Trace-element geochemistry of diamond-hosted olivine inclusions from the Akwatia Mine, West African Craton: implications for diamond paragenesis and geothermobarometry

Trace-element concentrations in olivine and coexisting garnets included in diamonds from the Akwatia Mine (Ghana, West African Craton) were measured to show that olivine can provide similar information about equilibration temperature, diamond paragenesis and mantle processes as garnet. Trace-element systematics can be used to distinguish harzburgitic olivines from lherzolite ones: if Ca/Al ratios of olivine are below the mantle lherzolite trend (Ca/Al < 2.2), they are derived from a harzburgitic mantle source, and syngenetic garnets are without exception subcalcic G10 garnets. For harzburgitic olivines that cannot be identified this way, Na and Ca contents can be used: olivine inclusions with < 60 µg/g Na and Na/Al < 0.7 are all harzburgitic, whereas those with > 300 µg/g Ca or > 60 µg/g Na are lherzolitic. Conventional geothermobarometry indicates that Akwatia diamonds formed and resided close to a 39 mW/m2 conductive geotherm. A similar value can be derived from Al in olivine geothermometry, with TAl-ol ranging from 1020 to 1325 °C. Ni in garnet temperatures is on average somewhat higher (TNi-grt = 1115–1335 °C) and the correlation between the two thermometers is weak, which may be not only due to the large uncertainties in the calibrations, but also due to disequilibrium between inclusions from the same diamond. Calcium in olivine should not be used as a geothermobarometer for harzburgitic olivines, and often gives unrealistic P–T estimates for lherzolitic olivine as well. Diamond-hosted olivine inclusions indicate growth in an extremely depleted (low Ti, Ca, Na, high Cr#) environment with no residual clinopyroxene. They are distinct from olivines from mantle xenoliths which show higher, more variable Ti contents and lower Cr#. Hence, most olivine inclusions in Akwatia diamonds escaped the refertilisation processes that have affected most mantle xenoliths. Lherzolitic inclusions are probably the result of refertilisation after undergoing high-degree melting first. Trivalent cations appear to behave differently in harzburgitic diamond-hosted olivine inclusions than lherzolitic inclusions and olivine from mantle xenoliths. Some divalent chromium is predicted to be present in most olivine inclusions, which may explain high concentrations up to 0.16 wt% Cr2O3 observed in some diamond inclusions. Strong heterogeneity of Cr, V and Al in several inclusions may also result in apparent high Cr contents, and is probably due to late-stage processes during exhumation. However, in general, diamond-hosted olivine inclusions have lower Cr and V than expected compared to mantle xenoliths. Reduced Na activity in depleted harzburgites limits the uptake of Cr, V and Sc via Na–M3+ exchange. In contrast, Al partitioning in harzburgites is not significantly reduced compared to lherzolites, presumably due to uptake of Al in olivine by Al–Al exchange.


Introduction
The subcontinental lithospheric mantle (SCLM) beneath cratons has been studied extensively as it is a key source of information about the geological and tectonic history of the early Earth. As the main source of diamonds, it is also an important economic reservoir. Olivine is a common inclusion in such diamonds (Sobolev et al. 2008;Stachel and Harris 2008), as well as the most common mineral in Earth's upper mantle, and may as such be an important tool in elucidating mantle and diamond formation processes. However, due to its low trace element contents and the lack of an empirical framework to interpret olivine data, its full potential has not been explored (De Hoog et al. 2010;Foley et al. 2013) and it is rarely used as an indicator mineral for diamond prospecting (e.g., Shchukina and Shchukin 2018).
Inclusions in diamonds are of particular interest because diamonds are robust containers shielding inclusions from secular processes in the Earth's mantle, and thus provide a window into early mantle processes that have been overprinted in mantle xenolith suites (Stachel and Harris 2008). For example, it has been noted that garnet inclusions in diamonds contain a much larger fraction of Ca-depleted garnets than mantle xenoliths from the same locality, and that olivine inclusions in diamonds can have much higher Cr 2 O 3 contents (up to 0.5 wt%) than commonly recorded in olivine from mantle xenoliths (up to 0.1 wt%; De Hoog et al. 2010;Hervig et al. 1980b;Sobolev et al. 2009;Stachel and Harris 2008).
Diamond formation is associated with garnet-bearing sections of the SCLM in which harzburgites predominate over lherzolites (Gurney et al. 1993). Harzburgitic assemblages with strongly Ca-depleted garnets (G10 garnets; Dawson and Stephens 1975;Grütter et al. 2004) are of particular interest, as these are indicators for diamondiferous kimberlites (Gurney 1984;Gurney et al. 1993). Peridotitic inclusions in diamonds have been subdivided into lherzolitic and harzburgitic paragenesis (i.e., mantle source lithologies) based on the presence or absence of cpx and the Ca-saturation of garnet (Sobolev et al. 1973;Stachel and Harris 2008). However, many diamonds contain olivine inclusions only and currently no criteria exist to date to determine their paragenesis. Attempts to use olivine in diamond exploration have mainly focussed on identifying olivine from kimberlite, i.e., as a kimberlite indicator mineral (e.g., Matveev and Stachel 2007;Shchukina and Shchukin 2018), but this gives little indication about diamond potential. An olivine classification scheme that would identify harzburgitic olivines would increase its potential for use as a diamond indicator mineral.
Inclusions in diamonds may also provide constraints on the pressure-temperature conditions of diamond formation. These conditions can be estimated based on the chemical composition of co-existing minerals within the diamond, assuming that they were trapped simultaneously (i.e., syngenetic) or at least under similar chemical and P-T conditions. The requirement of equilibrium between co-existing minerals does not apply to single-element thermometers, such as single cpx thermobarometry (Nimis and Taylor 2000), Al in olivine thermometry (De Hoog et al. 2010) or Ni in garnet (Canil 1996;Ryan et al. 1996), as these are assumed to be in equilibrium with a relatively constant source. However, few, if any, studies have evaluated the validity of olivine-based single-element thermometers for diamond-hosted inclusions.
A further source of uncertainty in interpreting trace element data is the influence of the chemical environment on trace element partitioning. For example, different exchange mechanisms appear to operate for Cr and Al in olivine in spinel vs. garnet peridotites (De Hoog et al. 2010;Witt-Eickschen and O'Neill 2005). As Na may act to charge balance trivalent cations (De Hoog et al. 2010;Hervig et al. 1986), the absence of clinopyroxene in harzburgitic lithologies prevalent in the mantle source of diamonds may affect trace element distributions and its use in tracing mantle processes and geothermometry.
This study aims to evaluate: diamond paragenesis based on the trace element compositions of olivine inclusions, the validity of trace element geothermometry, and the use of olivine to study mantle processes. The diamond suite used is from Akwatia, Ghana, in which olivine is a common inclusion and frequently co-exists with garnet (Stachel and Harris 1997a, b). It is, therefore, an ideal suite for the purpose of this study.

Previous work on trace elements in mantle olivine
Due to the low concentrations in olivine of many elements that are major or minor elements in co-existing minerals, trace element data for olivine are relatively scarce. Routine analytical settings for EMPA analysis often result in inadequate precision and detection limits for elements such as Na, Al, Ca, Cr and Ti in olivine, especially in mantle peridotites, where concentrations of these elements are particularly low. Therefore, analysis of these elements needs to be done by LA-ICP-MS (De Hoog et al. 2010;Foley et al. 2013) or SIMS (Hervig et al. 1986;Steele et al. 1981), or using a dedicated trace element routine by EPMA (Batanova et al. 2015). Alternatively, bulk analysis may yield excellent results, but extreme care needs to be taken to pick clean olivine grains clear of fractures and inclusions (Stead et al. 2017). Due to their even lower concentrations, most trace elements other than the above-mentioned are only achievable by LA-ICP-MS (Stead et al. 2017;Witt-Eickschen and O'Neill 2005), but this is a destructive technique usually not suitable for precious samples such as diamond-hosted inclusions.
Despite these analytical challenges, work on trace elements in olivine goes back to the early 1980s. A small set of trace elements in olivine from spinel peridotites was presented by Stosch (1981), who used temperature-dependent partitioning of Sc and Cr between olivine and cpx to derive single-element geothermometers. A set of pioneering studies by Hervig and collaborators (Hervig and Smith 1982;Hervig et al. 1980aHervig et al. , b, 1986Steele et al. 1981) presented trace-element data of olivine and co-existing minerals from a wide range of mafic to ultramafic rocks including kimberlite-derived lherzolites and harzburgites, as well as olivine inclusion in diamonds. They noticed temperature-dependent partitioning of elements such as Cr, Al and Na, and suggested the use of TiO 2 to trace mantle metasomatism. A large excess of Cr was reported in some olivine inclusions in diamonds and a different crystallisation environment was inferred (Hervig et al. 1980b). Temperature dependence of trace element partitioning in spinel peridotites was studied in more detail by Witt-Eickschen and O'Neill (2005), but no Al or Na was measured in their olivines. Sobolev et al. (2008Sobolev et al. ( , 2009) presented a large dataset of minor element data from olivine inclusions in diamonds, which showed a large variation in elements such as Ca and Cr, and distinct differences between diamond-hosted olivine inclusions and olivine from mantle xenoliths. De Hoog et al. (2010) presented a large database of olivine trace element data from mostly garnet-bearing lherzolitic mantle xenoliths from a variety of tectonic settings, which allowed them to calibrate several single-element geothermometers, of which the Al in olivine thermometer was the most promising, as well as identify geochemical parameters diagnostic for various mantle processes, such as melting and refertilisation. A review paper by Foley et al. (2013) expanded on the dataset by De Hoog et al. (2010) by including a wide suite of igneous rocks and showing olivine to be a sensitive tracer of melt metasomatism. Recent work has also provided data for supra-subduction zone xenoliths, an important reservoir (Ionov 2010;Pirard et al. 2013;Tollan et al. 2017) missing from previous compilations. The increase in interest of the behaviour of H in nominally anhydrous minerals has led to many studies about the interaction between trace element uptake in olivine with hydrogen (e.g., Berry et al. 2005Berry et al. , 2007Tollan et al. 2018), showing that trace element partitioning can be strongly influenced by the chemical environment.
Despite all the work mentioned above, olivine data from garnet peridotites are still scarce and existing datasets are often incomplete. For instance, garnet peridotite data in Foley et al. (2006) and Glaser et al. (1999) lacked Al and Na or Ca, whereas the large available dataset of olivine inclusions in diamonds (Sobolev et al. 2009) lacks Na and other trace elements such as V and Sc, whilst Ti is often near the detection limit of the EPMA technique. Due to incomplete datasets, trace element exchange mechanisms in olivine from garnet peridotite are still poorly constrained, and so are potential effects on empirically derived trace element geothermobarometers. This is particularly true for diamondhosted olivine inclusions.

