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Mass spectrometer correction factors for the determination of small isotopic composition variations of carbon and oxygen
Internatkkmul Joiimal
of Mass
Spectrometry
and Ion Physics
283
EIsevier PubIishing Company. Amsterdam. Printed in t!!e NetierIands.
MASS SPECTROMETER MINATION OF SMALL CARBON AND OXYGEN
CORRECTION FACTORS ISOTOPIC COiMPOSITION
FOR THE DETERVARIATIONS OF
P. DEINES Department of Geochemistry Pa. 16802 (UXA.)
and Mineralogy,
Tlze Pennsyicania
Stare Utiersity
University
Park,
(Received March 9th, 1970)
ABSTRACT
Mass spectrometer data of carbon and oxygen isotopic composition measuremen’s obtained by comparison of a sample with a standard have to be corrected for ditferences in the instrumental components used for the measurement of sample and standard and for extraneous ion current contributions to the measured mass peaks. The experimental determination of five different correction factors and their application in the data reduction are discussed.
INTRODUCTION
In recent years the field of stable carbon and oxygen isotope studies has experienced a rapid growth. The maximum isotopic composition variations occurring in these elements are a few percent, and usually variations of a few parts per thousand are of interest; however, with proper experimental methods variations of a few parts per ten thonsand have been suce%sfully measured. In order that results from one laboratory may be reliably compared with those of another at this kvel of precision, it is essential that in the reduction of the mass spectrometer data one consider all applicable correction factors. Generally little detail is given in reports of isotopic composition studies about the magnitude of the corrections that are applied, and how they were determined. It appears therefore appropriate to provide a summary discussion of the correction factors which should be considered-
THE LMASSSPECI-ROMETER
At .the present time the mass spectrometers used for the study of stable carII&. .?. Mass
Spectroin.
ion Phys., 4 (i970)
2831295
284
P. DEINES
bon and oxygen isotopic compositions are fairly well standardized, and are still quite similar in design to one first described by Nier’. The foilowing is 3 short description of the isotope ra
Private unpublisheci CommuItiifftion.
Int. J. _Mzss Sprctrom.
ion P~Jx., 4 (1970)
253-295
MASS
SPECTROMETER
CORRECTIOK
FACTORS
285
Liquid nitrogen cooled traps are provided between the diffusion pumps and the main part of the vacuum system_ With this type of mass spectrometer the isotopic composition measurement of a given carbon dioxide sample may be reproduced with a precision of + Cl.05O/e0 or better. The precision with which the isotopic composition of a solid carbonate may be determined is lower (0.1 “/,,), due to the fact that it includes isotopic composition v,ariations introdL_=d in the preparation of carbon dioxide from the solid sample.
MA!?23SPECTROMETFR
CORRECTION
FACTORS
The analytical results of carbon and oxygen isotope studies are conventionally reported in the “delta” (6) notation as per mil (part per thousand) deviations from a standard_ The delta values are defined as follows:
1 .$8* =i(~80/~60)swnd3rd Ywwa*ple -l1xlo3613C
=
(‘3C!12~)szimp~~
t
( 13C/12C)S_ndard
-
l
x
lo3
Generally, 13Cj12C and ‘“O/‘“O ratios are not directly measured in tie mass spectrometer. In our laboratory and most others the isotopic composition measurements are carried out on carbon dioxide gas, and the mass 45/44 and mass 46/ (44+45) ratios, which are related to the r3C/‘2C and 180/160 ratios, are determined. Data reduction may then be divided into three steps: (1) correction of the measured difference between the 45144 (46/(44 + 45)) ratio of sample and standard for various instrumental characteristics, (2) calculation of delta values with respect to the working standard in terms of 13C/12Cand 18O/16O ratios determined from the corrected 45[44 and 46/(44+45) ratios, (3) recaiculation of the delta value with respect to some conventional reportin,* standard. Steps two and three have been discussed by Craig’s’, Taylor’, Clayton et al.’ and Garlickg_ In the following the instrumental correction factors that should be considered will be discussed.
Decade Doltage divider correction If, as in our instrument, the ratio measuring circuit empioys two decade voltage dividers, the effect of differences in the two measuring circuits used to determine the sampIe and standard isotopic compositions respectively, has to be accounted for. This is accomplished with the decade voltage divider correction (DC)_ This correction may be determined simply by m~+euring the isotopic composition of a gas flowing &rough one leak into the mass spectrometer alternately fnt.
