Some micromechanical models of elastoplastic behaviors of porous geomaterials

专题18 阅读理解（科普类）1.C【2019·全国I】As data and identity theft becomes more and more common, the market is growing for biometric(生物测量)technologies—like fingerprint scans—to keep others out of private e-spaces. At present, these technologies are still expensive, though.Researchers from Georgia Tech say that they have come up with a low-cost device(装置)that gets around this problem: a smart keyboard. This smart keyboard precisely measures the cadence(节奏)with which one types and the pressure fingers apply to each key. The keyboard could offer a strong layer of security by analyzing things like the force of a user's typing and the time between key presses. These patterns are unique to each person. Thus, the keyboard can determine people's identities, and by extension, whether they should be given access to the computer it's connected to—regardless of whether someone gets the password right.It also doesn't require a new type of technology that people aren't already familiar with. Everybody uses a keyboard and everybody types differently.In a study describing the technology, the researchers had 100 volunteers type the word “touch”four times using the smart keyboard. Data collected from the device could be used to recognize different participants based on how they typed, with very low error rates. The researchers say that the keyboard should be pretty straightforward to commercialize and is mostly made of inexpensive, plastic-like parts. The team hopes to make it to market in the near future.28. Why do the researchers develop the smart keyboard?A. To reduce pressure on keys.B. To improve accuracy in typingC. To replace the password system.D. To cut the cost of e-space protection.29. What makes the invention of the smart keyboard possible？A. Computers are much easier to operate.B. Fingerprint scanning techniques develop fast.C. Typing patterns vary from person to person.D. Data security measures are guaranteed.30. What do the researchers expect of the smart keyboard？all 1o soisgitieoco oll.A. It'll be environment-friendly.B. It'll reach consumers soon.C. It'll be made of plasticsD. It'll help speed up typing.31. Where is this text most likely from?A. A diary.B. A guidebookC. A novel.D. A magazine.【答案】28. D 29. C 30. B 31. D【解析】本文是一篇说明文。

A Real-Time Traffic Simulation System Anthony Theodore Chronopoulos,Senior Member,IEEE,and Charles Michael JohnstonAbstract—This article studies the usefulness of parallel process-ing in real-time traffic-flow simulation based on continuum mod-eling of traffic putationalfluid dynamics(CFD’s) methods for solving simple macroscopic traffic-flow continuum models have been studied and efficiently implemented in traffic simulation codes(on serial computers)in the past.We designed a traffic-flow simulation code and mapped it onto a parallel computer architecture.This traffic simulation system is capable of simulating freeway trafficflow in real time.Tests with real traffic data collected from the freeway network in the metropolitan area of Minneapolis,MN,were used to validate the accuracy and computational rate of the parallel simulation system.The execution time for a2-h traffic-flow simulation of about200619 vehicles in an18-mi freeway,which takes2.35min of computer time(on a single-processor computer simulator),took only5.25s on the parallel traffic simulation system.This parallel system has a lot of potential for real-time traffic engineering applications. Index Terms—Freeway network,parallel,real time,traffic simulation.I.I NTRODUCTIONR ESEARCH in intelligent vehicle/highway systems (IVHS’s)traffic has generated considerable thrusts in the last two decades.The most recent advances in vehicle controllers and highway management technology seem to indicate that it is possible to start implementing such systems in everyday traffic.The main potential advantages are:1)significant increase in highway capacity and thus trafficvolume served;2)upgrading the highway safety;3)decreasing the environmental harm due to vehicle pol-lution;4)economic impact(savings in fuel,driving time,newtechnology generation,etc.).IVHS consists of both intelligent vehicles and intelligent or automated highways.Intelligent vehicles would allow an increase in highway capacity of up to300%.This would be the result of elimination of traffic congestion by increasing the speed and decreasing the intervehicle distance.The safety would result from(partial or entire)elimination of the human factor in vehicle control.It is assumed that the highway traffic management will be highly intelligent(entry/exit ramps,traffic signing,and incident detection).A very important component of an intelligent highways’management system is a traffic simulation system.Such a Manuscript received June23,1995;revised October6,1996.This work was supported in part by the NSF under Grant CCR-9496327.A.T.Chronopoulos is with the Department of Computer Science,Wayne State University,Detroit,MI48202USA(e-mail:chronos@).C.M.Johnston is with Concurrent Computer Corporation,Southfield,MI 48034USA.Publisher Item Identifier S0018-9545(98)00098-X.system,consists of a traffic-flow simulation code,which is able to simulate traffic on a freeway and arterials network and a computer system.This computer system consists of hardware and software.Input/output devices provide data of real-time traffic measurements from a network of traffic detectors(loops or cameras)and data on the road geometries or other traffic characteristics.The system uses a mathematical trafficflow model to perform traffic-flow simulation and predict the traffic conditions in real time.These predictions can be used for real-time traffic control and drivers’guidance.Accurate mathematical and computer modeling of the main characteristics of standard traffic-flow dynamics has been used in a better understanding of the collective behavior of the traffic,designing efficient control and management strategies, assessing the effects of roadway geometries,and in the design of new highway lanes.Traffic models can be characterized as either microscopic or macroscopic.The microscopic models which have been extensive studied are the so-called vehicle-follower models,where the behavior of each vehicle is specified in terms of the vehicle immediately ahead.Such models have been used in simulating mostly single-lane traffic and automatic longitudinal/lateral vehicle control of individual vehicles(see[1],[6],[10],[12],[24],and [25]).These models(in their continuum formulation)involve ordinary differential equations describing the movement of each individual vehicle following the vehicle ahead. Macroscopic or continuum traffic-flow models based on traffic density,volume,and speed have been proposed and analyzed in the past.See,for example,[14],[16]–[19],and [21]–[23].These models involve partial differential equa-tions(PDE’s)defined on appropriate domains with suitable boundary conditions,which describe various traffic phenom-ena and road geometries.The enhancement of computational efficiency in the contin-uum traffic models has been the focal point in the development of traffic simulation programs.One of the main goals of the traffic-flow simulation programs is to be used as a compu-tational component in a real-time traffic system.Such a system would be fed with real-time traffic input data,and it would predict traffic conditions in real time.These predicted traffic conditions would be used for traffic control and drivers’guidance.In past research,traffic simulation systems have been designed with their computational component being a single-processor computer.Junchaya and Chang(see[11])demonstrated that real-time traffic simulation is feasible on parallel computers.They con-sidered a traffic simulation model based on the macroparticle traffic simulation model(MTSM)(see[2]).This model uses macroscopic traffic relations to approximate the speed of a0018–9545/98$10.00©1998IEEEcluster of vehicles in a given link.Then,the vehicles are simulated individually.This means that this type of simulation allows car following and lane changing,as in microscopic simulations.Thus,this model combines macroscopic and mi-croscopic model characteristics.This model was implemented on a parallel computer system.The simulation tests space domain was a computer-generated(hypothetical)grid network. No real traffic data were used.The main objective of this paper is to demonstrate that the computational component in a real-time system is feasible for the macroscopic models.Some preliminary results on the issue of parallelizing computationalfluid dynamic(CFD) methods for transportation problems were presented in[5]. Such a real-time simulation system can be designed using a parallel computer as its computational component.We design such a computational component by parallelizing a CFD method to solve the momentum conservation(macroscopic) model(see[9],[18],and[23])and implementing it ontheCUBE2is as powerful as a SUN3/50workstation.We ran tests ontheandrepresents the number of cars entering or leavingthe trafficflow in a freeway with entries/exits.The traffic-flow,density,and speed are relatedby---alongthe roadway,where relaxationtimeaccordingto1are model parameters.Thesecond term on the right-hand side of(4)is the antici-pation parameter.As implied in this example,if downstreamdensity is higher due to congestion,speed has to be decreasedaccordingly.Conversely,if downstream density is lower,speedcan be increased.From(4)–(6),one derives a momentummodel for the trafficflow described by the following systemofPDE’s:(7)CHRONOPOULOS AND JOHNSTON:REAL-TIME TRAFFIC SIMULATION SYSTEM323 where,,and are the followingvectors:curve as in the case of the simple continuummodel.However,speed data are required for the boundaryconditions.If speed data are not available from the real trafficdata measurements,thena curve based on occupancydata([23])is used to generate the speed data.This is discussedin the next section.B.Volume-Density RelationA model curve is an indispensable part of the LWM.This relation can be used to express the volume as a functionof theflow density,i.e.,curve are used in the programs to convertdensity to volume and to convert volume to density.SVMdoes not requirea curve.However,if the speed dataare not available from the measured traffic data,thenacurve is used to compute the traffic speed.The method that we adopt for estimating traffic density andspeed is based on occupancy data[7].Laneoccupancynumber of vehicles that crossed the loop,theeffectivelength vehicle length,andintervehicle distance.(See Fig.1.)C.A Discrete ModelWe now apply the computer method(Lax)to discretizeSVM.This discrete model will be called Lax Momentummodel.For each traffic model,the road section(the spacedimension)is discretized using a uniform mesh.Letdensity(vehicles/mi/lane)at spacenodeflow(vehicles/h/lane)at spacenodespeed(mi/h)at spacenodeand volumevalueare computed directly from the density and volume atthe preceding timestep.To maintain numerical stability timeand space step sizes must satisfy the Courant–Friedrichs–Lewy(CFL)condition,where is the free-flow speed inorder to maintain numerical stability in the computation(see[9]).Typically,the space and timemeshes ft,ands are recommended for numerical stability[23].D.A Freeway ModelWe have used two schemes to add/subtract entry/exit(ramp)traffic volumes to the main-lane traffic volume in SVM.1)Point entry/exit scheme:ramp volumes are assumed tomerge into(diverge from or exit from)the freeway mainlane at a single space node.This treatment is necessaryto simplify the modeling and reduce computation timeat such main-lane nodes.2)Weaving entry/exit scheme:this is used when the ramp isdirectly connected to another freeway,and it is explainedin more detail below.The weaving scheme is outlined as follows.In the followingdiscussion,let us consider the traffic-flow volume in a freewaysection shown in Fig.2at afixed discrete time.In Fig.2,volume represents the through-traffic volumeflow fromlink,volume represents the diverging volume fromlink,and.is the merging volumefromlink,volume is the through-volume fromlink,and.It is obviousthatand.Because there are interchangesofand,traffic friction atlink,in this case,is greater than the case of a single entrance ramp or exit ramp.Thus,this must be taken into account by calibrating(locally)the parameter in the mathematical model for these spacenodes.Also,only merging dynamics at an entrance ramp mustbe employed,if.Similarly,only diverging dynamicsmust be employed,ifand324IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,VOL.47,NO.1,FEBRUARY1998Fig.2.Weaving flows in a freeway.term of the model.If the generationterm 0,the short weaving section is treated as a single on ramp.If the generationterm 0,it is treated as a single off ramp.The generation term thenbecomesCUBE2.Thefollowing terminology is introduced in order to evaluate the parallel simulation system.1)Number ofprocessorsis the time required to solvethe problem on a single-processor computer system.3)Parallel executiontime is the time required to solve the problemonis theratio is theratio.Fig.3.Real-time traffic simulation system architecture.B.TheCUBE2is a multiple-instruction multiple-data(MIMD)hypercube parallel computer system.A hypercube model is an example of a distributed-memory message passing parallel computer.Let be a positive integer.In a hypercube ofdimension ,thereare processors.These processors are labeledby .Twoprocessorsand are directly connected if the binary representationof,each processor is connectedto other processors.Thus,any two processors in a hypercube graph are connected by a maximum distanceof edges.Fig.4shows a hypercube graph ofdimension .The number of processors to