12th comparison between the Swedish National Kilogram and SP's principal kilogram mass standards.

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12th comparison between the Swedish

National Kilogram and SP’s principal

kilogram mass standards

SP Measurement Technology SP REPORT 2004:32

SP Swedish National T

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12th comparison between the Swedish

National Kilogram and SP’s principal

kilogram mass standards

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Abstract

The 12th comparison between the Swedish National Platinum-Iridium kilogram (Proto-type number 40) and the principal kilogram standards for mass has been performed at SP Swedish National Testing and Research Institute. The method used was a weighted least square method with restraint developed by Dr Leslie Pendrill <1>. Weighings for the pan-European key intercomparisons for 1 kg, EUROMET 509 and 510 were made together with the regular kilogram comparison.

Key words: Sweden, SP, mass standards, kilogram, comparison, traceability

Cover: Swedish National Kilogram K40, photograph by Mats Johansson.

SP Sveriges Provnings- och SP Swedish National Testing and Forskningsinstitut Research Institute

SP Rapport 2004:32 SP Report 2004:32 ISBN 91-85303-08-9 ISSN 0284-5172 Borås 2004 Postal address: Box 857,

SE-501 15 BORÅS, Sweden

Telephone: +46 33 16 50 00

Telex: 36252 Testing S

Telefax: +46 33 13 55 02

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Contents

Abstract 2 Contents 3 Preface 5 1 Introduction 7 1.1 History 7 1.2 Present day 7 2 Mass standards 8 2.1 K40 8 2.2 H 8 2.3 G1 8 2.4 MJV2 8 2.5 Me 9 2.6 Me2 9

2.7 Summary of weight properties 9

3 The balance and the weighing environment 10

3.1 Balance 10

3.2 Air tight chamber 10

3.3 Wobblestick and calibration weight 10

3.4 Atmospheric instruments 11

4 Procedure 12

4.1 Weighing dates 12

5 Calculations 13

5.1 Gravitational gradient 13

5.2 K40 Stability, drift model 13

5.3 Data acquisition and corrections 14

5.4 Model for a weighing process 15

5.5 Least squares fit 16

6 Results 17

6.1 Uncertainty estimation and calculation 17

6.1.1 Common contributions to the uncertainty 17

6.1.2 Individual contributions to the uncertainties 18

7 Tables and graphs showing mass change 19

7.1 National Kilogram K40 19

7.2 Gilded brass kilogram H 19

7.3 Stainless steel kilogram G1 20

7.4 Stainless steel kilogram MJV2 21

7.5 Stainless steel kilogram Me 22

8 Conclusions and Discussion 23

8.1 Summary of results 23

9 Acknowledgements 25

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Annex A Traceability chain for mass in Sweden Annex B Protocols from kg prototype handling Annex C Certificates of equipment used Annex D Control sheet for the comparisons

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Preface

The following report describes the work performed in connection with the 12th compari-son between the Swedish principal standards for one kilogram and the Swedish National Prototype for one kilogram, no 40 (K40). It was manufactured from a rod of 90% Plati-num and 10% Iridium in the 1880’s.

In general four mass standards for one kilogram made of stainless steel are used to main-tain the Swedish kilogram. Every 6 to 10 years a comparison with the ultimate Swedish reference K40 is performed.

In earlier times this interval was regulated by the Swedish act for weights and measures. After the act’s latest revision in 1972 it is up to the National Measurement Institute to decide when to do comparisons at the primary level.

The time chosen for this particular comparison fits nicely with the time schedule for the key comparisons EUROMET projects 509 and 510, thereby confirming the Swedish Best Measurement Capability as defined in the Mutual Recognition Agreement (MRA). The Swedish kilogram K40 is regularly calibrated at the International Bureau for Weights and Measures (BIPM) providing necessary traceability to the international kilogram pro-totype. The results for K40 from the latest, so called, 3rd verification was dated February 26th 1991. Since there is some time since the certificate was issued a drift model for mass gain since calibration until the date of the comparison is used.

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1

Introduction

1.1

History

The Metre Convention is a diplomatic treaty according to which every country signing it should have the metre and the kilogram as the only legal units for length and mass. Sweden was one among the 17 premier states signing this treaty in 1875.

Following the signing, the hard work to find a materialized artefact embodying these measures began. Finally it was found that the metre and the kilogram could best and most durably be materialized with a bar and a cylinder of an alloy of platinum-Iridium (90% Pt 10% Ir). Out of a batch of almost 50 prototypes the one with a mass most resembling the mass of 1dm3 of pure water at 4 ºC was chosen as the international prototype for one kilogram. The latter definition was proposed by the French chemist Lavoisier almost a century earlier, in the 1790’s. The international prototype is accompanied by 6 other kilo-gram prototypes called “temoins” (witnesses), or official copies, that are used for more routine measurements at the BIPM <2>.

Sweden was allotted copy no 40 (K40) of the kilograms and copy no 29 of the metres manufactured by BIPM. Professor Robert Thalén brought the prototypes for the metre and the kilogram from BIPM to Sweden in 1889 <3>.