J. Mass
Spectrom. 10.~ Pfzys., 4 (1970) 283-295
256
P. DEINES
with the %ample” and “standard” decade voltage dividers. If, for example, the unbaiance-indicating meter shows that the unbalanced portion of the signal is displaced towards higher ratiC;sby a fraction, fiC, of one divider step when the isotope ratio is determined with the “sample” decade voltage divider compared to the identical measurement with the ‘~at~dal-d” decade voltage divider, then this fraction has to be subtracted from isotope ratios measured with the “sample” decade voltage divider. If the unbalanced portion is dispiaced to higher ratios when the measurement is carried out with the “standard” decadevoltage divider, the fraction, DC, must be subtracted from the “standard” divider setting for every measurement carried out. The decade voltage divider correction is determined separately for the 45/44 (DC “) and 46/(4-4+45) ratio
Leak correction With this correction, the effect of possible fractionation differences in the viscous leaks and, combined with it, the effect of differences in background stemming from the leaks, is eliminated from the raw data. The Ieak correction is determined by measuring (using the same ratio-measuring circuit) the apparent isotopic composition difference when the sa.m* sample is flowing through both the ‘*sample” and the “standard” leaks. If the apparent isotope ratio of the gas flowing through the “sample” leak is found to be larger by a fraction, LC, of one decade voltage divider step than that cf the same gas flowin g through the “standard” leak, all measured “ssrnple” decade settings have to be reduced by this amount. The fraction has to be subtracted from the “standard” setting if a higher isotope ratio is measured for the gas flowing through the “standard” leak. The leak correction has to be determined separately for the 45144 (L-C J5) and 46/(44+45) ratio (LCG6). For our instrument the leak correction is generally smaller than
0.05 o/oo. Since the vo!tage divider correction and leak correction are of the same type, we rout&sly measure them combined rather than separately. A single sample of carbon dioxide is divided into two portions which are introduced into the “sample” and “standard” reservoirs. The apparent differences in 45/44 and 46/(44+45) ratios are determined using the two digerent branches of the ratio circuit for the measurement of the gas flowing through “sample” and “standard” leaks. Subsequently the two gases are exchanged, i.e. the gas contained in the “sample” reservoir is transferred to the “standard” reservoir and vice versa, and the measurement is repeated. The two sets of measuremenrs are averaged_ This eliminates the effect of possible small isotopic composition differences between the two gas portions. IJZLJ- Mass Spectrom. Zun Phys_, 4
(1970)
283-295
MASS SPECTROMETER
CORRECTiON
FACTORS
283
Corrections for extraneous ion current contributions Whereas the decade voltAge divider correction and leak correction result
from the fact that different instrumental
components
are used to measure the iso-
topic compositions of sample and standard gas, the corrections discussed in the following sections arise from ezctraneuz4.s ion current ContribuCons to the mass 44, 45, and 46 ion beam intensities of the gases analyzed. Minor ccntributions to the mass 45 and 46 ion beams of the sample gas come from the very strong adjacent mass 44 beam, from the background carbon dioxide in the mass spectrometer, and from carbon dioxide flowing through the second leak, which is not (in most instruments used for such studies) completely prevented from entering the mass spectrometei. The manner in which the relative importance of each of these contributions can be determined and how their effect on the isotopic composition measurement can be eliminated is discussed below. Each of the corrections is treated separately, and it is assumed for simplicity that all corrections except the one under consideration are zero_ Abundance sensitit;ity correction This correction adjusts the measured isotopic compositions for the overiap of the Iarge mass 44 peak onto the much smaller mass 45 and 46 peaks. This overlap is due mainly to ion scatter by the background gas of the mass spectrometer and is characterized by the abundance sensitit’ify, AS, which is defined as the inverse frac-
Fig. 1. Abundance sensitivityas a firactionof pressure.The relationshipwas meured underthe following conditions_ Ion source: triple filament surface ionization source, collimating slit width: 0.008 in. and 0.006 in; sample: strontium iodide; acceferating potential: 4 kV; pressurerange: 10-5-7.5x 1O-8torr, the pressurewas measuredover the cold trap of the analyzer tube with the aid of a Vexxo ion gauge; cokctor slit width: O-030 in. The ion currents were rneasurexiat the mass 88 and mass 89 positions. Each point represents the mean of five independent measurements. Int. 1. Mass Spectrom. Ion Phys., 4 (1970) 283-295
288
P. DEINES
tion of the number of ions or^mass M which are collected at mass M+ 1. It is a function of a number of instrumental parameters and depeads very strongly upon the operating pressure of the mass spectrometer. Figure 1 shows the measured AS, as a function of operating pressure, of another 6-inch radius, 60” degree deflection mass spectrometer at the mass 89 position (Deineslo). From this Figure it can be seen that at the normal operating pre5sure of 4x lo-’ torr in the isotope ratio mass spectrometer the AS can be expected to be of the order of l@ per mass unit at mass 89 and to be higher at mass 45. The peak overlap in the mass 44 to mass 46 range determined for t&e actual isotope ratio mass spectrometer described above is shown in Fig. 2. The inverse fraction of the mass 44 ion beam intensity is shown as a Pmction of distance (volts) from the major peak. If the contributions of the mass 45 and 46 peaks are subtracted one obtains directly the AS at the mass 45 and mass 4C positions*. OVERLA?
WOLTSI
MASS
ACCNPATING
44
CN
45
AND
45
POTENT&
Fig. 2. OverIap of mass 44 on mass 43 ar;d 46. The plot was determined undx the following experimental conditions_ Ion source: Nier type electron bombardment source, collimating slit width: 0.012 in. and 0.012 in.; sample: carbon dioxide, flowing into the instrument at a rate of 5 x lOI3 mokc~ulcs per set; pressore: 4 x IO-; torr, the pressure was measured over the cold trap of the analyzer tube with the aid of a Veeco ion gaailge.Cokctor sIit width: 0.036 in. Thz existence of a “nwtive” peak between the mass 44 and $5 ion beam ped! in this spedthat at this time secondary electrons were being lost from the ion collector. This may result fmm imperfect collector design or insufkient secondary okctron suppression. In some cass -such “*negative’*$e& inay be removed ‘by increasing the secondary electron suppressor voltage or by the application of a weak magnetic field in the collector region. St is advisable to attempt to eliminate this effect since it may impair the reproducibility of the isotopic composition measurements. l
indicates
MASS
SPECTROMETER
CORRECTION
289
FACTORS
In order that the abundance sensitivity correction may be derived we define the following: = mzss 45 ion beam intensity due to the sampie gas; = mass 44 ion beam intensity due to the sample gas; mass 45 ion beam intensity due to the standard gas; 1; = mass 44 ion beam intensity due to the standard gas; _4s4= = abundance sensitivity at the mass 45 position; 0: = decade setting of the 45/44ratio of the sample; this includes the fraction of one decade step that the sample trace is displaced from the unbaIanm signal of the standard ratio; 0; = the decade setting of the standard; 6R’ = raw ddta value for the 45/44 ratio calculated from the decade settings 0: and 0: ; SC2 = d&a va!ue for the 45/44 ratio corrected for peak overlap. 1,” 1’:
r,
=
With these detitions: 61’Zs= (D:[D$-I)
x lo3 and SC,’ = (i$!$
-1 ) x10”.