be active is chosen by the user,but must be a power of two.In Table I,we show a summary of interprocessor commu-nication times for neighbor processors and the basic floatingCHRONOPOULOS AND JOHNSTON:REAL-TIME TRAFFIC SIMULATION SYSTEM325Fig.4.Hypercube (of n dim =4)with Gray code mapping of linear arrays in its subcubes (of ndim =3).TABLE IC OMPUTATIONANDC OMMUNICATION T IMESON THEmCUBE2point operation timesforbe the number of processors available in the sys-tem.The parallelization of the discrete model is obtained by partitioning the space domain (freeway model)into equal seg-ments and assigning each segment to theprocessors .The choice ofindexesare computed byprocessorif the spacenode .This segment-processor mapping must be such that the communication delays for data exchanges,required in the computation,are minimized.Such a mapping of a linear array (of sets)onto a hypercube is achieved by the Gray code mapping (see [15]).To explain this mapping,weconsider)requiresthat the density/speed/volume ofnodesin order to compute density/speed/volume (at discrete time1).However,the processors are not interconnected in a linear array topology.Thus,we must map a linear array of nodes onto the hypercube.The same would be true if instead of 16single space node we considered a freeway section divided into 16segments forming a linear array.Then,the density/speed/volume at the boundaries of these segments must be sent between processors handling adjacent segments.The Gray code mapping is easier to explain by an example.Here,let the ordering of the nodes,onto which theindexesare mapped,be from left to right,and let the nodenumbers be in binary.For a hypercube ofdimension,the nodesare-bit numbers.For the 1-b case 0,1are mapped to 0,1.To get the 2-b case,we reflect the 1-b case numbers326IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,VOL.47,NO.1,FEBRUARY1998Fig.5.Parallel execution time (s)on n CUBE2.dt =1s and dx =200ft.Fig.6.Parallel execution time (s)on n CUBE2.dt =0:5s and dx =100ft.around the right-most number (1)to get:0,1is used to separate the reflected numbers from the preexisting ones.We add a prefix of 0(1)to the numbers on the left (right)(of to get 00,01,11,10.Inductively,we obtain the same waythe-bit Gray code numbers fromthe-bit code numbers.Fig.4,illustrates the GrayCHRONOPOULOS AND JOHNSTON:REAL-TIME TRAFFIC SIMULATION SYSTEM327Fig.7.Speedup on n CUBE2.dt=1s and dx=200ft.Fig.8.Speedup on n CUBE2.dt=0:5s and dx=100ft.328IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,VOL.47,NO.1,FEBRUARY1998Fig.9.Efficiency on n CUBE2.dt =1s and dx =200ft.Fig.10.Efficiency on n CUBE2.dt =0:5s and dx =100ft.code mapping of a linear array of 16nodes onto the hypercubeof.The nodes’sequence is marked by arrows.In the scheduling part of the parallelization,this sequence isgenerated (foreachdimension hypercube)only once,and it can be stored and reused.The parallelization of Lax Momentum with a space domain a network of freeways can be achieved in a similar way,by dealing with each member freeway one at time.Each member freeway is mapped onto a subcube of the hypercube.The issue of mapping automatically arbitrary networks onto aCHRONOPOULOS AND JOHNSTON:REAL-TIME TRAFFIC SIMULATION SYSTEM 329TABLE IIE RROR S TATISTICSFOR T RAFFIC F LOW V OLUME(I-494)TABLE IIIE RROR S TATISTICSFOR T RAFFIC F LOW S PEED(I-494)parallel computer system (likeanCUBE2parallel computer located at the SandiaNational Laboratory in Alburquerque,NM.As our test site,we considered a multiple-entry/exit freeway section in the Minneapolis freeway network.This is a section of Eastbound I-494.The Eastbound I-494section extends from the Carlson Parkway to Portland Avenue.It is 18mi long,and it has 21entry and 18exit ramps.To test the program,the time and space mesh sizeswere sand ft.The discrete model contains 425space nodes.In order to be able to test the simulation code on the full configuration,we also run a testwith sand ft.Then,the number of (space nodes)/(discrete times)doubles.From these results one could extrapolate the performance of the parallel system for a (36mi)freeway traffic simulated for 4h.Our tests are distinguished into two units:comparisons with real data and performance parisons with Real DataTraffic data are collected at the upstream/downstream boundaries of the freeway section and at check-station sites inside the freeway section.Let(10)Mean AbsoluteErrorObservedSimulated(11)Mean RelativeErrorObserved SimulatedObservedNormObservedSimulatedSimulated(14)The error statistics are summarized in Tables II and III.The relative errors are at a level about 10%for the volume,but are lower for the speed measurements.These error sizes are consistent with past simulations carried out by simulation systems based on a single-processor computer (see [3]).B.Performance AnalysisWe measure the execution time ,which consists of the time for input/output data and the computation time as follows.1)Time for input data:time for reading from the computer disk of the initial data by processor 0and then broad-casting them to all the processors.Initial data are:1)330IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,VOL.47,NO.1,FEBRUARY 1998TABLE IVP ARALLEL E XECUTION T IMES (IN S ECONDS)TABLE VP ARALLELE XECUTION T IMES (IN S ECONDS)volume/speed at entry/exit,upstream/downstream,and check-station sites and 2)an array of flags.2)Time for computation:time for discrete model compu-tations.3)Time for output data:time for gathering output data from all processors to processor 0and then processor 0writing to the disk.Output data are:1)volume/speed at every sixth space node (i.e.,about every 0.25mi)at every minute and 2)an array of errors.In a real-time simulation system,the output data are channeled to the traffic control and drivers’guidance devices.The parallel execution times are tabulated in Tables IV and V.We note that for the larger configurations about 16%of the processors are idle because our task scheduling strategy divides the freeway into equal segments and maps onto the processors.We are currently working to improve this task scheduling strategy.The parallel execution time is plotted in Figs.5and 6.This execution time is sufficiently fast to justify the usefulness of the proposed parallel system as part of a real-time traffic system.The parallel speedup and efficiency curves are givenin Figs.7–10.It can be seen that a parallel speedup of 27(57)is achievedfors(s)and ft(CUBE2parallel computer.A single processorofCHRONOPOULOS AND JOHNSTON:REAL-TIME TRAFFIC SIMULATION SYSTEM3312-h traffic-flow simulation of an18-mi freeway,with real input data,takes5.05s versus2.35min on a single-processor system time.This demonstrates that there is a great potential of using parallel processors in the design and implementation of real-time traffic systems.A CKNOWLEDGMENTThe comments of the anonymous reviewers,which helped improve the presentation of some parts of the paper,are gratefully acknowledged.R EFERENCES[1]J.G.Bender,“An overview of systems studies of automated highwaysystems,”IEEE Trans.Veh.Technol.,vol.40,no.1,pp.82–99,1991.[2]G.L.Chang,H.S.Mahmassani,and R.Herman,“A macropartitetraffic simulation model to investigate peak-period commuter decision dynamics,”Transport.Res.Rec.,vol.1005,1985.[3] A.T.Chronopoulos et al.,“Trafficflow simulation through high ordertraffic modeling,”put.Modeling,vol.17,no.8,pp.11–22, 1993.[4] A.T.Chronopoulos et al.,“Efficient trafficflow simulation computa-tions,”put.Modeling,vol.16,no.5,pp.107–120,1992. [5] A.Chronopoulos and G.Wang,“Trafficflow simulation through parallelprocessing,”Parallel Comput.,vol.22,pp.1965–1983,1997.[6]R.E.Fenton and R.J.Mayan,“Automated highway studies at the OhioState University—An overview,”IEEE Trans.Veh.Technol.,vol.40, no.1,pp.100–113,1991.[7] D.L.Gerlough and M.J.Huber,“Trafficflow theory,”Transport.Res.Bd.Special Rep.165,National Res.Council,Washington,DC,1975.[8]J.Gustafson,G.Montry,and R.Benner,“Development of parallelmethods for a1024-processor hypercube,”SIAM put., vol.9,pp.609–638,1988.[9] C.Hirsch,Numerical Computation of Internal and External Flows.New York:Wiley,1988,vol.2.[10]P.Ioannou,C.C.Chien,and J.Hauser,“Autonomous intelligent cruisecontrol,”in IVHS America1992Annu.Meet.,pp.97–112.[11]T.Junchaya and G.Chang,“Exploring real-time traffic simulation withmassively parallel computing architecture,”Transport.Res.C,vol.1, no.1,pp.57–76,1993.[12]J.L.Kim et al.,“The areawide real-time traffic control(ARTC)system:A new traffic control concept,”IEEE Trans.Veh.Technol.,vol.42,no.2,pp.212–223,1993.[13]S.K.Kim and A.T.Chronopoulos,“A class of Lanczos-like algorithmsimplemented on parallel computers,”Parallel Comput.,vol.17,pp.763–778,1991.[14]R.D.K¨u hne,“Microscopic distance strategies and macroscopic trafficflow model,”in Proc.Int.Conf.Control,Computers and Communication in Transportation,Paris,France,Sept.19–21,1989.[15]V.Kumar et al.,Introduction to Parallel Computing Design and Analysisof Algorithms.Redwood City,CA:Benjamin/Cummings,1994.[16] C.J.Leo and R.L.Pretty,“Numerical Simulation of macroscopiccontinuum traffic models,”Transport.Res.,vol.26B,no.3,pp.207–220, 1990.[17]M.H.Lighthill and G.B.Witham,“On kinematic waves:II a theoryof trafficflow on long crowded roads,”Proc.R.Soc.Ser.,vol.A229, no.1178,pp.317–345,1955.[18] A.S.Lyrintzis et al.,“Continuum Modeling of traffic dynamics,”in Proc.2nd Int.Conf.Appl.Advanced Tech.Transportation Eng., Minneapolis,MN,Aug.18–21,1991,pp.36–40.[19]L.Mikhailov and R.Hanus,“Hierarchical control of congested urbantraffic-mathematical modeling and simulation,”(IMACS)put.Simulation,vol.37,pp.183–188,1994.[20]n CUBE2Programmers Guide1992,n CUBE,Foster City,CA.[21]M.Papageorgiou and J.C.M.Banos,“Optimal control of multidesti-nation traffic networks,”in Proc.29th IEEE CDC,Honolulu,HI,Dec.1990,pp.1355–1361.[22]H.J.Payne,“FREEFLO:A macroscopic simulation model of freewaytraffic,”Tranport.Res.Rec.,vol.772,pp.68–75,1979.[23]P.Yi et al.,“Development of an improved high order continuum trafficflow model,”Transport.Res.Rec.,vol.1365,pp.125–132,1993. [24]S.Sheikholeslam and C. A.Desoer,“A system level study of thelongitudinal control of a platoon of vehicles,”Trans.AMSE,J.Dynamic Syst.,Meas.Contr.,vol.114,pp.286–292,1992.[25]S.J.Sklar,J.P.Bevans,and Stein,“Safe-approach vehicle-followingcontrol,”IEEE Trans.Veh.Technol.,vol.VT-28,no.1,pp.56–62,1979.Anthony Theodore Chronopoulos(SM’98)wasborn on October18,1956.He received the B.Sci.degree in mathematics from the University ofAthens,Athens,Greece,in1979and the Ph.D.degree in computer science at the University ofIllinois,Urbana-Champaign,in1987.He is an Associate Professor at the Department ofComputer Science,Wayne State University,Detroit,MI.He has published over25refereed journalpublications in the areas of computational science,parallel and distributed computing and applications in traffic-flow simulation,and helicopter aerodynamicssimulation.Charles Michael Johnston received the B.S.degreein mathematics from the University of Michigan,Ann Arbor,in1980and the M.S.degree in computerscience from Wayne State University,Detroit,MI,in1997.Currently,he is a Regional Specialist/Analyst forConcurrent Computer Corporation,Southfield,MI.Authorized licensed use limited to: University of Texas at San Antonio. 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Particle Size Distribution Analyzer TN168T T e e c c h h n n i i c c a a l l N N o o t t e e Powder DisperserEFFECT OF PSA300 POWDER DISPERSER ON SIZEAs in all particle analysis, sample selection and sample preparation remain critical to obtaining accurate results. This note addresses one aspect of sample preparation by showing the effects of varying disperser conditions on the obtainedparticle size distribution. In addition, we take advantage of the unique features of static image analysis to evaluate sample preparation strategies.IntroductionImage analysis is often considered areferee technique for particle sizing. The intuitive appeal of seeing particle picturesis compelling. In addition, the ability toextract more than size information, that is, shape, from images means that image analysis meets requirements not covered by other techniques. Naturally, methodsto improve image analysis results are important to extracting full value from this technique.The steps discussed here are examples ofthe steps used in developing a final method for analyzing a particular product. The HORIBA PSA300 Powder Disperser option is used to prepare microscope slides for static image analysis. With this device, sample particles are dispersedwith a controlled blast of air and allowedto settle on a microscope slide. In general,this method is quite gentle and distributesthe particles evenly across the microscope slide in a tightly controlled environment.It should be noted that not all static image analysis samples are best dispersed in this manner. For example, particle suspensions are often cast or spin coated onto the slide (1). Gels are spread onto a slide with a cover slip or razor blade (2). Some samples such as glass beads arefirst dispersed in a glycerin paste and then spread. But, for dry powders, the Powder Disperser is often the most convenient choice.In order to allow a single unit to be used with multiple sample types, the PSA300 Powder Disperser is quite flexible. In order to take advantage of this flexibility,the effect of various operating conditions on a particular sample type should beinvestigated. And, the effect of varying one operating condition, the starting pressure, is described here.Materials and MethodsA narrow size distribution fraction ofAvicel PH-101 microcrystalline cellulose was isolated by sieving. By using a narrow size fraction, one can ignore issues of sampling and counting a sufficient number of particles. The