Introduction

Experimental studies on garnet lherzolites have demonstrated that the solubility of Cr in clinopyroxene (cpx) is pressure (P) dependent (Brey et al. 1990). This relationship has previously been used empirically to calibrate the NT00 Cr-in-cpx geobarometer for chrome-rich (> 0.50 wt% Cr2O3) cpx derived from garnet lherzolites. Their geobarometer was calibrated using previously published data (Nickel 1986; Brey et al. 1990; Taylor 1998) obtained from experimental studies on a variety of synthetic fertile to refractory lherzolite starting compositions over a pressure–temperature (PT) range of 2–6 GPa and 900–1400 °C. The majority of the experiments used in the NT00 calibration were conducted at P < 4 GPa. The application of this geobarometer to natural and experimental datasets has confirmed its reliability from 2 to 4 GPa. As a result, the NT00 geothermobarometer has proved to be an important petrological tool for defining PT conditions and mantle lithospheric geotherms, essential for understanding both the thermotectonic and chemical evolution of the sub-continental lithosphere (Mather et al. 2011) and in assessing the diamond-bearing potential of kimberlites (Grütter et al. 2004; Cookenboo and Grütter 2010) in situations for which traditional two-phase geothermobarometry has not been feasible. To accurately study the lithosphere from which garnet lherzolites are sampled, which ranges in thickness up to 300 km (Gung et al. 2003; Lee et al. 2005), reliable P estimates above 4 GPa are critical. Application of the NT00 geobarometer to experimental and natural samples derived from P > 4 GPa suggest that it progressively and systematically underestimates P by as much as 1 GPa (Shirey et al. 2013; Ziberna et al. 2016). Despite this, the NT00 geobarometer has remained widely used and is currently the only available major element single crystal geobarometer for garnet lherzolites. A recent empirical correction of the Cr-in-cpx geobarometer was proposed by Nimis et al. (2020) as an interim measure by recalibrating the original NT00 geobarometer against pressures determined by the Al-in-orthopyroxene geobarometer of Nickel and Green (1985) with the modification by Carswell (1991). Although this correction results in an overall improved agreement with Al-in-orthopyroxene P estimates, it has larger uncertainties, especially at high P (> 4.5 GPa).

In the following study, the solubility of Cr in lherzolitic cpx is re-examined using experimental methods. We present data from twenty-nine new experiments conducted at 3–7 GPa and 1100–1400 °C, which form the basis of a high-P experimental database. This database is used in conjunction with similar experiments from Brey et al. (1990), Taylor (1998), and Walter (1998) to establish an updated Cr-in-cpx geobarometer more suitable for higher mantle pressures. The reliability of our updated calibration is rigorously tested on previously published well-equilibrated natural garnet lherzolite and garnet pyroxenite xenolith datasets from the Diavik-Ekati kimberlite pipes, with P estimates compared to the results obtained from various internally consistent two-phase geothermobarometers.

Methods

Experimental methods

We used three synthetic lherzolite compositions which are variants of the MORB-pyrolite composition of Green and Falloon (1998) (Table 1), recalculated to contain 40% less olivine. The MORB-pyrolite (MPY-40) starting composition is an estimate of the composition of the fertile upper mantle (Green, 2015) and formed the basis for all experimental compositions used in this study. A Cr-enriched MPY-40 composition (Cr-MPY-40) was used in several experiments between 3–4 GPa and 1200–1300 °C. This composition was used to broaden the range of the \({\text{ln}}\left( {\frac{{{\text{Cr}}\#^{{{\text{cpx}}}} }}{{T{ }\left( {\text{K}} \right)}}} \right)\) term (see below) in our calibration, and to synthesise garnet and cpx with Cr# values \(\left( {{\text{Cr}}\# = \left( {\frac{{{\text{Cr}}}}{{{\text{Cr}}{ + }{\text{Al}}}}} \right)} \right)\), similar to those found in depleted cratonic lherzolites (Cr#cpx 0.25–0.30). A Hawaiian pyrolite (Green 2015) (HPY-40) starting composition was used in several experimental runs to test the precision and accuracy of our geobarometer on a non MPY-40 starting composition.

