Multi-element ion-exchange chromatography and high-precision MC-ICP-MS isotope analysis of Mg and Ti from sub-mm-sized meteorite inclusions

The analytical improvement of new generation mass spectrometers has reached a level required for high-precision isotope analysis of very small and unique natural samples. The multi-element isotopic signatures of meteorite inclusions can potentially provide detailed insight into the origin of our solar system. As such, in-line separation and isotope analysis of multiple elements from such unique samples is highly desirable, but rarely accommodated by current chromatographic puri ﬁ cation procedures necessary for accurate isotope analysis using multiple collector inductively coupled plasma source mass spectrometry (MC-ICP-MS). Here, we report a new multi-element ion chromatographic puri ﬁ cation procedure, speci ﬁ cally developed for the separation of very small amounts of Mg ( (cid:1) 5 m g) and Ti (0.7 – 1 m g) from individual samples. Highly isotopically anomalous sub-mm sized materials, such as Ca – Al-rich inclusions in primitive meteorites, can be routinely analysed for their mass-independent m 26 Mg * , m 46 Ti * , m 48 Ti * , m 49 Ti * and m 50 Ti * isotope compositions with an estimated external reproducibility of 4.1, 11, 8.8, 18 and 12 ppm (2sd), respectively. These procedures consume signi ﬁ cantly less material than previous methods and as such represents a 6-to 10-fold improvement in precision. The method ensures >99.9% Mg and >97% Ti recovery, thereby allowing for the accurate determination of mass-dependent compositions with a precision better than (cid:1) 60 ppm amu (cid:3) 1 for both Mg and Ti. It can further be adapted to accommodate the in-line separation of e.g. Ca, Cr, Fe, Ni, W, Mo, Ru, V, Zr and Hf from the same sample matrices. Doping tests on a synthetic Ti standard demonstrate that isobaric interference can be adequately corrected for provided that atomic ratios are Ca/Ti < 0.07, V/Ti < 0.04 and Cr/Ti < 0.005 and Zr 2+ , Mo 2+ and Ru 2+ have no in ﬂ uence on Ti measurements when atomic ratios are Zr/Ti < 0.002, Mo/Ti < 0.01 and Ru/Ti < 0.001, which is ensured by the chromatographic procedures. Magnesium and titanium isotope data for terrestrial geostandards and isotopically anomalous chondrite meteorites (OC, CR, CV, and CI) and two CV CAIs are in excellent agreement with literature values, demonstrating the accuracy of our methods. The two CAIs plot on an extension of the mass-independent correlation line between m 46 Ti * and m 50 Ti * de ﬁ ned by inner solar system materials, suggesting residual nucleosynthetic e ﬀ ects in CAI precursors.


Introduction
Magnesium and titanium are both important elements in natural environments on Earth and throughout the solar system. While Mg is an important ingredient of terrestrial planets, 1 Ti is a major refractory element, which are enriched in the solar system's rst solids, Ca-Al-rich inclusions (CAIs), found in primitive meteorites. 2 Studying their isotope composition potentially provides constraints on, for example, the timing and efficiency of planetary differentiation processes, [3][4][5][6] mixing and transport of primitive components in the solar protoplanetary disk, 7-9 thermal processing of presolar dust, 10 nucleosynthetic sources that contributed to the astrophysical birth environment of our young Sun, 11 biogeochemical processes on Earth 12 and evaporation and condensation processes. 13,14 Given that Mg is a moderately volatile element and Ti a highly refractory one, potential differences in the degree of stable isotope fractionation may discern the condensation and/or evaporation history of CAIs. Also, the identication of planetary-scale mass-independent heterogeneity in both Mg (most likely associated with heterogeneities in the short-lived radioactive nuclide 26 Al [15][16][17] ) and Ti isotopes 10 calls for an evaluation of the large-scale mixing/unmixing processes of pre-solar components associated with the establishment of the protoplanetary disk and the formation of the rst planetesimals. The coupled isotope systematics of various elements (including Mg and Ti) from unique solar system components, including disk solids such as CAIs, AOAs (Amoeboid Olivine Aggregates) and chondrules from primitive meteorites, may aid in such a quest.
Ion chromatographic purication required for highprecision isotope analysis using Multi-Collector Inductively Coupled Plasma Mass Spectrometry (MC-ICP-MS) and Thermal Ionisation Mass Spectrometry (TIMS) is oen accomplished using chromatographic separation protocols tailored for specic elements involving a combination of various ion exchangers. [18][19][20] The combined analysis of the isotope composition of multiple elements extracted from the exact same sample matrices may, however, be very valuable for a critical evaluation of their prehistory. Such multi-element isotope analyses are especially advantageous when handling small and unique samples, such as sub-mm meteoritic inclusions.
With the advent of new generation high-precision mass spectrometers, such as the Thermo Scientic Neptune Plus MC-ICP-MS and its Jet/X cone interface, the precision of isotope measurements has increased signicantly. This has unlocked the possibility of precisely analysing very small amounts of analytes for the isotope composition of sub-mm inclusions in primitive meteorites. However, such an increase in analytical precision further tightens the demands on ion chromatographic purication protocols required to diminish the number of matrix elements generating instrumental interference and thus inaccurate measurements. It also puts constraints on the amount of impurities, known as 'blanks', introduced through chemical purication of the analyte. The scarcity of material available in small silicate samples calls for effective purication procedures that allow for the separation and high-precision isotope analysis of many elements from the same samples, while at the same time minimizing impurities introduced into the sample through chemical processing.
