Accessories in Kaiserstuhl carbonatites and related rocks as accurate and faithful recorders of whole rock age and isotopic composition

The accessories perovskite, pyrochlore, zirconolite, calzirtite and melanite from carbonatites and carbonate-rich foidites from the Kaiserstuhl are variously suited for the in situ determination of their U–Pb ages and Sr, Nd- and Hf-isotope ratios by LA-ICP-MS. The 143Nd/144Nd ratios may be determined precisely in all five phases, the 176Hf/177Hf ratios only in calzirtite and the 87Sr/86Sr ratios in perovskites and pyrochlores. The carbonatites and carbonate-rich foidites belong to one of the three magmatic groups that Schleicher et al. (1990) distinguished in the Kaiserstuhl on the basis of their Sr, Nd and Pb isotope ratios. Tephrites, phonolites and essexites (nepheline monzogabbros) form the second and limburgites (nepheline basanites) and olivine nephelinites the third. Our 87Sr/86Sr isotope data from the accessories overlap with the carbonatite and olivine nephelinite fields defined by Schleicher et al. (1990) but exhibit a much narrower range. These and the εNd and εHf values plot along the mantle array in the field of oceanic island basalts relatively close to mid-ocean ridge basalts. Previously reported K–Ar, Ar–Ar and fission track ages for the Kaiserstuhl lie between 16.2 and 17.8 Ma. They stem entirely from the geologically older tephrites, phonolites and essexites. No ages existed so far for the geologically younger carbonatites and carbonate-rich foidites except for one apatite fission track age (15.8 Ma). We obtained precise U–Pb ages for zirconolites and calzirtites of 15.66, respectively 15.5 Ma (± 0.1 2σ) and for pyrochlores of 15.35 ± 0.24 Ma. Only the perovskites from the Badberg soevite yielded a U–P concordia age of 14.56 ± 0.86 Ma while the perovskites from bergalites (haüyne melilitites) only gave 206Pb/238U and 208Pb/232Th ages of 15.26 ± 0.21, respectively, 15.28 ± 0.48 Ma. The main Kaiserstuhl rock types were emplaced over a time span of 1.6 Ma almost 1 million years before the carbonatites and carbonate-rich foidites. These were emplaced within only 0.32 Ma.


Introduction
The relationship between carbonatites and associated alkaline silicate rocks has always been and still is a matter of intense discussion. Most carbonatites that are associated with silicate rocks intrude the alkaline silicate rocks (e.g. Bell et al. 1999) and appear to be younger just like in the Kaiserstuhl. Results from experimental petrology and major, trace and isotope geochemistry do not provide a single answer to the generation of carbonatitic magmas but suggest that carbonatitic melts can be generated by partial melting directly from the mantle, by liquid immiscibility and/or fractional crystallization (see Jones et al. 2013 for a more recent review). The isotopic compositions do not unequivocally distinguish between the various possibilities mainly because the silicate rocks vary much wider in composition than the associated carbonatites (see, e.g. Bell 1998, andGittins andHarmer, 2003). A direct association of carbonatites and silicate rocks is only feasible where they overlap in isotopic composition. The advent of LA-ICP-MS (laser ablation inductively coupled plasma mass spectrometry) made the in situ analysis of trace elements and isotope ratios of minerals in polished mounts possible. This opened entirely new opportunities for in situ analysis of accessory minerals especially in carbonatites and alkaline rocks. These contain phases with incompatible trace element concentrations up to the level of major elements. Their in situ analysis is fast and accurate and can substitute conventional whole rock TIMS analysis to quite an extent in cases (e.g. Sylvester 2008). LA-ICP-MS analyses may even be superior because contamination of whole rocks by meteoric water, etc. is excluded. Perovskite (CaTiO 3 ), pyrochlore (Ca 2 Nb 2 O 7 ) and schorlomite (a Ti-rich variety of melanite) already found application (e.g. Kogarko et al. 2009;Mitchell et al. 2011;Yang et al. 2018) while other accessories, especially Zr-rich phases like zirconolite (CaZrTi 2 O 7 ) and calzirtite (Ca 2 Zr 5 Ti 2 O 16 ) still need more investigation (Wu et al. 2010). The latter phases are scarce in alkaline rocks and carbonatites; they have, however, great potential for in situ U-Pb geochronology and the determination of the (Rb)-Sr, Sm-Nd and Lu-Hf isotope systems (e.g. Rasmussen and Fletcher 2004;Wu et al. 2011).
The aim of the present study is to test and further explore the potential and proficiency for in-situ laser ablation analysis of five accessory phases from carbonatites and carbonaterich foidites, i.e. of perovskite, pyrochlore, calzirtite, zirconolite and melanite (andradite-rich garnet). These accessory phases were separated from intrusive, massive carbonatites and from carbonatite and bergalite dikes (haüyne melilitites- Braunger et al. 2018) from the young volcanic edifice Kaiserstuhl in the Rhine Graben in Germany. Known ages for the silicate-based intrusives and extrusives range between 16 and 18 Ma. Ages for the carbonatites and bergalites were not known before except for one apatite fission track age of 15.8 Ma from a carbonatite (Wagner 1976). In agreement with the geological findings absolute ages of the carbonatites and related rocks should be younger than those of the main edifice-building rocks of the Kaiserstuhl-by how much was not known before the present study. We evaluate the precision and accuracy of the mineral isotope compositions in comparison to conventional whole rock analyses and of the U-Pb geochronology in comparison to K-Ar, Ar-Ar and fission track ages. The new data should give tighter constraints on age and genetic relationships of the diverse rock types of the Kaiserstuhl complex.