sample used here passed through 53 micron sieve openings, but not 45 micron sieve openings. For a discussion on reconciling sieving results with image analysis data (or dispensing with sieve analysis altogether), see (3).Two slides were prepared with the PowderDisperser. The only difference between the two slides was the starting pressure condition. The dispersion conditions are tabulated on the following page.Condition High PD Low PD Starting Pressure (torr)100 500 Dispersion FlowNormal Normal Dispersion Time (msec ) 500 500Air Restoration Delay (sec )30 30 Nozzles Medium, Large Medium,LargeThe starting pressure reflects the pressure of the chamber into which the particles are dispersed. The velocity of the blast of air can be controlled by lowering thechamber pressure since the air velocity is controlled by the difference between atmospheric pressure (760 torr) and chamber pressure. Of course, thedispersion flow setting is a different way to manipulate velocity. A more complete study would examine the effect of multiple disperser conditions. The slides aredesignated High PD and Low PD to reflect the pressure difference.A third slide, denoted “Manual,” wasprepared by using a spatula and dropping the powder onto the slide without applying any dispersion energy.The three slides were then examined with the HORIBA PSA 300 Static ImageAnalysis System using the 5x objective.ResultsQualitative AnalysisThe qualitative conclusions discussed here are based on reviewing images from each slide at a number of positions on the slide. The single photos presented here are for illustrative purposes even thoughqualitative analysis should be performedover multiple regions of a slide.A representative image from the High PD slide is shown below in Figure 1. From this image, one sees that the particles are not touching and therefore particle separation during image processing is unnecessary. Most notably for the discussion at hand, there are a substantial number of fine particles (less 20 microns) that are much smaller than the main particles.Figure 1 Representative image of particles dispersed under high pressure differenceconditions (high PD). Note the presence of a substantial number of fine particles that are an artifact of the dispersion process.Here one can take advantage of the nature of image analysis to confirm the presence of the fine particles in the original sample. An image from theManual slide is shown in Figure 2. In this image, the particles tend to overlapsignificantly; better dispersion will provide superior results to any numerical algorithm for particle separation.Therefore, this slide is not optimal for automated image analysis. Note the near absence of fine particles. It is clear that the fine particles observed in the High PD slide are not part of the original sample. This is consistent with the fact that the sample was prepared by sieving which would tend to remove any fine particles. From this image along with two or three others from the same slide, one candevelop a qualitative idea of the particlesize and shape for comparison withimages obtained from other slidesprepared with the HORIBA SampleDisperser.Figure 2 Representative image of manuallydispersed particles. Note the lack of fineparticles and the significant overlap of analyteparticles that preclude good automated imageanalysis.Finally, a typical image from the Low PDslide is shown in Figure 3. Note that in thiscase, unlike the High PD slide but similarto the Manual slide there are almost nofine particles. In addition, unlike theparticles in the Manual slide, the particlesare well separated; automated particleseparation during image processing isunnecessary. It should be pointed out thatthe number of particles in each imagecould be increased. And, optimizing thenumber of particles in each frame wouldbe the next step in method development.From these photographs, it is clear thatthe High PD dispersion conditions areaffecting the particles under study. Theparticles prepared under the Low PDdispersion conditions are unaffected bydispersion. Therefore, quantitative imageanalysis should be performed on theparticles prepared under the Low PDdispersion conditions.Figure 3 Representative image of particlesdispersed under low pressure differenceconditions (low PD). Note the lack of fineparticles and the distinct analyte particles.This sample is most appropriate for accurateautomated image analysis.Quantitative AnalysisLet us now compare the results of staticimage analysis from each sample. Weconsider two different distributionweightings: number weighted and volumeweighted. For the volume weighteddistribution, the particle volume isestimated based on the area of theparticle in the image and an assumedspherical form. Spherical volume is chosensince it is specified in ISO 13322-1 (4).The ellipsoidal volume calculation from thePSA 300 could be more appropriate.However, the choice of model does notaffect the conclusions drawn here.HighPDLowPDManualNumberMedianSize(microns)12 70 66VolumeMedianSize(microns)81 80 662Here it is clear that the number mediansizes (D50) obtained from the Manualslide, 66 microns, and the Low PD slide,70 microns are similar. For the High PD slide, the large number of fine particles brought the median size down to 12 microns. The small number of large agglomerates which are really overlapping or touching particles did not substantially change the obtained median size of the Manual slide. So, that value was still accurate.On the other hand, the volume median sizes (D50) obtained from the High PD slide, 81 microns and Low PD slide, 80 microns, were quite similar. This is because the volume fraction of fine particles is small. But the volume of large agglomerates was substantial enough to significantly perturb the measured volume median particle size from the Manual slide.The small difference between the number median and volume median particle sizes for the Low PD slide is a direct consequence of using a sample with a narrow size distribution.Since these numerical results were obtained by analyzing 392 images, and from 4000 to 20000 particles, thestatistics are certainly better than those from manually inspecting four or five images. For a discussion on the effect ofthe number of analyzed particles on the accuracy of the determined size distribution parameters such as the median size, see references (4) and (5). Review of only the numerical results does not clearly show which set of results is correct. But manual inspection of only afew images did clearly show which set of numbers is most accurate.ConclusionsImage analysis allows inspection of the results of different dispersion settings and this feature should be exploited in order to evaluate the quality of the slides prepared for image analysis. Comparing imagesfrom an undispersed sample to images from a dispersed sample rapidly verifies the appropriateness of dispersion conditions.References(1) AN193 Measuring 10 Micron PSL onthe PSA300, available from/us/particle(2) AN190 Particle Characterization of Ointments and Creams Using Image Analysis, available from/us/particle(3) AN142 Determination of the Roundness of Globules in the Pharmaceutical Industry, available from /us/particle(4) ISO 13322-1, Particle Size Analysis– Image Analysis Methods – Part 1: Static Image Analysis Methods(5) TN155 The Effect of Sample Size on Result Accuracy using Static Image Analysis, available from/us/particleCopyright 2011, HORIBA Instruments, Inc. For further information on this documentor our products, please contact:HORIBA Ltd.2, Miyanohigashi,KisshoinMinami-Ku Kyoto 601-8510 Japan+81 75 313 8121HORIBA Scientific34 BunsenIrvine, CA 92618 USA1-888-903-5001HORIBA Jobin Yvon S.A.S.16-18, rue du Canal - 91165 Longjumeau FranceTel. +33 (0)1 64 54 13 00/us/particle******************。

Chapter 7Markets in ActionCheckpoint 7.1Price Ceilings7.1.1)A price ceilingA)is an illegal price.B)is the price that exists in a black market.C)is the maximum price that can legally be charged.D)Both answers A and B are correct.E)Both answers B and C are correct.Answer:CTopic:Price ceilingSkill:Level 1: DefinitionObjective:Checkpoint 7.1Author:SA7.1.2)If a price ceiling is set above the equilibrium price, thenA)there will be a surplus of the good.B)there will be a shortage of the good.C)there will be neither a shortage nor a surplus of the good.D)the price ceiling will generate revenue for the government.E)the price ceiling affects suppliers but not demanders.Answer:CTopic:Price ceiling, shortageSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SA7.1.3)A price ceiling in the market for fuel oil that is below the equilibrium price willA)lead to the quantity supplied of fuel oil exceeding the quantity demanded.B)lead to the quantity demanded of fuel oil exceeding the quantity supplied.C)decrease the demand for fuel oil.D)increase the supply of fuel oil.E)have no effect in the market for fuel oil.Answer:BTopic:Price ceiling, shortageSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SAChapter 7 Markets in Action 277Price(dollars per sliceof pizza)Quantity supplied(slices of pizzaper week)Quantity demanded(slices of pizzaper week) 11050220403303044020550107.1.4)The demand and supply schedules for pizza are in the table above. A price ceiling of $2 perslice results inA)a surplus of 20 slices of pizza.B)a shortage of 20 slices of pizza.C)a shortage of 40 slices of pizza.D)a shortage of 60 slices of pizza.E)neither a shortage nor a surplus.Answer:BTopic:Price ceiling, shortageSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SA7.1.5)The demand and supply schedules for pizza are in the table above. A price ceiling of $4 perslice results inA)a surplus of 20 slices of pizza.B)a shortage of 20 slices of pizza.C)a shortage of 40 slices of pizza.D)a shortage of 60 slices of pizza.E)neither a shortage nor a surplus.Answer:ETopic:Price ceiling, shortageSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SA278 7.1.6)The demand and supply schedules for pizza are in the table above. If the government sets amaximum legal price of $2 per slice of pizza, thenA)there is a shortage of 20 slices of pizza.B)this maximum price is an example of a price floor.C)this maximum price is an example of a price ceiling.D)Both answers A and C are correct.E)Both answers B and C are correct.Answer:DTopic:Price ceiling, shortageSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SABade/Parkin Foundations of Microeconomics , Fourth Edition·Chapter 7 Markets in Action 2797.1.7)The figure above illustrates the bagel market. Which of the following statements is correct?A)With a price ceiling of $1.00 per bagel, the quantity demanded is equal to the quantitysupplied.B)With a price ceiling of $3.00 per bagel, the quantity demanded is greater than thequantity supplied.C)With a price ceiling of $1.00 per bagel, there is a shortage of bagels.D)Answers A and B are correct.E)Answers B and C are correct.Answer:CTopic:Price ceiling, shortageSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SA7.1.8)The figure above illustrates the bagel market. Which of the following statements is correct?A)With a price ceiling of $1.00 per bagel, the price of a bagel is $1.B)With a price ceiling of $3.00 per bagel, the price of a bagel is $2.C)With no government intervention, the equilibrium price of a bagel is $2.D) Only answers A and B are correct.E)Answers A, B, and C are correct.Answer:ETopic:Price ceilingSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SA280 7.1.9)In a housing market with no rent ceilings, the equilibrium rent is that for which the quantityof apartments demandedA)equals the quantity supplied.B)is greater than the quantity supplied.C)is less than the quantity supplied.D)might be greater than, equal to, or less than the quantity supplied depending onwhether the supply curve is upward sloping, horizontal, or vertical.E)None of the above answers is correct because without rent ceilings there is noequilibrium rent.Answer:ATopic:Rent ceilingSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC7.1.10)Suppose the equilibrium rent in Denver is $1,050. A rent ceiling of $755 per month leads toA)a surplus of apartments in Denver.B)a shortage of apartments in Denver.C)no change in the Denver apartment market.D)fair prices in the Denver market.E)compared to the situation at the equilibrium rent, a decrease in the quantity ofapartments demanded and an increase in the quantity of apartments supplied.Answer:BTopic:Rent ceiling, shortageSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC7.1.11)Suppose the equilibrium rent in Boston is $1,500. A rent ceiling of $1,600 per month leads toA)a surplus of apartments in Boston.B)a shortage of apartments in Boston.C)no change in the Boston apartment market.D)fair prices in the Boston apartment market.E)compared to the situation at the equilibrium rent, a decrease in the quantity ofapartments demanded and an increase in the quantity of apartments supplied.Answer:CTopic:Rent ceiling, shortageSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JCBade/Parkin Foundations of Microeconomics , Fourth Edition·Chapter 7 Markets in Action 2817.1.12)An illegal market in which the price exceeds a legally imposed price ceiling is called aA)shortage market.B)surplus market.C)black market.D)fair market.E)subsidized market.Answer:CTopic:Price ceiling, black marketSkill:Level 1: DefinitionObjective:Checkpoint 7.1Author:JC7.1.13)One of the consequences of a rent ceiling set below the equilibrium rent isA)decreased search activity.B)increased search activity.C)the establishment of landlord unions.D)surpluses of apartments.E)the elimination of the deadweight loss that would otherwise exist in the housingmarket.Answer:BTopic:Rent ceiling, searchSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC7.1.14)The