Supplementary Material for “The effects of PorapakTM trap
temperature on 18O, 13C, and 47 values in preparing samples for
clumped isotope analysis”
Explanation of Supplementary Data Table S1:
In this paper we discuss both raw data and data corrected for the PPQ
fractionation using Equation 4. Raw data include 13C and 18O values, 45, 46, 47 and
48 values, and 47, and 48, as measured originally. Where corrected data is presented, it
is denoted with a lowercase n (13Cn and 18On, 45n, 46n, 47n, and 48n, 47n, and 48n).
Where available, we present sample weight, background pressure, and pre- and post-PPQ
trap pressure, which are used to calculate yield. These preparation line parameters are not
available for data measured prior to September 2014, and for a few samples where they
were not recorded. In all tables, data are separated into that measured in the ColdPPQ and
WarmPPQ configurations.
Guide to Tabs (subtables) in Supp_Data_TableS1.xlsx
 Table S1a. Reference Frame Parameters
o Includes reference frame parameters (SlopeEGL, SlopeETF, IntETF) for
original data and PPQ-corrected data, calculated using standard gases
found in Table S1b.
o Includes information about the dates of measurement sessions and
windows within those sessions, and the numbers of heated and
equilibrated gases used to calculate each reference frame.
 Table S1b. Gases
o Includes raw and corrected data for heated and equilibrated gases covering
May 2012- June 2015 in the windows where carbonate standards were
also run.
o Correction was done using d4X/dT (where 4X is 45, 46, or 47) values
calculated from November 2014 data with CM and OO combined, as
shown in Figure 2.
 Table S1c. CM
o Includes raw and corrected data for all analyses of CM standard from May
2012 – June 2015
o Analyses where the 13C value was clearly too low (below 1.5‰) are
marked in red and were excluded from averages (see below)
o Data in this table were used to make Figure 5.
 Table S1d. OO
o Includes raw and corrected data for all analyses of the OO standard from
November 2014 – June 2015
 Table S1e. PPQ Temp Test data
o Data in this table were used to make Figures 1, 2, 3, and 4, S1 and S2.
o Includes background, pre-PPQ, and post-PPQ pressure readings used to
calculate yield.
1
o “numcycle” lists the number of cycles for which the sample was analyzed
on the MAT253.
Removal of bad data:
Data was retrieved from older measurement sessions to compare long-term trends
in 47 for the CM standard (OO was only run after November 2014). A few of the older
analyses were deemed to be non-representative due to anomalous 13C values. From
independent (non-clumped isotope) measurement of CM on a Kiel III device, it was
determined that CM has a 13C value of 2.05 ± 0.04‰. In tests that varied the PPQ trap
temperature (November 2014), the measured 13C values for CM were all contained
within the range 1.7-2.1‰, even for the most fractionated samples (-40°C PPQ trap
temperature). Based on this range, we chose to eliminate any older analyses that had 13C
values below 1.4‰, which are clearly outside the range of variability studied here. If
these low values were caused by the temperature dependent PPQ trap fractionation, they
would require temperatures lower than -75°C. This is outside the expected temperature
range (-30°C ± 10°C) for the PPQ trap, and probably represents some other complicating
factor. Some of the bad samples can be attributed to new users being trained. Carrara is
also run as a diagnostic tool when problems with the sample preparation line are
suspected. Regardless of the cause of the low 13C values, the removal of these six bad
analyses does not change the overall mean 47 value substantially (0.418 ± 0.006‰ for
all replicates vs 0.410 ± 0.006‰ for only good replicates).
d4X/dT values for CM and OO in different measurement sessions:
Figure 2 shows the November 2014 “Stable Isotope Test” data for CM and OO.
d4X/dT values were calculated for CM and OO combined by fitting “4X offsets” rather
than 4X values, where offsets were calculated from the mean 4X value for all samples
measured between -20°C and -10°C. Table S2 summarizes the d4X/dT values for the
different time periods and carbonate standards. The first column (November 2014 CM +
OO) is what is shown in Figure 2.
Nov. 2014 Nov. 2014
CM + OO CM only
(n=15)
(n=9)
d45/dT 0.0103
0.0106
0.0100
June 2015 June 2015 June 2015 +
CM + OO OO only
Nov. 2014
(n=12)
(n=8)
CM+OO
(n=27)
0.0066
0.0057
0.0080
± 0.0008
± 0.0013
± 0.0005
± 0.0027
± 0.0044
± 0.0017
d46/dT 0.0378
0.0411
0.0335
0.0284
0.0258
0.0321
± 0.0025
± 0.0030
± 0.0033
± 0.0046
± 0.0068
± 0.0033
0.0519
0.0557
0.0467
0.0357
0.0317
0.0421
d47/dT
Nov. 2014
OO only
(n=5)
± 0.0035
± 0.0048
± 0.0035
± 0.0071
± 0.0108
± 0.0051
Table S2. d4X/dT values for different subsets of data, separated by sample type and time period. Grey
column is what is shown in Figure 2 and used in all calculations. There were not enough CM replicates run
in June 2015 to fit a separate line.
