Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 8
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In 1791 a new system of unitswas recommended to the French Academy of Sciences, including a unit thatwas the mass of a declared volume of distilled water in vacuo at the freezingpoint. This unit was based on natural constants but was not reproducibleenough to keep up with technological advances. Over the next hundred yearsthis definition of a mass unit was refined and a number of weights weremanufactured to have a mass equal to it. In 1879 Johnson Matthey and Co.of London successfully cast an ingot of an alloy of platinum and iridium,a highly stable material.
The water definition was abandoned and theplatinum-iridium weight became the standard kilogram (known as theMassInternational Prototype of the Kilogram). In 1889 forty copies of the kilogramwere commissioned and distributed to the major NMIs to be their primarystandard. The UK received Kilogram 18, which is now held at NPL (seeFigure 2.4). The International Prototype of the Kilogram is made of an alloyof 90% platinum and 10% iridium and is held at the Bureau International desPoids et Mesures (BIPM) in Paris, France.
A thorough treatise on massmetrology is given in chapter 10.Whereas the definition of length is given in terms of fundamental physical constants, and its realization is in terms of quantum mechanical effects,mass does not have these desirable properties. All mass measurements aretraced back to a macroscopic physical object. The main problem witha physical object as a base unit realization is that its mass could change due toloss of material or contamination from the surrounding environment. TheInternational Prototype Kilogram’s mass could be slightly greater or lesstoday than it was when it was made in 1884 but there is no way of provingthis [10].
It is also possible that a physical object could be lost or damaged.For these reasons there is considerable effort worldwide to re-define mass interms of fundamental physical constants [11,12]. The front-runners at thetime of writing are the Watt balance (based on electrical measurements thatFIGURE 2.4 Kilogram 18 held at the NPL, UK.1112C H A P T ER 2 : Some basics of measurementcan be realized in terms of Plank’s constant and the charge on an electron[13]) and the Avogadro method (based on counting the number of atoms ina sphere of pure silicon and determining the Avogadro constant [14]); moremethods are described in section 10.1.6. As with the metre, it is easy todefine a standard (for example, mass as a number of atoms) but as long as itcannot be reproduced better than the current method, a re-definition, evenusing well-defined physical constants, does not make sense.On the MNTscale, masses can become very small and difficult to handle.This makes them difficult to manipulate, clean, and ultimately calibrate.These difficulties are discussed in the following section, which considersmasses as force production mechanisms.2.5 ForceThe SI unit of force, a derived unit, is the newton – one newton is defined asthe force required to accelerate a mass of one kilogram at a rate of one metreper second, per second.
The accurate measurement of force is vital in manyMNT areas, for example the force exerted by an atomic force microscope ona surface (see section 7.3.5), the thrust exerted by an ion thrust space propulsion system [15] or the surface forces that can hamper the operation ofdevices based on microelectromechanical systems (MEMS) [16].Conventionally, force is measured using strain gauges, resonant structures and loadcells [17].
The calibration of such devices is carried out bycomparison to a weight. If the local acceleration due to gravity is known, thedownward force generated by a weight of known mass can be calculated. Thisis the principle behind deadweight force standard machines – the mass values oftheir internal weights are adjusted so that, at a specific location, they generateparticular forces.
At NPL, gravitational acceleration is 9.81182 m$s2, soa steel weight with a mass of 101.9332 kg will generate a downward forceof approximately 1 kN when suspended in air. Forces in the meganewtonrange (the capacity of the largest deadweight machines) tend to be generated hydraulically – oil at a known pressure pushes on a piston of knownsize to generate a known force [18].When measuring forces on the MNT scale, different measurement principles are applied compared to the measurement of macroscale forces. As themasses used for deadweight force standards decrease, their relative uncertainty of measurement increases.
For example at NPL a 1 kg mass can bemeasured with a standard uncertainty of 1 mg, or 1 part in 109. However, a 1 mgmass can only be measured with a standard uncertainty of, once again, 1 mg, or1 part in 103, a large difference in relative uncertainty. This undesiredAnglescaling effect of mass measurements is due to the limitations of theinstrumentation used and the small physical size of the masses.
Suchsmall masses are difficult to handle and attract contamination easily(typically dust particles have masses ranging from nanograms to milligrams). The limitation also arises because the dominant forces in themeasurement are those other than gravitational forces. Figure 10.1 inchapter 10 shows the effects of the sort of forces that are dominant ininteractions on the MNT scale. Therefore, when measuring force fromaround 1 mN or lower, alternative methods to mass comparison are used,for example, the deflection of a spring with a known spring constant.Chapter 10 details methods that are commonly used for measuring theforces encountered in MNT devices along with a description of endeavoursaround the world to ensure the traceability of such measurements.2.6 AngleThe SI regards angle as a dimensionless quantity (also called a quantity ofdimension one).
It is one of a few cases where a name is given to the unit one,in order to facilitate the identification of the quantity involved. The namesgiven for the quantity angle are radian (plane angle) and steradian (solidangle). The radian is defined with respect to a circle and is the angle subtended by an arc of a circle equal to the radius (approximately 57.2958 ).For practical angle measurement, however, the sexagesimal (degrees,minutes, seconds) system of units, which date back to the Babylonian civilization, is used almost exclusively [19].
The centesimal system introducedby Lagrange towards the end of the eighteenth century is rarely used.Other units referred to in this section require either a material artefact(for example, mass) or a natural standard (for example, length). No ultimatestandard is required for angle measurement since any angle can be established by appropriate sub-division of the circle. A circle can only have 360 .In practice basic standards for angle measurement either depend on theaccurate division of a circle or the generation of an angle from two knownlengths. Instruments that rely on the principle of sub-division includeprecision index tables, rotary tables, polygons and angular gratings [19].Instruments that rely on the ratio of two lengths include angular interferometers (see section 5.2.9), sine bars, sine tables and small angle generators.Small changes in angle are detected by an autocollimator [20] used inconjunction with a flat mirror mounted on the item under test, for examplea machine tool.
Modern autocollimators give a direct digital readout of angularposition. The combination of a precision polygon and two autocollimators1314C H A P T ER 2 : Some basics of measurementenables the transfer of high accuracy in small angle measurement to thesame accuracy in large angles, using the closing principle that all anglesadd up to 360 .Sometimes angle measurement needs to be gravity-referenced and in thiscase use is made of levels. Levels can be based either on a liquid-filled vial oron a pendulum and ancillary sensing system.2.7 TraceabilityThe concept of traceability is one of the most fundamental in metrology andis the basis upon which all measurements can be claimed to be accurate.Traceability is defined as follows:Traceability is the property of the result of a measurement whereby itcan be related to stated references, usually national or internationalstandards, through a documented unbroken chain of comparisons allhaving stated uncertainties.
[21]To take an example, consider the measurement of surface profile usinga stylus instrument (see section 6.6.1). A basic stylus instrument measuresthe topography of a surface by measuring the displacement of a stylus as ittraverses the surface. So, it is important to ensure that the displacementmeasurement is ‘correct’.
To ensure this, the displacement-measuringsystem must be checked or calibrated against a more accurate displacementmeasuring system. This calibration is carried out by measuring a calibratedstep height artefact (known as a transfer artefact). Let us suppose that themore accurate instrument measures the displacement of the step using anoptical interferometer with a laser source. This laser source is calibratedagainst the iodine-stabilized laser that realises the definition of the metre,and an unbroken chain of comparisons has been ensured. As we move downthe chain from the definition of the metre to the stylus instrument that weare calibrating, the accuracy of the measurements usually decreases.It is important to note the last part of the definition of traceability thatstates all having stated uncertainties.
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