Given these requirements, we present a novel multi-element chromatographic separation protocol that allows for highprecision isotope analysis of Mg and Ti from the same digestion aliquots of small silicate samples. We show that sub-mm meteoritic inclusions, such as highly isotopically anomalous CAIs, can be accurately and precisely measured for their Mg and Ti isotope compositions with a resolution signicantly exceeding that required to resolve mass-dependent and massindependent variability amongst most inner solar system materials.

Materials, reagents and sample digestion
Experimental and analytical procedures were carried out in ultra-clean laboratory environments with HEPA-ltered laminar ow hoods. All reagents were either purchased as ultrapure chemicals (HF, H 2 O 2 , and NH 4 OH) or puried through distillation (HNO 3 , HCl, acetone, and Milli-Q water). These reagents were all blank tested to ensure a sufficiently low level of impurities prior to chromatographic purication. CAIs were microdrilled using tungsten-carbide drill bits on a computerassisted New Wave Micromill at the Centre for Star and Planet Formation, University of Copenhagen. Whole-rock powders, crushed silicate rock specimens and microdrilled samples (0.1-2 mg) were digested in Savillex PFA beakers in a mixture of concentrated HF : HNO 3 (3 : 1) ($0.5 ml) for 2 days at 120 C and evaporated to dryness. To ensure complete dissolution of all samples, this step was followed by digestion in concentrated aqua regia (HCl : HNO 3 ¼ 3 : 1) ($0.5 ml) at 120 C for another 2 days, thereby also destroying any uorides formed during HF-HNO 3 digestion. The aqua regia treatment was repeated until there were no remaining solids. Prior to sample digestion all PFA beakers were pre-cleaned using the same mixture of acids as that used for sample digestion. Following decomposition, all samples were converted to NO 3 salts through two evaporation cycles with 7 M HNO 3 in preparation for chromatographic purication.

In-line chromatographic separation and purication of Mg and Ti
To ensure a minimum impurity contribution from resin and reagents, we developed a new low-level chromatographic separation protocol for in-line separation and purication of multiple elements from small amounts of silicate samples. This ensures a sample load of <5% of the full cation exchange capacity (CEC) of the 1 st chromatographic column, thereby preventing peak fronting during elution and thus ensuring the availability of sufficient ion exchange sites. 21 For the current setup of the exchanger columns, this corresponds to a typical sample load of approximately 1-2 mg (from which Si has been removed prior to chromatographic separation by volatilization through HF-HNO 3 digestion) depending on cation valences in individual sample matrices. The capacity of the exchanger columns can be scaled up to accommodate larger amounts of samples. This may be of relevance for the separation of elements, such as W, Mo, Ru, V, Zr and Hf, given their common presence in trace amounts in most types of sample matrices.
The ion chromatographic separation protocol involves a series of discrete ion chromatographic separation steps, as summarized in Fig. 1. It takes advantage of novel sample pretreatment procedures to ensure a high Cr recovery (>95%) 22 and is further rened from a Mg purication protocol for larger samples ($100 mg Mg), known to provide high-purity Mg for high-precision isotope analysis by MC-ICP-MS. 23 Although applicable to most types of inorganic sample matrices, the purication method described here is specically tailored for samples with highly anomalous isotope compositions whose measured isotope composition may be compromised by minute analyte impurity contributions. The protocol is well suited for sample matrices with particularly high amounts of Mg, Al, Ca and Fe, such as CAIs and chondrules.
Sample pre-treatment procedures for Cr speciation prior to using the 1 st column. The extremely sluggish kinetics of Cr speciation in acidic media at room temperature and the large differences in the selectivity of a cation exchanger for various Cr(III) species are known to be problematic for high Cr recovery through chromatographic Cr purication. 22 Fig. 2a). Prior to sample loading, the resin was cleaned in $7 M HNO 3 , 1 M HF, and MilliQ water, followed by $6 M HCl and distilled MilliQ water. To ensure sufficiently low impurity contributions from the resin, we dried down and screened the last 0.5 ml of cleaning 6 M HCl eluted from all columns for possible contaminants using an XSeries ICP-MS. The resin blank contributions were in all cases <0.5 ng Mg, <0.1 ng Ti, and <0.3 ng Cr. The resin was subsequently preconditioned in 0.5 M HNO 3 in preparation for sample loading.