2
In terms of actual ion currents 6R5 represents:
This exnression can be transformed to:
We define the abundance sensitivity correction at mass 45 as: AC5
= I -+I;/(I;
x A2?);
hence: 6C; = 6R’x
AC-.
Since the ratio of 1$/l,”is approximately eqral to 0.012 we obtain for the abundance sensitivity correction: ACSS = l+
I
0.012 x AIS= -
For the derivation of the abundance sensitivity correction of the 46/(44-!-45) ratio we def%nein addition the following quantities: Int. J.
Mass Spectrom. Ion Phys,
4 (1970)
283-295
290
P. DElNES
mass 46 ion beam intensity of the sample; mass 46 ion beam intensity of the standard; abundance sensitivity at the mass 46 position; decade setting of the 46/(44+45) ratio; this inctudes the fraction of one decade step that the sampIe trace is disp!aced from the unbalance signal of the standard ratio; = decade setting of the 46/(44+45) ratio of the standard; = raw delta value for the 46/(44-l-45) ratio calculated from the decade settings 07 and 0:; = deita value for the 46/(44+45) ratio corrected for peak overla;.
0: 6R6
se
With these definitions we obtain: 10’ and BC: =
6R6 = (DriD,*--ljx
-mc+-I3 __1x 1 L
103
qj(r;+-l;)
SR6 may be expressed in terms of ion currents as follows:
The contribution of the mass 4-4 ion beam to the mass 45 ion beam has been neglected in this case since its influence on the abundance sensitivity correction factor for the 46/(44+45) ratio is neghgibie- The expression for 6R6 may be rewritten as foIlowsr
We define the abundance sensitivity correction at mass 46 as: Ae6
=
I +@‘(I;
x AP6);
hence: SC: = 6R” x AC=. Since the @I: AC=
=
ratio is approximately equal to 0.004 is-
1 0.004x Ap6
-
our instrument the abundance sensitivities at the mass 45 and mass 46 positions were determin& to be ASu5 = 2.5 x 104 and AZ? = 7.5 x l@ respectively. With thesevalues the abundance sensitivity corrections are calculated to be AC5 = 1.0033 and AC6 = 1.0033. In
ht. 3. Merp Sjwctrom. Iori Phyz-) 4 1;1970)283-295
biASS SPECTROMETER
CORRECTION
291
FACTORS
Vaice mix5zg correction Since the ground glass surfaces of the solenoid valves of the inIet system do not seal perfectly a certain amount of standad gas enters the mass spectrometer while the sample is analyzed and vice versa. The valve mixing correction adjusts the measured isotopic compositions for this effect. In order to develop a valve mixing correction formula let us define the following:
_fl fi
SC,”
SC,”
= the fraction of the sample gas that is leaking into the mass spectrometer while the standard gas is anaiyzed; = the fraction of t’te standard gas leaking into the mass spectrometer while the sample gas is analyzed; = 45/44 ratio deluz value corrected for valve mixing; = 45/(44+45) ratio delta value corrected for vaIve mixing.
The measured delta value 6R5 can be expressed in terms of ion currents as follows:
The expression can be rewritten as: 6R5 = ac,’
l+f1+fz+fr
l-fifi f,(li2x,5xlo-3)'
Since (1 -!-sC: x 10e3) is cIose to unity and fi and fi are of the order of 0.01 to 0.02 the expression simplses to: 6R5 = bC,5 -_I 1 +f1 +fz We define the valve mixing correction for the
ve5
=
mass 45144 ratio as:
1+f1+-fz;
hence: SC,’ = 6R’ x VC4’. The measured 46/(44+45)
Transformation
ratio difference represents:
of the expression yields:
8R6 = SC:
1-fIf2 +f~f&+dc,6x
'o-3)
ht. J. Mass Spectrom. ion Phys, 4 (1970) 283-295
292
P. DEINES
Since under normal operating ccnditions CL f the mass spectrometer the ratios If/It as well as the expression (I+ SC$ x IO- ‘) do not depart from and (I~+Ifs)j(I~+I~) unity by more than a few percent, and the fractionsf, and f, are of the order of 0.01 to 0.02, the expression for dR6 simplifies to:
We define the -..:!:ze mixins correction for the mass 46/(44+45)
ratio as:
hence: EC,” = SPX
vcJ6
There are a variety of methods by which the valve mixing correction may be determmed. The method usually used by the author is outlined below. Two gases are introduced into “sample” and “standard” reservoirs respectively, and their pressure is adjusted to the normal operating conditions (the isotopic composition of the two gases is immaterial)_ While the sample gas is flowing into the mass spectrometer, the mass 44 ion beam intensity is observed_ The major portion of the ampliiied signal due to this ion beam is bucked out with a set of batteries and the peak top is displayed on the highest sensitivity scaie of the d.c. amplifier. The standard gas is then pumped from its reservoir and the drop in the mass 44 ion beam intensity of the sample gas is determined. The intensity drop, expressed as a fraction of the total mass 4% ion beam intensity, gives the quantity &. Next the standard gas is allowed to flow into the instrument and the drop in its mass 44 ion beam intensity when the sample gas is removed from its reservoir is observed. This ion-beam-intensity-change expressed as a fraction of the total mass 44 beam intensity yields fI. In our instrument these fractions lie generally in the range of 0.005 to 0.01 so that the vaIve mixing correction is of the order of 1.01 to 1.02, and occasionally as small 2s 1.005. Backgromd correction ‘i”his correction eliminates the effect of the carbon dioxide background of :he MLZSSspectrometer from the measured isotopic compositions. During any evacuation after breaking vacuum in the instrument for any reason, the mass spectrometer tube is heated whiIe it is pumped down to a pressure of -5 x IO-’ torr_ This reduces the intensity of all the individual hydrocarbon background peaks in the mass 40 to mass 50 range to below lo- la A_ ‘ihe remaining background carbon dioxide is generally higher, and of the order of 5 x 1O-‘2 A for the mass 44 peak_ As soon as the mt carbon dioxide sample is introduced into the mass spectrometer, this background rises to about 5 x IO-” -4, and remains rather constant at this value from then on (this background lnr_ J. Mass
Spearom.
ion
Phys-..
