A basic theoretical understanding of stable isotope fractionations can help researczzzhers plan and interpret both laboratory experiments and measurements on natural samples. The goal of this chapter is to provide an introduction to stable isotope fractionation theory, particularly as it applies to mass-dependent fractionations of non-traditional elements and materials. Concepts are illustrated using a number of worked examples. For most elements, and typical terrestrial temperature and pressure conditions, equilibrium isotopic fractionations are caused by the sensitivities of molecular and condensed-phase vibrational frequencies to isotopic substitution. This is explained using the concepts of vibrational zero-point energy and the partition function, leading to Urey’s (1947) simplified equation for calculating isotopic partition function ratios for molecules, and Kieffer’s (1982) extension to condensed phases. Discussion will focus on methods of obtaining the necessary input data (vibrational frequencies) for partition function calculations. Vibrational spectra have not been measured or are incomplete for most of the substances that Earth scientists are interested in studying, making it necessary to estimate unknown frequencies, or to measure them directly. Techniques for estimating unknown frequencies range from simple analogies to well-studied materials to more complex empirical force-field calculations and ab initio quantum chemistry. Mossbauer spectroscopy has also been used to obtain the vibrational properties of some elements, particularly iron, in a variety of compounds. Some kinetic isotopic fractionations are controlled by molecular or atomic translational velocities; this class includes many diffusive and evaporative fractionations. These fractionations can be modeled using classical statistical mechanics. Other kinetic fractionations may result from the isotopic sensitivity of the activation energy required to achieve a transition state, a process that (in its simplest form) can be modeled using a modification of Urey’s equation (Bigeleisen 1949).

Theoretical estimates of isotopic fractionations are particularly powerful in systems that are difficult to characterize experimentally, or when empirical …

Applying Stable Isotope Fractionation Theory to New Systems

The single-stage separation factors for boron isotopes between an ion-exchange resin and an external solution were determined, using an ion-exchange breakthrough operation. The lighter isotope boron-10 was considerably enriched in the anion-exchange resin phase. The separation factor was very much influenced by the boric acid concentration in the external solution, but not as much influenced by the kind of the anion exchange resin used and operation temperature. The separation factor increased with a decrease in the boric acid concentration of external solution from 1.008 (0.501 mol/l) to 1.016 (0.010 mol/l). The value of the separation factors obtained experimentally were compared with those estimated on the basis of the theory of the two-phase distribution of isotopes.