1.2

Present day

Since 1960 the kilogram is the last man made artefact embodying a quantity. Work is in progress to replace the kilogram with a definition relating the kilogram to “natural” quan-tities. In the future, the kilogram is expected to become a secondary unit either to electri-cal or atomic units. The technielectri-cal challenges in redefining the kilogram to another physi-cal quantity, while keeping the same accuracy as today, are enormous.

Thus there is a good chance that the Pt-Ir kilogram prototypes will be in use, and serve as the principal standards for mass, several years from now.

This report presents the work that was carried out at the National laboratory for mass in Sweden in autumn 2002. It is the 12th in an unbroken line of reports starting in 1895, each report thoroughly describing the procedures used to determine the mass of the principal mass standards in Sweden from the national prototype.

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2

Mass standards

2.1

K40

This artefact is the Swedish National Prototype for one kilogram. It is made of a 90% platinum 10% Iridium alloy in the shape of a cylinder 39 mm in diameter and 39 mm high. It has been in the ownership of the Swedish Government since its delivery. K40 is also at the top level of the traceability chain for mass in Sweden <Annex A>.

Over the years K40 has been calibrated at the BIPM several times, in 1889, 1948, 1991 following the international periodic verifications <4, 5, 6>. Upon request by the Swedish National Laboratory for Mass, additional calibrations were performed in the years 1956 <7> and 1984 <8>.

Between the years 1890 – 1934 the kilogram was housed at the Swedish Royal Academy of Sciences (KVA). In 1934 K40 was transferred from KVA in Frescati outside Stock-holm to the Royal Mint (MJV) situated at KungsStock-holmen in central StockStock-holm <9>. After the outbreak of World War II the kilogram was kept in a bombproof shelter in the base-ment of the Royal Mint. As a part of the Royal Mint’s centennial celebration in 1950, K40 was exhibited to the public <10>. In 1973 the kilogram was transferred to SP. When SP transferred to new premises in Borås 1976 K40 followed along. It has been located in a vault at SP since then. Two excursions to BIPM have been performed though, one between the years 1982 – 1985 <11>. Another was between the years 1988 – 1992 for the 3rd periodic verification of the National Prototypes <12>.

2.2

H

The kilogram mass standard ”H” was manufactured of gilded brass in the 1890’s by in-strument maker P.M. Sörensen in Stockholm <13>. The mass standard is of cylindrical shape with rounded edges. This mass standard has “always” accompanied the National Kilogram K40. However it is not entirely compatible with present day demands for preci-sion mass standards. From the report 1890 by Ångström <14> the volume of the mass standard at 15 ºC is 121.665 cm3 with a volume expansion coefficient of 58 10-6 K-1.

2.3

G1

G1 is a kilogram mass standard that was manufactured by Gragerts våg och viktservice AB in Stockholm, in the year 1974 <15>. The mass standard’s shape is cylindrical with the letters “G1” engraved at the top surface. A stainless steel alloy (DIN 4305, Uddeholm AB) was used, with a composition of 18% Cr, 10.5% Ni 2% Mn, 1% Si and 0.15% C.

2.4

MJV2

MJV2 is an example of first generation stainless steel kilogram mass standards. The Royal Mint purchased two copies in 1945. The copies were first used for the 6th compari-son of mass standards against the national kilogram in 1945 –1949 <16>. The mass stan-dard is in the form of a cylinder with the letters MJV2 engraved on the top face. The alloy is an austenitic stainless steel composed of 18.6% Cr, 8.5% Ni and 0.08% C according to an analysis performed by SP<17>.

Its sister weight, MJV1, was found to be unstable and was eventually scrapped in 1996 after the 11th comparison after considerable instability was detected<18>.

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2.5

Me

As a reinforcement of the traceability chain among the most accurate stainless steel kilo-grams in Sweden the kilogram mass standard “Me” was received from Mettler-Toledo Corporation in 1995. This mass standard is of the standardized OIML-shape and made out of an austenitic stainless steel alloy of low magnetic susceptibility.

2.6

Me2

SP purchased the kilogram mass standard Me2 in 2001 from Mettler-Toledo Corporation. This mass standard is a state of the art, high precision, OIML weight class E1. The aus-tenitic stainless alloy used has virtually no magnetic susceptibility nor magnetization as well as a density close to the desired value 8000 kg/m3. It underwent a laser marking procedure by Svenska Maskinskyltfabriken AB, Linköping in spring 2002 when the let-ters “Me2” were put on the top surface. Laser marking will possibly not affect a mass standard’s stability to the same extent as an engraving or a punch mark. But that remains to be further investigated in comparisons that will follow.

