# Introduction to Radioisotope Geochronology/Part 5 - Rocks to Ratios: Analytical Approaches
## Extracting Quantitative Isotope data From Minerals and Rocks

In this section we go through the steps that are needed to derive an accurate P/D ratio from a mineral of interest which can feed into the age equation, and combined with information about the rate of decay can be translated into a mineral date. Determining a P/D involves mass spectrometric analyses however even when a P/D ratio can be measured it will be not represent the P/D ratio of the sample analysed as this ratio will have fractionated during mass spectrometry (see below) and any chemical processes used to separate the elements of interest prior to mass spectrometry.

## 1. Principles of Isotope Dilution methodologies

Isotope dilution (ID) is the basic method for determining the ratio of two isotopes from two different elements (e.g., 238U/206Pb).

### Example: U-Pb ID-TIMS

ID-TIMS analyses of zircon (either as multi-grain fractions, single grains or grain fragments) involves dissolution of the zircon in the presence of tracer isotopes and is called isotope dilution. For U-Pb ID-TIMS analyses the most common tracers are 205Pb and 235U. 205Pb is an artificial isotope that does not occur in nature whereas 235U occurs naturally but an enriched form is used as a tracer. Natural U in the zircon assumed to have a 238U/235U = 137.88 (Steiger and Jager, 1977) therefore the tracer can be used to determine the number of moles of 238U and 235U in a sample. Since the tracer is added before dissolution, the tracer/sample isotope ratios stay constant despite incomplete recovery during chemistry and low ionization efficiency during analysis. Following dissolution the sample undergoes chemical purification using anion exchange chemistry that allows separation of the Zr and REEs from the Pb and U, and Pb and U from one another.
Following purification Pb and U are analysed separately by thermal ionisation mass spectrometry where the ratios of sample isotopes (204Pb, 206Pb, 238U, etc) to the tracer isotopes (205Pb, 235U) can be measured. As the amount of tracer isotope added to the same is known the number of atoms of each naturally occurring isotope in the sample determined based upon the measured ratio of sample isotope/tracer isotope ratio. . After corrections for mass fractionation, the minor contribution of common Pb and U from the reagents, the tracer and labware, the sample 206Pb/207Pb, 206Pb/238U and 207Pb/235U ratios can be determined and 206Pb/207Pb, 206Pb/238U and 207Pb/235U dates calculated. See section 5.2.3 for further discussion of the isotope dilution technique. Optimisation of this technique means that it is now possible to date zircons with <10 pg radiogenic Pb and obtain precision <0.1% on the U/Pb ratio for single grain analyses. It is a very labour intensive technique, each single U/Pb analyses takes several hours of mass-spectrometry and chemical purification in an ultra-clean lab environment, making it time consuming to develop high-n datasets.

