International Comparison CCQM-K15 – Emission level of CF4 and SF6
Final Report
Jin Seog Kim1, Dong Min Moon1, Kenji Kato2, Leonid A. Konopelko3, Yuri A. Kustikov3, Franklin R.
Guenther4
1
Korea Research Institute of Standards and Science (KRISS), Division of Chemical Metrology and
Materials Evaluation, P.O.Box 102, Yusung, Taejon, Republic of Korea
2
National Metrology Institute of Japan (NMIJ), 305-8565 Umezono 1-1-1, Tsukuba lbaraki, Japan
3
D.I. Mendeleyev Institute for Metrology (VNIIM) laboratory of state standards in Field of Analytical
measurement 19, Moskovsky prospekt, 198005 st-petersburg, Russia
4
National Institute of Standards and Technology (NIST), Chemical Science and Technology Laboratory,
100 Bureau Drive, Gaithersburg MD, USA
Field
Amount of substance
Subject
Comparison of measurement of carbon tetrafluoride and sulfur hexafluoride in nitrogen
Participants
KRISS(KR), NIST(US), NMIJ(JP), VNIIM(RU)
Organizing body
CCQM
Rationale
CF4 and SF6 are the global warming chemicals that are used in semiconductor companies. In Kyoto
protocol on climate change in 1997, those chemicals were included in the items to achieve its quantified
emission limitation and reduction commitments. Accordingly for the measuring of these gases, it is
necessary that measurement results are accurate and traceable, in particular because of the fact that
emission level CF4 and SF6 are the global warming source gases.
This part of project focuses a comparison to measurement capability for measuring CF4 and SF6 at emission
level. This key comparison will cover the comparability of the gas CRMs on the emission level (10. 10-6
mol/mol – 100 mmol/mol in Nitrogen or Air) of following chemicals; CF4, C2F6, CHF3, SF6, and NF3.
At the CCQM gas analysis working group meeting in April 2003, it was agreed that CCQM organize a
pilot study (CCQM-P51) for institutes that are participated as study level on CCQM-K15. Therefore,
CCQM-P51 was run in parallel to CCQM-K15. The CCQM-P51 was reported as a separated report.
Process of the comparison
The individual cylinders for this comparison were prepared by means of primary methods (gravimetry) at
the coordinating laboratory KRISS. The pressure in the cylinders was approximately 10 MPa when
distributed. Because of individual preparation of gas mixture, there are some differences in the actual
property values of these mixtures, which make working with a single reference value undesirable.
However, all property values of these mixtures are within the range of proposed values in protocol. The
nominal amounts of substance ratios of CF4 and SF6 in nitrogen, as used in this key comparison, are
summarized in table 1.
Table 1: Nominal amount of substance ratios
Component
Carbon tetrafluoride
Sulfur hexafluoride
Nitrogen
x (µmol/mol)
100
100
balance
The cylinders were shipped to participants between July and August 2003. Participated laboratories
carried out their measurements from September to November 2003. Reports were received until
December 31, 2003.
Measurement protocol
The measurement protocol requested each laboratory to perform at least 3 measurements, with
independent calibrations. The replicates, leading to a measurement were to be carried out under
repeatability conditions. The protocol informed the participants about the nominal concentration ranges,
given as 90 – 110 µmol/mol carbon tetrafluoride, 90 – 110 µmol/mol sulfur hexafluoride and nitrogen as
balance. The laboratories were also requested to submit a summary of their uncertainty evaluation used
for estimating the uncertainty of their result.
Measurement equation
The measurement model has been taken from the CCQM-K3 [1]. The gas mixtures have been prepared by
means of primary methods (gravimetry) [2].
Three groups of uncertainty components have been considered for the preparation:
1. gravimetric preparation (weighing process)
2. purity of the parent gases
3. stability of the gas mixtures (short term stability)
There has been no evidence that there would be relevant effect of adsorption, and the component of gas
mixtures has been known as very stable compounds, so that only the first two groups of uncertainty
components appear in the model for evaluating the uncertainty from gravimetric preparation.
u2(xgravp) = u2(xweighing) + u2(∆xpurity)
(1)
A second contributor to the uncertainty of the reference value of gas mixtures is the uncertainty from
verification. The verification process is used to confirm the gravimetric composition by high-precision
Gas Mass Spectrometer (Instrument Model: Finnigan MAT 271) as checking internal consistency
between prepared cylinders.
For a typical mixture of this project, the following results have been obtained, whereby for uver the
standard deviation s is used (Table 2).
Table 2: Uncertainty components for a typical mixture
Component
CF4
SF6
u (xgravp) (%, rel)
0.045
0.045
uver (%, rel)
0.075
0.075
The results from table 2 have been used to calculate the uncertainty in the assigned (reference) value
UgravR = kugravR
(2)
Where
2
u gravR = u 2 ( xgravp ) + u ver )
(3)
and k = 2. The relative uncertainty ugravR has been used to compute the combined standard uncertainty of
reference value for all mixtures.
Measurement methods
The following methods of measurement and calibration methods have been employed (Table 3 and 4) by
participants.
Table 3: Measurement and calibration methods for CF4
Laboratory
KRISS
NMIJ
VNIIM
NIST
Measurement method
Calibration method
Traceability
GC-AED
One point
own gravimetric standard
GC-TCD
Linear, 3 mixtures
own gravimetric standard
FT-IR
Linear, 2 mixtures
own gravimetric standard
GC-TCD
2nd order regression, 5
mixtures
own gravimetric standard
Table 4: Measurement and calibration methods for SF6
Laboratory
KRISS
NMIJ
VNIIM
NIST
Measurement method
GC-AED
GC-TCD
FT-IR
GC-TCD
Calibration method
One point
Linear, 3 mixtures
Linear, 2 mixtures
Linear, 3 mixtures
Traceability
own gravimetric standard
own gravimetric standard
own gravimetric standard
own gravimetric standard
Results
In the current comparison on gas mixtures, measurements were performed on individually prepared gas
mixtures with (slightly) different concentrations. Since the coordinating laboratory prepared these
mixtures using the same methods and materials, the individual gravimetric values can be adopted as
reference values. The difference between the gravimetric and analyzed values has been taken as degree
of equivalence, defined as
Di = xlab,i – xref,i
(4)
which is treated as same way as previously adopted methods [1]. The combined standard uncertainty of
the degree of equivalence can be expressed as
2
2
u ( Di ) = ulab
, i + uref , i
(5)
and the expanded uncertainty, at a 95% confidence level
2
2
U ( Di ) = k ulab
,i + u ref ,i
(6)
where k denotes the coverage factor. For all degrees of equivalence, k = 2 (normal distribution,
approximately 95% level of confidence).
