Isotope Geochemistry: Geochronology III - Mass Spectrometry & Isotope Ratios, Study notes of Geochemistry

Download Isotope Geochemistry: Geochronology III - Mass Spectrometry & Isotope Ratios and more Study notes Geochemistry in PDF only on Docsity! Isotope Geochemistry Chapter 4: Geochronology III 107 February 21, 2011 rupole mass spectrometers were employed for these instruments, largely because they are cheaper to manufacture and do not require as high a vacuum as a magnetic sector mass spectrometer. However, quadrupoles cannot achieve the same level of accuracy as magnetic sector instruments, and the initial generation of ICP-MS instruments was not used for the high precision isotope ratio measurements needed in geochronology and isotope geochemistry. These quadrupole ICP-MS instruments are used primarily for elemental analysis, with only some limited used for isotope ratio determination. Mag- netic sector ICP-MS instruments came on the market a decade after quadrupole ICP-MS instruments and now achieve accuracies competitive with thermal ionization instruments. Combined with their generally higher ionization efficiency and hence higher sensitivity, they produce results that are supe- rior to thermal instruments for several elements. As they continue to develop they may entirely replace thermal ionization instruments. After the ions are produced, they are accelerated by an electrostatic potential, typically in the range of 5-20 kV for magnetic sector mass spectrometers (in thermal ionization mass spectrometers, the filament with the sample are at this potential). The ions move through a series of slits between charged plates. The charge on the plates also serves to collimate the ions into a beam. Generally the potential on the plates can be varied somewhat; in varying the potential on the plates, one attempts to maximize the beam intensity by 'steering' as many ions as possible through the slits. Thus the source produces a nar- row beam of nearly monenergetic ions. The Mass Analyzer The function of the mass analyzer is two-fold. The main purpose is to separated the ions according to their mass (strictly speaking, according the their mass/charge ratio). But as is apparent in Figure 10.9, the mass analyzer of a sector mass spectrometer also acts as a lens, focusing the ion beam on the detec- tor. A charged particle moving in a magnetic experiences a force F = qv × B 4.46 where B is the magnetic field strength, v is the particle velocity, and q is its charge (bold is used to de- note vector quantities). Note that force is applied perpendicular to the direction of motion (hence it is more properly termed a torque), and it is also perpendicular to the magnetic field vector. Since the force is always directed perpendicular to the direction of motion, the particle begins to move in a circu- lar path. The motion is thus much like swinging a ball at the end of a string, and we can use equation for a centripetal force: F = m v 2 r 4.47 This can be equated with the magnetic force: m v 2 r = qv × B 4.48 The velocity of the particle can be determined from its energy, which is the accelerating potential, V, times the charge: Vq = 1 2 mv2 4.49 Solving 4.49 for v2, and substituting in equation 4.48 yields (in non-vector form): 2V r = 2Vq m B 4.50 Docsity.com Isotope Geochemistry Chapter 4: Geochronology III 108 February 21, 2011 Solving 4.50 for the mass/charge ratio: m q = B2r2 2V 4.51 relates the mass/charge ratio, the accelerating potential, the magnetic field, and the radius of curvature of the instrument. If B is in gauss, r in cm, and V in volts, this equation becomes: m q = 4.825 ×10−5 B 2r2 V 4.51a with m in unified atomic mass units and q in units of electronic charge. For a given set of conditions, a heavier particle will move along a curve having a longer radius than a lighter one. In other words, the lighter isotopes experience greater deflections in the mass analyzer. A typical radius is 27 cm and typically operating potential is 8 to 10 kV. Masses are selected for analysis by varying the magnetic field (note that in principle we could also vary the accelerating poten- tial; however doing so has a second order effect on beam intensity, which is undesirable), generally in the range of a few thousand gauss. It was shown in the 1950's that if the ions entered the magnetic field at an angle of 26.5° rather than at 90°, the effective radius of the mass analyzer doubles. This design trick, employed in all modern mass spectrometers, results in higher resolution (better separation between the masses at the collector). The Cornell instrument, for example, has an effective radius of 54 cm. An additional advantage of this ‘ex- tended geometry’ is that the ion beam is focused in the ‘z’ direction (up-down) in addition to the x-y di- rection. This is an important effect because it allows the entire ion beam to enter the detector, which in turn allows the use of multiple detectors. In addition, modern mass spectrometers have further modifica- tions to the magnet