Technical Supplement 2B
Ion Corrections
This is a very technical section for those interested in how  values are actually
generated in traditional mass spectrometer measurements. Skip this section unless you
have a detailed interest in these measurements.
Making the isotope measurements with a mass spectrometer is elegant, the realm
of physics. There are five overview steps involved with measurements:1) convert samples
into to a common denominator gas, for example combusting nitrogen-containing samples
to N2, 2) introduce the gas to the evacuated source region of a mass spectrometer where
ions are generated via close encounters with electrons boiling off a hot filament, 3)
accelerate and focus the ions through a magnetic field into discrete ion beams according
to mass, 4) measure the ion beam intensities in downstream collectors, and 5) calculate
the isotope compositions via automated software. Steps 4) and 5) concern us here, a
chance to see isotopes at work.
The details of the measurement and calculation are given in the attached tables, using
first a N2 example, followed by CO2 and SO2 examples. The following text gives some
guidance to these tables. For all the HCNOS gases, correction procedures presented here
are well-known and reliably implemented in routine laboratory practice.
Nitrogen
The details of the ion corrections are simplest for nitrogen gas N2 (Table A). Two
collectors count the two main N2 ion beams at mass 28 and mass 29. The ions involved
are 14N14N+ at mass 28, and 14N15N+ plus 15N14N+ at mass 29. Counted currents from the
ion beams can be combined to give the ratio
29
R = 2*(14N15N)/14N14N
where R denotes the isotope ratio and the ratio superscript (29 in this case) gives the
heavy mass used in the ratio calculation.
The algebra continues in simple steps, first canceling 14N in the numerator and
denominator, then substituting 15R for the isotope ratio 15N/14N, so that
29
R = 2*15R or 15R = 29R/2.
In practice, the mass spectrometer determines 15R as 29R/2 ratios for samples and
standards measured sequentially, then computer software calculates  values:
15N = [(15RSAMPLE/15RSTANDARD)-1]*1000
Similar steps apply for the  determinations for the other HCOS gases.
Calculations for carbon and sulfur isotopes typically are based on measurements of CO2
and SO2 gas, and the presence of additional oxygen in these molecules makes these
calculations more complex. Calculations for O2 and H2 are most like those for N2 because
these three molecules each contain only a single element. They are simple diatomic
molecules, and the ion corrections are correspondingly simple. But corrections for O2 and
H2 do differ somewhat than the simplest N2 corrections presented here, as follows. When
determining 18O values of O2, corrections are needed for 17O, similar to corrections
discussed below as part of 13C measurements. And for D (hydrogen) measurements,
corrections must be made for pressure-dependent formation of H3+ in the source region of
the mass spectrometer. Such corrections are calculated on a daily basis from routine and
reliable measurements.
CO2
The CO2 molecule contains multiple carbon and oxygen isotopes (Table B). There are
three CO2 ion beams at masses 44, 45 and 46 that contain various mixtures of these
isotopes, and are important in measurements of this gas. Most of the CO2 gas is mass 44,
with minor amounts of CO2 present at masses 45 and 46 constituting the heavy isotope
(isotopomer) varieties of this gas (Table B). The ion beam at mass 44 has just one kind of
CO2, 12C16O16O. But the ion beam at mass 45 is considerably more complicated with 3
parts, 13C16O16O, 12C17O16O, and 12C16O17O. The 45/44 ratio is thus composed of two
parts, the desired 13R term but also an undesired 17R term:
45
R = 13R + 2*17R
Just how serious is this extra contribution from 17O? Calculations show that it is
large enough to worry about. The calculations focus on determining the relative amounts
of each of these mass 45 gases from the known isotope abundances of the individual
isotopes. For example, for mass 45 that has 13C-containing CO2 (13C16O16O) the
individual isotope abundances in the standard of Table B are respectively 1.1056%,
99.7553% and 99.7553% for 13C, 16O, and 16O. Similarly for 17O-containing mass 45
(12C17O16O and 12C16O17O) these abundances are 98.8944%, 0.0385%, and 0.2062%.
Multiplying these individual abundances gives the relative strengths of ion beams
collected in the mass 45 collector:
13 16
C O16O = 1.1056*99.7553*99.7553 = 11,001.96
12 17
C O16O + 12C16O17O = 2*(98.8944*0.0385*99.7663) = 759.62
Expressing these numbers as percentages of the total ion beam measured in at mass 45
with the total ion beam having a relative intensity of 11001.96 + 759.62 = 11761.68, one
arrives at:
13 16
C O16O contribution = 100*11,001.96/11761.68 = 93.54%
12 17
C O16O + 12C16O17O contribution = 100*759.62/11761.68 = 6.46%.
