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National Measurement Institute

Mass and Related Quantities Research

NMI is responsible for maintaining and disseminating Australia's standard of mass (the kilogram), as well as the following quantities that are derived from or calibrated in terms of the kilogram: density, flow, force, humidity, pressure, viscosity and volume.

Some of our recent research in mass, force, pressure, gas flow and density research is described below.


Redefining the Kilogram through the Avogadro Constant

1 kg silicon sphereThe kilogram is the only remaining fundamental unit within the SI system that is defined in terms of a material artefact (a PtIr cylinder kept in Paris). It is proposed in the medium term to redefine the kilogram in terms of the Avogadro constant NA. By definition an Avogadro number of carbon-12 atoms weigh exactly 12 g, so the kilogram could be defined as the mass of 1000/12 x NA carbon-12 atoms if the Avogadro constant is known with an uncertainty of 0.01 ppm. The Avogadro constant is obtained from the ratio of the molar mass to the mass of an atom. For a crystal, the atomic volume is obtained from the lattice parameter and the number of atoms per unit cell. The atomic mass is then the product of the volume and density.

The preferred method for determination of the Avogadro constant is to use a highly polished 1 kg single crystal silicon sphere manufactured with out of roundness < 40 nm. Silicon is used because of its well-known crystal structure, its stability and its relative ease of use. The volume is determined from the diameter and roundness measurements. Accurate measurement of the mass then allows the density to be measured.

The nominal diameter of a 1 kg Si sphere is 93.6 mm. In order to obtain an uncertainty of 0.01 ppm in volume, the diameter must be known with an uncertainty of 0.3 nm, i.e. within one atom spacing. This requires optical interferometry against a precision etalon using stabilised laser light. The measurements are sensitive to many parameters, particularly temperature and pressure. An instability of range 2 mK will be sufficient to cause the silicon to expand by more than the permitted uncertainty. The refractive index of air and hence the wavelength of the light is sensitive to the air pressure. It is therefore necessary to carry out the measurements in near vacuum conditions (low pressure He).

Monoisotopic Silicon 28 (more than 99.99%) material has been produced in Russia, and then grown into a very high quality crystal boule in Germany, from which two spheres of very high quality (surface finish and roundness) have been produced in Australia by CSIRO – Australian Centre for Precision Optics, with the support of NMI.

Corrections must be applied for surface impurities such as oxide and adsorbed water. Typically silicon has an oxide layer 1 to 2 nm thick, which is a mixture of SiO and SiO2. It is also possible for the surface to adsorb some monolayers of water. A number of the key measurements are made in vacuum. Much of the adsorbed water is removed in vacuum. A further correction must be applied for the difference in bulk modulus between air and vacuum.

The project involves international collaboration between laboratories in Germany, Italy, Belgium, Japan, Australia and the USA. Currently the Avogadro constant is known with an uncertainty of <0.12 ppm. It is hoped that the uncertainty will be reduced to <0.05 ppm in the next five years and eventually <0.01 ppm after a further five years. Before a permanent and absolute of the kilogram is introduced, the relative stability of a silicon sphere and the existing PtIr artefact will be monitored.

Uncertainties in the Silicon Kilogram

The limiting factors currently are:

  • the variability from sample to sample of the isotopic abundances M(Si)
  • the content of impurities and vacancies (n)
  • realisation of accurate density standards (m,V)

The list below gives first the present estimated uncertainty followed by the ultimate uncertainties that can be expected if current methods are pursued to their limits:

  • molar mass: 0.2 ppm to ultimately 0.05 ppm
  • atoms per unit cell: 0.2 ppm to 0.01 ppm
  • mass: 0.05 ppm to 0.01 ppm
  • volume: 0.08 ppm to 0.02 ppm
  • lattice parameter: 0.05 ppm to 0.01 ppm

Magnetic Properties of Weights

For high precision weighing, the magnetic properties of mass standards are quite significant. This has become more important as the new types of mass comparators use magnetic forces whereas the old beam balances were non-magnetic. The magnetic forces that may be generated pose problems in weighing. A requirement of a recent OIML document is that permanent magnetisation and magnetic susceptibility should be measured or known before the standard is calibrated. This is especially important for older weights made when the magnetic properties of the alloys used was not considered to be so important. An investigation on suitable methods to measure these parameters is being carried out.