Table 1 Composition of starting mixtures used in experiments for the calibration of the Cr-in-cpx geobarometer
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Starting mixtures were prepared by blending oxide and carbonate powders and synthetic fayalite under acetone, using well-established techniques (Yaxley and Green, 1998). The starting mixtures were loaded into graphite crucibles enclosed with a graphite lid. The graphite capsule was contained in 2.3 × 3.5 mm outside diameter platinum (Pt) capsule which was triple crimped on each end, welded shut, and housed in 12.5 mm length MgO tubing. A 1 mm MgO disk was used to separate the Pt capsule from the thermocouple. Half-inch diameter NaCl sleeves were used as the pressure medium for all piston cylinder experiments. A 12.5 mm length cylindrical graphite furnace was placed between the MgO tubing and the outer NaCl pressure medium. For experiments near and above the NaCl solidus, a Pyrex glass tube was positioned between the NaCl pressure medium and the graphite furnace to prevent the melting of the NaCl.

All experiments were completed at the Research School of Earth Sciences, Australian National University. Experiments at 3, 3.5 and 4 GPa were performed on a 150-tonne end-loaded piston cylinder apparatus from 1100 to 1400 °C. Temperature was measured by a type B Pt–Rh thermocouple. The run durations of these experiments were typically > 120 h. For experiments at 5 and 6 GPa a modified ultra-high pressure, 500-tonne end-loaded piston cylinder was used. The T of these experiments ranged from 1100 to 1400 °C and was also measured with a type B Pt–Rh thermocouple. The run times of these experiments varied from 120 to 168 h. Experiments completed on the 500-tonne piston cylinder were typically pressurized over 1 h and then heated over 30 min. Experimental PT conditions for both piston cylinders were calibrated by the quartz–coesite transition (Bose and Ganguly 1995). A 1200-tonne, Kawai-style split sphere 6/8 multi-anvil apparatus was used for experiments conducted at 7 GPa. The same starting compositions and capsule materials were used as described above. All multi-anvil experiments used a 14/8 anvil cell configuration, and a G2 COMPRESS assembly. Further details of this assembly can be found in Leinenweber et al. (2012). Multi-anvil experiments were pressurized over a 24-h period and heated over 1 h. The T of the multi-anvil experiments was measured with a W–Re thermocouple. The run duration of multi-anvil experiments ranged between 6 and 48 h. The run conditions (P, T, starting composition, duration) of experiments completed in this study are listed in Table 2. The run conditions of the previously published experiments used in our calibration are listed in Table 3. These published experimental datasets are described in greater detail below.

Table 2 Summary of run conditions of the experiments used in this study
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Table 3 Summary of run conditions of previously published experiments used in our calibration
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In preparation for imaging and quantitative analyses, all capsules were removed from their assemblies and mounted in epoxy resin. Once set, capsule mounts were polished down to expose the experimental charge (starting material) and re-impregnated with epoxy under vacuum to seal any cracks. The capsule mounts were polished down to a ¼ µm grit using a diamond lapse and coated with a thin film of carbon for electron probe microanalysis.

Analytical methods

Quantitative analyses of the experimental run products were done by wavelength dispersive spectroscopy (WDS) on a JEOL JXA-8530F + electron probe micro analyser (EPMA) at the Centre for Advanced Microscopy (CAM), Australian National University. A 15 kV accelerating voltage, a beam current of 10 nA, and 1 µm spot size were used routinely for most mineral analyses. Counting times were 20 s (peak and background) for major elements and 30–40 s for minor elements with a total analytical time of approximately 2–3 min. The calibrations were made using a mix of synthetic and natural ASTIMEX Mineralogy standards as follows: Na (albite), Mg (periclase and olivine), Al (sanidine and pyrope), Si (sanidine and diopside), Ca (diopside), Ti (rutile), Cr (chromite), Mn (rhodonite), Fe (haematite and magnetite), and Ni (pentlandite). The limits of detection were typically 70–180 ppm, equivalent to 0.01–0.03 wt% oxide. The data correction was done using the ‘PAP model’ (Pouchou and Pichoir 1991). A total of 10–20 EPMA analyses were typically performed on cpx grains within each sample. Fewer analyses were performed for runs with low modal abundances of cpx. The number of analyses on garnet (grt), orthopyroxene (opx) and olivine (ol) grains typically ranged between 5 and 15 for each sample. Only cpx that crystallised in experiments containing garnet lherzolite or garnet pyroxenite assemblages were used in our calibration. The quality of major and minor element data for cpx was filtered following the strict protocols of Ziberna et al. (2016) whereby cpx analyses with totals < 98 and > 102 wt%, and cation totals < 3.98 and > 4.02 (calculated on the basis of six oxygens in clinopyroxene) were rejected. Published cpx analyses from the Walter (1998) and Taylor (1998) experimental datasets also adhere to the data quality protocols of Ziberna et al. (2016). Because the Brey et al. (1990) analyses were normalized to 100 wt% and four cations in clinopyroxene, it is not possible to apply these data quality protocols to their experiments. However, given that these experiments were used to calibrate the widely-used Brey and Köhler (1990) set of geothermobarometers, it is reasonable to conclude that they are of sufficient quality to be incorporated into the experimental dataset used in this study. The averages of the accepted mineral analyses (in oxide wt%) for each experiment completed in this study are listed in Table 4.