Here we see that although most (about 94%) of the signal in the 45 collector is due to
C, there is a substantial (6%) contribution from the heavy oxygen isotope, 17O. To
13
correct for this 17O contribution, modern mass spectrometers include measurement of a
third CO2 isotopomer at mass 46. The 17O contributions for the mass 45 ion beam are
estimated from the mass 46 measurements, as follows.
The mass 46 collections almost completely record the 18O contributions, with only
very minor contributions from 17O and 13C (about 0.2% of the total; Table B). Thus
measurements at mass 46 can estimate the 18O composition. With a known 18O
composition, 17O compositions can be estimated because isotope fractionations for 18O
are just about twice those for 17O. The two extra neutrons in 18O vs. 16O lead to an
approximately doubled fractionation relative to the fractionation caused by one extra
neutron in 17O vs. 16O. (In fact, the author’s father was one of the first to experimentally
verify this 2-for-1 rule; see Journal of Physical Chemistry 56: 897-901, 1952. Subsequent
investigations by Clayton and others focused on precise quantification of these so-called
“mass-dependent” fractionation effects for terrestrial vs. meteorite samples).
So we use the 18O signals measured at mass 46 to estimate and correct for the
17
small O contribution to the mass 45 signal. With this correction, the ion beam currents
measured in the mass 44 and 45 collectors give a ratio or 13R value used in the computer
calculation of 13C values. The exact equations for these calculations are given at the
bottom of Table B.
A side benefit of using CO2 for isotope work is that 18O values are routinely
measured from the 46/44 ion currents. Carbonates are decomposed in many laboratories
to CO2 for measurement of oxygen isotope values. Also oxygen in water can be measured
as oxygen in CO2 after suitable equilibration and exchange of the oxygen in water and
CO2. Thus, working with CO2 often has an advantage of giving information about both
carbon and oxygen isotope compositions.
Sulfur
The ion corrections for sulfur work are particularly complex for the SO2 molecule
because there are four sulfur isotopes and three oxygen isotopes involved (Table C). One
solution has been to prepare samples and standards in the same way to maintain constant
oxygen isotope compositions, while another solution used in some high-precision work
has been to fluorinate the sulfur to form SF6. Fluorination has the advantage that fluorine
has only one stable nuclide so that in SF6, all the isotope variations are due to sulfur
isotope variations. However, fluorination is a relatively difficult and hazardous laboratory
procedure, so that there is continued interest in the SO2 measurements that are routinely
made in most laboratories. At the time of this writing, new mass spectrometers are on the
market that will allow simultaneous measurement of SO+ and SO2+ ions formed in the
mass spectrometer from SO2 gas preparations. This simultaneous measurement should
allow routine oxygen isotope corrections for the SO2-based sulfur isotope work (Table
C), similar to those outlined above for the carbon isotopes.
A mass spectrometer equipped to measure isotope values of both SO+ and SO2+
ions collects data from four ion beams for masses 48, 50, 64 and 66. The isotope values
for SO+ are recorded in the 50/48 ratio (50R) and the isotope values for SO2+ are recorded
in the 66/64 ratio (66R). Final  values are calculated from these ratios. Table C tabulates
the various ions contributing to 50R and 66R, with oxygen isotopes contributing
appreciably to both ratios. Notes to Table C show that these ratios are composed of 18R
and 34R contributions, i.e.,
66
R = [2*(32S18O16O) + 34S16O16O]/ 32S16O16O = 2*18R + 34R, and similarly
50
R = (32S18O + 34S16O)/ 32S16O =
18
R + 34R
Inspection shows that 18R should be the simple difference between the ratio
measurements, 66R - 50R (Holt and Engelkemeir 1970). However, experience shows that
fractionation during formation of SO+ and SO2+ is not equivalent, so that the actual
equations should be 66R = 2*18R + 34R and 50R =  18R + 34R, where  is the
fractionation differential in the formation of SO+ vs. SO2+. Solution of these equations
requires knowledge of  that can be hard to measure. An alternative method for
calculating oxygen isotope contributions without estimation of  is given in the text
following Table C. Those calculations yield the following general formulas:
18O = 24.02*66 - 23.024*50 and
34S = 1.0908*66 - 0.0908*18.
