The Application Of The Regression Model For The Measurement Of Lu-Hf Isotopic System

In recent years,with the development of multi-receive inductively coupled plasma mass spectrometer（MC-ICP-MS）,the study of Lu-Hf isotopes has made great progress and has become a powerful tool for mineral-scale geochronology and isotopic tracer studies.Owing to the suitable half-life,the Lu-Hf isotopic system can be applied for a wider range than the Rb-Sr,Sm-Nd and U-Pb isotopic systems.The Lu-Hf isotopic system is mainly used for the analysis of mineral and whole rock samples with high Lu/Hf ratios,such as garnet and apatite.However,the application of the Lu-Hf isotopic system is limited by the low content of Lu and Hf in natural samples,which affects the application of Lu-Hf isotopic system in geological research.It is difficult to measure nanogram accurately and precisely or sub-nanogram levels of Lu and/or Hf using MC-ICP-MS.If the concentration of Lu and Hf is extremely low(normally<0.1μg g^-1 to several ng g^-1),it is hard to separate sufficient concentration of Lu and Hf from samples.Therefore,the isotope diluent（ID）method is very important in the isotopic system.It should be noted that the main prerequisite for the application of the isotope dilution method is the accurate isotopic composition of spike.Therefore,it is necessary to calibrate the isotopic composition of spike accurately before using the isotope diluent method.Compared to the sample preparation needed for conventional thermal ionization mass spectrometry（TIMS）and hot-secondary ionization mass spectrometry（SIMS）techniques,Lu and Hf chemical purification for MC-ICP-MS measurements can be greatly simplified,facilitating a much higher sample throughput and smaller sample size.However,recent research showed that the mass bias phenomenon is commonly existed during the measurements using MC-ICP-MS,including mass dependent fractionation（MDF）and mass independent fractionation（MIF）.This study is based on the MDF and MIF during the measurement of MC-ICP-MS,comparing different fractionation correction models.The regression model was chosen to determine the isotopic composition of spike and Yb isotope.Besides,this study focused on the MIF phenomenon within MC-ICPMS itself.Adopting the appropriate isotope fractionation correction model,we have determined the isotope ratios of Lu,Hf and Yb,the main achievements and conclusions are summarized as follows:（1）In this study,the regression model was successfully applied to the measurement of Lu and Hf isotopic composition in spike.In addition,the results of the regression model were compared with the SSB and C-SSBIN method,which require strict matrix matching,otherwise the results are unstable and have large errors.Since the regression model required the mixing of sample and standard,which minimize the influence of matrix effect and the instability of the instrument.Therefore,the regression model does not need strict matrix matching.This method has been proven to be consistent within the error range with the gravimetric isotope mixture model.The regression model is one of the efficient methods.The obtained precision of ¹⁷⁶Hf/¹⁷⁷Hf,¹⁷⁹Hf/¹⁷⁷Hf and¹⁸⁰Hf/¹⁷⁷Hf was improved significantly compared with the SSB and C-SSBIN method.With the precision of SSB method and regression model method of the spike Hf,～97.6Ma(¹⁷⁶Hf/¹⁷⁷Hf=0.237-0.243 and ¹⁷⁹Hf/¹⁷⁷Hf and ¹⁸⁰Hf/¹⁷⁷Hf were 2.90 and 391,respectively,which were kept fixed with the calibrated value of SSB method)offset of the calculated isochron age.While with the precision obtained by the regression model method,only～16 Ma(¹⁷⁶Hf/¹⁷⁷Hf=0.2401-0.2411,¹⁷⁹Hf/¹⁷⁷Hf and ¹⁸⁰Hf/¹⁷⁷Hf were2.8620 and 384.65,respectively,which were fixed with the calibrated value of regression model)offset of the calculated isochron age.Thus,with the application of the regression model,the calculated isochron Lu-Hf age was significantly improved.The calibration of spike broadened the application of the regression model.（2）In this study,the absolute Yb isotopic composition were analyzed by MC-ICP-MS using the NIST SRM 3143 Re standard solution as the internal standard.The results of absolute Yb isotope ratios in three Yb standard solutions are consistent.The agreement between the slopes of the three-isotope plots and the theoretical slopes also indicated that the obtained Yb isotopic composition was not affected by the MIF and polyatomic interferences.Therefore,the results were accurate and reliable.In addition,the Yb isotopic composition obtained by the regression model yields the ¹⁷⁶Hf/¹⁷⁷Hf,which is consistent with the recommended value.Therefore,the absolute Yb isotopic composition of this study is suitable for the Hf isotope analysis.（3）Based on the chemical separation method of Lu-Hf isotopic composition integrated by the previous studies,the concentrations of Lu and Hf and Hf isotopic ratio in international reference materials（BHVO-2,BCR-2 and JB-1）were analyzed by the Lu-Hf isotope dilution method.The results were consistent with the recommended value,which verified the reliability of the ID method of Lu-Hf.In order to verify whether the configured Lu-Hf isotope diluent can be successfully applied to the geological sample,and to explore the influence of the ID method on the accuracy of the content of Lu-Hf,the Lu-Hf spike was applied to the eclogite.The primary Lu-Hf isochron analysis and application of the selected garnet pyroxene samples were carried out by ID method.The isochron age of 434.74±4.45 Ma（MSWD=0.73）was obtained by the Lu-Hf isotope analysis of whole rocks and the selected garnets and clinopyroxene.In addition,by comparing the content of Lu and Hf elements obtained by the ID method with the conventional methods,it was obvious represented that the accuracy of the content of Lu and Hf obtained by the ID method is improved from1%to0.1%.Therefore,the calibrated Lu-Hf spike can be used for the Lu-Hf isotope analysis of geological samples.The main innovations of this study include:（1）Owing to the main advantage of regression model without strict matrix matching,this study finds that the regression model has better calibration effect than the conventional fractionation model in the isotopic composition calibration test of diluent.（2）The regression correction model can be applied not only for the natural isotope composition,but also for the isotopic composition of spike.（3）Hf spike was found to have mass-independent fractionation during the measurement and needed to be accurately corrected.（4）The calibratedspikes were successfully applied to the Lu-Hf analysis of garnet pyroxenitesamples,and the obtained the high accuracyisochrone age.