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Some peculiarities manifestation of the spin in isotope effects
MYSHKIN Vyacheslav F., PLEKHANOV Vladimir.G., IZHOYKIN Dmitry A.a,
KHAN Valery A.
National Research Tomsk Polytechnic University, 30, Lenina ave., Tomsk, 634050, Russia
a
[email protected]
Keywords: isotope effect, spin, thermodynamics, electron interactions, g-factor.
Abstract. The rewiev of 12 widely known isotope separation methods based on electron interactions is
executed. Thus it can be assumed that isotope effects based on spin interactions.
Introduction
Application field of isotopes are constantly expanding. Therefore the development of isotope
separation efficient methods is significantly actual. Isotope separation methods used the differences in
physical and chemical properties of isotopes: diffusion [1], electrolysis, evaporation, condensation
(crystallization), in chemical reactions [2], and isotope exchange. As a rule, these processes are related
to formation or destruction of electron coupling.
When the chemical bond formed or changed the redistribution of electron density between single
atoms occurred. Thus there is a change in the effective charges on atoms or molecular fragments. In
accordance with the valence bond method the bond between atoms forms using common electron pair.
Covalent bond contribution is significantly great even at great difference in atoms electronegativities.
Isotope species behavour laws can be explained in terms of electron properties, electron molecular
structures, reaction products and its interactions with the environment.
A great number of experimental results including Stern and Gerlach in the early 20th century show
the internal freedom degree of electron. A mechanical moment of electron related to this freedom
degree and independent of its orbital motion called «spin».
In accordance with the quantum mechanics the magnetic moment related to a rotating body. Spin
has the magnetic moment as confirmed by S-state hydrogen atomic beam splitting in two when passing
through the anisotropic magnetic field. In the S-state the orbital moment and magnetic moment are
zero. Therefore the reason of splitting is only spin magnetic moment. The probable values of the spin
moment projection on arbitrary allocated Z-axe are equal to s z    / 2 to electron. Appropriate
electron spin projections are equal in magnitude to Bohr magneton  z  e  2mc1    B [3].
The most detailed spin description performed by Dirac in relativistic approximation [4].
Schrodinger shows that electron in Dirac’s equation has two velocities: regular (measurable) and
motion with transient in time small amplitude (bounce). The orbital moment of bounce is spin [3].
Isotope effects
Let’s briefly discuss the isotope effects. The first metal isotopes studied by X-ray diffraction were
Li и 7Li. At the 4,2 K the crystal lattice parameters are aLi6=3,480A, aLi7=3,478А [5].
Significantly change of lattice parameters owing to replacement of the hydrogen by deuterium was
discovered in S and Se [6], HfH2 [7], UH3 and UD3 [8].
Atoms oscillate even through the absolute zero. It leads to relation between to interatomic distance
and mass. The more the particle vibration energy the more the mean distance between particles owing
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to potential curve asymmetry. Because of the "zero oscillation" the self-diffusion coefficient is more
than an order of magnitude at the transition from 7Li to 6Li when the cooling to zero. At the transition
from 12С to 13С the self-diffusion coefficient is three orders of magnitude less [9].
The vaporization enthalpy growth at the transition CD3OH, CH3OH, CH3OD shows that
intermolecular interactions become stronger [10]. Isotopic substitution weakens the dispersion
interactions owing to lesser polarizability of moleculs which contain deuterium.
Isotope thermodynamics. Substance-to-subctance contact leads to isotope redistribution. The
equilibrium fractionation factor α depends on -factors. The formulae for -factors calculation based
on total vibrational spectrum of molecules bound by paired electrons [11].
Isotope effects reason is nuclei mass difference. The formula for -factor calculation from
oscillations kinetic energy of isotope-substituting atom K [12].