In tables 5 and 6, the results of this comparison are presented. The table contains the following
information.
xgrav Assigned amount of substance fraction of a component
ugrav Standard uncertainty of the assigned value xgrav
xlab
Result as reported by the participant
klab Coverage factor as reported by participant
Ulab Expanded uncertainty as reported by participant
Di
Degree of equivalence, difference between laboratory value and the gravimetric value
U(Di) Expanded uncertainty of the degree of equivalence
The differences between gravimetric and reported value are given as degree of equivalence, that is the
difference between the value measured by the laboratory and the gravimetric value.
The uncertainties in the degrees of equivalence are given with k = 2 for all laboratories, taking into
consideration both the uncertainty reported from the laboratory as well as the uncertainty from gravimetry
(and validation). The combined standard uncertainty of a laboratory has been computed from Ulab and klab.
This implies that if a laboratory used a k value deviating from k = 2, this information has been appreciated
to obtain an estimate for the combined standard uncertainty of the result.
/
Table 5: Results for CF4
xgrav
ugrav
ME2233
100.398
NMIJ
ME2208
VNIIM
NIST
Lab
Cylinder
KRISS
(µmol/mol) (µmol/mol)
xlab
Ulab
(µmol/mol)
(µmol/mol)
0.171
100.35
0.15
99.872
0.175
100.08
ME2212
101.977
0.178
ME2195
100.815
0.171
xgrav
ugrav
klab
Di
U(Di)
(µmol/mol)
(µmol/mol)
2.01
-0.044
0.371
0.66
2
0.208
0.747
101.55
0.47
2.07
-0.427
0.575
100.7
1.30
2
-0.115
1.344
/
Table 6: Results for SF6
Lab
Cylinder
KRISS
ME2233
99.837
NMIJ
ME2208
VNIIM
NIST
(µmol/mol) (µmol/mol)
xlab
Ulab
(µmol/mol)
(µmol/mol)
0.170
99.9
0.26
99.473
0.169
99.41
ME2212
100.682
0.171
ME2195
99.111
0.168
klab
Di
U(Di)
(µmol/mol)
(µmol/mol)
2.06
0.063
0.421
0.67
2
-0.063
0.751
100.78
0.57
2.12
0.098
0.641
99.1
1.00
2
-0.011
1.055
/
Degrees of equivalence
The degrees of equivalence for carbon tetrafluoride and sulfur hexafluoride are shown in figure 1 and 2.
The error bars represent the expanded uncertainty at a 95 % level of confidence. All reported data from
participants overlap with the reference value.
Degree of Equivalence (% relative)
5
CCQM-K15 CF4 in Nitrogen
(Nominal Value: 100 µmol/mol)
4
3
2
1
0
-1
-2
-3
-4
-5
KRISS
NMIJ
VNIIM
NIST
/
Fig. 1. Degree of equivalence for CF4
/
Degree of Equivalence (% relative)
5
4
CCQM-K15 SF6 in Nitrogen
(Nominal Value: 100 µmol/mol)
3
2
1
0
-1
-2
-3
-4
-5
KRISS
NMIJ
VNIIM
NIST
/
Fig. 2. Degree of equivalence for SF6
Conclusions
There is good agreement between the results of the key comparison participants in this comparison for
both CF4 and SF6. The results for CF4 agree within 0.5 % relative, and for SF6 agree within 0.1 % relative.
Even though the concentration is as low as 100 µmol/mol, the comparability between participants on
gravimetric preparation plus comparison analysis is excellent for the laboratories that are participating in
this key comparison.
References
[1] Van der Veen A.M.H, De Leer E.W.B., Perrochet J.-F., Wang Lin Zhen, Heine H.-J.,Knopf D.,
Richter W., Barbe J., Marschal A., Vargha G., Deák E., Takahashi C., Kim J.S., Kim Y.D., Kim B.M.,
Kustikov Y.A., Khatskevitch E.A., Pankratov V.V., Popova T.A., Konopelko L., Musil S., Holland P.,
Milton M.J.T., Miller W.R., Guenther F.R., International Comparison CCQM-K3, Final Report
[2] International Organization for Standardization, ISO 6142:2001 Gas analysis - Preparation of
calibration gas mixtures - Gravimetric methods, 2nd edition
Coordinator
Jin Seog Kim
Korea Research Institute of Standards and Science (KRISS)
Division of Chemical Metrology and Materials Evaluation, 1 Doryong - Dong, Yusong - ku, Daejeon 305600, Rep. of Korea
phone +82 42 868 5352
fax +82 42 868 5042
E-mail [email protected]
Project reference
CCQM-K15
Completion date
December 2003
Annex 1:
Proposal of Degrees of Equivalence
The degree of equivalence of each laboratory with respect to the reference value is given by a pair of
numbers:
Di = (xi - xigrav)
and Ui, its expanded uncertainty (k = 2), both expressed in µmol/mol
Ui2 = 22(ui2 + uigrav2)
The degree of equivalence between two laboratories is given by a pair of numbers:
Dij = Di - Dj = (xi - xigrav) - (xj - xjgrav)
and Uij, its expanded uncertainty (k = 2), both expressed in µmol/mol
Uij2 = 22(ui2 + uj2 + uigrav2 + ujgrav2)
Table 7. Degree of equivalence for carbon tetrafluoride
Lab j ⇒
KRISS
Lab i
⇓
Di
Ui
µmol/mol
KRISS
-0.04
0.37
Dij
NMIJ
Uij
µmol/mol
Dij
VNIIM
Uij
µmol/mol
-0.25
0.83
NMIJ
0.21
0.75
0.25
0.83
VNIIM
-0.43
0.58
-0.38
0.68
-0.64
0.94
NIST
-0.11
1.34
-0.07
1.39
-0.32
1.54
Dij
Uij
µmol/mol
NIST
Dij
Uij
µmol/mol
0.38
0.68
0.07
1.39
0.64
