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International Comparison CCQM-K15 – Emission level of CF 4 and SF 6
Final Report
Jin Seog Kim^1 , Dong Min Moon^1 , Kenji Kato 2 , Leonid A. Konopelko 3 , Yuri A. Kustikov^3 , Franklin R. Guenther 4
(^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
CF 4 and SF 6 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 CF 4 and SF 6 are the global warming source gases.
This part of project focuses a comparison to measurement capability for measuring CF 4 and SF 6 at emission level. This key comparison will cover the comparability of the gas CRMs on the emission level (10. 10 - mol/mol – 100 mmol/mol in Nitrogen or Air) of following chemicals; CF4, C (^) 2F6, 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 CF 4 and SF 6 in nitrogen, as used in this key comparison, are summarized in table 1.
Table 1: Nominal amount of substance ratios
Component x ( μ mol/mol) Carbon tetrafluoride 100 Sulfur hexafluoride 100 Nitrogen 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:
- gravimetric preparation (weighing process)
- purity of the parent gases
- 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.
u^2 ( x (^) gravp ) = u^2 ( x (^) weighing ) + u^2 (∆ x (^) purity ) (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 u (^) ver the standard deviation s is used (Table 2).
Table 2: Uncertainty components for a typical mixture
Component u ( x (^) gravp ) (%, rel) u (^) ver (%, rel) CF 4 0.045 0. SF 6 0.045 0.
The results from table 2 have been used to calculate the uncertainty in the assigned (reference) value
U (^) gravR = ku (^) gravR (2)
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. x (^) grav Assigned amount of substance fraction of a component u (^) grav Standard uncertainty of the assigned value x grav x (^) lab Result as reported by the participant k (^) lab Coverage factor as reported by participant U (^) lab Expanded uncertainty as reported by participant D (^) i Degree of equivalence, difference between laboratory value and the gravimetric value U(D (^) i ) 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 U (^) lab and k (^) lab. 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. G Table 5: Results for CF 4
Lab Cylinder (^) ( μ mol/mol) x^ grav ( μ mol/mol)^ u^ grav (μmol/mol)^ x^ lab ( μ mol/mol)^ U^ lab k (^) lab (μmol/mol) D^ i (μmol/mol)^ U(D^ i^ )
KRISS ME2233 100.398 0.171 100.35 0.15 2.01 -0.044 0.
NMIJ ME2208 99.872 0.175 100.08 0.66 2 0.208 0.
VNIIM ME2212 101.977 0.178 101.55 0.47 2.07 -0.427 0.
NIST ME2195 100.815 0.171 100.7 1.30 2 -0.115 1.
G Table 6: Results for SF 6
Lab Cylinder (^) ( μ mol/mol) x^ grav ( μ mol/mol)^ u^ grav (μmol/mol)^ x^ lab ( μ mol/mol)^ U^ lab k (^) lab (μmol/mol) D^ i (μmol/mol)^ U(D^ i^ )
KRISS ME2233 99.837 0.170 99.9 0.26 2.06 0.063 0.
NMIJ ME2208 99.473 0.169 99.41 0.67 2 -0.063 0.
VNIIM ME2212 100.682 0.171 100.78 0.57 2.12 0.098 0.
NIST ME2195 99.111 0.168 99.1 1.00 2 -0.011 1.
G
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.