dead weight force machineRecalibration of Australia's Dead Weight Force Standard

The main primary standard for force in Australia is a dead weight force machine with a capacity of 550 kN. The uncertainty associated with the applied forces in the dead weight force standard is ±20 ppm. In order to maintain the stated uncertainty level, and to provide traceability of the weights to the international kilogram, periodic recalibration of the weights is necessary. Due to the high costs in terms of human resources and machine down-time associated with the dismantling of the machine, the approach adopted is to calibrate the masses and associated parts by weighing in situ using load cells.

The in situ weighing method developed at NMI uses load cells as mass comparators to determine the difference between two nominally equal masses. One is a reference weight of known mass value and the other is the test weight. The mass comparator designed at NMI was verified by comparing two nominally equal masses of about 500 kg each in a force loading test rig. The test results showed that the calculated mass differences agree with the known mass differences to within 2 ppm.


mercury manometerBarometric Pressure Standards

The primary standard for pressure in the region up to 7 MPa in gas has been a mercury manometer. This instrument uses the interferometry of light of known wavelength to measure the difference in heights of the two columns. Because free mercury surfaces are subject to small ripples, even under very good conditions, floats that contain a very shallow mercury pool are used to provide the reflecting surface for the interferometer. This instrument is now being refurbished to take advantage of the advances in interferometers that have occurred in the 25 years since it was originally built.

We are also investigating hysteresis effects in mercury columns that are used to measure very small pressures, that is for very small displacements of the mercury surface.

High Pressure Standards

High pressure standardsPressure balances for the higher pressure standards are traceable to national measurement institutes in Europe and the US. A research effort is currently underway to establish an independent national pressure scale to 500 MPa (5000 bar) at appropriate levels of uncertainty.

Pressure is a derived unit combining the SI units of mass, length and time. For the high pressure region, from a few atmospheres (bars) up to many hundreds of bar, NMI is establishing fundamental standards using piston gauges, in which a force due to masses acts on a well specified area, and fluid columns, in which pressure is a function of fluid density and depth. As the pressure increases, the effective area of pistons changes, as does the density of working fluids in fluid columns. These remain fundamental limitations and overcoming them is the main task of metrology in this pressure region. We are doing this because improvements in the accuracy of measurement of the national pressure standard flows down to users in industry, science and utilities resulting in better, more efficient, more competitive products and services.

Our target is to measure pressures with uncertainties approaching a few parts per million up to 3000 bar and beyond.

At NMI, three parallel fields of effort are directed towards this end:

  • mathematical modelling and numerical simulation of the piston under operating conditions
  • accurate dimensional characterisation of the cylindrical geometry of pistons 
  • establishment of high pressure mercury fluid columns

Controlled clearance gaugeControlled Clearance Gauge

A controlled-clearance piston gauge operates on the principle of controlling the clearance between the piston and the cylinder by applying an auxiliary (jacket) pressure to the cylinder’s outer surface. In theory, as the jacket pressure increases, it will reach a point at which the cylinder will come into contact with the piston. This would correspond to a zero fall rate of the piston and the effective area of the assembly is defined as the effective area of the piston. In practice, this condition cannot be achieved and one would use a flow model to relate the fall rate and the jacket pressure to estimate the point of zero clearance.

The newly acquired NMI controlled-clearance piston gauge (see picture) will be used to undertake experimental and analytical studies of the piston and cylinder system up to 250 MPa, and to calibrate first level reference standards to achieve a pressure uncertainty of 30 ppm or better at 1 sigma up to that pressure. Parametric studies on the effects of rotation speed and types of fluid for an optimum performance of the piston gauge will be followed by the development of mathematical models to analyse and evaluate the distortion of the piston and cylinder unit using the finite element method. The verification of numerical results by comparison with experimental or alternative numerical approaches, with other primary standards such as the mercury column, and participation in key and regional comparisons will be undertaken as part of the program that establishes the standard as an international measurement service.

