Jul 12, 1994 - Fig. 5. Chemical measurements have weak comparability because of lack of traceability years in its IMEP programmes (international measure-.
Fresenius J Anal Chem (1994) 350:277-283
Fresenius' Joumal of
© Springer-Verlag 1994
Stable isotope dilution: an essential tool in metrology P. De Bi~vre Institute for Reference Materials and Measurements, Commission of the European Community (JRC), B-2440 Geel, Belgium Received: 28 December 1993/Revised: 12 July 1994
Abstract. The potential role of isotope dilution (ID) in the future organization of traceability and therefore comparability of chemical measurements (amount measurements in SI terms) is described. Essential is that ID (e.g. in isotope dilution mass spectrometry IDMS), directly measuring in our SI unit for amount of substance (the mole), gives matrix-independent results and reduces a complicated chemical measurement to a simple physical measurement. It is possible to borrow from the ultra-high accuracy isotopic measurement techniques needed in the continuous improvement of the Avogadro constant in order to make high accuracy measurements of the amount of substance: both fields have in c o m m o n the determination of isotope abundance ratios with small but well known total uncertainties (conditions for so-called "absolute" measurements). In addition, the use of such ratio measurements in an isotope dilution procedure for amount measurements seems to constitute a form of direct traceability of amount measurements to the "Avogadro measurement procedure" and therefore to the closest realisation of the mole so far. All of this will have far-reaching consequences: Will enriched isotopes be available in a systematic, continuous, affordable supply to ensure the possibility of isotope dilution in the future? Will simpler and, above all, cheaper isotope mass spectrometers be available for the key laboratories of future measurement networks needed in the organization of the traceability of chemical measurements? Will the difference between "chemical" and "physical" measurements not gradually fade away in the organization of traceability of amount measurements? Is further development and application of IDMS but also of ID using other isotope-specific measurement techniques - not needed for all elements?
1 Introduction Metrology is the science - and art! - of the accurate measurement. The term is usually used for high accuracy
physical measurements of mass, time, length, etc. But it is virtually never used in chemistry. Some simple methods such as gravimetry are sometimes considered as metrology - weighing is the measurement method in this case. But, in general, chemical measurements or, better, measurements of amount of substance, are not considered as "metrology" nor have gained its status. However, as our measurement capability and insight in quantitative chemical measurements progresses, it is almost logical that more and more metrology will - and should - evolve. The time for metrology in chemistry has now come. And this opinion has penetrated the highest metrological authorities. It appears more and more that isotope dilution has developed into such a "metrological tool" thanks to the existence of "isotopes", i.e. element species which have exactly the same chemical properties and have, therefore - and exactly therefore - a great potential for accurate chemical assay.
2 Isotope dilution as "metrology" For many classical chemists, thinking in terms of elements which differ in chemical properties, isotopes are almost an unnecessary complication of nature, since they complicate chemical thinking. For many analytical chemists, isotope dilution is an analytical method amongst many, having its practical advantages and disadvantages. In fact, according to most, it has more disadvantages: it requires enriched isotopes (expensive), mass spectrometers (id) and requires careful - but not quantitative wet chemistry (slow, not "exciting"). The fact that in its basic characteristics (Fig. 1) it compares an unknown number of atoms or molecules in sample X to a known number in the "spike" Y through a ratio measurement [1, 2], is still not fully recognised. I f applied in this way, the isotope mass spectrometer can act for the present-day chemist as the balance did for the early chemist (Fig. 2) [1]. Other isotopes in both unknown and spike are simply related to these numbers by an isotope ratio determination and are correction terms in the process.
278 WHY ISOTOPE DILUTION M A S S SPECTROMETRY ?
[ mol
A NUMBER OF ATOMS
-
-
SI U N I T O F AMOUNT OF SUBSTANCE
only ratios measuring the same quantity (amount of substance) (Table 1) are involved: N x / N Y = R B (B stands for blend) a basic unit of our SI system, the mole, is used since (2) (3)
N x _ N x / N A _ nx
Ny
SPIKE
(:known number of atoms)
RATIO
:
1
unknown number known number
is determined by Isotope Dilution Mass Spectrometry 1
- ~
UNKNOWN
[:unknown
number of atoms)
Fig. 1. Isotope dilution mass spectrometry measures directly numbers of atoms
Nx/NA
ny
where N A is the Avogadro Constant in tool -1. Thus, n x = RB,ny. The determination of an unknown amount of substance nx is made by comparing it with a known amount ny of that substance through a ratio measurement RB. This could be called a "physical" measurement in the sense that it has become a simple, transparent measurement on a well defined system. However, there are no "physical" and "chemical" measurements. There are only measurements of simple (well-defined) and of more complex (less well defined) systems. Also the basic quantities we measure, do not distinguish between physical and chemical measurements (Table 1). The usual route which we use in analytical chemistry goes via equation (4): m x / M x (E) _ m x mx/My(E)
The full equation for polyisotopic IDMS is: N x _ R B-RY ~Rix Ny