This last formula also gives the conventional way of calculating 34S from 66 values
under the assumption that samples and standards are prepared with the same oxygen
isotope composition, so that 18 is zero and can be ignored. Experience using the newer
method based on combined 66 and 50 values requires further steps, detrending the
measured 66 and 50 values for any fractionation and then recalculating them vs. a
common reference value (Fry, in preparation). This detrending involves plotting 66 and
50 values vs. sample size to show trends related to fractionation, then using regression to
develop size-based corrections for fractionation, and finally using a common reference
value for both 66 and 50 corrections (Fry, in preparation).
Further Reading
Clayton, R.N., L. Grossman, and T.K. Mayeda. 1973. A component of primitive nuclear
composition in carbonaceous meteorites. Science 182:485-488.
Clayton, R.N., N. Onuma, and T.K. Mayeda. 1976. A classification of meteorites based
on oxygen isotopes. Earth and Planetary Science Letters 30:10-18.
Craig, H. 1957. Isotopic standards for carbon and oxygen and correction factors for massspectrometric analysis of carbon dioxide. Geochimica et Cosmochimica Acta 12:132149.
Ding, T., S. Valkiers, H. Kipphardt, P. De Bievre, P.D. P. Taylor, R. Gonfiantini and R.
Krouse. 2001. Calibrated sulfur isotope abundance ratios of three IAEA sulfur isotope
reference materials and V-CDT with a reassessment of the atomic weight of sulfur.
Geochimica et Cosmochimica Acta 65:2433-2437.
Epstein, S. and T. Mayeda. 1953. Variations of the 18O content of waters from natural
sources. Geochimica et Cosmochimica Acta 4:213-224.
Fry, A. and M. Calvin. 1952. The isotope effect in the decomposition of oxalic acid.
Journal of Physical Chemistry 56:897-901.
Fry, B., S.R. Silva, C. Kendall and R.K. Anderson. 2002. Oxygen isotope corrections for
online 34S analysis. Rapid Communications in Mass Spectrometry 16:854-858.
Giesemann, H.-J. Jaeger, A.L. Norman, H.R. Krouse and W.A. Brand. 1994. On-line
sulfur-isotope determination using an elemental analyzer coupled to a mass spectrometer.
Analytical Chemistry 66:2816-2819.
Halas, S. and W.P. Wolacewicz. 1981. Direct extraction of sulfur dioxide from sulfates
for isotopic analysis. Analytical Chemistry 53:686-689.
Holt, B.D. and Engelkemeir, A.G. 1970. Thermal decomposition of barium sulfate to
sulfur dioxide fro mass spectrometric analysis. Analytical Chemistry 42:1451-1453.
Hulston, J.R. and B.W. Shilton. 1958. Sulphur isotopic variations in nature. Part 4 –
Measurement of sulphur isotopic ratio by mass spectrometry. New Zealand Journal of
Science 1:91-102.
Lane, G.A. and M. Dole. 1956. Fractionation of oxygen isotopes during respiration.
Science 123:574-573.
Mariotti, A. 1983. Atmospheric nitrogen is a reliable standard for natural 15N abundance
measurements. Nature 303:685-687.
Puchelt, H., BR. Sables and T.C. Hoering. 1971. Preparation of sulfur hexafluoride for
isotope geochemical analysis. Geochimica et Cosmochimica Acta 35:625-628.
Rees, C.E. 1978. Sulphur isotope measurements using SO2 and SF6. Geochimica et
Cosmochimica Acta 42:383-389.
Rees, C.E., W.J. Jenkins and J. Monster. 1978. The sulphur isotopic composition of
ocean water sulphate. Geochimica et Cosmochimica Acta 42:377-381.
Santrock, J., S.A. Studley and J.M. Hayes. 1985. Isotopic analyses based on the mass
spectrum of carbon dioxide. Analytical Chemistry 57:1444-1448.
Table A. N2+ ion contributions at collectors for masses 28, 29 and 30, and calculation of
15N values from these measured values.
% Abundance in Reference Gas
14
15
N
N
99.6337%
0.3663%
Mass 28:
14
Mass 29:
15
Mass 30:
15
N14N+
N14N+
14 15 +
N N
N15N+
99.268742% of total N
0.729916% of total N
0.001342% of total N
Steps in calculating 15N for a sample of N2 gas measured against this reference:
1) Because so little of the 15N signal is in the mass 30 cup (for unenriched samples),
the calculation concerns only masses 28 and mass 29, i.e., mass 30 is ignored. But
importantly, for 15N enriched samples with artificially added 15N, mass 30
contributions must be factored in to calculate final 15N values (see section 2.6
above).
