The Ionic Radius of No³+

1. Introduction
Studies of the heaviest actinides and comparison with the properties of lanthanides are interesting because they help to understand the influence of relativistic effects on the chemical properties.  The relativistic effects influence the contraction of the 3+ lanthanides and actinides ionic radii by two ways: split- ting of outermost p orbitals and stabilization of p 1 /2 orbitals, and expanding the f 5/2 and f 7/2 orbitals which results in less effective shielding of the nuclear charge. For the heaviest actinides these might result in ionic radii different from non-relativistic extrap- olations. For example, in the case of Fm 3+ the relativistic effect is responsible for 8 pm contraction of the ionic radius, while for Er 3+ only 2.5 pm. The determination of the ionic radius of No 3+ ion is of key interest, particularly since the ionic radius of Lr 3+ has been determined. 1 This measurement would conclude the ionic radius determinations of the 3+ actinide ions. The ground state electronic configuration of nobelium is [Rn]5f 147s 2 . Energy of 5f 1/2 orbitals in nobelium (−15.43 eV) is more negative than 4 f 7 /2 orbitals in ytterbium (−14.67 eV) (homologue in lanthanide series) which causes that nobelium as the only one among f electron cations is very stable in the oxidation state 2+. The redox potential of the No 2+ /No 3+ cou- ple was determined to be 1.4 ± 0.2 V. 2 This aspect of nobelium chemistry provides special problems for the determination of the No 3+ ionic radius. In the determination experiment first No 2+ must be oxidized to the No 3+ .  This can be accomplished with the use of strong oxidizing agent such as KMnO 4 (1.5 V) or H 5 IO 6 (1.7 V). The second problem is to stabilize in the 3+ ox- idation state during the determination experiment. Ionic radii are usually obtained from X-ray diffraction data for oxides or fluorides.  However, these techniques require weighable quantities of the compound. Unfortunately, elements heavier than fermium are produced in quantities of few atoms at a time, so that experimental structural data for these elements are not available.  The values of ionic radii for Md 2+ , Md 3+ , No 2+ , and Lr 3+ were determined only by chromatographic meth- ods. 1.3.4 The ionic radii of Md 3+ and Lr 3+ were determined by comparing their elution positions with the positions of rare earth tracers and of actinides of known ionic radii. The ionic radii of Md 2+ and No 2+ were determined by comparison with crystallo- graphic radii of Ca 2+ , Sr 2+ , and Ba 2+ (Ref. 3,4). For the determination of ionic radius of No 3+ , Henderson 5 used ion exchange chromatography with KMnO 4 and H 5 IO 6 as oxidizing agents and α-HIB as eluent.  Unfortunately, these strong oxidants decomposed both the α-HIB and the ion ex- change resin and, therefore, the determination of No 3+ ionic ra- dius could not be accomplished using this approach. In our laboratory, samples of cryptomelane-type MnO 2 inor- ganic ion exchanger were synthesized. This sorbent is known to possess interesting ion exchange properties. The cryptome- lane MnO 2 phase has a well-defined 2 × 2 tunnel-framed struc- ture with exchangeable hydrogen, alkali, or alkali earth cations. 6 The presence of exchangeable ions in the tunnels requires that some of the manganese atoms must be present in oxidation states lower than 4. The formulae could be represented by HMn rVMn ll O 16 as postulated by Tsuji and Tamaura. 7 The av- erage tunnel diameter is 0.28 nm so the selectivity of the sor- bent is related to the steric effect in the tunnel structure. 8 Cryp- tomelane MnO 2 has been demonstrated to show excellent ion- exchange selectivity towards cations with crystal ionic radii of 130–150 pm, e.g. K + , NH + , Ba 2+ , and Ra 2+ (Ref. 6–8). For 3+ lanthanides and actinides the distribution coefficients are much lower, but strongly depend on the radius of cations.  Addition- ally, in acidic solutions the sorbent exhibits both ion exchange and strong oxidizing properties, so No 3+ should be stabilized in cryptomelane MnO 2 phase. In the present work, cryptomelane- type MnO 2 is used for the determination of No 3+ ionic radius by chromatographic methods.