(1)
(4)
my
where M(E) is the molar mass (atomic weight) of element E. We can also use the dimensionless atomic weight Ar(Si ) = m (Si)/u
Ry - R B ~ Riy
which only contains ratios [3], a very important feature for metrology. The above equation is consistent with the definition that ID is a method based on the measurement of an induced change in isotopic composition (addition of a spike). It is now interesting to observe that several of the basic characteristics of metrology are fulfilled in the ID measurement procedure:
(5)
where we express the mass m of one atom Si in u (unified atomic mass unit). The u is then expressed in kg. m o l - 1 . We conclude that measurements of amount o f substance (chemical measurements) can become "metrology" through the use of isotope dilution and determining ratios of numbers of particles. 3 Significance of the "mole" (symbol mol), our SI unit for amount of substance
OUA~4TITY
REALISATION OF SI UNIT IN TERMS OF
SYMBOL OF QUANTITY
MEASUREMENTIS A COMPARISON BETWEEN THE QUANTITY IN AN UNKNOWN TO THAT QUANTITY IN A REFERENCEMATERIAL
MEASURED AMOUNT IN UNKNOWN
One of the more basic discoveries in science has been the insight that matter has a particulate nature, constituted
,rt~ +(m- "r?~i
kg
THE INTERNATIONAL PROTOTYPE OF THE KILOGRAM AT S~VRES
k9
-
-
I
('t~-'n*bs)kg
AMOUNT OF SUBSTANCE
tool
mol THE NUMBEROF ATOMS IN 0.012 kg OF 12C -PHYSICAL MEASUREMENTS SMALL, KNOWN CORRECTIONS ONLY
Fig. 2. Isotope mass spectrometer is the modern chemist's balance
Table 1. Quantities and units of measurements. By convention physical quantities are organized in a dimensional system built upon seven base quantities, each of which is regarded as having its own dimension. These base quantities and the symbols used to denote them are as follows Physical quantity
Symbol for quantity
Name of SI unit
Symbol for SI unit
length mass time electric current thermodynamic temperature amount of substance luminous intensity
l m t I T
metre kilogram second ampere kelvin
m kg s A K
n
mole
tool
Iv
candela
cd
279 of "entities" and that chemical reactions take place by way of numbers of entities. Avogadro, Lavoisier, Dalton, Loschmidt a.o. found that these reactions could be studied through the ratios of these numbers, since these ratios would be the same on the atomic/molecular scale as they are on the macroscopic scale. Handling the individual entities was out of the question because of their unattainable small size and small "weight". Multiplying one entity by a number (the Avogadro or Loschmidt number) provided the possibility to work with "bunches" of entities, the size and weight of which were measurable on the human - macroscopic - scale. Such a "bunch" was chosen as the unit for measurements of amount of substance (1971). It was called the mole (symbol: mol) [4]. Hence the "bunch" has the dimension mol-~. Since comparisons of a few entities in samples X and Y could not be observed and measured, the "upscaling" to the macroscopic level was carried out using the number per "bunch" N A, because it leads to a ratio of "bunches" which could be observed NX/NA
Ny/N A
_ nx
(6)
ny
Chemists were interested in such ratios e.g. to study chemical reactions. These ratios could be experimentally approached through "weighing" (a first experimental approach to compare amounts of stubstance) and "correcting" the weighings by means of the concept of an atomic (and molecular) weight of an element E. A tool could be used which was available to everybody, the balance (Fig. 2):
m x / M x (E) _ n x my~My (E) F/y
QUANTITY
UNIT
I
REALIZATION
MASS
LENGTH, TIME
kg
m, s
I MEASUREMENT1 PROCEDURE j
ARTEFACT 1
L 'NSTRUMENT J •
~ BIPM
BIPM ./
NATIONAL STANDARDS INSTITUTES
•
/1\ //[\/l\ •
•
•
[]
/
\
\,
•
•
•
/I\ /l\ '
1
000
FIELD LABORATORIES
000
Fig. 3. Measurements of mass, length, time are traceable to the best realization of their basic SI unit
not only of scientific nature. It is necessary to realize across-border comparability of such measurements imposed by e.g. "Europe 1993" and by international trade where exchange and payment of goods is based on chemical "amount measurements". A situation where chemical measurement results are essentially declarations of isolated figures (Figs. 4 and 5), is highly unsatisfactory. It is believed that isotope dilution can play a role in the traceability of chemical measurements to the mole on the basis of its "metrological characteristics" described above. This model has been tested at IRMM over the last ten
(7)
Thus, measurements could be performed on the macroscopic scale, yielding ratios which were values on the atomic scale. They allowed the study of atomic and molecular scale phenomena with the resulting present-day chemical insight.
MEASUREMENTS OF AMOUNT (OF S U B S T A N C E ) NOT COMPARABLE: W H E R E IS T H E T R A C E A B I L I T Y ?
4 Traceability to the mole: a task to be considered?
All measurements of mass must be "traceable" to the prototype of the kg in Sbvres. This means that a path or "trace" must be demonstrated which is constituted by links which connect one measurement to another until the last "link" connects it to the "realisation" of the SI unit kg which is the prototype kg kept in S~vres by the BIPM. Similarly all measurements of length and time must be "traceable" i.e. traced back along many links, to the "realization" of the S! units for length, the metre, and time, the second (Fig. 3). [Those are not artefacts such as the kg but well-defined measurement procedures on welldefined instruments.] A similar system does not exist in chemical measurements or measurements of amount of substance [5, 6]. Why should there be one exception in the realization of Table 17 The requirement that "amount measurements" be comparable through a consistent traceability system is
J
•
j
'%
o f
o