4 i1970)
283-295
is measured with no gas
MASS
SPECTRO-METER
CORRECTION
FACTORS
293
flowing through either the “sample” or “standard” leaks). Since the normal operating mass 44 ion current is 2.5 x lo-’ A; the background carbon dioxide represents about 2 % of the measured ion beam intensities. Since the isotopic composition of the background gas can be quite diEerent from +Jlat of either or both of the gases analyzed, a correction for this extraneous contribution must be considered. For this purpose the folIowing additional quantities are defined: mass 44 background ion beam intensity with no gas flowing through either the sample or standard Ieak; mass 45 background ion beam intensity; mass 46 background ion beam intensity; I$Y;t = 1:/I;, f rat t ion of the mass 44 ion beam attributable to carbon dioxide background; (1: +1~)/(1~ i 1:) = (1: + Iz)/(Iz + Is), fraction of the mass 44 -!- 45 ion beam attributable to carbon dioxide background; (1: x It)/(IT x I;), background corrected ratio of the 45j44 ratios of sample and standard; (c x (1: fI~))/((l~-l-I:) x I:), background corrected ratio of the 46/(44+45) ratios of sample and standard; decade setting of the background 45144 ratio; decade setting of the background 46/(44+45) ratio. The ratio of the measured 45/44
This expression
ratios of sample and standard
represents:
may be rewritten as:
R5 = C; l+‘,‘l-r: 1 -&/I; We define the background
correction
for the 45/44 measurement,
BC4’,
as:
The ratios i,“/Iz and 1:/J; may be expressed in terms of the decade settings of background, sample, and standard respectively: GiG
=
fd-Dm> and I;&
= f,(D;/D;);
hence:
Inr. 3. Mass Spectrom.
Ion Phys., 4 (1970) 283-295
294
P. DEIXES
Tbe background corrected ,45/44ratio deha value follows as:
A similar expression may be derived for the background correction of the 46/ (44t45) measurement_ The ratio of the measured 46/(44+45) ratios of sample and standard represents in ‘terms of ion currents:
This expression may be rewritten as:
The background correction for the 46/(44+45)
ratio measurement is defined as:
The ratios &‘I,” and I$12 may be expressed in terms of divider settings of background, sample, and standard respectively.
hence:
The background corrected delta value for the 46/(44+45) then given by: Eb” = (R%BF-1)x
ratio measurement is
103_
Computation of a delta cake corrected for instrumental eflects The magnitudes of the above disctissed correction factors wiII vary from instrument to instrument. Thus regard&s of whether a certain correction factor was negligibfe at some time in the history of the instrument, it is advisable to check routinely all of the correction factors that have been discussed. A delta value that is corrected for decade voltage divider differences, leak differences, peak overlap, valve mixing, and background spectra may be caIcuIated as follows:
6C5 =
D:+DC+LC4’ DZ
1
xBes_l
xvCxAC4sX103
1
and
C I’_ J.&fats 6C6 =
D:1DC”%LCf6
Spectrom_
x~C46_l
.G
roi Phys.,
4 (1970) 283-295
1
xVCxAC46X103
MASS
SPECTROMETER
CORRECTION
295
FACTORS
VC stands for the valve mixing correction, which is the same for the 45/44 and 46/(44+45) ratio measurements. The If: indicates that the signs of the decade divider and leak corrections have to be chosen correctly. The delta values that have been adjusted for instrumental effects may then be corrected for 13C and “0 contributions and expressed as 6 ’ 3C and 6’*0 delta values according to the procedures of Craig’ *.
REFEREXCES
I A. 0. NIER,RCC.ScLInstr., 18 (1947) 398. J. i&i.MC-, S. EP~IN,
2 C. R. McKw>m, 21 (1950) 724.
R. A. ALEX AND H.
C. UEY, Rec.
Sci. Znsfr.,
3 R. K. W~LVLESS _tim H. G. THODE, J. Sci. Znstr., 30 (1953) 395. 4 K. HABFAS, 2. instrumentenk., 68 (19600) 82. 5 H. CRXIG, Geochim. Cosmochim. Acra, 12 (1957) 133. 6 H. CRAIG, Science, 133 (1961) 1833. 7 H. P. TAYLOR, in H. L. BARE~E~ (Editor), Geochemistry of Hy&othermaZ
Ore Deposits, Ho&s, Rinehart and Winston, Inc., New York, 1967, pp. 309-142. 8 R. N. Cuyro~, B. F. JONFS AND R. A. BERSZR, Geochim. Cosmochim. Acta, 32 (1968) 415. 3 G. D. GXRLICK, in K. H. WEDEPOHL (Editor), Wunribook ofGeochemistry, Vol. II/I, SpringerVerlag, Berlin, 1969, pp. 8-B-l - S-B-27. 10 P. Du?zs, Instrumental Factors Limiting the Precision and Accuracy of Strontium Isotopic Composition Measurements, M. S. Thesis in Geochemistry, The Pennsylvania State University, 1964.