2.7

Summary of weight properties

Volumes and densities

Table 1 Properties of SP’s principal one kilogram mass standards

Name Year of acquisi-tion SP’s in-ventory no Volume at 0 ºC /cm3 (unc, k=1) Volume expan-sion coefficient / K-1 Density at 20 ºC /kg·m-3 (unc, k=1) Ref., year, Certificate No K40 1890 600354 46.411 5 25.869 · 10-5+ 5.65 · 10-9 · ∆t 21435.4 BIPM, 1889 H 1890 121.563 58 · 10-6 8216.7 <19>, 1894 G1 1974 601364 124.578 (1) 43.5 · 10-6 8020.1 (1) BIPM, 1984, No 42 MJV2 1945 601354 126.657 (1) 48 · 10-6 7887.7 (1) BIPM, 1956, No 113 Me 1995 601380 125.317 (3) 48 · 10-6 7972.1 (2) SP, 1996, 01-B96074 Me2 2001 602618 124.828 (3) 48 · 10-6 8011.0 (2) SP, 2002, P200140-50

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3

The balance and the weighing environment

3.1

Balance

The balance used for all comparison weighings is a fully automatic commercial balance of the type Sartorius C1000S working according to the principle of electromagnetic force compensation. This particular balance has been in use since 1991 and served during the 11th comparison between the mass standards and the National kilogram <20>.

At present, some ten years after its acquisition, the balance is well characterized regarding internal heat generation, short- and long-term stability etc. This makes it possible to fulfil the special demands that this kind of measurements have.

3.2

Air tight chamber

To keep the environment as stable as possible, minimizing external influences from pres-sure change, an airtight chamber was used to enclose the balance and the mass standards. The chamber is the same that was used during the 11th comparison and is described in detail in that report <21>.

3.3

Wobblestick and calibration weight

In the previous comparison the need to dismantle the vacuum chamber for sensitivity checks resulted in higher uncertainties as well as substantially more work <22>. To be able to make sensitivity checks of the balance during the weighing process an item called “wobblestick” was purchased from Nor-Cal Inc<23>. This makes it possible to manipu-late small objects within the air tight chamber. Together with a specially “wrinkled” 10 mg weight it was possible to check the balance sensitivity during the weighings without opening the chamber.

Figure 1. Pedestal and “wrinkled” 10 mg weight.

Figure 2. Wobblestick, an instrument used to manipulate small objects such as the sensitivity

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3.4

Atmospheric instruments

The displaced air volumes of a platinum- (46 cm3) and a stainless steel kilogram (125 cm3) differ by a large amount. Since all objects are “floating” in air, air buoyancy, this volume difference gives rise to systematic weighing errors. These errors are from the difference in mass of the displaced air volume, which is about 90 mg. For this reason it is crucial to know the air density as well as the mass standard density with good accuracy and make a correction accordingly.

The air density was determined by using the BIPM formula for calculation of air density from common air parameters <24, 25>.

The measured air parameters were pressure, temperature and relative humidity (dew point). An auxiliary measurement was made to determine the CO2 content as well.

Table 2. Instruments used to check the atmospheric parameters

Quantity Instrument used s/n Inventory no Calibration ref1

Temperature Systemteknik 1228 6629 600 031 MTvP201555

Temp (switch) Burster 1634 601 154 MTvP201555

Pressure Druck DPI 141 775 / 00-03 601 797 P200140-61

Pressure (extra) Texas 145-01 2908 / 6915 600 211 P200140-60

Humidity Protimeter DP989M 315127 601 024 F2 09783 A

Dew point (extra) EG&G 660 0000736 / 903 600 068 F2 11160

Dew point (extra) Thommen HM30 1005578 601798 F2 11161B

CO2 content TSI 8551 50595 300 910 KMo300910

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4

Procedure

The mass standards were set up in the C1000S balance in a way that minimized the num-ber of times K40 had to be moved. Before each comparison a simple protocol was written and signed by two persons thereby securing that all weight positions were thoroughly checked. See annex D for an example.

Each run was performed during a prolonged time with a pre-run for a period of 12 – 20 hours before the actual comparison took place. The actual weighing scheme was to read the balance indication for position 1 Æ 2 Æ 3 Æ 4 Æ 1 … etc. Every position was weighed 30 times with time stamps so that the drift correlated with temperature increase could be monitored.

The software used to govern the balance and weight handler is essentially the same as of the 11th comparison. The weighing sequence is described in detail in <26>.

The influence of balance linearity can have a role when there are large differences in display indication between standard and test weight. To minimize the effects from the weighing differences between K40 and the stainless steel mass standards due to air buoy-ancy an additional 100 mg sheet weight was put on each of the stainless mass standards.

4.1

Weighing dates

Several weighings were performed during the dates in the tables below:

Table 3. Start and stop times for weighings where K40 was used as reference

Start date 2002- Start time End date 2002- End time Balance pos “N” Balance pos “1” Balance pos “2” Balance pos “3” 08-28 23:42 08-29 06:10 K40 MJV2 K55 Me 08-29 22:13 08-30 04:41 K40 MJV2 K651 Me 08-30 23:46 08-31 06:13 K40 Me Me2 MJV2 09-03 08:34 09-03 15:03 K40 Me Me2 MJV2 09-03 23:15 09-04 05:43 K40 Me Me2 MJV2

The kilograms K55 and K651 are kilogram prototypes owned by NPL, <27> and were circulated during the intercomparison EUROMET 509.