Table 4 Major element analyses by WDS EPMA data for the experimental run products
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Results

Our experiments were generally successful at synthesising a garnet lherzolite, and/or garnet pyroxenite equilibrium assemblage. The size of crystals produced from our experiments typically varied from 10 to 40 µm (Fig. 1a). Garnet and orthopyroxene were usually the largest of these phases (> 25 µm). Back-scattered electron (BSE) images were used to qualitatively identify inhomogeneous regions within crystals prior to WDS analysis. Well equilibrated runs contained phases with well-defined grain boundaries (Fig. 1a) and cation abundances that were approximately homogenous across the entire experimental charge. The presence of significant Fe3+ in garnet and clinopyroxene is unlikely given that our experiments equilibrated in reducing conditions (controlled by the graphite furnace at around the CCO buffer) not suitable for appreciable Fe2+ oxidation. Further, the lack of large deviations on the X2+ and X3+ sites of garnet and clinopyroxene (Table 4) are inconsistent with the presence of large quantities of Fe3+.

Fig. 1
figure 1

BSE image of equilibrated experimental run products. (a) Experiment PT.60 (5 GPa, 1250 °C), (b) CRPT.22 R (3.5 GPa, 1250 °C)

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Clinopyroxene

The size of cpx crystals ranged from < 10 to 30 µm. Compositional zoning and inclusions were not commonly observed in cpx, however, the well-equilibrated rims of the crystals were preferred for microanalysis. The concentration of Cr2O3 and Al2O3 wt% in cpx was consistent with the values expected for a natural cratonic garnet lherzolite and non-cratonic garnet-spinel lherzolite source, with values ranging from 0.57 to 2.0 wt% Cr2O3 and 1.7 to 6.3 wt% Al2O3 (Fig. 2). Na2O in cpx ranged from 0.77 to 3.56 wt %. High Al2O3 cpx were produced from low-P high-T runs, and high Na2O cpx from low-P low-T runs. The Cr# of cpx increased with increasing P, ranging from ca. 0.1‒0.15 at 3 GPa to ca. 0.15‒0.20 between 5 and 7 GPa. The CaO abundance in cpx was comparable to previously published analyses (e.g. Taylor 1998), and ranged from approximately 10 to 20 wt%, which is consistent with the concentrations expected for the PT range of our experiments. The Cr:Na ratio of cpx ranged from 0.11 to 0.76, with a mean value of 0.33.

Fig. 2
figure 2

Clinopyroxene Cr2O3 and Al2O3 wt% classification diagram of Ramsay (1992). Field a: Cratonic garnet-lherzolite. Field b: Non-cratonic garnet and garnet-spinel-lherzolite. Field c: Eclogite, pyroxenite source

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Olivine

The size of experimental olivine crystals ranged from 15 to 40 µm. The Mg# (Mg/(Mg + Fe)) of olivine ranged from 0.84 to 0.96. Olivine grains did not display compositional zoning and crystals were typically free of inclusions.

Garnet

Garnet crystals ranged in size from 20 to > 40 µm. All microanalyses were performed on the well equilibrated rims of these crystals. Well equilibrated garnet displayed well-defined grain boundaries and had cation totals \(\cong\) 8. Garnet synthesized from the Cr-MPY starting composition contained numerous Cr-spinel inclusions (Fig. 1b). The presence of spinel in Cr-enriched systems at high pressures is well known and has been discussed in considerable detail by Klemme (2004). The presence of Cr-rich spinel in these experiments is not expected to affect the solubility of Cr in cpx in equilibrium with garnet. These inclusions were typically < 5 µm and were not quantitatively analysed, and were avoided in the garnet analyses. The concentration of Ca and \(\Sigma\)Fe in garnet decreased with increased P and T, and Mg increased with increased P and T. Cr2O3 contents in the experimental garnets ranged from 1.22 to 5.97 wt %, and the Cr# ranged from 0.03 to 0.17, which broadly covers the range observed in most natural lherzolitic garnets.