opportunity cost of an apartment in a rent controlled market is equal toA)the rent charged for the apartment.B)the opportunity cost of searching for the apartment.C)the rent charged for the apartment plus the opportunity cost of searching for theapartment.D)nothing because of the surplus of apartments when there are rent controls.E)the rent charged for the apartment minus the opportunity cost of searching for theapartment.Answer:CTopic:Rent ceiling, searchSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC282 7.1.15)A rent ceiling in a housing marketA)makes all rents lower than the ceiling illegal to charge.B)is set above the equilibrium rent in order to have an effect.C)increases the time people spend searching for housing.D)Both answers B and C are correct.E)Both answers A and C are correct.Answer:CTopic:Rent ceiling, searchSkill:Level 3: Using modelsObjective:Checkpoint 7.1Author:SA7.1.16)In a market with a rent ceiling set below the equilibrium rent, the producer and consumersurplusA)both increase.B)both decrease but generally not to zero.C)do not change.D)are eliminated.E)are both totally converted into deadweight loss.Answer:BTopic:Rent ceiling, efficiencySkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC7.1.17)The deadweight loss in a housing market with a rent ceiling set below the equilibrium rent istheA)loss to those who cannot find apartments and the gain to landlords who charge blackmarket rents.B)loss to those who cannot find apartments and the loss to landlords who cannot offerhousing at the lower rent ceiling.C)loss to landlords and the gain to tenants who pay a fairer rent.D)loss to tenants and the gain to landlords who have the incentive to offer moreapartments for rent.E)gain to landlords and to tenants because now a fairer rent is charged.Answer:BTopic:Rent ceiling, deadweight lossSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JCBade/Parkin Foundations of Microeconomics , Fourth Edition·Chapter 7 Markets in Action 2837.1.18)Rent ceilings set below the equilibrium renti.create a deadweight loss.ii.increase search activity.iii.encourage landlords to charge a high price for new locks and keys, called ʺkey money.ʺA)i only.B)ii only.C)i and iii.D)i and ii.E)i, ii, and iii.Answer:ETopic:Rent ceiling, deadweight lossSkill:Level 3: Using modelsObjective:Checkpoint 7.1Author:SA7.1.19)In a housing market with a rent ceiling set below the equilibrium rent, as time passes thesupply of apartmentsA)decreases.B)increases.C)does not change.D)becomes fixed by the government.E)increases while the demand for apartments decreases.Answer:ATopic:Rent ceiling, change in supply over timeSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC7.1.20)Which of the following is an example of the unfairness of rent control?A)Voluntary exchange is encouraged by rent control.B)Racial discrimination in renting is discouraged by rent control.C)Newcomers have a more difficult time finding apartments.D)Rich people do not get apartments in these markets.E)Too many people rent apartments.Answer:CTopic:Rent ceiling, unfairnessSkill:Level 2: Using definitionsObjective:Checkpoint 7.1Author:JC284 7.1.21)Suppose the city of Chicago imposes a rent control program that fixes rents at $400 below theequilibrium rent. With this planA)the quantity of apartments demanded will increase.B)the quantity of apartments supplied will increase.C)young people and poor people will have an easier time finding apartments.D)the deadweight loss in Chicago ʹs apartment market will be eliminated.E)there will be a surplus of apartments offered for rent.Answer:ATopic:Rent ceiling, unfairnessSkill:Level 3: Using modelsObjective:Checkpoint 7.1Author:JC7.1.22)Rent controlsA)create a deadweight loss.B)increase maintenance by landlords.C)benefit people who live in rent controlled apartments.D) Both answers A and C are correct.E) Both answers B and C are correct.Answer:DTopic:Rent ceiling, unfairnessSkill:Level 4: Applying modelsObjective:Checkpoint 7.1Author:SACheckpoint 7.2Price Floors7.2.1)A price floor isA)the highest possible legal price that can be charged for a good or service.B)usually equal to the equilibrium price established before the government imposed theprice floor.C)the lowest legal price at which a good or service can be traded.D)a legal price of zero that can be charged for a good or service.E)almost always equal to the price ceiling.Answer:CTopic:Price floorSkill:Level 1: DefinitionObjective:Checkpoint 7.2Author:JCBade/Parkin Foundations of Microeconomics , Fourth Edition·Chapter 7 Markets in Action 2857.2.2)A price floor set above the equilibrium priceA)creates a surplus.B)creates a shortage.C)creates excess demand.D)balances supply and demand.E)has no effect.Answer:ATopic:Price floor, surplusSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.3)A price floorA)changes the equilibrium price if it is imposed in black markets.B)changes the price and quantity if it is set below the equilibrium price.C)changes the price and quantity if it is set above the equilibrium price.D)does not create a black market if it is set above the equilibrium price.E)changes the price and quantity only if it equals the equilibrium price.Answer:CTopic:Price floor, surplusSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.4)Suppose the equilibrium price of a gallon of milk is $4. If the government imposes a pricefloor of $5 per gallon of milk, theA)quantity supplied of milk falls short of the quantity demanded.B)quantity supplied of milk exceeds the quantity demanded.C)supply increases.D)demand decreases.E)price of milk remains $4 per gallon.Answer:BTopic:Price floor, surplusSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.5)Suppose the current equilibrium wage rate for housekeepers is $8.60 per hour. An increase inthe minimum wage to $7.50 per hour leads toA)a surplus of housekeepers.B)a shortage of housekeepers.C)no change in the market for housekeepers.D)an increase in the quantity of housekeepers supplied.E)unemployment of housekeepers.Answer:CTopic:Minimum wage, employmentSkill:Level 2: Using definitionsObjective:Checkpoint 7.2Author:JC7.2.6)Suppose the equilibrium wage rate for apricot pickers is $6.00 per hour and at that wage ratethe equilibrium quantity of apricot pickers employed is 14,000. If the minimum wage is set at $6.50 per hour, then theA)quantity of apricot pickers employed increases.B)quantity of apricot pickers employed decreases.C)quantity of apricot pickers employed does not change.D)wage rate for apricot pickers decreases.E)quantity of apricot pickers demanded does not change and the quantity of apricotpickers supplied does not change.Answer:BTopic:Minimum wage, employmentSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:JC7.2.7)Suppose the current equilibrium wage rate for landscapers is $5.65 in Little Rock; $6.50 in St.Louis and $8.05 in Raleigh. An increase in the minimum wage to $6.50 per hour results inunemployment of landscapers inA)Little Rock and St. Louis.B)only Raleigh.C)Little Rock, St. Louis, and Raleigh.D)only Little Rock.E)St. Louis and Raleigh.Answer:DTopic:Minimum wage, employmentSkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:JC7.2.8)Suppose the equilibrium wage rate for apricot pickers is $9.00 per hour in California and atthat wage rate the equilibrium quantity of apricot pickers is 14,000. If the minimum wage is set at $7.50 per hour, then theA)quantity of apricot pickers employed increases.B)quantity of apricot pickers employed decreases.C)quantity of apricot pickers employed does not change.D)wage rate for apricot pickers increases.E)some apricot pickers are unemployed.Answer:CTopic:Minimum wage, employmentSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:JCWage rate(dollars per hour)Quantity demanded(workers)Quantity supplied(workers)9 40010008 600 9007 800 80061000 70051200 5007.2.9)The labor demand and labor supply schedules are given in the table above. If a minimumwage of $8 per hour is imposed,A)a surplus of 300 workers occurs.B)there is no shortage or surplus of workers.C)900 workers are employed.D)Both answers B and C are correct.E)Both answers A and C are correct.Answer:ATopic:Minimum wage, employmentSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.10)The labor demand and labor supply schedules are given in the table above. If a minimumwage of $6 per hour is imposed,A)a surplus of 300 workers occurs.B)a shortage of 300 workers occurs.C)there is no surplus or shortage of workers.D)the quantity demanded is 1,000 workers.E)there is unemployment of 700 workers.Answer:CTopic:Minimum wage, employmentSkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.11)The figure above shows the labor market in a region. For a minimum wage to change thewage rate and amount of employment, it must beA)left to the forces of supply and demand.B)set above $6 an hour.C)set equal to $6 an hour.D)set below $6 an hour.E)set at $12 per hour.Answer:BTopic:Minimum wage, employmentSkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:SA7.2.12)The figure above shows the labor market in a region. If a minimum wage of $8 an hour isimposed, then there are ________ unemployed workers.A)20,000B)40,000C)60,000D)80,000E)zeroAnswer:BTopic:Minimum wage, employmentSkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:SA7.2.13)The figure above shows the labor market in a region. If a minimum wage of $8 an hour isimposed, then the quantity of labor supplied is ________ and the quantity of labor demanded is ________.A)60,000; 60,000B)80,000; 40,000C)40,000; 60,000D)60,000; 40,000E)40,000; 40,000Answer:BTopic:Minimum wage, employmentSkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:SA7.2.14)The figure above shows the labor market in a region. In which of the following cases wouldthe amount of unemployment be the largest?A)when the market is at its equilibrium, with no minimum wageB)when a minimum wage of $4 an hour is imposedC)when a minimum wage of $6 an hour is imposedD)when a minimum wage of $8 an hour is imposedE)None of the above because the market will adjust so that there is no unemployment.Answer:DTopic:Minimum wage, unemploymentSkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:MR7.2.15)One result of the minimum wage isA)a black market for labor that pays more than the minimum wage.B)a black market for labor that pays less than the minimum wage.C)decreased job search activity.D)a decrease in unemployment among poor and unskilled workers.E)an increase in employment among poor and unskilled workers.Answer:BTopic:Minimum wage, black marketSkill:Level 2: Using definitionsObjective:Checkpoint 7.2Author:JC7.2.16)An increase in the minimum wage to $15 per hour would lead toA)an increase in search activity for many workers.B)a decrease in search activity for many workers.C)a decrease in unemployment.D)no change in unemployment.E)no change in employment.Answer:ATopic:Minimum wage, searchSkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:JC7.2.17)Suppose the marginal benefit a cherry orchard derives from hiring Lauren to pick cherries is$8 per hour. If the wage rate that Lauren earns is $7 per hour, then the orchardʹs surplus from Laurenʹs labor is ________ per hour.A)$7B)$15C)$1D)$8E)$0Answer:CTopic:Demand for labor, surplusSkill:Level 2: Using definitionsObjective:Checkpoint 7.2Author:JC7.2.18)The surplus for workers from a job is equal to theA)marginal cost of work.B)wage rate.C)marginal cost of work minus the wage rate.D)wage rate minus the marginal cost of work.E)marginal benefit of hiring a worker minus the wage rate.Answer:DTopic:Supply of labor, surplusSkill:Level 1: DefinitionObjective:Checkpoint 7.2Author:JC7.2.19)An efficient allocation of labor occurs when theA)marginal benefit to workers exceeds the marginal benefit to firms.B)marginal benefit to firms exceeds the marginal benefit to workers.C)marginal cost to workers is equal to the marginal benefit to firms.D)marginal cost and marginal benefit of both workers and the firms are equal to zero.E)marginal benefit of workers exceeds the marginal cost to firms by as much as possible.Answer:CTopic:Minimum wage, efficiencySkill:Level 3: Using modelsObjective:Checkpoint 7.2Author:SA7.2.20)If the minimum wage is set above the equilibrium wage, after taking into account theresources lost in job search, the firmsʹ surplus ________ and the workersʹ surplus ________.A)increases; increasesB)increases; decreases.C)decreases; increasesD)decreases; decreasesE)does not change; decreasesAnswer:DTopic:Minimum wage, efficiencySkill:Level 2: Using definitionsObjective:Checkpoint 7.2Author:JC7.2.21)A minimum wage set above the equilibrium wageA)decreases the deadweight loss in the market.B)decreases the workersʹ surplus because workers must spend resources looking for jobs.C)increases the firmʹs surplus.D)increases the marketʹs efficiency.E)has no effect on the market.Answer:BTopic:Minimum wage, efficiencySkill:Level 2: Using definitionsObjective:Checkpoint 7.2Author:SA7.2.22)Labor unions ________ increases in the minimum wage because an increase in the minimumwage ________ the demand for union labor.A)support; increasesB)support; decreasesC)oppose; increasesD)oppose; decreasesE)support; has no effect onAnswer:ATopic:Minimum wage, supportSkill:Level 2: Using definitionsObjective:Checkpoint 7.2Author:JC7.2.23)In the figure above, if the wage rate is $6 per hour, then theA)firmsʹ surplus is the area d+e+f.B)workersʹ surplus is the area a +b +c.C)deadweight loss equals zero.D)Only answers A and C are correct.E)Answers A, B, and C are correct.Answer:ETopic:Minimum wage, efficiencySkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.24)In the figure above, if the minimum wage rate is $8 per hour, then after taking account ofresources lost in job search, the workersʹ surplus