Table 4. Start and stop times for weighings where MJV2 was used as reference

Start date 2002- Start time End date 2002- End time Balance pos “N” Balance pos “1” Balance pos “2” Balance pos “3” 08-20 16:22 08-20 22:35 MJV2 Me Me2 61 08-23 21:30 08-24 03:42 MJV2 Me Me2 61d 08-24 19:18 08-25 01:30 MJV2 Me Me2 61d 09-11 22:49 09-12 05:16 MJV2 G1 Me2 H

The kilograms are 61 and 61d are manufactured of stainless steel, owned by NPL, and were circulated during the key intercomparison EUROMET 510.

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5

Calculations

5.1

Gravitational gradient

A factor influencing high precision mass determination when masses have very different shape and / or density is the difference in height of centre of mass for different artefacts. This is not a large effect but comes from the property that the gravitational acceleration reduces as one moves outward from the earth’s surface.

To calculate the magnitude of this effect the expression for the difference in gravitational force ∆F = m·∆g associated with the gravitational gradient ∆g is used. Modelled with a conceptual expression ∆F = ∆m·g it is assumed that ∆F depends on some apparent mass difference ∆m instead of a difference in gravitational acceleration ∆g. According to work made by NPL <28> the relative gradient of the gravitational acceleration can be set to 3,14·10-10 mm¯¹ near the sea level. The apparent mass difference can be calculated from the relation below:

g

g

m

m

=

eq 5-1 where the value of the right hand expression is given by the NPL figure. A recalculation factor 109 µg/kg leads to an apparent mass gradient of 0,314 µg/mm. There exist other models as well <29> but in this work the NPL-figure is used.

The centre of gravity for a Pt-Ir kilogram is about 19 mm above the bottom whereas in the case of a standard stainless steel kilogram the centre of gravity can vary depending on its shape as seen in the following table.

Table 5. Centre of gravity for Sweden’s principal kilogram standards

Mass standard Distance base-centre of gravity / mm Difference to K40 / mm correction ∆m / µg ) K40 19.5 0.0 MJV2 27.2 7.7 2.4 G1 27.5 8.0 2.5 H 26.8 7.3 2.3 Me 40.2 20.7 6.5 Me2 40.2 20.7 6.5

5.2

K40 Stability, drift model

Even though all kilogram prototypes display excellent stability over time there must be means to estimate the mass change since last calibration at the BIPM. In this work a model described by Richard Davis, BIPM has been used <30>. From minute examina-tions of the BIPM official prototype No 25 the following conclusions were drawn after having used the cleaning washing procedure in connection with calibration:

Mass increase first 3 months: 0.0032 mg Annual increase thereafter: 0.001 mg/yr Increase in uncertainty: 0.0004 mg/yr

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K40 had a mass value of 1 kg - 0.035 mg with an uncertainty of 0.002 3 mg

(k=1, 12 degrees of freedom), by the time of the third verification of the National proto-types according to the calibration certificate dated May 18 1993 <31>.

The 12th comparison was performed an estimated 11.49 years after the 3rd verification meaning that the corrected values used according to the above mentioned model were 1 kg - 0.0206 mg with an estimated uncertainty (k=1) of 0.0051 mg. These were the mass and uncertainty values used for K40 throughout this comparison.

Simulated K40 mass change since 3rd verification

-40 -30 -20 -10 1990-09-04 1992-09-03 1994-09-03 1996-09-02 1998-09-02 2000-09-01 2002-09-01 date m - 1 kg (µg)

Figure 3. Simulated mass change of K40 since 3rd verification. Note the bend 3 months after the

3rd verification. The other two points show the time for the 11th and 12th comparisons

re-spectively.

5.3

Data acquisition and corrections

From the weighing sequence described in section 4 the input data consists of four time series of balance indications

1. Measurement of time, balance indication and air density which are logged quantities for each point.

2. Correction for heat expansion and each weight’s volume (density) according to:

V(t) = V(tref ) · α · ∆t eq 5-2

where:

∆t is t - tref, where tref is 0 or 20 °C depending on original weight data

α is the coefficient of volume expansion for each weight (see section 2.7).

3. Calculation of each weight’s mean volume and standard deviation during one meas-urement series. The weight volume has an uncertainty of type A expressed as a stan-dard deviation.

4. Adjustment of the balance readouts for air buoyancy and mass of sensitivity weight for each measurement point, deflections.

5. Feed the deflection values into a weighted least squares fit to get the mass corrections to the nominal mass of 1 kg.

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5.4

Model for a weighing process

A fictitious counterweight cw can be used when modelling the weighing even though there is a system of electromagnetic force compensation in a modern balance.

Figure 4 Symbolic view of a weighing model with a mass standard a counter weight and

a sensitivity weight.

It is easy to see that the balance indication is the difference in apparent mass between the masses put on the load carrier to the left and the counterweight.

I = m + Tm – ρa · (Vm + VTm) – mcw + ρa · Vcw eq 5-3 However the really interesting part is the deflection.

I’ = m – mcw eq 5-4

that results in

I’ = I - Tm + ρa · (Vm + VTm) – ρa · Vcw eq 5-5 If all deflections I’ are indexed,

I’N(ti) , I’1(tj) , I’2(tk) , I’3(tl) eq 5-6

there are four curves described, one for each weight handler position, for each compari-son.