Aer the 5-7 day equilibration procedure described above, the sample was loaded directly onto the column in 0.5 M HNO 3 + 3 wt% H 2 O 2 + 0.01 M HF. Titanium was subsequently collected together with Fe, Al, V, Re, W and Mo by elution in 4 ml of 1 M HF (Table 1). This was followed by Mn elution using a 95% acetone + 0.5 M HCl mixture. 24 Calcium was nally separated from the residual sample matrix by unloading Mg, Ca, Ni, Cr, Na and K from the cation exchanger using 10 ml of 3 M HNO 3 and eluting directly onto a pre-cleaned faster-owing Bio-Rad column containing 0.7 ml DGA-N (TrisKem) resin. The high affinity of Ca for the DGA resin in 3 M HNO 3 (ref. 25) ensures its efficient separation from Mg, Cr, Ni, Na and K, which is collected for further purication. The pore-volumes of DGA and AG50w-x8 resin were subsequently emptied into the collected aliquot using 2 ml of 1 M HNO 3 and 3 ml of 6 M HCl, respectively. Calcium can be unloaded from the DGA column using a few column volumes of 0.001 M HCl. Alternatively, Ca can be cleaned up in a separate step by eluting Mg, Na, K, Cr and Ni together with Ca from the cation exchanger in 4 ml of 6 M HCl (instead of 3 M HNO 3 elution directly onto DGA) and later eluting Mg, Na, K, Cr and Ni through a 0.5 ml DGA column in 5 ml of 1 M HNO 3 , while efficiently retaining Ca. Chromatographic recoveries from this 1 st column, as asserted on elution aliquots around the collected Ti and Mg/Cr cuts for different types of sample matrices (including BHVO-2, BIR-1, BCR-2, chondrites (CCs & OCs) and CAIs), were >99% for Ti and Cr and >99.95% for Mg.
2 nd Mg/Cr column (M1). The second step in the Mg/Cr separation reuses the resin and column from the rst step aer conditioning of the resin bed. Samples were converted to the Cl form by using two consecutive dissolution-evaporation cycles in 6 M HCl. This time we employed a sample pretreatment procedure which promotes the formation of neutral, mono-and divalent Cr(III)-Cl complexes with low cation exchanger selectivities, thereby allowing for efficient elution of Cr (>97.5%) from the column. 22 This speciation was ensured by sample exposure to 10 M HCl on a hotplate at 130 C for $1 day. To effectively minimize any back-reaction of the Cr species to its Cr(H 2 O) 6 3+ form prior to column loading, this 10 M HCl sample aliquot was allowed to cool down for no more than 10 minutes and diluted to 0.5 M HCl using cold (about 5 C) distilled MQ water. The sample was subsequently loaded onto the column at room temperature. Cr (in the form of Cr(III)-Cl complexes) was then unloaded from the column together with Na and K in 15 ml of 0.5 M HNO 3 ( Table 1, Fig. 2b). The residual sample matrix, consisting of Mg and Ni, was eluted in 4 ml of 6 M HCl in which elution tests showed that >99.9% of the Mg is collected in the 1 st ml of 6 M HCl eluant. To ensure a robust elution sequence, this separation step was designed such that Mg is  , and Na and K were eluted using 6 ml of 0.5 M HNO 3 , followed by collection of Cr in 3 ml of 6 M HCl (Fig. 1). The Cr pre-treatment procedure and the cation exchange step may be repeated on the Na/K elution cut in order to recover the last 3% Cr. This approach should result in a total Cr recovery of >94%, thereby avoiding signicant mass-dependent isotope fractionation effects. 22 3 rd Mg column (M2). The third Mg purication column involves in the separation of Ni using 260 ml of Ni specic resin (TrisKem) loaded onto a custom-made column made from Pasteur pipettes with an inner diameter of 3.5 mm ( Table 1). The Mg/Ni aliquot from the preceding column was converted to the Cl form by using two consecutive dissolution-evaporation cycles in 6 M HCl, redissolved in 0.5 M HCl on a hotplate to ensure complete dissolution and subsequently diluted to 0.1 M HCl using NH 4 OH and distilled MilliQ water to obtain a 1.5 ml loading solution of 0.2 M NH 4 OH + 0.1 M HCl at pH > 9. This alkaline solution allows the complexation of Ni with dimethylglyoxime (DMG) bound to the resin, which would otherwise be irreversibly destroyed by reaction with H + in acidic solutions. Magnesium was loaded onto the column and collected in 5 ml of 0.2 M NH 4 OH + 0.1 M HCl. Following this separation procedure, NH 4 salts were destroyed by sample exposure to HCl/ HNO 3 (3 : 1) on a hotplate at 130 C and subsequently converted to the Cl form using $6 M HCl in preparation for the nal Mg purication step. The resin-bound Ni-DMG complex can be destroyed and Ni can be eluted with a few column volumes of an acidic solution, such as 2 M HNO 3 . The chromatographic Mg recoveries from this column were >99.99%. 4 th (nal) Mg column (M3). Magnesium was nally puried from residual organics introduced during chromatography that may generate dri and signal spikes during data acquisition using MC-ICP-MS. To this effect, samples were loaded in 300 ml of 0.5 M HCl on a pre-cleaned 100 ml AG50w-x8 200-400 mesh (Bio-Rad) resin-lled Savillex micro-column (ID ¼ 1.6 mm; length ¼ 50 mm) (Table 1). Organics, together with potential Al,  Diagram showing the effect that impurity contribution (known as 'blanks' with isotopically normal composition) from chemical purification of an analyte has on the maximum isotope anomaly, which can be accurately determined within the stated uncertainty. For example, a procedural Ti 'blank' contribution of 0.8 ng introduced into a 1 mg Ti sample through chemical purification provides an anomaly/uncertainty contrast of 1250. With a stated external reproducibility of 12 ppm for m 50 Ti*, this allows for the accurate analysis of materials with anomalies in m 50 Ti* of up to 15 000 ppm.