2) 29R = mass 29/mass 28 = (2*15N14N)/14N14N = 2*15R, and 15R = 29R/2.
3) 15N vs. laboratory standard = (15RSAMPLE/15RSTANDARD)-1)*1000 =
(((29RSAMPLE/2)/(29RSTANDARD/2))-1)*1000 = ((29RSAMPLE/29RSTANDARD) -1)*1000
4) If the sample is measured as1 relative to a lab standard whose isotope ratio value
is R1, and the lab standard is measured as 2 vs. atmospheric air, the international
standard for N2 work, then the following equations apply:
1 = [(RSAMPLE/R1) - 1]1000
2 = [(R1/RAIR) -1]1000
and the  value of the sample expressed vs. the atmospheric N2 standard is given
as: NAIR = [(RSAMPLE/RAIR) - 1]1000 or
NAIR = [(1 + 1000)*(2 + 1000) - 1,000,000]/1000.
Table B. CO2+ ion contributions at collectors for masses 44, 45 and 46, and calculation of
13C values from these measured values.
% Abundance in CO2 reference gas
12
C
C
16
O
17
O
18
O
13
98.8944%
1.1056%
99.7553%
0.0385%
0.2062%
Mass 44:
12 16
C O16O+
Mass 45:
13 16
C O16O+
12 17 16 +
C O O
12 16 17 +
C O O
93.54%
6.46%
Mass 46:
12 18
99.8%
C O16O+
C O18O+
12 17 17 +
C O O
13 16 17 +
C O O
13 17 16 +
C O O
100%
12 16
0.2%
Masses 47-49: low abundance and ignored (see Table A in Technical Supplement 2A
also found in the Chapter 2 folder on this CD).
Steps in calculating 13C for a sample of CO2 gas (as outlined by Santrock et al. 1985):
1) 45R = (13C16O16O + 2*12C17O16O)/12C16O16O or
45
R = 13R + 2*17R.
2) 46R = (2*12C16O18O + 2*13C16O17O + 2*12C17O17O)/12C16O16O or
46
R = 2*18R + 2*13R*17R + 2*17R2
3) 17R = K*(18Ra), K = 0.0099235, a = 0.516 (note: this formulation precisely gives the
rule discussed in the text that 17O is normally fractionated about half as much as 18O).
4) Combine equations 1-3 to express 18R in terms of known and measured values,
-3*K2*(18R2a) + 2*K*(45R)*(18Ra) + 2*(18R) – 46R = 0.
5) Solve equation 4) for 18R and determine 17R using equation 3).
6) Determine 13R using 17R, 45R and equation 1.
7) In most cases, 13C values are measured vs. a laboratory standard and need to be
recalculated vs. a primary standard, e.g. vs. VPDB. (Note: VPDB is Vienna PDB, an
updated version of the original PDB standard, and distributed from the International
Atomic Energy Agency in Vienna, Austria. The original PDB standard was exhausted
several decades ago, and was originally a fossil carbonate skeleton of Belemitella
americana collected near the PeeDee River of South Carolina). If the sample is measured
as1 relative to a lab standard whose isotope ratio is R1, and the lab standard is measured
as 2 vs. VPDB, then the following equations apply:
1 = [(RSAMPLE/R1) - 1]1000
2 = [(R1/RVPDB) -1]1000
and the  value of the sample expressed vs. the VPDB standard is given as
CVPDB = [(RSAMPLE/RVPDB) - 1]1000 = [(1 + 1000)*(2 + 1000) - 1,000,000]/1000.
Table C. Ion contributions in a hypothetical reference SO2 reference gas that has isotope
abundances characteristic of international reference standards, VCDT for 34S and
VSMOW for 18O. The SO+ ion contributions are given for masses 48 and 50, and SO2+
ion contributions for masses 64 and 66.
% Abundance in SO2 Reference Gas
32
S
S
34
S
36
S
16
O
17
O
18
O
33
95.0396%
0.7486%
4.1972%
0.0146%
99.76206%
0.0379%
0.20004%
Mass 48:
32 16
S O+
100%
Mass 50:
32 18
S O+
33 17 +
S O
34 16 +
S O
4.342941%
0.006481%
95.650578%
Mass 64:
32 16
100%
S O16O+
Mass 66:
32 16
S O18O+
32 18 16 +
S O O
32 17 17 +
S O O
33 17 16 +
S O O
33 16 17 +
S O O
34 16 16 +
S O O
8.323819%
0.000300%
0.012422%
91.663460%
Calculation of formulas for determining 34S and 18O from measured 50 and 66 values:
1)Write the ion contributions at mass 66, ignoring those species that have two rare
isotopes, i.e.,
66
R = [2*(32S18O16O) + 34S16O16O]/ 32S16O16O = 2*18R + 34R, and 34R = 66R - 2*18R
2) 34S = [(34RX - 34RSTD)/ 34RSTD]*1000,
where subscripts X and STD denote sample and standard =
[(66RX - 2*18RX) - (66RSTD - 2*18RSTD)]/ (66RSTD - 2*18RSTD)] * 1000.