### Example: Isochron methods

Isochron techniques involve analysis of multiple samples assumed to be the same age, have a spread in parent/daughter ratio, and have remained closed systems. In order to maximize the likelyhood that the samples are the same age and have the same initial isotopic composition it is preferable to design an appropriate sampling strategy. For example, Re-Os geochronology is often attempted on laminated organic rich shales so it is essential to have multiple samples from the same restricted stratigraphic interval (e.g., (Kendall et al., 2004), to avoid samples that span an amount of time much larger than uncertainties. In some cases, such as working with core samples, this is not always possible (Kendall et al., 2006; Schaefer and Burgess, 2003). This could be a complicating factor if there is temporal variation in the initial isotopic composition of the daughter element, and/or represents a significant amount of time, especially in condensed sections. In U-Pb in carbonates, different cement domains can have very different U-Pb ratios but is difficult to know a priori whether the cements are all exactly the same age and have the same initial ratios. In both of these cases, deviations from the assumption of the same age and initial ratio lead to increased scatter and uncertainties in calculated dates.
Sample dissolution and purification techniques are similar to the procedures for U-Pb ID-TIMS. Prior to isotope ratio mass spectrometry samples undergo dissolution and chemical purification. For multi-element systems (such as Re-Os, U-Pb and Lu-Hf) isotopic tracers are added prior to dissolution for the isotope dilution (see above) whereas for systems where only daughter isotopes are measured (i.e., Pb-Pb), direct measurements of the isotope ratios are made. The isotopic composition is determined via thermal ionization mass-spectrometry although it is also possible to use solution mode ICPMS for most elements.
The accuracy and precision of isochron techniques is largely controlled by a spread in initial parent/daughter ratio, closed system behaviour, and an identical initial isotopic composition for all samples. For precipitates such as carbonates and phosphates there is often no significant detrital input however this is not the case for organic-rich shales targeted for Re-Os where there is potential that significant concentrations of initial Os from multiple sources. This has been demonstrated in several studies (Creaser et al., 2002; Kendall et al., 2004) however it is possible to limit the detrital Os contribution by selective dissolution of the organic component using a CrO3-H2SO4 dissolution approach. Kendall et al (Kendall et al., 2004) compared two dissolution methods (aqua regia vs. CrO3-H2SO4 dissolution) on greenschist facies organic rich shale from the Old Fort Point Formation in Western Canada. Both dissolution techniques were used on the same powders, however the aqua regia method yielded scattered data and a resulting “isochron” regression with an MSWD of 65 and a large “age” uncertainty (9%) in comparison to the CrO3-H2SO4 dissolution method which yielded an isochron with much less scatter (MSWD = 1.2) and a relatively low uncertainty (0.8% 2 sigma) (Kendall et al., 2004).

## 2. Principles of Sample Relative to a Reference Material methodologies

An alternative approach to determine the P/D ratio of a given decay system is to measure the P/D ratio directly by mass spectrometry

### Example: U-Pb Microbeam techniques

U-Pb geochronology by microbeam techniques has revolutionized geochronology over the past two decades. The two major techniques are Secondary Ion Mass Spectrometry (SIMS), typified by the SHRIMP (Sensitive High Resolution Ion Microprobe), and Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). Both of these techniques (collectively termed ‘microbeam’ techniques) offer high-spatial resolution analyses using either a focused ion beam to sputter a volume of zircon (SIMS) or a laser that is used to vaporise a volume of zircon (LA-ICP-MS). Microbeam techniques allow in-situ analysis of very small volumes and thus high-spatial resolution; a typical volume of zircon analyzed by an ion-probe is cylindrical, 20-30 microns in diameter and several microns deep, with somewhat larger volumes for LA-ICPMS (Kosler and Sylvester, 2003). In addition the analyses can be done relatively rapidly (many 10’s analyses per day for LA-ICPMS and SIMS). Furthermore, these techniques allow analysis of remaining mineral for other isotopes/elements of interest (Hf, O, REE’s) and can be made on the same zircon grains in close proximity to the volume analyzed for geochronology.
Fundamental to the microbeam U-Pb zircon methods is use of a primary standard against which the U/Pb ratio of the unknown zircon is calibrated. For SIMS techniques this calibration involves the analyses of standard zircon to develop a calibration curve for a known U/Pb ratio (which is determined via ID-TIMS analyses) and against which analyses of unknown zircons can be compared. This is achieved through analytical sessions where a standard zircon is repeatedly analysed interspersed with analyses of unknown zircons (this is termed sample-standard bracketing). During the course of a single analytical session, the measured ratio/date of a standard can drift by several percent. For LA-ICPMS the approach is somewhat similar in that sample-standard bracketing is employed in order to determine the inter-elemental fractionation which is then applied to the unknown zircons. In both SIMS and LA-ICPMS techniques the 207Pb/206Pb ratio is a direct measurement, for SIMS mass-dependent fractionation appears to be minimal and the measured ratio is commonly used whereas in LA-ICPMS analyses mass dependent fractionation is quantifiable and is corrected for either using sample-standard bracketing and/or using a solution with known 205Tl/203Tl ratio to correct for mass bias on Pb isotopic ratios. For further details of microbeam techniques see Ireland and Williams (Ireland and Williams, 2003) for a review of SIMS U-Pb geochronology and Kosler and Sylvester (Kosler and Sylvester, 2003) for a review of LA-ICPMS geochronology
The benefit of the high spatial resolution provided by microbeam techniques is a tradeoff in that the precision of individual spot analyses using LA-ICPMS and SIMS is lower than ID-TIMS by approximately an order of magnitude (Ireland and Williams, 2003; Kosler and Sylvester, 2003). In-situ techniques are without question essential tools for characterizing complex (zoned) zircons from volcanic and metamorphic rocks and for characterizing detrital populations which in some cases can provide robust estimates of the minimum age of a sequence.