KRISS NMIJ VNIIM NIST
0
1
2
3
4
5 CCQM-K15 CF 4 in Nitrogen (Nominal Value: 100 μmol/mol)
Degree of Equivalence (% relative)
G
Fig. 1. Degree of equivalence for CF 4
G
KRISS NMIJ VNIIM NIST
0
1
2
3
4
5
CCQM-K15 SF 6 in Nitrogen (Nominal Value: 100 μmol/mol)
Degree of Equivalence (% relative)
G
Fig. 2. Degree of equivalence for SF 6
Conclusions
There is good agreement between the results of the key comparison participants in this comparison for
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: D (^) i = ( x (^) i - x (^) i grav) and U (^) i , its expanded uncertainty ( k = 2), both expressed in μmol/mol U (^) i^2 = 2 2 ( u (^) i^2 + u (^) i grav^2 )
The degree of equivalence between two laboratories is given by a pair of numbers: D (^) ij = D (^) i - D (^) j = ( x (^) i - x (^) i grav) - ( x (^) j - x (^) j grav)
and U (^) ij , its expanded uncertainty ( k = 2), both expressed in μmol/mol U (^) ij^2 = 2 2 ( u (^) i^2 + u (^) j^2 + u (^) i grav^2 + u (^) j grav^2 )
Table 7. Degree of equivalence for carbon tetrafluoride
Lab j ⇒ KRISS NMIJ VNIIM NIST
Lab i ⇓ D^ i U^ i D^ ij U^ ij D^ ij U^ ij D^ ij U^ ij D^ ij U^ ij μmol/mol μmol/mol μmol/mol μmol/mol μmol/mol KRISS (^) -0.04 0.37 -0.25 0.83 0.38 0.68 0.07 1. NMIJ (^) 0.21 0.75 0.25 0.83 0.64 0.94 0.32 1. VNIIM (^) -0.43 0.58 -0.38 0.68 -0.64 0.94 -0.31 1. NIST (^) -0.11 1.34 -0.07 1.39 -0.32 1.54 0.31 1.
Table 8. Degree of equivalence for sulfur hexafluoride
Lab j ⇒ KRISS NMIJ VNIIM NIST
Lab i ⇓ D^ i U^ i D^ ij U^ ij D^ ij U^ ij D^ ij U^ ij D^ ij U^ ij μmol/mol μmol/mol μmol/mol μmol/mol μmol/mol KRISS (^) 0.06 0.42 0.13 0.86 -0.03 0.77 0.07 1. NMIJ (^) -0.06 0.75 -0.13 0.86 -0.16 0.99 -0.05 1. VNIIM (^) 0.10 0.64 0.03 0.77 0.16 0.99 0.11 1. NIST (^) -0.01 1.06 -0.07 1.14 0.05 1.29 -0.11 1.
Measurement report of KRISS
Method
The instrument used for CF 4 and SF 6 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: 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 Value (mg) Distribution Standard uncertainty (mg)
- Resolution of balance (^1) Rectangular 0.
- Accuracy of balance including linearity 1 Rectangular 0.
- Incorrect zero point 1 Rectangular 0.
- Drift(thermal and time effects) 1 Rectangular 0.
- Instability due to draught Negligible
- Location of cylinder on the balance pan Negligible
- Uncertainties in the weights used 0.05 Rectangular 0.
- Buoyancy effects on the weights used 1.68 Rectangular 0. Total (mg) 1.
Quantity X (^) i
Estimate x (^) i
Evaluation type (A or B)
Distribution Standard uncertainty u(x (^) i)
Sensitivity coefficient c (^) i
Contribution u (^) i(y)
Asample 1892.33 A 0.8343 0.053 0.
Cstd 100.207 B normal 0.041 1.0015 0.
f rep 0.
B normal 0.00021 100.3608 0.
Astd 1889.43 A 0.6436 -0.0531 0.
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 X (^) i
Estimate xi
Evaluation type (A or B)
Distribution Standard uncertainty u(xi )
Sensitivity coefficient ci
Contribution u (^) i (y)
Asample 1163.98 A 0.9684 0.086 0.
Cstd 100.075 B normal 0.041 0.9982 0.
f rep 1.00024 B normal 0.00073 99.8716 0.
Astd 1166.35 A 0.4637 -0.0856 0.
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.
G G G G G G G G G G G G G G G G
Measurement report of NMIJ
Method
Table 1 shows the summary of our instruments used for this comparisonUG G
Table 1. Summary of Instruments
Component CF 4 SF 6
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. 90 oC 30 oC
Calibration G 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, FT- IR, 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.