2
-35
-30
-25
-20
PPQ Trap Temperature (°C)
-15
8.08
8.03
4.23
4.03
3.83
OO d46 (‰)
3.43
-10
Figure S1. 4X offsets (left axis) and 4X values (right axes) vs PPQ trap temperature for data from three
different time periods. Points are color-coded by sample type and shape-coded by measurement period.
Black lines are fitted to November 2014 data only and are identical to those shown in Figure 2.
Fractionation observed in stable isotopes:
3
OO d47 (‰)
12.44
11.64
11.24
12.04
6.08
6.48
-40
5.68
-0.5
-1.0
Nov 2014
Jan 2015
June 2015
CM d47 (‰)
0.0
6.88
0.5
1.1
-0.8
1.3
3.63
1.7
1.5
-0.4
-0.6
CM d46 (‰)
-0.2
1.9
0.0
0.2
7.93
5.18
7.98
OO d45 (‰)
5.33
5.28
5.23
CM d45 (‰)
8.13
5.38
0.05
0.00
-0.05
-0.10
-0.15
-0.20
d45 (‰) offset
d46 (‰) offset
d47 (‰) offset
CM OO
4.87
4.77
4.72
4.67
8.18
7.79
OO d18O (‰)
7.40
5.85
5.46
5.07
Nov 2014
Jan 2015
June 2015
CM d18O (‰)
0.0
-0.2
-0.6
CM OO
-1.0
d18O (‰) offset
0.2
0.4
1.77
4.62
OO d13C (‰)
4.82
2.02
1.92
1.87
1.82
CM d13C (‰)
1.97
0.00
-0.10
-0.20
d13C (‰) offset
0.05
We chose to look at 45, 46, and 47as a more “raw” representation of changing
isotopic compositions. 13C and 18O values are more familiar ways to define isotopic
composition. Figure S2 shows 13C and 18O offsets vs. PPQ trap temperature for the
November 2014 data shown in Figure 2, demonstrating that the same pattern also applies
to those isotope quantities.
-40
-35
-30
-25
-20
-15
-10
PPQ Trap Temperature (°C)
Figure S2. 13C and 18O offsets (left axis) and real values (right axes) vs PPQ trap temperature for data
from three different time periods. Points are color-coded by sample type and shape-coded by measurement
period. Black lines are fitted to November 2014 data only.
Idealized calculations of fractionation behavior:
We can use idealized data to test the range and magnitude of the effects of
shifting 45, 46, and 47 on raw 47, 47-RFAC and the reference frame parameters, and to
interrogate compositional effects.
Effect of fractionation on raw 47
4
-30
-20
-10
d18O (‰ VPDB)
0
10
20
30
We can create synthetic data points (representing carbonates or gases) covering a
range of compositions by varying the 13C and 18O values between -30‰ and +30‰.
Raw 47 values usually range between -1.5‰ and 0.5‰ over this range of compositions.
For each composition trio (13C, 18O, 47), we can calculate 45, 46, and 47 using the
function “get_dx” (below). Next, we shift 45, 46, and 47 based on the November 2014
slopes shown in Figure 2 and Table S2, as if the sample was run at -30°C (a 10°C shift)
using the function “get_new”. Finally, we calculate a new composition (13Cn, 18On,
47n) using the function “get_D47”. We can then plot the shift in 47 per degree shift
(d47/dT) relative to composition (Figure S3).
Over the tested range, changing the 13C and 18O values had a much bigger
effect on d47/dT than changing 47-RFAC, probably due to the larger possible range of
variation.
For a single 47 value (-0.5‰), the largest d47/dT value (0.0059 ‰/°Cb20) occurs for
the most depleted composition (13C, 18O = -30‰, -30‰), and the smallest d47/dT
value (0.0026 ‰/°Cb20) occurs for the most depleted composition (13C, 18O = +30‰,
+30‰). This same pattern is found for any 47 value. For a single stable isotopic
composition (0‰, 0‰), d47/dT varied from 0.00424 to 0.00415 ‰/°Cb20 for raw 47
values of -1.5‰ and +0.5‰ (Figure S4). For the mean isotopic compositions of CM (1.97, -2.27, 0.414) and OO (4.80, -0.34, 0.704), d47/dT is 0.00416 and 0.00401,
respectively.
