ISSN 1425-7351 I'll! PL9800491
fNCT — RAPORTY IChTJ. SERIA B nr 7/97
STUDIES ON FRACTIONATION OF YTTERBIUM ISOTOPES IN Yb(III)-ACETATE/Yb-AMALGAM SYSTEM EVEN-ODD EFFECT
Wojciech Dembiriski, Marek Poninski, Rudolf Fiedler
INSTYTUT CHEMII ITECHNIKI JADROWEJ INSTITUTE OF NUCLEAR CHEMISTRY AND TECHNOLOGY
WARSZAWA RAPORTY IChTJ. SERIA B nr 7/97
STUDIES ON FRACTIONATION OF YTTERBIUM ISOTOPES IN Yb(III)-ACETATE/Yb-AMALGAM SYSTEM. EVEN-ODD EFFECT
Wojciech Dembinski, Marek Poninski, Rudolf Fiedler
Warszawa 1997 EDITORIAL BOARD Wiktor Smulek, Ph.D., Ewa Godlewska, Sylwester Wojtas
ADDRESS OF THE EDITORIAL OFFICE Institute of Nuclear Chemistry and Technology Dorodna 16, 03-195 Warszawa, POLAND phone: (+4822) 11 06 56; tlx: 813027 ichtj pi: fax: (+4822) 11 15 32; e-mail: [email protected]
UKD: 541.1, 541.2, 546 INIS:B12.20 KEY WORDS: YTTERBIUM, ISOTOPE EXCHANGE, ISOTOPE SEPARATION, ISOTOPE EFFECTS, EVEN-ODD EFFECT, YTTERBIUM AMALGAM
Papers are published in the form as received from the Authors Studies on fractionation of ytterbium isotopes in Yb(lll)-acetate / Yb-amalgam system. Even-odd effect
The fractionation of ytterbium isotopes with the even and odd numbers of neutrons was investigated in a Yb(lll)-acetate / Yb-amalgam exchange system. The light isotope was preferentially fractionated to the amalgam phase. The values of the unit separation
gain per mass difference, e, were found to be -0.00054 for 176/171Yb and -0.00069 for
i76/i74yb fne difference which amounted to 0.00015 is an evidence for the occurrence of the so-called "even-odd" effect. It was also found that the chemical isotope shift of ytterbium was mirrored by the optical isotope shift in its atomic spectra.
Badanie podziatu izotopdw iterbu w ukladzie Yb(lll)-octan / Yb-amalgamat. Efekt parzysto-nieparzysty
Badano proces podziatu izotop6w iterbu o parzystej i nieparzystej ilosci neutron6w w ukladzie Yb(lll)-octan / Yb-amalgamat. Stwierdzono, ze w uWadzie tym faza amalgamatu wzbogaca si? w izotop Izejszy. Znaleziono nast^pujqce wartosci jednostkowych stopni podziaki, e : -0.00054 dla pary 176/171Yb oraz -0.00069 dla pary i7e/i74Yb R6znica wynosza.ca 0.00015 Swiadczy o wyst^powaniu w tym uWadzie tzw. efektu parzysto-nieparzystego. Pokazano, ze chemiczny efekt izotopowy jest podobny do optycznego efektu izotopowego w widmach atomowych.