· responses to the analyte contents, y 1 , y 2 , y 3 , · standard uncertainties of the responses, u ( y 1 ), u ( y 2 ), u ( y 3 ).
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.
Parameters and its uncertainty of the analytical function xk = b 0, k + b 1, 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 SF 6 +CF 4 /N 2. The unit of concentration is μmol/mol.
component R 1 R 2 R 3 R 4 x U ( k =2) x U ( k =2) x U ( k =2) x U ( k =2) SF 6 95.0675 0.0568 98.4846 0.0551 102.7958 0.0536 108.1698 0.
CF 4 94.0018 0.0564 97.3807 0.0548 101.6437 0.0534 106.9577 0.
G
Table 8. Combination of analytes and standared gases.
Analyte Combination
SF 6 R 1 , R 2 , R 3 CF 4 R 1 , R 3 , R 4
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 ). G
G
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 −ρ air ( V (^) R − VM ). (1)
where m R and m M are the mass of cylinders, V R and V M 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 E 2 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, m gas, 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 air air R M air Ml
cyl cyl M M air R M air R M m m V V V
m m m m V V V V
= ′− − − − − ⋅ ∆
∆ −∆ ′ = ′− − − + −
( ' )( ) '
( ) ' ( ' )
ρ ρ ρ
ρ ρ G , (2)
where,
m M ; mass of cylinder before filling , m ’M ; mass of cylinder after filling , ρ air ; air density before filling , ρ’ air ; air density after filling , V R ; volume of cylinder before filling , V M ; volume of mixture cylinder before filling , V ’M ; volume of mixture cylinder after filling , ∆V M ; volume of mixture cylinder expanded by filling high-pressure dilution gases ( ∆V M = V ’M - V M).
The term ( ρ (^) air −ρ' air )( VR − VM )can be ignored, being compared to the term ( mM ′^ − mM ). It has
been assumed in this comparison that the term ρ ' air ⋅∆ VMl 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 = mM ′ − mM =∆ mcyl −∆ m cyl ′. (3)
The standard uncertainty of u ( m gas) includes the following sources of uncertainty.
- Resolution of balance
- Incorrect zero point
- Drift (thermal and time effects)
- Location of cylinder on the balance pan
(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
Table 10. Molar mass and its standard uncertainty of each component.
Component Molar mass Standard uncertainty
Type of Uncertainty
Distribution
i g/mol g/mol (A or B)
CF 4 88.0043^ 4.6E-04^ B Rectangular
SF 6 146.0554^ 2.9E-03^ B Rectangular
N 2 28.01340^ 2.3E-04^ B Rectangular
The mole fractions x (^) i 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.
∑ ∑
∑ ∑ = =
=
^ ⋅
P
A
n
i
iA i
A
P
A
n
i
iA i
iA A i x M
m
x M
x m x 1 1
, 1 1
,
, ,^ ( eq. 3 of ISO6142)
∑ ∑ ∑∑ = = = =
P
A
iA
n
i (^) iA
i A
P
i (^) A
i i
n
i (^) i
i i (^) x u x
x u m m
x u M M
x u x 1
,
2
2
(^1) ,
2
2
1
2
2
1
(^2) ( ) ( ) ( ) ( ), (eq. A.5 of ISO6142)
where,
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 i xi u ( xi )^2 ( )
2 1^ A
P i A
i (^) u m m
x (^) ⋅
∂
∂ ∑= ∑∑= = ⋅
∂
P ∂ A iA
n i iA
i (^) u x x
x 1 ,
2
2 1 , ( )^2 ( )
2 1^ i
n i (^) i
i (^) u M M
x (^) ⋅
∂
∂ ∑=
SF 6 4609.98 0.84 0.828 0.078 0. SF 6 +CF 4 /N 2 (1-step dilution) (^) CF 4 4558.45^ 1.52^ 1.51^ 0.078^ 0.
SF SF^6 98.4846^ 0.0551^ 0.0201^ 0.019^ 0.
