J. Nig. Soc. Phys. Sci. 2 (2020) 180–185 Journal of the Nigerian Society of Physical Sciences Original Research Mass Resolution of Ca, K Isotopes and CO, N2 and C2H4 Isobars in Isotopes Separator On-Line trap Mass spectrometry B M Dyavappa∗ Department of Physics, Government First Grade College for Women, Kolar, Karnataka, India Abstract In Isotopes separator on-line trap, ions are trapped, cooled, accumulated, bunched and isotopes or isobars are separated, cyclotron frequencies are determined, which are followed by time of flight mass resolution. The mass resolution of isotopes in Penning trap mass spectrometry is achieved by the direct excitation of axial motion of ions, driven by RF field at the pure cyclotron frequencies of ions. The design and working of Isotopes separator on-line trap which is used for high-accuracy mass spectrometry in the mass resolution of calcium isotopes (40Ca+, 42Ca+, 44Ca+), potassium isotopes (39K+, 41K+) and [28(CO)]+, [(28N2)]+, [28(C2H4)]+ isobars found in mixtures is achieved from time of flight mass spectrometry are presented here. Keywords: Mass spectrometry, Mass resolution, Isotope online Penning trap, Resonance spectrum, RF excitation. Article History : Received: 09 May 2020 Received in revised form: 17 July 2020 Accepted for publication: 20 July 2020 Published: 01 August 2020 c©2020 Journal of the Nigerian Society of Physical Sciences. All rights reserved. Communicated by: O. J. Oluwadare 1. Introduction The stable six isotopes of calcium are 40Ca, 42Ca, 43Ca, 44Ca, 46Ca and 48Ca out of which 43Ca, 46Ca, 48Ca are rare isotopes found in trace amounts and hence cannot be identified in the isotope-ratio mass spectrum obtained from stimulations. The mass resolving powers of 40Ca+, 42Ca+, 44Ca+ are deter- mined from [1, 2, 3] (M.R.P.)Ca+ = mCa+ δmCa+ (1) where mCa+ →mass of Ca +and δmCa+ →full width at half max- imum in mass spectrum. The mass spectrum of ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ of isobars is obtained by time of ∗Corresponding author tel. no: +919483113600 Email address: dyavappabm@gmail.com (B M Dyavappa ) flight mass spectrometry simulations. The isobars are identified from identifying the values of time of flight in mass spectrum and calculating the mass from [4, 5] m = 2qV [ t f d ]2 , (2) where m → mass of ion, q → charge state of ion, t f → time of flight of ion, d → distance travelled by the ion before reach- ing the detector. This is compared with the estimated values of masses of the isobars and the corresponding isobar is iden- tified from approximately equating to the estimated value of its mass. The mass determination of 4119 K + isotope in Penning trap mass spectrometry is achieved by the excitation of axial motions of same charge state of 3919 K +and 4119 K +ions by driv- ing Radio Frequency (RF) field at the pure cyclotron frequen- cies fc (3919 K + ) , fc(4119 K+ ) of 3919 K +and 4119 K + ions respectively as the 180 Dyavappa / J. Nig. Soc. Phys. Sci. 2 (2020) 180–185 181 magnetic field is known. The mass of most abundant isotope m(3919 K+ ) = 38.963707 amu is well known and hence the mass of less abundant isotope m(4119 K+ ) of 41 19 K + can be determined from the following equation [6]: m(4119 K+ ) = fc (3919 K + ) fc(4119 K+ ) m(3919 K+ ). (3) 2. Theory The isotope-ratio mass spectrum of Ca isotopes is drawn by using data from the Mass Spectrometry Data Base. The accu- racy of mass measurements in penning trap is determined by the resolving power of masses of isotopes. The resolving power of masses of isotopes of ions is defined as the ratio of the centre frequency of the resonance line to the full width at half maxi- mum of the resonance line. Therefore the mass resolving power (M.R.P.) of masses of isotopes of ions is given by [1, 2, 3] (M.R.P.)ion = m δm = f0 ∆ f1/2 , (4) where m → mass of ion and δm → full