Mass and volume measurements on a Si sphere performed at the NMISA Mass laboratory

Ronél Steyn

rsteyn@nmisa.org

Content

1. Redefinition of the kg2. Introduction3. Mass measurements4. Volume measurements5. Mass results6. Volume results7. Conclusion

Redefinition of the kilogram

IPKKibble balance (Watt balance)

Si Sphere

Introduction

• In 2017 NMISA received a Si sphere from PTB –Braunschweig, to monitor the stability of mass measurements over a period of time.

• The NMISA Mass laboratory has a Si sphere which is not well characterised and was intercompared with the PTB sphere.

Mass measurements• A Mettler Toledo AT10 005

comparator was used for measurements.

• Weighing range:

1 000 g to 10 000 g

• Readability: 0,01 mg

• Ring weights were used to support the Si spheres and Stainless Steel check weight

• The spheres were compared against stainless steel reference standards and Bouyancycorrection were added

Weighing equation

The weighing equation used for calculating the mass between the reference and test mass pieces is given by

𝑚𝑡 = 𝑚𝑟 + ∆𝑚 −𝑚𝑟𝑖𝑛𝑔 + 𝐶𝑏

where:

mt = mass of test weight

mr = mass of reference weights

∆𝑚 = average difference in mass

𝑚𝑟𝑖𝑛𝑔 = mass of ring weight

Cb = Buoyancy correction

Volume comparator

• A Mettler VC1005 automated volume comparator was used for volume measurements

• Weighing range:

1 g to 1 000 g

• Double wall glass container with distilled water in the outer bath and FC-40 in the inner bath• FC-40 is a fluorinert colourless

liquid with density of 1,87 g/ml

Volume measurement procedure

• FC-40 fluid is thermally stable within a temperature range of -57 ᵒC to 165 ᵒC which makes it suitable for constant temperature measurements

• ClimaLog to measure:• air temperature• relative humidity• air pressurefor applying buoyancy corrections

Volume measurement procedure

• Temperature sensor close to where weighing occurs

• Fluid density was calibrated with external weights

• Data processing on a computer

Volume measurements

• Compares the test mass to the reference mass (known volume) and detects the volume difference between the mass pieces

• Results include volume and density

Volume measurements

• Use conventional mass to determine the volume

• The conventional mass of a body is equal to the mass mc of a standard weight that balances this body under “conventional” conditions:• ambient temperature tref = 20 ᵒC

• air density 𝜌air = 1,2 kg.m-3

• and standard weight density 𝜌std = 8000 kg.m-3

• For a weight of mass 𝑚 and volume 𝑉 this definition may be expressed as

Volume measurements

• The weighing equation that was used to calculate the volume difference Δ𝑉between the reference and test weight is given by

∆𝑽 =(𝒎𝒄𝒕−𝒎𝒄𝒓) 𝟏 −

𝟏. 𝟐𝟖𝟎𝟎𝟎

𝝆𝒇 − 𝟏. 𝟐−

𝑩∆𝒎𝒘

𝝆𝒇 − 𝟏. 𝟐

where:

• 𝑚𝑐𝑡, 𝑚𝑐𝑟 = conventional masses for the test and reference respectively

• Δ𝑚𝑤 =

• B = is the balance correction factor

• 𝜌air = the air density

• 𝜌bw = is the density of the balance’s internal weights

The volume 𝑉𝑡 of the test weight is found by adding Δ𝑉 to the volume 𝑉𝑟 of the reference

𝐕𝐭 = 𝐕𝐫 + 𝚫𝐕

Volume measurements

• 200 g stainless steel reference standard was used to determine the density of the spheres

• When a 1 kg silicon sphere is weighed in the liquid, its apparent mass becomes much less because of the buoyancy force acting on the sphere

• A coefficient of thermal expansion of 10,0 ppm/ᵒC was assumed for the Si sphere

•

• SIT FOTO IN!!!!!!!!

Mass measurement results

Nominal Value

g

Measured Value

NMISAg

Uncertainty

g

MassReference

valueg

Uncertainty

g

Si sphere, SiQPkg_03_b

1 000 1 000,046 36 0,000 15 - -

Checkweight, #5

1 000 1 000,001 53 0,000 13 1 000,001 47 0,000 25

Mass measurements

• The results of the check weight measurement were 60 µg (0,000 06 g heavier than expected

• Two values are well in agreement to within their associated uncertainties

• The higher uncertainty could be attributed to the comparator used

• Although ring weights had to be used to accommodate the spheres on the weighing pan which was not ideal but the measurements obtained reasonable results

Volume measurement results

Nominal Value

g

Measured Value

NMISAcm3

Uncertainty

cm3

Reference value

cm3

Uncertainty

cm3

Si sphere, SiQPkg_03_b

1 000 429,805 0,032 429,350 0,019

Check weightMV-E-170 (200. g)

200 24,954 11 0,000 50 24,954 10 0,000 50

Volume measurements

• The volume results agree to the expected values as confirmed with the check weight used, and within the uncertainty of measurements.

• The PTB Si-sphere measured had a known density value (provided with the sphere) which was used to validate the determined volume values.

• Improvement on the mass measurements and a more accurate value for the coefficient of thermal expansion will improve the volume measurements.

• The volume measurements could be further improved by using another sphere as a standard instead of the stainless steel OIML shaped weight were the differences in volumes are big.

Conclusion

• The calibration procedures used for mass and density measurements proved to be fit for purpose using the equipment available

• The laboratory will continue to improve the large measurements uncertainties on mass and volume measurements on Si spheres.

• Several possible improvements had been identified to enable the laboratory to adequately monitor the stability of Si-spheres. They include:• reducing the size and weight of the ring weights

• improvement of buoyancy corrections

• more accurate values for coefficient of thermal expansion for Si sphere during the volume measurements

• direct comparison between two spheres will be much more accurate and will improve the measurement uncertainties drastically as proved by measurements done at the PTB

Thank you