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1、附录A论述压痕测试法和原子力显微镜的SI可跟踪力计量学摘要:本文论述压痕测现状试法和原子力显微镜(AFM)的微小力计量学的现状并特别针对全国科学与技术研究会(NIST)提出的新的电力和自重力的标准。这些标准提供计量学的基础结构所以压痕测试法和原子力显微镜的使用者可根据国际上认可的计量单位表示的力对材料,工作表面和纳米设备进行微机械测试。关键字:原子力显微镜,压痕测试法,微小力校准1.SI计量学和可追踪性国际单位系统(SI)的计量等级是很简单的。国家计量院(NMIS)维持着反映实际物体计量单位的原始标准。NMIS校准secondary artifacts.这些secondary artifact

2、s和transfer artefacts传播与NMI,而且校准其他的传感器和仪器,他们反过来校准其他的传感器和仪器。每个校准与原始标准有换算关系,在传递结束后为了确保单位的实际值,随着单位从一个设备传到另一个设备的误差在每个阶段被估计。这是SI传递的基本。力派生与国际单位制,这意味着力的原始标准起源于由SI的基本单位(kg,m,s)组成的牛顿的定义。力的原始标准是由质量artefact与适当的长度和时间的单位表示的当地的地心引力组成的。这类里是根据重力的名称而来的,很多根据重力另传感器测力的机器被发明了。事实上,由于测试材料和工业产品时力的测量标准的原因,NIST仍保持着静重式力标准机,在美国

3、这些机器在力的计量等级上起着重要的作用。同样,世界上很多其他国家计量院(NMIS)留用重力测量设备。对这些设备进行相互比较,即几个NMI轮流校准相同高稳定度的secondary artifact 形成相互承认的排列,这些排列保证了统一的国际测量标准而且给商业和贸易带来了方便。2.微机械测试,标准和力的计量法微机械的特性测试技术的应用刺激了压痕测试法和原子力显微镜的测量法和校准标准的发展,如附着力,硬度 弹性模量,薄膜,涂料,微机电设备和系统,纳米材料的扩展阵列。这些机械特性大部分是由压痕测试法和原子力显微镜对力和位移的测量测出来的,利用摩擦计和张力计研制出了功能相似的测量法2.1国际标准近几年

4、,压痕技术扩展到更小的力和位移的领域。通过分析这些力-位移数据可以测定出样品的硬度和弹性模量。这种测量方式通常被称为instrumented或压痕深度检测。当用于微小力和深度测量时这种技术被称为纳米压痕测试。位移分辨率大于1nm,力的分辨率大于1µN是纳米压痕测试的特征。仪器和数据分析的进步另纳米压痕测试法能测量材料非常细微的力学性能,特别是对薄膜和涂料如汽车涂料,增加切断刀具寿命的TIN涂料,计算机硬盘驱动曲面。如果厂家生产用一种纳米压痕测试法规格测量的刀具的话市场上会出现混乱,因为目前只有一种国际测试标准(美国没有)使用于纳米压痕测试,而且检验这种测试仪器的程序目前还不充分。有一

5、种被认可的国际标准(ISO/DIS 14577-1,2,3)称为金属材料-硬度和材料参数的压痕测试,但它只使用于大批材料的测试。涉及薄膜测试的文件的第四部分(ISO/DIS 14577-4)还没有被认可。2.2微机械的计量学受到以上标准化工作的影响NMI开始研究国际单位制框架内可追踪的可以测量和传播微小力的方法。在这里我们对这些工作做简单的综述。本文仅仅是为了提供目前技术发展水平的情况。从纳到微级的我们的工作,用静电力秤(EFB)得到的10-8 N 到 104 N的力已经得到NIST的认证而且用于校准secondary force artifact基于Veeco,Inc.,而且随后被Asylu

6、m Research Molecular Force Probe所用,因此说明原子力显微镜材料测试仪器的校准是符合国际单位制的。除了美国,在英国的国家物理实验所研制出了另一个静电力秤系统,此系统可以令NIST EFB得到改进,预计2005年的九月可以实现。同时,德国的PTB也研制了cantilever-type force cells 基于压阻应变传感,这些设备与测力计和刚度计一样得到了校准。在更高的量级,从几百微牛顿到几百万牛顿,NMI正研制基于自重力的原始力校准系统。PTB利用传统的电子秤的秤盘上的精确的压力传感器。两个系统已经宣布,这种秤是根据力的范围进行分类。NIST利用重力对力传感器