Ti, Fe and Na blanks, were eluted from the column in 0.3 ml of 1 M HF followed by 1 ml of 0.5 M HNO 3 . The puried Mg fraction was nally collected in 0.65 ml of 6 M HCl and converted to the NO 3 form through two evaporation-dissolution cycles with $7 M HNO 3 in preparation for mass-spectrometric analysis using MC-ICP-MS. Magnesium recoveries from this column were >99.99%, thereby ensuring a nal chromatographic Mg recovery of >99.9%. Total procedural blanks were typically <5 ng (n ¼ 29), which is insignicant compared to the amount of Mg processed through the columns ($5 mg). We note that with a reproducibility of 4.1 ppm for m 26 Mg*, such a low blank level allows for accurate analysis of materials with m 26 Mg* anomalies up to 4100 ppm ( Fig. 3), i.e. about 4 times more anomalous than most CAIs (m 26 Mg* $ 1000 ppm) and well within the range of most solar system materials, as well as the rare and extremely anomalous FUN (Fractionation and Unidentied Nuclear effects, m 26 Mg* down to $À2000 ppm) CAIs found in primitive meteorites. 2 nd Ti column (T1). Titanium (together with Zr and Hf) was separated from Al, Fe, V, Ru, Mo and W on a pre-cleaned 600 ml AG1-x8 200-400 mesh (Bio-Rad) anion exchange column (ID ¼ 3.5 mm; length ¼ 62 mm) ( Table 2, Fig. 4a). The sample was loaded in 0.4 ml of 1 M HF + 0.2 M HNO 3 and Al, Fe, and Ru (and some V) were eluted in 3 ml of 3 M HF, followed by V elution in 6 ml of 1 M HF + 0.2 M HNO 3 . Titanium (incl. Zr and Hf) was subsequently collected using 3 ml of 3 M HCl + 0.03 wt% H 2 O 2 and converted to the NO 3 form using $7 M HNO 3 . When drying down from 3 M HCl, care was taken not to exceed 110 C, thereby avoiding the loss of Ti in the form of TiCl 4 (boiling temperature of 136 C (ref. 26)). Chromatographic Ti recoveries from this column were >99.3%, as asserted on >40 samples.
3 rd Ti column (T2). Titanium was then separated from Zr and Hf (and potential Ca blanks introduced through the chemistry) using a pre-cleaned 260 ml DGA-N (50-100 mm, TrisKem) column (ID ¼ 3.5 mm; length ¼ 27 mm) ( Table 2, Fig. 4b). The sample is loaded in 0.4 ml of 1 M HNO 3 + 0.5 wt% H 2 O 2 and collected in another 5 ml of 1 M HNO 3 + 0.5 wt% H 2 O 2 . In preparation for the nal purication step, the sample was subsequently subjected to three evaporation-dissolution cycles in $7 M HNO 3 to make sure that only trace H 2 O 2 was present in the loading solution, which is known to reduce the selectivity of the cation exchanger for Ti through the formation of anionic species. Chromatographic Ti recoveries from this column were >99.7%. 4 th (nal) Ti column (T3). Titanium was nally puried from potential organics and Ca and Cr blanks introduced into the sample during chromatography using the same type of precleaned micro-column as that used for the nal Mg purication step (Savillex column (ID ¼ 1.6 mm; length ¼ 50 mm) containing 100 ml AG50w-x8 200-400 mesh, Bio-Rad) ( Table 2). The samples were loaded in 300 ml of 0.5 M HNO 3 aer which organics and residual Na were eluted with another 1 ml of 0.5 M HNO 3 . Titanium was nally collected and separated from potential Ca, Cr and Fe blanks using 1 ml of 0.1 M HF. The puried Ti was then converted to the NO 3 form through three evaporation-dissolution cycles in $7 M HNO 3 in order to sufficiently reduce the HF concentration in preparation for isotope analysis using MC-ICP-MS. Titanium recoveries from this column were >99.2%, thereby ensuring a nal chromatographic Ti recovery of >97%. Total procedural blanks were typically <0.8 ng Ti (n ¼ 12), which is insignicant compared to the amount of Ti processed through the columns ($1 mg). The   reproducibility of 12 ppm in m 50 Ti* allows for the accurate analysis of materials with m 50 Ti* anomalies up to 15 000 ppm (Fig. 3), i.e. well within the range of most solar system materials, including FUN-type CAIs.

Mg isotope analysis using MC-ICP-MS
High-precision Mg isotope analysis was performed using the Thermo-Finnigan Neptune Plus MC-ICP-MS located at the Centre for Star and Planet Formation (Natural History Museum of Denmark, University of Copenhagen), using procedures based on Bizzarro et al. 2011. 23 In brief, puried Mg was introduced into the plasma source by means of an Apex IR desolvating nebuliser in a 2% HNO 3 run solution at 50 ml min À1 using a Thermo Fisher Jet sample cone and skimmer X-cone interface in high-resolution mode. The typical sensitivity of the instrument was $200 V ppm À1 of 24 Mg and samples were typically analysed at $50 V. Magnesium isotope data were acquired in static mode using three Faraday collectors connected to ampliers with 10 11 ohm feedback resistors. Samples and standards were analyzed 10 times with each analysis consisting of 100 cycles of 16.78 second integrations separated by a total of 822 seconds of on-peak zero blank measurements in clean 2% HNO 3 solution.