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1. INTRODUCTION 9 2. EXPERIMENTAL 9 2.1. REAGENTS g 2.2. ANALYSIS 2.3. SEPARATION PROCESS 2.4. OCCURRENCE AND STABILITY OF Yb2+ 2.5. CASCADE PROCEDURE 12 3. DISCUSSION 14 4. REFERENCES 16 TABLES 75 FIGURES
NEXT PAGE(S) left BLANK 1. INTRODUCTION
The phenomenon called "even-odd effect" or "even-odd staggering of the isotopes" was first announced by Fuji et al. (1989) [1]. They found that in the red-ox exchange system of U(IV)-U(VI), the unit separation factor for the 238/235u isotope pair did not fit the linear interpolation between 238/234u and 238/236u. This meant that the
experimental results did not follow the relation: ln(q) « Am/(mi-m2) derived by Bigeleisen and Mayer [2] on the basis of quantum effects in the molecular vibration of isotopic species. Nishisawa et al. observed the same difference in the behavior of even and odd isotopes of Sr and 8a [3], Zn [4] and Mg [5] in liquid-liquid extraction systems with dicyclohexano-18-crown-6 (DC18C6). The even-odd staggering of Gd isotopes was also announced by Nomura et al. [6] in cation exchange displacement chromatography with EDTA and malonic acid as eluents, however with the reservation that the measurement errors were too large to conclude about the deviation from the theoretical relation of the mass dependence. Parallel unsuccessful attempts to find the even-odd effect in fractionation of Sr [7] and Ba [8] by the cation displacement chromatography have been reported. It should be stressed here that studies on the even-odd isotope staggering in the chemical exchange reaction represent a challenge for the analysts who measure the isotope ratio by mass spectrometry. Nowadays it is not sufficient to measure the difference between isotope ratios in enriched and depleted fractions but it is necessary to measure much smaller differences between isotope ratios of the chosen isotope pairs in both enriched and depleted fractions. For these reasons it is also advisable to study the phenomena rather in red-ox (electron) exchange reactions than in univalent (ligand) exchange reactions. The former offer a higher absolute value of the isotope effect expressed by natural logarithm of the unit separation factor (Inq). More experimental data are needed to offer reasonable interpretation of the phenomenon. This is because the energy value of hyper fine interactions connected with isotope nuclear spin (I), nuclear magnetic moment (n), as well as electric quadruple moment (Q) are considered to be too small to change the orbital coupling at the molecular level, the more so, as values of I, n and Q vary strongly with Z and A. However, the theory of the phenomenon is being developed. Recently Bigeleisen [9,10] has announced that in addition to classic mass shift the nuclear field shift must be taken into consideration whereas the nuclear spin effect can be neglected. The direction of the nuclear field term can be opposite to that of the mass term and its absolute value can be higher. The nuclear field shift is presumably responsible for the fractionation of the heavy isotope into the U(IV) phase in U(IV)<->U(VI) the red-ox exchange system. It was also observed that chemical isotope shifts of uranium isotopes were mirrored by isotope shifts in their atomic spectra. The latter are related to charge, size and shape of the nuclei and electron density at the nuclei. For our studies we have selected ytterbium from the rare earth region because of its interesting nuclear and chemical properties. The natural isotope composition of ytterbium is shown in Table 1 along with its isobars. Ytterbium has five and two isotopes with even and odd mass numbers, respectively. The latter have different spin numbers (l171 = 1/2; Ii73= 5/2) and different sign of nuclear magnetic moment expressed in nuclear magnetons (^171 = + 0.49188; Hi7i = - 0.67755). Such a composition is rather unique for the periodic system and after successful chemical fractionation may offer more information on the even-odd effect than for example in the case of barium with two odd isotopes (133 and 135) with the same spin number (3/2) and nearly the same value of the magnetic moment
(|*133 = + 0.8329; n135 = + 0.9311). From the chemical point of view ytterbium belongs to a characteristic group of 14 rare earth elements with the general electronic configuration of free atoms: [Xe]4fn5d°6s2. In the solution chemistry of Ln the valence 3+ with the configuration [Xe]4f1+U is typical, however a few exceptions occur. Cerium forms stable Ce4+ ions, europium forms relatively stable Eu2+ ions, ytterbium and samarium form much less stable Yb2+ and Sm2+. The latter two, because of the very low value of the standard red-ox potential (Table 2, uranium is included for comparison) are reoxidized by water itself or according to [11,12] by H+ ions with evolution of hydrogen. The instability of Yb does not permit to study the fractionation of its isotopes in red-ox exchange reactions utilizing counter-current extraction or displacement chromatography as it was done for U(IV/VI) [1], Ce(lll/IV) [13,14] , Eu(ll/lll) [15]. Ytterbium, however, forms amalgams. This inspired us to elaborate a new separation process based on the reduction of Yb(lll) by means of the sodium amalgam to produce the ytterbium amalgam, Yb(Hg). The isotope effect in such system should reflect the three electron exchange reaction; Yb(lll)oYb(0). 2. EXPERIMENTAL
2.1. Reagents
Yb2C3 of purity grade 99.99 was supplied by Aldrich Chemical Co. The mean content of the isobars amounted to: Er - 20 ppm, Lu - 3 ppm. Acetate solutions of Yb+3 were obtained by dissolving the oxide in an excess of acetic acid:
3.5M HAc/1M Yb. The final pH of 0.1M Yb(Ac)3 solution in 0.05M HAc was about 4.5. Sodium amalgam of concentration 2-^3.5M Na was prepared by dissolving
sodium in mercury purified by digestion with a 5% Hg(NO3) solution in 8% HNO3 followed by washing with bi-distilled water and drying under vacuum. After dissolution the Na amalgam was washed with xylene and absolute ethanol.