is the area ________ and the firmsʹ surplus is the area ________.A)e; cB)d; bC)a; fD)f; aE)a + b + c + d + e; fAnswer:CTopic:Minimum wage, efficiencySkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SA7.2.25)In the figure above, if the minimum wage is $8 per hour, thenA)resources used in job-search activity increase compared to the situation before theminimum wage.B)it is legal to hire workers for a wage below the minimum wage because otherwiseunemployment would result.C)the deadweight loss is minimized.D)Both answers A and B are correct.E)Both answers B and C are correct.Answer:ATopic:Minimum wage, efficiencySkill:Level 4: Applying modelsObjective:Checkpoint 7.2Author:SACheckpoint 7.3Price Supports in Agriculture7.3.1)Which of the following is true regarding a price support set above the equilibrium price?i.The price support increases the price consumers pay.ii.The price support creates a deadweight loss.iii.The price support decreases output.A)i and iiB)i and iiiC)iii onlyD)i, ii, and iiiE)i onlyAnswer:ATopic:Price supportSkill:Level 2: Using definitionsObjective:Checkpoint 7.3Author:CD7.3.2)A price support leads to inefficiency becauseA)output is more than the efficient, equilibrium quantity.B)the marginal benefit of the last unit produced is larger than the marginal cost.C)the price charged is less than the equilibrium price.D)producer surplus is less than consumer surplus.E)producers must pay a subsidy to the government.Answer:ATopic:Price support, deadweight lossSkill:Level 2: Using definitionsObjective:Checkpoint 7.3Author:CD7.3.3)Suppose the government imposes a price support that is above the equilibrium price. As aresult,A)total revenue increases.B)consumer surplus increases.C)the marginal cost of the last unit produced decreases.D)the government has effectively imposed a price ceiling.E)the subsidy the government pays decreases.Answer:ATopic:Price support, deadweight lossSkill:Level 2: Using definitionsObjective:Checkpoint 7.3Author:CDCheckpoint 7.4Integrative Questions7.4.1)The shortage created by a rent ceiling below the equilibrium rent is smallest when thedemand for housing is ________ and the supply of housing is ________.A)elastic; elasticB)elastic; inelasticC)inelastic; elasticD)inelastic; inelasticE)unit elastic; unit elasticAnswer:DTopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:MR7.4.2)A regulation that sets the highest price at which it is legal to trade a good is aA)production quota.B)price floor.C)price support.D)price ceiling.E)subsidyAnswer:DTopic:IntegrativeSkill:Level 1: DefinitionObjective:IntegrativeAuthor:MR7.4.3)A regulation that sets the lowest price at which it is legal to trade a good is aA)search ceiling.B)price floor.C)production ceiling.D)price ceiling.E)subsidyAnswer:BTopic:IntegrativeSkill:Level 1: DefinitionObjective:IntegrativeAuthor:MR7.4.4)If the government imposes an effective ________, output decreases and ________ increases.A)price support; consumer surplusB)price floor; consumer surplusC)price support; total revenueD)price floor; marginal benefit to consumersE)price ceiling; efficiencyAnswer:CTopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:CD7.4.5)If the government imposes an effective ________, a deadweight loss ________.A)price floor; does not occurB)price ceiling; does not occurC)price ceiling; occursD)price support; does not occurE)Both answers C and D are correct.Answer:CTopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:CD7.4.6)Producers favor a ________ because ________.A)price ceiling; the equilibrium price increasesB)price support; the deadweight loss is minimizedC)price ceiling; total revenue increasesD)price support; total revenue increasesE)price ceiling; consumer surplus increasesAnswer:DTopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:CD7.4.7)In order to have an impact, a ________ must be set below the equilibrium price and whenthis occurs, ________.A)price ceiling; consumer surplus increasesB)price floor; consumer surplus decreasesC)price ceiling; producer surplus decreasesD)price support; total revenue increasesE)price support; consumer surplus increasesAnswer:CTopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:CD7.4.8)Which of the following describes a difference between a price support and a price ceiling?A)A price support creates a deadweight loss while a price ceiling does not.B)A price ceiling is a regulated price while a price support is a regulated quantity.C)A price support decreases the quantity while a price ceiling does not.D)A price ceiling increases the price above the equilibrium price while a price supportdoes not.E)A price support attempts to raise the price above the equilibrium price while a priceceiling does not.Answer:ETopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:CD7.4.9)Both price supports and a price floor canA)create a deadweight loss.B)decrease output below the equilibrium quantity.C)decrease the price below the equilibrium price.D)increase consumer surplus.E)have no effect on producer surplus.Answer:ATopic:IntegrativeSkill:Level 3: Using modelsObjective:IntegrativeAuthor:MR7.4.10)Which of the following is true?i. A price ceiling set above the equilibrium price has no effects.ii. A price ceiling set below the equilibrium price creates a surplus.iii. A price floor set above the equilibrium price has no effects.A)Only iB)Only iiC)Only iiiD)i and iiE)ii and iiiAnswer:ATopic:IntegrativeSkill:Level 2: Using definitionsObjective:IntegrativeAuthor:CO7.4.11)Which of the following is true?i. A price ceiling is inefficient but fair.ii. A price floor is inefficient and unfair.iii. A price support increases the quantity produced.A)Only iB)Only iiC)Only iiiD)i and iiE)ii and iiiAnswer:BTopic:IntegrativeSkill:Level 2: Using definitionsObjective:IntegrativeAuthor:CO。

Laser technologyR. E. Slusher Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974 Laser technology during the 20th century is reviewed emphasizing the laser’s evolution from science to technology and subsequent contributions of laser technology to science. As the century draws to a close, lasers are making strong contributions to communications, materials processing, data storage, image recording, medicine, and defense. Examples from these areas demonstrate the stunning impact of laser light on our society. Laser advances are helping to generate new science as illustrated by several examples in physics and biology. Free-electron lasers used for materials processing and laser accelerators are described as developing laser technologies for the next century.[S0034-6861(99)02802-0]1. INTRODUCTIONLight has always played a central role in the study of physics, chemistry, and biology. Light is key to both the evolution of the universe and to the evolution of life on earth. This century a new form of light, laser light, has been discovered on our small planet and is already facilitating a global information transformation as well as providing important contributions to medicine, industrial material processing, data storage, printing, and defense. This review will trace the developments in science and technology that led to the invention of the laser and give a few examples of how lasers are contributing to both technological applications and progress in basic science. There are many other excellent sources that cover various aspects of the lasers and laser technology including articles from the 25th anniversary of the laser (Ausubell and Langford, 1987) and textbooks (e.g., Siegman, 1986; Agrawal and Dutta, 1993; and Ready, 1997).Light amplification by stimulated emission of radiation (LASER) is achieved by exciting the electronic, vibrational, rotational, or cooperative modes of a material into a nonequilibrium state so that photons propagating through the system are amplified coherently by stimulated emission. Excitation of this optical gain medium can be accomplished by using optical radiation, electrical current and discharges, or chemical reactions. The amplifying medium is placed in an optical resonator structure, for example between two high reflectivity mirrors in a Fabry-Perot interferometer configuration. When the gain in photon number for an optical mode of the cavity resonator exceeds the cavity loss, as well as loss from nonradiative and absorption processes, the coherent state amplitude of the mode increases to a level where the mean photon number in the mode is larger than one. At pump levels above this threshold condition,the system is lasing and stimulated emission dominates spontaneous emission. A laser beam is typically coupled out of the resonator by a partially transmitting mirror. The wonderfully useful properties of laser radiation include spatial coherence, narrow spectral emission, high power, and well-defined spatial modes so that the beam can be focused to a diffraction-limited spot size in order to achieve very high intensity. The high efficiency of laser light generation is important in many applications that require low power input and aminimum of heat generation.When a coherent state laser beam is detected using photon-counting techniques, the photon count distribution in time is Poissonian. For example, an audio output from a high efficiency photomultiplier detecting a laser field sounds like rain in a steady downpour. This laser noise can be modified in special cases, e.g., by constant current pumping of a diode laser to obtain a squeezed number state where the detected photons sound more like a machine gun than rain. An optical amplifier is achieved if the gain medium is not in a resonant cavity. Optical amplifiers can achieve very high gain and low noise. In fact they presently have noise figures within a few dB of the 3 dB quantum noise limit for a phase-insensitive linear amplifier, i.e., they add little more than a factor of two to the noise power of an input signal. Optical parametric amplifiers (OPAs), where signal gain is achieved by nonlinear coupling of a pump field with signal modes, can be configured to add less than 3 dB of noise to an input signal. In an OPA the noise added to the input signal can be dominated by pump noise and the noise contributed by a laser pump beam can be negligibly small compared to the large amplitude of the pump field.2. HISTORYEinstein (1917) provided the first essential idea for the laser, stimulated emission. Why wasn’t the laser invented earlier in the century? Much of the early work on stimulated emission concentrates on systems near equilibrium, and the laser is a highly nonequilibrium system. In retrospect the laser could easily have been conceived and demonstrated using a gas discharge during the period of intense spectroscopic studies from 1925 to 1940. However, it took the microwave technology developed during World War II to create the atmosphere for thelaser concept. Charles Townes and his group at Columbia conceived the maser (microwave amplification by stimulated emission of radiation) idea, based on their background in microwave technology and their interest in high-resolution microwave spectroscopy. Similar maser ideas evolved in Moscow (Basov and Prokhorov, 1954) and at the University of Maryland (Weber,1953). The first experimentally demonstrated maser at Columbia University (Gordon et al., 1954, 1955) was based on an ammonia molecular beam. Bloembergen’s ideas for gain in three level systems resulted in the first practical maser amplifiers in the ruby system. These devices have noise figures very close to the quantum limit and were used by Penzias and Wilson in the discovery of the cosmic background radiation.Townes was confident that the maser concept could be extended to the optical region (Townes, 1995). The laser idea was born (Schawlow and Townes, 1958) when he discussed the idea with Arthur Schawlow, who understood that the resonator modes of a Fabry-Perot interferometer could reduce the number of modes interacting with the gain material in order to achieve high gain for an individual mode. The first laser was demonstrated in a flash lamp pumped ruby crystal by Ted Maiman at Hughes Research Laboratories (Maiman, 1960). Shortly after the demonstration of pulsed crystal lasers, a continuouswave (CW) He:Ne gas discharge laser was demonstrated at Bell Laboratories (Javan et al., 1961), first at 1.13 mm and later atthe red 632.8 nm wavelength lasing transition. An excellent article on the birth of the laser is published in a special issue of Physics Today (Bromberg, 1988).The maser and laser initiated the field of quantum electronics that spans the disciplines of physics and electrical engineering. For physicists who thought primarily in terms of photons, some laser concepts were difficult to understand without the coherent wave concepts familiar in the electrical engineering community. For example, the laser linewidth can be much narrower than the limit that one might think to be imposed by the laser transition spontaneous lifetime. Charles Townes won a bottle of scotch over this point from a colleague at Columbia. The laser and maser also beautifully demonstrate the interchange of ideas and impetus between industry, government, and university research.Initially, during the period from 1961 to 1975 there were few applications for the laser. It was a solution looking for a problem. Since the mid-1970s there has been an explosive growth of laser technology for industrial applications. As a result of this technology growth, a new generation of lasers including semiconductor diode lasers, dye lasers, ultrafast mode-locked Ti:sapphire lasers, optical parameter oscillators, and parametric amplifiers is presently facilitating new research breakthroughs in physics, chemistry, and biology.3. LASERS AT THE TURN OF THE CENTURYSchawlow’s ‘‘law’’ states that everything lases if pumped hard