E L S EVI E R
Mass Spectrometry
and Ion Processes
International Journal of Mass Spectrometry and Ion Processes 173 (1998) 55-63
A primary xenon isotopic gas standard with SI traceable values for
isotopic composition and molar mass
S. Valkiers, Y. Aregbe, P.D.P. Taylor, P. De Bibvre
Institute for Reference Materials and Measurements, European Commission
JRC, B-2440 Geel, Belgium
Received 11 July 1997; accepted 24 October 1997
Abstract
A metrological certification measurement was made on a large batch of xenon separated from the terrestrial atmosphere by
Messer Griesheim (Duisburg, Germany). The measurements were performed using the same procedure for measurements of
amount ratios as developed for the improvement of the Avogadro constant NA. During the measurement, the gas effusion from
the expansion vessel into the ion source was continuously monitored by measuring experimental values for [m(iE)/m(E)] -~ to
enable correction for mass discrimination. Synthetic mixtures were made of enriched Xenon isotopes and measured. They did
not reveal a significant correction factor for residual unknown errors within the measurement uncertainty of 5 × 10 -4. Thus, an
isotopic composition and a molar mass (atomic weight) value M(Xe) = 131.29276 ± 0.00033 g mol-I for xenon in this batch
was established by procedures confirmed by kinetic gas theory at this level. The measured isotope amount ratios were compared
to previous measurements on atmospheric xenon. They are in good agreement but now have considerably smaller relative
combined uncertainties: n(124Xe)/n(132Xe)=O.O03 536(12); n(126Xe)/n(132Xe)=0.003 307 7(72); n(128Xe)/n(132Xe) =
0.070989(29); n(129Xe)/n(132Xe)=0.98112(41);
n(13°Xe)/n(132Xe)=O.151290(47);
n(131Xe)/n(132Xe) = 0.789055(76);
n( 134Xe)/n(132Xe) = 0.387 819(69); n( 136Xe)/n(132Xe) = 0.329 16(17). Published by Elsevier Science B.V.
Keywords: Primary isotopic gas standard; Isotopic composition; Xenon; Isotope amount ratios; Gas isotope mass spectrometry;
Traceability; SI; Avogadro constant
I. Introduction
The isotopic composition and molar mass
(atomic weight) of Xe were measured by Nier
in 1950 [1] and Valkiers et al. in 1993 [2].
These measurements were not calibrated by
means of synthetic mixtures of xenon isotopes.
Xenon in air is still deemed the best reference
material by IUPAC [3] so far. High precision
measurements of atmospheric and radiogenic
Xe have been made by Mazor [4] and Ozima
and Podosek [5]. It seemed to be useful to the
authors to perform new measurements of the
0168-3659/98/$19.00 Published by Elsevier Science B.V.
PII S 0 1 6 8 - 1 1 7 6 ( 9 7 ) 0 0 2 7 4 - 7
isotopic composition and of the molar mass
(numerically equal to the atomic weight) of natural Xe in view of the fact that a high precision,
high accuracy, isotopic measurement procedure
and gas isotope mass spectrometer have been
developed and are available from the attempts
to redetermine and improve the value of the
Avogadro constant [6-9]. Also a need exists to
measure isotope amount ratios of Xe (and other
gases such as krypton) with an uncertainty of 1
part in 10-4 [ 10-13 ] and there are other important
applications for this gas measurement capability
in both geological and atmospheric sciences.
56
S. Vallders et al./International Journal Of Mass Spectrometry and Ion Processes 173 (1998) 55-63
Table 1
Experimentally observed values for [m(iSiF4)/m(28SiF4)] ~ and for ~ versus theoretical ones as predicted by kinetic gas theory where 4~ = 0.5.