Samples
The alluvial Birim diamond fields near Akwatia, Ghana, are located within Birimian (Early Proterozoic) metasedimentary rocks forming the south-eastern part of the West Africa Craton (Chirico et al. 2010; see also Electronic Supplement, Fig. S1). Akwatia diamonds show little evidence of transport and are associated with metamorphosed ultramafic rocks with a composition resembling komatiite or boninitetype volcanic rocks, similar to occurrences at Dachine in French Guyana and at Wawa in Ontario, Canada (Canales and Norman 2003). The eruption age of the diamonds is around 2.2 Ga (Gurney et al. 2010). They contain abundant silicate inclusions of peridotitic ( Fig. 1), the most abundant of which is olivine (66% of inclusions are monomineralic olivine, another 15% occur in bimineralic and tri-mineralic assemblages; Stachel and Harris 1997b). The diamonds are dominantly derived from an initially strongly depleted but subsequently refertilised mantle source (Stachel and Harris 1997a).
This study presents new major and trace element data for 28 olivine inclusions from 25 Akwatia diamonds, as well as for garnets coexisting with 23 of the olivines. Of these inclusions, 5 are of lherzolitic paragenesis (co-existing with Fig. 1 Photographs of Akwatia diamonds containing silicate mineral inclusions. Left: diamond with red inclusions of pyrope garnet; right: diamond with pale-green to transparent olivine inclusions. Diamond size ca. 3 mm lherzolitic garnet or cpx), 19 are harzburgitic (co-existing with harzburgitic garnet) and 4 belong to the peridotitic suite but are of unknown paragenesis (no co-existing garnet or cpx).
Silicate inclusions were extracted by crushing the host diamond, embedded in epoxy and polished to a ¼ µm finish. Most inclusions were euhedral to subhedral in shape and mostly 100-500 µm in size; typical examples are shown in Fig. 3. No spatial information about the inclusions was recorded, other than that none of the inclusions were touching.

Electron microprobe
Major and minor elements were measured by electron probe Cameca SX-100 in the School of GeoSciences, University of Edinburgh. Major elements Mg, Si and Fe were measured using a 10 nA beam current at 15 kV and a counting time of 60 s on both peak and background, whereas minor elements were measured using a higher beam current of 80 nA and longer counting times of 240 s (Na, Al, Ca, Cr) or 120 s (Mn, Ni) on both peak and background. Calibration standards were forsterite (Mg, Si), fayalite (Fe), wollastonite (Ca), Mg spinel (Al), jadeite (Na) and pure metals for the remaining elements (Cr, Ni, Mn). Accuracy and precision were monitored by repeat analysis of San Carlos olivine from USGS (USNM# 111312/44;Jarosewich et al. 1980), in-house olivine standard DC0212 (see De Hoog et al. 2010, for preparation and details) and an in-house Cr-diopside standard, the latter mainly to monitor elements which are low in olivine (Na, Al, Ca, Cr). Four or five analyses were performed for each olivine to test their homogeneity.

Ion microprobe-olivine trace elements
Trace elements were measured by secondary ion mass spectrometry (SIMS) using the Cameca ims-4f at Edinburgh Ion Microprobe Facility. A 10 nA 16 O − primary beam was focussed and impacted onto the samples at 14.5 kV; sputtered high-energy (75 ± 25 eV) positive secondary ions were collected at low mass resolution in six cycles of 5 s for each isotope, except 47 Ti, which was measured for 15 s/cycle. Spot size was approximately 15 × 20 µm. The following isotopes were measured (those in brackets were used for interference corrections, see details below): 7  A small contribution of 30 Si 16 O 2 -62 Ni was considered negligible due to the high Ni content of olivine. Average molecular production rates for SiO + /Si + and MgSi + / Si + were 0.29% and 0.11%, respectively. As a check for the validity of the MgMg correction on V and Cr, it was measured on mass 48 as 24 Mg 24 Mg after correction 48 Ca, 48 Ti and 30 Si 18 O and compared to MgMg measured on mass 49 (see step 3 above). The difference in V concentration calculated using MgMg measured on mass 48 or 49, respectively, was generally < 3%, showing that the analytical uncertainty added due to the interference corrections was small.
Although the measurements could have been made using high mass resolution of ca. 3000 (M/ΔM) to resolve molecular interferences, this would have been detrimental for the analysis of elements with low signals, in particular Sc, Ti and V.
Calibration was performed using in-house olivine standard DC0212 (LA-ICP-MS value, Table 3 in De Hoog et al. 2010), which was measured at least once every 4-8 analyses, using 30 Si as an internal standard. Standard deviation of 15 repeats on the standard was better than 5% for all elements except P (10%) and Sc (20%). To verify that SIMS data gave similar results as LA-ICP-MS data, olivine grain from selected Kaalvallei xenoliths from De Hoog et al. (2010) was re-analysed by SIMS. Agreement is overall excellent (Electronic Supplement, Fig. S2).

Ion microprobe-garnet trace elements
Selected trace elements in garnet were measured (Ti, Sc, Ni, V, Co)  To use Ni in garnet as a thermometer, accuracy of the Ni content is essential. Therefore, in-house garnet standards that were prepared specifically for this application were used for calibration (Ivanic 2007). Nickel contents of the standards range from 41 to 140 µg/g and they have major element contents representative of those observed in mantlederived garnets. The same standards were used to calibrate TiO 2 and Cr 2 O 3 . Working curves for Ni, Ti and Cr show excellent correlations (r 2 = 0.995-0.999; Electronic Supplement, Fig. S3). 57 Fe was used as internal standard using FeO contents measured by electron probe micro-analysis. Sc and Co were calibrated using two garnet standards (KP1, Binge Binge Point, and DDI, Dutsen Dushowo; Irving and Frey 1978). As V content is not known for any of the garnet standards in this study, it was measured by SIMS Cameca ims-4f at EIMF, University of Edinburgh. A 16 O − beam of 5 nA was impacted onto the samples at 14.5 kV; sputtered positive ions were collected with 75 V energy offset in 10 cycles of 5 s for each isotope. Spot size was approximately 30 × 25 µm. Measured isotopes were 30 Si, 45 Sc, 47 Ti, 51 V, 52 Cr, 55 Mn and 60 Ni. Molecular interferences were negated using high mass resolution (M/ΔM ca. 2400 at 5% peak width). Basaltic glasses GSE1-G and GSD1-G were used for calibration (Jochum et al. 2005). Vanadium contents of KP1 and DDI garnet standards were determined as 41 and 134 µg/g, respectively. Other elements agreed well with the data by Irving and Frey (1978).