Orthopyroxene

Orthopyroxene produced from our experiments ranged in size from 10 to > 50 µm. Orthopyroxene crystals were unzoned and typically free of inclusions. The concentration of Al2O3 in orthopyroxene decreased with increasing P, ranging from 4.33 wt% at 3 GPa to 0.72 wt% at 7 GPa. The concentration of Cr2O3 also decreased with increasing P ranging from 1.17 wt% at 3 GPa to 0.31 wt% at 7 GPa. The concentration of SiO2 and MgO in orthopyroxene increased with P, whereas CaO concentrations increased with increased T. The Mg# of our experimental orthopyroxene ranged from 0.86 to 0.95. The concentration of Na2O ranged between 0.09 and 0.45 wt% and decreased marginally with increasing P. The highest Na2O concentration in orthopyroxene were typically found in samples that equilibrated at low P (< 4 GPa).

Geobarometer calibration

The Cr-in-cpx geobarometer is based on the P dependent exchange of Cr between lherzolitic grt and cpx, expressed by Nimis and Taylor (2000) as:

$${\text{CaMgSi}}_{2} {\text{O}}_{6} + {\text{CaCrAlSiO}}_{6} = \frac{1}{2}\left( {{\text{Ca}}_{2} {\text{Mg}}} \right){\text{Cr}}_{2} {\text{Si}}_{3} {\text{O}}_{12} + \frac{1}{2}\left( {{\text{Ca}}_{2} {\text{Mg}}} \right){\text{Al}}_{2} {\text{Si}}_{3} {\text{O}}_{12}$$
(1)

Or

$${\text{di}} + {\text{CaCrTs}} = { }\frac{1}{2}{\text{uv}}_{2} {\text{kn}}_{1} + \frac{1}{2}{\text{grs}}_{2} {\text{pyrp}}_{1}$$
(2)

where diopside (di) and the CaCr Tschermak components in cpx (CaCrTs) react to give uvarovite (uv), knorringite (kn), grossular (grs), and pyrope (pyp) components in coexisting garnet. The corresponding equilibrium constant for this reaction is defined as:

$${\text{K}} = \frac{{\left[ {a_{{{\text{grs}}_{2} {\text{pyp}}_{1} }}^{{{\text{grt}}}} } \right]^{\frac{1}{2}} \cdot \left[ {a_{{{\text{uv}}_{2} {\text{kn}}_{1} }}^{{{\text{grt}}}} } \right]^{\frac{1}{2}} }}{{\left[ {a_{{{\text{di}}}}^{{{\text{cpx}}}} } \right] \cdot \left[ {a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} } \right]}}$$
(3)

However, development of this geobarometer through an equilibrium constant requires thermodynamic data that is overcomplicated given the intended purpose of this geobarometer and, in some instances, are unavailable (see Nimis and Taylor, 2000 for discussion). As an alternative, we have continued to pursue this geobarometer in a similar manner to NT00 by using only the activity of the CaCrTs component of cpx. We have calculated \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) using the same formulation as the original NT00 calibration, which is defined as:

$$a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} = {\text{Cr}} - 0.81 \cdot {\text{Cr}}\#^{{{\text{cpx}}}} \cdot \left( {{\text{Na}} + {\text{K}}} \right)$$
(4)

The basis on which \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) in cpx is estimated is explained in greater detail in Nimis and Taylor (2000). Multiple linear regressions of our experimental dataset, which includes experiments completed in this study (Table 2) and the previously published experiments of Taylor (1998), Walter (1998) and Brey et al. (1990) (Table 3), using T(K), Cr#cpx, and \(- T{ }\left( {\text{K}} \right){\text{ ln}}\left( {a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} } \right)\) gave the following expression for P (Fig. 3):

$$P\left( {{\text{GPa}}} \right) = 11.03 + \left( { - T{ }\left( {\text{K}} \right){\text{ ln}}(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} ) \times 0.001088{ }} \right) + \left( {1.526 \times {\text{ln}}\left( {\frac{{{\text{Cr}}\#^{{{\text{cpx}}}} }}{{T{ }\left( {\text{K}} \right)}}} \right)} \right){ }$$
(5)
Fig. 3
figure 3

Variation in \({ - }{\rm T}({\text{K}}),\;\ln \,{(}a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} )\) and \(\ln \,\left( {\frac{{{\text{Cr}}\#^{{{\text{cpx}}}} }}{{T({\text{K}})}}} \right)\) plot against experimental P (kbar) using the experiments described in Tables 2 and 3

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where \({\text{Cr}}\#^{{{\text{cpx}}}} = \left( {\frac{{{\text{Cr}}}}{{{\text{Cr}} + {\text{Al}}}}} \right)\), \({ }a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} = {\text{Cr}} - 0.81 \cdot {\text{Cr}}\#^{{{\text{cpx}}}} \cdot \left( {{\text{Na}} + {\text{K}}} \right),{ }\) with all mineral components calculated assuming six oxygen anions per formula unit in clinopyroxene.