Measurements for Si samples of natural composition. Uncertainties are standard uncertainties
[m(29SiFa)/m(28SiF4)] 4,
[m(3°SiF4)/m(28SiF 4)] 4,
Theoretical
Observed
~b observed
1.004 80
1.009 57
1.004 69(20)
1.009 11 (31 )
0.489(21 )
0.476(16)
2. A primary standard for xenon isotopic
measurements
The establishment of a primary isotopic gas
standard (PIGS) of measurement was thus indicated. A primary standard of measurement,
according to the international vocabulary of
metrology (VIM) [14], is a "standard that is
designated or widely acknowledged as having
the highest metrological qualities and whose
value is accepted without reference to other standards of the same quantity". Ratio measurements
of amount of substance have been carried out at
IRMM to a combined uncertainty of a few parts
in 10 5 for n(iSi)/n(28Si) ratios as an essential part
of three successive and successful attempts to
improve the Avogadro constant. The combined
uncertainty of the measurements was verified
against synthetic isotope mixtures of enriched
Si isotopes [19] prepared to an uncertainty of 1
part in 10 5 on the isotope amount ratio, and by
verifying the closeness of the actual effusion
behaviour of SiF4 in the gas inlet of the Avogadro
II amount comparator, to ideal gas behaviour as
governed by kinetic gas theory [7,8,15]. That was
done by comparing measured values for ~b in
[m(iSiF4)/m(28SiF4)] 4' to those calculated from
theory which prescribes q5 = 0.5 (see Table 1
and Table 2).
This proves that:
(a) the conditions in the inlet system and ion
source of the Avogadro spectrometer are
very close to permitting ideal gas behaviour;
(b) the effect of the isotope fractionation at
the pinholes in the gold foil where the gas
leaks into the ion source does not affect the
combined uncertainty of the measured values
for the isotope amount ratios to more than 5 x
10-4;
(c) the method of measuring isotope amount
ratios is independent o f these ratios over a
large range of values for these ratios;
(d) the method is largely independent of the
chemical identity of the gas molecules.These
conclusions encouraged us to apply the same
measurement procedure (gas inlet, software,
mass spectrometric techniques, data reduction) [ 15-19] on isotope amount ratio measurements in an attempt to establish a Xe
PIGS.
There are significant limitations in the present
published ability to achieve measurements with
such low uncertainty. First, the quantitative
Table 2
Experimentally observed values for [m(iE)/m(JE)] ~ and for ~, versus theoretical ones (as prescribed by kinetic gas theory where ~ = 0.5).
Measurements for gaseous fluorides of C, Te, S, and Ge samples of natural isotopic composition. E can stand for either an element or an element
compound. Uncertainties are standard uncertainties
[m( 13CF4)/m( 12CF4)] i/2.
Ira( 126TeF6)/m( 13°TeF6)] 1/2
[m( 335F6)/m(32SF6)] 1/2
[m(34SF6)/rn(32SF6)] i/2
[m(72GeF 4)/m(74GeF4)] 1/2
Theoretical
Observed
q~ observed (theoretical = 0.500)
1.005 67
0.991 77
1.003 42
1.006 83
0.993 31
1.00562(10)
0.991 78(8)
1.00347(4)
1.00685(1)
0.99293(41)
0.4960(87)
0.4993(48)
0.5073(58)
0.501 53(80)
0.528(28)
X Valkiers et aL/lnternational Journal o f Mass Spectrometry and Ion Processes 173 (1998) 55 63
determinations of practical corrections necessary
to deal with isotope fractionation in the gas introduction system are not so well understood nor
adequately documented in literature. Second, rigorous data treatment and data reduction concepts
required to identify and correct subtle error components at very small uncertainties ( < 10 -3) are
not found in published literature. Third, at present there are no isotopic reference materials of
xenon or krypton. Except 'Xe (Kr) in air' which
are certified to an uncertainty of only 5 x 10 -3. In
this paper, the concept 'accuracy' rather than
precision is stressed here because some of the
applications of Xe isotopic measurements envisaged require inter-comparability of results from
different laboratories and at different points in
time. In such situations knowledge of an SI-traceable value provides a powerful common basis for
measurement comparability across borders in
space and time.
This xenon primary isotopic gas standard
(IRMM-2000) meets the criteria for a primary
standard because its values are based on a comparison with gravimetrical synthetic mixtures of
enriched Xe isotopes (see below) as well as on
the Avogadro measurement procedure which
contains a self-calibration against theoretical
values provided by kinetic gas theory. An
essential quality of a primary standard is
intrinsic, long-term stability [20]. It is expected
that it will provide a useful 'anchor' for any
xenon isotopic measurements. Also, calculational and parametric evaluation techniques
developed in this work are expected to provide
spin-off benefits for other high precision
measurements on other gaseous compounds of
elements.