Major elements
The olivine inclusions presented here are a subset of a larger suite of inclusions documented previously by Stachel and Harris (1997b). New major element data presented here (Table 1) agree well with previous data but show less scatter due to the improved analytical protocol (Fig. 2a, b). The olivines span a range of forsterite contents from 90.3 to 94.2% (median 92.9%); most show very little variation in Fo contents (< 0.1%) with maximum variations up to 0.3% in only few olivines. The lowest Fo values (90.3-92.9%) are from lherzolitic inclusions, whereas harzburgitic olivines range from 92.6 to 94.3% (average 93.2%). This is identical to the average mode of 93.2% for harzburgitic olivines from a global database of olivine inclusions in diamonds (Stachel and Harris 2008), and slightly higher than the average of 92.9% from a large suite of diamond-hosted inclusions from Sobolev et al. (2009), which also included lherzolitic inclusions (Fig. 2b).
MnO contents range from 0.081 to 0.112 wt% (median 0.093 wt%), apart from one high value of 0.15 wt%, and show a well-defined negative correlation with Fo contents (Fig. 2a), which overlap with the diamond inclusions from Sobolev et al. (2009). NiO contents show a narrow range from 0.36 to 0.43 wt% (median 0.404 wt%), which is higher than the global array of NiO contents in olivine inclusions in diamonds (0.36-0.38 wt%; Stachel and Harris 2008;Sobolev et al. 2009). There is no correlation of NiO with Fo content, although the spread in NiO contents is larger for the olivines with the highest Fo contents (Fig. 2b). Lherzolitic olivines are near the high end of the range (0.40-0.43 wt%), with the exception of anomalous lherzolitic olivine (G201-202), which also has low Fo and high MnO.
Duplicate ion microprobe analyses of olivine generally show excellent reproducibility for most elements (e.g., Mn, Ni, Co, Ti) but occasionally large differences for Cr and V, and, to a lesser extent, Na, Al and Ca. This variability was confirmed by high-resolution line scans across several olivines by EPMA (Fig. 3) as well as a Cr map of one of the grains (Electronic Supplement, Fig. S4). The patterns are mostly highly irregular for Cr but flat for Mn, whereas Ca and Al correlate with Cr for some inclusions (G106-113, G112-129; Fig. 3) and are flat in others (G105-111; Fig. 3). The variability in Cr and V may be due to the presence of nano-inclusions of chromite, which have been reported in a olivine inclusion in diamond from Yakutia (Sobolev et al. 2008), but no such inclusions could be observed in Akwatia olivines even at very high magnification using BSE imaging. Hence, if such inclusions exist they must be smaller than 0.1 µm, in which case their presence cannot explain the large variability under the ion microprobe beam (which is tia diamonds analysed at lower precision (Stachel and Harris 1997b), whereas small plus signs represent diamond-hosted olivine inclusions from Sobolev et al. (2009) ca. 10 × 15 µm in diameter, i.e., many orders of magnitude larger) unless they are distributed highly heterogeneously. A Cr concentration map of inclusion G106-113 (Electronic Supplement; Fig. S4) does show considerable heterogeneity on a scale of 2-10 µm, which is consistent with the variability in EPMA and SIMS Cr data. The origin of this heterogeneity will be discussed later. Healed micro-fractures in two olivine grains are distinctly different and show high contents of Cr, Ca and Al as well as small bright spots in BSE imaging, presumably microinclusions of chromite.

Garnet
Major element compositions of garnets in this study were presented by Stachel and Harris (1997b) and are summarised here. The garnets show variable but high Cr 2 O 3 contents (4.3-20.6 wt%, Cr# 0.13-0.66) and are some of the most Table 2 Trace-element concentrations of olivine inclusions by SIMS All concentrations in µg/g. Fo = forsterite content of olivine (data for G30-40, G32-46, G37-60, G38-63 from Stachel and Harris 1997b). Inclusions with the same name as the row above indicate repeat analyses of the same grain. Inclusions with the same number in the sample name following the letter G are from the same diamond. The analysis marked with plus signs (G120-147) overlapped a healed microfracture par. paragenesis: l lherzolitic, h harzburgitic, p peridotitic, l-Ti Ti-rich lherzolite  Cr-rich garnets reported in the literature. Mg# range from 83.6 to 89.1%. CaO contents are variable (1.0-6.3 wt %) and 27 out of 32 garnets are subcalcic, i.e., these are harzburgitic or G10 garnets (Table 3). MnO contents span a relatively narrow range (0.22-0.35 wt%) and show a positive correlation with FeO. Newly obtained trace element data (Table 3) show that Ti contents of garnets span an extremely wide range from 4 to 4600 µg/g, although harzburgitic garnets all have Ti contents < 470 µg/g (< 0.078 wt% TiO 2 ). Scandium and V contents are high (130-560 µg/g and 250-505 µg/g, respectively). Cobalt (40-48 µg/g) shows very little variation. A weak negative correlation exists between V and Mg#, as well as a weak positive correlation between Sc and Cr, but no other elements show any correlation, including V and Cr. Nickel contents range from 75 to 141 µg/g.

Conventional major-element geothermobarometry
Equilibrium pressures and temperatures of diamond-hosted inclusions at the time of their entrapment can be estimated based on the chemical composition of co-existing minerals in the same diamond, assuming that they were trapped simultaneously or at least under similar chemical and P-T conditions, and that they are not touching other inclusions, in which case they would record the temperature of the mantle at the time of eruption (Phillips et al. 2004). All Akwatia inclusions reported here were non-touching, and for most diamonds it was possible to calculate temperature estimates, but pressure estimates could only be derived for the few diamonds that contained garnet-opx pairs or cpx, the only assemblages that can be reliably used as geobarometers. A summary of P-T estimates is given in Table 4. Note that equilibrium temperatures have been rounded to the nearest five degrees to reflect uncertainty in geothermometer calibrations and chemical analyses upon which the calculations are based. Most geothermobarometer calibrations have an accuracy of 15-30 °C and 2-3 kbar (e.g., Brey and Köhler 1990;Krogh 1988;Nimis and Taylor 2000). The estimated pressures and temperatures span the whole range of conditions expected for diamonds sampled along a 38-40 mW/m 2 conductive geotherm (Hasterok and Chapman 2011), i.e., from 1100 °C at 45 kbar to 1300 °C at 65 kbar, and all fall within the diamond stability field, as required for inclusions in diamonds. We will now compare the results from various geothermobarometers in detail.
Simultaneous P-T information could be obtained from seven single cpx inclusions (present in four of the studied diamonds; mineral data from Stachel and Harris 1997b). Using the single clinopyroxene geothermobarometer from Nimis and Taylor (2000), we obtained values of T cpx NT00 = 1185-1200 °C and P cpx NT00 = 53-54 kbar for three pyroxenes (in two different diamonds, G50 and G201) and 1300-1310 °C at 59-60 kbar for two others (in a single diamond, G23). Two anomalously K-rich cpx (0.7 wt% K 2 O) in a single diamond (G41) with no other inclusions gave relatively low T cpx NT00 of 1150-1235 °C at 58 kbar, but the high K 2 O contents are outside the calibration range of Nimis and Taylor (2000). Overall, the single-cpx results are about 50 °C cooler than the Kalahari geotherm of Rudnick and Nyblade (1999) and fall close to a 39 mW/ m 2 model conductive geotherm (Hasterok and Chapman 2011) (Fig. 4).
For cpx co-existing with garnet (in diamonds G50 and G201), temperature estimates ( T grt-cpx Kr88 ) based on garnet-cpx Mg-Fe exchange thermometry (Krogh 1988) are about 35 °C cooler than T cpx NT00 for both diamonds using the same P cpx NT00 barometer (i.e., agree within error, which are ± 25 °C and ± 30 °C for T grt-cpx Kr88 and T cpx NT00 , respectively). Two diamonds (G126 and G209) contained opx in addition to garnet and olivine; therefore, equilibration pressures could be calculated using Al-opx thermobarometry   differ by 55 °C (i.e., agree within error due to the larger uncertainties of these geothermometers of 60 °C and 40 °C, respectively), resulting in a P Al-opx BKN estimate of 50-55 kbar. Two more diamonds contained garnet and opx but no olivine. Diamond G104 contained single garnet and opx inclusions giving a P Al-opx BKN at T grt-opx Ha84 estimate of 1210 °C at 58 kbar. Diamond G111 contained two garnets and three opx, which resulted in an wide range of P-T estimates (1160-1450 °C and 43-78 kbar) due to the range in Al 2 O 3 contents in three co-existing opx (0.92-1.19 wt%). As the Mg# of the two garnet inclusions was also significantly different (Mg# 89.9 vs. 90.3), inclusions in this For all other diamonds, only temperatures could be estimated due to the lack of cpx and opx. The most common co-existing mineral pair is garnet-olivine. T grt-ol OW79 results for garnet and olivine inclusions range from 975 to 1440 °C at a fixed pressure of 55 kbar, and most cluster around 1100-1300 °C (average 1210 °C). In general, if multiple garnets and/or olivines were present within a diamond, they fall within 50 °C with only a few exceptions. An updated calibration of the garnet-olivine Fe-Mg exchange thermometer  Stachel and Harris 1997b): Mg# = atomic Mg/(Mg + Fe), Cr# = atomic Cr/(Cr + Al), Ca_int (CaO intercept value) indicates how far a garnet is removed from the harzburgite-lherzolite division (Ca_int = 3.375) after Grütter et al. (2004). Garnet types: G10 harzburgitic, G9 lherzolitic, G11 high-Ti lherzolitic (Grütter et al. 2004  by Wu and Zhao (2007) resulted in similar temperatures within 50 °C.
In conclusion, where P and/or T estimates could be derived from multiple inclusions in a single diamond, these estimates generally agree within uncertainty of the geothermobarometer calibrations. A few inclusions are clearly anomalous, as they result in anomalous P-T estimates (e.g., olivine G126-156, and all three opx inclusions in diamond G111), which indicates these were not in equilibrium with the other inclusions in the host diamond, so were trapped in an evolving chemical environment and/or at different P-T conditions.