-30
-20
-10
0
d13C (‰ VPDB)
10
20
30
Figure S3. d47/dT (point size) plotted for different compositions (13C and 18O values). The mean
compositions of CM (green circle with cross) and OO (blue circle with X) are plotted for comparison, and
are scaled appropriately. Smallest and largest points are equal to d47/dT values of 0.0027 and 0.0059
‰/°Cb20. CM has a d47/dT value of 0.0042 and OO has a d47/dT value of 0.0040. Shown for raw 47 = 0.500‰.
5
Difference in Raw D47 per degree below -20C (‰ / °Cb20)
0.00410 0.00415 0.00420 0.00425 0.00430
d13C and d18O = 0‰ (VPDB)
-1.5
-1.0
-0.5
RawD47 (‰)
0.0
0.5
Figure S4. d47/dT vs 47 for a single stable isotopic composition (13C, 18O = 0‰).
Effect of fractionation on Reference Frame Parameters
We can calculate gas compositions to make up a synthetic reference frame with
parameters chosen to represent typical instrumental conditions (RF1: SlopeEGL = 0.02,
SlopeETF = 1.08, IntETF = 1.0). For 47 values ranging from -60‰ to +60‰
(representing a similar range of bulk isotopic compositions as varying 13C and 18O
values between -30‰ and +30‰) we can calculate an accompanying raw 47 value that
would perfectly define RF1. In order to get stable isotopic compositions, either 45 or 46
must be known. We therefore assume 45 = 0‰ for all samples and calculate 46 to be
internally consistent with the 47/47 pairs by solving “D47_optimize”. From there we
can also calculate 13C and 18O values for the idealized standard gases using the
function “get_D47”.
Using these synthetic heated and equilibrated gas compositions as the “true”
values (values measured if run through a PPQ trap at -20°C or higher), we then can
perturb them as if they were measured at -30°C using “get_new” with Tstart=-20 and
Tend=-30 and the November 2014 combined d4X/dT values (Table S2, left-most
column). With the new 45, 46, and 47 values, we can recalculate 47, and determine new
reference frame parameters (RF2) for gases as if they were run at -30°C.
All three parameters that make up the reference frame shift as a result of the
fractionation (RF2: SlopeEGL = 0.02015, SlopeETF = 1.0797, IntETF = 1.0355). When
run at -30°C, both 47 and 47 decrease, so the heated and equilibrated gas lines move
downwards. Samples with lighter bulk isotopic composition (lower 47 and 47 values)
are more affected by the fractionation than those with heavier bulk isotopic compositions
(higher 47 and 47 values) (Figure S3), so the 47 value of a synthetic gas with a 47
value of -60‰ decreases more than one with a 47 value of +60‰. This causes an
6
1.0
increase (steepening) of the SlopeEGL parameter (0.02015 vs 0.02). This has an effect of
~0.009‰ on the calculated 47-RFAC value.
Again, because isotopically lighter samples are more affected than isotopically
heavier samples, the heated gases, which have lower 47 values, are shifted down by
more than the equilibrated gases. This causes a slight stretching in the empirical transfer
function (ie. the intercepts are farther apart than they were before), which is reflected in a
slight decrease in the SlopeETF parameter (1.0797 vs 1.08). This has an effect of
<0.001‰ on the calculated 47-RFAC value.
The biggest change comes in the IntETF parameter. Because all gases were
shifted to lighter 47 values by ~0.03 to 0.05‰ (depending on their composition), the
intercepts of both the heated and the equilibrated gas lines also shifted lighter by
~0.033‰. This is reflected in a large increase in the IntETF parameter (1.036 vs 1.0).
This has an effect of 0.036‰ on the calculated 47-RFAC value.
-0.5
-2.0
-1.5
-1.0
D47 (‰)
0.0
0.5
HG -20C
EG -20C
HG -30C
EG -30C
-60
-40
-20
0
d47 (‰)
20
40
60
Figure S5. 47 vs 47 for synthetic reference frame. RF1 (dashed lines, -20°C) has parameters (0.2, 1.08,
1.0). RF2 (solid lines, -30°C) has values of (0.02015, 1.07966, 1.0355). HG lines represent 1000°C
stochastically scrambled gases and EG lines represent CO2 equilibrated with water at 25°C.