3. The material for a xenon PIGS
The PIGS material is a high purity xenon separated from atmospheric air. It has a purity of
about 0.999999 mol(Xe) per mol(gas). It consists of one homogenized batch supplied by the
57
Messer Griesheim company (W6rthstral3e 170,
D-47053 Duisburg, Germany), and is bottled in
1 1 aluminium pressure cans at a pressure of 1.2 x
106 Pa. Messer Griesheim developed technological procedures to ensure minimum adsorption/
interaction with the inner walls of the containers
used. In order to avoid possible mass fractionation effects during sampling gas from the can, a
special valve (Messer Griesheim 795.08312) is
mounted on the cans.
The measured isotopic composition of the
PIGS is considered to be representative for the
isotopic composition of atmospheric xenon (as
far as one can define the 'true' atmospheric
xenon because slight deviations can even occur
in the isotopic composition of atmospheric xenon
depending on the geographic spot from which it
has been collected). Also, isotopic fractionation
during the separation of xenon from air cannot be
completely excluded from occurring but careful
extraction as performed by Messer-Griesheim
should minimise this effect to an undetectable
level.
4. The measurement procedure used
Prior to the admission of Xe gas to the mass
spectrometer, the expansion vessel (volume 2 l,
degassed previously at a temperature of 75°C)
was filled to a pressure of about 0.9 Pa yielding
an amount of Xe gas sufficient for one isotope
amount ratio measurement lasting about 1.2 h
[10]. Temperature and pressure readings were
controlled by a carefully laid-out data acquisition system built up for the measurements in
the framework of the redetermination of the
Avogadro constant, taking into account adsorption and desorption effects in the inlet system of
the Avogadro II amount comparator [21,22]. The
measurement procedure used for the isotope
amount ratio measurements of xenon is the
same as described in a similar measurement of
silicon [8,9,17] and nitrogen [15] and is repeated
in short here for the convenience of the reader.
58
S. Valkiers et al./lnternational Journal Of Mass Spectrometo' and Ion Processes 173 (1998) 5 5 - 6 3
The instrument is the Avogadro II 'amount
comparator' which was developed for the
redetermination of the Avogadro constant from
isotope amount ratio measurements on SiF4 calibrated by means of synthetic mixtures of
enriched Si isotopes [ 19]. The vacuum conditions
in the ion path of this spectrometer represent a
considerable improvement over those in previous
instruments and have been described elsewhere
[8]. The ion currents arising from the isotopically
distinct molecules were measured by using a
single Faraday cup in the peak jumping mode
and by calculating the weighted mean ratios of
the recorded ion currents at mass positions m/e =
124 (124Xe) to 136 (136Xe). During the measurement, the sample in the expansion vessel of the
spectrometer changes in isotopic composition as
a function of time because the effusion from the
expansion vessel through the gold foil at the inlet
of the spectrometer [21] is mass dependent. The
influence of possible adsorption and desorption
effects in the inlet system is also taken into
account, although in the case of xenon this effect
is very small and therefore does not affect the
isotope measurement results [22]. Extrapolation
of the measurement results to time t = to, the time
at which the sample starts to leak into the ion
source, is therefore necessary to determine the
initial isotopic composition of the sample [9,17].
The nine ion currents are measured twice in a
symmetrical sequence for each scan. For every
cycle, consisting of 15 scans, the logarithmically
interpolated mean currents and corresponding
uncertainties are calculated and printed out
together with the values for the derived ratios
as a function of time t. Extrapolation to t = to
then yields one value for the isotope amount
ratio investigated [9]. Use is thereby made of
the equation which relates the measurement
result (ratios at time to) to what is actually
measured (ion currents):
ln(R/Ro)
ln[i(JE)/io(JE)] - OlEi-- 1
(1)
with R -- N(iE)/N(JE), i.e. the ratio between the
number of atoms of the isotope with m a s s m(iE)
and the number of atoms of the isotope with mass
m(/E), R0 is the same ratio extrapolated to time t
= t0, I(/E) is the measured current transported by
ions of the isotope with mass m(/E), I0(/E) is
the same current extrapolated to time t = to,
c~Ei =kE/kE/ !S the effusion fractionation factor,
equal to [m('E)/mfE)] -~ with 4~ = 1/2 in case of
ideal gas behaviour.