General geology of the Kaiserstuhl
The Miocene Kaiserstuhl alkaline complex (Fig. 1a) is located in the SW of Germany, in the southern part of the Rhine rift valley. Wimmenauer (1966) and Keller (1984a, b) distinguished five rock groups (Fig. 1b) on the basis of petrography and major element anlysis: (1) olivine nephelinites and limburgites (ne-basanites), (2) tephrites and essexites (renamed to nepheline monzogabbro by Braunger et al., 2018) as the dominant rock types of the complex, (3) phonolites, (4) a group of bergalites and hauynophyres, both considered as a petrogenetic links between carbonatites and the alkaline rocks and (5) carbonatites. Carbonatites, bergalites and related rocks intrude all other silicate rock types and are, therefore, geologically younger (Fig. 2b) Wimmenauer (2003); essexites are the subvolcanic equivalents to tephrites b overview on Kaiserstuhl rock types with the division into five groups (olivine nephelinites + limburgites, tephrites, phonolite, bergalites + hauynophrs and carbonatites after Wimmenauer (1966) and Keller (1984a, b). The colour coding corresponds to the three groups that were distinguished by Schleicher et al. (1990) on the basis of Sr-, Nd-and Pb-isotope ratios. The fields in the figure correspond to those in Fig. 11 of Keller et al. (1990) with carbonatite compositions added from their Table 8. The field of olivine nephelinites contains one specimen directly from the Kaiserstuhl and four from its immediate surroundings. A much more comprehensive data set on whole rock major and trace elements from the Kaiserstuhl can be found in Braunger et al. (2018) (calcite carbonatite dykes; Lehnert 1989) and lapilli tuffs (Keller 1981(Keller , 1989. Keller (1984a) distinguished a Narich (K 2 O/Na 2 O < 0.8) and K-rich (K 2 O/Na 2 O > 0.8) series. Olivine nephelinites, limburgites, bergalites and hauynophyres belong to the former series, tephrites, phonolites and essexites to the latter. Based on whole rock Sr-, Nd-and Pb-isotope ratios Schleicher et al. (1990) distinguished olivine nephelinites and limburgites as one group with the most positive εNd values, bergalites, hauynophyres and carbonatites as a second group with less positive εNd but similarly low 87 Sr/ 86 Sr ratios and tephrites, phonolites and essexites with highest 87 Sr 86 Sr ratios as a third group. The differences were interpreted such that olivine nephelinites, carbonatites and related foidites stem from a similar mantle source with no modification of the isotopic composition by subsequent processes and that the tephrite to phonolite family stems from another mantle source with modification of the isotopic composition by crustal processes. Essentially the same distinction was made by Wang et al. (2014) and Braunger et al. (2018) whereby several rock types were renamed to correspond to modern nomenclature. The latter authors argue that rare basanitic lamprophyres (monchiquites) are the primitive rock types for the tephritic to phonolitic group and that olivine melilititic magmas are the primary magmas for the other group. They model the derivation of the differentiated magmas by fractional crystallization accompanied by an increase in oxygen fugacity. The Miocene age of the Kaiserstuhl complex with ages between 16 and 18 Ma has been established with bulk rock K-Ar and Ar-Ar age determinations and the fission track method in the main silicate rock types by Lippolt et al. (1963), Wagner (1976), Baranyi et al. (1976), Schleicher (1986) and Kraml et al. (2006).