enough. Indeed thousands of materials have been demonstrated as lasers and optical amplifiers resulting in a large range of laser sizes, wavelengths, pulse lengths, and powers. Laser wavelengths range from the far infrared to the x-ray region. Laser light pulses as short as a few femtoseconds are available for research on materials dynamics. Peak powers in the petawatt range are now being achieved by amplification of femtosecond pulses. When these power levels are focused into a diffraction-limited spot, the intensities approach 1023 W/cm2. Electrons in these intense fields are accelerated into the relativistic range during a single optical cycle, and interesting quantum electrodynamic effects can be studied. The physics of ultrashort laser pulses is reviewed is this centennial series (Bloembergen, 1999).A recent example of a large, powerful laser is the chemical laser based on an iodine transition at a wavelength of 1.3 mm that is envisioned as a defensive weapon (Forden, 1997). It could be mounted in a Boeing 747 aircraft and would produce average powers of 3 megawatts, equivalent to 30 acetylene torches. New advances in high quality dielectric mirrors and deformable mirrors allow this intense beam to be focused reliably on a small missile carrying biological or chemical agents and destroy it from distances of up to 100 km. This ‘‘star wars’’ attack can be accomplished during the launch phase of the target missile so that portions of the destroyed missile would fall back on its launcher, quite a good deterrent for these evil weapons. Captain Kirk and the starship Enterprise may be using this one on the Klingons!At the opposite end of the laser size range are microlasers so small that only a few optical modes are contained in a resonator with a volume in the femtoliter range. These resonators can take the form of rings or disks only a few microns in diameterthat use total internal reflection instead of conventional dielectric stack mirrors in order to obtain high reflectivity. Fabry-Perot cavities only a fraction of a micron in length are used for VCSELs (vertical cavity surface emitting lasers) that generate high quality optical beams that can be efficiently coupled to optical fibers (Choquette and Hou, 1997). VCSELs may find widespread application in optical data links.4. MATERIALS PROCESSING AND LITHOGRAPHYHigh power CO2 and Nd:YAG lasers are used for a wide variety of engraving, cutting, welding, soldering, and 3D prototyping applications. rf-excited, sealed off CO2 lasers are commercially available that have output powers in the 10 to 600 W range and have lifetimes of over 10 000 hours. Laser cutting applications include sailclothes, parachutes, textiles, airbags, and lace. The cutting is very quick, accurate, there is no edge discoloration, and a clean fused edge is obtained that eliminates fraying of the material. Complex designs are engraved in wood, glass, acrylic, rubber stamps, printing plates, plexiglass, signs, gaskets, and paper. Threedimensional models are quickly made from plastic or wood using a CAD (computer-aided design) computer file.Fiber lasers (Rossi, 1997) are a recent addition to the materials processing field. The first fiber lasers were demonstrated at Bell Laboratories using crystal fibers in an effort to develop lasers for undersea lightwave communications. Doped fused silica fiber lasers were soon developed. During the late 1980s researchers at Polaroid Corp. and at the University of Southampton invented cladding-pumped fiber lasers. The glass surrounding the guiding core in these lasers serves both to guide the light in the single mode core and as a multimode conduit for pump light whose propagation is confined to the inner cladding by a low-refractive index outer polymer cladding. Typical operation schemes at present use a multimode 20 W diode laser bar that couples efficiently into the large diameter inner cladding region and is absorbed by the doped core region over its entire length (typically 50 m). The dopants in the core of the fiber that provide the gain can be erbium for the 1.5 mm wavelength region or ytterbium for the 1.1 mm region. High quality cavity mirrors are deposited directly on the ends of the fiber. These fiber lasers are extremely efficient, with overall efficiencies as high as 60%. The beam quality and delivery efficiency is excellent since the output is formed as the single mode output of the fiber. These lasers now have output powers in the 10 to 40 W range and lifetimes of nearly 5000 hours. Current applications of these lasers include annealing micromechanical components, cutting of 25 to 50 mm thick stainless steel parts, selective soldering and welding of intricate mechanical parts, marking plastic and metal components, and printing applications.Excimer lasers are beginning to play a key role in photolithography used to fabricate VLSI (very large scale integrated circuit) chips. As the IC (integrated circuit) design rules decrease from 0.35 mm (1995) to 0.13 mm (2002), the wavelength of the light source used for photolithographic patterning must correspondingly decrease from 400 nm to below 200 nm. During the early 1990s mercury arc radiation produced enough power at sufficiently short wavelengths of 436 nm and 365 nm for high production rates of IC devices patterned to 0.5 mm and 0.35 mmdesign rules respectively. As the century closes excimer laser sources with average output powers in the 200 W range are replacing the mercury arcs. The excimer laser linewidths are broad enough to prevent speckle pattern formation, yet narrow enough, less than 2 nm wavelength width, to avoid major problems with dispersion in optical imaging. The krypton fluoride (KF) excimer laser radiation at 248 nm wavelength supports 0.25 mm design rules and the ArF laser transition at 193nm will probably be used beginning with 0.18 mm design rules. At even smaller design rules, down to 0.1 mm by 2008, the F2 excimer laser wavelength at 157 nm is a possible candidate, although there are no photoresists developed for this wavelength at present. Higher harmonics of solid-state lasers are also possibilities as high power UV sources. At even shorter wavelengths it is very difficult for optical elements and photoresists to meet the requirements in the lithographic systems. Electron beams, x-rays and synchrotron radiation are still being considered for the 70 nm design rules anticipated for 2010 and beyond.5. LASERS IN PHYSICSLaser technology has stimulated a renaissance in spectroscopies throughout the electromagnetic spectrum. The narrow laser linewidth, large powers, short pulses, and broad range of wavelengths has allowed new dynamic and spectral studies of gases, plasmas, glasses, crystals, and liquids. For example, Raman scattering studies of phonons, magnons, plasmons, rotons, and excitations in 2D electron gases have flourished since the invention of the laser. Nonlinear laser spectroscopies have resulted in great increases in precision measurement as described in an article in this volume (Ha¨nsch and Walther 1999).Frequency-stabilized dye lasers and diode lasers precisely tuned to atomic transitions have resulted in ultracold atoms and Bose-Einstein condensates, also described in this volume (Wieman et al., 1999). Atomicstate control and measurements of atomic parity nonconservation have reached a precision that allows tests of the standard model in particle physics as well as crucial searches for new physics beyond the standard model. In recent parity nonconservation experiments (Wood et al., 1997) Ce atoms are prepared in specific electronic states as they pass through two red diode laser beams. These prepared atoms then enter an optical cavity resonator where the atoms are excited to a higher energy level by high-intensity green light injected into the cavity from a frequency-stabilized dye laser. Applied electric and magnetic fields in this excitation region can be reversed to create a mirrored environment for the atoms. After the atom exits the excitation region, the atom excitation rate is measured by a third red diode laser. Very small changes in this excitation rate with a mirroring of the applied electric and magnetic fields indicate parity nonconservation. The accuracy of the parity nonconservation measurement has evolved over several decades to a level of 0.35%. This measurement accuracy corresponds to the first definitive isolation of nuclear-spin-dependent atomic parity violation.。

Effect of Si doping on strain,cracking,and microstructure in GaN thin films grown by metalorganic chemical vapor depositionL.T.Romano a)and C.G.Van de WalleXerox Palo Alto Research Center,Palo Alto,California94304J.W.Ager IIIMaterials Sciences Division,Lawrence Berkeley National Laboratory,California94720W.Go¨tz and R.S.KernLumiLeds Lighting,San Jose,California95131͑Received20December1999;accepted for publication14February2000͒The effect of Si doping on the strain and microstructure in GaNfilms grown on sapphire bymetalorganic chemical vapor deposition was investigated.Strain was measured quantitatively byx-ray diffraction,Raman spectroscopy,and wafer curvature techniques.It was found that for a Siconcentration of2ϫ1019cmϪ3,the threshold for crack formation duringfilm growth was2.0␮m.Transmission electron microscopy and micro-Raman observations showed that cracking proceedswithout plastic deformation͑i.e.,dislocation motion͒,and occurs catastrophically along the lowenergy͕11គ00͖cleavage plane of GaN.First-principles calculations were used to show that thesubstitution of Si for Ga in the lattice causes only negligible changes in the lattice constant.Thecracking is attributed to tensile stress in thefilm present at the growth temperature.The increase intensile stress caused by Si doping is discussed in terms of a crystallite coalescence model.©2000American Institute of Physics.͓S0021-8979͑00͒03410-1͔I.INTRODUCTIONGrowth of III–V nitrides for device applications is pri-marily done on sapphire substrates using metalorganic chemical vapor deposition͑MOCVD͒.1Since the thermal ex-pansion coefficient of sapphire is larger than that of GaN,a compressive stress estimated at greater than1GPa would be expected to develop in afilm that was grown stress free at the growth temperature͑typically1000°C͒.2Typically, smaller,but still compressive stresses are observed.2–6An interesting effect has been observed with Si doping.Highly Si doped GaN is desired to form low resistance n-type con-ductive layers in nitride-based light emitting diodes,lasers, and optoelectronic devices.However,the maximum amount of Si doping appears to be limited by cracks that develop in films with high Si concentration.7,8Ex situ Raman and x-ray diffraction͑XRD͒studies performed on Si doped GaNfilms have shown that the compressive strain observed at room temperature in MOCVD-grownfilms decreases with increas-ing Si concentration.6It has also been suggested that the reduction of compressive stress observed at room tempera-ture in moderately Si doped samples(ϳ3ϫ1018cmϪ3)is due to the formation of dislocations in the basal plane.5Re-cently,in situ wafer curvature measurements have shown that undoped GaNfilms are in tension at the growth temperature.9We perform here a detailed study of the effect of Si doping on the strain and microstructure of MOCVD-grown GaNfilms.First-principles calculations were used to deter-mine the change in lattice constant expected for Si substitut-ing for Ga in GaN.Film strain was measured with threecomplementary techniques:XRD,wafer curvature,andmicro-Raman spectroscopy with1␮m lateral resolution.The microstructure was evaluated with transmission electron mi-croscopy͑TEM͒,scanning electron microscopy͑SEM͒,andatomic force microscopy͑AFM͒.Strain gradients in the vi-cinity of cracks were measured with micro-Raman spectros-copy.The experimental observations are discussed in termsof a crystallite or domain coalescence model developed forthe growth of polycrystallinefilms.10II.EXPERIMENTA.SamplesGaNfilms were grown in conventional MOCVD reac-tors on͑0001͒sapphire substrates similar to studies de-scribed elsewhere using trimethylgallium,ammonia,and hy-drogen as a carrier gas.11Silane was introduced into the gasstream to achieve Si doping in the range from3ϫ1016to5ϫ1019cmϪ3.The standard deposition procedure for Si-dopedfilms͑Afilms͒was sequential growth of:͑1͒a lowtemperature͑LT͒nucleation layer,͑2͒a100nm high tem-perature͑HT͒undoped layer,and͑3͒1–2.5␮m HT Si-doped layer.Some samples͑Bfilms͒were made without the un-doped HT layer͑i.e.,silane was introduced immediately after growth of the LT nucleation layer͒.The totalfilm thickness h was varied between1and3.0␮m.Hall-effect and secondary ion mass spectrometry mea-surements were used to determine the electron and Si con-centrations͓Si͔.In all the samples the quantitative agreementbetween͓Si͔and the carrier concentration indicated that allthe Si was electrically active and it was therefore inferred toa͒Electronic mail:romano@parc.xeroxJOURNAL OF APPLIED PHYSICS VOLUME87,NUMBER111JUNE200077450021-8979/2000/87(11)/7745/8/$17.00©2000American Institute of Physicsreside on the Ga site.The surface roughness and microstruc-ture of thefilms were measured by a combination of AFM, SEM,and TEM.Samples for TEM were prepared in the standard way by mechanically thinning and ion milling to electron transparency.B.Strain determination from x-ray diffractionThe a and c lattice constants were measured by XRD using the(101គ5)and͑0002͒reflections,respectively.The strain values can then be obtained from the equations ⑀aϭa/a0Ϫ1͑1͒and⑀cϭc/c0Ϫ1.