示300飞机:表示造册有效号。
与WDM手册的有效性相对应,如:,查线路图册时,仅在符合PS691的飞机图册中使用:是表示波音公司生产飞机的总数的序列号,表示波音公司生产各种民用飞机中B2932是第25787架:表示波音公司生产B737-300飞机的线号,表示波音公司生产B737-300飞机中,B2932是这种类型飞机的第2302架:表示使用AIPC中的有效号,与AIPC相对应的,如:,仅在符合002的有效性的部件方可使用:表示为该机飞机的交机日期:应该是该架飞机的两台发动机的序号,如:B2932的上述是旧版(PDF)使用时要参考的某些信息,如果用PMA的话,输八飞机号就可以了,因为不可用的手册都会打斜线如:B2932的AMM/SSM/WDM在BA V公司下的B737-300手册下查,IPC在目录SHENZHEN AIRLINES737-300/400/500 的下面查,其它飞机的说明,参考查阅说明表:IPC的使用以内网手册为说明参考:B2691/B2692/B5073/B5075/B5078/B5079AIPC,D638A001-ILF-0101,20061010,34FRONT MATTER:是手册的使用说明:如:中27为章节/系统,21为大的部件,03为子部件,10为段或图号,如下图:如下图,则说明IPC表格的含义(FRONT MATTER/EXPLANATION OF PARTS LIST DATA),理解下面的内容,就基本可以使用IPC了:表示图号与项目号,如上图中的5为图号,35为部件的项目号表示件号(P/N):表示件号的名称,1234567和小圆点对应以确定是第几级的子目录表示有效性从三位数到三位数和前面的:相对应表示每个ASSY有多少个UNITS,有的也用RF和AF表示,上面的图解有说明如何使用IPC,FRONT MATTER上有简单的说明:为了更好的说明查找件号的方法,我们下面作个例子:飞机B2691的IDG1.如果已知飞机上的IDG 件号,反查IPC确定并检查有效性就行方法为:已知飞机B2691 /有效性号为505(可在或AIPC--FRONTMATTER--中找到)/IDG 属于24章/已知件号为:*可通过B2691---AIPC---FRONT MATTER-PART NUMBER ALPHA UNMERICAL INDEX或PART NUMBER NUMERICAL ALPHAINDEX---在24-11-11中,有三个图都有IDG,它们的项目号分别为10、5、1等,再到其中24-11-11-01A 5中确定有效性/即从413到700均可用(这是手册给的方法)*我们一般在已知条件的情况下,用搜索方式来查找并确定有效性/可用2.如果不知件号,知道B2691/上述已找到有效号为505/IDG在24章*1.找到B2691---AIPC-----------到24-11-11-01----在学习IPC时,FRONT MATTER 就是手册的使用说明,其中较有用的是:(最为重点)考核内容:B2692件号的查找:ACM-----空气循环机FCU-----APU燃油控制组件EDP-----发动机驱动泵EMDP-----电动马达驱动泵EEC-----发动机电子控制器主轮、前轮发动机起动机发动机点火电嘴厕所冲洗活门机组氧气瓶etc.件号清单数据解答。
Springer Series inmaterials science121Springer Series inmaterials scienceEditors:R.Hull R.M.Osgood,Jr.J.Parisi H.WarlimontThe Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles,physical properties,materials theory and design.Recognizing the increasing importance of materials science in future device technologies,the book titles in this series reflect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials.Please view available titles in Springer Series in Materials Scienceon series homepage /series/856H.Julian Goldsmid Introductionto Thermoelectricity With140Figures123Professor H.Julian GoldsmidUniversity of New South Wales,School of Physics 2052Sydney,AustraliaE-mail:hjgoldsmid@.auSeries Editors:Professor Robert HullUniversity of VirginiaDept.of Materials Science and Engineering Thornton HallCharlottesville,V A22903-2442,USA Professor R.M.Osgood,Jr. Microelectronics Science Laboratory Department of Electrical Engineering Columbia UniversitySeeley W.Mudd BuildingNew Y ork,NY10027,USA Professor Jürgen ParisiUniversit¨a t Oldenburg,Fachbereich Physik Abt.Energie-und Halbleiterforschung Carl-von-Ossietzky-Straße9–1126129Oldenburg,GermanyProfessor Hans WarlimontDSL Dresden Material-Innovation GmbH Pirnaer Landstr.17601257Dresden,GermanySpringer Series in Material Science ISSN0933-033XISBN978-3-642-00715-6e-ISBN978-3-642-00716-3DOI10.1007/978-3-642-00716-3Springer Heidelberg Dordrecht London New Y orkLibrary of Congress Control Number:2009929170c Springer-V erlag Berlin Heidelberg2010This work is subject to copyright.All rights are reserved,whether the whole or part of the material is concerned,specifically the rights of translation,reprinting,reuse of illustrations,recitation,broad-casting,reproduction on microfilm or in any other way,and storage in data banks.Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September9,1965,in its current version,and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law.The use of general descriptive names,registered names,trademarks,etc.in this publication does not imply,even in the absence of a specific statement,that such names are exempt from the relevant protective laws and regulations and therefore free for general use.Printed on acid-free paperSpringer is part of Springer Science+Business Media()PrefaceThis book has been written at a time when thermoelectric energy conversion is showing great promise.It was in1953that Ifirst carried out the experiments on bismuth telluride that demonstrated the potential of thermoelectric refrigeration. The present-day thermoelectric modules are based on the work that was carried out during the late1950s and the early1960s on bismuth telluride and its alloys. Since that time,there have been significant advances in materials for thermoelectric generation,but at all temperatures the efficiency of energy conversion using thermo-couples has fallen far short of that expected for an ideal thermodynamic machine. At last,with the advent of nanostructured thermoelements,there is the promise that substantial