* An IBM-FORTRAN computer program for the reduction of mass spectrometer data of carbon and oxygen isotopic composition measurements is available from the author upon request. Znt. J. MQSS Spectrom.
ion P&s.,
4 (1970) 283-295
of Mass
Spectrometry
and Ion Physics
283
EIsevier PubIishing Company. Amsterdam. Printed in t!!e NetierIands.
MASS SPECTROMETER MINATION OF SMALL CARBON AND OXYGEN
CORRECTION FACTORS ISOTOPIC COiMPOSITION
FOR THE DETERVARIATIONS OF
P. DEINES Department of Geochemistry Pa. 16802 (UXA.)
and Mineralogy,
Tlze Pennsyicania
Stare Utiersity
University
Park,
(Received March 9th, 1970)
ABSTRACT
Mass spectrometer data of carbon and oxygen isotopic composition measuremen’s obtained by comparison of a sample with a standard have to be corrected for ditferences in the instrumental components used for the measurement of sample and standard and for extraneous ion current contributions to the measured mass peaks. The experimental determination of five different correction factors and their application in the data reduction are discussed.
INTRODUCTION
In recent years the field of stable carbon and oxygen isotope studies has experienced a rapid growth. The maximum isotopic composition variations occurring in these elements are a few percent, and usually variations of a few parts per thousand are of interest; however, with proper experimental methods variations of a few parts per ten thonsand have been suce%sfully measured. In order that results from one laboratory may be reliably compared with those of another at this kvel of precision, it is essential that in the reduction of the mass spectrometer data one consider all applicable correction factors. Generally little detail is given in reports of isotopic composition studies about the magnitude of the corrections that are applied, and how they were determined. It appears therefore appropriate to provide a summary discussion of the correction factors which should be considered-
THE LMASSSPECI-ROMETER
At .the present time the mass spectrometers used for the study of stable carII&. .?. Mass
Spectroin.
ion Phys., 4 (i970)
2831295
284
P. DEINES
bon and oxygen isotopic compositions are fairly well standardized, and are still quite similar in design to one first described by Nier’. The foilowing is 3 short description of the isotope ra
Private unpublisheci CommuItiifftion.
Int. J. _Mzss Sprctrom.
ion P~Jx., 4 (1970)
253-295
MASS
SPECTROMETER
CORRECTIOK
FACTORS
285
Liquid nitrogen cooled traps are provided between the diffusion pumps and the main part of the vacuum system_ With this type of mass spectrometer the isotopic composition measurement of a given carbon dioxide sample may be reproduced with a precision of + Cl.05O/e0 or better. The precision with which the isotopic composition of a solid carbonate may be determined is lower (0.1 “/,,), due to the fact that it includes isotopic composition v,ariations introdL_=d in the preparation of carbon dioxide from the solid sample.
MA!?23SPECTROMETFR
CORRECTION
FACTORS
The analytical results of carbon and oxygen isotope studies are conventionally reported in the “delta” (6) notation as per mil (part per thousand) deviations from a standard_ The delta values are defined as follows:
1 .$8* =i(~80/~60)swnd3rd Ywwa*ple -l1xlo3613C
=
(‘3C!12~)szimp~~
t
( 13C/12C)S_ndard
-
l
x
lo3
Generally, 13Cj12C and ‘“O/‘“O ratios are not directly measured in tie mass spectrometer. In our laboratory and most others the isotopic composition measurements are carried out on carbon dioxide gas, and the mass 45/44 and mass 46/ (44+45) ratios, which are related to the r3C/‘2C and 180/160 ratios, are determined. Data reduction may then be divided into three steps: (1) correction of the measured difference between the 45144 (46/(44 + 45)) ratio of sample and standard for various instrumental characteristics, (2) calculation of delta values with respect to the working standard in terms of 13C/12Cand 18O/16O ratios determined from the corrected 45[44 and 46/(44+45) ratios, (3) recaiculation of the delta value with respect to some conventional reportin,* standard. Steps two and three have been discussed by Craig’s’, Taylor’, Clayton et al.’ and Garlickg_ In the following the instrumental correction factors that should be considered will be discussed.
Decade Doltage divider correction If, as in our instrument, the ratio measuring circuit empioys two decade voltage dividers, the effect of differences in the two measuring circuits used to determine the sampIe and standard isotopic compositions respectively, has to be accounted for. This is accomplished with the decade voltage divider correction (DC)_ This correction may be determined simply by m~+euring the isotopic composition of a gas flowing &rough one leak into the mass spectrometer alternately fnt.