͑2͒To calculate these strains,the lattice constants a0and c0of the relaxed,unstrained bulk material must be known.Among the reported values,it is our opinion that the ones that most closely approximate the‘‘true’’lattice constant of pure GaN are the values measured for undoped homoepitaxial layersgrown on top of bulk single crystals with values of a0ϭ3.1878Åand c0ϭ5.1850Å.12These values are extremely close to the values of a and c measured for bulk single crys-tal GaN grown under high pressure in the presence of Mg (a0ϭ3.1876Åand c0ϭ5.1846Å͒.13C.Strain determination from Raman measurementsIn-plane strain(⌬a/aϭ⑀a)was measured with a lateral spatial resolution of1␮m with micro-Raman spectroscopy using shifts of the E2phonon.The E2phonon line in GaN is sensitive to strain in the layer,and its frequency can be ac-curately measured using Raman spectroscopy.In Ref.14,the following relationship was derived between the measured shift of the phonon line⌬E2and the stress in the layer:⌬E2ϭ␴aϫ͑Ϫ2.4Ϯ0.2cmϪ1/GPa͒.͑3͒The stress␴a is related to the strain⑀a through the expres-sion⑀aϭ␴a/M f,͑4͒where M is the biaxial modulus of GaN,which is defined as M fϭc11ϩc12Ϫ2c132/c33.͑5͒Elastic constants for GaN were taken from Ref.15,yielding a value for Mϭ478GPa.As discussed in Ref.14,the Raman measurements pro-duce an accurate assessment of the slope of the stress versus phonon shift curve,but the absolute magnitude of stresses and strains depend on the choice of a reference lattice con-stant.The standard used in the Raman shift measurements͑a bulk single crystal͒has lattice constants slightly larger than the homoepitaxialfilms which we choose as our reference,as discussed above.The relationship between the measured Ra-man shift and strain is then⑀aϭ0.00062Ϫ0.00086⌬E2.͑6͒D.Strain determination from curvature measurementsWafer curvature measurements of thefilms were per-formed in a Tencor laser system using a sapphire substrate as a reference.The curvature␬is equal to the inverse of the radius of curvature.The stress in thefilm,␴a,is related to the curvature␬by Stoney’s Equation16͑see Ref.9͒␴a hϭM s d Al2O32␬/6,͑7͒where h is the thickness of the GaNfilm,d Al2O3is the sub-strate thickness͑430␮m in our case͒,and M s is the biaxial modulus of the substrate͓see Eq.͑5͔͒.We have used the value M sϭ610GPa for Al2O3,as derived from the elastic constants in Ref.17.Equation͑7͒thus allows us to deter-mine the stress in thefilm,and the strain can subsequently be derived using Eq.͑4͒.III.RESULTSA.StrainThe a and c lattice constants were measured for all the films by XRD.The results for the2␮mfilms are shown in Fig.1for samples A͑undoped prelayer͒and B͑no undoped prelayer͒.The a lattice constants are found to be smaller͑and c lattice constants larger͒than the value found for bulk single crystals forfilms with͓Si͔Ͻ1018cmϪ3,whereas the a lattice constant is greater͑and c lattice constants smaller͒than the bulk values for SiϾ1018cmϪ3.The values for the single crystal lattice parameters a sc and c sc are noted in Fig.1from Ref.12.Figure2͑a͒is a combined plot of the in-plane strain⑀a measured by XRD,Raman,and curvature techniques as a function of Si doping for2␮m thick,A and Bfilms.The strains were calculated as discussed in Sec.II.Thefigure shows that our three different techniques for measuring the strain produce consistent results.Some exceptions are noted forfilms at the highest͓Si͔,where cracks were presentand FIG.1.a and c lattice constants measured by x-ray diffraction for2␮m thick GaNfilms as a function of͓Si͔.Inverted triangle symbols are Afilms ͑with undoped interlayer͒,diamond symbols are Bfilms͑no undoped inter-layer͒.Hatched open symbols are the a lattice constants,solid symbols are the c lattice constants.a sc and c sc are the values for the bulk lattice con-stants͑from Ref.12͒.The solid line through the points is a guide and not meant to imply the transition is continuous.found to cause local strain variations.XRD and wafer curva-ture measure strain over a macroscopic area,whereas the Raman microprobe is able to measure local strain variations.Strain variations around cracks will be discussed in Sec.III C.Figure 2͑a ͒shows that the in-plane strain increases with ͓Si ͔and the values of the strain for A and B films are comparable in magnitude.At low ͓Si ͔the films are in com-pression,which is expected to occur on cooling,due to the difference in thermal expansion coefficients between GaN and sapphire.However,as the Si concentration increases,the films are found to be in in-plane tension.The transition from compressive to tensile strain occurs at a ͓Si ͔between 1018–1019cm Ϫ3.Figure 2͑b ͒shows a comparison of the strain for the 1and 2␮m thick films in which only the Raman measurements are shown for simplicity.The 1␮m thick films clearly exhibit a lower strain than the 2␮m thick films for doping concentrations exceeding 1018cm Ϫ3.B.Extended defect structure observed by TEMThe defect structure was investigated by TEM for A and B samples with different ͓Si ͔.It was found that the density and the type of dislocations in the films were dependent on the doping level and presence of the undoped prelayer.The TEM images shown in Fig.3are for films grown at a doping concentration and thickness for which cracking was not ob-served.Figures 3͑a ͒and 3͑b ͒were obtained using a diffrac-tion vector g -5g ͑g ϭ0002͒weak beam condition,at a tiltapproximately ten degrees from the ͕112គ0͖towards the ͕101គ0͖zone.Figure 3͑a ͒is for a 1␮m thick film with ͓Si ͔ϭ2ϫ1019cm Ϫ3grown on a 100nm undoped prelayer.The image shows a broad band of contrast near the interface between the undoped prelayer and the doped overlayer.This contrast is due to the interference of overlapping regions with different c and a lattice constants across the doped/undoped interface as measured by XRD.18The broad fringe contrast was not observed for a 1␮m thick film with ͓Si ͔ϭ5ϫ1018cm Ϫ3as shown in Fig.3͑b ͒,where there was no significant lattice constant change between the undoped and doped layer.The threading dislocations in both of the images either have mixed or screw character with a compo-nent of the burgers vector b along the ͗0001͘direction.Dislocations with burgers vector b parallel to the ͗112គ0͘direction are imaged in Fig.3͑c ͒(g ϭ101គ0)for the same region of film shown in Fig.3͑a ͒.The combination of both images in Fig.3͑a ͒and 3͑c ͒show that the threading disloca-tions are unperturbed at the boundary between the undoped and doped layers and no additional dislocations are created.In addition,no dislocations along the basal plane were ob-served.This observation is consistent with the difficulty of generating misfit dislocations ͑on the basal plane ͒at lattice mismatched interfaces found previously for thick InGaN lay-ers on GaN 19and thin films with high In content in quantum well structures.20By comparison a 3.0␮m thick film grown without an undoped prelayer for ͓Si ͔ϭ5ϫ1018cm Ϫ3is shown in Fig.3͑d ͒using diffraction conditions g ϭ101គ0.It can be observed that predominately basal plane dislocations are found within a 1␮m thick region above the LT buffer layer.The presence of dislocations on the basal planes in-creases the probability of defect interactions with threading dislocations.This may explain the decrease in dislocation density at the film surface with increasing ͓Si ͔observed by other groups.5However,for the films in our study no such trend was observed for films grown with an undoped prelayer since basal plane dislocations were typically not present.As discussed above,the dislocations that were gen-erated in the undoped prelayer extended unperturbed to the surface resulting in a defect density at the surface of ϳ1010/cm 2for ͓Si ͔up to 2ϫ1019cm Ϫ3.C.CrackingCracking was observed for both A and B films with a doping level of 2ϫ1019cm Ϫ3for h у2␮m.The cracks were found to either extend partially (h ϭ2␮m)or completely from the film/substrate interface to the surface (h ϭ2.5␮m).The SEM micrographs in Fig.4for an A film that was 2␮m thick,shows that the crack occurs ontheFIG.2.͑a ͒Comparison of in-plane strain ⑀a measured for 2␮m thick GaN films as a function of ͓Si ͔by XRD ͑squares ͒,micro-Raman spectroscopy ͑triangles ͒,and wafer curvature ͑circles ͒.The circles with a cross are A films and the open circles are B films.The trend of increasing tensile strain with increasing ͓Si ͔is observed by all three techniques.The solid line through the points is a guide and not meant to imply the transition is con-tinuous.͑b ͒Comparison of in-plane strain ⑀a as a function of ͓Si ͔for 1and 2␮m thick films as measured by micro-Raman.Solid circles are 1␮m thick,A films;circles with a cross are 2␮m thick,A films;open circles are 2␮m thick,B films.The solid line through the points is a guide and not meant to imply the transition is continuous.prismatic ͕11គ00͖cleavage planes 21of the GaN ͑i.e.,parallel to the growth direction ͒and extends into the substrate.Fig-ures 5͑a ͒–5͑c ͒are TEM micrographs of a subsurface crack in the same film.Dislocation images taken in the same region along g ϭ101គ0͓Fig.5͑a ͔͒and g ϭ0002͓Fig.5͑b ͔͒near the ͗112គ0͘zone,show that no additional dislocations are gener-ated near the crack.This suggests that plastic deformation does not take place to promote crack formation.The widest part of the crack is revealed using the imaging conditions in Fig.5͑b ͒to be ⌬L ϳ50nm and the average crack spacing L is shown in Fig.5͑c ͒to be ϳ10␮m.As shown in the AFM image and corresponding line scan in Fig.6,the surface of the film that grows over the cracks is higher than the region between the cracks.The lighter contrast lines are the position of the cracks below the film surface indicating the crack pattern and a crack spacing of ϳ10␮m for parallel cracks,consistent with the TEM results.For the position measured in Fig.6,the surface of the overgrown film was ϳ16nm higher above the crack compared to the region between the cracks.Typical values for the root mean square roughnessbetween the cracks was found to be ϳ3nm whereas the surface height over the cracks typically ranged between 10–20nm.The subsurface cracking suggests that the films cracked during growth at high temperature,which is consis-tent with our measurements showing tensile strain in these films.Micro-Raman measurements of strains around a crack in a 2.5␮m thick ͑A film ͒with ͓Si ͔ϭ2ϫ1019cm Ϫ3are shown in Fig.7.The inset in Fig.7is a SEM showing that the crack extends from the film substrate to the film surface.At dis-tances far away from the crack ͑Ͼ75␮m ͒,the in-plane strain is ϩ0.015͑tensile ͒.The strain decreases near the crack,and parts of the film are in a small amount of compression ͑Ϫ0.005͒at the crack location.We attribute the compressive strain at the crack to thermal stresses occurring on film cool down ͑we assume the cracking occurred at the growth tem-perature ͒.Several groups 22–24have studied the elastic stress field around surface cracks in thin films.We apply here the model in Ref.23,assuming that by symmetry,a surface crack in a stressed film is equivalent to asemi-infiniteFIG.3.TEM images for 1␮m thick,A films with ͓Si ͔ϭ2ϫ1019cm Ϫ3in ͑a ͒and ͑c ͒;and ͓Si ͔ϭ5ϫ1018cm Ϫ3in ͑b ͒.The images in ͑a ͒and ͑b ͒were using a diffraction vector g -5g (g ϭ0002)weak beam conditions.A 3.0␮m thick B film with ͓Si ͔ϭ5ϫ1018cm Ϫ3is shown in ͑d ͒.The images in ͑c ͒and ͑d ͒are dark field images with g ϭ101គ0.edge.22The adjustable parameters used in the model includethe elastic constants and thickness of the film and substrate,and the value of the film stress away from the crack.The elastic constants used for GaN were taken from measure-ments by Polian et al.25and the sapphire elastic constants were from Tefft.17A film thickness of two microns was ob-tained from the SEM measurement and the in-plane strain away from the crack was taken from our micro-Raman mea-surement to be ϩ0.0015͑equivalent to a tensile biaxial stress of 560MPa ͒.As shown in Fig.7,there is good agreement of the elastic cracking model ͑solid line ͒and the values of strain measured by micro-Raman.Therefore,we conclude that cracking of the film leads to elastic relaxation in the vicinity of the crack which is consistent with the lack of dislocations observed near the cracks ͑Fig.5͒.This is in con-trast with the well-studied case of stress gradients in SiO 2/Si devices,where film stresses have been observed to lead to both dislocation generation and cracking.26IV.FIRST-PRINCIPLES CALCULATIONSThe observed dependence of strain on Si concentration could,in principle,be due to a change in lattice constant induced by Si incorporation.Incorporation of dopant impu-rities has two distinct effects on the lattice constant.27The first effect is purely a size effect,and is related to the differ-ence in atomic radius between the impurity and the host atom that is replaced by the Si.The second effect is an elec-tronic effect,related to deformation potentials.In the case of n -type doping,the donors contribute electrons to the conduc-tion band.The energy of the system can therefore be lowered if the conduction band energy can be decreased ͑on an abso-lute energy scale ͒.Such a shift in the position of the conduc-tion band can occur if the volume of the material is changed;hydrostatic strain indeed leads to a change in theconductionFIG. 4.SEM micrographs of a crack in a 2␮m thick,A film with ͓Si ͔ϭ2.0ϫ1019cm Ϫ3.͑a ͒The crack extends to sapphire substrate and ͑b ͒extends along the ͕11គ00͖cleavage plane of theGaN.FIG.5.TEM micrographs of a subsurface cracking in a GaN film ͑h ϭ2.0␮m,͓Si ͔ϭ2ϫ1019cm Ϫ3,no undoped interlayer ͒:High magnification image showing crack that is overgrown and extends into sapphire substrate with diffraction vector ͑a ͒g ϭ0002and ͑b ͒g ϭ101គ0.Lower magnification image in ͑c ͒showing distance between twocracks.FIG.6.