5. I s o t o p e a b u n d a n c e s and m o l a r mass o f the
new xenon PIGS
A credible PIGS needs to fulfil the following
criteria:
1. Fully calibrated isotope amount ratios measured to (very) small (ISO/BIPM Guide)
uncertainties.
2. Homogeneity of the sub-samples of this
standard
3. Wide and open availability of the samples in
adequate amounts so that different laboratories can refer to the 'same' values as carried
by a stable gas.
4. Full, documented uncertainty budgets. A
detailed uncertainty budget for the preparation
of the mixtures is given in Ref. [10]. The first
criterion implies gravimetrically prepared
synthetic mixtures of enriched Xe isotopes
which have not so far been prepared for
xenon. Such mixtures were prepared in collaboration between IRMM and NMi [10]
despite the demanding requirements on
weighing gases to sufficiently small combined
uncertainties (10 -3 relative or better) and
despite the high cost of enriched Xe isotopes.
It required working with microgravimetric
techniques to minimize the cost of expensive
enriched Xe isotopes. For the mixtures, the
amounts of the enriched Xe isotopes were
chosen such that the prepared amount ratios
were close to those for natural xenon. Correction factors Kres for possible residual effects
59
S. Valkiers et al./lnternational Journal of Mass Spectromet~ and Ion Processes 173 (1998) 55-63
Table 3
Correction factors Kre~ = Rmp/Robs for one of the synthetic xenon isotope mixtures (no. 3). Uncertainties are standard uncertainties [23]. All
uncertainties indicated are uncertainties U=k.u,. where u, is the combined uncertainty, and k is the coverage factor/c = 1.
Isotope amount ratios
from gravimetric preparation
(Xenon isotope mixture 3)
n( 124Xe)/n(132Xe)
n( t26Xe)/n(mXe)
n( 12SXe)/n(132Xe)
n( 129Xe)/n(132Xe)
n( 13°Xe)/n(132Xe)
n( 131Xe)/n(132Xe)
n( 134Xe)/n(132Xe)
n( 136Xe)/n(t32Xe)
Correction factors
K,e~ = R prep/Robs
Rprep
0.003 560 4(31)
0.003 497 2(17)
0.091 484(12)
I. 1O0 01 ( 11)
O. 154 193( 11 )
0.790 580(12)
0.397 706(15)
0.496 916(76)
0.998 7(11)
0.999 17(61)
1.000 22( 13)
1.000 35 (14)
1.000 422(85)
1.000 345(20)
0.999 588(43)
0.999 46(16)
(Kres is the amount ratio prepared/amount ratio
observed) for the measurement procedure can
be determined with these mixtures (see
Table 3 and Fig. 1). All measurements made
on the PIGS (Tables 4 - 6 ) were verified
against these gravimetrically prepared synthetic mixtures of enriched xenon. The applied
measurement procedure and the corresponding
detailed uncertainty budget is described in other
1.010
works [7,10,15]. All PIGS bottles and synthetic
isotope mixtures were measured in the same
series of tightly controlled measurements in
order to minimise the (always possible) effect
of any instrumental drift.
In Fig. 2(a)-2(d) the absolute isotope amount
ratios of the PIGS (IRMM-2000) are compared
with previously published values [ 1-3,25-27].
K,.,- factors for mixture 3
1.008
o
1.005
IJ
~
1.000
0.998
0.995
i
129/132
--
i
i
130/132
131/132
i
m (JXe)/m
i
i
i
134/132
1361132
(l~ZXe)
Fig. 1. Correction factor Kr~ (Kres= prepared amount ratio/observed amount ratio, for major abundant isotopes) for residual, but so far unknown,
errors versus m( Xe)/m( 132Xe) for synthetic mixture number 3, U = k.uc where uc is the combined uncertainty, and k is the coverage factor k = 3.
