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In a neutral atom the number of extranuclear electrons is equal to the numberof protons. The protons in the nucleus of an atom therefore determine howmany electrons that an atom can have when it is electrically neutral. Thenumber of electrons and their distribution about the nucleus in turn determinethe chemical properties of that atom.

Nuclear systematics

The number of protons (Z) is called the "atomic number" and the number ofneutrons (N) is the "neutron number".

The atomic number Zalso indicates the number of extranuclear electrons in aneutral atom.The sum of protons and neutrons in the nucleus of an atom is the "massnumber" (A). We can therefore represent the composition of the nuclei ofatoms by means of a simple relationship:

A = Z + N

The composition of atoms is conveniently described by specifying the numberof protons and neutrons that are present in the nucleus.

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We are now in a position to define several additional terms. Referring to thechart of the nuclides, we see that each element having a particular atomicnumber Zis represented by several atoms arranged in a horizontal row havingdifferent neutron numbers. Such atoms, which have the same Z but differentvalues of N, are called "isotopes".

Because they have the same Z, isotopes are atoms of the same chemicalelement.

They have very similar chemical properties and differ only in their masses.Nuclides, which occupy vertical columns on the chart of the nuclides, are called

"isotones". They have the same value of Nbut different values of Z. Isotonesare therefore atoms of different elements.

Isotopes are therefore defined as atoms whose nuclei contain the samenumber of protons but a different number of neutrons. The termisotopes is derived from Greek (meaning equal places) and indicates thatisotopes occupy the same position in the Periodic Table. Isotopes can bedivided into stable and unstable (radioactive) species. The number of stable

isotopes is about 300; while over 1200 unstable ones have been discovered sofar. There will be moremark my words!

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6-carbon-12------------------------------------------------------------------------* Atomic Mass: 12.0000000 +- 0.0000000 amu* Excess Mass: 0.000 +- 0.000 keV* Binding Energy: 92161.753 +- 0.014 keV* Beta Decay Energy: B- -17338.083 +- 1.000 keV"The 1995 update to the atomic mass evaluation" by G.Audi and A.H.Wapstra, Nuclear Physics A595 vol. 4 p.409-480, December 25,1995.

------------------------------------------------------------------------* Atomic Percent Abundance: 98.89%* Spin: 0+* Stable IsotopePossible parent nuclides:Beta from B-12Electron capture from N-12------------------------------------------------------------------------6-carbon-13

------------------------------------------------------------------------* Atomic Mass: 13.0033548 +- 0.0000000 amu* Excess Mass: 3125.011 +- 0.001 keV* Binding Energy: 97108.065 +- 0.016 keV* Beta Decay Energy: B- -2220.445 +- 0.270 keV"The 1995 update to the atomic mass evaluation" by G.Audi and A.H.Wapstra, Nuclear Physics A595 vol. 4 p.409-480, December 25,1995.------------------------------------------------------------------------* Atomic Percent Abundance: 1.11%* Spin: 1/2-* Stable IsotopePossible parent nuclides:Beta from B-13Electron capture from N-13

R.R.Kinsey, et al.,The NUDAT/PCNUDAT Program for Nuclear Data,paper submitted to the 9 th International Symposium of Capture-Gamma_raySpectroscopy and Related Topics, Budapest, Hungary, Octover 1996.Data extracted from NUDAT database (Jan.

14/1999)

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The stability of nuclides is characterized by several important rules, two ofwhich are briefly discussed here.

1) Symmetry rule- in a stable nuclide with low atomic number, the number ofprotons is approximately equal to the number of neutrons, or the neutron-

to-proton ratio, N/Z, is approximately equal to unity. In stable nuclei withmore than 20 protons or neutrons, the N/Z ratio is always greater than unity,with a maximum value of about 1.5 for the heaviest stable nuclei. Theelectrostatic Coulomb repulsion of the positively charged protons growsrapidly with increasing Z. To maintain the stability in the nuclei, electricallymore neutral neutrons than protons are incorporated into the nucleus.

http://www.triumf.ca/safety/rpt/rpt_2/node3.html

http://www.triumf.ca/safety/rpt/rpt_2/node3.htmlhttp://www.triumf.ca/safety/rpt/rpt_2/node3.html

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In the beginningIn 1931 Harold Urey predicted on theoretical grounds that there should be adifference in the vapor pressures of the isotopes of hydrogen. His interest in

hydrogen had been aroused by a suggestion of Birge and Menzel that it mayhave naturally occurring isotopes.