advances will be made.The basic principles of thermoelectric devices have not changed over the years and the theory presented in thefirst few chapters will always be applicable as new materials are discovered.A review of existing thermoelectric materials is presented with a chapter devoted to bismuth telluride showing how improvements in its syn-thesis and composition have led to the present-day performance.It is not always appreciated that the behaviour of a specific alloy is strongly dependent on the man-ner in which it is prepared and a chapter is devoted to the production of materials, the stress being on principles rather than on experimental detail.The assessment of the transport properties of thermoelectric materials presents special problems.The chapter on measurement techniques includes a discussion of the errors that can arise when the so-calledfigure of merit is determined for non-uniform specimens.Indeed,I myself was led astray in the interpretation of ex-perimental observations on polycrystalline samples of anisotropic material before I realised the extent of the problem.It is usual to make use of modules rather than simple thermocouples.There is an outline of the method of selecting commercial modules for any particular applica-tion and a discussion of the problems that arise from attempts to miniaturise the size of modules so as to economise on space and material.Throughout the book,I have tried to emphasise practical considerations.A full understanding of the behaviour of nanostuctured thermoelectric materi-als requires the mastery of difficult theoretical concepts but it is hoped that the elementary treatment in this book will allow the reader to comprehend the basic principles.It is expected that the so-called bulk nanostructures willfind their way into commercial production in the very near future.vi Preface It is only during the past2or3years that I have appreciated the potential of the synthetic transverse thermoelement and I have included a chapter that reviews this unusual configuration.I have also included discussions of energy conversion using the transverse thermomagnetic effects and the thermionic effects in solids and in vacuum.The latter,in particular,will lead to greatly improved efficiencies if they live up to their theoretical promise.This book draws on my experience of thermoelectricity and its applications over the past55years.During that time I have been supported by many people and I acknowledge with gratitude the help that I have received from all of them.In1953,as a very junior scientist at the Research Laboratories of the General Electric Company,I was encouraged by my group leader,R.W.Douglas,to look into the possibility of using the Peltier effect in semiconductors as a practical means of refrigeration.He continued to support the project,in spite of scepticism from some of his senior colleagues,and the success of bismuth telluride as a thermoelectric material stems from his foresight.I received support from many others in the Solid Physics Group over the next few years and should mention particularly D.A.Wright, who supervised my Ph.D.studies,and Ray Drabble,who helped me to understand transport theory.In my academic life between1964and1988,first as Reader in Solid State Physics at the University of Bath and then as Professor of Physics at the University of New South Wales,I was fortunate to be working in institutions that had been founded to promote applied science.I was encouraged to continue my research on thermo-electricity and was joined by some excellent students.I am sure that I learned much more from them than they did from me.I acknowledge the support that I have received over much of my career from Marlow Industries.Raymond Marlow enabled me to work closely with his com-pany and kept me in touch with practical developments.In recent years,I have been stimulated by my contact with George Nolas and Ted V olckmann and I appreciate the fact that I am still able to work with Jeff Sharp and Jim Bierschenk.Perhaps,my greatest inspiration has been the work of Abram Ioffe and I greatly valued the opportunity,in2005,to join in the celebration of the125th anniversary of his birth in the town of Romny in Ukraine.This was made possible through an invitation from Professor L.I.Anatychuk and I am most appreciative of his encour-agement for me to continue with my research.Over the whole of my career I have received enthusiastic