7、进行校准,这个传感器是我们曾用以证明压痕力的力的单元,我们也建立和测试了自己设计的基于电容的力单元。3NIST的SI可传递的微小力的等级为了利用国际单位制对牛顿的定义了解力的单位,力必须由国际单位制的基本单位组成的单位来表示。从基本单位获得单位通常是不确定度最小的途径,但这并不是唯一的方法,例如,电子力可以由国际单位制的长度单位结合适当的电的单位测量。电的单位从国际单位制获得,也可以由基于约瑟夫效应和量子霍而效应的伏特和欧姆表示,所以它可以由很多种不确定度很小的力学测量方法,这与质量的情况不一样,力的电子显示方法有用瓦特秤的电磁力和用伏特秤的电工力。虽然这些秤实验最初是想用力学量单位对电子单位

8、下定义,但是量为基础的电子标准的可行性让这些秤实验代替了公斤。承认基本的计量学趋势,基于电子力的原始标准的发展曾是NIST做小力计量学实验室的主要的目标。图1用基于小于10-5N的力的由长度,电容,电压组成的单位表示的力表示了NIST微小力计量学的计量等级。我们从对电子力的描述和如何与自重力核对考试。接下来的是关于能连接电子力的力的单位的传播。最后我们用对更大规模的自重力系统的简单论述和它的为证实从压痕检测仪器测出的力校准传播导出量的使用下结论。3.1 10-8N到10-4N的微小力的原始标准:NIST的电子力秤。在NIST,我们从电力学了解了微小力的原始标准,而且为了用电容器的布置了解力建造

9、了一系列不断精致的系统。根据图2,图3的NIST电子力秤和EFB可以对原始标准说明,从图中可以看到,这个秤安装在直径大约为1m的专门设计的真空室里的专用的安装台上。EFB安装在安装台上的三条腿上,三条腿从真空室地板伸出通过可伸缩的到空的凸缘的风箱。这些安装台的腿由真空室下面的花岗岩支撑,如图3所示。因而,真空室和设备是通过风箱接触的。这个实验可以在空气或惰性气体里进行,但是在真空中进行可以避免空气的对流对敏感的秤的悬架的影响。而且在真空中进行实验减小折射量的调整和另电容的间隙保持不变。EFB由一个电子力发生器组成,它能沿垂直轴移动(Z轴);根据当地的地心引力调整,当电压传到一对同轴的圆柱体时力

10、就会产生。当内部的圆柱体沿Z轴移动时外部的高电压圆柱体会固定不动,改变重叠的程度。电容的大小随着两个圆柱体的重叠程度而变化。因为同轴的布置,内表面的电容倾斜度完全对称,所以产生的电子力指向Z轴,为了保证轴的对称,内部的圆柱体悬挂在有一系列弯曲轴的平衡力平行四边形连接装置。这个装置提供准确运动的轴,方便地根据重力进行调整,对非轴向力不敏感,做涨力实验时轴向硬度达到0.001Nm-1。3.2用EFB校准力在传统的力的等级,测力传感器是与应变仪安装的,应变仪使力的变化转换成电阻的变化。在这个力的等级,AFM的悬臂作成压阻的模式,这样就成了应变仪的半导体,所以这些悬臂功能上与测力传感器是一样的。压电A

11、FM悬臂不是规范,很少的样本能够通过商业获取。但这样的装置可以通过使用常用的半导体制造技术获得。附录Review of SI traceable force metrology for instrumented indentation and atomic force microscopy and Douglas T SmithAbstract:This paper reviews the current status of small force metrology for quantitative instrumented indentation and atomic force micr

12、oscopy (AFM), and in particular focuses on new electrical and deadweight standards of force developed at the National Institute of Standards and Technology (NIST). These standards provide metrological infrastructure so that users of instrumented indentation and AFM can achieve quantitative nanomecha