Corrections for instrumental mass bias were obtained by sample-standard bracketing with sample/standard peak intensities matching to better than 5%. Stable Mg isotope ratios are reported in parts per million (ppm) deviation relative to the composition of the Mg reference standard DTS-2B 27 23), assuming that instrumental mass discrimination follows the exponential mass-fractionation law. Data reduction was conducted offline using the freeware soware package Iolite. 28

Ti isotope analysis using MC-ICP-MS
High-precision Ti isotope analysis was performed by standardsample-standard bracketing using the Thermo-Finnigan Neptune Plus MC-ICP-MS located at the Centre for Star and Planet Formation (Natural History Museum of Denmark, University of Copenhagen). Following Ti purication, the samples were dissolved in 0.3 M HNO 3 + 0.001 M HF and introduced into the plasma source by means of an Apex HF desolvating nebuliser (with Ar + N 2 ) at a sample uptake rate of 30-45 ml min À1 . To enhance ion transmission and sensitivity, we used a Thermo Fisher Jet sample cone and skimmer X-cone interface. The measurements were performed on the low mass side of peak shoulders. We used high mass resolution mode, dened as mass resolving power > 8000(m/(m 0.95 À m 0.05 )), measured in the center cup. These conditions are sufficient to efficiently lter out slightly heavier polyatomic interference from e.g. 36 Fig. 5 for a 0.1 ppb solution of Ti, V and Cr); see Section 4.4 for detailed discussion on the measurement conditions. For a 250 ppb run solution, this resulted in a typical sensitivity of $12 V of 48 Ti. Standard and sample intensities were matched to within 5% and tune settings were optimized before each analytical session to maximize the sensitivity and signal stability.
Ti isotope data were acquired in dynamic mode by peak jumping using Faraday collectors connected to ampliers with 10 11 ohm feedback resistors for 46,47,48,49,50 Ti, 51 V, 52 Cr and 44 Ca and a 10 13 ohm feedback resistor to monitor doubly charged 91 Zr 2+ at half-mass 45.5. Each sequence consisted of a number of repeated measurements on a sample bracketed by standards and blanks, each consisting of one cycle of 33.6 seconds of integration for 44 Ca in line 1 followed by 200 cycles of 2.1 seconds of integration for Ti isotopes, 51 V and 52 Cr in line 2 ( Table 3). A peak centering procedure was automatically performed prior to each standard analysis. With a sample uptake time of 100 seconds, this corresponds to a total effective analysis time of 8.9 hours for 10 repeats.
Aer correction for isobaric interference, stable Ti isotope ratios were calculated as parts per million (ppm) deviation from the composition of the Origins Laboratory Ti reference standard (OL-Ti) 29  Due to potential matrix effects and isobaric interferences, isotope analysis by MC-ICP-MS requires sufficient ion exchange chromatographic purication of analytes to ensure measurement accuracy. 32 The need for such chemical processing of samples prior to data acquisition, however, unavoidably results in small impurity contributions, known as 'blanks', introduced either through (1) release from the ion exchange resins, (2) the chemical reagents used for sample digestion and during chromatographic purication, or (3) other exogenous contributions introduced during sample handling. Blanks introduced through chromatographic purication can potentially dilute the true isotopic signature of the 'puried' element and thus generate false results. This delicate balance between chemical purication and blank contributions becomes increasingly important when handling samples that are highly isotopically anomalous. This is because of the large isotopic contrast between the sample and typical 'Earth'-like blanks. Amongst some of the most isotopically anomalous samples are the rst solids known to have formed in our solar system, namely Ca-Alrich inclusions (CAIs) in primitive chondritic meteorites. These inclusions commonly exhibit large mass-dependent and/or mass-independent anomalies in the permil range in a wide range of elements and thus contain important isotopic ngerprints of the very earliest evolution of our solar system. 10,15,[33][34][35][36][37] As such, the chemical and analytical procedures described here were optimized to obtain accurate and precise isotope data from isotopically anomalous materials.
Taking advantage of the increased precision of modern mass spectrometric techniques and thus the small amount of sample that can be precisely analysed simultaneously requires sufficient reduction of procedural blanks introduced through chemical processing. Minimizing procedural blanks demands a sufficient reduction in the amount of resins and acid used through chromatographic purication. Thus, in order to ensure effective separation of most of the sample matrix during the rst purication step, the rst column ensures a removal of >75% of matrix elements (Fe, Al, Ti, Ca, V and Mn) from Mg and Cr for a variety of rock samples (Table S1 †). Ti is effectively separated from the residual matrix in its 2 nd purication step, requiring subsequent removal of only Zr. This effectively minimizes the amount of resins and reagents required in the subsequent purication steps, thereby reducing major blank contributions.
The separation of Mg from elements that may generate doubly charged interference (e.g. 48 Ca 2+ , 48 Ti 2+ , 50 Ti 2+ , 50 V 2+ , 50 Cr 2+ and 52 Cr 2+ ) and/or affect the instrumental mass bias of the sample as compared to the bracketing standard during analysis (e.g. Al, Fe, Na, Ni, Mn and Ca) is critical for reliable and accurate Mg isotope measurements using MC-ICP-MS. 23,38 Ca is specically known to be problematic for isotope analysis of meteoritic materials, as it may induce signicant isobaric interference on mass 24 from doubly charged 48 Ca and can result in apparent m 26 Mg* anomalies. 32,38 Thus, in handling sample matrices with high Ca levels compared to Mg, such as CAIs, efficient separation of Ca from Mg is important. Cation to Mg ratios were monitored in puried samples processed through the chromatographic separation protocol and found to be <$0.001 (examples are given in Table S1 †).