support from my wife Joan and it is to her that I dedicate this book.Kingston Beach Julian Goldsmid Tasmania,AustraliaJune2009AcknowledgmentsAll the diagrams in this book are original but several are based on material that has been published elsewhere.The permission of the following publishers to use this material is gratefully acknowledged.American Physical Society.CRC Taylor and Francis.Elsevier.Institute of Electrical and Electronics Engineers.Institute of Thermoelectricity.Wiley VCH.ContentsList of Symbols (xiii)1The Thermoelectric and Related Effects (1)1.1Introduction (1)1.2Relations Between the Thermoelectric Coefficients (3)1.3Effects in a Magnetic Field (5)References (6)2Theory of Thermoelectric Refrigeration and Generation (7)2.1The Transport Effects (7)2.2Thermoelectric Refrigerators and Heat Pumps (8)2.3Thermoelectric Generators (13)2.4Multi-Stage Devices (15)2.5Application of the Thermomagnetic Effects (17)References (21)3Thermoelectric Properties of Metals and Semiconductors (23)3.1Transport by Electrons (23)3.2Metals and Semiconductors (29)3.3Bipolar Effects (34)3.4Phonon Conduction (36)3.5Phonon Drag (39)References (41)4Optimisation and Selection of Semiconductor Thermoelements (43)4.1Power Factor (43)4.2The Materials Parameter,ˇ (44)4.3Mobility and Effective Mass (46)4.4The Lattice Thermal Conductivity in Pure Crystals (47)4.5The Effect of Temperature (50)4.6The Importance of the Energy Gap (51)4.7Non-Parabolic Bands (53)4.8Thermomagnetic Materials (55)4.9Superconductors as Passive Thermoelements (60)References (61)5Minimising the Thermal Conductivity (63)5.1Semiconductor Solid Solutions (63)5.2Phonon Scattering by Point Defects (64)5.3Boundary Scattering (70)5.4Scattering of Electrons and Phonons (72)5.5Fine-Grained Material with Large Unit Cells (74)5.6Phonon-Glass Electron-Crystal (76)References (78)6The Improvement of a Specific Material–Bismuth Telluride (79)6.1Pure Bismuth Telluride (79)6.2Band Structure of Bismuth Telluride (82)6.3Diffusion in Bismuth Telluride (86)6.4Solid Solutions Based on Bismuth Telluride (87)6.5Practical Developments (90)6.6Extension of the Temperature Range (93)6.7Recent Advances (96)References (97)7Methods for the Production of Materials (99)7.1General Principles (99)7.2Growth From the Melt (100)7.3Sintering (105)7.4Thick and Thinfilms (109)References (110)8Measurement Techniques (113)8.1General Considerations (113)8.2Electrical Conductivity (114)8.3Seebeck Coefficient (118)8.4Thermal Conductivity (121)8.5Thermal Diffusivity (126)8.6The Figure of Merit (128)8.7Thermomagnetic Measurements (135)References (138)9Review of Thermoelectric Materials (139)9.1Bismuth and Bismuth–Antimony (139)9.2Lead Telluride and Related Compounds (148)9.3Silicon–Germanium Alloys (151)9.4Skutterudites and Clathrates (154)9.4.1Skutterudites (154)9.4.2Clathrates (156)9.5Oxides (159)9.6Other Thermoelectric Materials (160)9.6.1Zinc Antimonide (160)9.6.2Half-Heusler Compounds (161)9.6.3Metal Silicides (162)9.6.4Boron Carbide (163)References (164)10Thermoelectric Modules and Their Application (167)10.1The Modular Concept (167)10.2Heat Transfer Problems (171)10.3Electrical Contact Resistance (174)10.4Applications of the Peltier Effect (176)10.5Transient Cooling (179)10.6Seebeck Devices (182)References (188)11Transverse Devices (191)11.1Features of Transverse Coolers and Generators (191)11.2Synthetic Transverse Thermoelements (192)11.3Materials for Transverse Thermoelements (195)11.4Alternative Configurations (200)References (201)12Properties of Nanostructured Materials (203)12.1Theory of Nanostructures (203)12.2Thermal Conduction in Low-Dimensional Materials (208)12.3Observations on Nanostructures (213)12.4Preparation of Nanostructures (216)References (219)13Thermionic Energy Conversion (221)13.1Vacuum Thermoelements (221)13.2Thermionic Emission in Solids (228)References (233)Bibliography (235)Index (237)Index of Elements,Compounds and Alloys (241)List of SymbolsA Cross-section area,mean atomic weight,parameter for point-defectscatteringA M Parameter for mass-defect scatteringA0Richardson constanta Lattice constanta H Scattering law dependent parameter in Hall coefficientB Magneticfield,parameter for umklapp scatteringB K Parameter in Keyes relationC Parameter for scattering by normal processes,concentrationc Diameter of defectc V Specific heat per unit volumeD Diffusion coefficient in liquidD Specific detectivityd Width,electrode spacing,barrier