Urey, working with Murphy and Brickwedde, promptly planned and carried outan experiment to detect 2H and 3H by spectroscopic means in the residual

volume of gas produced by evaporating about 6 liters of liquid hydrogen.

The results immediately confirmed the presence of 2H but 3H was not found.Urey named the newly discovered isotope "deuterium" because it has nearlytwice the mass of hydrogen. The specific reason for this was not yet known

because the existence of neutrons was not established until 1932. In 1934,Harold Urey won the Nobel Prize for chemistry for his discovery of deuterium.

2) Oddo-Harkins rule- states that nuclides of even atomic numbers are moreabundant than those with odd numbers. The most common of the four possiblecombinations is even-even, the least common odd-odd. The same relationshipshows that there are more stable isotopes with even than with odd protonnumbers.

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During W.W.II, he used his knowledge of isotope fractionation to developmethods for the separation of 235U by gaseous diffusion.

When the war ended, he turned his attention to the possibility that the stable

isotopes of oxygen may be fractionated by natural processes. He suggestedthat such fractionation might occur during the formation of calcium carbonate inthe oceans and that the extent of fractionation depends on the temperature. Outof these ideas has developed the oxygen isotope method of measuring thetemperature of deposition of skeletal calcium carbonate.

The research inspired and led by Harold Urey has evolved into an importantbranch of isotope geology that deals with the fractionation of the stable isotopesby physical and chemical reactions occurring in nature. The group of elementswhose isotopes are especially susceptible to natural isotope fractionation

includes hydrogen, carbon, nitrogen, oxygen, and sulfur.

These are among the most abundant elements in the Earth, and they areintimately associated with the biosphere, the hydrosphere, and the lithosphere.Consequently, the study of fractionation of their isotopes provides information

on a great variety of important biological, geological, and meteorologicalprocesses occurring in many different environments.

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Beginning with the classic paper of Urey (1947), in which he calculated stableisotope fractionation factors between species of geochemical interest, there hasbeen an increasing use of stable isotope variations in natural materials forstudies in the Earth and cosmic sciences.

Equilibrium fractionation factors that measure the distribution of a rare stableisotope between two species have been determined directly by laboratoryexperiments and also by calculations using the methods of statisticalthermodynamics. They have also been inferred from regularities in the stable

isotope ratios of natural materials.

These fractionation factors have been used in geochemistry, meteorology,oceanography, water and aqueous chemistry, cosmochemistry, paleontology,and other scientific fields for a variety of purposes.

In his 1947 paper, Harold Urey reviewed theoretical and experimental resultsfrom studies on isotopes of various elements in a publication entitled"Thermodynamic Properties of Isotopic Substances"wherein he concluded

that isotopes and their compounds have different thermodynamic propertiesthat vary primarily as a function of temperature.

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As a result of the small but significant differences in the thermodynamicproperties of isotopes of the same element, Urey suggested that fractionationsof the isotopes of oxygen and carbon among water, CO2, and carbonate shellmaterial were sufficiently large as to be useful in discerning the CO2 contents ofancient atmospheres and the paleotemperatures of the oceans.

Not only did this suggestion generate a plethora of studies concerning possiblepaleoclimates of the earth, but it also led to the birth of stable isotopegeochemistry, a discipline which is now an integral part of many studies in theearth sciencesand my personal favorite...

Light stable isotope geochemistry

1) They have low atomic mass. Isotopic variations have now been found forheavy elements like Cu, Sn, W, and Fe.