Accurate and precise mass spectrometric analysis of Ti is further compromised by direct isobaric interference from Ca (on masses 46 ( 46 Ca $ 0.004%) and 48 ( 48 Ca $ 0.187%)), V (on mass 50 ( 50 V $ 0.2497%)) and Cr (on mass 50 ( 50 Cr $ 4.3452%)) and potential doubly charged interference from Zr (on masses 46, 47 and 48), Mo (on all Ti isotopes) and Ru (on masses 48, 49 and 50) ( Table 3). Therefore, the chromatographic purication procedure was designed to ensure sufficient separation of these elements from Ti. However, Ca blanks may be especially problematic, since Ca can be introduced through general sample handling from gloves and pipette tips. Thus, all chromatographic columns used in the purication of Ti were designed to separate potential Ca blanks introduced on the sample from Ti. The last column further ensures the effective separation of potential Ca and Cr blanks from the puried Ti fraction. Moreover, all reagents used in the chromatographic chemistry, as well as analytical solutions, were blank tested in order to ensure a sufficiently low Ca blank introduced on the samples. Finally, to eliminate potential interference from chlorides ( 35

Efficiency of the multi-element ion chromatographic separation protocol
Our protocol allows for the efficient separation of multiple elements from the same sample aliquots (Fig. 1). Fig. 2 and 4 show the high resolution achieved for individual elution peaks as exemplied by a synthetic CAI composition. The elution proles of other types of sample matrices (including a dunite (DTS-2B), basalt (BIR-1), lherzolite (J11), ordinary chondrite (Tennasilm), a CAI, and synthetic mixtures) were equally well resolved, demonstrating the reproducibility and efficiency of the chromatographic procedures in separating multiple elements from various types of sample matrices. The efficiency of the chromatographic protocol in separating elements other than Mg, Ti and Cr was evaluated by measuring K, Ca, V, Fe, Ni, Zr, Mo, Ru, Hf, and W eluted from the respective columns. Their recoveries were found to be near 100% for K, Ca, V, Fe, Ni, Zr, Mo, Hf and W, and >92% for Ru in their respective collection aliquots (Tables 1 and  2). The lower recovery of Ru most likely results from complications associated with chemical speciation and redox conditions in the eluting acid, thereby distributing Ru species with variable selectivity over the column. Prior to future isotope work on these elements, their purity in the collected aliquots needs to be addressed and further purication for some is required.

Accuracy and reproducibility of Mg isotope measurements
The procedures described here for Mg purication and analysis are optimized to handle considerably smaller samples than previous high-precision Mg isotope protocols, 23 i.e. 20 times less. This is attained by minimizing the amount of resin and reagents used in the chemical processing of the sample and optimizing the chromatographic separation scheme, as well as by taking advantage of the Jet and X cone interface. Our results show that isotopically anomalous samples, such as CAIs, can be routinely analysed to an external long-term reproducibility for their stable Mg isotope composition of AE61 ppm (2sd) on m 25 Mg and AE4.1 ppm for the mass-independent m 26 Mg* component ( Table 5). This is comparable to, although less precise, the protocols designed for high-precision Mg isotope analysis of larger samples. 23 The typical internal standard error in each repeated measurement was on the order of 5-15 ppm for m 25 Mg and 4-6 ppm for m 26 Mg*, whereas the external precision (2se) for 10 repeated measurements on the same aliquot was on the order of 3-10 ppm for m 25 Mg and 2-5 ppm for m 26 Mg*. This level of precision is adequate to resolve the oen very large isotope differences (a few &) between refractory inclusions, such as AOAs and CAIs, in primitive meteorites. 15,33,34 5 mg Mg typically consumed during a full analysis corresponds to the amount of Mg typically found in a spherical CAI of about 350 mm in diameter. This allows for the measurement of the Mg isotope  composition of inclusions in non-CV carbonaceous chondrites, such as CR, CO and CM chondrites, which have previously been inaccessible to high-precision isotope analysis by MC-ICP-MS due to their small sizes. An external reproducibility of 4.1 ppm on m 26 Mg* restricts the Mg blank contribution (with m 26 Mg* $ 0) allowed on a sample with e.g. a very extreme anomaly in m 26 Mg* of 5000 ppm (such as a canonical CV CAI fragment with an anomalously high 27 Al/ 24 Mg ratio of 13.5) to <1&. Thus, for typical 5 mg Mg required for high-precision isotope analysis following the present analytical procedures, this corresponds to a maximum blank level of 5 ng Mg (Fig. 3), which is fullled by our ion chromatographic procedures.