0.94
0.32
1.54
-0.31
1.46
0.31
1.46
Table 8. Degree of equivalence for sulfur hexafluoride
Lab j ⇒
KRISS
Lab i
⇓
Di
Ui
µmol/mol
Dij
NMIJ
Uij
µmol/mol
Dij
VNIIM
Uij
µmol/mol
KRISS
0.06
0.42
NMIJ
-0.06
0.75
-0.13
0.86
VNIIM
0.10
0.64
0.03
0.77
0.16
0.99
NIST
-0.01
1.06
-0.07
1.14
0.05
1.29
0.13
0.86
Dij
Uij
µmol/mol
NIST
Dij
Uij
µmol/mol
-0.03
0.77
0.07
1.14
-0.16
0.99
-0.05
1.29
0.11
1.23
-0.11
1.23
Measurement report of KRISS
Method
The instrument used for CF4 and SF6 determination is HP6890 GC/ AED(2350G )
Configuration of analysis system: gas cylinder -> regulator -> MFC -> sample injection valve -> column > detector -> integrator -> area comparison -> results
Gas Chromatograph with AED,
Carrier gas : Helium
Cavity & Transfer Line Temp. : 250°C, Oven Temp. : 30°C
Column: Polaplot Alumina, 50m, 0.53mm, 0.025mm film thickness
Measurement Wavelength : C(193nm), S(181nm)
Carrier Flow : 4mL/min, Split Ratio : 5:1
Sample loop: 0.5cc, Sample Flow Rate: 100 mL/min
Calibration
Calibration Standards
The calibration standards for CCQM K-15 were prepared by gravimetric method in KRISS. All source
gases were analyzed impurities for purity analysis. The primary standards with 0.05% ~0.15% overall
uncertainty are used.
Instrument Calibration
One-point calibration method used to determine the composition of a sample gas mixture by comparing
with a primary reference gas mixture with similar concentration prepared by gravimetric method.
Sample Handling
The sample cylinders were stood for more than one week at room temperature before measurements. We
used mass-flow controllers to transfer sample gases.
Evaluation of uncertainty
They estimated the uncertainty in the gravimetric methods and measurements. Their uncertainties are
given in Tables.
Uncertainty evaluation of weighing
1
Uncertainty related to the balance & the weights
1. Resolution of balance
2. Accuracy of balance including linearity
3. Incorrect zero point
4. Drift(thermal and time effects)
5. Instability due to draught
6. Location of cylinder on the balance pan
7. Uncertainties in the weights used
8. Buoyancy effects on the weights used
Total (mg)
Value
(mg)
1
1
1
1
Negligible
Negligible
0.05
1.68
Distribution
Standard
uncertainty (mg)
Rectangular
Rectangular
Rectangular
Rectangular
0.289
0.577
0.289
0.289
Rectangular
Rectangular
0.025
0.97
1.235
2
Uncertainty related to the gas cylinder
1. Loss of metal, paints or labels from surface of
cylinder
2. Loss of metal from threads of valve/fitting
3. Dirt on cylinder, valves or associated fitting
4. Adsorption/desorption effects on the external
cylinder surface
5. Buoyancy effects on the cylinder itself
5.1 Cylinder temperature differs from surrounding
air due to e.g. filling with gas
5.2 Change of cylinder volume during filling
5.3 Change of density of surrounding air due to
change in temperature, air, pressure, humidity
and CO2 content
6. Uncertainty in determination of external cylinder
volume
Total (mg)
Value
(mg)
Distribution
Standard
uncertainty (mg)
0.1
Rectangular
0.058
0.5
0.1
Rectangular
Rectangular
0.289
0.058
0.1
Rectangular
0.058
0.6
Rectangular
0.346
1.1
Rectangular
0.635
Negligible
Negligible
0.783
G
G
G
3
Uncertainties related to the component gases
1. Residual gases in cylinder
2. Uncertainties of leakage of gas
2.1 Leakage of air into the cylinder after evacuation
2.2 Leakage of gas from the cylinder valve during
filling
2.3 Escape of gas from cylinder into transport lines
3. Gas remaining in transfer system when weight loss
method is used
4. Absorption/reaction of components on internal
cylinder surface
5. Reaction between components
6. Insufficient homogenization
Value(mg)
Distribution
Standard
uncertainty(mg)
0.057
Rectangular
0.033
1
Rectangular
0.289
1
Rectangular
0.289
Negligible
Negligible
Negligible
Negligible
Negligible
Total (mg)
Total uncertainties in weighing (1.519 mg: standard uncertainty)
G
G
G
Model used for evaluating measurement uncertainty for CF4 & SF6:
Model equation
Csample = Asample × Cstd/Astd
Cfinal = Csample ×G ™Œ—
Typical evaluation of the measurement uncertainty for CF4:
0.410
Quantity
Xi
Estimate
xi
Evaluation
type
(A or B)
Asample
Cstd
frep
1892.33
100.207
0.99993
3
1889.43
A
B
B
Astd
Distribution
normal
normal
A
Standard
uncertainty
u(xi)
Sensitivity
coefficient
ci
Contribution
ui(y)
0.8343
0.041
0.00021
0.053
1.0015
100.3608
0.0442
0.0411
0.021
0.6436
-0.0531
0.0342
Standard
uncertainty
u(xi)
Sensitivity
coefficient
ci
Contribution
ui(y)
0.9684
0.041
0.00073
0.4637
0.086
0.9982
99.8716
-0.0856
0.0833
0.0409
0.073
0.0397
Asample : the peak area of sample
Cstd : the concentration of standard gas (1×10-6 mol/mol)
Astd : the peak area of standard
frep : the factor of reproducibility in analysis.