Isotope mixture rectification. The substance transition between condensed and gaseous phase
related to intermolecular bonds destruction has isotope selectivity. The method based on isotope effects
appears in difference of saturation vapor pressure in liquid-vapor equilibrium state. The α-factors were
estimated for equilibrium evaporation of С2Н6, С2Н4, СН3ОН, С3Н8О, СН3С1, ССl4, С6Н6 [13].
Isotope-selective processes by sorption of Cu and Zn on the amorphous ferric hydroxide are
studied experimentally from solutions with different content of Cu (65Cu/63Cu) and Zn (66Zn/64Zn). The
heavy isotope adsorbed better on the hydroxide surface which is related to a shorter metal-oxygen
electron bonds and to a lesser metal coordination number on a surface respectively to dissolved ion. Cu
isotope fractionation is greater than for Zn isotope [14].
It is shown that hydrogen isotope distribution at thermal desorption from PdHxDy depends on
difference between energies of corresponding transient state of atom-atom recombination reaction [15].
At liquid-ice phase transition the intermolecular interactions formation occurred. Water freezing
or melting related to change in isotope composition [16]. It is shown that thermodynamic factor of
isotope separation for ion crystal growth from water solution for monatomic ions Li+ and Ca2+ is
defined by the equilibrium between ions in solution and on growing crystal surface [17].
Chemical isotope exchange in the gas–liquid system is used for light elements isotope separation
from 30th of 20th century [18]. Mills and Urey study the isotope exchange reaction between dissolved
inorganic carbon (H2CO3, HCO3-, CO32-) and gaseous CO2. Carbon-13 turns to the gas phase by HCN
and NaCN contact. An estimated value of separation factor between 12C and 13C is α = 1,026-1,030 at
298 К [19], between 12С and 14С is α = 1,035 [20]. Isotope separation factors 13C and 18O for CO2calcite system at 900 С and 12,5 kbar are +2.70±0.36% and +3.30 ± 0.16% respectively [21].
Isotope exchange in the liquid–liquid system between the R2C(ОН) in organic solvent and K13CN
water solution occurred with the separation factor  = 1,035-1,040 and large velocity [22].
In paper [23] the experimentally measured equilibrium constant for isotope-exchange reaction for
lithium 7Li(s) + 6LiCl(aq)  6Li(s) + 7LiCl(aq) at 296.6K is k = 1.046±0.013.
Extraction is the selective subctance selection related to dissolve matter transfer from one liquid to
nonmiscible [24]. There is a change of Gibbs free energy. Chemical systems thermodynamic
parameters related to electron structure of molecules participating in chemical interactions [25]. For the
isotope effect estimation the statistical thermodynamics based on partition function are used [26].
First papers of carbon isotope separation by ion-exchange resin related to carbon isotope effect
investigation by 14C-labeled aminoacids separation on cationite [27]. For carbon isotope separation
used the formate-ions [28] which are placed into a resin « Dowex-2» in the acetate  = 1,0062-1,0032
in the temperature range 279–308 K. There are methods of uranium isotope separation in U4+-cationite
systems by complex former elution [29] with  = 1,000060,00005 for 235U/238U [30].
Generally the problem of isotope separation in nonequilibrium conditions considered in [31].
Filling of upper vibrational levels in nitrogen molecules at nonequilibrium vibrational exchange
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between 14N2() and 14N15N() molecules is isotope-selective. Thus there is enrichment of products of
dissociation or chemical reaction N2(12) + O  NO + N by 15N [32].
The difference between vibrational temperatures in the V - V-exchange related to vibrational energy
transfer from light molecules into heavier. Required difference between vibrational and transitional
temperatures can be created both at the expense of molecular vibrations exciation and at cooling of
transitional and rotational degrees of freedom of gas previously heated by a nozzle [33].
The selective excitation of isotope species is common for all methods of laser isotope separation at
dissociation. Experiments of isotope selective multiphoton dissociation at selective breakup of
molecular orbital by resonant IR radiation executed for elements from hydrogen to osmium [34].