In addition to the reproducibility test, our analysis shows that three terrestrial rock standards (J11, BIR-1 and BCR-2) are all within the error of the bracketing standard DTS-2B (Table 5)

Optimization of Ti mass-spectrometric analytical protocols
Interference corrections and doping tests. Given that the accuracy and precision of Ti isotope analysis are compromised by direct isobaric interference from 46,48 Ca, 50 V and 50 Cr, as well as doubly charged interference from 92,94,96 Zr, 92,94,96,98,100 Mo and 96,98,100 Ru, we monitored 44 Ca, 51 V and 52 Cr in order to correct for direct isobaric interference on masses 46, 48 and 50. Doubly charged interference from 92,94,96 Zr was further monitored at half-mass 45.5 ( 91 Zr 2+ ). Their intensities were subtracted from the intensities of 46 Ti, 48 Ti and 50 Ti isotopes. To test the performance of our interference correction routines and evaluate their inuence on our measurements, we performed doping tests on a pure 250 ppb Alfa Aesar Ti standard solution. The doped solutions were analysed for their isotope composition by bracketing against a Ti pure aliquot of the Alfa Aesar Ti solution. The results show that our interference correction routines are sufficient up to a cation/Ti atomic ratio of 0.07 for Ca, 0.04 for V, and 0.005 for Cr (Fig. 6). Further doping tests showed that uncorrected interference from doubly charged Zr, Mo and Ru is insignicant at atomic ratios Zr/Ti < 0.002, Mo/Ti < 0.01 and Ru/Ti < 0.001 (Table 4), i.e. comparable to or higher than the ratios found in typical unprocessed CAIs and most types to rocky materials. Residual Zr, Mo and Ru, present in the puried Ti samples, should therefore not affect the measurement accuracy. Measured Ca/Ti, V/Ti and Cr/Ti atomic ratios in  standards and samples were all insignicant for the precision of our measurements (Table S2 †).
Peak-shoulder-atness testoptimizing measurement position. The accuracy, reproducibility and precision of highresolution Ti-isotope measurements are strongly dependent on the alignment of detectors and the measurement position on peak shoulders. This is due to the combined effects of magnet dri, tailing from comparatively large interfering molecular interference on the high mass side of Ti peaks, small peak misalignments typically on the scale of a few millimass units, and variations in the peak shape among the detectors used to determine an isotope ratio (Fig. 7). The main analytical challenge is nding a position sufficiently far away from the centre of the peaks to robustly resolve interference, while not moving so far down a peak shoulder that a combination of magnet instabilities and asymmetric decreases in signal intensity compromises the measurement of the isotope ratios of interest. Hence, to ensure a sufficiently at measurement plateau that minimizes these effects, we performed a series of short-term repeated measurements (each of 8.4 second integrations) interspaced with 1 millimass unit on the low-mass side of peak shoulders before each analytical session. In contrast to traditional peak atness denitions that describe the effective peak atness for a single isotope in a single cup, we employ a ratiobased denition that provides a probe of the actual measurement protocols, including a partial data reduction pipeline. The peak-shoulder-at plateau is dened as the mass range where the internally normalized mass-fractionation corrected isotope ratios approach constant values. Fig. 8 shows an example of such a peak-shoulder-atness test and the sufficiently at shoulder plateau around the typical measurement position at X.926 mass units.
Instrumental dri due to magnet instabilities between two peak centers (prior to each standard measurement) was typically less than 1 millimass unit, which is much less than the peak-shoulder-at plateau of >15 millimass units on the lowmass shoulder. With a typical measurement position in the middle of the shoulder plateau at X.926 mass units, this ensures a at peak plateau of >7 millimass units on either side of the shoulder measurement position, i.e. sufficient to neglect measurement inaccuracy associated with magnet instabilities during an analytical session.
Optimizing Ti analytical protocols. The observation of largescale m 50 Ti* heterogeneity in the solar protoplanetary disk 10 suggests that the Ti isotopic signature of sub-mm-sized disk solids, such as chondrules and CAIs, may provide a tool for disentangling the very earliest processing and transport of material in the solar system. To this effect, and contrary to Trinquier et al. 2009 (ref. 10) and Zhang et al. 2011 (ref. 18) who positions 47 Ti in the central Faraday cup, our cup conguration positions 49 Ti in the central Faraday cup. This conguration allows for the optimization of the peak shape for 50 Ti in Faraday cup H1, since high mass resolution is generally easier to achieve close to the axial Faraday cup i.e. the centre cup for our instrument. This ensures optimal resolution in H1 to robustly resolve 36 Ar 14 N + interference on 50 Ti, while at the same time allowing for the 36 Ar 16 O + (+ 38 Ar 14 N + ) interference on the high-mass side of the 52 Cr peak to be sufficiently resolved. Using this analytical setup with an integration time of 2.1 seconds in 200 cycles typically resulted in internal standard errors in each repeated measurement of 30-40 ppm for d 49 Ti and 25-30 ppm for m 50 Ti*. The internal precision (2se) for 10 repeats was typically on the order of 15-30 ppm for d 49 Ti and 7-10 ppm for m 50 Ti*. The initial tests with longer integration times and fewer cycles (i.e. 4.2 seconds Â 100 cycles and 8.2 seconds Â 50 cycles) had no effect on the internal precision of individual measurements.