2.2. Analysis
Ytterbium was determined gravimetrically by oxalate precipitation and calcination at 850°C for 2 h or by a spectrographic method using a Carl Zeiss (Jena) spectrograph PGS-2.
The concentration of Yb(ll) was determined by titration with 0.05 N K2Cr2O7 using barium diphenyloamine sulphonate as indicator. Titration was performed in presence of ferric ammonium sulphate, phosphoric acid and sulphuric acid. The reagents solution was deaerated by a stream of argon. Yb(ll) was also determined spectrophotometrically using a Beckman DU 68 spectrophotometer and 0.25 cm quartz cells. The isotope ratios, 176/17lYb and 176/ 174Yb, were measured by means of a MAT 262 (Finnigan MAT) mass spectrometer. This instrument is equipped with 7 Faraday cup detectors. Six of them can be moved for an optimal adjustment to select masses. The method of total evaporation of the sample was applied, thus under normal conditions there should be no mass fractionation effect [16].
2.3. Separation process
The separation was performed in a 100 ml separation cell shown in Figure 1. At the beginning of the experiment the cell contained 50 ml of 0.1M Yb(lll) acetate solution and 260 g Hg. The content of the cell was stirred by means of a magnetic bar. The solution was deaerated with a stream of argon. The sodium amalgam, -2.5M Na(Hg), was then slowly pumped underneath the surface of mercury by means of a peristaltic pump. At the end of the experiment the amalgam (A) and solution (S) phases were separated. The Yb(Hg) was washed with ethyl alcohol and etched with 4M HCI for few hours at 60nC in order to reextract ytterbium. Then oxalates were precipitated and Yb,>O3 was obtained by calcination at 850"C. The ytterbium oxides recovered from fractions A and S were used to obtain 0.1M Yb(Ac)3 solutions for next separation stages. The aim of the experiment was to extract 50% of the ytterbium ^rom the initial solution to the ytterbium amalgam in a time as long as possible in order to establish isotope equilibrium. In general two competing reactions occurred in the studied chemical system: 1) reduction, of Yb(lll) with the sodium amalgam to Yb(Hg) with Yb(ll) as an intermediate stage: Yb3+ + 3Na -> Yb2* + 2Na + Na+ -> Yb° + 3Na+ (1) 2) reoxidation and back extraction of ytterbium :
2+ 3+ Yb° + 3H2O -^ Yb + 2H2O + 1/2H2 -» Yb + 6OH" + 3/2H2 (2) as well as:
Na + H2O -> Na* + 1/2H2 (3) The rate of reaction (1) depends mostly on the rate of delivering the Na(Hg) to the system. The rates of reactions (2) and (3) depend on pH and first of all on the kind and concentration of the ligand and counter ions which influence the effective red-ox potential. Following the literature suggestion [17-19] we have chosen for our studies acetates, however, citrates and ascorbic acid have also been used in our preliminary experiments. To find optimum conditions for the separation procedure a series of experiments were performed. Some of them are presented in Table 3 and Figure 2. As can be seen in Table 3, for given conditions a total time of 45 min and the final pH value 6.25, as in D-16, offer the best compromise. At higher pH white hydrolysis products precipitate at the surface of mercury. At lower pH the rate of reoxidation is probably too high to obtain Yb(Hg) of the desired concentration. Taking this into account the conditions of D-16, slightly modified, were adopted for cascade multiplication. The course of such an experiment, called "the unit separation procedure, u.s.p", is shown in Figure 3. The final concentration of ytterbium in the mercury was about 0.11% (by weight) or 0.078M, and the molecular fraction of ytterbium in the amalgam, Xi, amounted 0.0013.
10 2.4. Occurrence and stability of Yb2+
A deep yellow Yb(ll) acetate appears upon the addition of first drops of the Na-amalgam. UV-Vis absorption spectra of Yb(ll) exhibit two bands at 260 and 351 nm[20], 246 and 352 nm [21]. Our measurements, shown in Figure 4, revealed absorption bands at 252 and 351 nm which are consistent with the literature data. The concentration of Yb(ll) in the solution was determined by oxidimetry or by measurement of absorbance at 252 and 351 nm. The values of molar absorptivity calculated from oxidimetric and photometric data were £252= 920 and €351 = 479. It was estimated that the concentration of Yb(ll) in the course of the experiment was 0.015-J-0.025M for pH = 5-^-6. The results however were not very precise because of the high rate of Yb(ll) decay. The rate of its reoxidation in the samples of D-16, at pH = 6 was determined by measuring changes in the absorbance at 252 and 351 nm. The results, shown in Figure 5, suggest that the reoxidation follows the first order 1 kinetic equation: ln(C0/C) = -k t with constant k = 0.09 min' (TV2 = 8 min).