2. Experimental
2.1. Synthesis  of   Cryptomelane   Manganese   Dioxide. Manganese dioxide samples were synthesized according to the procedure used by Tsuji and Abe. 9 The precipitates were ob- tained by adding 250 cm 3 of 0.5 M KMnO 4 in 1 M H 2 SO 4 to 250 cm³ of 1 M MnSO 4 solution containing 1 M of H 2 SO 4 at 60 °C. The precipitates were then aged overnight, filtered, and washed with water. The product was dried at ca 70 °C for three days, and then ground and sieved. The samples were trans- formed to the H + form by percolating 6 M HNO 3 solution. 2.2. Radioactive Tracers.  The radionuclides of 89 Sr, 46 Ca, 90Y, 177 Lu, 169Yb, 170 Tm, 166mHo, 152 Eu, and 241 Am were pur- chased from Isotope Products in Swierk, Poland.  All tracers were stored in 6 M HNO 3 solutions to prevent them from hy- drolysis. were obtained by 18 O irradiation of 248 Cm target in reaction: 248 Cm( 18 O, α3n) 259 No .
The experiments were carried out at Philips cyclotron at the Paul Scherrer Institute, Villigen (Switzerland). Target of 0.730 mg cm − 248 Cm was irradiated for 2.5 h with 18 O 5+ ions. The beam energy on target was 99 MeV, and the beam intensity was 1 × 10 12 particles per second. Under these conditions, 259 No is produced with the cross section of about 30 nb.  The target contained 10% of Gd thus producing simultaneously 165,167 Yb and 165,167 Lu. The reaction products recoiling out from the target were stopped in He gas and transported to the chemistry collec- tion site by a KCl aerosol-seeded gas-jet system.  The aerosol with reaction products was collected on a glass filter. 2.4. Chromatographic Procedure. A small glass column (3 mm × 5 cm) was filled with 0.5 g cryptomelane MnO 2 (0.01– 0.05 mm) and preconditioned with solution of HNO 3 . The lan- thanides and americium tracers were dissolved in 0.5 M HNO 3 , evaporated, and dissolved in 20 µ L of 0.5 M HNO 3 and 0.05 M H 5 IO 6 . Next, the solution was placed on the top of the column. The radionuclides were subsequently eluted from the column with 0.5 M HNO 3 solution at a flow rate of 0.1 cm 3 min − 1 . Drop fractions from the column were collected and measured by γ spectrometry or by liquid scintillation counting ( 46 Ca, 90 Y). The same chromatographic procedure was used in nobelium experiments. The aerosol, together with the reaction products, was dissolved in 2 cm³ of 0.5 M HNO 3 , evaporated, and dis- solved in 20 µ L of 0.5 M HNO 3 and 0.05 M H 5 IO 6 . The drops from the column were collected on stainless steel disc and evap- orated on a hot plate.  After evaporation the samples were in- serted into the detector array for α spectroscopy, consisting 6 Si(Au)-surface barrier detectors, for 2.5 h measurement.  The α events, together with the detector numbers and the associ- ated time, were recorded. Spontaneous fission events were also recorded. Before α measurement the γ activity was measured by Ge(Li) detector for 1 min. The whole procedure, from the end of bombardment until the start of α spectroscopy, lasted about 40 min. The distribution coefficient ( K d ) between two phases in chromatographic system is defined as:
where V m and V s are the volumes of the mobile and the station- ary phase, respectively, and V f is the free column volume.