A fit to a second-degree polynomial equation with respect to time

I’(t)= a + b ·t + c ·t2 eq 5-7 for the deflections I’ giving the corrected indication for each mass standard is created. This can readily be done with the standard tools supplied with mathematical software packages such as Excel, Mathlab or Mathcad.

Differences at pre determined times t1 t2 t3 ... tM which are mean times between weighings

for each pair of weights according to the design are made:

(

)

N M i i N i N

M

I

t

I

t

m

h

d

1 1 ' ' 1 1

(

)

(

)

1

+

=

= eq 5-8

(

)

21 1 ' 1 ' 2 21 ( ) ( ) 1 h m t I t I M d M j j j ⎟⎟+∆ ⋅∆ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − =

= eq 5-9

(

)

32 1 ' 2 ' 3 32

(

)

(

)

1

h

m

t

I

t

I

M

d

M k k k

+

=

= eq 5-10

(

)

3 1 ' 3 ' 3

(

)

(

)

1

N M l l l N N

I

t

I

t

m

h

M

d

+

=

= eq 5-11

The term ∆m · ∆h gives a mass correction based on the vertical gravitational gradient as described in section 5.1. The four different dis make up the vector d together.

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5.5

Least squares fit

Written in matrix form the design for the differences mentioned above can be described in matrix form as A= 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 − − − −

where each column symbolizes a mass standard and each row symbolizes a comparison. Row 0 symbolizes the reference standard and is used to create the restraint together with the weighting element W00.

The difference vector d is fed into the weighted least squares fit:

c = (AT · W · A)-1 · AT · W · d eq 5-12

Where the c-vector contains the mass corrections to the nominal mass of 1 kg for all four weights.

W is the weighting matrix constructed with the diagonal elements:

=

2 2

)

(

1

1

)

(

j j ii

d

s

d

s

W

i ≠ 0 eq 5-13

and all off-diagonal elements = 0

The normalization condition is

Wii =1 for i ≠ 0

The restraint for this fitting is given by the element W00, which is the mathematical

weighting assigned to the reference. The figure used in this work is 106. It is chosen by the experimenter from experience and thus tells something about the experimenter’s con-fidence in the reference.

This design A with its associated least squares fit is based on the same technique as used when performing subdivision of mass standards. <32, 33>]

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6

Results

6.1

Uncertainty estimation and calculation

One of the most extensive tasks to do in a comparison of this type is the uncertainty cal-culation. Several standard publications have been issued to give guidance how to deter-mine measurement uncertainty in calibration <34, 35>.

The uncertainty for each weight consists of a number of components. Some components are common for all mass standards, such as balance parameters and air density. Other components are individual for each mass standard like, for example, the result of a weighing process or the result of density determination. In subsection 6.1.1 through 6.1.2 the method for presenting uncertainties according to EA-4/02 is used <36>.

6.1.1

Common contributions to the uncertainty

Table 6. The reference (K40) and balance uncertainty components uref and ubal.

Symbol Quantity Estimated1 unc. (k=1) Divisor Standard un-certainty Sensitivity coefficient Contribution / mg MS Ref. Mass 0.0054 mg 1 0.005400 mg 1 0.0054 δmD Ref. Drift 1 0.000000 mg 1 0.0000

δmC Bal. scale div 0.0006 mg 1 0.000577 mg 1 0.0006

δmS Bal. sensitivity 0.0030 mg 1 0.003000 mg 1 0.0030

total (k=1) 0.006 2 mg

or 6.2 µg

1 The estimated uncertainty is based on the assumption that the drift is taken care of and the balance scale division has a rectangular distribution. Uncertainty from balance sensi-tivity and reference mass are taken to have normal distributions.

2 2 mD MS uref = +

δ

eq 6-1 2 2

mS

mC

u

bal

=

δ

+

δ

eq 6-2

Table 7. Air density uncertainty uair.

Quantity Estimated uncertainty (k=1) Relative sen-sitivity1 ci/ρa Relative un-certainty in air density Uncertainty in air density / kg·m-3

Unc based on vol-ume difference2 / mg Pressure 4 Pa 1.00·10-5 3.775·10-5 0.00005 0.0036 Temp 0.035 °C -4.00·10-3 1.386·10-4 0.00017 0.0131 Dew pt 0.27 °C -3.00·10-4 8.07·10-5 0.00010 0.0077 CO2 35 ppm 0.4 1.385·10-5 0.00002 0.0013 Formula 6.00·10-5 6.00·10-5 0.00007 0.0057 Total (k=1) 0.000 21 0.0167 mg Or 0.21 µg/cm³ 16.7 µg

1 The relative sensitivity transforms an absolute uncertainty into a relative uncertainty in air density. Multiplied with the reference density used (1.200 kg·m-3) gives the absolute uncertainty in air density.

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Common uncertainty components 0 5 10 15 20 Ref. Ref. drift scale div.

sens press temp dew pt. CO2

CIPM-formula

total

contribution / µg

Figure 5. Uncertainty components shown graphically.