2.5. Cascade procedure
After phase separation the ytterbium was recovered and a pair of new stock solutions were prepared for next stage of the separation procedure. To attain 5-stages separation a simple cascade procedure with two branches: solution (S) and amalgam (A), shown in Figure 6, was applied. To preserve a constant concentration of ytterbium along the cascade the separation at first stage was done by repeating u.s.p. 12 times, in order to collect a sufficient amount of ytterbium for next separation stages. At the second stage u.s.p was repeated 6 times (3 in branch A and 3 in branch S). At the last stage the initial volume of the 0.1M ytterbium solution had to be reduced to 10 ml. The "S" and "A" fractions from the last separation stage were analyzed for the i76/i7iyb gnd us/ i74yb jsotope ratjo The resu|ts are snOwn in Figure 7. The values of the process separation factor (5 stages) Q, unit separation factor q = Q1/s and unit separation gain, divided by isotope mass difference, s = (1/Am)lnq are shown in Table 4.
11 3. DISCUSSION
It follows from the obtained data :
176/171qA/s = 0.99729; 176/171e = - 0.00054
176/174qA/s = 0.99863; 176/174e = - 0.00069 that in the studied exchange system the light isotopes are preferentially fractionated to the amalgam phase. This finding is in agreement with the general statement of B-M theory [2] that the heavy isotope concentrates in the chemical species that forms stronger bonds with the chemical element involved in the isotope exchange reaction.
The separation factor q formally corresponds to the isotope equilibrium in three or two electron exchange reactions presented by reaction (1).
L H n L H n Yb(Hg) + Yb(Ac)p «• Yb(Hg) + Yb(Ac)p (4)
H n where: L and H are the light and the heavy isotope, respectively, Yb(Ac)p - Yb(ll) or Yb(lll) acetate complexes
In the present state of the studies it is difficult to guess which complex is mostly responsible for the isotope fractionation. Their composition is rather variable because the pH and concentration of sodium ions increase in the course of the experiment. The sequence of the red-ox reactions occurring in the chemical system is not exactly known as well; reactions (1) and (2) represent a rather simplified picture. Direct reduction of Yb(lll) to Yb, beside the two step reduction, should also be taken into consideration. For example, no Yb(ll) was observed [17] when the amalgamation was performed by the falling drop method, providing a very short contact time.
In any case, the mean value of the RPFR (reduced partition function ratio) for acetate complexes should be higher than the RPFR value for ytterbium dissolved in mercury. The latter value should rather referred to intermetallic compounds of general structure Yb(Hg)n than to a homogeneous solution. 176/171 176/174 The difference between the value of E and e (amounting to 0.00015) may be taken as evidence for the occurrence of the even-odd effect in ytterbium isotope fractionation. Thus ytterbium has become the first element of the rare earth group and the sixth element of all elements that demonstrate such an effect.