High P experiments from Walter (1998) and Brey et al. (1990) were used in our calibration to increase the number of data points at pressures above 5 GPa. Both experimental datasets used complex starting compositions similar to those listed in Table 1, which resulted in similar phase compositions to those reported in Table 4 at comparable PT conditions. The Walter (1998) experiments also provided a greatly extended T range, which widened the surface of the \({\text{ln}}\left( {\frac{{{\text{Cr}}\#^{{{\text{cpx}}}} }}{{T{ }\left( {\text{K}} \right)}}} \right)\) axis in Fig. 3. Although the experiments of Walter (1998) were completed at near- solidus temperatures (see Table 3), these experiments provide an important constraint for cpx with low aCaCrTs. The inclusion of these experiments into our calibration improved the overall fit of our geobarometer regression equation to the experimental dataset. Thus the inclusion of these experiments in our dataset and calibration increases the R2 of the geobarometer regression equation from approximately 0.93 to 0.963, with only a very slight change in estimated P (< 0.1 GPa) relative to that based solely on our new experiments when applied to natural cpx from Diavik. Some lower pressure experiments of Taylor (1998) were also incorporated into our experimental dataset to help strengthen the performance of our calibration at P < 3 GPa. These experiments were performed using an HPY-40 starting composition which produced cpx with similar compositions as those reported in Table 4. The temperatures for the Taylor (1998) experiments ranged between 1050 and 1250 °C. Similarly, including the Taylor (1998) experiments in our calibration increases the R2 value from 0.94 to 0.96, again with only minimal differences in estimated P (< 0.1 GPa) relative to a calibration based solely on our new experiments when applied to natural cpx from Diavik. The improved statistics and extended compositional range covered justify the inclusion of these additional experimental data in our calibration dataset.

Propagation of uncertainties

The measured PT conditions of multi-anvil, belt and piston cylinder experiments, and the measured major and minor oxide concentrations by WDS are all subject to small but cumulative uncertainties. In addition, experimental P between 4 and 7 GPa are subject to a higher degree of uncertainty than experiments below 4 GPa. To accurately determine the error of the estimated P of our updated geobarometer we have propagated all analytical and experimental uncertainties. In Eq. (5), uncertainties exist in the Cr, Na, and Al abundances measured by WDS, and the experimentally determined P and T. As suggested by Ziberna et al. (2016), the influence of analytical uncertainties on the very minor K contents can safely be neglected. The experimental P of piston cylinder experiments conducted below 4 GPa is subject to an estimated uncertainty of approximately 3%. For experiments P between 4–6 GPa and above 6 GPa this estimated uncertainty increases to approximately 5 and 7.5%, respectively. The W–Re and Pt–Rh thermocouples used to measure experimental T are highly precise and have an uncertainty of ~ 1%. Using the conventional WDS EPMA analytical procedure described above, the maximum uncertainty in the measured concentrations of Cr2O3, Na2O, and Al2O3 are 5.4, 2.2, and 4.1%, respectively. These uncertainty values were obtained by performing repeated measurements on an ASTIMEX Mineralogy Cr-diopside standard using the analytical conditions described in the methods section. The uncertainty in estimated P for our updated geobarometer calibration was determined by taking the square root of the sum of the squares of these errors (in percentage), which is defined by the following equation:

$$\delta P = \sqrt {(\delta P{\text{exp}})^{2} + (\delta T{\text{exp}})^{2} + (\delta {\text{Cr}})^{2} + (\delta {\text{Na}})^{2} + (\delta {\text{Al}})^{2} }$$

This approach results in uncertainty values of \(\pm\) 0.31 GPa for P estimates below 4 GPa, \(\pm\) 0.35 GPa between 4–6 GPa, and \(\pm\) 0.41 GPa for P estimates above 6 GPa.

Compositional effects

We investigate compositional effects on the performance of our updated Cr-in-cpx geobarometer by comparing the difference of the experimental P and the calculated P for our updated geobarometer (Pexp − Pcalc) against the concentration of various cations in cpx. We also compare the difference between the Brey and Köhler (1990) (BKN90) calculated P and the calculated P of our updated geobarometer (PBKN90 − Pcalc) with the composition of natural cpx from xenoliths sampled by the Diavik-Ekati kimberlite pipes.