Light stable isotope geochemistry primarily involves accounting for variations inthe isotopic composition of H, C, N, O, Si and S in a variety of natural

substances. These elements are comprised of one very abundant isotope andone or more minor isotopes the ratios of which vary differentially in naturalsubstances. The stable isotope ratios of these elements are particularly usefulin the earth sciences for the following reasons:

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2) The relative mass difference between the rare (heavy) and abundantisotope is large. For example compare the values of 12.5 and 8.3 percent forthe pairs 18O-16O and 13C-12C respectively, with the value of only 1.2 percent forthe 87Sr-86Sr. The relative mass difference between D and H is almost 100 percent and hydrogen isotope fractionations are, accordingly, about 10 times largerthan those of the other elements of interest.

3) They form chemical bonds that have a high degree of covalentcharacter. Attesting to the importance of bond type to isotopic fractionation, the48Ca/40Ca ratio varies little in terrestrial rocks despite the large relative mass

difference (only D-H is larger) between the isotopes.

4) The abundance of the rare isotope is sufficiently high (tenths to a fewpercent) to assure the ability to make precise determinations of theisotopic ratio by mass spectrometry. Depending on the instrument used, theanalytical error of deuterium analyses is up to ten times larger than those of the

other elements because of the low abundance of deuterium (about 160ppm) innature.

5) Unlike radiogenic isotopes, the isotopic composition of these elementsin natural substances is not a function of time or the chemical behavior of

the parent element.

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6) These elements are significant components of most rocks, mineralsand fluids as well as forming the basis of most forms of life.

7) The distribution of the isotopes of these elements among differentphases varies primarily as a function of temperature, but because of their

low atomic masses and large relative mass differences, mass-dependentfractionations of isotopes of these elements among phases is much morepronounced than those of heavier elements.

8) The occurrence of more than one oxidation state as with C, N, and S or

of very different types of bonds as in H-O, C-O or Si-O also enhances themass-dependent fractionation of isotopes; the isotopic compositions of mostcations in geological materials do not vary much, not only because of theirsmall relative mass differences, but also because they tend to occur in a limitednumber of oxidation states and in similar atomic environments.

9) The great abundance of these elements in most substances coupledwith the ability to determine precise relative isotope ratios using gas-source mass spectroscopy allows determination of the isotopiccomposition of many geologically relevant materials.

N l i i i i i i f i l i l h b d

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Natural variations in isotopic ratios of terrestrial materials have been reportedfor other light elements like Mg and K, but such variations usually turn out to belaboratory artifacts.

The case of Mg is fairly straightforward. Aside from the fact that its bonds aredominantly ionic in character, the same atomic environment (an octahedron ofoxygen almost always surrounds magnesium) in nature. SS effect?

Thus with little or no possibility of site preference in magnesium compounds,conditions are not favorable for isotopic fractionation of this element in nature.

In any event, variations in stable isotope ratios of light elements other than the

seven mentioned are small in terrestrial substances. The reasons for this arenot completely understood and are only loosely discussed in terms ofcharacteristics such as those noted. These characteristics are only observedand are not rigorously tied to theoretical principles.

E i l h i i f l i i f li h bl

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(1) Semi-empirical calculations using spectroscopic data and the

methods of statistical mechanics.

(2) Laboratory calibration studies.

(3) Measurements of natural samples whose formation conditionsare well known or highly constrained.

Essential to the interpretation of natural variations of light stableisotope ratios is knowledge of the magnitude and temperaturedependence of isotopic fractionation factors between the commonminerals and fluids. These fractionation factors are obtained in

three ways:

Ki ti d E ilib i i t ff t

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Kinetic and Equilibrium isotope effectsKinetic isotope effects

Kinetic isotope effects are common both in nature and in the laboratory andtheir magnitudes are comparable to and sometimes significantly larger thanthose of equilibrium isotope effects.

Kinetic isotope effects are normally associated with fast, incomplete, orunidirectional processes like evaporation, diffusion, and dissociation reactions.

The examples of diffusion and evaporation are explained by the different

translational velocities of isotopic molecules moving through a phase or acrossa phase boundary. Kinetic theory tells us that the average kinetic energy (K.E.)per molecule is the same for all ideal gases at a give temperature.