12 It follows from the relations
1176/174 „ I ^ 1176/171 el that the separation of the even-even isotope pair is more efficient (by the factor 1.27) than the separation of the even-odd pair. An opposite relation was observed in the fractionation of uranium isotope [1,9]. In the red-ox exchange systems U(VI) <-> U(VI) and U(VI) <-> U(lll) it was found that the even-odd isotope pair was separated more efficient (by the factor 1.16) than the even-even isotope pair, according to: 238/236 238/234 238/235 I e| =| e| = I-0.0037I < I-0.0043I = I el
Similar differences between the behavior of ytterbium and uranium isotopes occur in their atomic spectra. For comparison we have taken the changes in the nuclear charge radius, 8 2 2 2 [(1/2)5 2 2 [(1/2)8(r >]176|174 = i-0.0045! > I-0,00401 = [(1/5)1 5 13 In fact the total separation factor, Inq, should be breakdown into the vibrational term, lnq(0), and the field shift effect, lnK(fS). Till now the contribiution of the nuclear field term to the total separation factor was calculated by Bigeleisen [10] for U[IV]/U[VI] exchange. In general, considering the uranium fractionation data [1,9,10], it was concluded that the nucleus with the odd number of the neutrons will behave in chemical reactions as though it has a smaller atomic mass, It was also told that the nuclear field shift leads to concentration of heavy isotope into the chemical species with the smaller electron density at the nucleus or the smallest number of s electrons at the bonding or valence orbitals. In fact, to normalize the uranium fractionation data in term of mass dependence (Inq « Am/m2) the value 234.5 should be taken for 235U. However, to normalize the ytterbium fractionation data the value 172 should be taken for 171Yb. Thus it should be concluded that ytterbium isotope with the odd number of the neutrons will behave in chemical reactions as though it has a higher atomic mass. This discrepancy in the properties of uranium can result from the specific differences in the structure of even and odd mass nuclei but also from the kind of molecular orbitals formed in the isotope exchanging species. To elucidate the phenomena the further studies are necessary. Fractionation data for another ytterbium isotope pairs as well as better understanding of the electron structure of the isotope species are of the interest. Acknowledgment This work was financially supported by the Polish State Committee for Scientific Research under the contract 3TO9A05209. 4. REFERENCES [1]. Fuji Y., Nomura M., Okamoto M., Onitsuka H., Kawakami F., Takeda K.: Z. Naturforsch., 44a, 395 (1989). [2]. Bigeleisen J., MayerM. G.: J.Chem.Phys., 15, 261 (1947). [3], Nishisawa K., Nakamura K., Yamamoto T., Masuda T.: Solv.Extr.lon.Exch., 11, 389 (1993). 14 [4], Nishisawa K., Nakamura K., Yamamoto T., Masuda T.: Solv.Extr.lon.Exch., .12, 1073 (1994). [5]. Nishisawa K., Nishida K., Miki T., Yamamoto T.: Sep.Sci.Tech., 31(5), 643-654 (1996). [6]. Nomura M., Fuji Y., Kawakami F., Okamoto M.: J.Nucl.Sci.Tech., 29(11), 42-49 (1992). [7]. Oi T., Hose M., Kakihana H.: Sep.Sci.Tech., 27(5), 631-643 (1992). [8]. Kondoh A., Oi T., Hose M.: Sep.Sci.Tech., 3J.(1), 39-48 (1996). [9]. Bigeleisen J.: J.Am.Chem.Soc, 118,3676-3680 (1996). [10]. Bigeleisen J.: Proc.Natl.Acad.Sci. USA, 93, 9393-9396 (1996) [11]. Stubblefield C, Eyring L: J.Am.Chem.Soc., 77, 3004-3005 (1955). [12]. Greenwood N., Earnshaw A.: Chemistry of elements, Pergamon Press, N.Y. 1984, p. 1465. [13). Dembiriski W., Goroncek K., Phuc N.: J.Radioanal.Nucl.Chem., Articles, 149(1). 