Novel Piston Characterisation

The most widely used means of realising a physical standard of pressure is using piston gauges in which a force due to masses acts on a well specified area. To achieve target uncertainties of a few parts per million, the diameter, roundness and straightness of a typical piston-cylinder of diameter around 2 to 8 mm needs to be measured with an uncertainty of a few nanometers.

To develop a new instrument capable of measuring diameters up to 10 mm with an uncertainty of 10 to 20 nm we have adopted an approach based on the independent metrology of dimensional and form parameters such as diameter, roundness and straightness, which are then processed to combine them in a single Cartesian coordinate frame.

Diameter will be measured using two sensitive displacement probes and a commercial laser interferometer measuring system mounted on sophisticated multi-axis tables under computer control. The refractive index of air is required for laser wavelength calculation and will need to be determined with an uncertainty of better than 0.5 parts per million. The target uncertainty for temperature is 0.1 °C.

Mercury Column

A 9 m high mercury fluid column is currently being established to generate accurate pressures up to around 60 atmospheres (bar). This prototype will be studied to determine the feasibility of establishing much higher columns (100 m+), achieving much higher ultimate pressures (3000 bar+).

The density of the mercury fluid, the height of the pressure column, its temperature and the value of the gravitational field are all critical parameters in the instrument to be developed. Two fluid columns will be used in parallel to measure the height of the pressure side accurately and conveniently. Temperature control to about 0.02 °C will be required to approach the target accuracies, and lasers will be used to measure the height of the base mercury column and the small offsets between the two parallel columns with uncertainties initially of the order of 30 micrometre, reducing to 3 micrometre with further developments. For the prototype column, the uncertainties arising from the temperature of the mercury (range 0.1 °C), its thermal expansion, compressibility, chemical purity and isotopic variability have already been incorporated into the uncertainty of the mercury density.

The uncertainty in pressure generated up to a few hundred bar is expected to be initially around 80 ppm, reducing to around 10 ppm with planned developments, but for very high pressures (above around 3000 bar) the density of the mercury (which changes with pressure) will need to be known more accurately than currently.

Gas Flow 

The current national standard for gas flow is a mercury-wetted piston prover. A second standard being developed is a conventional bell prover that needs to be modified to enable the distance of travel of the bell to be measured more accurately than the existing method, as provided by the manufacturer: a simple pointer on a scale. It is intended to use a series of flags on a bar whose distance apart can be well determined. These will interrupt a light beam and thus cause pulses to be produced, the interval between which can be timed. The diameter of the bell will be determined by strapping, using tapes measured against length standards.

Investigations into the properties of small sonic nozzles are done using another primary standard that uses a deformable membrane that sweeps out a known volume. This instrument has been described in the literature. Work on the thermal properties of nozzles during their operation and the effect that this has on the flows that they pass has been done. It is hoped to extend this work to investigate the influence of gases of different molecular properties on the performance of the nozzles.

N Bignell and YM Choi (2001) Volumetric Positive Displacement Gas Flow Standard. Flow Measurement and Instrumentation 12, 245–251
N Bignell and YM Choi (2002) Thermal Effects in Small Sonic Nozzles. Flow Measurement and Instrumentation 13, 17–22


NMI has long been involved with the measurement of the absolute density of water and the comparative density of mercury as well as with the measurement of the effect of dissolved gases on the density of water. A new table for the density of water from 0 °C to 40 °C based on this work and that of several other national laboratories was accepted by CIPM.

Current work in density is directed to measuring the density of silicon spheres with relative uncertainties of 1 in 10 million. This work is directed mainly at the determination of the value of the Avogadro constant and ultimately at replacing the mass standard as an artefact (see above).

JB Patterson and EC Morris (1994) Measurement of Absolute Water Density, 1 °C to 40 °C. Metrologia 31, 277–288
M Tanaka, G Girard, R Davis, A Peuto and N Bignell (2001) Recommended Table for the Density of Water between 0 °C and 40 °C based on Recent Experimental Reports. Metrologia 38, 301–309
MK Fen, E Jaatinen, BR Ward and MJ Kenny (2001) A New Solid Density Standard with a Relative Uncertainty of 1 in 107. Fourth Conference of the Metrology Society of Australia, Broadbeach, Queensland, pp 131–133