Fundamental studies on the ion-exchange separation of boron isotopes

FT-IR and Raman spectroscopic study of hydrated borates

Indirect photometric chromatography

...................................................... Introduction...................................................................^ Basic Concepts ................................................................................................................................................2 Aclmowledgements...........................................^ Hydrogen...............................................................................................................................................^ Reference materials and reporting of isotope ratios......................................................................................5 Ranges in isotopic composition......................................................................................................................5 Water...................................................................................................................................... Silicates............................................................................................................................................^ Hydroxides...........:...............................................................................^ Organic hydrogen....................................................................................................................................8 Methane .................................................................................................................................................10 Hydrogen gas......................................................................................................................................... 10 Lithium................................................^ Reference materials and reporting of isotope ratios.................................................................................... 11 Ranges in isotopic composition.................................................................................................................... 11 Marine sources ......................................................................................................................................11 Non-marine sources............................................................................................................................... 13 Lithium in rocks.................................................................................................................................... 13 Phosphates............................................................................................................................................. 13 Silicates....... ... . ........... . .... . .. .. . . .... . ....... .._ Reagents............................ .. ..... ... . ... .. ... . . ..............J^ Boron......................................................................... Reference materials and reporting of isotope ratios.................................................................................... 15 Ranges in isotopic composition.................................................................................................................... 15 Marine sources ......................................................................................................................................15 Non-marine sources............................................................................................................................... 16 Igneous rocks......................................................................................................................................... 19 Metamorphic rocks................................................................................................................................ 19 Sediments............................................................................^ Organic boron........................................................................................................................................19 Carbon ......................................................................................20 Reference materials and reporting of isotope ratios....................................................................................20 Ranges in isotopic composition....................................................................................................................20 Carbonate and bicarbonate ...................................................................................................................20 Carbon dioxide......................................................................................................................................25 Oxalates...............................................................................26 Carbon monoxide..................................................................................................................................26 Organic carbon ......................................................................................................................................26 Elemental carbon...................................................................................................................................28 Ethane ....................................................................................................................................................28 Methane .................................................................................................................................................28 Nitrogen............................................................ Reference materials and reporting of isotope ratios....................................................................................29 Ranges in isotopic composition....................................................................................................................29 Nitrate................................................................................................................................ Nitrite............................................................................................ Nitrogen oxide gases.......................................................................................30 Nitrogen gas ................................................................................................30 Organic nitrogen....................................................................................................................................32 Nitrogen in rocks...................................................................................................................................34 Ammonium.................................................................................................................................^ Oxygen ........................................................... Reference materials and reporting of isotope ratios....................................................................................36 Ranges in isotopic composition....................................................................................................................37 Oxygen gas.............................................................................................................................................39 Water........................................................^ Carbon monoxide..................................................................................................................................41 Carbon dioxide ......................................................................................................................................41 Carbonates .............................................................................................................................................41 Nitrogen oxides.....................................................................................................................................42 Other Oxides..........................................................................................................................................42 Phosphates .............................................................................................................................................42 Silicates...................................................... Sulfates..................................................................................^ Plants and animals.................................................................................................................................43 Magnesium.....................................................................................................................................^ Reference materials and reporting of isotope ratios....................................................................................44 Ranges in isotopic composition....................................................................................................................44 Marine sources ......................................................................................................................................44 Elemental magnesium...........................................................................................................................46 SiHcon..............................................................^ Reference materials and reporting of isotope ratios....................................................................................46 Ranges in isotopic composition....................................................................................................................46 Igneous rocks.........................................................................................................................................47 Metamorphic rocks................................................................................................................................47 Vein quartz and silicified rocks ............................

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Compilation of minimum and maximum isotope ratios of selected elements in naturally occurring terrestrial materials and reagents

Raman spectra of polyborate ions in aqueous solution

Boron isotopic composition of fumarolic condensates and sassolites from Satsuma Iwo-jima, Japan

A fundamental equation for chromatography is derived starting from a very simple concept that the chromatographic movement of species can be expressed as the sum of the movement caused by the external force and the movement caused by the internal concentration gradient and its transformations into appropriate forms are discussed in the cases of ion exchange (or gas) chromatography and ionic migration, without or with a counterflow. By solving the fundamental equation, making appropriate assumptions, a comprehensive expression which describes the concentration profile is derived for two-isotope systems in any kind of chromatography.

Theory of Chromatographic Separation of Isotopes

Ion exchange, isotope exchange and isotope separation

Fundamental equations for the ion exchange separation factor of the isotopes A and B are derived : a)for the system having the molecules or ion associations[math] b)for the system having stepwise series of complexes[math] According to the prediction based on these fundamental equations, some experimental works have been done to obtain larger separation factors for the isotopes Li, N and U. The results are as follows : a)[math]1,005-1,008 for the system of a weaker electrolyte, LiOH, in the external solution with the strongly acidic and very highly cross-linked cation exchange resins. The separation factor reaches 1,012 when acetone is added to the same system to reduce the dissociation constant of LiOH. 1,013-1,015 for the system of strong electrolyte, LiCL, in the external solution with the weakly acidic inorganic cation exchanger, Ionite C (zirconium phosphate typ). 1,016 for the system of LiOH in the aqueous external solution with Ionite C. The value 1,022 is obtained by adding acetone to the same system. b)[math]1,027-1,029 for the system of weak electrolyte, NH3 , in the external aqueous solution either with strongly acidic cation exchange resins or with Ionite C. The addition of organic solvent such as ethanol or acetone gives better results especially with very highly cross-linked cation exchange resins. c)[math]The values 1,000 28-1,000 40 are estimated from break through experiments with hydrochloric acid solutions containing greater part of uranous together with smaller part of uranyl ions.

Hidetake Kakihana

Papers

Raman spectra of polyborate ions in aqueous solution

Boron isotopic composition of fumarolic condensates and sassolites from Satsuma Iwo-jima, Japan

Theory of Chromatographic Separation of Isotopes

Ion exchange, isotope exchange and isotope separation

A fundamental study on the ion exchange separation of lithium, nitrogen and uranium isotopes