Принципы нанометрологии, страница 67

Mechatronics 5 199–211[28] Burnham N A, Colton R J, Pollock H M 1993 Interpretation of force curvesin force microscopy Nanotechnology 4 64–80[29] Tabor D 1991 Gases, liquids and solids; and other states of matter (Cambridge University Press: Cambridge)[30] Lamoreaux S K 1997 Demonstration of the Casimir force in the 0.6 to 6 mmrange Phys. Rev. Lett. 78 5–8[31] Pratt J R, Smith D T, Newell D B, Kramar J A, Whitenton E 2004 Progresstoward Système International d’Unités traceable force metrology for nanomechanics J. Mat.

Res. 19 366–379[32] Choi I-M, Kim M-S, Woo S-Y, Kim S-H2004 Parallelism error analysis andcompensation for micro-force measurement Meas. Sci. Technol. 15 237–243[33] Nesterov V 2007 Facility and methods for the measurement of micro andnano forces in the range below 105 N with a resolution of 1012 N(development concept) Meas. Sci. Technol. 18 360–366[34] Leach R K, Chetwynd D G, Blunt L A, Haycocks J, Harris P M, Jackson K,Oldfield S, Reilly S 2006 Recent advances in traceable nanoscale dimensionand force metrology in the UK Meas.

Sci. Technol. 17 467–476.[35] Jones C W, Kramar J A, Davidson S, Leach R K, Pratt J R 2008 Comparison ofNIST SI force scale to NPL SI mass scale Proc. ASPE, Oregon, USA[36] Gates R S, Pratt J R 2006 Prototype cantilevers for SI-traceable nanonewtonforce calibration Meas. Sci. Technol. 17 2852–2860[37] Tortonese M, Barrett R C, Quate C F 1993 Atomic resolution with an atomicforce microscope using piezoresistive detection Appl.

Phys. Lett. 62 834–836[38] Cumpson P J, Clifford C A, Hedley J 2004 Quantitative analytical atomicforce microscopy: a cantilever reference device for easy and accurate AFMspring-constant calibration Meas. Sci. Technol. 15 1337–1346309310C H A P T ER 1 0: Mass and force measurement[39] Pratt J R, Kramar J A, Shaw G, Gates R, Rice P, Moreland J 2006 Newreference standards and artifacts for nanoscale property characterizationProc. 11th NSTI Nanotech, Boston, USA, 1st–5th June[40] Behrens I, Doering L, Peiner E 2003 Piezoresistive cantilever as portablemicro force calibration standard J.

Micromech. Microeng. 13 S171–S177[41] Cumpson P J, Hedley J, Zhdan P 2003 Accurate force measurement in theatomic force microscope: a microfabricated array of reference springs for easycantilever calibration Nanotechnology 14 918–924[42] Cumpson P J, Hedley J 2003 Accurate analytical measurements in theatomic force microscope: a microfabricated spring constant standard potentially traceable to the SI Nanotechnology 14 1279–1288[43] Cumpson P J, Hedley J, Clifford C A 2005 Microelectromechanical device forlateral force calibration in the atomic force microscope: Lateral electricalnanobalance J. Vac.

Sci. Technol. B 23 1992–1997[44] Stalder A, Dürig U 1995 Nanoguitar: Oscillating string as force sensor Rev.Sci. Instrum. 66 3576–3579[45] Fukuzawa K, Ando T, Shibamoto M, Mitsuya Y, Zhang H 2006 Monolithicallyfabricated double-ended tuning-fork-based force sensor J. Appl. Phys. 99 094901[46] Sazonova V, Yaish Y, Üstünel H, Roundy D, Arias T A, McEuen P L 2004 Atunable carbon nanotube electromechanical oscillator Nature 431 284–287[47] Nesterov V, Mueller M, Fremin L L, Brand U 2009 A new facility to realizea nanonewton force standard based on electrostatic methods Metrologia 46277–282[48] Argento C, French R H 1996 Parametric tip model and force-distance relation for Hamaker constant determination from atomic force microscopyJ. Appl.

Phys. 80 6081–6090[49] Sparnaay M J 1958 Measurement of attractive forces between flat platesPhysica 24 751–764[50] Oberhauser A, Hansma P, Carrion-Vazquez M, Fernandez J M 2001 Stepwiseunfolding of titin under force-clamp atomic force microscopy PNAS 98 468–472[51] Oberhauser A F, Marszalek P E, Erickson H P, Fernandez J M 1998 Themolecular elasticity of the extracellular matrix protein tenascin Nature 393181–185[52] Fulton A, Isaacs W 1991 Titin, a huge, elastic sarcomeric protein witha probable role in morphogenesis Bioassays 13 157–161[53] Degertekin F L, Hadimioglu B, Sulchek T, Quate C F 2001 Actuation andcharacterization of atomic force microscope cantilevers in fluids by acousticradiation pressure Appl.