7
1.0
0.6
0.4
0.0
0.2
True D47 (‰)
0.8
HG -20C
EG -20C
HG -30C
EG -30C
-1.0
-0.8
-0.6
-0.4
Measured D47 Intercept (‰)
-0.2
0.0
Figure S6. Measured 47 intercept vs True 47 for synthetic reference frame. RF1 (dashed lines, -20°C) has
parameters (0.2, 1.08, 1.0). RF2 (solid lines, -30°C) has values of (0.02015, 1.07966, 1.0355).
Effect of fractionation on 47-RFAC
We can now compare the 47-RFAC values calculated in RF1 and RF2 to assess the
effect of the fractionation on 47-RFAC. The same range of carbonate values used above
(13C and 18O between -30‰ and +30‰) was used to calculate 47-RFAC for shifted data
using RF2 and for original data using RF1. Compared with the range of d47/dT values
(0.0026 to 0.0059 ‰/°Cb20) found for a single 47 value (-0.5‰), the range in d47RFAC/dT values was much reduced (-0.0009 to +0.0008 ‰/°Cb20), and is centered around
zero. 47-RFAC is therefore, on average, unaffected by the shift as long as gases and
carbonates are prepared at the same PPQ trap temperature.
At the average composition of CM, d47-RFAC/dT equals -0.00017 ‰/°Cb20. For
OO, d47-RFAC/dT equals -0.00025 ‰/°Cb20. This means for samples with most earth
surface compositions (±5‰ in 13C and 18O values), running a sample at -30°C vs.-20°C
only changes 47-RFAC by < 0.003‰, well within the error of a typical clumped isotope
measurement, while raw 47 changes are much larger (~0.04‰).
8
0.006
0.005
0.004
0.003
0.002
0.001
0.000
-0.001
Difference in D47per degree below -20 (‰ /° Cb20
dD47raw / dT
dD47RFAC / dT
-60
-40
-20
0
d
47
20
40
60
(‰)
Figure S7. d47/dT and d47-RFAC/dT vs 47 for a range of isotopic compositions. 13C, 18O = +30‰ (30‰) is the bottom right (top left) point in the diamond shape. The bottom center point of the diamond
represents 13C = +30‰, 18O = -30‰, and the top center is 13C = -30‰, 18O = +30‰. Points for CM
(green with cross) and OO (blue with X) show d47/dT and d47-RFAC/dT values for the two standards.
Functions used in idealized calculations:
In all these functions, ratios of VPDB (R13_VPDB, R17_VPDB, R18_VPDB) are from
the accepted value of VPDB, and stochastic ratios in “refgas” (stR45_refgas,
stR46_refgas, stR47_refgas) are calculated based on the established isotopic composition
of the reference tank at U of M (13C = -3.69‰, 18O = 3.94‰ VPDB).
############# “get_dx” is a function that calculates small deltas (d45, d46,
d47) from a given d13C, d18O, D47raw.
get_dx <- function(d13C, d18O, D47raw) {
#### calculate ratios R13, R18, and R17 using d13C and d18O
R13 = (d13C/1000+1)*R13_VPDB
R18 = (d18O/1000+1)*R18_VPDB
R17 = R17_VPDB * (R18/R18_VPDB)^beta
#### use R13, R18, and R17 to get R45 and R46
R45 = R13+2*R17
R46 = 2*R18 + 2*R13*R17 + (R17)^2
9
#### calculate first two small delta values
d45 = (R45/stR45_refgas-1)*1000
d46 = (R46/stR46_refgas-1)*1000
#### Calculate abundances of isotopes in sample gas
C12 = 1/(1+R13); C13 = R13/(1+R13)
O16 = 1/(1+R17+R18); O17 = R17/(1+R17+R18); O18 = R18/(1+R17+R18)
#### Calculate abundances of isotopologues in sample gas assuming STOCHASTIC
distribution
st44 = C12*O16^2
st45 = C13*O16^2+2*C12*O16*O17
st46 = 2*C12*O16*O18+2*C13*O16*O17+C12*O17^2
st47 = 2*C13*O16*O18+2*C12*O17*O18+C13*O17^2
#### Calculate the raw ratios of isotopologues in sample gas assuming
STOCHASTIC distribution
stR45 = st45/st44; stR46 = st46/st46; stR47 = st47/st44
#### solve the D47 definition equation for R47
#### to make it simpler, do some intermediate calculations first
C = (-(R46/stR46-1)-(R45/stR45-1))*1000
#### solve the for R47, use that to get d47
R47 = ((D47raw-C)/1000+1)*stR47
d47 = (R47/stR47_refgas-1)*1000
return(c(d45,d46,d47))
}
############# “d4xnew” is a function to calculate new small delta values (d45,
d46, d47) given old delta values and PPQ temp for a single sample, and the
slopes along which it fractionates. Slopes come from Figure 2 (slopes =
c(0.0103, 0.0378, 0.0519)).