For our experimental database, the Pexp − Pcalc ranges between −0.68 and 0.93 GPa, with a mean difference of −0.017 GPa. The variation in Pexp − Pcalc does not show any major correlation with the changes in the abundances of major cations in cpx. This is contrast to the original NT00 calibration, which has a Pexp − Pcalc that ranges between −0.33 GPa at lower P and > −1 GPa (−1.76) at 7 GPa (Fig. 4 a, b). The NT00 calibration also shows strong systematic correlations between Al, Cr, and Na with Pexp − Pcalc (Fig. 4 d, f, h) in contrast to our revised calibration (Fig. 4 c, e, g). Additionally, the variation in Pexp − Pcalc for our updated calibration does not show any major systematic correlation with \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) (Fig. 5a) whereas the original NT00 calibration exhibits a strong increase in Pexp − Pcalc with decreasing \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) (Fig. 5b). The calculated pressures using the BKN90 Al-in-orthopyroxene geobarometer and our updated calibration (PBKN90 − Pcalc) for xenoliths from the Diavik-Ekati kimberlite pipes are generally in good agreement with a mean difference of −0.23 GPa and ranging between −3.1 and + 2.9 GPa in the worst-case examples. Two major trends are observed from the comparison of PBKN90 − Pcalc with the composition of cpx. Firstly, PBKN90 − Pcalc is typically high for cpx that are strongly enriched in Al (> 0.20 Al cations per six oxygen anions in clinopyroxene) (Fig. 6a). Similarly, departures from agreement between the two geobarometers are also observed for cpx with low Cr# (< 0.10) (Fig. 6b). These compositions typically correspond to high temperature, off-craton cpx derived from spinel-garnet bearing peridotites. Secondly, PBKN90 − Pcalc increases with increasing Na in cpx. For cpx with > 0.20 Na cations, the PBKN90 − Pcalc was typically > 1 GPa. One highly sodic cpx (> 0.35 Na cations) recorded a PBKN90 − Pcalc of 3 GPa (Fig. 6c). Highly sodic cpx are commonly observed in eclogite xenoliths. The magnitude of PBKN90 − Pcalc is generally higher at very low levels of \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) (Fig. 6d). This trend reflects the increase in uncertainty of P estimates at high P (> 6 GPa) and low \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\). The relationship between PBKN90 − Pcalc with \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) and \(\left( {\frac{{a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} }}{{{\text{Cr}}\#^{{{\text{cpx}}}} }}} \right)\) does not exhibit any systematic trends or systematic differences which may otherwise suggest a bias or error in the calibration (Fig. 6e).

Fig. 4
figure 4

Comparison between Pexp − Pcalc and the composition of cpx using our updated Cr-in-cpx geobarometer and the original NT00 geobarometer. Diagram is constructed using cpx from the experiments listed in Tables 2 and 3. Pcalc is calculated P in GPa using either the updated geobarometer presented in this study (filled circles) or the original NT00 geobarometer (open circles) pressure for both geobarometers were made using the fixed experimental T

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Fig. 5
figure 5

Comparison between Pexp − Pcalc and the \(\left( {a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} } \right)\) of cpx using our updated Cr-in-cpx geobarometer and the original NT00 geobarometer. Diagram is constructed using cpx from the experiments listed in Tables 2 and 3. Symbols as Fig. 4

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Fig. 6
figure 6

Comparison between PBKN90 − Pcalc and the composition of cpx using our updated Cr-in-cpx geobarometer and the original NT00 geobarometer. Diagram is constructed using cpx and xenolith data from the Diavik-Ekati kimberlite pipes. BKN90 is Brey and Köhler (1990) Al-in-orthopyroxene equilibration P, calculated using the T estimates of the Brey and Kohler two-pyroxene solvus geothermometer. See Comparison and application for Diavik-Ekati sample references

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We therefore recommend the following updated compositional filters when applying our updated Cr-in-cpx geobarometer to natural xenolith and xenocryst cpx:

  • The Cr2O3–Al2O3 cpx source lithology discrimination diagram of Ramsay (1992) (Fig. 5 of Nimis and Taylor, 2000) should be used as a first pass filter for removing high alumina cpx which may have been derived from high-temperature, off-craton spinel bearing peridotites. We suggest that P estimates on cpx outside of fields a and b on Fig. 2 should be interpreted with caution. The Cr2O3–Al2O3 relationship in cpx should also be used to test equilibrium with garnet. Cpx from the on-craton grt-peridotite field are preferred for single grain Cr-in-cpx geobarometry.