Analytical methods
The samples for this study (Table 1) are from the Freiburg collection of Prof. J. Keller. They stem from the central intrusive carbonatites (soevites from the Orberg at Schelingen and the Badberg, Fig. 1) and from alvikite and bergalite dykes in the intrusive center W of Badberg (Brettel gang group). Soevites are calcitic intrusive carbonatites, alvikites are fast quenched calcitic dyke rocks and bergalites are calcite-rich melilititic dyke rocks (renamed by Braunger et al. 2018 as haüyne melilitite). The Schelingen soevite consists of calcite up to 30 cm, magnetite, almost pure forsterite, Ba-phlogopite, apatite and pyrochlore. The Badberg soevite consist of coarse-grained calcites with Ba-phlogopite, magnetite and apatite and pyrochlore, Nb-perovskite and lattrapite (perovskite-lueshite group, CaTiO 3 -NaNbO 3 with Fe 2 O 3 …) as accessories. Alvikites from the Brettel dike system have (comb-layered) calcite (Katz and Keller 1981) as their main phase with perovskite, pyrochlore, zirconolite, calzirtite and melanite as accessories. The bergalite dikes from Oberbergen consist of hauyne, melilite, perovskite, nepheline, calcite, mica, magnetite and apatite. The Brettel carbonatite dike contains rounded calcites up to 2 cm and magnetite up to 1 cm and olivine, zirconolite, calzirtite, pyrochlore, Nb-perovskite and baddeleyte. More details of all rock types are described in Keller et al. (1990). The samples were first placed into cold 2.5 M HCl to dissolve the carbonates. The undissolved rest was sieved and sorted according to their magnetic and gravitational properties. The non-magnetic and heavy fractions were hand-picked for accessory minerals (see Table 1). The handpicked minerals were embedded in epoxy and polished. Grain sizes varied between 100 and 200 µm (see secondary electron images, Fig. 2). Generally, one analysis was performed on each individual grain with a laser spot size varying between 20 to 100 µm. Multiple grains were analysed for each mineral species to test for compositional variation, isotopic homogeneity and to obtain a high precision by statistics for isotope analysis and U-Pb age determination. Prior to analysis, the polished minerals were characterized by secondary electron (SE), back scattered electron (BSE) and cathodoluminescence (CL) imaging with an electron microscope (JEOL JSM 6490) to identify and avoid altered or fractured areas and mineral inclusions during LA-ICP-MS analysis (Fig. 2). All analyses were performed at the Institut für Geowissenschaften of the Goethe University, Frankfurt am Main.

Major and trace element analyses
The major elements were analyzed with an Electron Microprobe (JEOL JXA-8900RL) at the Goethe University, Frankfurt am Main. The analyses were carried out in WDS (Wavelength Dispersive Spectroscopy) mode with an accelerating voltage of 15 kV, a beam current of 20 nA and a spot size of 10 μm. The counting time was 30 s with a background measurement time from 10 to 30 s depending on the element. The standards were natural minerals and metals; a ZAF correction was employed to the raw data. For the elevated abundances of REE, U and Th in pyrochlores, we had to perform an off-line ZAF correction using the abundances of trace elements (such as Th, Ce and U) obtained from laser ablation ICP MS.
The trace elements were analyzed using an Element 2 sector field ICP MS, Thermo Finnigan, coupled to a RESOLution M-50 Excimer (193 nm) laser from Resonetics. Helium (about 0.6 l/min) was used as carrier gas in the two-volume ablation cell and was mixed with about 0.8 l/min Ar, and 5 ml/min N 2 after the cell and before introduction into the plasma. Depending on the size and element concentration of the grains, the laser spot size was varied from 20 to 60 μm with a fluence of 3-4 J/cm 2 and a repetition rate of 5-10 Hz. The ablation time was 33 s with 20 s for background measurements. The following isotopes were analyzed for determining the abundances of trace/major elements: 29 44 Ca for internal standardization and NIST SRM612 soda lime glass as the external calibration standard. The signal intensities were corrected for the gas blank background and the final element concentrations were calculated by comparing the Ca-normalized signals of the internal standard with that of the NIST SRM612 glass following Pearce et al. (1997). The Ca content of each mineral was determined beforehand by electron microprobe analysis (EPMA).