The total combined common standard uncertainty 2 2 2 air bal ref common

u

u

u

u

=

+

+

eq 6-3

is calculated to be 17.8 µg for all mass standards with a density near 8000 kg/m3 or a volume of 125 cm3. For the mass standard H made of gilded brass with slightly higher density, this figure amounts to 18.3 µg. Uncertainties in temperature and dew point are the dominant uncertainty components.

6.1.2

Individual contributions to the uncertainties

Apart from the common contribution there is an individual contribution for each mass standard, which might differ slightly depending on the conditions during the weighing sequence. 2 2 common individual u u u= + eq 6-4

Table 8. Total uncertainty (k=1) calculated from the individual and common components

respec-tively Mass standard Standard de-viation of the mean / mg Common contribution / mg Uncertainty (k=1), / mg (±) MJV2 0.0031 0.0178 0.018 Me 0.0035 0.0178 0.019 Me2 0.0098 0.0178 0.021 G1 0.0024 0.0178 0.019 H 0.0035 0.0183 0.019

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7

Tables and graphs showing mass change

In this section both the total drift over time as well as drift during this comparison where applicable for each mass standard are shown. The weights in section 2.4 MJV2, 2.5 Me and 2.6 Me2 used K40 as reference. Therefore a correction from the difference in height of centre of mass was applied after calculation of the mean mass value. The weights in section 2.2, H and section, 2.3 G1 used MJV2 as reference. No correction for difference in centre of mass was applied since it is almost at the same level.

7.1

National Kilogram K40

Mass for the Swedish National Kilogram K40 1894-1991

1948 1984 1991 1889 1956 -0,060 -0,040 -0,020 0,000 1885 1905 1925 1945 1965 1985 2005 m - 1 kg / mg 2. verification 1. verification 3. verification

Figure 6. K40 mass values and uncertainties (k=1), from all verifications and auxiliary weighings.

7.2

Gilded brass kilogram H

Mass for the gilded brass kilogram H 1894-2002

1894 1924 1935 1945 1965 1980 1988 1996 2002 1914 1915 1904 6,60 6,70 6,80 6,90 1885 1905 1925 1945 1965 1985 2005 m - 1 kg (mg)

Figure 7. H mass values. The value from 1955 <37> has been excluded from the graph due to its

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7.3

Stainless steel kilogram G1

Below is the graph from the mass development of G1from purchase and onwards

Mass for the stainless kilogram G1 1984-2002

2,20 2,30 2,40 2,50 1980 1985 1990 1995 2000 2005 2010 m - 1 kg (mg)

Figure 8. G1 mass values BIPM value

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7.4

Stainless steel kilogram MJV2

Mass for the stainless kilogram MJV2 1945-2002

1945 1955 1956 1956 1965 1988 1996 2002 0,40 0,50 0,60 1940 1950 1960 1970 1980 1990 2000 m - 1 kg (mg)

Figure 9. MJV2 mass values. The values in 1956 were given without uncertainty <38>.

Table 9. Mass drift of MJV2 during 12th comparison.

Date m -1 kg / mg unc k=1 / mg 2002-08-29 0.444 0.018 2002-08-30 0.444 0.018 2002-08-31 0.446 0.018 2002-09-03 0.431 0.018 2002-09-04 0.433 0.018 MJV2 mass 12th comp 0,410 0,420 0,430 0,440 0,450 0,460 2002-08-28 2002-09-01 2002-09-05

Figure. 10 MJV2 mass change during 12th comparison

The mean value from above (m – 1 kg = 0.440 mg) was then corrected for the height of centre of mass for this particular mass standard (0.0024 mg) to become

m – 1 kg = 0.442 mg.

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7.5

Stainless steel kilogram Me

Mass for the stainless kilogram Me 1996-2002

0,50 0,60 0,70 1994 1996 1998 2000 2002 2004 m - 1 kg (mg) Figure 11. Me mass values. In 1998 a comparison was made with the mass standard MJV2 as

reference <39>.

Table 10. Mass drift of Me during 12th comparison.

Date m - 1 kg / mg unc k=1 / mg 2002-08-29 0.639 0.018 2002-08-30 0.639 0.018 2002-08-31 0.642 0.018 2002-09-03 0.624 0.018 2002-09-04 0.628 0.018 Me mass 12th comp 0,610 0,620 0,630 0,640 0,650 0,660 2002-08-28 2002-09-01 2002-09-05

Figure 12. Me mass change during 12th comparison

The mean value from above (m – 1 kg = 0.634 mg) was then corrected with the height of centre of mass for this particular mass standard (0.0065 mg) to become

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8

Conclusions and Discussion

In August – September 2002 the 12th comparison of the Swedish principal kilograms against the Swedish National prototype K40 was performed. The equipment used was essentially the same as in the 11th comparison in 1994 – 1996 except that the refractome-ter was omitted. The BIPM formula for air density was used for air density derefractome-termination in this work. A drift model for the National kilogram’s mass was used based on work by BIPM on kilogram number 25.

To check the balance sensitivity during the comparison a “wobblestick” was used to-gether with a specially (de)formed 10 mg wire weight. During the course of the compari-son the weighing results showed excellent reproducibility, indicating that knowledge about the present mass for the Swedish principal mass standards has been gained with good confidence.