  • P estimates on highly sodic cpx (> 0.20 Na cations) should be interpreted with caution regardless of Cr2O3 concentration in cpx. This filter should be used in conjunction with the Cr2O3–Al2O3 cpx source lithology discrimination diagram to determine whether a sodic cpx was derived from an eclogitic source. P estimates on eclogitic cpx should be discarded.

  • The Cr#cpx protocol of Ziberna et al. (2016) should be used to filter cpx with unsafe Cr# values, whereby Cr#cpx outside of the range 0.10–0.65 should be discarded.

  • We recommended the same data quality protocols as discussed above (see Ziberna et al. 2016), whereby cpx analyses with totals < 98 and > 102 wt%, and cation totals < 3.98 and > 4.02 (calculated on the basis of six oxygens in clinopyroxene) should be avoided.

  • The \(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}}\) range of the Cr-in-cpx geobarometer is extended to a lower concentration than suggested by NT00 and Ziberna et al. (2016). We recommend a lower limit of 0.005 for \(\left( {\frac{{a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} }}{{{\text{Cr}}\#^{{{\text{cpx}}}} }}} \right)\) in cpx, and analyses with below 0.005 should be discarded.

Comparison and applications

Garnet-lherzolite and garnet-pyroxenite xenoliths from the Diavik kimberlite pipe

An extensive database of analyses of cpx from garnet lherzolite and garnet pyroxenite xenoliths from the Diavik and Ekati kimberlite pipes within the Lac De Gras field in Canada’s Northwest Territories (Aulbach et al. 2007; Creighton et al. 2010; Yaxley et al. 2017) has been used to test our updated Cr-in-cpx geobarometer. This database also includes a large dataset of cpx analyses sourced from heavy mineral concentrate (Supplementary File 1). A garnet peridotite/pyroxenite source for cpx from heavy mineral concentrate was confirmed through the use of the Cr2O3–Al2O3 cpx source lithology discrimination diagram of Ramsay (1992). PT estimates were calculated using the original NT00 calibration and our updated calibration of the Cr-in-cpx geobarometer in combination with the NT00 en-in-cpx geothermometer. For xenoliths, PT estimates were also determined using the BKN90 Al-in-orthopyroxene geobarometer and BKN90 two-pyroxene solvus geothermometer, and Nickel and Green (1985) Al-in-orthopyroxene geobarometer paired with the Taylor (1998) two-pyroxene solvus geothermometer. The P estimates for the various calibrations range from 3 to 7 GPa. The P estimates were broadly comparable below 4.5–5 GPa, however, the estimates on high P samples (≥ 4.5 GPa) showed an increasingly significant difference between the NT00 and our updated calibration of the Cr-in-cpx geobarometer (Table 5). The PT estimates for well-equilibrated xenoliths determined by our updated calibration were typically comparable to the Brey and Köhler (1990) estimates (Table 5). Xenoliths derived from P > 6.5 GPa provided a higher equilibration P when our updated calibration was applied. Similar observations were made for comparisons to the Nickel and Green (1985) and Taylor (1998) geothermobarometer (Table 5).

Table 5 Comparison of estimated PT conditions (in GPa, °C) for selected equilibrated mantle xenoliths from various kimberlite pipes
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The PT estimates for the Diavik-Ekati xenoliths and xenocrysts using both the NT00 original and our revised Cr-in-cpx geobarometer [Eq. (5)] were used to construct paleogeotherms using the FITPLOT algorithm (Mather et al. 2011) (Fig. 7). Paleogeotherms were calculated assuming a 40 km crustal thickness (Davis et al. 2003; Snyder, 2008), and mantle isentrope of 1330 °C. The PT estimates using our modified calibration constitute a steep paleogeotherm that intersects the mantle isentrope approximately between 235 and 250 km (Fig. 7a). The estimates using the NT00 calibration form a shallower paleogeotherm that intersects the isentrope at the slightly shallower depth of approximately 210–220 km (Fig. 7b). The estimated depth to the lithosphere-asthenosphere boundary (LAB) using our updated calibration is comparable to LAB estimates of ~ 190‒250 km for the central Slave Craton derived previously from geothermobarometry on mantle xenoliths and xenocrysts (Griffin et al. 1999, 2004; Aulbach et al., 2018) and from various geophysical techniques, including magneto-telluric (MT) methods (Jones et al., 2003), seismic tomography (Bank et al. 2000), and through strain rate measurements (Eaton et al. 2009).