In situ analysis of Sr-, Nd-and Hf-isotopes
The isotope analyses were performed using a Thermo Finnigan Neptune MC-ICP-MS equipped with 9 Faraday detectors and attached to a RESOLution M-50 excimer laser (193 nm) from Resonetics. The laser spot size was varied from 45 to 100 μm with a fluence of 1.5 J/cm 2 , using a repetition rate of 6 Hz.
Sr-isotope analyses were carried out on perovskites and pyrochlores. The isotope ratios were measured in a static multi-collector mode with 60 s ablation time for 30 integrated blocks using a cup configuration as suggested by Ramos et al. (2004). The nine Faraday detectors were set to measure the isotopes from 83 Kr to 88 Sr with monitoring the masses 83.5, 85.5 and 86.5 to evaluate double charged ions of 167 Er 2+ , 171 Yb 2+ and 173 Yb 2+ respectively. At high abundance levels of the HREE different double charged Yb and  Yb,and 174 Yb/ 173 Yb. Gas blanks were measured frequently throughout the sequence to monitor Kr and other possible interferences on the selected mass range. The gas blank was subtracted directly from the signal of each individual analysis prior to interference and mass bias correction. For correction of the Rb interference on mass 87, we monitored 85 Rb and used the natural 87 Rb/ 86 Rb ratio of 0.38564, the respective Sr mass bias (βSr = 86 Sr/ 88 Sr measured relative to 86 Sr/ 88 Sr true ; 0.1194) and a βRb/βSr correction factor (~ 0.93). The latter was empirically determined ( 87 Rb/ 85 Rb mass bias / 86 Sr/ 88 Sr mass bias) from soda-lime glass SRM-NIST610 (interference of 87 Rb on 87 Sr > 300%; 87 Sr/ 86 Sr ~ 0.709) analyses at the beginning of the analytical session. Due to the low abundances of Rb and the high Sr contents, the interferences of 87 Rb on 87 Sr were negligible in most cases. The monitored 83 Kr, after 166 Er interference subtraction, was used to check the potential interferences of Ca dimers (e.g., 43 Ca 40 Ca) and Ca argides (e.g., 44 Ca 40 Ar). However, as shown before (Ramos et al. 2004;Vroon et al. 2008;Wu et al. 2011) no interferences were imposed and a correction was not necessary. For Sr mass bias correction, an exponential law was used, assuming the natural ratio of 86 Sr/ 88 Sr = 0.1194. For the HREE mass bias, we used a ß factor of 1.31 as obtained from the analysis of Yb isotopes in zircon. To monitor the accuracy and reproducibility of our method, we used in house standard plagioclase megacrysts from the Miringa volcano (Biu plateau, Nigeria; named Mir' a) and Mir' b), previously analyzed by IDFTIMS (Rankenburg, 2004). Our measurements during several separate sessions yielded 87 Sr/ 86 Sr ratios of 0.703043 ± 0.00029 (n = 4) and 0.703087 ± 0.000024 (n = 12), respectively. The values given by Rankenburg et al. (2004) are 0.703096 respectively 0.703044. For instrumental mass bias correction, we used the exponential law assuming the natural ratio for 86 Sr/ 88 Sr of 0.1194.
The Sm-Nd-isotopes were analyzed in perovskite, pyrochlore, zirconolite, calzirtite and melanite. Data were collected in static mode using nine faraday cups for monitoring 142 Nd,143 Nd,144 Nd,145 Nd,146 Nd,147 Sm,148 Nd,149 Sm,150 Nd with an ablation time of 62 s for integrating 60 blocks. The only significant interference for Nd-isotope analysis is 144 Sm on 144 Nd, while the effect of the other isobaric mass (i.e.: 142 Ce on 142 Nd) is negligible. For mass bias correction, the exponential law was applied, using the natural 146 Nd/ 144 Nd ratio of 0.72190. The results were then normalized to an off-set correction factor, calculated from the deviation of the measured in-house standard from its accepted values. We used Merck 500 ppb as our in-house standard and obtained an average of 0.511722 (± 0.000002, n = 2) for 143 Nd/ 144 Nd. NIST 610 was measured several times to monitor instrumental offset. During two sessions we obtained 146 Nd/ 144 Nd = 0.511912 ± 0.000035 (n = 6) and 0.511931 ± 0.000018 (n = 15). These values are close the value of 0.511908) suggested by Foster and Vance (2006). If necessary, a small correction was performed to account for the offset between our analyses and the accepted value.
The Hf isotopes were determined in calzirtites from alvikites. The masses 172 Yb, 173 Yb, 175 Lu, 176 Hf, 177 Hf, 178 Hf, 179 Hf, 180 Hf and 181 Ta were measured in static mode on 9 detectors with 58 s ablation time, integrating 55 blocks. All analytical and correction procedures are described in detail by Gerdes and Zeh (2009 Gerdes and Zeh, 2009). Instrumental bias correction was by exponential law using 179 Hf/ 177 Hf = 0.7325 (Patchett and Tatsumoto, 1980). Because of the low abundances of Lu in calzirtites (Table 2), the interference of 176 Lu was negligible. For instrumental offset correction we used GJ1 as our reference and measured it twice before, during and after our analytical sequence. The average of 176 Hf/ 177 Hf(t)d for our internal standard (GJ1) during measurement is 0.282000 ± 16 (2σ, n = 6), which was adapted to 0.282003 ± 18 (2σ) as obtained by Gerdes and Zeh (2009).

Sr-and Nd-isotope dilution analysis
As a comparison for LA-ICP-MS analysis about 7.7 mg of perovskites and 1.69 mg of pyrochlores were handpicked from the Badberg respectively Schelingen soevites and each divided into two beakers. The grains were first leached in 6 M HCl at room temperature in an ultrasonic bath and afterwards washed with MQ water twice, each time for about 20 min. Prior to dissolution, a 149 Sm: 150 Nd double spike was added. The minerals were dissolved in 100 μl of HF:HNO 3 (3:1) on a hot plate at 120 °C for one day. Just before entire evaporation, 100 μl of perchloric acid (HClO4) was added to each beaker at a temperature set to 150 °C for one day. After evaporation to dryness 0.5 ml of 6 M HCl was added to each beaker at a temperature of 130 °C for one day. The procedure was repeated a second time. Finally 1 ml of 2 M HCl was added to each beaker for preparing the samples for Sr and Sm:Nd chromatographic separation. Sr and LREE were separated using the following chromatographic procedure: after washing out most major and minor elements with 3 ml of 2.2 M HCl, Sr and LREE were separated by 6 ml of 3 M HCl and 10 ml 6 M HCl, respectively, using cation exchange resin (column 1, Bio Rad 50Wx8); the Nd and Sm