Typical evaluation of the measurement uncertainty for SF6:
Quantity
Xi
Estimate
xi
Evaluation type
(A or B)
Asample
Cstd
frep
Astd
1163.98
100.075
1.00024
1166.35
A
B
B
A
Distribution
normal
normal
Asample : the peak area of sample
Cstd : the concentration of standard gas (1×10-6 mol/mol)
Astd : the peak area of standard
frep : the factor of reproducibility in analysis.
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
Measurement report of NMIJ
Method
Table 1 shows the summary of our instruments used for this comparison7/ /
Table 1. Summary of Instruments
Component
CF4
SF6
Principle
GC-TCD
GC-TCD
Equipment
GC-14B with pre-amplifier
(Shimadzu)
GC-14B with pre-amplifier
(Shimadzu)
Data collection
GCsolution ver.2 (Shimadzu)
GCsolution ver.2 (Shimadzu)
Column
Porapack Q
( i.d.3 mm, length 6 m, packed,
stainless steel )
Porapack Q
( i.d.3 mm, length 6 m, packed, stainless
steel )
Oven temp.
o
90 C
o
30 C
Calibration
/
Preparation method:
All calibration gas mixtures were prepared by gravimetric method using an electronic mass-comparator
( Mettler Toledo model KA10-3/P, capacity 15 kg , readability 1 mg ) with automatic loading system of
cylinders. The difference on the indication of the mass-comparator between mixture and reference
cylinders can be automatically weighed.
Purity analyses :
The impurities in a nominally “pure” parent gas are determined with GC-PID, GC-FID, GC-TCD, FTIR, GC-HID, and, moisture meter. The mole fraction of the major component is conventionally calculated
from equation (1) in ISO6142:2001.
Table 2, 3 and 4 show the results of impurity analyses.
Table 2. Purity table for nitrogen used as parent gas.
Component
Mole fraction
µmol/mol
Standard uncertainty
µmol/mol
Type of
Uncertainty
method
N2
999999.81
0.94
-
-
C3H8
0.024
0.014
B
GC-FID
H2 O
0.138
0.936
B
Moisture meter
CH4
0.018
0.011
B
GC-FID
SF6
0.0079
0.0046
B
GC-HID
CF4
0.0047
0.0027
B
FT-IR
Table 3. Purity table for sulfur-hexafluoride used as parent gas.
Component
Mole fraction
µmol/mol
Standard uncertainty
µmol/mol
Type of
Uncertainty
method
N2
14.5
8.4
A
GC-TCD
C3H8
0.0239
0.0138
B
GC-FID
CH4
0.0185
0.0107
B
Moisture meter
SF6
999985.5
8.4
-
-
Table 4. Purity table for sulfur-hexafluoride used as parent gas.
Component
Mole fraction
µmol/mol
Standard uncertainty
µmol/mol
Type of
Uncertainty
method
CF4
999977.9
30.2
-
-
N2
13.5
25.6
A
GC-TCD
O2
8.5
15.9
A
GC-TCD
C3H8
0.0239
0.0138
B
GC-FID
SF6
0.0079
0.0046
B
GC-TCD
Measurements sequence and mathematical model:
Each measurement #k consists of the following procedure.
1) Inject 3 calibration standards into the column. Record the retention times and peak areas. The
following calibration data set can be obtained;
· analyte contents, x1, x2, x3,
· standard uncertainties of the analyte contents, u(x1), u(x2), u(x3),
· responses to the analyte contents, y1, y2, y3,
· standard uncertainties of the responses, u(y1), u(y2), u(y3).
2) Inject the sample with the same manner as the calibration standards. Record the retention times and
the peak areas. The response yk and its standard uncertainty u(yk) can be obtained.
3) Parameters and its uncertainty of the analytical function xk = b0,k + b1,k yk were calculated with
ISO6143 implementation software ”B_LEAST version 1.11”. After that, the analytical content xk and
standard uncertainty u(xk) of sample cylinder were calculated from peak area yk and its uncertainty
u(yk).
The analytical functions were validated by Goodness-of-fit. For all analytical functions of our
measurements in these comparison values of Goodness-of-fit were less than 2.
Concentration of calibration standards
The following calibration standards were prepared for analyses of P-41.
Table 5. Concentration and its expanded uncertainty [k=2]
of calibration standards SF6+CF4 /N2. The unit of concentration is µmol/mol.
R1
component
R2
R3
R4
x
U (k=2)
x
U (k=2)
x
U (k=2)
x
U (k=2)
SF6
95.0675
0.0568
98.4846
0.0551
102.7958
0.0536
108.1698
0.0734
CF4
94.0018
0.0564
97.3807
0.0548
101.6437
0.0534
106.9577
0.0728
/
Table 8.
Combination of analytes and standared gases.
Analyte
Combination
SF6
R1, R2, R3
CF4
R1, R3, R4
Stabilization
The sample cylinder was kept in air conditioned storage of about 24 oC.
Injection device
A automatic by-pass-type injector (gas-sampling valve) with an injection capacity of 5 ml was used as
injection device at room temperature.
A pressure regulator was attached to the cylinder. The flow rate of
sample gas was controlled with a valve (Swagelok SS-SS2). /
/
Mass flow controller :
none
Dilution:
None
Evaluation of uncertainty
a. Uncertainty related to the balance and the weights.:
b. Uncertainties related to the gas cylinder:
The “apparent” mass difference between reference and mixture cylinders including Al-weighing-pans on
the balance, mcyl, is expressed as,
∆mcyl = mR − mM − ρair (VR −VM )
.