Fig. 7
figure 7

Paleogeothermal gradients for the Lac De Gras (Diavik-Ekati) kimberlite field (Canada). The paleogeotherms were constructed using FITPLOT (Mather et al. 2011) using PT data derived from (a) our revised Cr-in-cpx geobarometer [Eq. (5)], and (b) the original Nimis and Taylor (2000) calibration. T for both geobarometers were calculated using the NT00 en-in-cpx single crystal geothermometer, with the final PT estimate solved by iteration. See text and Supplementary File 1 xenocryst data. See text for FITPLOT input parameters and sample references. Shaded margin is the FITPLOT error only. Graphite-diamond transition from Kennedy and Kennedy (1976)

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Cr diopside xenoliths and xenocrysts from the Argyle lamproite pipe

Equilibration PT conditions were also calculated for a suite of Cr-diopside xenocrysts from heavy mineral concentrate (Jaques et al. 2018) and mantle peridotite xenoliths (Luguet et al. 2009) from the Argyle lamproite pipe in Western Australia. This provides a practical example of the usefulness of single-crystal geothermobarometry as the garnet in the Argyle mantle peridotites is typically retrogressed and altered (Jaques et al. 1990). A FITPLOT paleogeotherm was calculated for a crustal thickness of 42 km crustal thickness (Kennett et al. 2011) and other parameters as above using our revised Cr-in-cpx geobarometer and the original NT00 geobarometer (Fig. 8). The FITPLOT paleogeotherm based on our Cr-in-cpx calibration is steeper than that generated from the NT00 calibration and results in an estimated LAB 210‒215 km compared with 200 km for the NT00 calibration (Fig. 8). The estimated LAB depth at 210‒215 km compares well with s wave seismic tomography models which indicate a present-day lithospheric thickness of ~ 200‒250 km (Fishwick and Rawlinson, 2012; Hoggard et al. 2020).

Fig. 8
figure 8

Paleogeothermal gradients for the Argyle lamproite (Australia). The paleogeotherms were constructed using FITPLOT (Mather et al. 2011) using PT data derived from (a) our revised Cr-in-cpx geobarometer [Eq. (5)], and (b) the original Nimis and Taylor (2000) calibration. T for both geobarometers were calculated using the NT00 en-in-cpx single crystal geothermometer, with the final PT estimate solved by iteration. See text for xenocryst references. See text for FITPLOT input parameters. Shaded margin is the FITPLOT error only. Graphite-diamond transition from Kennedy and Kennedy (1976)

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Conclusions

An updated high-P experimental dataset that includes mineral data from new experiments conducted between 3–7 GPa and 1050–1400 °C, and published data from Brey et al. (1990), Taylor (1998) and Walter (1998) has been used to re-examine the solubility of Cr in cpx in garnet-bearing lherzolites. Statistical treatment of this dataset has derived an alternative calibration for the widely used Nimis and Taylor (2000) Cr-in-cpx geobarometer. Our modified calibration addresses the progressive and systematic underestimation of P above 4 GPa by the original NT00 Cr-in-Cpx geobarometer calibration. The empirical recalibration of NT00 geobarometer proposed by Nimis et al. (2020) appears to provide a closer approximation for pressures in the 4.5–6 GPa interval but still carries significant uncertainties at higher pressure due to the small number of xenoliths equilibrated at and above 6 GPa. The improved reliability and precision of our calibration for P estimates > 5 GPa has been demonstrated through application to cpx from garnet-lherzolite and garnet-pyroxenite xenoliths from the Diavik-Ekati kimberlite and Argyle lamproite pipes. The estimated paleogeotherms constructed using our new PT estimates differ slightly from previous estimates based on the NT00 geobarometer, resulting in a modest but significant increase in the estimated lithospheric thickness beneath these kimberlites and lamproite. Our updated paleogeotherms for Diavik-Ekati and Argyle are in line with estimates from seismic tomography and MT surveys. Application of the new calibration of the Cr-in-cpx geobarometer can be expected to result in higher P estimates for Cr-diopside xenoliths and xenocrysts derived from garnet-lherzolites equilibrated at pressures beyond 5 GPa relative to the NT00 version. These estimates will lead to deeper estimates of the depth to the LAB beneath many cratons, which will allow the nature of the cratonic lithosphere to be more accurately studied in future investigations.