U-Th-Pb geochronolgy
In situ U-Th-Pb isotope analyses were carried out on perovskites from the Badberg soevite and from bergalites, on pyrochlores from the Schelingen soevite and on calzirtites and zirconolites from alvikites. Analyses were performed with a Thermo Finnigan Element 2 ICP MS connected with a Resonetics laser ablation system. Data were collected in time resolved-peak jumping-pulse counting mode over 810 mass scans with 19 s of background scanning followed by 30 s of sample ablation. Depending on the size of the grain and U content, the ablation spot varied from 30 to 65 μm. Off-line data processing was performed for correcting background signals, common Pb, interferences of 204 Hg, elemental fractionation during ablation and instrumental mass discrimination, using an Excel © spreadsheet by Zeh (2006, 2009). For the correction of mass discrimination and elemental fractionation during ablation, we normalized the data to zircon GJ-1 (Jackson et al. 2004), which was repeatedly measured during each analytical sequence. As secondary standards and for quality control of the analysis we used zircon 91,500 (Wiedenbeck et al. 1995) and Ice River perovskite (Heaman 2009); the latter was particularly used for monitoring matrix effects observed in perovskite. The concordia and weighted average age diagrams were plotted, using Isoplot 4.

Mineral major and trace element compositions
Minerals are partly oscillatory zoned and vary in composition from grain to grain. Selected analyses for major and trace elements of the perovskites, pyrochlores, zirconolites, calzirtites and garnets are given in Table 2. Totals are always lower than 100% when Fe is calculated as FeO. However, when all Fe is calculated as Fe 2 O 3 and trace elements are recalculated to oxides, the totals always reach more than 99 wt%. A confirmation for the existence of Fe 3+ in such accessories is the report of Fe 2 O 3 analysed directly in zirconolites (see review by Williams and Gieré, 1996). Also, high Fe 2 O 3 in the accessories of Kaiserstuhl carbonatites is not surprising considering the high oxgygen fugacity (above the FMQ buffer) calculated by Braunger et al. (2018) for the Kaiserstuhl carbonatites. The range of trace element variations shown in Fig. 3 depicts the minimum and maximum values for each mineral species. Zirconolites and calzirtites have the overall highest trace element contents followed by pyrochlores, perovskites and melanites (Fig. 3). Calzirtites show fairly flat chondrite normalized REE patterns whereas they are negatively inclined for all other phases except for La that is lowered in pyrochlore, zirconolite and melanite. Perovskites Per01 and 03 (  Fig. 3 within one compositional range. The perovskites from bergalites lie within this range for soevitic perovskites, esp. also the REE (Fig. 3c).  Yb  290  290  318  249  211  210  29  13  15  Lu  34  42  38  23  19  204  4  2  2  Hf  528  705  645  1158  1063  1477  14  13  15  U  31,136  37,573  40,986  2640  2307  2718  26  26  33  Th  29,993  20,365  36,262  943  428  325  38  45  62  Pb  56  29  67  14  12  17 0.2 0.5 1.1