(1)
where mR and mM are the mass of cylinders, VR and VM are the volume of cylinders, and
ρ air is the air
density. Before weighing, the adjustment curves between the difference of indications on the electronic
mass comparator ∆I and ∆m have been investigated by using standard mass pieces with the uncertainly
corresponding to OIML class E2 and by air density measurement. This curve had good linearity. After
that, the difference of indication ∆Icyl between reference and mixture cylinders was measured. The ∆mcyl
was obtained by substituting ∆Icyl to the adjustment curves. The standard uncertainty of ∆Icyl, u(∆Icyl),
was
calculated from the pooled estimate standard deviation sp= 5 mg divided by √n where n=3. The
deviation undergoes a simulated filling process.
To obtain the mass of filled gas, mgas, from the “difference” of apparent mass differences ∆mcyl
between before and after fillings, eq.(1) is recalled. When ∆m’cyl is the apparent mass difference after
filling gas and ∆m’cyl is before filling,
′ = m′M − mM − ρair(VR −VM ) + ρ'air (VR −V'M )
∆mcyl − ∆mcyl
= m′M − mM − (ρair − ρ'air )(VR −VM ) − ρ'air⋅∆VMl
/ ,
(2)
where,
mM ; mass of cylinder before filling ,
m’M ; mass of cylinder after filling ,
ρair ; air density before filling ,
ρ’air ; air density after filling ,
VR ; volume of cylinder before filling ,
VM ; volume of mixture cylinder before filling ,
V’M ; volume of mixture cylinder after filling ,
∆VM ; volume of mixture cylinder expanded by filling high-pressure dilution gases (∆VM =V’M V M) .
The term ( ρ air − ρ 'air )(VR − VM ) can be ignored, being compared to the term
been assumed in this comparison that the term
ρ 'air ⋅∆VMl
(m′M − mM ) . It has
could be ignored in eq.(2), although we have
never measured the expansion of 10 L Al cylinder by filling high-pressure gas. As the result,
′
m gas = m ′M − m M = ∆ m cyl − ∆ m cyl
.
(3)
The standard uncertainty of u(mgas) includes the following sources of uncertainty.
<Balance>
•Resolution of balance
•Incorrect zero point
•Drift (thermal and time effects)
•Location of cylinder on the balance pan
• Resolution of balance
• Uncertainties in the weights used
• Buoyancy effects on the weights used.
• Accuracy of balance including linearity
< Mechanical handling of cylinder>
•Loss of metal, paints or labels from surface of cylinder:
•Loss of metal from threads of valve /fitting :
•Dirt on cylinder, valves or associated fitting:
•Absorption/ desorption effects on the external cylinder surface:
< Buoyancy effects on the cylinder itself >
•Cylinder temperature differs from surrounding air due to e.g. filling with gas .
•Change of density of surrounding air due to changes in temperature, air pressure, humidity and carbon
dioxide content
The results of the mass measurements are tabulated in the following table.
Table 9. Example of mass and its standard uncertainty of gas filled into cylinder
in the preparation of gas mixtures.
component
i
SF6+CF4/N2
SF6+CF4/N2
Parent gas
mass / g
mgas
Standard uncertainty / mg
u(mgas)
SF6
23.1975
4.2
CF4
13.8213
4.6
N2
956.2897
4.3
SF6 + CF4 / N2
23.3093
4.9
N2
1037.5833
4.6
c. Uncertainties related to the component gases
The following uncertainty sources are negligible in this comparison. In our fillings, weight loss method
was not used.
•Residual gas in cylinder
(The cylinders were evacuated to about 1 Pa before filling,)
•Leakage of air into the cylinder after evacuation
(The leak check was done with vacuum gauge.)
•Leakage of gas from the cylinder valve during filling
(The leak check was done with high-pressure gauge.)
•Escape of gas from cylinder into transport lines
•Absorption/reaction of components on internal cylinder surface
(There are no reactive gases in this comparison.)
•Reaction between components
(There are no reactive gases in this comparison.)
•Insufficient homogenization
(After fillings, the homogenization treatments were performed with a rotating platform. These
calibration standards were used for measurements after more than one day.)
The results of impurity analyses are described in the tables of the section “Calibration standard”. This
table shows the following sources.
•Impurities in the component gases: described in above tables.
•Impurities present in the balance gas (or in other components) : described in above tables.
•One or more of the mixture components present in other component gases ;
The molar masses and their uncertainties are calculated from the atomic weights given in the IUPAC
publication on the Atomic weights of the Elements (2001). In these calculations, it is assumed that the
standard uncertainties of atomic weights of elements are parenthetic values divided by the square root of
3.
Table 10. Molar mass and its standard uncertainty of each component.
Component
Molar mass
Standard
Type of
uncertainty
Uncertainty
Distribution
i
g/mol
g/mol
(A or B)
CF4
88.0043
4.6E-04
B
Rectangular
SF6
146.0554
2.9E-03
B
Rectangular
N2
28.01340
2.3E-04
B
Rectangular
The mole fractions xi of the component i in the final gas mixture are calculated using eq.(3) of ISO6142.
These standard uncertainties u(xi) were calculated from (A.5) of the same ISO.


x ⋅m
xi = ∑  n i , A A

A=1
 ∑ xi , A ⋅ M i
 i =1
P
n
 ∂x
u 2 ( xi ) = ∑  i
i =1  ∂M i
where,
2








mA

∑
 n
A=1
 ∑ xi , A ⋅ M i
 i =1
P
2






,
P
P n 

 ∂x 
∂x
 ⋅ u 2 ( M i ) + ∑  i  ⋅ u 2 ( m A ) + ∑∑  i

m
∂
∂
i =1 
A=1 i =1  xi , A
A 

( eq. 3 of ISO6142)
2

 ⋅ u 2 ( xi , A ) , (eq. A.5 of ISO6142)


xi is the mole fraction of the component i in the final mixture, i =1,…, q-1, q, q+1,…, n ;
P is the total number of the parent gases ;
N is the total number of the components in the final mixture ;
MA is the mass of the parent gas A determined by weighing , A=1,…, r-1, r, r+1,…, P.
xi,A is the mole fraction of the component i, i =1 ,…, n in the parent gas A, A=1,…, r-1, r, r+1,…, P.