width at half maximum in mass spectrum, f0 → centre frequency of the resonance line, ∆ f1/2 → full width at half maximum of the resonance line. The mass spectrum of ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ of isobars is obtained by time of flight mass spectrometry simula- tions. In time of flight mass spectrometry ions are accelerated by an electric field of known strength E with potential V and all those ions which have the same charge state q, will have same kinetic energy with velocity v due to the acceleration. The spe- cific charge (q/m) of ions is given by [7] q m = 1 2 [ E2 B2V ] = 1 2 [ v2 V ] , (5) where q → charge state of ion, m → mass of ion, B → Mag- netic field, E → Electric field, V → electric potential, v → velocity of ion. The velocity of the ion accelerated by electric field depends upon its specific charge q/m the time taken by the particle to reach the detector is called time-of-flight t f and it can be measured. The specific charge of ions is determined through the measurement of time to reach the detector in time-of-flight mass spectrometry. Heavier ions reach the detector slower than the lighter ones as the mass of moving ion is m ∝ t2f . The time is measured from the instant the ion leaves the cooler ion trap to the instant that reaches the detector, it is used to find specific charge of it and the ion is determined from the known parame- ters. The time-of-flight is given by [4] t f = d √ 2V √ m q ⇒ m q = 2V [ t f d ]2 ⇒ q m = 1 2V [ d t f ]2 . (6) ∴ m = 2qV [ t f d ]2 , (7) where d → distance traveled by the ion, V → electric potential,m is mass and q is charge state of ion. When the ions are excited by continuously sweeping the RF field, the motional frequen- cies of ions respond to the external RF at a given step, conse- quently some of the ions gain enough energy to escape the trap. This change in the motion of ions due to RF field drive causes increase in kinetic energy in the radial plane and can be detected by a time-of-flight technique. The mass resolution of isotopes of ions is related to specific charge and cyclotron angular fre- quency as [6] m δm ∝ q m B ( tRF √ N ) = ωc ( tRF √ N ) = 2π fc ( tRF √ N ) ⇒ fc∝ 1 m , (8) where q→ charge state of ion, m→ mass of ion, B→ Mag- netic field, tRF→ time of RF drive, N→ number of cycles of RF field, ωc→ cyclotron angular frequency. The resolving power of masses of isotopes of ions is proportional to the time of ex- citation of RF field, which results in the motional resonances of the isotopes of ions that can be observed in motional resonances spectrum. The lifetime of unstable isotopes limit the time of ex- citation as they are in very short duration of time. The temporal stability of the magnetic field due to shielding current in pair of coils of wire limit the radial confinement of the stable and long-lived isotopes. The exchange of the ions of isotopes in the trap is required for comparison of cyclotron frequencies of two different ions and measured at different times during which the magnetic field strength changes. Superconducting magnets re- quire temperature and pressure stabilization to reduce temporal variation of the magnetic field strength. The mass determina- tion in isotopes separator on-line trap is on the basis of the fact that the two ions of isotopes whose charge state is same but their masses are different. The ratio of their cyclotron frequencies is equal to the inverse of ratio of their masses kept in the same magnetic field [6]. Therefore if the charge state of two ions of isotopes is q1=q2 kept in the same magnetic field B then fc1 fc2 = m2 m1 , (9) where fc1 and fc2 are cyclotron frequencies of isotopes of ions of an element with masses m1 and m2 respectively. 