I would also like to add that on top of the problems with IRMS linearity described below, the sample preparation system can be non-linear and can change with time even if it was once linear.  Frequently I have encountered EA-IRMS users who assume that since their reference gas test is linear then their results should be linear.  This is not the case as all EA-IRMS systems I have ever seen exhibit some non-linearity even if the IRMS ref gas is linear over the same range.  This effect does not appear to be constant but can change from day to day.  The phenomena was first described by:

 Fry, B., W. Brand, F.J. Mersch, K. Tholke, and R. Garritt.  1992. Anal. Chem: 64, 288-291. 

This paper describes a dual mixing model that has worked well on several systems to correct for the non-linearity.  We have referred to this as the "Fry correction" and on every analysis analyze variable weight standards to do this correction.  We then check with quality control standards at a different isotope ratio and weights to check this correction.  This approach seems to work well to correct for the inherent EA-IRMS system non-linearity.

Paul Brooks.

John Eiler wrote:
[log in to unmask]" type="cite">This is all quite well put; it is worth adding that a sufficiently precise measurement will show that the detectors and solid-state components of the counting boards are not strictly linear.  E.g., the resistivity of the resistors through which we register ion currents can vary as a function of the voltage you put across them.  

On Jul 26, 2010, at 2:12 AM, Willi A. Brand wrote:


Linearity in the stable isotope measurement world means that the ratio of two ion currents from one source is independent of the intensity of the ion beams.
I would like to widen this a bit: The ratio measured should be identical to the ratio in the original gas in the sample. Hence, I exclude from the discussion any effect related to the chemistry that converts the original whatever-nature-sample to the measurement gas.

- The first thing to realize is that the gas that is present in the ion source during ionization is not the same as the one in the inlet system. Due to the viscous leak, the ratio in the ion source differs from that in the reservoir by a factor close to sqrt(m2/m1); (see Halsted R. E. and Nier A. O. (1950) Gas Flow through the Mass Spectrometer Viscous Leak. Review of Scientific Instruments 21(12), 1019-1021.) In the paper, Figure 3 is a good illustration of the situation: For an original hydrogen 3/2 ratio of 0.042 one observes a measured ratio of 0.0515 when a viscous leak is used. For a molecular leak, the original ratio in the reservoir is observed. As shown in this Figure 3 there is a pressure component that can affect linearity.
- The second point is that the molecules must be ionized for analysis. The ionization probabilities for different isotopologues are close, but they are not identical. The ionization probablility largely depends on the ionization cross section, which is a geometrical relation where the molecular velocities play a role. The latter are different for different masses and may change with pressure. I think, however, that this has only a very minor effect on linearity.
- 3rd, and probably very important is the fact that the ions initially move at thermal velocities inside a magnetic field (generated by the source magnets, which are present to collimate the electron beam). Once the electric field has started to accelerate the ions, this influence becomes smaller. The overall effect is called predispersion, reflecting that the molecules with different masses (but the same energy) enter the mass spectrometer with different probabilities. They are discriminated against by the alpha slit. The time the ions spend in or near their origin depends on the number of ions produced. This space charge shields the external field, hence slower ions spend more time inside the space charge dominated area and are affected by the magnetic field slightly more.
- 4th, and probably most important in daily analysis practice are ion-molecule reactions in the ion source. These can produce ions with the same mass but different nature. The best known ion-molecule reaction is the formation of H3+ in the ion source, when H2+ reacts with H2 to form H3+ and a hydrogen radical. In general, ion source chemistry has not been studied very systematically so far, but I deem it responsible for most linearity effects as well as instrument drifts (provided it is not due to a poor electronic component). Typically, H+ is transferred to a neutral molecule, producing m+1 ions that interfere with the minor isotope. The most common reactions are protonation of CO2 with the proton originating from traces of H2O+, or ionized organics, mostly generated from pump oil.

The points 3 and 4 are the most common sources of non-linearity. They can be distingished from each other rather easily: Point 3 should scale with relative mass difference whereas point 4 is a mass specific isobaric interference. One often has good linearity for the 46/44 ratio while the 45/44 non-linearity is too large and variable. This means that the physical ion source conditions are good but that there still is water or other contaminants interfering.

For those who want to learn more, I have given some more insight in chapter 38 in Pier de Groot's Handbook (WA Brand, 'Mass Spectrometer Hardware for Analyzing Stable Isotope Ratios', Chapter 38 in 'Handbook of Stable Isotope Analytical Techniques', ed. P. deGroot, Elsevier Science ( ISBN: 0-444-51114-8) 2004 ). In addition, Magnus Wendeberg and I have contributed a chapter to a new Elsevier encyclopedia (Magnus Wendeberg and Willi A. Brand, “Isotope ratio mass spectrometry (IRMS) of light elements (C, H, O, N, S): The principles and characteristics of the IRMS instrument” in Encyclopedia of Mass Spectrometry Vol 5, ed. Dwight E. Matthews, Elsevier, Amsterdam) which is scheduled to be published in September.

Best regards    Willi

On 7/24/2010 03:40, Gerard Olack wrote:
[log in to unmask]" type="cite">
Hi Robert-

Changes in pressure in the source?  There is always some source chemistry going on, and more molecules, more chemistry.  No, I've studied this directly-so I hope those who know chime in...but you did ask for any ideas ;)

Take care,


Robert Panetta <[log in to unmask]> wrote:

On the heels of the discussion launched by Daniel, can anyone explain (or
provide a good reference) why there is a mass-dependent linearity effect in
the first place? I was quite surprised to learn a few months back that it is
not isolated to IRMS: I sat in on a seminar about analyzing isotope-labeled
compounds by other MS techniques (such as ion trap) and very clearly, the
enrichment of a compound increased linearly with the amount injected. The
presenter had no explanation for it and just tossed it as the quirks of mass
spec, but it's curious that this seems to be a universal trait.
Any thoughts?

Willi A. Brand, Stable Isotope Laboratory      [log in to unmask]
Max-Planck-Institute for Biogeochemistry (Beutenberg Campus)
Hans-Knoell-Str. 10, 07745 Jena, Germany      Tel: +49-3641-576400
P.O.Box 100164,      07701 Jena, Germany      Fax: +49-3641-577400
WMO/IAEA Experts Workshop on Observations of Greenhouse Gases and Related Tracers:

Mr. Paul D. Brooks,
Dept. Integrative Biology MC3140,
3060 Valley Life Sciences Building,
UC Berkeley, 94720-3140.

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