pole faces to produce a linear focal plane, which is helpful in the multiple collectors currently in use. Collisions of ions with ambient gas result in velocity and energy changes and cause the beam to broaden. To minimize this, the mass spectrometer is evacuated to 10-6 to 10-9 torr (=1mm Hg ≈ 10-3 atm). Where very high resolution is required, an energy filter is employed. This is simply an electrostatic field. The electric field force is not propor- tional to velocity, as it the magnetic field. Instead, ions are deflected according to their energy. The radius of curvature is given by: R = 2V V2 4.52 where V2 is the electrostatic potential of the energy filter and V is the energy of the ions (equal to the accelerating potential). Ion Figure 4.19. A double focusing or Nier-Johnson mass spectrometer with both magnetic and electrostatic sec- tors. After Majer (1977). Docsity.com Isotope Geochemistry Chapter 4: Geochronology III Spring 2011 111 February 21, 2011 the 14C position. If the 14C/12C ratio is 10-14, some 107 more 12C would be detected at the 14C position than 14C atoms! The techniques involved in accelerator mass spectrometry vary with the element of interest, but most applications share some common features that we will briefly consider. Figure 4.23 is an illustration of the University of Rochester accelerator mass spectrometer. We will consider its application in 14C analy- sis as an example. A beam of C– is produced by sputtering a graphite target with Cs+ ions. There are several advantages in producing, in the initial stage, negative ions, the most important of which in this case is the instability of the negative ion of the principal atomic isobar, 14N. The ions are accelerated to 20keV (an energy somewhat higher than most conventional mass spectrometers) and separated with the first magnet, so that only ions with m/q of 14 enter the accelerator. The faraday cup FC 1 (before ac- celerator) is used to monitor the intensity of the 12C beam. In the accelerator, the ions are accelerated to about 8 MeV, and electrons removed (through high-energy collisions with Ar gas) to produce C4+ ions. The reason for producing multiply-charged ions is that there are no known stable molecular ions with charge greater than +2. Thus the production of multiply charged ions effectively separates 14C ions from molecular isobaric ions such as 12CH2. The now positively charged ions are separated from resid- ual ions through two more magnetic sectors, and an electrostatic one (which selects for ion energy E/q). The final detector distinguishes 14C from residual 14N, 12C, and 14C by the rate at which they lose energy through interaction with a gas (range, effectively). Analytical Strategies Isotopic variations in nature are very often quite small. For example, variations in Nd (neodymium) isotope ratios are measured in parts in 10,000. There are exceptions, of course. He and Os isotope ra- tios, as well as Ar isotope ratios, can vary by orders of magnitude, as can Pb in exceptional cir- Figure 4.23. The accelerator mass spectrometer at the University of Rochester. F.C. 1, 2, & 3 are faraday cups, T of F detectors are time of flight detectors. After Litherland (1980). Docsity.com Isotope Geochemistry Chapter 4: Geochronology III Spring 2011 112 February 21, 2011 cumstances (minerals rich in uranium). These small variations necessitate great efforts in precise measurements. In this section we will briefly discuss some of the methods employed in isotope geo- chemistry to reduce analytical error. We will exclude, for the moment, the problem of contamination. We will also exclude, for the most part, a discussion of instrument and electronics design, though these are obviously important. One technique used universally to reduce analytical errors is to make a large number of measurements. Thus a value for the 3He/4He ratio reported in a paper will actually be the mean of perhaps 100 indi- vidual ratios measured during a 'run' or analysis. Any short-term drift or noise in the instrument and its electronics, as well as in the ion beam intensity, will tend to average out. The use of multiple collec- tors and simultaneous measurement of several isotopes essentially eliminates errors resulting from fluc- tuations in ion beam intensity. This, however, introduces other errors related to the relative gains of the amplifiers. A final way to minimize errors is to measure a large signal. It can be shown that the uncer- tainty in measuring x number of counts is x . Thus the uncertainty in measuring 100 atoms is 10%, but the uncertainty in measuring 1,000,000 atoms is only 0.1%. These 'counting statistics' are the ultimate limit in analytical precision, but they come into play only for very small sample sizes. In mass spectrometry of gaseous elements such as H, O, N, S, and C (the latter does not, of course, always occur as a gas; however, it is always converted to CO2 for analysis), the instruments are de- signed to switch quickly between samples and standards. In other words, a