3. Experimental Procedure 3.1. Design The isotopes separator on-line trap consists of three ion traps connected end to end together in an order of RF Paul trap, Cooler Penning trap and Precision Penning trap as shown in Figure 1 [8, 9]. The RF quadrupole ion trap consists of 4 rods structure to which a RF field is applied for alternate rods, and 181 Dyavappa / J. Nig. Soc. Phys. Sci. 2 (2020) 180–185 182 this is used for beam preparation and hence it is also called beam buncher. The Cooler Penning trap is a large cylindrical Penning trap which is placed in the homogeneous magnetic field of superconducting magnets, which is used to cool the ions. The Precision Penning trap is a Quadrupole Penning trap in which ions are detected through time of flight. Figure 1. Schematic diagram of Isotopes separator on-line trap [8, 9] 3.2. Working A quadrupole Penning trap is designed with three-electrode infinite hyperboloid revolution of structure, which consists of two end-cap electrodes and a ring electrode, a homogeneous magnetic field is superposed on electrostatic quadrupole field. The magnetic field B confines ion beam of isotopes of charge state q and different masses in the radial direction, while the electric field quadrupole potential VDC , confines ions in the ax- ial direction, as it prevents the ions from escaping along the magnetic field lines. The motion of trapped ions in a Penning trap is not a simply pure cyclotron motion with frequency fc but a combination of three harmonic Eigen motions, viz. an ax- ial oscillatory motion with frequency fz, two circular motions called modified cyclotron motion with frequency f ′ c and mag- netron motion with frequency fm which are related to each other as [1] fc = f ′ c + fm. (10) The precise value of pure cyclotron frequency in an isotope sep- arator on-line trap is [6] fc = ( q m ) B 2π ⇒ fc ∝ 1 m ( ∵B, q → constants ) (11) The motion of ions of isotopes can be driven by oscillating elec- tric field which changes the amplitudes of the oscillatory mo- tion of ions and azimuthal electric quadrupole field causes the excitation of ion oscillatory motion directly at the side band fre- quency fc. The mass determination of ion of unknown isotope in isotopes separator on-line trap mass spectrometry is achieved by the direct excitation of axial oscillatory motions of same charge state ions of isotopes at their pure cyclotron frequencies from the relation m2 = m1 fc1 fc2 as the magnetic field is known [6]. 3.3. Cooling and bunching in RF quadrupole ion trap A RF field is applied to the 4 rods structure which creates an oscillating quadrupole electric field that confines the ions of isotopes or isobars along the symmetry axis of trap. The rods are segmented and an appropriate shape DC potential is applied to the segments to drag the ions close to the end of the 4-rods structure where the ions are trapped. The first step is stopping and preparation of the high energy of ≈ 30 − 60keV ion beam of isotopes or isobars. The ions of isotopes or isobars are de- celerated electro statically by applying repelling potential and then injected into the central region of 4-rods structure being filled with buffer gas. The RF quadrupole ion trap cools the ion beam of isotopes through buffer gas cooling by collisions. The ions of high energy of ≈ 30 − 60keV lose kinetic energy up to a few keV due to the collision with the buffer gas, and then finally accumulated as a small ion cloud of isotopes or iso- bars in the trapping region. Thus cooled ions of isotopes or isobars are accumulated in beam buncher and enter into cooler Penning trap later, where contaminants are removed. The cold ion cloud bunch of selected isotopes or isobars of an element can be ejected out off the trapping region, transported and then injected into the cooler trap through a potential adaption in a pulsed drift tube. 3.4. The cooler trap The cooler trap is a large cylindrical Penning trap placed in the homogeneous magnetic