13、nical testing of materials, engineered surfaces and micro and nanoscale devices in terms of forces that are expressed in internationally accepted units of measure with quantified uncertainty. Keywords: atomic force microscopy, instrumented indentation, micronewton/nanonewton force calibration1. SI m

14、etrology and traceabilityThe hierarchy of metrology within the International Systemof Units (SI) is conceptually simple: primarystandards thatreflect a practical physical realization of a unit of measure aremaintained bynationalmeasurement institutes (NMIs) wherethey are used to calibrate secondary

15、artefacts; these secondaryor transfer artefacts are disseminated from the NMI and usedto calibrate other sensors or instruments, which in turn areused to calibrate yet other sensors and instruments. Eachcalibration is a comparison back to the primary standard, andtheuncertainty associated with propa

16、gating the unit from onedevice to the next is evaluated at each step in order to placebounds on the actual value of the unit after its propagationthrough this chain. This is the essence of the SI traceability.Force is a derived unit in the SI, meaning that primarystandards of force are derived from

17、the definition of the newtonusing a combination of base SI units (kg, m and s). Typically,a primary standard of force is fashioned from a traceable massartefact combined with a suitably accurate estimate of the localgravity expressed in appropriate units of length and time. Thistype of force is refe

18、rred to by the name deadweight, and avariety of schemes and machines have been devised that usedeadweights to apply known forces to sensors. In fact, becauseof the importance of force measurement standards to the testingof materials and manufactured products, deadweight machinesare maintained at NIS

19、T 1, and these machines sit atop thehierarchy of force metrology in the United States. Likewise,many other NMIs around the globe maintain deadweightforce calibration facilities. Round robin comparisons betweenfacilities, where several NMIs take turns calibrating thesame highly stable secondary artef

20、act, form the basis ofmutual recognition arrangements. 2. Nanomechanical testing, standards andforce metrologyThe development ofmeasurement and calibration standards forinstrumented indentation and AFM is largely motivated by thegrowing use of nanomechanical testing to evaluate propertiessuch as adh

21、esion, hardness and elastic modulus of chemicallyengineered surfaces, thin films and coatings,microelectromechanicaldevices and systems and an expanding arrayof nanostructured materials 2. Most of these mechanicalproperties are evaluated from force and displacementmeasurements recorded using either

22、instrumented indentationor atomic force microscope (AFM)-based materials testinginstruments. Functionally similar measurements (e.g., forcedisplacement data) are also made using surface forcesapparatus 3, tribometers and tensiometers, as well as otherinstruments 4.2.1. International standardsIn rece

23、nt years, indentation techniques have been extendedto significantly smaller applied forces and displacements.Analyses of these forcedisplacement data permit thedetermination of both the specimen hardness and the elasticmodulus 5. This type of measurement is commonly referredto as instrumented or dep

24、th-sensing indentation. When usedat small forces and depths, the technique is referred to asnanoindentation. Displacement resolution greater than 1 nmand force resolution larger than 1 N is the characteristicof nanoindentation, with mechanical property informationobtained at indentation depths as sm

25、all as 10 nm.Improvements in instrumentation and data analysis havemade nanoindentation the method of choice for measuringthe mechanical properties of very small volumes of material,particularly for thin films and coatings such as auto paint,TiN coatings for extending the life of cutting tools andsu

26、rface films on computer hard disk drive surfaces. Problemsarise in the marketplace if a manufacturer tries to makeproperties measured by nanoindentation part of a productspecification, because there is currently only one internationalstandard test method (and none in the United States) forperforming

27、 the nanoindentation tests, and procedures forverifying the performance of such testing machines arepresently inadequate. There is an approved internationalstandard in ISO (ISO/DIS 145771, 2, 3) entitled metallicmaterialsinstrumented indentation test for hardness andmaterials parameters but it deals

28、 solelywith the testing of bulkmaterials. A fourth part of the document (ISO/DIS 145774),which deals specifically with the testing of thin films.2.2. Fundamental force metrology for nanomechanicsMotivated by the above standards work, the NMIs have startedto investigate methods for realizing and diss

29、eminating smallforce in a fashion that is traceable within the establishedframework of SI units. We offer a brief overview of theseefforts in this section. The review is not complete and ismerely intended to provide an indication of the current stateof the art.Beginning with our own work in the nano