Consider the isotopic molecules 12C16O and 12C18O that have molecular weightsof 28 and 30, respectively. Solving the expression equating the kinetic energies

(K.E. = 1/2 Mv2) of both isotopic species, the ratio of velocities of the light toheavy isotopic species is (30/28)1/2, or 1.034.

That is, regardless of T, the average velocity of 12O16O molecules is 3.4 percentgreater than the average velocity of 12C18O molecules in the same system. This

and other such velocity differences lead to isotopic fractionations in a variety ofways.

M l l ith l l l f ti ll diff t

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Molecules with lower molecular mass can preferentially diffuse outof a system and leave the reservoir enriched in the heavy isotope.

In the case of evaporation, the greater average translational

velocities of lighter molecules allows them to break through theliquid surface preferentially, resulting in an isotopic fractionationbetween vapor and liquid.

For example, the 18O value of water vapor above the ocean (18O= 0) is typically around -13, whereas at equilibrium the valueshould only be about -9 depending on the temperature ofevaporation.

The magnitude of the isotopic fractionation reduces to the value ofthe equilibrium fractionations as the vapor phase approachessaturation or equilibrium vapor pressure. At that point the rates ofmolecular transfer between liquid and vapor and between vaporand liquid are equal. Condensation, on the other hand, isdominantly an equilibrium process.

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M l l t i i th h i t t bl d h

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Molecules containing the heavy isotope are more stable and havehigher dissociation energies than those containing the lightisotope. Therefore it is easier to break such bonds as 12C-H and32S-O than to break bonds like 13C-H and 34S-O.

If youre a bacterium, which molecule are you going to eat?

Kinetic isotope effects arising from these differences indissociation energies can be extremely large in dissociation andbacterial reactions that occur in nature. While it is very importantto be aware of kinetic isotope effects, they are relatively rare in

high-temperature processes occurring on Earth.

O th th h d t i t h b

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On the other hand, transient processes can occur wherebydiffering rates of isotopic exchange between coexisting mineralsthemselves or between the minerals and an external fluid canresult in assemblages that are grossly out of isotopic equilibrium.

Such examples are not explained by kinetic isotope effects butrather by a series of equilibrium isotope exchange reactions thathave not gone to completion.

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Background terminologyIsotopes, ratios, deltas and permil ()

Stable isotopes are measured as the ratio of the two mostabundant isotopes of an element.

For oxygen it is the ratio of 18O, with an abundance of 0.204%, to16O which represents 99.796% of oxygen. Therefore the 18O/16Oratio is about 0.00204.

Fractionation processes will modify this ratio in any given

compound containing oxygen, but these differences are seen inthe 5th or 6th decimal place.

Measuring the absolute isotope ratio or abundance is very difficultand requires some expensive toys.

Doing this on a reg lar basis o ld be heino sl diffic lt and lab

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Doing this on a regular basis would be heinously difficult and labto lab comparisons would be a nightmare. So what labs do ismeasure an apparent or relative ratio by gas source massspectrometry.

The apparent ratio differs from the true ratio due to operationalvariation (called machine error, m). This variation m differs fromlab to lab and even day to day on one machine.

By measuring a known reference on the same mass spec at thesame time, we compare the sample to the reference.

Isotopic values are then expressed as the difference between the

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Isotopic values are then expressed as the difference between themeasured ratios of the sample and reference over the measuredratio of the reference. This allows us to cancel the error (m) andpresent the ratio in delta notation:

18Osample

m(18O16O

)sample m(18O16O

)reference

m(18

O16

O

)reference

The value may also be defined as follows:

where Rx=(D/H)x, (13C/12C)x, (18O/16O)x, (34S/32S)x, and so forth,and Rstd is the corresponding ratio in a standard. Note that R isalways written as the ratio of the heavy (rare) isotope to the light(common) isotope.

x

xR STDRSTDR

3

10 ,

Because fractionation processes do not yield huge variations in

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Because fractionation processes do not yield huge variations inisotope values, -values are expressed as the parts per thousandor permil () difference from the reference. This yields the

equation:

18

Osample

18O16O

sample

18O16O

reference 1

x1000

VSMOW

VSMOW (Vienna Standard Mean Ocean Water) is the reference

used. A - value that is positive, 20 indicates that the samplehas 20 or 2% more 18O than the reference. Some people say"enriched" by 20.