d4xnew <- function(d4all, Tstart,Tend, slopes){
d45new
d46new
d47new
d4xnew
=
=
=
=
d4all[1]+slopes[1]*(Tend-Tstart);
d4all[2]+slopes[2]*(Tend-Tstart);
d4all[3]+slopes[3]*(Tend-Tstart);
as.numeric(c(d45new, d46new, d47new));
return(d4xnew)
}
############## “get_D47” is a function to calculate new raw D47 given small
delta values and reference frame parameters. d4all is a 3x1 vector of d45, d46,
d47. RF is also a 3x1 vector of the 3 reference frame parameters
get_D47 <- function(d4all,RF){
#### calculate R values from small deltas
R45 = (d4all[1]/1000+1)*stR45_refgas
R46 = (d4all[2]/1000+1)*stR46_refgas
R47 = (d4all[3]/1000+1)*stR47_refgas
#### Calculate the ratios of stable isotopes in the sample gas
R18 = solve_for_R18(R45,R46) # see below for this function
R17 = R17_VPDB*(R18/R18_VPDB)^beta
R13 = R45 - 2*R17
10
#### Calculate d13C, d18O
d13C = (R13/R13_VPDB-1)*1000
d18O = (R18/R18_VPDB-1)*1000
#### Calculate abundances of isotopes in sample gas
C12 = 1/(1+R13); C13 = R13/(1+R13)
O16 = 1/(1+R17+R18); O17 = R17/(1+R17+R18); O18 = R18/(1+R17+R18)
#### Calculate abundances of isotopologues in sample gas assuming STOCHASTIC
distribution
st44 = C12*O16^2
st45 = C13*O16^2+2*C12*O16*O17
st46 = 2*C12*O16*O18+2*C13*O16*O17+C12*O17^2
st47 = 2*C13*O16*O18+2*C12*O17*O18+C13*O17^2
#### Calculate the raw ratios of isotopologues in sample gas assuming
STOCHASTIC distribution
stR45 = st45/st44; stR46 = st46/st46; stR47 = st47/st44
#### Calculate raw D47
Cap47 = ((R47/stR47-1)-(R46/stR46-1)-(R45/stR45-1))*1000
return(c(d13C, d18O, Cap47))
}
############### “solve_for_R18” is a function to find R18 by solving the
“R18_optimize” function using the inputs R45 and R46, which are single values.
solve_for_R18 <- function(R45,R46) {
#### start with a guess for R18 of the VPDB composition, calculate R17
R18_in = R18_VPDB
#### solve the R18 optimize function
R18 <- optimize(R18_optimize, c(0.00170,0.00230),tol=0.000000001,
R45sam=R45, R46sam=R46)
return(R18)
}
############## This is the “R18_optimize” function that is used to solve for
R18.
R18_optimize <- function(R18_in, R45sam, R46sam){
R17_in <- R17_VPDB*(d18_in/R18_VPDB)^beta
(R46sam-2*(R45sam-2*R17_in)*R17_in-R17_in^2-2*R18_in)^2
}
############## “D47_optimize” is a function to optimize to calculate new delta
values given a guess at small delta values and PPQ temp for a single sample
D47_optimize <- function(d45,d46,d47,D47target){
# calculate R values
R45 = (d45/1000+1)*stR45_KIS
R46 = (d46/1000+1)*stR46_KIS
R47 = (d47/1000+1)*stR47_KIS
#### Calculate the ratios of stable isotopes in the sample gas
11
R18 = solve_for_R18(R45,R46)
R17 = R17_VPDB*(R18/R18_VPDB)^beta
R13 = R45 - 2*R17
####
C12
C13
O16
O17
O18
Calculate abundances of isotopes in sample gas
= 1/(1+R13)
= R13/(1+R13)
= 1/(1+R17+R18)
= R17/(1+R17+R18)
= R18/(1+R17+R18)
#### Calculate abundances of isotopologues in sample gas assuming STOCHASTIC
distribution
st44 = C12*O16^2
st45 = C13*O16^2+2*C12*O16*O17
st46 = 2*C12*O16*O18+2*C13*O16*O17+C12*O17^2
st47 = 2*C13*O16*O18+2*C12*O17*O18+C13*O17^2
#### Calculate the raw ratios of isotopologues in sample gas assuming
STOCHASTIC distribution
stR45 = st45/st44
stR46 = st46/st44
stR47 = st47/st44
#### Calculate Big Deltas
Cap47 = ((R47/stR47-1)-(R46/stR46-1)-(R45/stR45-1))*1000
return((D47target-Cap47)^2)
}
12