Results of calculating the standard uncertainty and contributions are tabulated in the following table. The
concentration and its uncertainty were tabulated in Table 11.
Table 11. Examples of contributions to the standard uncertainties on mole fraction from mass
measurement, impurity analyses, and, molar mass in pre-mixtures and final-mixtures. The unit of values
is µmol/mol.
Gas mixture
SF6+CF4/N2
(1-step dilution)
SF6+CF4/N2
(2-step dilution)
2
 ∂x i 
 ⋅ u 2 ( m A )
i =1 
A 
P
P
2
 ∂xi 
 ⋅ u 2 ( xi , A )

i =1 
i, A 
n
2
 ∂xi 
 ⋅ u 2 ( M i )
i =1 
i 
n
i
xi
u(xi)
SF6
4609.98
0.84
0.828
0.078
0.0982
CF4
4558.45
1.52
1.51
0.078
0.0442
SF6
98.4846
0.0551
0.0201
0.019
0.000054
CF4
97.3807
0.0548
0.0199
0.019
0.000053
∑  ∂m
∑∑  ∂x
A=1
∑  ∂M
d. Uncertainties related to the analysis
GC-TCD was used for analyses. This detector is one of universal type detector. In the chromatograph at CF4
analysis, the resolution of peaks between N2 and CF4 , R, is about 1.3. Here, R = 2(tN -tCF4)/(W N +W CF4),
2
2
which tN2 and tCF4 are retention time and WN and WCF4 are the times corresponding to the bottom of each
2
triangle-approximate peak. This R value means that N2 peak scarcely influences the quantitative analysis of CF4.
Final analytical function x is the average of all measurements.
J
x = ∑ xk J
,
(4)
k =1
where J is the number of measurement #k and xk is the analyte content at each measurement #k described in the
previous section “Instrument calibration”.
The standard uncertainty of analyte content u(x) is evaluated from the following equations;
u 2 ( x) = u 2 ( x) ISO 6143 + u 2 ( x) between − day ,
(5)
J
u 2 ( x) ISO 6143 = ∑ u 2 ( xk ) J ,
(6)
k =1
J
u 2 ( x) between − day = ∑ ( x k − x) 2 ( J − 1) .
k =1
These uncertainties include the following source of uncertainty ;
(7)
·Repeatability and selectivity of the analyzer ,
·Appropriateness of the calibration curve (model and its residuals) .
Model used for evaluating measurement uncertainty for CF4:
Typical evaluation of the measurement uncertainty for CF4:
Quantity
Xi
Estimate
xi
(µmol/mol)
Evaluation
type
(A or B)
Distribution
Standard
uncertainty
u(xi)
(µmol/mol)
0.223
Sensitivity
coefficient
ci
Contribution
ui(y)
(µmol/mol)
xk=1
100.03
A
normal
1/√3
0.129
xk=2
100.33
A
normal
0.404
1/√3
0.233
xk=3
99.870
A
normal
0.250
1/√3
0.144
A
normal
0.135
1
0.135
between-day
x
100.08
0.33
Model used for evaluating measurement uncertainty for SF6:
Typical evaluation of the measurement uncertainty for SF6:
Quantity
Xi
Evaluation
type
(A or B)
Distribution
Standard
uncertainty
u(xi)
(µmol/mol)
0.105
Sensitivity
coefficient
ci
Contribution
ui(y)
(µmol/mol)
xk=1
99.444
A
normal
1/√3
0.061
xk=2
98.944
A
normal
0.243
1/√3
0.140
xk=3
99.827
A
normal
0.276
1/√3
0.159
A
normal
0.260
1
0.260
betweenday
x
/
/
/
/
/
/
/
/
/
Estimate
xi
(µmol/mol)
99.41
0.34
Measurement report of VNINM
Method
IR absorption spectrometry was used.
Instrument: FTIR spectrometer FSM1201 made by Monitoring Ltd.,
St. Petersburg, Russia: spectral range 400 – 7800 cm-1, resolution 1, 2, 4, 8, 16 cm-1.
IR gas cell: optical path length 100 mm.
Data collection was fully automated.
/
Calibration
Calibration standards
Pure components used for preparation of the calibration standards.
Characteristics of pure substances are shown in table 1.
Table 1 – Description of pure components
Component
Molar fraction, ppm
Standard uncertainty, ppm
SF6
999460
СF4
998300
N2
999988,5
Note: 500 ppm of CF4 was found out in pure SF6
160
124,6
0,812
Relative
standard
uncertainty, %
0,0160
0,0125
0,0000812
Binary pre-mixtures were prepared: SF6/N2 with molar fraction 0,491 % and СF4/N2 with molar fraction
0,994 %. Two calibration standards each comprising three components were prepared using these
mixtures with characteristics shown in table 2.
Table 2 – Characteristics of calibration standards
Cylinder #
Measured component
0470
0633
SF6
CF4
N2
SF6
CF4
N2
Molar fraction,
ppm
101,76
104,26
the rest
95,36
95,76
the rest
Relative standard
uncertainty, %
0,074
0,114
0,076
0,118
-
/
/
Instrument calibration:
/
Calibration used was liner regression for CF4 or SF6 concentrations vs absorbance magnitude at 1283
and 948 cm-1 respectively. Classic Least Squares (CLS) method was used to deduce absorbance
magnitude from IR spectra.
Each standard was measured several times at different temperature and pressure conditions. For
calibration purposes all concentrations were reduced to standard temperature and pressure conditions.
Sample handling
Prior to measurements cylinders were stabilized to room temperature. For each measurement the gas cell
was evacuated, then filled up with the investigated gas sample, and then cell pressure equalized to the
atmospheric pressure. Evacuation and filling up processes were manually controlled.