169-176(1991). [14], Dembinski W., Goroncek K.: J.Radioanal.Nucl.Chem.,Lett, 175, 437 (1993). [15]. Dembinski W., Mioduski T.: J.Radioanal.Nucl.Chem.,Lett., 199. 159 (1995). [16]. Fiedler R., Donohue D., GrabmuellerG., Kurosawa A.: Int.J.Mass Spectrom. Ion Processes, 132, 207-205 (1994). [17]. Barret M., Sweasey D., Topp N.: J.lnorg.Nucl.Chem., 24, 571-586 (1962). [18], Kamenskaya A.N., Mikheev N.B., Strekolov A.I.: Zh.Neorg.Khim., 28(7), 1711 (1983). [19], Kamenskaya A.N.: Zh.Neorg.Khim., 29(2), 439 (1984). [20]. Faraggi M., Tendler Y.: J.Chem.Phys., 56(7), 3287-3293 (1972). [21], Christensen R. J., Espenson J. H., Butcher A. B.: Inorg. Chem., 12(3), 564 (1973). [22]. King W. H.: Isotope Shifts in Atomic Spectra, Pergamon Press, New York and London 1984, pp. 158-159. [23]. King W. H.: Isotope Shifts in Atomic Spectra, Pergamon Press, New York and London 1984, pp.142-143. 15 Table 1. Natural aboundance of ytterbium and its isobars, [%] z 68 69 70 71 72 M Erbium Thulium Ytterbium Lutetium Hafnium 168 27.7 0.14 169 100 170 14.88 3.03 171 14.34 172 21.88 173 16.18 174 31.77 0.18 175 97.5 176 12.65 5.15 Table 2. Standard red-ox potential [11] Ce Sm Eu Yb U 2+ 4+ E(MO2 /M );V 0.607 E^/M^V 1.61 -0.41 EtM^/M2*)^ -1.000 -0.360 -1.205 -2.483 -2.414 -2.407 -2.267 -1.798 16 Table 3. Separation experiments 50ml,0.1MYb(Ac)3 D-9 D-13 D-14 D-15 D-16 D-17 D-18 Concentration of Na in Na(Hg), [M] 1.28 1.39 3.68 2.31 3.9 2.84 2.44 Rate of Na addition, [mmol Na/min} 0.47 0.48 0.57 0.58 0.41 0.38 0.21 Total time [min] 35 35 30 30 45 20 85 Final pH 7.25 7.03 6.55 6.2 6.25 5.48 6.25 Time of pH stabilization [min] - 10 10 15 20 - 45 Extraction of Yb to Yb(Hg), [%] <20 29 45 55 48 <5 14 Table 4. Fractionation of Yb isotopes in amalgam/acetate system Phase Sample R(176/171) R(176/174) RSD [%] RSD [%] Yb-5 0.892641 0.400571 Amalgam Yb-6 0.892579 0.400557 R-A* 0.892610 0.024 0.400564 0.01 Yb-7 0.904623 0.403343 Solution Yb-8 0.904984 0.403304 R-S* 0.904803 0.087 0.403323 0.056 QA/S 0.98652 0.093 0.99316 0.055 QA/S 0.99729 0.018 0.99863 0.01 8=(1/Am)lnq -0.00054 6.7 -0.00069 7.4 counted from two independent measurements : (5;6) and (7;8) 17 Figure 1. Separation cell 4.5 5 10 15 20253035404550 time [min] Figure 2. pH vs. time in separation experiments 18 6.5 .. - -< < 20 •"7 / PH / 15 5.5 r / / o • ^ X 0.47 mmol / Na/min 5 4.5 r HAc] / iV 0 5 10 15 20 25 30 35 40 45 time [min] Figure 3. Unit separation experiment 3.5 — 3.30; t=0r 3 2.5 CO •8G 1.58 (0 0.5 200 250 300 350 400 wave lenght [nm] Figure 4. Absorption spectra of Yb(ll) acetate 19 (a) i ln(Ao/A«) = ().O95* t 0,i N R2 = 0.9965 1,0 \ k. \ 2,0 [V \ 2,5 V 10 15 20 25 30 time [min] (b) 0,2 ln(/VAO = 0.087*t |_ R2 = 0.9999 0,4 0,6 — 0,8 1,0 1,2 1,4 5 10 15 time [min] Figure 5. Reoxidation of Yb(ll). (a) absorbance at 252 nm, (b) absorbance at 351 nm 20 Stage 1 [Yb(Ac)3 12x50ml Yb(Hg) | Yb(Ac)3 y Yb(Ac)3 [YbCA^T] Stage 2. Yb(Hg) Yl?(Ac)3 - Yb(Hg) | Yb(Ac); 6x50 ml i Yb(AC)3 Yb(Ac)3 Stage 3. Yb(Hg) ArVl 1 Yb(Hg) ||Yb(Ac), 4x40ml Ac)ai > Stage4. 2x20ml Yb(Ac)3 Yb(Ac)3 Stage 5. 2x10ml Yb(Hg) YWAcW > «— YtXHg) Yb(Ac)3 1 to mass 1 to j I to mass 1 pectromet»v i ; waste j spectrometry "A" • "S" Figure 6. Cascade procedure 21 (a) 0.405 SOLUTION 0.404 •" 0.403 FEED •H 0.402 >'> -• j AMALGAM T" | 0.401 -/•"• '__ T' 0.400 ') • * f r ' 0.399 J -r , • 0.398 —i— —l— —1— Yb-5 Yb-6 Yb-4 Yb-7 Yk>« 0.915 (b) 0.91 SOLUTKJN 0.905 t "8 FEED i" •H 0.9 — n _ A UALGAM £ 0.895 MM •!• 0.69 - 0.885 — — 0.88 1 —t— —y— —(— Yb-5 Yb-6 Yb-3 Yb-4 Yb-7 Yb-8 Figure 7. Shift in Yb isotope ratio after 5-stages separation: (a) 176/174; (b) 176/171 isotopes pair 22