A sample that is lower than the reference by the same amountwould be indicated as 18Osam le = -20VSMOW.

Over the years stable isotope geochemists have developed a

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Over the years, stable isotope geochemists have developed acertain uniformity in the presentation of their data. However, thereare still a few noteworthy differences. Some workers write(18O/16O), (D/H), and so forth, whereas others write 18O and

D, and so forth, the latter being more common.

In the earlier literature D values were given in percent, but,because so many laboratories now report both D and 18O

values for the same substances (primarily water), it has becomestandard practice to report both values in per mil to avoidconfusion. 13C values reported from most laboratories in theSoviet Union (now Russia) are given in percent.

The standards were called Standard Mean Ocean Water (SMOW)

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The water and carbonate standards have changed to ViennaStandard Mean Ocean Water (VSMOW) for both oxygen andhydrogen, a belemnite from the Cretaceous Pee Dee Formation,South Carolina (VPDB) for carbon (and, sometimes for oxygen incarbonates).

The standards were called Standard Mean Ocean Water (SMOW)for both oxygen and hydrogen, a belemnite from the CretaceousPee Dee Formation, South Carolina (PDB) for carbon (and,sometimes for oxygen in carbonates), air (Air) for nitrogen, troilite

from the Canyon Diablo iron meteorite (CDT) for sulfur, NBS BoricAcid Standard for boron, and the Caltech Rose Quartz Standard(NBS-28) for silicon.

St bl i t t d d d t

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Stable isotope standards and measurementNBS is now the National Institute of Standards and Technology (www.nist.gov)IAEA United Nations International Atomic Energy Agency (www.iaea.or.at)

ISOGEOCHEM http://www.uvm.edu/~geology/geowww/isogeochem.html

Oxygen-18 and deuterium in waterIn 1961 Harmon Craig proposed the Standard Mean Ocean Water (SMOW)standard which was not really standard seawater, but a calculated seawatervalue relative to NBS-1. You can read about the absolute isotope abundances

if youd like, but for our purposes you need to know that the SMOW standardand today the VSMOW standard are defined as having 18O and D values of0.0.

For waters that are highly depleted in 18O relative to VSMOW, a water standard

with much lower values is used. Standard Light Antarctic Precipitation, or SLAPis defined as having a 18O value of -55.50VSMOW and D value of -428.0VSMOW.

Measurement of 18O and D values is not quite straightforward You can't just

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Measurement of O and D values is not quite straightforward. You can t justpour the water sample into a mass spectrometer. Because water moleculescling to the guts of machines, 18O values are determined by equilibrating waterwith CO2 and then comparing the CO2 to a standard CO2.

For rapid equilibration the pH should be less than 4.5. The 18O value of thewater sample is derived by compensating for the equilibrium offset(fractionation factor). The fractionation factor () is generally assumed to be1.0412 (Friedman and O'Neil, 1977). Therefore the CO2 in equilibrium withwater is enriched by 41.2. We'll go over the actual process of measuring 18O

values in the lab soon.

Measurement of deuterium can take place in three ways, measurement ofelemental hydrogen reduced with uranium or zinc, reduction in a Cr furnace, ormeasurement of hydrogen that has been equilibrated with water using a

platinum catalyst.

The fractionation factor

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The fractionation factor,

The isotope fractionation factor between two substances, A and B, A-B,

is defined as:

where Ra is the ratio of the heavy (rare) isotope to the light (common) stableisotope in phase A, such as D/H, 11B/10B, 13C/12C, 18O/16O, 30Si/28Si or 34S/32S. Ifthe isotopes are randomly distributed over all the positions in substance A andB, is related to the equilibrium constant, K, for isotope exchange reactions by

A B aR

b

R

,

1

nKwhere n is the number of atoms exchanged. Rather than determining theabsolute ratios, ca. 18O/16O, in every phase, it is easier and more precise tomeasure the difference in absolute ratios between two substances. At

equilibrium, is related, to the very good approximation that the isotopes arerandomly distributed among all possible sites in the molecule, to the equilibriumconstant K for the isotope exchange reaction between the two substances(Biegeleisen, 1955).