3. Results
The selectivity for the cations on cryptomelane MnO 2 strongly depends on the ionic radii of the exchanged cations. Because the diameter of the tunnel in the MnO 2 phase (280 pm) is similar to diameters of the metal cations, the selectivity of the sorbent is associated with the steric effect.  The hydrated 3+ metal cations with diameter much larger than 280 pm must be dehydrated before entering the ion exchange phase. Therefore, the selectivity of the cyptomelane MnO 2 depends linearly on free energy of hydration, 10 which is also linearly related to the reciprocal of crystal ionic radius. The linearity of log K a on ionic radii for f electron cations was also found by Tsuji et al. 11 There are numerous data for ionic radii of the cations. The values com- monly used are Shannon radii. 12  In case of heaviest actinides (Es 3+ , Fm 3+ , Md 3+ , and Lr 3+ ) all available experimental ionic radii are given in the Templeton and Dauben 13 scale. In order to allow comparison we also used the Templeton and Dauben scale to present the ionic radii of the lanthanides and actinides cations studied. As mentioned earlier 1 it is known that the co- ordination number (CN) for the heavy trivalent lanthanides and actinides is 8.  Although there is no experimental data on the CN of Md 3+ , No 3+ , and Lr 3+ , it is assumed that CN is also 8. Then, the log K d vs. (1/r) should be linear for the respective cations.  A plot of log K d versus reciprocal crystal ionic radius for lanthanides, yttrium, and americium is shown in Figure 1. There is a good linear correlation for all the cations studied. The chromatographic columns calibrated previously for lanthanides tracers were used in experiments with nobelium. We performed 11 accumulation and chromatographic cycles during which we observed the decay of 22 atoms of 259 No.  In Figure 2, the sum α spectra of all No fractions obtained in the elution processes are given. The analysis of 259 No α spectra is difficult since its α branch consists of five lines covering the energy range from 7.455 to 7.685 MeV. 14 The possible interference is only from 250 Fm (7.390 and 7.430 MeV). Other possible interfering nu- clides decayed within experimental time (40 min). Taking into account the FWHM of the α spectra (25 keV) and the possi- ble interference at 7.430 MeV, the events in the range 7.460– 7.690 MeV were considered. From the γ -spectroscopy measure- ment the elution positions of 165,167 Yb and 165,167 Lu, produced in the na Gd + 18 O reaction, were obtained to make sure that the col- umn behaved as in the calibration runs, and to give markers in the elution so that all elutions could be compared on the same basis.  During synthesis of 259 No also Fm, Es, and Cf nuclides were produced as transfer products. In collected fractions max- imum of 250 Cf activity was found near Eu 3+ fraction and 255 Fm close to Dy 3+ so the elution positions of actinides are consistent with the elution positions of respective lanthanides. The sum of the elution curves from the experiments where 259 No was detected is presented in Figure 3.  The elution curve is presented in the K d scale because V f and V s of the column were not identical.  As shown in the Figure 3 two maxima are ob- served. First — small one is probably related to the nonoxidized No 2+ because it is seen between the fractions where cations Ca 2+ and Sr 2+ are eluted. The value of No 2+ radius (105 pm) is be- tween radii of the Ca 2+ (100 pm) and Sr 2+ (118 pm). The second maximum corresponds to No 3+ and is eluted near the fraction where Ho 3+ and Y 3+ are eluted. The logarithm of distribution coefficient of No 3+ was converted to an ionic radius from the slope and intercept of the line, yielding 89.4 ± 0.7 pm in Tem- pleton and Dauben scale or 90.0 ± 0.7 pm in Shannon scale.  The error limits on radius value represent the uncertainty in the elu- tion positions as measured from separate experiments and the distribution of the observed No data points.  Unfortunately, the uncertainty in the determination of No 3+ radius is much larger than the error of determination in the case of Md 3+ and Lr 3+ radii (±0.1 pm). 1 This results from the slower kinetics observed on the cryptomelane MnO 2 than on the ion exchange resin as well as from the lower selectivity of cryptomelane MnO 2 to M 3+ cations compared to the selectivity of complexation with α -HIB. The No 3+ radius value determined lies between radii of Md 3+ and Lr 3+ , closer to that of Md 3+ . Acknowledgement.  The author likes to thank A. Türler, S. Hübner, B. Eichler, R. Eichler, S. Yakushev, B. Wlodzimirska, and K.Zuchowska for their advise and assistance in the experi- ments.  The research was supported by the grant from the State Committee for Scientific Research of Poland nr. 7T 09A 073 20.