Two-stage selective photodissociation is useful for separation of nitgrogen isotopes [35], boron at
simultaneous СО2-laser and UV radiation on the NH3, ВС13 molecules. Isotope selective reactions of
ВС13 with oxygen [36] and SF6 with hydrogen [37] were performed using dissociation.
If at electron excitation molecule is on coupling term crossing with dissociable there are the
predissociation [38]. Selective predissociation firstly used for hydrogen isotope separation [39].
In the magnetic field the paramagnetic terms split. Therefore it is possible to cross the stable and
unstable terms and predissociation of molecules from high vibrational levels of stable term. Magnetic
predissociation of rotational levels of Вr2 in 3П1u–state was founded lower the dissociation boundary to
50-1000 sm-1 occurred at 150-300 kilogauss because of crossing of upper branch from 3П1u-term and
lower branch from unstable term 1Пu [40].
For calcium isotope separation by laser photoionization the radiation of dye laser and argon laser
[41]. The possibility of efficiency enhancement of two-stage ionization is excitation of atoms electrons
into states close to the ionization boundary. Further the ionization by electric field is taken place [42].
In the electric field greater than 3 kV/cm the energy levels nearest to ionization potential turn into
continuum and the remainder levels turn into autoionization.
Theoretical analysis [43] and experiments [44] show that two-stage laser influence can selectively
ionized the atoms with 100%-efficiency. Among the papers on laser isotope separation by selective
photoionization the paper cycle [45] is widely known. It dedicates to rare earth elements. By the
selective two-stage ionization the enrichment was: 102Pd - to 18%, 104Pd - to 70%, 105Pd - to 60% [46].
Isotope separation at photochemical processes based on possibility of molecules excitation at 10-810-12 s by laser radiation [47]. For H and D separation the oscillations of molecules mixture (СН3ОН
and CD3OD) are selectively excited by laser radiation on 2,7 micron at 100 torr and ~300 K.
Vibrationaly excited methanol reacts with the Вr2 vapor and leave the gaseous phase. As a result of
laser radiation at 60 s (90 W) the content of CD3OD in gaseous phase changes from 50% to 95%.
Chlorine isotope separation is implemented in a laser-produced reaction of CSC12 with
dietoxyethylene [48]. Argon laser radiation (4657,84 А) was absorbed mainly by CS37Сl37Cl molecules
and laser radiation (4705,5 А) by GS35Сl36Cl. In the first case 35С1 concentration in CSCl2 molecules
increase from 75 to 80% and in the second case 35С1 concentration in CSCl2 decrease to 64%.
Radical processes in magnetic field occurred in the solution make it possible to separate magnetic
and nonmagnetic isotopes. There is magnetic isotope effect [49]. It is shown that primary elementary
photoreaction of uranyl is selective on electron spine.
Plasma isotope separation. At the carbon dioxide dissociation in the Townsend discharge the
isotope 13C accumulate in undissociated CO2. Separation degree is 1,028±0,008 [50]. At the glow
discharge nondissociated part of carbon dioxide enriches on 13C on the average 1,020+0,008 times.
We study the plasma reaction of partial carbon oxidation in a magnetic field in the mixture argon–
oxygen [51]. In the magnetic field 0,2 T maximal concentration 13CO 1,41% is observed when magnet
(height 10 cm) placed on 13–16 cm from the plasma flow onset. In the magnetic field 1,2 T maximal
concentration 13CO 1,7% is observed when magnet (height 5 cm) placed on 16–27 cm from the plasma
flow onset. Content of 13C in CO produced without magnetic field is not differing from natural content.
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Processes leads to isotope selectivity at carbon oxidation in the magnetic field are discussed in
papers [52, 53]. Calculations performed by the developed model shown that the 13CO concentration on
the outlet of plasmachemical reactor should be significantly higher. One reason for the small isotope
effect is an excessive amount of oxygen supplied to the plasma-forming mixture.
Summary
In all of these the electron-electron interactions can be observed. These show the importance of
accounting of the spin component in the isotope separation methods.
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