Phys. Lett. 78 1628–1630[54] Dushkin C D, Yoshimura H, Nagayama K 1996 Note - Direct measurementof nanonewton capillary forces J. Colloid Interface Sci. 181 657–660[55] Choi J-H, Kim M-S, Park Y-K 2007 Quantum-based mechanical force realization in the piconewton range Appl. Phys. Lett. 90 90 073117Appendix ASI units of measurementand their realization at NPLQuantityUnit (symbol)DefinitionRealisationTimesecond (s)The second is the durationof 9 192 631 770 periodsof the radiationcorresponding to thetransition between the twohyperfine levels of theground state of thecaesium 133 atom.Lengthmetre (m)The metre is the length ofthe path travelled by lightin a vacuum during a timeinterval of 1/299 792 458of a second.Masskilogram (kg)The kilogram is the unit ofmass; it is equal to themass of the internationalprototype of the kilogram.The second is realized byprimary caesiumfrequency standards toabout 2 parts in 1015. Themajority are traditionalcaesium-beam designsbut the latest use lasers tocontrol and detect theatoms.At NPL the metre iscurrently realized throughthe wavelength of the633 nm radiation from aniodine-stabilized heliumneon laser, with anuncertainty of about3 parts in 1011.Kilogram masses and submultiples of 1 kg, madefrom similar materials,may be compared on theNPL precision balance to1 mg.(Continued)311312Appendix AQuantityUnit (symbol)DefinitionRealisationElectric currentampere (A)The ampere is thatconstant current which, ifmaintained in two straightparallel conductors ofinfinite length, of negligiblecircular cross-section, andplaced 1 m apart invacuum, would producebetween these conductorsa force equal to 2 10 7N per metre of their length.Thermodynamictemperaturekelvin (K)The kelvin is the fraction of1/273.16 of thethermodynamictemperature of the triplepoint of water.Amount of substancemole (mol)The mole is the amount ofsubstance of a system thatcontains as manyelementary entities asthere are atoms in0.012 kg of carbon 12.The ampere is realized, viathe watt, to about 0.08 mAusing NPL’s currentweighing and induced-emfmethod.

The ohm isrealized at NPL viaa Thomson-Lambertcalculable capacitor toabout 0.05 mU andmaintained via thequantized Hall resistanceto about 0.01 mU. The voltis maintained to 0.01 mVusing the Josephsoneffects ofsuperconductivity.Triple point of water cellsare used at NPL to realizethe triple pointtemperature witha reproducibility of 0.1 mKvia the InternationalTemperature Scale interms of which platinumresistance and otherthermometers arecalibrated within the range0.65 K to 3000 K.Measurements of amountof substance do notrequire the mole to berealized directly from itsdefinition. They are madeusing primary methodsthat give results expressedin moles by combiningmeasurements made inother SI units. The numberof entities in one mole isknown to 1 part in 107.(Continued)Appendix AQuantityUnit (symbol)DefinitionRealisationLuminous intensitycandela (cd)The candela is theluminous intensity, ina given direction, ofa source that emitsmonochromaticradiation of frequency540 1012 Hz andthat has a radiantintensity in that directionof 1/683 W$sr 1.The candela has beenrealized at NPL with anuncertainty of 0.02 %,using a cryogenicradiometer that equatesthe heating effect of opticalradiation with that ofelectric power.

A solidstate photometer has beendeveloped to evaluate lightof other frequenciesaccording to the spectralluminous efficiency curveof the human eye with anuncertainty of 0.1 %.313This page intentionally left blankAppendix BSI derived unitsExamples of SI derived units expressed in terms of baseunitsDerived quantitySI derived unit nameSymbolAreaVolumeSpeed, velocityAccelerationWavenumberDensityCurrent densityMagnetic field strengthConcentrationLuminanceRefractive indexsquare metrecubic metremetre per secondmetre per second squaredreciprocal metrekilogram per cubic metreampere per square metreampere per metremole per cubic metrecandela per square metreunitym2m3m$s 1m$s 2m 1kg$m 3A$m 2A$m 1mol$m 3cd$m 21SI derived units with special names and symbolsDerived quantitySI derivedunit nameSymbolPlane angleSolid angleFrequencyForceradiansteradianhertznewtonradsrHzNIn terms ofother unitsIn terms ofbase units11s 1m$kg$s2(Continued)315316Appendix BDerived quantitySI derivedunit nameSymbolPressureEnergyPowerElectric chargeElectric potential differenceCapacitanceElectric resistanceElectric conductanceMagnetic fluxMagnetic flux densityInductanceLuminous fluxIlluminanceActivity (of a radionuclide)Absorbed dosepascaljoulewattcoulombvoltfaradohmsiemensweberteslahenrylumenluxbecquerelgrayPaJWCVFWSWbTHlmlxBqGyIn terms ofother unitsIn terms ofbase unitsN$m 2N$mJ$s 1m 1$kg$s 2m2$kg$s 2m2$kg$s 3s$Am2$kg$s 3$A 1m 2$kg 1$s4$A2m2$kg$s 3$A 1m 2$kg 1$s 3$Am2$kg$s 2$A 1kg$s 2$A 1m2$kg$s 2$A 2Cdcd$m 2s 1m2$s 2W$A 1C$V 1V$A 1A$V 1V$sWb$m 2Wb$A 1cd$srlm$m 2J$kg12IndexAAbbe criterion, 134Abbe error, 40, 41, 92, 94, 274,283, 284Abbe offset, 40, 107, 283Abbe Principle, 40, 41, 82, 275absorption index, 130accuracy, 15, 16acoustic noise, 51acousto-optic frequency shifter,88active vibration isolation, 51ADC.

See analogue-to-digitalconverteradded-mass method, 192adhesion force, 190, 198AFM. See atomic force microscopeamplitude distribution curve, 222,226amplitude-wavelength space, 117analogue probe, 266angle, 13angular distribution of scatter,153angular interferometer, 98angular power spectrum, 242aperture correction, 78, 81, 127area-integrating, 123areal material ratio, 239, 240, 241areal parameter, 164, 235, 240areal surface texture, 116, 121,159, 229areal topography measuring, 123area-scale fractal complexity,256arithmetic mean of the absoluteheight, 236arithmetic mean peak curvature,250arithmetical mean deviation of theassessed profile, 219ARS.