3) This expression is complex, but can be solved because the oxygen and sulfur isotope
compositions of the standard are known, i.e., 66RSTD and 18RSTD are known. So, the next
steps involve algebraic rearrangements, starting with the numerator. First, group the
terms in the numerator by 66R and 18R terms,
(66RX - 2*18RX) - (66RSTD - 2*18RSTD) = (66RX - 66RSTD) - 2*(18RX - 18RSTD)
Now the numerator has separate 66R and 18R terms:
(66RX - 66RSTD) and - 2*(18RX - 18RSTD).
4. For these new numerator terms, rewrite the denominator, 66RSTD - 2*18RSTD, in terms of
66
R and then in terms of 18R. So, rewrite the denominator for the new numerator 66R
terms as:
66
RSTD - 2*18RSTD = 66RSTD*(1 - 2*18RSTD/66RSTD)
and rewrite the denominator for the new numerator 18R terms as:
66
RSTD - 2*18RSTD = 2*18RSTD*([66RSTD/(2*18RSTD)] -1).
5) Following the logic of treating the 66R terms separately than the 18R terms, one can
now write:
34S = {[(66RX - 66RSTD)/66RSTD*(1-2*18RSTD/66RSTD)] –
2*(18RX - 18RSTD)/[2*18RSTD*([66RSTD/(2*18RSTD)] -1)]}*1000
Or 34S = a*66 – b*218
where a = 1/(1-2*18RSTD/66RSTD) and b = 1/([66RSTD/(2*18RSTD)] -1).
6) The values of 66RSTD and 18RSTD can be calculated from the isotope abundances for
standards given at the top of this section, i.e.,
66
RSTD = 2*18R + 34R = 2*(0.200045/99.763) + (4.1972/95.0396) = .048173 and
18
R = (0.200045/99.763) = 0.002005.
Substituting these numerical values for 66RSTD and 18RSTD, one obtains:
34S = 1.0908*66 -0.0908*18
This result, derived by Hulston and Shilton (1958), gives 34S values in terms of
measured 66values when oxygen isotope values are equal in sample and standards.
7) The 34S values also can be derived as a function of measured 50 values instead of 66
values, by following steps 1-6 above but rewriting equations in terms of 50R instead of
66
R. The result for 50 is:
34S = 1.045404*50 -0.045404*18O.
8) Finally, one combines the last two equations to obtain:
18O = 24.02*66 -23.02*50.
This gives the oxygen isotope composition of the sample in terms of measured 66 and 50
values. The calculated 18O value can then be used to correct measured 66 or 50 values
to obtain 34S values.
9) Note that values measured in this way relative to a tank of SO2 standard gas need to be
recalculated vs. combusted standards measured with the samples, then these values have
to be recalculated vs. the international standard, VCDT. Steps for these recalculations are
similar to those given above in Table A, step 4, with S substituted for N.
10) Using different assumed values for the standards will yield slightly different
coefficients in the equations above. Especially, the oxygen isotope value of the reference
SO2 gas used in the isotope measurements is unknown, and not easily measurable. Using
the sulfur isotope values at the front of this table, one can calculate that the coefficient in
front of the 66 term could vary from 1.086 to 1.096 respectively for SO2 18O values of 50 and +50o/oo versus SMOW, values that span the likely range of oxygen isotope
compositions in the reference SO2 gas. These calculations indicate that a compromise
value of 1.091 seems realistic until the oxygen isotope compositions of SO2 are directly
measured. Another way of saying this is that even for a very large 50o/oo 18O deviation
from the standard, using a value of 1.091 should mean that any 18O-related error is small,
+0.25o/oo. Finally, it seems possible that one could prepare SO2 of known oxygen
isotope composition via equilibration with water, in a similar manner to the well-known
CO2 equilibrations (Epstein and Mayeda 1953, Craig 1957). Measurement of such a
sample should allow precise assessment of this coefficient, as needed.