Different authors report equilibrium fractionation factors as ln 103ln K

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Different authors report equilibrium fractionation factors as , ln, 103ln, K,lnK, , and (see appendix 1, ONeil, 1986). For simplicity, isotope exchangereactions are usually written such that only one atom is exchanged. Forexample, the oxygen isotope exchange reaction between CO2 and water vaporcan be written:

12

16

C 2O 218

H O 1218

C 2O 216

H O

The equilibrium constant for this reaction is

K

1218

C 2O 1216C 2O 2

16

H O 218

H O

This formalism is normally used in the calculation of fractionation factors from

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This formalism is normally used in the calculation of fractionation factors fromspectroscopic and thermodynamic data. C18O2 means that both oxygen atomsin the molecule are 18O. The equilibrium constants for these reactions arewritten are equal to the fractionation factor:

K 2CO

18O16

O

2H O

18O

16O

Values of are normally very close to unity, typically 1.00X. Commonly, isotopicfractionations are discussed in terms of the value of X, in per mil (per mil

fractionations). For example, the sulfur isotope fractionation factor betweenZnS and PbS at 200C is 1.0036. It is accepted parlance to state that at 200C(1) the sphalerite-galena fractionation is 3.6 (or 3.6 per mil), or (2) sphalerite is

enriched in34

S by 3.6 per mil relative to galena.

In terms of quantities actually measured in the laboratory ( values), this

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In terms of quantities actually measured in the laboratory ( values), thisexpression becomes:

AB

1 A

1,000

1 B1,000

1,000 A1,000

B,

Values of are usually close to unity, so that isotopic fractionations areexpressed as per mil fractionations. For example, for oxygen isotopesbetween quartz and water at 200C is 1.0110 so that the fractionation of oxyegnisotopes between quartz and H2O is +11; that is, quartz is enriched in

18O by11 relative to water. Similarly, for oxygen isotopes between water andquartz at 200C is 0.9890 so that water is depleted in 18O by 11 relative to

quartz.

As with any equilibrium constant, is related to the energy of any exchange

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As with any equilibrium constant, is related to the energy of any exchangereaction as ln. The energies involved in any reaction having an equilibriumconstant close to unity are small, i.e. ln (quartz-water) = 0.011 at 200C. For = 1.0X, 1000ln is approximately equal to X so that for the quartz-waterexchange reaction at 200C, 1000ln = +11. Thus, 1000ln is approximately

the per mil fractionation. From equation (6), defining A-B as A-B:

1000lnAB A B AB (6)provided A-B is within about 2 percent of unity. Therefore, the differencebetween the values of two coexisting phases is approximately equal to the permil fractionation.

103ln and the valueIt is a useful mathematical fact that

3

10 ln(1.00X)X

For the 34S example mentioned above where a = 1.0036, 103ln = 3.6. That is,103ln is the per mil fractionation. This logarithm function has addedtheoretical and experimental significance. For perfect gases, ln varies as 1/T-2and 1/T-1 in the high- and low-temperature limits, respectively (Bigeleisen andMayer, 1947). In addition, smooth and often linear curves have been found to

be obtained when 103

ln is plotted against 1/T-2

for experimentally determinedfractionation factors between mineral pairs or mineral-water pairs.

The per mil fractionation, 103ln, is then of prime importance in stable isotope

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The per mil fractionation, 10 ln, is then of prime importance in stable isotopegeochemistry. This quantity is very well approximated by the value:

AB A B 103 lnAB

That is, merely subtracting values will be an excellent approximation to theper mil fractionation and identical to it within the limits of analytical error forvalues of both s and s, which are less than about 10.