30、 to micro range,a primary realization of force in the regime between 108 Nand 104 N based on an electrostatic force balance (EFB)has been demonstrated at NIST 11 and used to calibratea secondary force artefact based on a Veeco, Inc.1, contactmode piezolever AFM cantilever 12. This secondary artefact

31、was subsequently employed to calibrate an Asylum ResearchMolecular Force Probe, thereby demonstrating the first suchcalibration of an AFM materials test instrument to preserve anunbroken link to the SI 13.Outside the United States, another electrostatic balancesystem has been proposed and designed a

32、t the NationalPhysical Laboratory (NPL) in the United Kingdom. Thisbalance promises improvements in resolution over the NIST1 Commercial equipment and materials are identified in order to adequatelyspecify certain procedures. In no case does such identification implyrecommendation or endorsement by

33、the National Institute of Standards andTechnology, nor does it imply that the materials or equipment identified arenecessarily the best available for the purpose.EFB 14 and is expected to be operational in September 2005.Also at NPL, work has been reported on a spring constantartefact 15, and a micr

34、o-electromechanical spring balancethat may yield a traceable spring constant 16. Meanwhile,the Physikalisch-Technische Bundesanstalt (PTB) in Germanyhas developed active cantilever-type force cells based onpiezoresistive strain sensing 17. These devices have beencalibrated both as force cells and st

35、iffness artefacts.At larger force levels, ranging from hundreds ofmicronewtons up to several millinewtons, NMIs aredeveloping primary force calibration systems based ondeadweights. PTB uses a precision scan stage to press sensorsagainst the weighing pan of a conventional electromagneticcompensation

36、balance 18. Two different systems have beenreported, the size of balance employed depending on the forcerange of interest 19. NIST has used wire deadweights tocalibrate a modified force transducer as a transfer standardfor instrumented indentation 20. This sensor is one of asmall number of force cel

37、ls that we have attempted to use forindentation force verification 21. We have also built andtested capacitance-based force cells of our own design 22.3. SI traceable hierarchy of small force at NISTIn order to realize the unit of force using the SI definition ofthe newton, the observed force must b

38、e expressed in termsof measured quantities that are themselves expressed in termsof some combination of the SI base units. Deriving a unitfrom realizations of the base units is typically the path ofleast uncertainty, but this need not always be the case. Forinstance, electrical forces may be measure

39、d in terms of the SIunit of length in combination with appropriate electrical units.Electrical units are themselves derived units in the SI, butthey may also be linked to practical representations of the voltand ohm based on the Josephson and quantized Hall effects.Because of this, theymay be measur

40、ed through a large dynamicrange with little loss of relative uncertainty, unlike the situationwith mass. Electrical realizations of force may be achievedusing electromagnetic forces, along the lines of watt balanceexperiments 23, 24 or using electrostatic forces, along thelines of volt balance exper

41、iments 25. Although such balanceexperiments were originally conceived to define electricalunits in terms of SI mechanical quantities, the availability ofquantum-based electrical standards has placed these balanceexperiments at the forefront of efforts to replace the kilogram26. Acknowledging this tr

42、end in fundamental metrology, thedevelopment of a primary standard based on electrical forcehas been a central goal of the NIST small force metrologylaboratory from its conception 27.The block diagram of figure 1 lays out a proposedhierarchy of NIST small force metrology, with a primaryrealization o

43、f force based on a combination of length,capacitance and voltage for forces below 105 N.We begin thesection with a description of the electrostatic force realizationand how it is checked against the deadweight force. Theproblem of disseminating the unit of force through appropriatetransfer artefacts

44、 that can interface with the electrostatic forceis treated next. Finally, we conclude the section with a briefreview of our larger scale deadweight system and its use inthe calibration of a transfer artefact for the verification of theforce readout of instrumented indentation equipment.3.1. A primar

45、y standard of small force between 108 N and104 N: the NIST electrostatic force balanceAt NIST, we realize a primary standard of small force fromelectrostatics, and have constructed a series of increasinglyrefined systems to realize force using a coaxial cylindricalcapacitor arrangement 11, 28. The p

46、resent version of thisprimary standard, referred to as the NIST electrostatic forcebalance, or simply the EFB, is shown in the photo of figure 2and schematically in the drawing of figure 3.As shown in the photo and drawing, the balance has beenassembled on a custom optical table in a specially desig