Mineral isotope compositions
The results of single-spot measurements of isotope ratios are presented in Fig. 4 a-c, their average values with 2σ deviations are given in Table 3. Figure 4a shows the results for 87 Sr/ 86 Sr and Sr contents in perovskites and pyrochlores from bergalites, soevites and alvikites. Because of the very low abundances of Rb in perovskites and pyrochlores (Table 1) the measured values correspond to the initial 87 Sr/ 86 Sr ratios. The Sr-concentrations of pyrochlores from the Schelingen carbonatite range from about 1000-1900 ppm (n = 13) and the 87 Sr/ 86 Sr ratios vary between 0.70359 and 0.70370. The Sr-concentrations and 87 Sr/ 86 Sr ratios in perovskites from alvikites and the Badberg soevite completely overlap and range from 1500 to 2800 ppm (n = 19) and 0.70356 to 0.70366. Perovskites in bergalites have Sr-concentrations between 2200 and 3000 ppm (n = 23) and 87 Sr/ 86 Sr ratios of 0.70364-0.70382. The latter are highest both in concentration levels and isotope ratios of all measured mineral grains. The averaged 87 Sr/ 86 Sr ratios (Table 3) are lowest in the pyrochlores (0.70361). They overlap within the error with the somewhat higher average (0.70365) of the perovskites from alvikite and of the Badberg soevite from Badberg. The latter only marginally overlaps with the high average of 0.70371 of the perovskites from bergalites. Element concentrations were high enough to determine the 143 Nd/ 144 Nd isotope ratios in all phases that were separated from bergalites, alvikites and soevites. The results of single measurements are shown in Fig. 4b) in a diagram of εNd (t) versus Nd concentration and averaged values are given in Table 3. Neodymium concentrations are lowest in calzirtite and garnets (around 400 ppm), significantly higher in perovskites (~ 5000 ppm) followed by zirconolite (7000 ppm) and then pyrochlore (15,000 ppm). The 143 Nd/ 144 Nd values are time corrected (15 Ma) and the corresponding εNd values calculated according to the chondritic value of 143 Nd/ 144 Nd = 0.512638 (Bouvier et al. 2008). In general, the 143 Nd/ 144 Nd values of all phases overlap closely within their 2σ errors and give an average of 0.512774 (n = 83). In detail, the values of one group of garnets lies below those of all other phases while a second group falls within their range. The garnet group with the lower values does not differ in texture or major element composition from the other garnet group. Also, the perovskites from the bergalites form a group on the low side of the Nd isotope range of all other phases.
The Lu-Hf isotopes could be analyzed only in calzirtites from alvikites. The results for 16 analyses are shown in Fig. 4c in a 176 Hf/ 177 Hf versus 176 Lu/ 177 Hf diagram. The average is 0.28301 ± 2 ( Table 3) that corresponds to εHf(t) = + 8.3.
A larger number of individual analyses of an isotopically homogeneous material statistically yields an accurate average value with a low 2σ error that corresponds to the value obtainable by isotope solution. Indeed, the duplicate isotope dilution measurements for the Sr and Nd isotope ratios of perovskites and pyrochlores correspond within the isotope dilution error to the average values from LA-ICP-MS measurements (Fig. 4a,b and Table 4).

U-Th-Pb geochronology
U-Pb ages were determined for perovskites, pyrochlores, calzirtites and zirconolites from the soevites and alvikites. Error ellipses of all individual measurements are shown in concordia diagrams (Fig. 5a-d); derived U-Pb and  . 5b). The Zr-rich minerals calzirtite and zirconolite from alvikites give similar concordia ages of 15.5 (± 0.1) and 15.66 ± 0.16 Ma and 206 Pb/ 238 U ages of 15.5 (± 0.08) respectively 15.67 ± 0.11 Ma (Fig. 5c, d and Table 5). Perovskites from the bergalites did not yield a concordia age because of their low U and high common lead abundances. They only gave a lower but not an upper intercept value. Instead, their 206 Pb/ 238 U and 208 Pb/ 232 Th yielded averaged ages of 15.28 ± 0.48 Ma and 15.26 ± 0.21 Ma, respectively (Fig. 5e, f and Table 5). Calzirtite, zirconolite, pyrochlore and perovskites from bergalites give the same ages within error around 15.45 Ma whereas the perovskites from soevite give a younger age of 14.56 Ma. This age with a large 2σ error barely overlaps with that of the other phases. Pyrochlores from soevite give an older age consistent with that from the other accessories. Analogous to the various isotope ratios, the average of a larger number of U-Pb analyses statistically gives a very good precision and accuracy of the in-situ age values. A precision of around ± 0.2 Ma is significantly better than the ± 0.7 Ma of the previous methods employed in the Kaiserstuhl. The exception is the age of 14.56 Ma with its large error of ± 0.86 Ma for the perovskites from the Badberg. This large error could be due to the relatively low U and Pb abundances in these perovskites compared to zirconolite, pyrochlore and calzirtite and the larger variability of the trace elements compared to the pervoskites from the bergalites (Fig. 3).

Accessories as accurate and reliable age monitors of their whole rocks
Existing age data for the Kaiserstuhl tephrites, essexites and phonolites are shown in Fig. 6 together with our new data on the accessories from the carbonatites and bergalites. The former fall in the time span between 16.2 and 17.8 Ma and mark the main intrusive and extrusive activity in the Kaiserstuhl. Age data for the carbonatites and related rocks were not available before our study except for one younger apatite fission track age of 15.8 ± 0.5 from a carbonatite (Wagner 1976).
We obtained significantly younger ages for the carbonatites and bergalites. Perovskites from the Badberg gave the youngest age of 14.56 Ma but with a large error. Still, the age overlaps within error with the more precise ages of the other phases (Fig. 6). These span the time range between 15.35 and 15.67 Ma (Table 5 and Fig. 6) including the 208 Pb/ 232 Th and 206 Pb/ 238 U ages of the perovskites from the bergalites. The bergalite dykes intrude the carbonatites and are thus geologically younger. However, this is not resolvable with our methods. Pyrochlores, calzirtites and zirconolites yield the most precise age data with errors of only 0.1-0.2 Ma. Perovskite ages are less precise because of their relatively lower U and lead contents.
The K-Ar and Ar-Ar age data for the Kaiserstuhl from the literature entirely stem from the geologically older extrusive tephrites and intrusive phonolites and essexites while our in-situ age determinations are from members of the  Wimmenauer (2003). Errors for the K-Ar ages are around ± 0.7 Ma (2σ). The black, up-side down triangle with the white dot is the average of four ages obtained by Kraml et al. (2006) from minerals of the phonolitic Limberg T3 tephra: apatite by fission track, apatite and titanite each by (U-Th)/He) and sanidine by laser Ar-Ar. Coloured symbols are the results from the present study.) geologically younger carbonatite and carbonate-rich foidite family (Fig. 1b)