S. Valkiers et al./lnternational Journal o f Mass Spectrometry and Ion Processes 173 (1998) 55-63
60
Table 4
Observed isotope amount ratios of the primary isotope gas standard (IRMM-2000) with the correction factors K. All uncertainties indicated are
uncertainties U =k.uc where uc is the combined uncertainty, and k is the coverage factor k = 1
n( 124Xe)/n(132Xe)
n( 126Xe)/n(132Xe)
n(128Xe)/n(132Xe)
n( 129Xe)/n(132Xe)
n( 13°Xe)/n(132Xe)
n(131Xe)/n(132Xe)
n( 134Xe)/n(132Xe)
n( 136Xe)/n(132Xe)
Observed amount
ratios of the PIGS
from the direct
measurement using
the Avogadro procedure
Correction factors
Kres = Rprer,/Robs
0.003 541 01(96)
0.003 310 4( 13)
0.070 973 4(27)
0.980 778(26)
0.151 226 4(89)
0.788 783(20)
0.387 979(16)
0.329 343(18)
0.998 7(11)
0.999 17(61 )
1.000 22(13)
1.000 35(14)
1.000 422(85)
1.000 345(20)
0.999 588(43)
0.999 46(16)
Table 5
Absolute isotope amount ratios of the PIGS (1RMM-2000). All uncertainties indicated are expanded uncertainties U = k.ur where uc is the
combined uncertainty, and k is the coverage factor k = 3
n( IZ4Xe)/n(t32Xe)
n( 126Xe)/n(132Xe)
n( 1~SXe)/n(132Xe)
n(l:gxe)/n(132Xe)
n( 13°Xe)/n(132Xe)
n( 131Xe)/n(132Xe)
n( 134Xe)/n(132Xe)
n( 136Xe)/n(132Xe)
Absolute amount
ratios of the PIGS
from the direct
measurement using
the Avogadro procedure
Amount ratio
of the IUPAC
selected from the
'best measurement'
of xenon [1,3]
0.003 536(12)
0.003 307 7(72)
0.070 989(29)
0.981 12(41)
0.151 290(47)
0.789 055(76)
0.387 819(69)
0.329 16(17)
0.003 570(77)
0.003 347(76)
0.071 36(47)
0.9833(78)
0.151 7(11)
0.787 6(55)
0.388 3(25)
0.329 8(19)
Table 6
Absolute isotopic composition and molar mass M(Xe) (numerically equal to atomic weight) of the PIGS IRMM-2000. All uncertainties
indicated are expanded uncertainties U = k.u,. where uc is the combined uncertainty, the coverage factor k = 3. The xenon atomic masses
used in the calculations are taken from Ref. [24]
Isotope
Amount fraction x 100
Mass fraction x 100
124Xe
126Xe
128Xe
129Xe
t3°Xe
t3tXe
132Xe
134Xe
136Xe
0.095 2
0.089 0
1.9102
26.4006
4.071 0
21.2324
26.908 6
10.435 7
8.857 3
0.089 8
0.085 3
1.8609
25.9204
4.0279
21.1697
27.033 9
10.643 3
9.168 6
Molar mass of xenon, M(Xe) = (131.292 75 + 0.000 34) g tool -t.
Uncertainty
+_ 0.000 3
_ 0.000 2
_+ 0.000 8
_+ 0.0082
+_. 0.001 3
_+ 0.0030
___0.003 3
_+ 0.002 1
_+ 0.004 4
S. Valkiers et al,/lnternational Journal o f Mass Spectrometry and lon Processes 173 (1998) 55 63
61
(a) 0.157
IUPAC'93
0.155
O,I I 9
v
o
0.153
Clarke'64~l
IRMM 2000
O19
~,
II~MM~
1-
-
~ × 0.151
asford'73
4
Nier'50
0.149
0.147
0.0705
I - -
0.0707
0,0709 0.0711 0.0713 0,0715 0,0717
128
132
0.0719
n(xe)ln(xe)
(b) r
~
lUPAC'93
0.793
0.792
0.791
o~
19
~x 0.790
0.789
IRMM-2000
0.788 I
0.787
0.786
0.785
0.784
0.975
I
' Podosek'71
v'~ ~sford'73
r" ;.
p
Nier'5(
Clarke '64
I IRMM'93
i
I
0.980
0.985
129
0.995
0.990
132
1.000
n(xel/n(xe)
(c)
0.3320
IUPAC93
0.3315
CIa'ke'64
0.3310
lw
e~119
~x
0.3305
.l
v
Pi
0.33o0
-t-
~losek71
I
"-, i,' RM
'
.