field of ≈5T superconducting mag- nets. The ions transported from the RF quadrupole ion trap are captured in the cylindrical Penning trap and cooled through mass selection technique. The cooler cylindrical Penning trap is optimized for high quality mass selection to resolve isotopes or isobars. Isotopes are different species of the same element with same atomic number (same number of protons and elec- trons) but differ in mass number (the number of nucleons) and hence specific charge (charge to mass ratio) will be different for different isotopes with same charge state, therefore the isotopes travel with different velocities and take different time durations to reach the detector. When ions of isotopes which have same charge state but different masses are trapped in constant mag- netic field, then heavier ions of the same charge state reach at lower speeds as [6] fc = q m B ∝ 1 m ∝ v ∝ d t ( ∵B, q are constants ) (12) ∴ m ∝ t (∵d is constant) (13) Isobars are different elements with same mass numbers (same number of nucleons) but differ in atomic number (the number 182 Dyavappa / J. Nig. Soc. Phys. Sci. 2 (2020) 180–185 183 of protons and electrons) and hence specific charge (charge to mass ratio) will be different for different isobars, therefore the isobars travel with different velocities and take different time durations to reach the detector. For ions of isobars which have same mass but different charge state in constant magnetic field, the velocity of ions with higher charge state will also increase [6]. fc = q m B ∝ q ∝ v ∝ d t (∵B, m are constants)(14) ∴ q ∝ 1 t (∵d is constant) (15) The cooled and clean bunches of ions are transferred into the precision Penning trap, which are used for highly accurate mass measurements. 3.5. Precision Penning trap mass spectrometer An azimuthal RF field of frequency fRF drives the motion of ions, the amplitude of the cyclotron motion of the stored ions increases due to resonance of driving frequency of RF field with cyclotron frequency ( f RF = fc) in Quadrupole Penning trap. The RF generator switched to sweep mode is used to feed RF energy into the trap through the antenna. The RF power is kept very low of the order of a few mV to weakly probe the motion of the trapped ion cloud. If the RF power is kept high, then it will resonantly drives the trapped ion cloud in the trap and causes to escape from the trap. When the ions are excited by continuously sweeping the RF field, the motional frequencies of ions respond to the external RF at a particular step, consequently some of the ions gain enough energy to escape from the trap, then the signal height is reduced and appears as a dip in the motional resonance spectrum, which is directly proportional to the number of ions lost from the trap. The cooled ions are ejected from the trap due to the excitation of the motion of ions by RF field, and drift through the inhomogeneous fringe magnetic field B to reach the detector of ions. The magnetic moments of the orbits of ions also increase due to magnetic field. An axial force arising from the inhomogeneous magnetic field increases the axial momenta of the ions by orbital magnetic moments. The time-of-flight of ions is determined as a function of the frequency of the RF field, as ions in resonance with the RF field reach the detector faster than those ions that are not in resonance. The mass can be extracted in conjunction with a reference mass measurement after the determination of the frequency of stored ion from the time-of-flight detection technique . 