Accessories as accurate fingerprints of the isotopic composition of their host rocks
Based on the Sr, Nd and Pb isotope characteristics Schleicher et al. (1990 a,b) distinguished three groups of volcanics and subvolcanics in the Kaiserstuhl (see above "General Geology"). The Sr and Nd isotope fields are outlined in Fig. 7a (Fig. 7b) whereas the fractionated alkaline rocks align oblique to the mantle array and lie partly outside.
Our new isotope data on accessories in carbonatites and bergalites are in accord with this division. They appear, however, to be more precise and accurate and allow finer distinctions than whole rock data. This is especially apparent for the 87 Sr/ 86 Sr ratios. The new mineral 87 Sr/ 86 Sr values overlap with the values of the primary magma field and fully overlap with the carbonatite whole rocks (Fig. 7a). The field for the bergalites, however, lies at somewhat higher 87 Sr/ 86 Sr ratios than the values for the perovskites from bergalites and the carbonatite field. This may reflect a meteoric influence in the easily weathering bergalites as suggested by Hubberten et al. (1988) on the basis of whole rock oxygen isotopes. Combined with the Nd-isotope ratios the field for carbonatite and bergalite accessories falls somewhat removed from the previously established carbonatite-bergalite field onto the edge of the mantle array (Fig. 7b), Both the Sr and Nd isotope ratios are lower possibly also reflecting a meteoric influence in the whole rocks. Furthermore, the perovskites from bergalites plot somewhat away from the pyrochlores and perovskites from carbonatites to even lower Nd values. The Hf-isotopes could only be determined in calzirtites from the bergalites. Combined with their Nd-isotopes they plot in an εHf versus εNd diagram within the field of oceanic  The outlined fields with black symbols depict the range of whole rock data after Schleicher et al. (1990) The colored symbols are our own new data. a Comparison of the 87 Sr/ 86 Sr ratios and Sr contents of whole rock and minerals. b Comparison of the 143 Nd/ 144 Nd and 87 Sr/ 86 Sr isotope ratios of whole rocks and and pyrochlores and perovskites from carbonatites and bergalites. Also shown are the mantle array and the right-hand edge of the HIMU field. c εHf vs εNd for calzirtites from bergalites. They plot within the field of oceanic island basalts just above the terrestrial array. Fields of MORB and OIB are from Dobosi et al. (2003) and Vervoort and Blichert-Toft (1999). The Terrestrial Array is from Vervoort and Blichert-Toft (1999) island basalts above the terrestrial array in the quadrant for long time depletion (Fig. 7c).