.
Nk~50
-t
Basfom"73
I
0.3290
0.3285
0.3280
0.388
i
i
.
0.387
O.387
0.388
.
.
.
0.388 0.389
134
132
0.389
0.390
0.390
n(xe)ln(xe)
13~
Fig, 2. (a) Three-isotope plot for n( 130 Xe)/n( 132 Xe) to n( 128 Xe)/n( 132 Xe). (b) Three-isotope plot for n( 131 Xe)/n(~Xe)
to n(129Xe)/n(l~ZXe). (c)
Three-isotope plot for n(IS4Xe)ln(~S2Xe) to n(IS6Xe)/n(IS2Xe). (d) Three-isotope plot for n( 126 Xe)/n( 132 Xe) to n(124Xe)/n(132Xe).
62
S. Valkiers et al./lnternational Journal o['Mas~ Spectrometry and Ion Processes 173 (1998) 55-63
(d)
0.0035
0.003,5
e,,l~
~x 0.0034
IUPAC'93
v
o.oo~
~x 0.0o33
Nier'b~.
,
I
-]- Clarke'64
'
im
po LIEt
• IRMM'93
0.0033
0.0032
i
•
I
+
-
I
--
I
I
I
I
I
I
I
0.0033 0.0034 0.0034 0.0035 0.0035 0.0036 0.0036 0.0037 0.0037 0.00,,~ 0.0038
n/'124'~ ,,.,/132~
~, Xe/" ~, X e /
Fig. 2. Continued
6. Conclusions
'Calibrated' measurements have been performed on xenon in order to achieve a PIGS for
that element. The gas is available in 1 1 pressure
cans which all have been verified for their isotopic identity with cans stored at IRMM as a PIGS
IRMM-2000 from Messer Griesheim in Duisburg. It can be used for accurate amount ratio
measurements
of
xenon
in
geological,
atmospheric and other studies.
Because the measurements on the synthetic
isotope mixtures of enriched xenon as well as
the PIGS were measured on the 'Avogadro II
amount comparator', the same instrument as
used for the redetermination of the Avogadro
constant [9] and self-calibrated against kinetic
gas theory, the PIGS is traceable to the Avogadro
constant and the SI. This measurement method
used in the certification measurements of this
PIGS meets the BIPM/CCQM for a 'primary
method of measurement'. This means that all
measurements of isotope amount ratios of Xe
which are calibrated against IRMM-2000 are
traceable to the SI by means of two links only
in the traceability chain. The isotope amount
ratios of Xe here described are in agreement
with the previously recognised 'best measurement' by Nier [1] and IUPAC [23], but have
considerably smaller uncertainties.
In the (near) future PIGSs of other gases
(nitrogen, krypton, oxygen, carbon dioxide, sulphur hexafluoride, etc.) will be made available
from IRMM to serve as an 'anchor' for various
differential measurement applications where
reproducibilities of the order of 10 -4 have been
attained. The xenon PIGS is the first one
available in the planned series.
Acknowledgements
A special tribute is due to Paul Vercammen
from Belgian Valve and Fittings (Zaventem,
Belgium) for assistance in selection (and delivery) of the high-tech valves and ampoules needed
for this project. Without this 'top' equipment, the
preparation of the synthetic Xe isotope mixtures
would not have been possible. Also the assistance
ofR.M. Wessel (NMi-Delft) in the preparation of
the gas mixtures is gratefully acknowledged. The
careful maintenance and monitoring of the mass
spectrometer hardware and software by D. Vendelbo, P. Hansen, R. Damen and G. Van Baelen
are warmly acknowledged.
References
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