A new mass standard (OIML class E1) was brought into the traceability chain with this comparison. A new feature with this mass standard is the laser marking “Me2” on the top face. Whether this marking method influences the mass standard’s long time stability remains to be seen.

Looking at a larger view one could compare the consistency between the mass standards MJV2, G1 and Me. This has been done in an auxiliary measurement with MJV2 as stan-dard in 1998 when a high precision mass stanstan-dard from Estonia was calibrated at SP. Again this shows a good agreement as can be seen in Figure 8 and Figure 11.

Simultaneously with this comparison two international intercomparisons were made. EUROMET 509 deals with the mass determination of the Platinum Iridium kilograms K55 and K651 provided by NPL (UK). The project EUROMET 510, also piloted by NPL (UK) used the stainless steel kilograms 61 and 61d. EUROMET 510 is also registered as a key intercomparison aimed to tie all National Measurement Institutes results together, thereby stating the Best Measurement Capability for each laboratory <40>.

From the results in the preliminary report draft A <41>, there is an indication that the drift model used for K40 might exaggerate the mass change slightly, however within the uncertainty for the comparison. It is hard to quantify the result on this level due to the uncertainties involved.

8.1

Summary of results

When performing the measurements the atmospheric parameters were logged. The values in the following table are not taken from the automatic logs obtained during the meas-urements, but excerpts from notes taken during each part of the comparison to give an estimate of the environmental conditions during the comparison measurements and its contribution to the uncertainty.

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Table 11. Summary of results from measurements of atmospheric parameters.

Quantity Min value Max value

Estimated1 unc (k=1)

Contribution to uncer-tainty in air density

/ kg·m-3 Pressure 99280 Pa 101015 Pa 4 Pa 0.00005 Temperature 20.285 ºC 20.374 ºC 0.035 °C -0.00017 Dew point 10.0 ºC 12.0 ºC 0.3 °C -0.00010 CO2 406 ppm 409 ppm 35 ppm 0.00002 BIPM-formula 0.00007 Air Density 1.17251 kg/m³ 1.19097 kg/m³ 0.000 21

1 The estimations are based on values in calibration certificates and repeatability of in-struments.

As can be inferred from the tables in section 4.1, and the graphs in section 7 each mass standard obtains several mass values with aid of the calculations described in detail in section 5. The mean values from these results corrected for centre of mass were taken as each mass standard’s actual mass value.

Table 12. Masses for the Swedish principal mass standards for one kilogram, 2002

Mass standard Real mass, m - 1 kg / mg Uncertainty (k=1), / mg (±) Density at 20 °C / kg·m-3 Uncertainty in density, (k=1) / kg·m-3 MJV2 0.442 0.018 7887.6 Me 0.641 0.019 7972.1 0.2 Me2 -0.120 0.021 8011.0 0.2 G1 2.396 0.019 8020.1 H 6.848 0.019 8216.7

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9

Acknowledgements

The authors want to thank Mr Rauno Pykkö, SP, KM for help with CO2 measurements. Svenska Maskinskyltfabriken AB for help with laser marking of the mass standard “Me2”.

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10

References

1 ”11th Comparison Between the Swedish National Kilogram and SP Principal Standards for One Kilogram”, Johansson B., Källgren H., Pendrill L., SP-Report 1996:50, 1996

2 La Troisème Vérification périodique des prototypes Nationaux du Kilogramme, Extrait des Procès-verbaux du Comité international des poids et mesures 82e session, BIPM, 1993 3 ”Jämförelse mellan Svenska Riksprototypen för Kilogrammet och några Staten tillhöriga

Hufvudlikare och Normalvigter”, Ekstrand Å. G., Ångström K., KVA handlingar, 27, 5, 1895, p 3

4 Comité Consultatif pour la masse et les grandeurs apparentées, Rapport de la 5e session, BIPM, 1993, ISBN 92-822-2132-6

5 Reference 2

6 ”The Third Periodic Verification of National Prototypes of the kilogram 1988-1992”, Girard G., Metrologia, 31, 1994, 317-336

7 ”Sjunde jämförelsen mellan svenska riksprototyperna för metern och kilogrammet och mynt- och justeringsverkets huvudlikare”, Swensson T., Glansholm D., Walldow E., KVA handlingar fjärde serien, 7, 3, 1958

8 ”10th Comparison of Swedish National Kilogram with National Testing Institute principal kilogram standards” Pendrill L., Källgren H., SP-Report 1988:38, 1988

9 ”Femte jämförelsen mellan Svenska riksprototyperna för metern och kilogrammet och mynt och justeringsverkets huvudlikare”, Grabe A., Swensson T., Walldow E., KVA handlingar tredje serien, 15, 5, 1935, p 3 10 Reference 7 p 9 11 Reference 8 p 15 12 Reference 4 – 6 13 Reference 3 p 12 14 Reference 3 p 14 15 Reference 8 p 18