J. Mass
Spectrom. 10.~ Pfzys., 4 (1970) 283-295
256
P. DEINES
with the %ample” and “standard” decade voltage dividers. If, for example, the unbaiance-indicating meter shows that the unbalanced portion of the signal is displaced towards higher ratiC;sby a fraction, fiC, of one divider step when the isotope ratio is determined with the “sample” decade voltage divider compared to the identical measurement with the ‘~at~dal-d” decade voltage divider, then this fraction has to be subtracted from isotope ratios measured with the “sample” decade voltage divider. If the unbalanced portion is dispiaced to higher ratios when the measurement is carried out with the “standard” decadevoltage divider, the fraction, DC, must be subtracted from the “standard” divider setting for every measurement carried out. The decade voltage divider correction is determined separately for the 45/44 (DC “) and 46/(4-4+45) ratio
Leak correction With this correction, the effect of possible fractionation differences in the viscous leaks and, combined with it, the effect of differences in background stemming from the leaks, is eliminated from the raw data. The Ieak correction is determined by measuring (using the same ratio-measuring circuit) the apparent isotopic composition difference when the sa.m* sample is flowing through both the ‘*sample” and the “standard” leaks. If the apparent isotope ratio of the gas flowing through the “sample” leak is found to be larger by a fraction, LC, of one decade voltage divider step than that cf the same gas flowin g through the “standard” leak, all measured “ssrnple” decade settings have to be reduced by this amount. The fraction has to be subtracted from the “standard” setting if a higher isotope ratio is measured for the gas flowing through the “standard” leak. The leak correction has to be determined separately for the 45144 (L-C J5) and 46/(44+45) ratio (LCG6). For our instrument the leak correction is generally smaller than
0.05 o/oo. Since the vo!tage divider correction and leak correction are of the same type, we rout&sly measure them combined rather than separately. A single sample of carbon dioxide is divided into two portions which are introduced into the “sample” and “standard” reservoirs. The apparent differences in 45/44 and 46/(44+45) ratios are determined using the two digerent branches of the ratio circuit for the measurement of the gas flowing through “sample” and “standard” leaks. Subsequently the two gases are exchanged, i.e. the gas contained in the “sample” reservoir is transferred to the “standard” reservoir and vice versa, and the measurement is repeated. The two sets of measuremenrs are averaged_ This eliminates the effect of possible small isotopic composition differences between the two gas portions. IJZLJ- Mass Spectrom. Zun Phys_, 4
(1970)
283-295
MASS SPECTROMETER
CORRECTiON
FACTORS
283
Corrections for extraneous ion current contributions Whereas the decade voltAge divider correction and leak correction result
from the fact that different instrumental
components
are used to measure the iso-
topic compositions of sample and standard gas, the corrections discussed in the following sections arise from ezctraneuz4.s ion current ContribuCons to the mass 44, 45, and 46 ion beam intensities of the gases analyzed. Minor ccntributions to the mass 45 and 46 ion beams of the sample gas come from the very strong adjacent mass 44 beam, from the background carbon dioxide in the mass spectrometer, and from carbon dioxide flowing through the second leak, which is not (in most instruments used for such studies) completely prevented from entering the mass spectrometei. The manner in which the relative importance of each of these contributions can be determined and how their effect on the isotopic composition measurement can be eliminated is discussed below. Each of the corrections is treated separately, and it is assumed for simplicity that all corrections except the one under consideration are zero_ Abundance sensitit;ity correction This correction adjusts the measured isotopic compositions for the overiap of the Iarge mass 44 peak onto the much smaller mass 45 and 46 peaks. This overlap is due mainly to ion scatter by the background gas of the mass spectrometer and is characterized by the abundance sensitit’ify, AS, which is defined as the inverse frac-
Fig. 1. Abundance sensitivityas a firactionof pressure.The relationshipwas meured underthe following conditions_ Ion source: triple filament surface ionization source, collimating slit width: 0.008 in. and 0.006 in; sample: strontium iodide; acceferating potential: 4 kV; pressurerange: 10-5-7.5x 1O-8torr, the pressurewas measuredover the cold trap of the analyzer tube with the aid of a Vexxo ion gauge; cokctor slit width: O-030 in. The ion currents were rneasurexiat the mass 88 and mass 89 positions. Each point represents the mean of five independent measurements. Int. 1. Mass Spectrom. Ion Phys., 4 (1970) 283-295
288
P. DEINES
tion of the number of ions or^mass M which are collected at mass M+ 1. It is a function of a number of instrumental parameters and depeads very strongly upon the operating pressure of the mass spectrometer. Figure 1 shows the measured AS, as a function of operating pressure, of another 6-inch radius, 60” degree deflection mass spectrometer at the mass 89 position (Deineslo). From this Figure it can be seen that at the normal operating pre5sure of 4x lo-’ torr in the isotope ratio mass spectrometer the AS can be expected to be of the order of l@ per mass unit at mass 89 and to be higher at mass 45. The peak overlap in the mass 44 to mass 46 range determined for t&e actual isotope ratio mass spectrometer described above is shown in Fig. 2. The inverse fraction of the mass 44 ion beam intensity is shown as a Pmction of distance (volts) from the major peak. If the contributions of the mass 45 and 46 peaks are subtracted one obtains directly the AS at the mass 45 and mass 4C positions*. OVERLA?
WOLTSI
MASS
ACCNPATING
44
CN
45
AND
45
POTENT&
Fig. 2. OverIap of mass 44 on mass 43 ar;d 46. The plot was determined undx the following experimental conditions_ Ion source: Nier type electron bombardment source, collimating slit width: 0.012 in. and 0.012 in.; sample: carbon dioxide, flowing into the instrument at a rate of 5 x lOI3 mokc~ulcs per set; pressore: 4 x IO-; torr, the pressure was measured over the cold trap of the analyzer tube with the aid of a Veeco ion gaailge.Cokctor sIit width: 0.036 in. Thz existence of a “nwtive” peak between the mass 44 and $5 ion beam ped! in this spedthat at this time secondary electrons were being lost from the ion collector. This may result fmm imperfect collector design or insufkient secondary okctron suppression. In some cass -such “*negative’*$e& inay be removed ‘by increasing the secondary electron suppressor voltage or by the application of a weak magnetic field in the collector region. St is advisable to attempt to eliminate this effect since it may impair the reproducibility of the isotopic composition measurements. l
indicates
MASS
SPECTROMETER
CORRECTION
289
FACTORS
In order that the abundance sensitivity correction may be derived we define the following: = mzss 45 ion beam intensity due to the sampie gas; = mass 44 ion beam intensity due to the sample gas; mass 45 ion beam intensity due to the standard gas; 1; = mass 44 ion beam intensity due to the standard gas; _4s4= = abundance sensitivity at the mass 45 position; 0: = decade setting of the 45/44ratio of the sample; this includes the fraction of one decade step that the sample trace is displaced from the unbaIanm signal of the standard ratio; 0; = the decade setting of the standard; 6R’ = raw ddta value for the 45/44 ratio calculated from the decade settings 0: and 0: ; SC2 = d&a va!ue for the 45/44 ratio corrected for peak overlap. 1,” 1’:
r,
=
With these detitions: 61’Zs= (D:[D$-I)
x lo3 and SC,’ = (i$!$
-1 ) x10”.