Genetic relationships amongst the Kaiserstuhl magmatic rocks
The intrusion and extrusion of the Kaiserstuhl magmatic rocks coincided with the updoming of the Moho underneath the Kaiserstuhl to 24 km depth, i.e. hot mantle material was rising underneath the Kaiserstuhl. This occurred during the uplift and N-S compression of the southern Rhine Graben segment in the late Aquitan and Burdigal (21-16 Ma; see overview by Keller et al. (2002), Lutz and Cleintuar (1999), Larroque and Laurent (1988). Schleicher et al. (1990Schleicher et al. ( , 1991 deduced the genetic relationships of the various intrusives and extrusives from the Sr-, Nd-and Pb isotopic compositions and embedded them into a history of updoming of the mantle underneath the Kaiserstuhl: (a) they proposed that parental, primary olivine nephelinites stem from the upwelling of a long-time depleted mantle that was reenriched in incompatible elements in the cause of the rifting processes and that the derivative tephrites, essexites and phonolites are the products of AFC processes in the crust.
(b) They also suggested that the carbonatites and bergalites stem from a second depleted mantle source whose isotopic composition was continuously, even though little modified by metasomatism in the process of the continued updoming of the asthenosphere. The carbonatites, bergalites and related magmas are not primary mantle melts but are differentiation products of olivine nephelinite magmas at high pressures. Prove for high-pressure crystal fractionation in the mantle is the presence of clinopyroxene megacrysts in olivine nephelinite tuffs in the Kaiserstuhl (Keller 1978;Ulianov et al. 2007). Keller (1978) demonstrated experimentally that these clinopyroxenes are high-pressure liquidus phases of the olivine nephelinites at around 2 GPa. The crystallisation of mainly clinopyroxene drives the residual liquids towards bergalitic and eventually carbonatitic melts. Whole rock REE patterns from olivine nephelinites to bergalites and carbonatites from Braunger et al. (2018) and Keller et al. (1990) are in qualitative agreement with such a model. Similarly, Braunger et al. (2018) postulated two mantle sources with distinct prevailing oxygen fugacities. In their model, basanitic lamprophyres (monchiquites) are the primitive rocks for the tephrite to phonolite series with fractional crystallization of mainly clinopyroxene, amphibole and olivine accompanied by an increase in oxygen fugacity. Olivine melilititic magmas are the primary magmas for the bergalites (hauyne melilitites) and more fractionated rocks. These differentiates developed by fractional crystallization of mainly olivine, spinel/magnetite, melilite, perovskite and nepheline at even higher oxygen fugacities.
The model of Schleicher et al. (1990) contains the geological findings that the carbonatite-foidite group is younger than the tephrite-phonolite group. We have shown here that the time difference is considerable and almost one million years and that the time span for the emplacement of the tephrite-phonolite group is much longer than for the carbonatite-foidite group. Reasons for these differences may lie in processes connected with the updoming of the mantle underneath the Kaiserstuhl and in the differences of the properties of silicate and carbonatite melts. For the generation of the strongly Si-undersaturated primary melts the depth of partial melting and melt segregation is roughly constant in the mantle but the portion of the melting peridotite is renewed in an upwelling mantle with time. Because of the relative properties of small melt fractions of silicic or carbonatitic melts as metasomatizing agents Green (2015) hypothesized that a carbonate-bearing melt moves slower than a silicate melts and also slower than an upwelling mantle. If so and if partial melting is intermittent, an earlier melting process may tap a long-time depleted mantle portion (required by positive εNd) that was refertilized in incompatible elements by a relatively water-rich, CO 2 -poor melt. The generated parental melts will differentiate into tephritic to phonolitic compositions. The second melting would occur in a depleted mantle that was metasomatised by a more carbonatitic melt. The resulting parental melts with higher CO 2 /(CO 2 + H 2 O) reach their volatile-saturated liquidus at higher pressures than those with lower CO 2 /(CO 2 + H 2 O) during uprise. They precipitate Si-rich phases like clinopyroxene and differentiate eventually to foidites and carbonatites.

Summary and conclusions
We have shown that accessories from young carbonatites and carbonate-rich foidites are accurate and precise recorders of the age and isotopic compositions of their host rocks. Depending on the trace element abundances and patterns (mother/daughter element ratios) the investigated phases are variously suited for U-Pb geochronology and the determination of their Sr-, Nd-and Hf-isotope ratios. a) Zirconolite and calzirtite have highest U contents and highest U/Pb ratios. They yield the most precise ages with 2σ errors of only 0.1 Ma followed by pyrochlore with an error of 0.2 Ma. Errors of 206 Pb/ 238 U ages are of similar size or less. Perovskites with lower U/Pb ratios appear to be less suited because they either yield concordia ages with a much higher error or no age at all. Still, meaningful ages may be obtained from 206 Pb/ 238 U and 208 Pb/ 232 Th geochronology. b) Perovskites and pyrochlores have the highest Sr-contents. They yield 87 Sr 86 Sr ratios with a precision very close to that of isotope dilution measurements. c) All accessory phases perovskite, pyrochlore, zirconolite, calzirtite and melanite are suitable for the precise determination of the Nd-isotopes. d) The Hf-isotopes could only be determined with high precision in calzirtites. They have the largest positive Zr-Hf anomalies compared to all other phases.
Zircon, baddeleyite zirconolite, calzirtite and perovskite have been previously used to determine precise U-Pb ages and isotope ratios by SIMS and TIMS for various rock types from 130 -2000 Ma old carbonatite complexes (Wu et al. 2010 andHeaman 2009). Our results show that this is also possible for a young volcanic complex like the Kaiserstuhl by LA ICPMS. They also confirm the findings of previous studies that precise data can be obtained from calzirtites and zirconolites (Wu et al. 2010) and perovskites and pyrochlores (Ghobadi et al. (2018).
Our new Sr-isotope ratios confirm the results of Schleicher et al. (1990) that olivine nephelinites and carbonatites with their associated carbonate-rich foidites entirely overlap which suggests a close genetic relationship between them. However, Schleicher et al. (1990) also pointed out that the olivine nephelinites had more negative εNd values and lower 206 Pb/ 204 Pb ratios. They resolved this by suggesting that the mantle source underneath the Kaiserstuhl was continuously modified by incoming melts or fluids during the updoming of the Moho. Indeed, our results show that at least 1 Ma passed after the intrusion and extrusion of the main silicate rock types of the Kaiserstuhl until the carbonatites and bergalites were emplaced providing time for the modification of the carbonatite mantle source. This source has not directly produced the calcic carbonatites of the Kaiserstuhl as partial melts. Direct partial melting products of a carbonatized peridotitic mantle at low degrees are rather dolomitic (Wallace and Green 1988) that cannot reach the Earth's surface because of decarbonatization reactions on the way up.