6 +CF 4 /N 2
(2-step dilution) (^) CF 4 97.3807^ 0.0548^ 0.0199^ 0.019^ 0.
d. Uncertainties related to the analysis
GC-TCD was used for analyses. This detector is one of universal type detector. In the chromatograph at CF 4 analysis, the resolution of peaks between N 2 and CF 4 , R , is about 1.3. Here, R = 2( t N2- t CF4)/( W (^) N2+ W (^) CF4),
which t N2 and t CF4 are retention time and W N2 and W CF4 are the times corresponding to the bottom of each
triangle-approximate peak. This R value means that N 2 peak scarcely influences the quantitative analysis of CF 4.
Final analytical function x is the average of all measurements.
x x J
J
k
∑ k
=
1
, (4)
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 ( x )= u ( x ) ISO + u ( x ) between − day
2 6143
2 2
u x u x J
J
k
ISO ∑ k
=
1
2 6143
1
=
u x − x x J
J
k
between day k.^ ( 7 )
These uncertainties include the following source of uncertainty ;
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-^. IR gas cell: optical path length 100 mm. Data collection was fully automated. G 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 Relative standard uncertainty, % SF 6 999460 160 0, СF 4 998300 124,6 0, N 2 999988,5 0,812 0, Note: 500 ppm of CF 4 was found out in pure SF 6
Binary pre-mixtures were prepared: SF (^) 6/N 2 with molar fraction 0,491 % and СF4/N 2 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 Molar fraction, ppm
Relative standard uncertainty, % SF 6 101,76 0, CF 4 104,26 0,
N 2 the rest - SF 6 95,36 0, CF 4 95,76 0,
N 2 the rest - G GGGG Instrument calibration: GGGG Calibration used was liner regression for CF 4 or SF 6 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. G
Evaluation of uncertainty
Table 3 – Evaluation of uncertainty of molar fraction SF 6 in the three component gas mixture (101,76 ppm
Value Хi Estimation, x (^) i
Standard uncertainty u(x (^) i), %
Pure components Molar fraction of SF (^) 6, ppm 999460 0, Molar fraction of N2, ppm 999988,5 0, Molar mass SF 6 *), g/mol 145,9991 0, Molar mass N 2 *), g/mol 28,01288 0, Preparation of the pre-mixture SF 6 / N 2 – 0,4910 % Mass of empty cylinder, g 1289,1919 0, Mass SF (^) 6, g 30,4152 0, Mass N 2 , g 1182,0685 0, Preparation of the final mixture with SF 6 Mass of empty cylinder, g 635297,53 0, Mass of the pre-mixture with SF 6 , g 9,7060568 0, Mass N 2 , g 444,54645 0, Total standard uncertainty 0, Expanded standard uncertainty ( k=3) 0,
GGGG Table 4 – Evaluation of uncertainty of molar fraction SF 6 in the tree component gas mixture (95,36 ppm – баллон № 0632)
Value Хi Estimation, x (^) i
Standard uncertainty u(x (^) i), %
Pure components Molar fraction of SF (^) 6, ppm 999460 0, Molar fraction of N2, ppm 999988,5 0, Molar mass SF 6 *), g/mol 145,9991 0, Molar mass N 2 *), g/mol 28,01288 0, Preparation of the pre-mixture SF 6 / N 2 – 0,4910 % Mass of empty cylinder, g 1289,1919 0, Mass SF (^) 6, g 30,4152 0, Mass N 2 , g 1182,0685 0, Preparation of the final mixture with SF 6 Mass of empty cylinder, г 529,601103 0, Mass of the pre-mixture with SF 6 , g 9,181457 0, Mass N 2 , g 449,52304 0, Total standard uncertainty 0, Expanded standard uncertainty ( k=3) 0,
*) Molar mass of pure components SF 6 and N 2 were calculated taking into consideration the measured values of molar fractions of admixtures and molar masses of the main component and admixtures.