/
Evaluation of uncertainty
Table 3 – Evaluation of uncertainty of molar fraction SF6 in the three component gas mixture (101,76 ppm
– cylinder № 0470)
Value Хi
Estimation,
Standard uncertainty u(xi), %
xi
Pure components
Molar fraction of SF6, ppm
999460
0,016
Molar fraction of N2, ppm
999988,5
0,0000812
Molar mass SF6 *), g/mol
145,9991
0,00027
Molar mass N2 *), g/mol
28,01288
0,00143
Preparation of the pre-mixture SF6/ N2 – 0,4910 %
Mass of empty cylinder, g
1289,1919
0,000152
Mass SF6, g
30,4152
0,00579
Mass N2, g
1182,0685
0,000795
Preparation of the final mixture with SF6
Mass of empty cylinder, g
635297,53
0,000279
Mass of the pre-mixture with SF6, g
9,7060568
0,0177
Mass N2, g
444,54645
0,0021
Total standard uncertainty
0,0247
Expanded standard uncertainty (k=3)
0,074
/
Table 4 – Evaluation of uncertainty of molar fraction SF6 in the tree component gas mixture (95,36 ppm –
баллон № 0632)
Value Хi
Estimation,
Standard uncertainty u(xi), %
xi
Pure components
Molar fraction of SF6, ppm
999460
0,016
Molar fraction of N2, ppm
999988,5
0,0000812
Molar mass SF6 *), g/mol
145,9991
0,00027
Molar mass N2 *), g/mol
28,01288
0,00143
Preparation of the pre-mixture SF6/ N2 – 0,4910 %
Mass of empty cylinder, g
1289,1919
0,000152
Mass SF6, g
30,4152
0,00579
Mass N2, g
1182,0685
0,000795
Preparation of the final mixture with SF6
Mass of empty cylinder, г
529,601103
0,000327
Mass of the pre-mixture with SF6, g
9,181457
0,0186
Mass N2, g
449,52304
0,00208
Total standard uncertainty
0,0253
Expanded standard uncertainty (k=3)
0,076
*) Molar mass of pure components SF6 and N2 were calculated taking into consideration the measured
values of molar fractions of admixtures and molar masses of the main component and admixtures.
Table 5 – Evaluation of uncertainty of molar fraction CF4 in the three component gas mixture (104,26
ppm – cylinder № 0470)
Value Хi
Standard uncertainty u(xi), %
Estimation,
xi
Pure components
Molar fraction of CF4, ppm
998300
0,0125
Molar fraction of N2, ppm
999988,5
0,0000812
Molar mass CF4 *), g/mol
87,9047
0,00046
Molar mass N2 *), g/mol
28,01288
0,00143
Preparation of the pre-mixture СF4/ N2 – 0,9938 %
Mass of empty cylinder, g
1453,91733
0,000135
Mass СF4, g
36,80977
0,00484
Mass N2, g
1166,6743
0,000805
Preparation of the final mixture with СF4
Mass of empty cylinder, g
635297,533
0,00028
Mass of pre-mixture with CF4, g
4,912485
0,035
Mass N2, g
444,54645
0,0021
Total standard uncertainty
0,038
Expanded standard uncertainty (k=3)
0,114
Table 6 – Evaluation of uncertainty of molar fraction CF4 in the three component gas mixture (95,76 ppm
– cylinder № 0632)
Value Хi
Estimation,
Standard uncertainty u(xi), %
xi
Pure components
Molar fraction of CF4, ppm
998300
0,0125
Molar fraction of N2, ppm
999988,5
0,0000812
Molar mass CF4 *), g/mol
87,9047
0,00046
Molar mass N2 *), g/mol
28,01288
0,00143
Preparation of the pre-mixture СF4/ N2 – 0,9938 %
Mass of empty cylinder, g
1453,91733
0,000135
Mass СF4, g
36,80977
0,00484
Mass а N2, g
1166,6743
0,000805
Preparation of the final mixture with СF4
Mass of empty cylinder, g
529,601103
0,000327
Mass of the pre-mixture with CF4, g
4,5529471
0,037
Mass N2, g
449,52304
0,00208
Total standard uncertainty
0,0394
Expanded standard uncertainty (k=3)
0,118
*) Molar mass of pure components SF6 and N2 were calculated taking into consideration the measured
values of molar fractions of admixtures and molar masses of the main component and admixtures.
Table 7 – Results of measurements of molar fraction SF6 and CF4 in cylinder № МЕ 2212
Measurement # 1
Component
CF4
SF6
Measurement # 2
Component
CF4
SF6
Measurement # 3
Component
CF4
SF6
Measurement # 4
Component
CF4
SF6
Measurement # 5
Component
CF4
SF6
Measurement # 6
Component
CF4
SF6
Measurement # 7
Component
CF4
SF6
Measurement # 8
Component
CF4
SF6
Measurement # 9
Component
CF4
SF6
Date
(dd/mm/yy)
13.11.03
Result
(µmol/mol)
101,83
101,17
Standard deviation
(% relative)
0,12
0,07
Number of
replicates
3
3
Date
(dd/mm/yy)
18.11.03
Result
(µmol/mol)
101,48
100,72
Standard deviation
(% relative)
0,06
0,03
Number of
replicates
3
3
Date
(dd/mm/yy)
19.11.03
Result
(µmol/mol)
101,87
101,18
Standard deviation
(% relative)
0,03
0,14
Number of
replicates
3
3
Date
(dd/mm/yy)
20.11.03
Result
(µmol/mol)
101,43
100,57
Standard deviation
(% relative)
0,05
0,08
Number of
replicates
3
3
Date
(dd/mm/yy)
21.11.03
Result
(µmol/mol)
101,38
100,60
Standard deviation
(% relative)
0,05
0,15
Number of
replicates
3
3
Date
(dd/mm/yy)
28.11.03
Result
(µmol/mol)
102,02
101,36
Standard deviation
(% relative)
0,08
0,15
Number of
replicates
3
3
Date
(dd/mm/yy)
01.12.03
Result
(µmol/mol)
101,28
100,60
Standard deviation
(% relative)
0,11
0,12
Number of
replicates
3
3
Date
(dd/mm/yy)
02.12.03
Result
(µmol/mol)
101,50
100,65
Standard deviation
(% relative)
0,05
0,12
Number of
replicates
3
3
Date
(dd/mm/yy)
03.12.03
Result
(µmol/mol)
101,12
100,19
Standard deviation
(% relative)
0,06
0,06
Number of
replicates
3
3
Table 8 – Estimation of uncertainty of molar fraction SF6 in gas mixture in cylinder № МЕ 2212,
presented for comparison
Source of uncertainty
Type of
evaluation
В
Preparation of SF6 in final
mixture
Formation of calibration curve
В
А
Standard deviation of the result
of measurement of molar
fraction SF6
Total standard uncertainty
Expanded uncertainty (k=2,120, Р=95 %)
Standard uncertainty,
u(xi), %
0,025
Coefficient
sensitivity
1
0,236
0,377
of
1
1
Contribution
Ui(y, %)
0,025
0,236
0,126
0,27
0,57
Table 9 – Estimation of uncertainty of molar fraction СF4 in gas mixture in cylinder № МЕ 2212,
presented for comparison
Source of uncertainty
Type of
evaluation
В
Preparation of CF4 in final
mixture
Formation of calibration curve
В
А
Standard deviation of the result
of measurement of molar
fraction CF4
Total standard uncertainty
Expanded uncertainty (k=2,069, Р=95 %)
Standard uncertainty,
u(xi), %
0,040
Coefficient
sensitivity
1
0,186
0,297
1
1
of
Contribution
Ui(y, %)
0,040
0,186
0,100
0,22
0,46
/
Table 10 – Result of measurements
Received values of molar fraction and expanded uncertainty of CF4 and SF6 in three component gas
mixture.