Ni in garnet thermometry
Estimates of equilibrium temperatures for garnets can be obtained from their Ni contents assuming equilibrium with mantle olivine (Canil 1999a;Griffin et al. 1989;Ryan et al. 1996), which is the case for all garnet inclusions presented here. Depending on the calibration used, temperatures range from 1175 to 1480 °C (Ryan et al. 1996 calibration) or 1115-1335 °C (Canil 1999a calibration). These ranges are smaller than the range obtained by grt-olivine Mg-Fe exchange thermometry, but extend to higher T for the Ryan et al. (1996) calibration. Temperature estimates for multiple garnets within a single diamond generally agree within 25 °C, compared to an uncertainty of the thermometers of ± 50 °C Canil 1999a).
The discrepancy between the two Ni-grt calibrations has been reported in the literature before, but has not been resolved (Canil 1996;Griffin and Ryan 1996). One possibility is that the difference is due to the Ryan et al. (1996) calibration not taking variation of Ni contents of co-existing olivine into account. As Ni contents of Akwatia olivines are higher than average mantle (Stachel and Harris 1997a), this may have introduced a bias towards higher temperatures. However, even when taking the differences in Ni contents into account (3140 and 2900 µg/g Ni, respectively), the two calibrations still differ by ca 75 °C. As T Ni-grt Can99 has negligible pressure dependence (Canil 1999a), uncertainty in equilibrium pressure cannot explain the difference. Because Ryan et al. (1996) estimates resulted in temperatures for several garnets that were well above the mantle adiabat and thus unreasonably high, and the Canil (1999a) estimates agree best with major-element-based P-T estimates (see previous section), we used the latter calibration in the remainder of this study.

Trace element thermometry of olivine
Aluminium, Cr and Ca in olivine have been calibrated as single-mineral geothermobarometers for garnet-bearing peridotites (Bussweiler et al. 2017;De Hoog et al. 2010;Köhler and Brey 1990). However, the calibrations only involved lherzolitic assemblages and were not tested on cpx-free rocks with subcalcic garnets. This could potentially lead to inaccuracies, particularly for Ca, as the activity of this element is no longer buffered by a Ca-saturated co-existing phase, which is essential for the accuracy of single-mineral geothermometers (De Hoog et al. 2010). In Al-Opx

Fig. 4 Estimated P-T equilibration conditions of silicate inclusions in
Akwatia diamonds colour-coded by diamond specimen whereas different symbols represent different geothermobarometer combinations (see Table 4 for data and abbreviations, note that only diamonds with olivine inclusions have been plotted). Error ellipses represent 95% confidence intervals of analytical uncertainties propagated through geothermobarometrical equations. Also plotted are the Kalahari geotherm and convective mantle adiabat of Rudnick and Nyblade (1999), 38 and 40 mW/m 2 conductive geotherms (Hasterok and Chapman 2011), and the diamond-graphite transition (Kennedy and Kennedy 1976) Page 15 of 28 100 addition, Cr 2 O 3 contents of Akwatia garnets are on average much higher, and thus Al 2 O 3 contents lower, than those used for calibration of the Al-ol thermometer (De Hoog et al. 2010). Even though the Al-ol thermometer has a correction for Cr#, its validity has not been tested using the high Cr# observed in this study (0.47-0.90 compared to 0.33-0.75 in the mantle xenolith database). Therefore, we compared T Al-ol DH10 and T Ca-ol DH10 (De Hoog et al. 2010) using (1) measured Ca and Al contents, with (2) using Ca and Al corrected for the deviation of CaO and Al 2 O 3 of co-existing garnets from average CaO and Al 2 O 3 in garnet from the calibration of De Hoog et al. (2010) (e.g., Ca corr = Ca ol / CaO grt × CaO avg , where CaO grt = CaO (wt%) in co-existing garnet and CaO avg = average CaO (wt%) of garnet used in T Ca-ol DH10 calibration, which was 5.02 wt%). Note that the Al 2 O 3 content of garnet is inversely correlated with its Cr 2 O 3 content. As the T Al-ol DH10 formulation also incorporates a Cr# correction, we used the Al-ol formulation without Cr# correction from Eq. 13 in De Hoog et al. (2010) to avoid incorporating the effect of Cr# twice.
When using a fixed pressure of 55 kbar, the range of T Al-ol DH10 is 1005-1295 °C with an average of 1195 °C. After correcting for garnet Al 2 O 3 content, the range is a little smaller (1045-1280 °C) and the average is slightly higher (1205 °C), but well within the uncertainty of the thermometer, which is ± 20 °C (De Hoog et al. 2010). This indicates that the effect of high Cr contents of garnet on T Al-ol DH10 is negligible. For T Ca-ol DH10 the range is 980-1370 °C with an average of 1160 °C. If the thermometer is corrected for CaO content of garnet, the range is much reduced (1115-1350 °C) and the average is considerably higher (1255 °C). Thus, Ca-ol temperatures without correction are significantly biased towards low temperatures, but after correction they are higher than T Al-ol DH10 . As T Al-ol DH10 and T Ca-ol DH10 have different P sensitivities, this difference could be due to the arbitrary P taken for this comparison. However, the difference is also visible when P can be calculated, as in two harzburgitic diamonds (G209 and G126) in which olivine co-exists with garnet and opx. In diamond G209, Al and Ca in olivine lead to P-T estimates of 1170 °C at 57 kbar and 1520 °C at 93 kbar, respectively. In diamond G126, in which two pairs each of garnets and olivines were present, there is a considerable range in T Al-ol DH10 at P Al-opx BKN (1205-1320 °C and 55-65 kbar) and an equally large range in T Ca-ol DH10 at P Al-opx BKN (1475-1620 °C and 79-94 kbar). This suggests not only that not all inclusions in the latter diamond were in equilibrium, as was already shown in the section on traditional geothermometry, but also that T Ca-ol DH10 estimates for both diamonds are unreasonably high.
Anomalously high Ca contents in olivine are also indicated by a plot of D ol/gt Al vs. D ol/gt Ca (Fig. 5a). Both these parameters are similarly sensitive to temperature, so one would expect these to correlate strongly. This is indeed the case for lherzolitic mantle xenoliths (De Hoog et al. 2010), but many Akwatia olivine inclusions fall towards the high Ca/ Al side, and will, therefore, show too high T Ca-ol DH10 values. This latter may be due to the CaO correction for subcalcic garnets being inaccurate (i.e., equilibration temperature is not linearly correlated with D ol/gt Ca ), but we note that several lherzolitic inclusions (which avoid the calibration issues mentioned above) also plot above the mantle lherzolites array. In addition, comparison of T Ca-ol DH10 with the single cpx thermobarometer ( T cpx NT00 ; Nimis and Taylor 2000) also gives inconsistent results.
Therefore, we suspect the high Ca/Al olivines were affected by transient heating events at the time of their entrapment in the diamond. Calcium diffuses faster than Al and during heating, Ca will diffuse into the olivine, resulting in Ca zoning with increasing concentrations towards the olivine rim . When these zoned olivines are trapped in diamond, they would homogenise due to diffusion during storage in the mantle, but cannot re-equilibrate with other silicate minerals. This would result in high Ca/Al ratios and anomalous T Ca-ol DH10 values. In summary, the Cr# correction of T Al-ol DH10 is valid for the high Cr# of garnet and olivine in the Akwatia suite, and this single-element thermometer can be used reliably for diamond inclusion suites. However, Ca-based geothermobarometers (De Hoog et al. 2010;Köhler and Brey 1988) should only be applied to olivine inclusions in diamonds that are undoubtedly of lherzolitic paragenesis (see "Discussion" for criteria), but, as shown above, even for those samples, results are often still unreliable.

Comparison between major and trace-element based geothermometers
Nickel in garnet temperatures show very little correlation with Mg-Fe exchange garnet-olivine temperatures, despite both thermometers being based on the same mineral pairs. Only about half the values fall within 50 °C of each other. The T grt-ol OW79 range is much larger than the T Ni-grt Can99 range (460 vs. 220 °C, respectively) and several values of T grt-ol OW79 are outside the diamond stability field (< 1050 °C) or above the mantle adiabat (> 1360 °C), indicating that these T estimates are unreliable. Only the average of both thermometers agrees well (1215 °C and 1210 °C, respectively), but for T grt-ol OW79 this value is dependent on the pressure assumed in the calibration (55 kbar in this study).
There are several possible explanations for the discrepancies between T grt-ol OW79 and T Ni-grt Can99 . Both methods assume equilibrium between garnet and olivine inclusions from the same diamond, whereas in reality they may have become encapsulated during different stages in the growth of their host diamond that were associated with fluctuations in the chemical environment or formation temperature. As Ti contents of garnet and olivine correlate well (Fig. 7), the assumption of equilibrium appears justified, but geothermometers are highly sensitive to small variations in concentrations of the elements involved, so even when minerals appear to be close to equilibrium, they may still yield erroneous temperatures. Also, due to differences in their diffusivities, some elements may be in equilibrium, whereas others are not.
A further thermometer based on equilibrium between garnet and olivine is T Al-ol . Figure 5b  In summary, even though most geothermobarometers give similar pressure-temperature ranges on average, correlation between different calibrations is poor. This is partially due to either inaccuracies based on calibrations potentially not being applicable to harzburgitic paragenesis inclusions (e.g., T Ca-ol DH10 ) or large uncertainties associated with some of the calibrations (e.g., T grt-ol OW79 ). However, discrepancies exceed expectations even taking these factors into account. In some instances, the main factor appears to be disequilibrium between mineral inclusions in the same diamond, which suggest that the diamonds grew in an environment with evolving P-T conditions and/or chemistry (e.g., Bulanova 1995). From this perspective, single-mineral calibrations (cpx; P cpx NT00 at T cpx NT00 ) or calibrations that are only weakly reliant on co-existing mineral composition (e.g., T

Ni-grt
Can99 , T Al-ol DH10 ) are therefore preferable when studying diamond inclusion suites.