͑a ͒AFM image of the surface of the film ͑shown in Fig.5͒and ͑b ͒corresponding line scans associated with the overgrown subsurfacecracks.FIG.7.Micro-Raman measurements of in-plane strain across a crack ͑cf.inset ͒in a GaN film grown on sapphire ͑h ϭ2.5␮m,͓Si ͔ϭ2ϫ1019cm Ϫ3,no undoped interlayer ͒.The solid line is the expected elastic strain relax-ation predicted by the model of Atkinson et al.,Ref.23.band energy,with a proportionality factor given by the de-formation potential.Such strain also bears a cost,of course,because of the elastic energy associated with the deforma-tion.This elastic energy,however,varies as the square of thestrain,whereas the energy gain due to the deformation varieslinearly with the strain;the system can therefore lower itsenergy by undergoing a deformation.The size effect can be addressed by studying the relax-ation of host atoms around the impurity.Even though we aredealing with wurtzite semiconductors,we treat the materialas isotropic.Our results indeed indicate that the anisotropyof the atomic relaxations is very small compared to the mag-nitude of the overall relaxations.It is customary to define aparameter␤size which relates the fractional change in the lattice constant to the impurity concentration⌬a/aϭ␤size͓Si].͑8͒The calculations were performed using density-functionaltheory in the local-density approximation,ab initio pseudo-potentials,and a supercell geometry.This is the same com-putational approach that we have successfully applied to thestudy of the atomic and electronic structure of a wide varietyof defects and impurities in nitride semiconductors.28,29Thecalculations show that the nitrogen atoms surrounding the Sidonor relax inwards by about0.10Åaround the Si Ga͑in the positive charge state͒.In order to determine the change inlattice constant,we follow a procedure described in Ref.27.The idea is to use Vegard’s law͑i.e.,a linear interpolation͒toestimate the contribution of atom-size differences to the ob-served lattice parameter.The end-point structures for the in-terpolation are pure GaN͑0%Si͒and a hypothetical zinc-blend SiN compound.Following this approach,we obtain avalue␤sizeϭϪ1.6ϫ10Ϫ24cm3.The negative sign of␤size in-dicates that the incorporation of Si atoms to the lattice results in a decrease of the lattice constant.The deformation-potential effect can be derived by per-forming a minimization of the sum of the elastic energy cost ͑quadratic in the strain͒and the energy gained due to lower-ing of the conduction band,occupied with a certain number of electrons͑linear in the strain͒.Similar to the parameter ␤size defined in Eq.͑8͒,one can define a parameter␤e, where the subscript indicates the deformation-potential effect for electrons⌬a/aϭ␤e n͑9͒and n is the electron concentration.Note that the carrier con-centration n is not necessarily equal to the donor concentra-tion,because of compensation or incomplete ionization. However,as discussed in Sec.II A,the samples studied in the present work show complete electrical activation of the Si donors and since most of the donors are ionized at room temperature,we can assume nϭ͓Si͔.The shift of the conduction band minimum is describedby the‘‘absolute’’deformation potential a c,as defined inRef.27.␤e can be calculated as␤eϭϪa c/3B,͑10͒where B is the bulk modulus of GaN.The absolute deforma-tion potential a c was calculated in Ref.30(a cϭϪ6.0eV).We thus obtain␤eϭ1.5ϫ10Ϫ24cm3,the positive sign indi-cating that placing electrons in the conduction band results in an expansion of the lattice.We conclude that for Si the size effect and deformation-potential effects have similar magnitudes but are of opposite sign,resulting in a very small net strain effect for Si Ga.As-suming complete ionization,we can write⌬a/aϭ␤tot͓Si͔, with␤totϭ␤sizeϩ␤eϭϪ0.1ϫ10Ϫ24cm3.For͓Si͔ϭ2ϫ1019 cmϪ3͑the maximum concentration used in this work͒the expected in-plane strain isϪ2ϫ10Ϫ6.This value is much smaller than the range of strain values observed as a function of͓Si͔͑Ϫ1.1ϫ10Ϫ3–2.5ϫ10Ϫ3,as reported above͒.There-fore,we conclude that the changes in lattice constant as a function of͓Si͔cannot be attributed to lattice distortions caused by the substitution.V.DISCUSSIONA.Effect of silicon on the lattice constantIn Sec.IV we argued,based onfirst-principles calcula-tions,that incorporation of silicon does not affect the lattice constant of the GaN overlayer.This result can actually be confirmed purely based on the measured lattice constants by invoking the theory of elasticity.From the theory of elasticity we know that the strains are related by the expression:⑀cϭϪD⑀a,͑11͒where Dϭ2c13/c33.Theoretical15and experimental25deter-minations of the elastic constants have produced a consistent and reliable value for D,namely Dϭ0.51.This corresponds to a value of Poisson’s ratio␯ϭ0.20,which is also well accepted.31Here we systematically use the elastic constants derived by Wright,15which are very close to the experimen-tal values of Polian et al.25Combining Eqs.͑1͒,͑2͒,and͑13͒,we can use a given pair of measured a and c values for a strained layer to derive the unstrained lattice constants of that layer,by assuming the above value of D,and a particular value for the c/a ratio;for the latter,we have chosen1.6265.For all of the layers ex-amined in the present study,the a0lattice constant extracted from this analysis is within0.0010Åof the value a0ϭ3.1878Åquoted above for pure GaN͑with a systematic deviation towards larger values͒.This deviation is very small,when compared to lattice-constant variations reported in the literature͑see,e.g.,Ref.32͒.This result confirms our conclusion that the effect of silicon incorporation on the lat-tice constant of our layers is very small.Figure8shows c versus a for all the1and2␮mfilms in our study.The solid line corresponds to the prediction from the theory of elasticity,for a biaxially strainedfilm with given bulk lattice constants͑a0ϭ3.1878Åand c0ϭ5.1850Å͒.The deviation from the solid line is smaller than the measured variation in a and c͑see Fig.1͒.This indicates that the measured values are due to variations in the strain induced on thefilm rather than a change in the bulk lattice constants.B.Dependence of strain on silicon concentrationThe increase in tensile strain with Si doping is puzzling.We have shown above that incorporating Si in the GaN lat-tice ͑substituting on a Ga site ͒has a negligible effect on the lattice constant of the GaN lattice.Silicon must therefore play a different role in introducing strain in the material.Recently Hearne et al.9reported in situ wafer curvature mea-surements that show that tensile strains occur in GaN films at the growth temperature.The films in their study were nomi-nally undoped,and exhibited tensile stresses up to 0.6GPa at the growth temperature.At room temperature the films in the study by Hearne et al.were found to be in compression,which is consistent with our results for films with ͓Si ͔Ͻ1018cm Ϫ3.Thermal cycling between 1000and 450°C showed that plastic relaxation of the growth stress does not occur during the cool down.9This is consistent with our results on films that were cracked without creating additional dislocations.Except for cracking,there was no obvious effect of Si on the microstructure for films grown with the undoped prelayer.Furthermore,the cracks generated during the growth occurred without the creation of dislocations.One possible explanation of the film stress present during growth may be as a consequence of film coalescence.The intrinsic stresses that develop during the growth of polycrystalline films have been investigated for many years.33,34Tensile stress is often found in these films and attributed to attractive forces between the grains.Nix and Clemens 10have recently developed a quantitative model for this process.In this model,tensile film stress increases monotonically with de-creasing crystallite size.In our study,the GaN films are single crystal.However,the surface structure,as measured by AFM,was found to depend on the Si concentration.We measured the surface roughness of two Si doped films with a thickness of 20nm grown on undoped prelayers by AFM.Increasing ͓Si ͔from 5ϫ1017to 5ϫ1019cm Ϫ3leads to a doubling of the root mean square surface roughness ͑from 5.5to 11.0nm ͒.Thesefilms showed no evidence of cracks.It is possible that gaps on the surface,due to the roughness,coalesce in a similar way as the crystallites described in the model by Nix and Clemens ͑NC ͒.Limited surface diffusion of atoms on the growing surface would cause adatoms to attach to the strained crystal at their point of arrival,and the film would grow in a strained state.If we associate the observed film roughness with an effective crystallite size,then as the roughness increased the effective crystallite would decrease.According to the NC model,this would predict a higher ten-sile stress with increasing roughness ͑high ͓Si ͔͒.The cause for the increased surface roughness with increasing ͓Si ͔is not understood.The presence of Si may limit the surface diffusion of the Ga and N atoms on the growing surface.The presence of Si on the surfaces of AlGaN 35and InGaN 36has been shown to lead to GaN quantum dot formation 35and spiral growth.36The competition for N atoms to form SiN may also play a role in the limited surface diffusion of the Ga and N atoms.It has been found that the growth rate of SiN grown by MOCVD was found to be three times higher when increasing the temperature from 800to 1080°C.37,38VI.CONCLUSIONSCrack formation in GaN films doped with Si was studied by measuring the strain and comparing to the microstructure.The strain was found to increase with film thickness and Si concentration.Crack formation along the ͕11គ00͖cleavage planes was found to be the major strain relief mechanism and occurred without creating additional dislocations.This sug-gests that plastic deformation is difficult in these materials at the temperatures used during growth.First-principles calcu-lations showed that silicon incorporation does not affect the lattice constant of the GaN crystal.It was proposed that the increase in tensile stress with increasing ͓Si ͔is related to the presence of tensile stress due to crystallite coalescence,in accordance with a model established recently by Nix and Clemens.10ACKNOWLEDGMENTSWe acknowledge helpful discussions with John Northrup,Stacia Keller,William Nix,Rowland Cannon,and Michael Drory.Some of this work was performed under a Cooperative Research and Development Agreement ͑CRADA ͒between Berkeley Lab and Hewlett Packard Laboratories.The Berkeley Lab portion of this work was supported by the Director,Office of Science,Office of Ad-vanced Scientific Computing Research,Advanced Energy Projects and Technology Research ͑AEPTR ͒Division,of the U.S.Department of Energy under Contract No.DE-AC03-76SF00098.We acknowledge support by DARPA Contract No.MDA972-96-3-0014.1S.Nakamura,The Blue Laser Diode:GaN Based Light Emitters and La-sers ͑Springer,Berlin,1997͒.2J.W.Ager III,T.Suski,S.Ruvimov,J.Krueger,G.Conti,E.R.Weber,M.D.Bremser,R.F.Davis,and C.P.Kuo,Mater.Res.Soc.Symp.Proc.449,775͑1997͒.3K.Hiramatsu,T.Detchprohm,and I.Akaksaki,Jpn.J.Appl.Phys.,Part 132,1528͑1993͒.ttice constants c and a ͑in angstrom ͒for all the 1and 2␮m films examined in the present study.The solid line is the prediction from elasticity theory for strained films with lattice constants a 0ϭ3.1878and c 0ϭ5.1850Å.A different choice of bulk lattice constants would produce a line parallel to the one shown in the figure.。

第23卷第21期岩石力学与工程学报23(21)：3577～3583 2004年11月Chinese Journal of Rock Mechanics and Engineering Nov.，2004岩土材料弹塑性损伤模型及变形局部化分析*杨强陈新周维垣(清华大学水利水电工程系北京 100084)摘要常规的弹塑性模型由于没有考虑到损伤和塑性的耦合作用，难以模拟破坏时由于内部损伤的累积导致的变形局部化剪切带的形成过程，因而，不能很好地反映实际结构的细观破坏机理。

作者采用一种宏细观结合的思路，基于细观损伤力学提出了一个适用于岩土材料弹塑性损伤模型，研究均质材料在外部环境作用下由于损伤和塑性的耦合导致的局部化剪切带的形成过程。

对基体材料服从Drucker-Prager准则的球形孔洞体胞单元提出了一个塑性损伤屈服面，为了反映岩土材料在拉应力和压应力作用下不同的孔洞形成机理，分别采用了球形拉应力和塑性应变的成核机制来建立孔隙率的演化方程，根据塑性损伤屈服面和孔隙率的演化方程，导出了关联流动法则下的岩土材料塑性损伤本构方程。

将笔者提出的岩土材料弹塑性损伤模型，通过用户子程序嵌入到大型商业有限元软件MRAC中。

为了研究塑性和损伤的耦合作用，分别采用Gurson弹塑性损伤模型和Mises弹塑性模型，对Tvergaard 关于自由表面有周期性分布微小形状缺陷的半无限大板在平面应变拉伸作用下剪切带的形成进行了数值模拟，计算结果表明弹塑性损伤本构模型在模拟变形局部化方面具有明显的优势。

采用作者提出的岩土材料弹塑性损伤模型，对平面应力条件下有一个缺陷单元的均质岩土材料单轴受压试件的局部化剪切破坏进行了数值模拟。

关键词岩土力学，岩土材料，体积孔隙率，Drucker-Prager准则，成核机制分类号 TU 452 文献标识码 A 文章编号1000-6915(2004)21-3577-07ELASTO-PLASTIC DAMAGE MODEL FOR GEOMATERIALSAND STRAIN LOCALIZAION ANALYSESYang Qiang，Chen Xin，Zhou Weiyuan(Department of Hydraulic and Hydropower Engineering，Tsinghua University， Beijing 100084 China)Abstract Elasto-plastic models can not explain the micro mechanism of shear band formation caused by damage evolution in ductile material due to the neglecting of the interaction between damage and plastic flow. An elasto-plastic damage model for geo-materials based on micromechanics is proposed and the micro mechanism of shear band formation in homogeneous geo-material is studied. A macroscopic yield criterion for porous geo-materials with matrices of Drucker-Prager yield criterion is given，and a plastic strain-controlled void nucleation model as well as a tensile volumetric stress-controlled nucleation model are proposed for the compressive and tensile stresses，respectively. Moreover，the constitutive relationship of the elasto-plastic damage model with plastic normality flow rule is deduced. This elasto-plastic damage model for geo-materials is embeded into the commercial FEM software MARC as a user’s subroutine. A tensile plane strain specimen with initial shape imperfection on its upper bound which was first analyzed by Tvergaard is investigated through the elasto-plastic damage model and Mises elasto-plastic model，respectively. It is shown that the shear band development is only found in Gurson elasto-plastic damage model. Shear band formation due to void nucleation and growth in a plane stress specimen of homogeneous geo-material with one defect element subjected to uniaxial compression is 2003年12月8日收到初稿，2004年2月8日收到修改稿。