Принципы нанометрологии, страница 8

In the meantime, it wasfound that the speed of light in a vacuum is constant within all experimentallimits, independent of frequency, intensity, source movement and time. Alsoit became possible to link optical frequencies to the time standard. Thisenabled a redefinition of the metre as [7]:the length of the path travelled by light in a vacuum in a timeinterval of 1/c of a second, where c is the speed of light given by299 792 458 m$s1Together with this definition, a list of reference frequencies was given,with associated uncertainties [8]. These included spectral lamps, forexample. The krypton spectral line was unchanged but it received anattributed uncertainty. More convenient and precise, however, are stabilizedlaser systems. Such a current realization of the metre can have an uncertainty in frequency of one part in 1011.

Figure 2.3 shows an iodine-stabilizedhelium-neon laser held at NPL. This new definition was only possiblebecause it could be realized with a chain of comparisons.As discussed, the speed of light in a vacuum is generally regarded asa universal constant of nature, therefore, making it ideal as the basis fora length standard. The speed of an electromagnetic wave is given byc ¼ nl(2.1)where n is the frequency and l is the wavelength of the radiation.

Therefore,length can be disseminated by measuring frequency or wavelength, usuallyusing either time of flight measurements or interferometry (see chapter 4).Note that length can be considered to be a base quantity that is realized ina manner that is based upon the principles of quantum mechanics. Theemission of electromagnetic waves from an atom (as occurs in a laser – seesection 2.9) is a quantized phenomenon and not subject to change providedcertain conditions are kept constant. This is a highly desirable property ofa base unit definition and realization [9].Note that the modern definition of length has become dependent on thetime definition.

This was proposed earlier; in the seventeenth centuryChristiaan Huygens proposed to define the metre as the length of a bar with910C H A P T ER 2 : Some basics of measurementFIGURE 2.3 An iodine-stabilised helium-neon laser based at NPL, UK.a time of oscillation of one second. However, this failed because of thevariation of local acceleration due to gravity with geographic location. Most ofthe measurements that are described in this book are length measurements.Displacement is a change in length, surface profile is made up of height andlateral displacement, and coordinate measuring machines (CMMs, seechapter 10) measure the three-dimensional geometry of an object.2.4 MassIn 1790, Louis XVI of France commissioned scientists to recommenda consistent system for weights and measures. 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).