Thermal structure of diamond source mantle
Taking into account the uncertainties in geothermometry results discussed earlier, the Akwatia dataset can be used to provide constraints on the thermal structure of the mantle beneath the West Africa Craton at the time of diamond formation (> 2.2 Ga). In total, five diamonds were available for which pressure estimates could be calculated (opx or cpx present), and six different thermometer-barometer combinations were used to calculate P-T estimates (Fig. 4). When multiple inclusions of the same type were present, separate P-T estimates were calculated for each inclusion. Considerable scatter is observed, with variation in T estimates for single diamonds ranging from 100 up to 300 °C, whereas the minimum pressure variation is 4 kbar, but can be as high as 16 kbar. Some of the variation may be explained by uncertainty in the P-T calculations, which can be large especially for pressure-sensitive thermometers (e.g., T Al-ol DH10 ) and temperature-sensitive barometers (e.g., P Al-opx BKN ). The propagated analytical uncertainties (not considering errors inherent in the calibration of the used geothermobarometers) are indicated in Fig. 4 by error ellipses, and even with our high-precision EPMA data, this can lead to uncertainty in pressure estimates of up to 10 kbar. Due to its low temperature sensitivity, P cpx NT00 gives much smaller uncertainties on individual P-T calculations than other geobarometers, but like other geothermometers gives inconsistent results; the P-T range for each diamond using P cpx NT00 is no smaller than when using P BK90 estimates.
Nevertheless, several observations can be made. First, as one would expect, all P-T estimates fall within the diamond stability field. Second, the paleogeotherm of the West Africa Craton is somewhat cooler than the Kalahari geotherm (based on the Kaapvaal and Zimbabwe cratons; Rudnick and Nyblade 1999) and scatters around 38-40 mW/m 2 conductive geotherms (Hasterok and Chapman 2011), in agreement with the smaller dataset from Stachel and Harris (1997b). This scatter could reflect actual temporal or spatial variations in heat flow beneath the West Africa Craton, but note that several diamonds (G50, G201) cover nearly the whole range of heat flow estimates. Third, the diamonds of the Akwatia field were derived from a continuous mantle section from the diamond-graphite boundary (ca. 140-km depth) down to ca. 200 km. This latter depth is the expected thickness of the lithosphere for a heat flow of 38-39 mW/m 2 (Hasterok and Chapman 2011).
Similar estimates can be derived from olivine data alone, as T Al-ol DH10 is insensitive to mantle lithology and gives similar results to other geothermometers. However, T Al-ol DH10 alone does not give an accurate P-T estimate. P Ca-ol KB90 has been calibrated as a geobarometer De Hoog et al. 2010), but combining this with T Al-ol DH10 gives unreasonably large uncertainties due to the shallow intercept of the two geothermobarometers in P-T space. As an alternative, for sufficiently large suites of diamond-hosted olivines the range of T Al-ol DH10 values can be used to determine the thermal state of the mantle at the time of olivine entrapment. Essentially, by calculating T Al-ol DH10 using pressure from a certain conductive geotherm T, a range of P-T conditions is calculated which can then be compared with the stability field of diamond and the mantle adiabat temperature as additional constraints. Calculating T Al-ol DH10 for all olivines from the Akwatia inclusion suite using a 40 mW/m 2 conductive geotherm of Hasterok and Chapman (2011) results in a T range of 1005-1295 °C (ignoring one outlier of 930 °C), whereas the 40 mW/m 2 geotherm intercepts the diamond-graphite transition intercepts at 1100 °C and 46 kbar. Thus, the T Al-ol DH10 data is incompatible with a 40 mW/m 2 conductive geotherm, as it would imply that some olivine inclusions were trapped inside the graphite stability field. Using a 38 mW/m 2 conductive results in a range of 1042-1355 °C (ignoring one outlier), whilst it intercepts the diamond-graphite transition at 950 °C and 44 kbar and the mantle adiabat at 1370 °C. Thus, P-T estimates of all inclusions fall within the diamond stability field and below the mantle adiabat. A 39 mW/m 2 also results in an acceptable P-T range, whereas using cooler conductive geotherms results in temperature estimates above the mantle adiabat. Thus, based on T Al-ol DH10 data alone, we can determine the paleogeotherm to be a 38-39 mW/m 2 conductive geotherm. This is the same result as obtained by traditional geothermobarometry.

Diamond paragenesis
Peridotitic inclusions in diamonds can be subdivided into lherzolitic and harzburgitic parageneses (representing mantle source lithologies) based on the presence or absence of cpx, or Ca-saturation of garnet (Sobolev et al. 1973;Stachel and Harris 2008). Harzburgitic assemblages with strongly Ca-depleted garnets (G10 garnets; Dawson and Stephens 1975;Grütter et al. 2004) are of particular interest, as these are indicators for diamondiferous kimberlites (Gurney 1984;Gurney et al. 1993). However, many diamonds contain olivine inclusions only and no criteria exist to determine their paragenesis. Here we evaluate diamond paragenesis based on the trace element composition of its olivine inclusions.

Ca-Al systematics
A strong positive correlation exists between Ca and Al in grt-lherzolite mantle olivine due to the temperature dependence of concentrations of both elements in olivine and relatively constant CaO and Al 2 O 3 activities in co-existing garnet and cpx (De Hoog et al. 2010). Indeed, lherzolitic olivines from Akwatia plot close to the mantle xenolith Ca-Al array (De Hoog et al. 2010, Sobolev et al. 2009), with two exception of two inclusions, which plot towards the high Ca/Al side.
In contrast to lherzolitic olivines, Ca and Al contents of harzburgitic and peridotitic (paragenesis undetermined) Akwatia olivines show significant scatter (Fig. 6a), most having low Ca/Al values. This scatter could be caused by olivines equilibrating along different geothermal gradients and the difference in pressure dependence of Ca and Al partitioning (De Hoog et al. 2010;Köhler and Brey 1990). However, although the exact origin of the Akwatia suite of alluvial diamonds is unclear, they are likely of similar age and unlikely to reflect large temporal variations in geothermal gradients needed to significantly shift Ca-Al trends (see Ca-Al correlation for various conductive geotherms; Fig. 6a). More likely, Ca contents in olivine reflect low but variable Ca activity of the mantle environment, as indicated by CaO undersaturation of co-existing garnets (Stachel and Harris 1997b). A large fraction of low-Ca garnets was also observed in the diamond inclusions dataset from Sobolev et al. (2009).
The different location of lherzolitic and harzburgitic olivines in Al-Ca space allows olivine compositions to be used to determine host diamond paragenesis. All olivines with Ca/Al < 2.2 are of harzburgitic origin (Fig. 6a). In addition, since olivine in equilibrium with clinopyroxene has at least 100 µg/g Ca in the P-T range where diamond is stable (> 1050 °C; Fig. 6a), olivines with < 100 µg/g Ca must also be harzburgitic, even if they fall on the mantle olivine Al-Ca array. Note that this applies to olivine inclusions in diamonds only, as low-T lherzolite xenoliths also have Ca < 100 µg/g, but these were sourced from the graphite stability field (De Hoog et al. 2010). All olivines with > 300 µg/g Ca and Ca/ Al ≥ 2.2 are of lherzolitic paragenesis. For olivines that fall on or near the mantle array and have 100-300 µg/g Ca, their paragenesis is uncertain (i.e., peridotitic). Following these rules, 12 out of 19 harzburgitic olivine inclusions are correctly classified as such, whereas seven cannot be classified.
Of the four peridotitic olivine inclusions (paragenesis undetermined), two are harzburgitic according this classification. All five lherzolitic inclusions are identified correctly.
As the distinction is based on generally applicable traceelement partitioning data, these rules can also be applied to other diamond-hosted inclusions suites. When applied to the diamond-hosted inclusion suites from Sobolev et al. (2009), the majority of olivines from Yakutia mines (299 out of 505, or 59%) are harzburgitic, whereas only 20 are lherzolitic (4%), the remainder being of unidentified origin (peridotitic). In contrast, olivines from the Majhgawan mine, India, and from Argyle, Australia, as well as the majority of inclusions from Snap Lake, Canada, cannot be classified (i.e., are peridotitic). As no Na data were reported, further refinement using the scheme below based on Na-Ca and Na-Al systematics is unfortunately not possible for the Sobolev et al. (2009) dataset.