47、ned freestanding vacuum chamber approximately 1min diameter. Theoptical table on which the EFB is mounted sits on three legsthat protrude from the chamber floor through flexible bellowsthat terminate in blank flanges. These table legs are supportedfrom below the chamber by a large granite block, as

48、indicatedschematically in figure 3. Thus, the only contact between thevacuum chamber and the experiment is through the relativelycompliant bellows. The experiment can operate in air, or withanother inert gas, but vacuum operation eliminates convectiveair currents that tend to perturb the large and c

49、ompliant balancesuspension. Also, operation in vacuum eliminates the need tocorrect for the index of refraction in the interferometer anddielectric constant of the gap in the capacitance.Functionally, the EFB consists of an electrostatic forcegenerator that acts along a vertical axis (the z-directio

50、n) alignedwith the local gravity to within a few milliradians 11. Forcesare generated when voltages are applied to the pair of nested,coaxial cylinders (items 3 and 4, figure 3). The outer highvoltagecylinder is fixed while the inner electrically-groundedcylinder is free to translate along the z-axi

51、s, varying thedegree of the overlap. The capacitance of this geometryis in principle a linear function of the overlap of the twocylinders. For a perfectly coaxial arrangement, the in-planecapacitance gradient possesses radial symmetry, so that the3.2. Force calibration using the EFBAt conventional f

52、orce levels, force cells are equipped withstrain gauge transducers that convert changes in mechanicalforce to changes in electrical resistance. At the forcelevels considered here, AFM cantilevers can be dopedwith piezoresistive patterns that achieve the semiconductorequivalent of a strain gauge tran

53、sducer, so that these cantileversare functionally equivalent to a force cell. Piezoresistive AFMcantilevers are not the norm and few examples are availablecommercially, but such devices can be made using commonsemiconductor fabrication techniquesReferences1 Jabbour Z J and Yaniv S L 2001 The kilogra

54、m and themeasurements of mass and force J. Res. Natl Inst. Stand.Technol. 106 252 Bhushan B (ed) 2004 Handbook of Nanotechnology(Heidelberg: Springer)3 Israelachvili J 1992 Intermolecular and Surface Forces2nd edn (Boston, MA: Academic)4 Joyce S A and Houston J E 1991 A new force sensorincorporating

55、 force-feedback control for interfacial forcemicroscopy Rev. Sci. Instrum. 62 7105 Oliver W C and Pharr G M 1992 An improved technique fordetermining hardness and elastic modulus using load anddisplacement sensing indentation experiments J. Mater. Res.77 15646 VanLandingham M R, Villarrubia J S and

56、Meyers G F 2000Nanoindentation of polymers: an overview ACS Polym.Preprints 41 14127 Hsu S 2004 Private communication, Chair VAMAS TWG 29,see the VAMAS website 8 Lawall J and Kessler E 2000 Michlelson interferometry with10 pm accuracy Rev. Sci. Instrum. 71 26699 Villarrubia J 1996 Scann

57、ed probe microscope tipcharacterization without calibrated tip characterizers J. Vac.Sci. Technol. B 14 151810 ISO group TC 164/SC 3/WG 1 and ASTM E28.06.11 2002Metallic MaterialsInstrumented Indentation Test forHardness and Materials Parameters ISO/DIS 14577-1, 2,and 311 Newell D B, Kramar J A, Pra

58、tt J R, Smith D T andWilliams E R 2003 The NIST microforce realization andmeasurement project IEEE Trans. Instrum. Meas. 52 50812 Pratt J R, Newell D B, Kramar J A, Mulholland J andWhitenton E 2003 Probe-force calibration experimentsusing the NIST electrostatic force balance Proc. AmericanSociety fo

59、r Precision Engineering 2003 Winter TopicalMeeting (University of Florida) p 6413 Pratt J R, Smith D T, Newell D B, Kramar J A andWhitenton E 2004 Progress towards Systeme InternationaldUnites traceable force metrology for nanomechanicsJ. Mater. Res. 19 36614 Leach R K, Oldfield S, Awan S A, Blackburn J andWilliams J M 2004 Design of

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