4. Results and Discussion 4.1. Mass spectrum of Calcium isotopes The isotope ratio mass spectrum of Calcium isotopes shows 3 peaks as shown in Figure 2. The tallest peak corresponds to Table 1. Mass resolving powers of calcium isotopes Ions of Calcium isotopes Mass Resolving Power 40 20Ca + 794.0675 42 20Ca + 789.60086 44 20Ca + 900.089 40Ca+ as specific charge of it is lesser than that of both of 42Ca+ and 44Ca+, the second short peak next to it corresponds to 42Ca+ as its specific charge is greater than that of 40Ca+ and the third short peak next to it corresponds to 44Ca+ as its specific charge is greater than that of 42Ca+. The mass resolving powers of 40Ca+, 42Ca+, 44Ca+ are [10] (M.R.P.)40 20Ca + = mCa+ δmCa+ = 39.961765 39.981125 − 39.9307996 = 794.06751 ≈ 794.0675 (16) (M.R.P.)42 20Ca + = mCa+ δmCa+ = 41.9586 41.9802842 − 41.9271452 = 41.9586 0.053139 ≈ 789.60086 (17) (M.R.P.)44 20Ca + = mCa+ δmCa+ = 43.9555 43.9763821 − 43.9275475 = 43.9555 0.0488346 ≈ 900.089 (18) Therefore the mass resolving powers of 40Ca+, 42Ca+, 44Ca+ as calculated from equation (1) are 794.0675, 789.60086 and 900.089 respectively as presented in Table 1. Figure 2. Isotope ratio mass spectrum of ions of 40Ca+, 42Ca+, 44Ca+ isotopes drawn by using isotope-ratio Mass Spectrometry Data Base 4.2. Mass spectrum of CO, N2 and C2H4 isobars The ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ of isobars can be produced by collisions of isobars with electrons. The 183 Dyavappa / J. Nig. Soc. Phys. Sci. 2 (2020) 180–185 184 Table 2. Masses of Isobars calculated from Mass spectrum of ions Ions of Isobars Mass (amu)[ 28 (CO) ]+ 27.99489[( 28 N2 )]+ 28.00699[ 28 (C2 H4) ]+ 28.031297 mass spectrum of ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ isobars obtained by time of flight mass spectrometry simula- tions is shown in Figure 3. The mass spectrum consists of three peaks, one corresponds to each of ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ of isobars [11]. The isobars are identified from identifying the values of time of flight of isobar in mass spec- trum and the mass of corresponding isobar is calculated from the value of time of flight. This accurate value of mass is com- pared with the estimated values of masses of the isobars and the corresponding isobar is identified from approximately equat- ing it to the estimated value of its mass. The masses of ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ of isobars are calculated from time of flight using equation (19) as shown below. From Figure 3 the time of flight that corresponds to first peak is t f = 762.27882 ns, then m = 2qV [ t f d ]2 (19) m = 2 × 1.6 × 10−19 × 25 [ 762.27882 × 10−9 10 × 10−3 ]2 (20) ⇒m = 46.48552 × 10−31kg = 27.99489 amu = mCO (21) From Figure 3 the time of flight that corresponds to second peak is t f = 762.43137ns, then m = 2 × 1.6 × 10−19 × 25 [ 762.43137 × 10−9 10 × 10−3 ]2 (22) ⇒m = 46.504128×10−31 kg = 28.00699 amu = mN2 (23) From Figure 3 the time of flight that corresponds to third peak is t f = 762.77432 ns, then m = 2 × 1.6 × 10−19 × 25 [ 762.77432 × 10−9 10 × 10−3 ]2 (24) ⇒m = 46.54597×10−31kg = 28.031297 amu = mC2 H4 (25) The ions of isobars [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ are identified from mass spectrum as shown in Figure 3. The mass of the isobar that corresponds to the first, second and third peaks were calculated using equation (19) as 27.99489 amu, 28.00699 amu and 28.031297 amu with corresponding time of flight of 762.27882 ns, 762.43137 ns and 762.77432 ns respectively as presented in Table 2. Figure 3. Mass spectrum of ions [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ of isobars drawn by using Mass Spectrometry Data Base 4.3. Mass spectrum of K isotopes The mass determination of 4119 K + isotope in Penning trap mass spectrometry is achieved by the excitation of axial mo- tions of same charge state of 3919 K +and 4119 K +ions by driving RF field at the pure cyclotron frequencies fc (3919 K + ) and fc(4119 K+ ) respec- tively as the magnetic field is known. As the mass of most abun- dant isotope m(3919 K+ ) = 38.963707amu is well known, and hence the mass of less abundant isotope m(4119 K+ ) can be determined. The pure cyclotron frequencies of fc (3919 K + ) and fc(4119 K+ ) from Fig- ure 4 are 98.426156 kHz and 93.624975 kHz respectively. The mass of ion 4119 K + of potassium isotope is given by [6] fc (3919 K + ) fc(4119 K+ ) = m(4119 K+ ) m(3919 K+ ) (26) ⇒ m(4119 K+ ) = fc (3919 K + ) fc(4119 K+ ) m(3919 K+ ) = 98.426156 × 103 93.624975 × 103 ×38.963707 × 1.66 × 10−27 (27) ∴ m(4119 K+ ) = 67.996595 × 10 −27kg = 40.9618amu (28) The mass of 4119 K + calculated using equation (27) is 40.9618amu as presented in Table 3. 