Na-Al-Ca systematics
Although many olivine inclusions can be successfully classified using Ca-Al systematics, a significant proportion of harzburgitic inclusions could not be classified due to overlap of harzburgitic and lherzolitic inclusions (peridotite field in Fig. 6a). As harzburgites are depleted in Na as well as Ca, Na-Al-Ca systematics may be used to provide additional constraints on mantle paragenesis. Sodium shows welldefined trends with Al and Ca in olivines from lherzolitic mantle xenoliths, as Na activity is buffered by co-existing clinopyroxene and therefore, like for Ca and Al, temperature is the main control on Na contents of olivine (De Hoog et al. 2010). In contrast, Akwatia olivines have very low Na contents relative to Al (Fig. 6b) and Ca (Fig. 6d). Even most lherzolitic olivine inclusions fall below the xenolith-based Al-Na and Ca-Na arrays of grt-lherzolites (De Hoog et al. 2010). Akwatia clinopyroxene inclusions have low jadeite contents (1-3%) compared to clinopyroxene from mantle xenoliths (4-14%; De Hoog et al. 2010) and clinopyroxene in diamonds elsewhere (7 ± 4%; Stachel and Harris 2008), which probably causes the relatively low Na contents of lherzolitic olivine inclusions from Akwatia. Harzburgitic olivine inclusions have even lower Na contents. Therefore, Na-Al systematics allow us to distinguish between harzburgitic and lherzolitic olivines: olivines with Na > 60 µg/g or Na/ Al > 0.75 are lherzolitic, whereas olivines with Na ≤ 60 µg/g and Na/Al ≤ 0.75 are harzburgitic (Fig. 6b). Following these rules, all 19 harzburgitic inclusions are correctly classified as such, and so are all five lherzolitic inclusions. Of the four peridotitic olivine inclusions (paragenesis undetermined), three are classified as harzburgitic, whereas the remaining one is uncertain due to heterogeneity in its Al and Na contents. Na-Ca systematics show similar patterns, so olivine inclusions with < 60 µg/g Na and < 300 µg/g Ca are harzburgitic (Fig. 6d).
Combining the Ca-Al, Na-Ca and Na-Al classifications, all harzburgitic and lherzolitic inclusions are classified successfully, and all peridotitic (unspecified) inclusions were classified as harzburgitic. Harzburgitic olivines dominate the Akwatia suite, which matches the distribution of the Akwatia garnet inclusions, as well as the distribution of diamondhosted inclusions suites worldwide (Gurney 1984;Stachel and Harris 2008).

Implications for olivine as a diamond indicator mineral
Olivine can potentially be used as a diamond indicator mineral. Previous use of olivine in diamond exploration has mainly focussed on identifying olivine from kimberlite, i.e., as a kimberlite indicator mineral (e.g., Matveev and Stachel 2007;Shchukina and Shchukin 2018), but this provides little indication of diamond potential. Diamond formation is associated with garnet-bearing sections of the SCLM in which harzburgites predominate over lherzolites (Gurney et al. 1993). Olivines with a harzburgitic paragenesis, following the identification scheme presented earlier, are derived from the same source as G10 garnets. However, since we only compared the olivine inclusions to olivines from garnet peridotite xenoliths with equilibrium temperatures > 1050 °C, it is possible that olivines from lower temperature xenoliths, or from other lithologies, have Al-Ca-Na systematics that would identify them as harzburgitic, whereas in fact they could be derived from, e.g., low-T lherzolites. Indeed, we note that a few lherzolitic mantle xenoliths plot inside the fields we have identified as harzburgitic (Fig. 6). These are xenoliths that have equilibrium temperatures just over 1050 °C, and thus are very close to the graphite-diamond transition. In addition, olivines from low-T lherzolite xenoliths would overlap with our harzburgite field as well (De Hoog et al. 2010). Thus, more stringent filtering needs to be applied to be certain that an olivine of unknown origin is derived from the same source as G10 garnets.
We recommend that the dataset is first filtered to olivines of mantle origin (Fo = 92-95% and NiO > 0.3 wt%; Fig. 2) with Al > 40 µg/g, Ca < 300 µg/g and Na < 60 µg/g. This removes most lherzolites and low-T peridotites, as well as olivines of non-mantle origin. Then 'G10' olivines are those from the filtered dataset that have at least two of the 100 Page 20 of 28 following three ratios: Ca/Al < 2.2, Al/Na > 1.5 and Ca/ Na < 5. This results in a proportion of harzburgitic inclusions not being identified as such, but no olivines from mantle xenoliths are incorrectly identified as harzburgitic. Applying this scheme to the 28 Akwatia olivine inclusions results in 11 'G10' olivines, whereas none of the olivines from De Hoog et al. (2010), including garnet and spinel peridotites, kimberlites and picrites, were classified as 'G10' olivines.
If Na has not been measured, as is the case for much of the literature, including the high-precision EPMA technique employed by several groups (Batanova et al. 2015;Sobolev et al. 2008), the filtering can be simplified to Al > 40 µg/g, Ca < 300 µg/g and Ca/Al < 2.2. This results in less olivines identified positively as 'G10' olivines. As an example, when applied to the diamond-hosted inclusion suites from Sobolev et al. (2009), for Yakutian kimberlites just over one-third of olivine inclusions is classified as 'G10'. This proportion drops considerably for the other localities (diamonds from elsewhere in Russia, as well as Canada), and to none at all for diamond-hosted olivine inclusions from India and Australia. Unfortunately, due to Na missing from the Sobolev et al. (2009) dataset, it is impossible to determine if the latter suites are lherzolitic or harzburgitic. Of all peridotite xenoliths from the same Yakutia, only one contains 'G10' olivine. Therefore, the usefulness of this olivine classification scheme as a diamond indicator mineral needs further evaluation, but including Na in analytical setups would be beneficial as it is more useful to constrain diamond paragenesis than Ca.

Melt depletion and refertilisation
The Ti content of olivine serves as a proxy for bulk rock TiO 2 content (De Hoog et al. 2010;Hermann et al. 2005), which is an important indicator of melt depletion and refertilisation of mantle rocks (e.g., Bizimis et al. 2000, Rehfeldt et al. 2008. Low Ti contents of Akwatia olivines, particularly the harzburgitic inclusions, indicate that their mantle source was highly depleted in fusible elements. Titanium contents in olivine correlate well with TiO 2 contents of coexisting garnet (Fig. 7a), although they are offset from the mantle xenolith array (discussed below). The low Ti contents of the garnets were taken as evidence by Stachel and Harris (1997a) that the Akwatia diamond source rocks avoided refertilisation through a melt. The olivine data support this view. About half the harzburgitic olivines have < 1 µg/g Ti, which equates to < 4 µg/g in the bulk rock (De Hoog et al. 2010), and the lowest values are 0.2 µg/g Ti. These Ti contents are lower even than those in olivine from highly depleted supra-subduction zone peridotites (0.8-2 µg/g; supra-subduction zone (SSZ) spinel harzburgites from Kamchatka (Ionov 2010) and metasomatised mantle xenoliths (dunites, wehrlites and websterites) from the Kimberley kimberlite (Rehfeldt et al. 2008) Ionov 2010; Tollan et al. 2017) and indicate extremely high degrees of melting in excess of 30%. Similarly low Ti contents were reported for olivine in grt-spinel lherzolites from Kaalvallei, Kaapvaal Craton (De Hoog et al. 2010). In contrast, Ti contents of lherzolitic olivine inclusions are similar to those of olivine from grt-lherzolite xenoliths, indicating that either their source rocks did not experience extensive melt depletion or that they were refertilised by Ti-bearing melts before entrapment of the inclusions into their host diamonds.
One peculiar feature of the Akwatia dataset is that Ti in olivine vs. garnet appears to be offset relative to the mantle xenolith data (Fig. 7A), i.e., Ti in olivine is about four times lower than expected based on Ti in co-existing garnet. This is true for lherzolitic as well as harzburgitic olivine. This offset is difficult to explain as one would expect D gt/ol Ti to be relatively constant, with only a small dependence on temperature and garnet composition. A change in Ti substitution from the octahedral to the tetrahedral site was reported in wet versus dry mantle olivine, and the presence of Na appears to enhance uptake of Ti in olivine (Tollan et al. 2018). As Na contents in Akwatia olivines inclusions are relatively low, we cannot exclude a crystal-chemical control on Ti partitioning. Nevertheless, the broad correlation with of Ti in Akwatia olivine inclusion with TiO 2 in co-existing garnet does indicate that Ti in olivine does follow a similar pattern as the mantle xenolith database and reflects that of the bulk rock (De Hoog et al. 2010).
To investigate whether lherzolitic olivines were refertilised by melt infiltration or instead escaped melt depletion altogether, we compared olivine TiO 2 contents with their Cr# (Fig. 7b). Cr# of olivine serves as an indicator of melt depletion is, as it correlates with Cr# of co-existing chromite (De Hoog et al. 2010), which increases with increasing degrees of melt extraction (e.g., Dick and Bullen 1984;Hellebrand et al. 2001). This is also illustrated by comparing Ti and Cr# of fertile spinel lherzolites with residual supra-subduction zone harzburgites (Fig. 7b). It is thought that most garnet peridotites from the subcontinental lithosphere underwent low-pressure melting in the spinel stability field (Brey and Shu 2018;Stachel et al. 1998) and would, therefore, show a similar Cr#-TiO 2 trend. Cooling after melting would not change Cr# of olivine much, as Al and Cr have similar temperature and pressure dependence (De Hoog et al. 2010). Most Akwatia olivines, including lherzolitic inclusions, have Cr# of 0.6-0.7 with some higher Cr# values up to 0.9 (Fig. 6c). This suggests that the mantle source of the olivines had very high Cr#, consistent with the high Cr 2 O 3 contents of garnet inclusions in the Akwatia diamonds (Stachel and Harris 1997a). No Cr# values lower than 0.45 are present, in contrast to the diamond-hosted inclusion suites from Sobolev et al. (2009), in which over a quarter of inclusions has Cr# < 0.45. This is again consistent with the mantle source of Akwatia diamonds having high Cr#, and a very high degree of melt depletion. Importantly, lherzolitic inclusions have similar Cr# as harzburgitic inclusions (Fig. 7b), which suggests these also experienced large degrees of melt depletion, which is at odds with their high TiO 2 contents. This indicates that lherzolitic olivine was affected by small degrees of metasomatism by Ti-bearing melts prior to entrapment in the diamond, which would increase Ti contents of the strongly depleted mantle, including olivine, but would not affect Cr# significantly (De Hoog et al. 2010;Rehfeldt et al. 2008). Harzburgitic Akwatia olivine inclusions escaped refertilisation (as indicated by their low Ti and high Cr#, Fig. 7b), presumably due to isolation from the surrounding mantle by the diamond host, and consequently were encapsulated into their host diamonds prior to any major refertilisation.
A similar pattern of TiO 2 vs. Cr# can be seen for Akwatia garnet inclusions, but Cr# tend to be lower for lherzolitic garnets than harzburgitic ones, and would therefore also be consistent with a partial melting trend for lherzolitic garnets. This difference in behaviour between olivine and garnet is likely due to the poor correlation between Cr# of olivine and garnet inclusions from the same diamond. This is a common feature also noted in mantle xenoliths (De Hoog et al. 2010), where a much better correlation between the Cr# of olivine and cpx was observed than with garnet. This is probably due to the pressure dependence of Cr# in garnet in equilibrium with Cr-spinel (Grütter et al. 2006) and the fact that the Cr# of spinel in equilibrium with garnet increases further with depth until spinel becomes exhausted (Klemme 2004). Confirmation that lherzolitic inclusions probably record melt refertilisation comes from cpx inclusions in the Akwatia diamonds. These have Cr# from 27 up to 41%, which is considerably higher than cpx from strongly depleted suprasubduction zone harzburgitic xenoliths (Ionov 2010), which have Cr# ranging from 16 to 25%. Therefore, the high Cr# of Akwatia cpx is due to their formation during melt infiltration with the Cr# of cpx being imposed by the composition of the ambient mantle.