16 ”Sjätte jämförelsen mellan svenska prototyperna för metern och kilogrammet och mynt- och justeringsverkets huvudlikare”, Grabe A., Swensson T., Walldow E., KVA handlingar fjärde serien, 1, 7, 1950 17 Reference 8 p 17 18 Reference 1 p 30 19 Reference 3 p 14 20 Reference 1 p 9 21 Reference 1 p 8 22 Reference 1 section 2.3

23 Nor-Cal Products, Inc., P.O. Box 518, 1967 So. Oregon, Yreka, CA 96097,

http://www.n-c.com

24 "Equation for determination of the density of moist air",' Giacomo P., Metrologia, 18, 1982, p33-40

25 "Equation for the Determination of the Density of Moist Air 1981/91", Davis R. S., Metrologia, 29, 1992, 67-70

26 Reference 1 p 17-19

27 National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom, www.npl.co.uk

28 ”Initial Stages in Determining the UK Mass Scale: From the National Prototype Kilogram to the Stainless Steel Reference Kilograms”, Havard D. C., Lewis S. L., NPL report MOM 98, 1995 p 25

29 "Absolute determination of the vertical gradient of gravity", Hipkin R. G., Metrologia, 36, 1999, 47-52

30 BIPM Calibration of 1 kg mass standards in Platinum-Iridium since 3rd periodic verification Davis R.S, Coarasa, CCM 2002-09

31 BIPM certificate No 22 dated May 18 1993 32 Reference 1 p 23

33 ”Neddelning av Kilogrammet”, Pendrill L., SP-Rapport 1989:22, SP, 1989 34 ISO guide to uncertainty in measurement, (GUM)

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36 Reference 35 37 Reference 7 p 27 38 Reference 7 p 22-24 39 SP Reference No 98V12652 40 BIPM, MRA www.bipm.fr

41 After a comparison is completed the first draft (draft A) of the report is confidential. Only the part taking laboratories may review it. Draft B i a more public draft followed by the final report.

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Traceability chain for mass in Sweden

Spårbarhetskedjan för massa

K40 1 kg MJV2 1 kg 1 år 1 år

Vid behov, vanligen 6 år

Me 1 kg Me2 1 kg 3 år E1 1 mg-10 kg 1 mg-10 kgE1k E1kk 1 mg-2 kg 1 mg-2 kgE11 E22 1 mg-2 kg 1 mg-2 kgE23 G 1 kg 1 kgH 2 år 1 år 1 år 1 år E26 5 - 50 kg 1 - 20 kgS 1 år 2 år 2 år 2 år B 50 kg 10 vikter K 500 kg 10 vikter E25 5 - 50 kg F14 1 mg-2 kg LS 50 kg E2 20 kg F1 500 kg

Cirkel betecknar enstaka vikt, kvadrat betecknar viktsats

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Kontrollblankett för komparationsvägning

Förinställd starttidpunkt för vägningarna datum:_______________ klockslag:______________

Position kilogramvikt Tilläggsvikt Notering

N ______________ _____________________ ____________________ 1 ______________ _____________________ ____________________ 2 ______________ _____________________ ____________________ 3 ______________ _____________________ ____________________

Före komparationen Känslighetskontroll, våg 6 enligt metod 32

Visad massa känslighetsvikt _________________ mg Osäkerhet i visad massa ________________ mg

Före komparationen med öppna kranar på burken daggpunktsbestämning och tryck

Operatör:___________ datum:_______________ klockslag:______________

EG&G 660 visar (okorrigerat) ________________ °C inv. nr: 600068 Protimeter DP989 visar (okorr) ________________ °C inv. nr: 601024

Thommen HM 30 visar (okorr) ________________ % inv. nr: 601798, 601799 Druck DPI 141 visar okorr. ________________ hPa inv. nr: 601797

Thommen HM 30 visar okorr. ________________ hPa inv. nr: 601798, 601799

Texas 145 visar (heltal) ________________ inv. nr: 600211

Efter komparationen med öppna kranar på burken daggpunktsbestämning och tryck

Operatör:___________ datum:_______________ klockslag:______________

EG&G 660 visar (okorrigerat) ________________ °C Protimeter DP989 visar (okorr) ________________ °C Thommen HM 30 visar (okorr) ________________ % Druck DPI 141 visar okorr. ________________ hPa Thommen HM 30 visar okorr. ________________ hPa Texas 145 visar (heltal) ________________

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Example of a sheet showing weight placement on the handler for each comparison. N 3 2 1 MJV2 E 510 61 Me2 Me Datum ____________ Placerat ____________ Kontrollerat ____________ N 3 2 1 MJV2 E 510 61d Me2 Me Datum ____________ Placerat ____________ Kontrollerat ____________

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SP Measurement Technology SP REPORT 2004:32

ISBN 91-85303-08-9 ISSN 0284-5172

technical investigation, measurement, testing and certfi cation, we perform

research and development in close liaison with universities, institutes of technology and international partners.

SP is a EU-notifi ed body and accredited test laboratory. Our headquarters are in Borås, in the west part of Sweden.

SP Swedish National Testing and Research Institute Box 857

SE-501 15 BORÅS, SWEDEN

Telephone: + 46 33 16 50 00, Telefax: +46 33 13 55 02 E-mail: info@sp.se, Internet: www.sp.se

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