## 3. Principles of Mass Spectrometry

In general, a mass spectrometer consists of three components: ion source, magnet, and detector. Ionisation of the analyte is accomplished through a variety of ways and in geochronology, the primary ionisation techniques are thermal ionisation, secondary ion, and inductively-coupled plasma ionisation. Ionisation is accomplished by stripping atoms of electrons resulting in positively charged particles. There are three general methods for ionization in mass spectrometry: thermal, plasma, and secondary ion.

### 2.1 Ionization

Thermal ionization mass spectrometry (TIMS) is a highly sensitive isotope ratio mass spectrometry characterization technique that exploits the thermal ionization effect, in which a chemically purified sample is heated to cause ionization of the atoms of the sample. The ions are accelerated using a large voltage and focused into a beam (More details), then separated into individual beams based on the mass/charge ratio of the ions, and those different ion beams are detected using discrete detectors...
Plasma ionisation mass spectrometry (PIMS) utilizes an inductively coupled plasma to ionize the sample and use a variety of ways to separate and analyze the mass spectra. Sector field ICP-MS instruments (SF-ICP-MS) use a magnetic field to separate ions of a given mass/charge ratio. They use an induced plasma source generated by supplying an alternating current (AC) of radio frequency (r.f.) to a copper coil and feeding a plasma gas (usually argon through the center of the coil through a glass torch). This plasma is ignited by a Tesla coil and stabilized by the AC of r.f. Material introduced to the plasma is ionized and focused using a series of charged metal plates (known as ion optics) that force the ion into a narrow beam. This beam is accelerated up to 10 keV using a high-extraction potential and is directed to the electrostatic analyzer and electromagnet. The kinetic energy of the ion beam is normalized by directing the ion beam through the source slit into the electrostatic analyzer. This device applies an electric field to normalize the kinetic energy of the ion beam before entering the electromagnet. Mass separation occurs as the ion beam is directed into perpendicular to the magnetic field and cross the field in different in arcing trajectories according to their mass/charge ratio. In some instruments, the electrostatic analyzer is placed after the electromagnet.
Secondary ion mass spectrometry (SIMS) is an technique to analyze the chemical and isotopic composition of solid materials by bombarding the surface with a of focused ion microbeam and collecting the ejected secondary ions.

### 1.2 Mass separation

Following ionization, an electric field focuses and accelerates a stream of ions along a flight tube set in a high vacuum into an electromagnetic field. This magnetic field splits the ion beam based on the mass to charge ratio of the individual ions. This design of mass spectrometer is referred to as a sector instrument. Many sector instruments also host an electrostatic analyzer placed along the ion flight path either before or after the magnet, in which the ion beam is filtered and focused according to the kinetic energy of the individual ions. Once ions streams have been separated according to the mass/charge ratio they enter the detector. The detector records the current produced when an ion strikes it. Single-collector instruments are able to measure a single mass at a time and can scan a mass range by adjusting the current to the electromagnet. Multi-collector instruments utilize a suite of detectors to analyze a variety of masses simultaneously. Aside from the method of ionization, most mass spectrometers used for geochronology share this same basic design.

### 1.3 Mass detection

Faraday Cups
Ion Counters
Energy Filters
Static vs. Dynamic Detection

### 1.4 Sources of Bias (and how to correct for them)

Mass Fractionation
Detector Lineartity
Detector Gain