Another obstacle towards optimizing measurement precision during Ti isotope analysis in dynamic peak jumping mode is the idle times (prior to actual measurement) needed for ampliers and magnets to settle when jumping between peaks in two cup conguration lines. Conventional analytical protocols for Ti isotope analysis utilize consecutive peak-jumping between two cup conguration lines for a given number of cycles, 10,18 thereby measuring each line an equal number of times. This approach, however, uses a relatively large volume of sample solution because of the idle time necessary for magnet stabilization between two peak jumps. Our analysis shows that an idle time of at least 3 seconds is required for magnet and amplier stabilization (Fig. 9). For 200 cycles at 2.1 second integration with 10 repeated measurements at 250 ppb Ti, this corresponds to 3-4 mg of Ti consumed during a full analysis. Thus, in order to minimize sample consumption during analysis, without compromising the time spend on the actual Ti isotope measurements (as well as V and Cr) in line 2, we measured the Ca interference in line 1 only once at the beginning of each repeated measurement at 33.6 seconds of integration. This limits the amount of Ti consumed per 10 repeats Fig. 9 Test showing the influence of the idle time necessary for the magnet and amplifiers to settle prior to the actual isotope measurements when jumping between peaks in lines 1 (Ca interference) and 2 (Ti isotopes). Internally 49 Ti/ 47 Ti normalized mass-fractionation corrected Ti isotope ratios approach constant values after an idle time of $3 seconds.
to 0.75-1 mg, i.e. 4 times less than that by the conventional mode. Hence, the precision of the actual Ti isotope measurements stays the same, because all Ti isotopes are measured in line 2. Although compromising the effectiveness of the Ca interference correction routine, considerably less material is being consumed. This is highly desirable when dealing with very small and unique samples, such as sub-mm-sized CAIs.
Reproducibility and accuracy of Ti isotope measurements. Similar to Mg, we used the CV CAI 'A3' to assert the external reproducibility of our chemical and analytical procedures for $1 mg Ti. Our results show that the stable mass-dependent Ti (m 49 Ti) isotope composition can be routinely measured to a precision of AE60 ppm amu À1 (2sd, Table 6), which is a factor of 10 better than recent stable Ti isotope data acquired by standard-sample bracketing. 31 Although 6 times larger than the external reproducibility obtained from Ti double-spike techniques, 29 this level of precision is adequate to resolve the m 49 Ti variability observed amongst terrestrial magmatic rocks. 4,5 Contrary to double-spike measurements, our approach further enables the combined analysis of both mass-dependent and nucleosynthetic effects on the Ti isotope composition of extraterrestrial rocks. The mass-independent m 46 Ti*, m 48 Ti*, m 49 Ti* and m 50 Ti* components can be measured to a precision of 11, 8.8, 18 and 12 ppm, respectively (2sd, Table 6). This is similar to or 2 times better than previous analytical methods on 6-10 times more material. 10 Thus, the 15 000 ppm accuracy limitation on m 50 Ti* of our Ti procedures (Fig. 3) fully allows the accurate determination of minor inner solar system isotope signatures, as well as the extreme isotopic signatures in FUNtype CAIs and most hibonite crystals found in carbonaceous chondrites. 7,40,41 Finally, both stable and mass-independent Ti isotope data for terrestrial geostandards (BIR-1, BCR-2 and BHVO-2) are normal within error, demonstrating the accuracy of our methods.
Correlated Ti isotope anomalies in bulk meteorites and CAIs. Signicant departures from mass-dependent Ti isotope fractionation have previously been observed for m 46 Ti* and m 50 Ti* in meteorites and their components. 9-11,42 While inner  solar system materials (bulk chondrites and achondrites) range in m 50 Ti* from À200 to +500, 10,42 refractory inclusions (normal CAIs) span a range from $+500 to +1600. 10 44 We note that natural mass-dependent isotope fractionation, which diverges from kinetic processes (i.e. follows the exponential fractionation law used for mass bias correction), can potentially generate apparent excesses or decits in m 46 Ti* and m 50 Ti*. However, inappropriate mass bias correction associated with mass-dependent fractionation in Ti isotopes can only explain up to $3 ppm variability in both m 50 Ti* and m 46 Ti* per 100 ppm amu À1 variation in m 49 Ti. Hence, stable isotope fractionation can only explain $1% of the variability in m 50 Ti* for CAIs, which instead must originate from nucleosynthetic effects.

Conclusions
We have developed a new multi-element ion chromatographic separation protocol, specically tailored to handle small amounts of isotopically anomalous material, such as Ca-Al-rich inclusions in primitive meteorites, for which impurity contributions must be minimized. We present rened analytical procedures for high-precision Mg and Ti isotope analysis using MC-ICP-MS. The high-precision isotope analysis results of a range of isotopically anomalous chondritic meteorites and refractory inclusions are identical to data previously reported for the same types of materials, demonstrating the accuracy of our methods. Data for terrestrial geostandards are within the error of the OL-Ti standard used for standard-sample bracketing. We show that the protocols allow for the accurate determination of the extreme mass-dependent and massindependent Mg and Ti isotopic signatures found in both normal CAIs and FUN-type CAIs, as well as some anomalous hibonite crystals in CM chondrites (m 26 Mg* up to AE4000 ppm and m 50 Ti* up to 15 000 ppm). Finally, our results support the observation of correlated anomalies in m 46 Ti* and m 50 Ti* for inner solar system materials, which extend to include two CAIs (31E and A3) with highly divergent mass-independent Ti isotope compositions. Such effects cannot be explained by massdependent stable isotope fractionation and must invoke variable nucleosynthetic effects in CAIs.

Conflicts of interest
There are no conicts to declare.