Trivalent cation behaviour and mantle oxidation state
Vanadium and Cr can occur in several oxidation states and may, therefore, provide information on the redox condition of their environment (e.g., Papike et al. 2005). Vanadium and Cr in Akwatia olivine inclusions (Fig. 8a) are rather scattered instead of the excellent correlation observed in olivines from mantle xenoliths (De Hoog et al. 2010;Ionov 2010;Witt-Eickschen and O'Neill 2005), showing high and variable Cr/V values instead. Akwatia harzburgitic garnets also exhibit high Cr/V compared to garnets from mantle xenoliths, in which both elements have a narrow compositional range in their major hosts cpx and garnet, and their concentrations in olivine are largely controlled by equilibration temperature of the xenoliths (De Hoog et al. 2010). Based on their equilibration temperatures, Akwatia olivine inclusions are expected to have > 5 µg/g V and > 150 µg/g Cr, but nearly all harzburgitic olivine inclusions have lower V. Chromium in olivine is also lower than expected when considering the high Cr# of co-existing garnets.
One possible explanation for the offset of Akwatia inclusions from the mantle array is that Cr and V contents are controlled by fO 2 . Under typical oxidation conditions in the upper mantle (IW to NNO buffers; Berry et al. 2003) most V will occur as V 3+ or V 4+ and Cr as Cr 3+ (Canil 2002;Papike et al. 2005). V 4+ has an ionic radius close to Ti 4+ , which has very low compatibility in olivine. V 2+ would probably be highly compatible in olivine, having an ionic radius very close to Fe 2+ , but occurs only at very low oxidation states (below the IW buffer). Cr 2+ has a similar ionic radius and charge to Fe 2+ and Mn 2+ , and therefore expected to be more compatible in olivine than Cr 3+ . Indeed, in peridotite melting experiments, olivine-melt   . A similar increase in compatibility of Cr 2+ in olivine at low oxidation fugacity was observed in Cr-spinel bearing lithologies (Li et al. 1995).
Based on the crystal-chemically induced relationship between oxygen fugacity and pressure, in average lithospheric mantle fO 2 decreases from about ΔQMF = − 1 to − 2.9 between 100-and 200-km depth (Canil et al. 1994), i.e., remains well above the IW buffer and the stability field of V 2+ (Canil et al. 1994;Luth and Stachel 2014;Stagno et al. 2013). fO 2 estimates based on Cr-spinel-olivine pairs in Akwatia diamonds (Cr-spinel compositions from Stachel and Harris 1997b) using the Ballhaus et al. (1991Ballhaus et al. ( ) calibration (with 1994Ballhaus et al. 1994) average to ΔQMF = − 1.6 ± 1.3. This is close to the EMOD buffer (enstatite + magnesite = olivine + diamond), and probably an overestimate of oxygen fugacity due to inaccuracies of the Ballhaus et al. (1991) calibration at high pressures. Nevertheless, even at this relatively high oxidation state, some Cr 2+ would likely be present in Akwatia olivines due to the high temperatures of equilibration and high MgCr 2 O 4 contents of syngenetic chromite (Berry et al. 2003;Li et al. 1995;Stachel and Harris 1997b). Three Akwatia diamonds with olivine as well as Cr-spinel inclusions can be used to estimate the Cr 2+ content following Li et al. (1995). Using average T Al-ol DH10 of 1140 °C and ΔQMF = − 2, ca. 80-130 µg/g Cr 2+ is divalent out of 117-327 µg/g total Cr present in these olivine inclusions. These estimates suggest that a significant fraction of Cr 2+ is present in most Akwatia olivines, which is in agreement with spectroscopy measurements of Cr oxidation state in olivine inclusions from South African diamonds (Sutton et al. 1993), in which one-third of total Cr was present as divalent Cr. This Cr 2+ would add to total Cr in olivine, as it is incorporated following a exchange reaction different to Cr 3+ . Indeed, some Akwatia olivines have very high Cr contents (up to 1090 µg/g Cr or 0.16 wt% Cr 2 O 3 ). High Cr contents have also been observed in olivine inclusions from other diamond suites (Hervig et al. 1980b;Sobolev et al. 2009). More reducing conditions are required to get higher Cr contents, and must be around QMF-3 to reach 0.16 wt% observed in some Akwatia olivine inclusions, which is still within the range of oxidation states in cratonic mantle (Luth and Stachel 2014). We note, however, that the Li et al. (1995) calibration is only valid for olivine in equilibrium with Cr-spinel. Many olivines probably had no Cr-spinel in their assemblage when they were trapped in the diamond, as the 39 mW/m 2 conductive geotherm intersects the Cr-spinel out boundary at about 1150 °C and 52 kbar ), whereas most olivine inclusions were derived from higher P-T conditions. Thus, the amount of divalent Cr in olivine from Cr-spinel-free assemblages remains uncertain.
In addition, despite the high Cr contents of some Akwatia olivines, most olivines have in fact relatively low Cr contents considering their equilibration temperature and high Cr# in co-existing garnet. This is demonstrated in Fig. 8b., where D ol/grt Cr ranges from 0.001 to 0.009 for harzburgitic olivine inclusions in Akwatia diamonds, compared to 0.005-0.016 for olivine from the mantle xenolith database equilibrated at similar temperatures. A similar pattern of low D ol/grt values can be observed for V and Sc (not shown), but not for Al (Fig. 5b). As Sc is not affected by oxidation state but otherwise has a similar geochemical behaviour as Cr and V, any redox-sensitive processes should be clearly visible in changes in Cr/Sc and/or V/Sc (Canil 1999b(Canil , 2002. No such difference is observed for V, and only a small difference for Cr/Sc, probably related to the presence of divalent Cr, as discussed above. Thus, Cr, Sc and V all have low D Ol/grt values for harzburgitic olivines, whereas lherzolitic inclusions are similar or higher than olivines from mantle xenoliths (Fig. 8b). We interpret the difference between harzburgitic and lherzolitic inclusions as a change in exchange mechanisms for trivalent cations due to the exhaustion of clinopyroxene. Trivalent cations in olivine need to be charge balanced, e.g., by monovalent ions or vacancies on the M site (where Mg and Fe reside) or by trivalent ions on the Si site (De Hoog et al. 2010;Kurosawa et al. 1997;Witt-Eickschen and O'Neill 2005). A strong correlation between #Na (nr. of atoms per functional unit) and #[Al + Cr] close to 1:1 was observed for lherzolitic mantle olivine, suggesting that Na plays an important role in the charge balance of trivalent cations in garnet lherzolites (De Hoog et al. 2010). In harzburgites, where cpx has been exhausted during partial melting, Na activity in the residue has decreased strongly. Indeed, for Akwatia olivines, #Na is strongly depleted relative to #[Cr + Al], indicating that other substitution mechanisms must be active in Na-undersaturated olivine (Fig. 8d).
The difference in substitution mechanisms is further illustrated in Fig. 8a, c and d. Chromium and V behave similarly in garnet peridotite and spinel peridotite xenoliths. Lherzolitic olivine inclusions fall on that trend (Fig. 8a), or slightly above, which can be explained by the presence of Cr 2+ . However, all other olivine inclusions are strongly depleted in V compared to mantle xenoliths equilibrated under similar P-T conditions (high-T GP lherzolites in Fig. 8a). Low V contents are difficult to explain with a change in oxidation state, as V 2+ would, like Cr 2+ , become more compatible in olivine relative to co-existing pyroxene and spinel (Li et al. 1995;, and requires oxygen fugacities below the IW buffer, which are unlikely to occur in cratonic mantle (Luth and Stachel 2014). Therefore, we conclude that the lack of Na for charge balance reduces the amount of V in harzburgitic olivine. Figure 8d shows that #Na is significantly lower than the amount required to charge balance trivalent cations (expressed as #[Al + Cr], note that for simplicity of the discussion we have ignored Li, Sc and V in this figure, as their contribution is insignificant relative to Na, Al and Cr), and therefore other substitution mechanisms than Na-M 3+ must play a role.
It is worth noting that of the trivalent cations, Al partitioning into olivine appears to be least affected by the absence of cpx, which is important for its use as a singleelement thermometer ( T Al-ol DH10 ). Its concentrations are similar in harzburgitic and lherzolitic inclusions, as well as olivines from mantle xenoliths (Fig. 8c). It is also relatively unaffected by the presence of spinel, which has a strong effect on the distribution of Cr and V (Fig. 8a, c). Whilst in garnet peridotites the Na-Al exchange mechanism appears to be dominant (De Hoog et al. 2010), in spinel peridotites a Tschermak-style substitution of Al occurs, i.e., Al on the M site is not charge balanced by Na, but by another Al replacing Si (De Hoog et al. 2010;Witt-Eickschen and O'Neill 2005). It appears that Tschermak substitution becomes important in garnet harzburgites if little Na to charge-balance Al is present.