5. Conclusion The mass resolving powers of 40Ca+, 42Ca+, 44Ca+ are 794.0675, 789.60086 and 900.089 respectively. The ions of isobars [28(CO)]+, [(28N2)]+ and [28(C2H4)]+ are identified in mass spectrum which correspond to time of flights of 762.27882 ns , 762.43137 ns and 762.77432 ns respectively. The pure cyclotron frequencies 184 Dyavappa / J. Nig. Soc. Phys. Sci. 2 (2020) 180–185 185 Table 3. Masses of potassium isotopes calculated from Mass spectrum of potassium ions Ions of Potassium isotopes Interchange Cyclotron frequency values Mass (amu) 39 19 K + 98.426156 kHz 38.963707 41 19 K + 93.624975 kHz 40.9618 Figure 4. Time of flight detection of cyclotron resonance of isotopes of potas- sium ions 3919 K +and 4119 K + at magnetic field 0.25T by RF excitation from 90-105 kHz drawn by using Mass Spectrometry Data Base of ions 3919 K + and 4119 K +from motional resonance spectrum are 98.426156 kHz and 93.624975 kHz respectively and hence the mass of ion of less abundant potassium isotope 4119 K + is deter- mined to be 40.9618 amu. Acknowledgments We thank the referees for the positive enlightening com- ments and suggestions, which have greatly helped us in making improvements to this paper. References [1] K. Blaum, Yu. N. Novikov & G. Werth, “Penning traps as a versatile tool for precise experiments in fundamental physics”, Contemporary Physics, 51 (2010) 149. [2] A. Pelander, P. Decker, C. Baessmann & I. Ojanperä, “Evaluation of a High Resolving Power Time-of-Flight Mass Spectrometer for Drug Anal- ysis in Terms of Resolving Power and Acquisition Rate”, Journal of The American Society for Mass Spectrometry, 22 (2011) 379-385. [3] W. A. M. Wilfried & R. A. C. Correa, Interpretation of MS-MS mass spec- tra of drugs and pesticides, Wiley series on mass spectrometry, Wiley. [4] Time-of-flight mass spectrometry, Wikipedia, https://en.wikipedia.org/wiki/Time-of-flight_mass_spectrometry [5] Mass Analyzer time of flight, https://phys.libretexts.org [6] F. Wenander, “Charge breeding of radioactive ions with EBIS and EBIT”, JINST 5 (2010) C10004. [7] S. K. Singh, Electricity and mag- netism, http://cnx.org/content/col10909/1.13/, http://creativecommons.org/licenses/by/3.0/, 122 (2009) [8] F. Herfurth, J. Dilling, A. Kellerbauer, G. Bollen, S. Henry, H. J. Kluge, E. Lamour, D. Lunney, R. B. Moore, C. Scheidenberger, S. Schwarz, G. Sikler & J. Szerypo, “A linear radiofrequency ion trap for accumu- lation, bunching, and emittance improvement of radioactive ion beams”, arXiv:nucl-ex/0011021 (2000) [9] M. Mukherjee, D. Beck, K. Blaum, G. Bollen, J. Dilling, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, H. J. Kluge, S. Schwarz, L. Schweikhard & C. Yazidjian, “ISOLTRAP: An on-line Penning trap for mass spectrometry on short-lived nuclides”, Eur. Phys. J. A 35 (2008) 31. [10] S. F. Boulyga, “Calcium isotope analysis by mass spectrometry”, Mass Spectrometry Reviews, 29 (2010) 685. [11] Y. Ishida, M. Wada, Y. Matsuo, I. Tanihata, A. Casares, & H. Wollnik, “A time-of-flight mass spectrometer to resolve isobars”, Nucl. Instr. and Meth. in Phys. Res. B 219-220 (2004) 468. [12] A. Finlay, Integration of a Multi Reflection Time of Flight Isobar Separa- tor into the TITAN Experiment at TRIUMF, M.Sc. thesis, The University of British Columbia (2017). 185