number of ratios of a sam- ple will be measured, then the inlet valve will be switched to allow a standard gas into the machine and a number of ratios of the standard will be measured. This process can be repeated several times during an analysis. The measurement of standards thus calibrates the instrument and any drift in instrument response can be corrected. However, this is not practical for solid source instruments because switch- ing between sample and standard cannot be done quickly. It is also impractical for noble gas analysis because of the small quantities involved, and the difficulty of completely purging a standard gas from the instrument. Mass Fractionation One of the most important sources of error in solid source mass spectrometry results from the ten- dency of the lighter isotopes of an element to evaporate more readily than the heavier isotopes (we will discuss the reasons for this later in the course when we deal with stable isotope fractionations). This means that the ion beam will be richer in light isotopes than the sample remaining on the filament. As the analysis proceeds, the solid will become increasingly depleted in light isotopes and the ratio of a light isotope to a heavy one will continually decrease. This effect can produce variations up to a per- cent or so per mass unit (though it is generally much less). This would be fatal for Nd, for example, where natural isotopic variations are much less than a percent, if there were no way to correct for this effect. Fortunately, a correction can be made. The trick is to measure the ratio of two isotopes that are not radiogenic; that is a ratio that should not vary in nature. For Sr, for example, we measure the ratio of 86Sr/88Sr. By convention, we assume that the value of this ratio is equal to 0.11940. Any deviation from the value is assumed to result from mass fractionation in the mass spectrometer. The simplest as- sumption about mass fractionation is that it is linearly dependent on the difference in mass of the iso- topes we are measuring. In other words, the fractionation between 87Sr and 86Sr should be half that be- tween 88Sr and 86Sr. So if we know how much the 86Sr/88Sr has fractionated from the 'true' ratio, we can calculate the amount of fractionation between 87Sr and 86Sr. Formally, we can write the linear mass frac- tionation law as: α(u,v) = Ruv N Ruv M −1       Δmuv 4.53 Docsity.com Isotope Geochemistry Chapter 4: Geochronology III Spring 2011 113 February 21, 2011 where α is the fractionation factor between two isotopes u and v, ∆m is the mass difference between u and v (e.g., 2 for 86 and 88), RN is the 'true' or 'normal' isotope ratio (e.g., 0.11940 for 86/88), and RM is the measured ratio. The correction to the ratio of two other isotopes (e.g., 87Sr/86Sr) is then calculated as: € Rij C = Rij M (1+α(i, j)Δmij ) 4.54 where RC is the corrected ratio and RM is the measured ratio of i to j and € α(i, j) = α(u,v) 1−α(u,v)ΔMvj 4.55 If we choose isotopes v and j to be the same (e.g., to both be 86Sr), then ∆mvj = 0 and α(i,j) = α(u,v). A convention that is unfortunate in terms of the above equations, however, is that we speak of the 86/88 ratio, when we should speak of the 88/86 ratio (= 8.37521). Using the 88/86 ratio, the 'normalization' equation for Sr becomes: € 87Sr 86Sr       c = 87Sr 86Sr       M 1+ 8.37521 88Sr /86 Sr( )M −1           2         4.56 A more accurate description of mass fractionation is the power law. The fractionation factor is: α = Ruv N Ruv M       1/Δmuv −1 4.57 The corrected ratio is computed as: Ri, j C = Ri, j M 1+α[ ]Δmi , j 4.58 or: € Ri, j C = Ri, j M 1+αΔmi, j + 1 2 Δmi, j (Δmi, j −1)α 2 +…       4.59 Since α is a small number, higher order terms may be dropped. Finally, it is claimed that the power law correction is not accurate and that the actual fractionation is described by an exponential law, from which the fractionation factor may be computed as: and the correction is: € α = ln Ruv N /Ruv M[ ] m j ln(mu /mv ) 4.60 € Ri, j C = Ri, j M mi m j         αm j = Ri, j M 1+αΔmi, j −α mi, j 2 2m j +α 2 mi, j 2 2 +…       4.61 The exponential law appears to provide the most accurate correction for mass fractionation. However, all of the above laws are empirical rather than theoretical. The processes of evaporation and ionization are complex, and there is yet no definitive theoretical treatment of mass fractionation during this proc- ess. Simultaneous Correction of Mass Fractionation and Gain Bias in Multiple Collection We can now return to the question of correcting for the differing gains of amplifiers when more than one collector is used. I mentioned we could calibrate the gains electronically, or that we could measure one isotope in each cup and use this intensity as a calibration. A simplistic approach to the latter method would put us at the mercy of fluctuations in the ion beam intensity, whereas eliminating fluc- tuations in ion beam intensity is one principal advantage of multiple collection (the other advantage is Docsity.com