widthd t Tunneling widthE ElectricfieldE F Fermi energyE g Energy gape Electron chargeF n Fermi–Dirac integralF NE Function proportional to thermomagneticfigure of meritf Fermi distribution function,measure of reduction of lattice conductivityin calculations for Si–Gef0Equilibrium Fermi distribution functionG Reciprocal lattice vectorG Bulk modulusg Density of electron states,ratio of space occupied by insulation to that ofthermoelementsh Planck’s constant,h=2I Electric currentI q Current for maximum cooling powerI Current for maximum COPi Electric current densityxiiii1Electric current density in a thermionic devicej Heatflux densityK Thermal conductanceK c Thermal conductance of end platesK s Transport integralk Boltzmann’s constant,segregation coefficientk Wave vector for charge carriersk0Parameter in Callaway’s theoryL Length,Lorenz number,latent heatl Vector parallel to temperature gradientl e Mean free path of charge carriersl t Mean free path of phononsM.1C ZT m/1=2,mean atomic mass,Average mass of unit cellm Mass of free electron,slope of liquidusm Density-of-states effective massm I Inertial massm N Density-of-states mass for a single valleyN Nernst coefficient,total number of modes of vibration,number of unit cells per unit volume,number of couples in a moduleN0Bose–Einstein functionN A Avogadro’s numberN v Number of valleys in an energy bandn Subscript for electronsn Electron concentration,ratio of layer thicknesses in a synthetic transverse thermoelementn L Number of vibrational modes per unit volume and frequencyP Ettingshausen coefficient,Poisson’s ratiop Porosity factor,proportion of specular reflection of phononsp Subscript for positive holesp Phonon momentumq Rate of heatflowq L Phonon wave vectorq max Maximum cooling powerq1Rate of heatflow from sourceR Electrical resistance,gas constant,responsivityR H Hall coefficientR L Load resistancer Scattering law parameterr c Electrical contact resistance for unit areaS Righi–Leduc coefficients Compatibility factorT TemperatureT1Temperature of heat sourceT2Temperature of heat sinkT m Mean temperature,melting pointTTemperature difference,difference between liquidus and solidus temperatures TTemperature difference between sink and source T maxMaximum temperature difference tTime uVelocity of carriers VV oltage,mean atomic volume V qV oltage for maximum cooling power vSpeed of sound,speed of zone WEnergy in a mode of vibration,thermal resistance wElectrical power x…!=kT yParameter in Callaway’s theory ZThermoelectric figure of merit for couple Z NEThermomagnetic or Nernst–Ettingshausen figure of merit,Z NE iIsothermal thermomagnetic figure of merit Z Transverse figure of merit zFigure of merit for single material z dPhonon drag figure of merit z 1D One-dimensional figure of merit z 2D Two-dimensional figure of merit ˛Seebeck coefficient ˛dPhonon drag Seebeck coefficient ˛IThermionic parameter replacing Seebeck coefficient ˛TThermal expansion coefficient ˇChasmar and Stratton’s materials parameter ˇ1 =R 2H B2 ˇ0Materials parameter for a 2D conductor ˇ00Materials parameter for a 1D conductor ˇIMaterials parameter for a solid-state thermionic deviceGamma functionGr¨u neisen’s parameter •Atomic diameter "Energy,emissivity,surface roughness "mParameter in melting rule ÁEfficiency,reduced Fermi energy ÁgReduced energy gap ÁrReduced efficiency DDebye temperature ÄThermal diffusivityWavelength of phonons 0Smallest phonon wavelengthThermal conductivity e Electronic thermal conductivityI Thermal conductivity of insulation,thermionic quantity replacing thermalconductivityL Lattice conductivityCarrier mobilityFrequencyReduced energyPeltier coefficientd Phonon drag Peltier coefficientElectrical resistivityd DensityElectrical conductivity,Stefan–Boltzmann constantI Thermionic quantity replacing electrical conductivity0Parameter that depends on mobility and effective massThomson coefficient,relaxation time0Scattering law constantd Relaxation time for phonon drage Relaxation time for charge carrierseff Effective relaxation time for charge carriersN Relaxation time for normal processesR Relaxation time for umklapp processes˚Work functionCoefficient of performance,angle of transverse thermoelement to normal to layersq Coefficient of performance at maximum cooling powers Coefficient of performance of each stage of a cascadeMaximum coefficient of performanceCompressibility!Angular frequency!D Debye angular frequency。