Component
Result
(µmol/mol)
CF4
101,55
SF6
100,78
N2
the rest
The coverage factor is based on 95 % confidence.
Expanded
Uncertainty, %
0,46
0,57
-
Coverage factor1
2,069
2,120
-
Measurement report of NIST
Method
CF4 and SF6 measurements: HP5890 Gas Chromatograph, thermal conductivity detector, 3.7m x 0.32 cm
packed column of 80/100 mesh Silica Gel, 3 ml gas sample loop on a 6 port gas sampling valve, peak
area responses determined using HP Chemstation software and sent to excel spreadsheet.
Calibration
Calibration Standards=/
Primary standards by gravimetry. CF4 and SF6 weighed into 150 ml volume stainless steel vessels and
weighed on a Mettler single pan balance with a 0.0001 g resolution. 6-Liter volume aluminum cylinders
weighed on a Mettler 30000-K top-loading balance with a 0.1 g resolution. Purity analysis by GC and
FTIR. CF4 and SF6 transferred from 150 mL vessels into gas cylinders. Vessels weighed before and
after transfer. Residual in system purged into cylinder with pure dry nitrogen. Purity analysis done by
FTIR and GC/TCD.
Instrument Calibration:
CF4: 2nd order regression calibration curve using 3-5 primary gravimetric standards (PSM) used:
concentrations of 52.85, 84.21, 99.20, 116.3, and 444.2 x 10-6 mol/mol (nmol/mol); measurement
sequence: September 29,2003 - K15sample, PSM1, PSM2, PSM3, K15sample ; on October 27-28,2003 K15sample, PSM1, K15sample, PSM2, K15sample, PSM3, K15sample, PSM4, K15sample, PSM5, K15sample . K15
sample used as a control to correct for instrument drift due to temperature and pressure fluctuations.
SF6: Linear regression calibration curve using 3 primary gravimetric standards (PSM) used:
concentrations of 109.5, 98.96, and 84.76 10-6 mol/mol (nmol/mol); measurement sequence: K15sample,
PSM1, K15sample, PSM2, K15sample, PSM3, K15sample. K15 sample used as a control to correct for
instrument drift due to temperature and pressure fluctuations.
Sample Handling:
Cylinders transferred to laboratory in which measurements were taken to equilibrate temperature.
CF4 and SF6: low dead volume stainless steel regulator attached to cylinder, sample flow of 30 mL/min to
purge sample loop with flow dropped to ambient pressure before injection onto column
Evaluation of measurement uncertainty
Model used for evaluating measurement uncertainty for CF4:
Typical evaluation of the measurement uncertainty for CF4:
Quantity
Xi
Estimate
xi
Evaluation
type
(A or B)
Distribution
Relative
Standard
uncertainty
CF4 wt std
N2 wt std
CF4 purity
N2 purity
CF4 in N2
0.00022g
0.07 g
< 0.01
< 0.0005
<0.05x10-
A
A
B
B
B
Gaussien
Gaussien
rectangular
rectangular
rectangular
0.084 %
0.008 %
0.01 %
0.0005 %
0.05 %
Bal Resolut
Weights
0.0001 g
B
A
rectangular
Gaussien
0.04 %
0.002 %
6
Sensitivity
coefficient
ci
Contribution
ui(y)
Acc balance
Metal loss
Repeat Anal
Cal curve
80 pa cts
A
B
A
A
Gaussien
rectangular
Gaussien
Gaussien
0.001 %
0.02 %
0.37 %
0.53 %
Model used for evaluating measurement uncertainty for SF6:
Typical evaluation of the measurement uncertainty for SF6:
Distribution
Estimate
Evaluation
Quantity
xi
type
Xi
(A or B)
SF6 wt std
0.00022g
A
Gaussien
N2 wt std
0.07 g
A
Gaussien
SF6 purity
< 0.01 %
B
rectangular
N2 purity
<0.0005%
B
rectangular
SF6 in N2
<0.05x10B
rectangular
6
Bal Resolut
Weights
Acc balance
Metal loss
Repeat Anal
Cal curve
0.0001 g
80 pa cts
B
A
A
B
A
A
Gaussien
Gaussien
rectangular
Gaussien
Gaussien
Relative
Standard
uncertainty
0.060 %
0.008 %
0.01 %
0.0005 %
0.05 %
0.03 %
0.002 %
0.001 %
0.02 %
0.37 %
0.31 %
Sensitivity
coefficient
ci
Contribution
ui(y)