2
In terms of actual ion currents 6R5 represents:
This exnression can be transformed to:
We define the abundance sensitivity correction at mass 45 as: AC5
= I -+I;/(I;
x A2?);
hence: 6C; = 6R’x
AC-.
Since the ratio of 1$/l,”is approximately eqral to 0.012 we obtain for the abundance sensitivity correction: ACSS = l+
I
0.012 x AIS= -
For the derivation of the abundance sensitivity correction of the 46/(44-!-45) ratio we def%nein addition the following quantities: Int. J.
Mass Spectrom. Ion Phys,
4 (1970)
283-295
290
P. DElNES
mass 46 ion beam intensity of the sample; mass 46 ion beam intensity of the standard; abundance sensitivity at the mass 46 position; decade setting of the 46/(44+45) ratio; this inctudes the fraction of one decade step that the sampIe trace is disp!aced from the unbalance signal of the standard ratio; = decade setting of the 46/(44+45) ratio of the standard; = raw delta value for the 46/(44-l-45) ratio calculated from the decade settings 07 and 0:; = deita value for the 46/(44+45) ratio corrected for peak overla;.
0: 6R6
se
With these definitions we obtain: 10’ and BC: =
6R6 = (DriD,*--ljx
-mc+-I3 __1x 1 L
103
qj(r;+-l;)
SR6 may be expressed in terms of ion currents as follows:
The contribution of the mass 4-4 ion beam to the mass 45 ion beam has been neglected in this case since its influence on the abundance sensitivity correction factor for the 46/(44+45) ratio is neghgibie- The expression for 6R6 may be rewritten as foIlowsr
We define the abundance sensitivity correction at mass 46 as: Ae6
=
I +@‘(I;
x AP6);
hence: SC: = 6R” x AC=. Since the @I: AC=
=
ratio is approximately equal to 0.004 is-
1 0.004x Ap6
-
our instrument the abundance sensitivities at the mass 45 and mass 46 positions were determin& to be ASu5 = 2.5 x 104 and AZ? = 7.5 x l@ respectively. With thesevalues the abundance sensitivity corrections are calculated to be AC5 = 1.0033 and AC6 = 1.0033. In
ht. 3. Merp Sjwctrom. Iori Phyz-) 4 1;1970)283-295
biASS SPECTROMETER
CORRECTION
291
FACTORS
Vaice mix5zg correction Since the ground glass surfaces of the solenoid valves of the inIet system do not seal perfectly a certain amount of standad gas enters the mass spectrometer while the sample is analyzed and vice versa. The valve mixing correction adjusts the measured isotopic compositions for this effect. In order to develop a valve mixing correction formula let us define the following:
_fl fi
SC,”
SC,”
= the fraction of the sample gas that is leaking into the mass spectrometer while the standard gas is anaiyzed; = the fraction of t’te standard gas leaking into the mass spectrometer while the sample gas is analyzed; = 45/44 ratio deluz value corrected for valve mixing; = 45/(44+45) ratio delta value corrected for vaIve mixing.
The measured delta value 6R5 can be expressed in terms of ion currents as follows:
The expression can be rewritten as: 6R5 = ac,’
l+f1+fz+fr
l-fifi f,(li2x,5xlo-3)'
Since (1 -!-sC: x 10e3) is cIose to unity and fi and fi are of the order of 0.01 to 0.02 the expression simplses to: 6R5 = bC,5 -_I 1 +f1 +fz We define the valve mixing correction for the
ve5
=
mass 45144 ratio as:
1+f1+-fz;
hence: SC,’ = 6R’ x VC4’. The measured 46/(44+45)
Transformation
ratio difference represents:
of the expression yields:
8R6 = SC:
1-fIf2 +f~f&+dc,6x
'o-3)
ht. J. Mass Spectrom. ion Phys, 4 (1970) 283-295
292
P. DEINES
Since under normal operating ccnditions CL f the mass spectrometer the ratios If/It as well as the expression (I+ SC$ x IO- ‘) do not depart from and (I~+Ifs)j(I~+I~) unity by more than a few percent, and the fractionsf, and f, are of the order of 0.01 to 0.02, the expression for dR6 simplifies to:
We define the -..:!:ze mixins correction for the mass 46/(44+45)
ratio as:
hence: EC,” = SPX
vcJ6
There are a variety of methods by which the valve mixing correction may be determmed. The method usually used by the author is outlined below. Two gases are introduced into “sample” and “standard” reservoirs respectively, and their pressure is adjusted to the normal operating conditions (the isotopic composition of the two gases is immaterial)_ While the sample gas is flowing into the mass spectrometer, the mass 44 ion beam intensity is observed_ The major portion of the ampliiied signal due to this ion beam is bucked out with a set of batteries and the peak top is displayed on the highest sensitivity scaie of the d.c. amplifier. The standard gas is then pumped from its reservoir and the drop in the mass 44 ion beam intensity of the sample gas is determined. The intensity drop, expressed as a fraction of the total mass 4% ion beam intensity, gives the quantity &. Next the standard gas is allowed to flow into the instrument and the drop in its mass 44 ion beam intensity when the sample gas is removed from its reservoir is observed. This ion-beam-intensity-change expressed as a fraction of the total mass 44 beam intensity yields fI. In our instrument these fractions lie generally in the range of 0.005 to 0.01 so that the vaIve mixing correction is of the order of 1.01 to 1.02, and occasionally as small 2s 1.005. Backgromd correction ‘i”his correction eliminates the effect of the carbon dioxide background of :he MLZSSspectrometer from the measured isotopic compositions. During any evacuation after breaking vacuum in the instrument for any reason, the mass spectrometer tube is heated whiIe it is pumped down to a pressure of -5 x IO-’ torr_ This reduces the intensity of all the individual hydrocarbon background peaks in the mass 40 to mass 50 range to below lo- la A_ ‘ihe remaining background carbon dioxide is generally higher, and of the order of 5 x 1O-‘2 A for the mass 44 peak_ As soon as the mt carbon dioxide sample is introduced into the mass spectrometer, this background rises to about 5 x IO-” -4, and remains rather constant at this value from then on (this background lnr_ J. Mass
Spearom.
ion
Phys-..
4 i1970)
283-295
is measured with no gas
MASS
SPECTRO-METER
CORRECTION
FACTORS
293
flowing through either the “sample” or “standard” leaks). Since the normal operating mass 44 ion current is 2.5 x lo-’ A; the background carbon dioxide represents about 2 % of the measured ion beam intensities. Since the isotopic composition of the background gas can be quite diEerent from +Jlat of either or both of the gases analyzed, a correction for this extraneous contribution must be considered. For this purpose the folIowing additional quantities are defined: mass 44 background ion beam intensity with no gas flowing through either the sample or standard Ieak; mass 45 background ion beam intensity; mass 46 background ion beam intensity; I$Y;t = 1:/I;, f rat t ion of the mass 44 ion beam attributable to carbon dioxide background; (1: +1~)/(1~ i 1:) = (1: + Iz)/(Iz + Is), fraction of the mass 44 -!- 45 ion beam attributable to carbon dioxide background; (1: x It)/(IT x I;), background corrected ratio of the 45j44 ratios of sample and standard; (c x (1: fI~))/((l~-l-I:) x I:), background corrected ratio of the 46/(44+45) ratios of sample and standard; decade setting of the background 45144 ratio; decade setting of the background 46/(44+45) ratio. The ratio of the measured 45/44
This expression
ratios of sample and standard
represents:
may be rewritten as:
R5 = C; l+‘,‘l-r: 1 -&/I; We define the background
correction
for the 45/44 measurement,
BC4’,
as:
The ratios i,“/Iz and 1:/J; may be expressed in terms of the decade settings of background, sample, and standard respectively: GiG
=
fd-Dm> and I;&
= f,(D;/D;);
hence:
Inr. 3. Mass Spectrom.
Ion Phys., 4 (1970) 283-295
294
P. DEIXES
Tbe background corrected ,45/44ratio deha value follows as:
A similar expression may be derived for the background correction of the 46/ (44t45) measurement_ The ratio of the measured 46/(44+45) ratios of sample and standard represents in ‘terms of ion currents:
This expression may be rewritten as:
The background correction for the 46/(44+45)
ratio measurement is defined as:
The ratios &‘I,” and I$12 may be expressed in terms of divider settings of background, sample, and standard respectively.
hence:
The background corrected delta value for the 46/(44+45) then given by: Eb” = (R%BF-1)x
ratio measurement is
103_
Computation of a delta cake corrected for instrumental eflects The magnitudes of the above disctissed correction factors wiII vary from instrument to instrument. Thus regard&s of whether a certain correction factor was negligibfe at some time in the history of the instrument, it is advisable to check routinely all of the correction factors that have been discussed. A delta value that is corrected for decade voltage divider differences, leak differences, peak overlap, valve mixing, and background spectra may be caIcuIated as follows:
6C5 =
D:+DC+LC4’ DZ
1
xBes_l
xvCxAC4sX103
1
and
C I’_ J.&fats 6C6 =
D:1DC”%LCf6
Spectrom_
x~C46_l
.G
roi Phys.,
4 (1970) 283-295
1
xVCxAC46X103
MASS
SPECTROMETER
CORRECTION
295
FACTORS
VC stands for the valve mixing correction, which is the same for the 45/44 and 46/(44+45) ratio measurements. The If: indicates that the signs of the decade divider and leak corrections have to be chosen correctly. The delta values that have been adjusted for instrumental effects may then be corrected for 13C and “0 contributions and expressed as 6 ’ 3C and 6’*0 delta values according to the procedures of Craig’ *.
REFEREXCES
I A. 0. NIER,RCC.ScLInstr., 18 (1947) 398. J. i&i.MC-, S. EP~IN,
2 C. R. McKw>m, 21 (1950) 724.
R. A. ALEX AND H.
C. UEY, Rec.
Sci. Znsfr.,
3 R. K. W~LVLESS _tim H. G. THODE, J. Sci. Znstr., 30 (1953) 395. 4 K. HABFAS, 2. instrumentenk., 68 (19600) 82. 5 H. CRXIG, Geochim. Cosmochim. Acra, 12 (1957) 133. 6 H. CRAIG, Science, 133 (1961) 1833. 7 H. P. TAYLOR, in H. L. BARE~E~ (Editor), Geochemistry of Hy&othermaZ
Ore Deposits, Ho&s, Rinehart and Winston, Inc., New York, 1967, pp. 309-142. 8 R. N. Cuyro~, B. F. JONFS AND R. A. BERSZR, Geochim. Cosmochim. Acta, 32 (1968) 415. 3 G. D. GXRLICK, in K. H. WEDEPOHL (Editor), Wunribook ofGeochemistry, Vol. II/I, SpringerVerlag, Berlin, 1969, pp. 8-B-l - S-B-27. 10 P. Du?zs, Instrumental Factors Limiting the Precision and Accuracy of Strontium Isotopic Composition Measurements, M. S. Thesis in Geochemistry, The Pennsylvania State University, 1964.
* An IBM-FORTRAN computer program for the reduction of mass spectrometer data of carbon and oxygen isotopic composition measurements is available from the author upon request. Znt. J. MQSS Spectrom.
ion P&s.,
4 (1970) 283-295