Chromium heterogeneity: syn-eruptive hydrogen loss?
A complicating factor to the interpretation of V and Cr contents of Akwatia olivines is the large within-grain variability observed for both elements, whereas most other trace elements show no such variability (Fig. 3). Complex oscillatory zoning patterns of P, Cr and Al have been recorded in olivines from basaltic lavas and spinel peridotite xenoliths Milman-Barris et al. 2008), whereas other elements showed no such zoning (note that V was not measured in these studies). This indicates slow diffusion of Cr and Al in olivine relative to Ca, Mn and Ni and thus points to Cr-Al zoning in Akwatia olivine inclusions being a primary growth feature. However, Akwatia olivines do not show oscillatory zoning, as element mapping shows that Cr is seemingly randomly distributed (Electronic Supplement Fig. S4). In addition, growth zoning is at odds with a likely mantle residence of > 1 Ga for these diamonds (assuming Early Archean formation of harzburgitic diamonds and exhumation at about 2.2 Ga; Gurney et al. 2010;Stachel and Harris 1997b), as it is inconceivable that such zoning patterns are preserved in olivine at mantle conditions (T > 1000 °C) for billions of years. Therefore, the Cr and V variability must be a relatively recent feature.
One possible explanation is related to the loss of hydrogen from olivine inclusions during diamond ascent in kimberlitic magma. Although the unresorbed shapes of Akwatia diamonds indicate that residence time in the magma was short, it has been suggested that the source of these diamonds were komatiites (Canales and Norman 2003), which have slower magma ascent rates than kimberlites (e.g., Russell et al. 2012). The following reaction was proposed by Ingrin and Skogby (2000) to explain possible hydrogen loss from mantle minerals during ascent to the surface: but if Cr 2+ is present, this reaction would be preceded by: as Cr 2+ oxidises at lower oxygen fugacity than Fe 2+ (Schreiber et al. 1987). As hydrogen diffuses very fast in olivine and, therefore, readily escapes into the boundary layer between olivine and diamond, this process results in oxidation of the olivine inclusion. The presence of methane (CH 4 ), detected in thin fluid layers around silicate inclusions in diamonds, has been interpreted as the result of H 2 escaping from the inclusions and reacting with the diamond host to form CH 4 (Smith et al. 2018). It also explains the observation that no hydroxyl has been detected in diamond-hosted olivine inclusions (Matsyuk and Langer 2004), whereas the maximum solubility of H 2 O in olivine equilibrated at 5-6 GPa is ca. 150-200 ppm (Demouchy and Bolfan-Casanova 2016). This amount of H 2 O is enough (on a 1:1 atomic equivalent) to oxidise 870-1160 µg/g Cr 2+ , which is higher than Cr 2+ present in the olivine inclusions, as calculated in the section on 'Mantle oxidation state' above.
As the solubility of Cr 3+ in the oxidised olivine is much lower than that of Cr 2+ (Li et al. 1995), the reaction may lead to local oversaturation of Cr, resulting in precipitation of chromite, which would also affect the distribution of Al and V, both of which are more compatible in chromite than olivine. However, no chromite micro-inclusions were observed by BSE imaging (with a maximum resolution of ca. 100 nm), and sub-µm chromite inclusions are generally extremely rare in olivine inclusions in diamonds (Sobolev et al. 2008). The spatial distribution of Cr (Electronic Supplement, Fig. S4) shows that its distribution is highly heterogeneous on a 2-10 µm scale, so if areas with excess Cr are the result of Cr being concentrated in sub-100 nm inclusions of chromite, their density would need to average ca. one nanocrystal per 2 µm 2 , but with a highly irregular distribution. More work is needed to fully understand the origin of Cr heterogeneity, and if it is present in other diamond-hosted olivine inclusion suites, particularly those where high Cr contents have been reported.

Summary and conclusions
• Diamond-hosted olivine inclusions from the Akwatia diamond suite were used to determine diamond paragenesis (lherzolitic vs. harzburgitic), study mantle processes such (1) Fe 2+ + OH − = Fe 3+ + O 2− + 1∕2 H 2 (2) Cr 2+ + OH − = Cr 3+ + O 2− + 1∕2 H 2 as melting and refertilisation, and determine physical conditions of diamond formation (pressure, temperature, oxidation state). • Trace element compositions of olivine inclusions can be used to determine the paragenesis of host diamonds. Olivines with Ca > 300 µg/g, Ca/Al > 2.2, and Na > 60 µg/g or Na/Al > 0.75 are lherzolitic (and coexist with G9 or G11 garnets), whereas olivines with Ca < 100 µg/g or Ca/Al < 2.2, Na ≤ 60 µg/g and Na/ Al ≤ 0.75 are harzburgitic (and co-exist with G10 garnets). • To use olivine as a diamond indicator mineral, additional screening is required, as some lherzolitic low-T mantle xenoliths may have olivine that fall into the harzburgitic diamond inclusion field. We recommend that the dataset is first filtered to olivines of mantle origin (Fo = 92-95% and NiO > 0.3 wt%) with Al > 40 µg/g, Ca < 300 µg/g and Na < 60 µg/g. Then 'G10' olivines are those from the filtered dataset that have at least two of the following three ratios: Ca/Al < 2.2, Al/Na > 1.5 and Ca/Na < 5. If Na has not been measured, the filtering can be simplified to Al > 40 µg/g, Ca < 300 µg/g and Ca/Al < 2.2. This results in less olivines identified positively as 'G10' olivines. • Trace-element thermometry for harzburgitic olivine is hampered by variation in the concentration of elements which are assumed to be constant in co-existing minerals, which affects Ca in particular. Aluminium appears to be little affected, so T Al-ol estimates are equally reliable for harzburgitic as lherzolitic olivine. Ca-ol thermometry can only be applied to lherzolitic olivines, but even those often give anomalously high temperature estimates. Trace element thermometers (T Ni-grt , T Al-ol ) result in similar average temperatures as major element exchange thermometry but good linear correlations are not observed, indicating the possibility of disequilibrium between different silicate inclusions in the same diamond. • Based on traditional geothermobarometry, the diamonds of the Akwatia field were derived from a continuous mantle section from the diamond-graphite boundary (ca. 140-km depth) down to ca. 200 km along a 38-39 mW/m 2 conductive geotherm. Similar results can be obtained from Al-ol thermometry, with T Al-ol ranging from 1020 °C at 45 kbar to 1325 °C at 65 kbar, using the assumption that the olivine suite is derived from within the diamond stability field at temperatures below the mantle adiabat. • Titanium in olivine correlates well with Ti in garnet, and is highest in lherzolitic olivine, whilst being extremely depleted (< 1 µg/g) in many harzburgitic olivines, which indicates strong melt depletion with no cpx left in the residue. Lherzolitic olivines have similar Cr# as harzburgitic olivines, so their high Ti contents are indicative of melt refertilisation during an ancient metasomatic event that occurred before trapping of the inclusions in the diamond. • A proportion of Cr in olivine is present as divalent Cr, due to the low oxidation state and high temperature of the mantle source. However, in harzburgitic olivine Cr and V are commonly lower than expected based on the equilibration temperatures. This is due to the absence of cpx in harzburgitic lithologies and the resulting low Na activity, which reduces the uptake of Cr and V via the Na-M 3+ exchange mechanism, which dominates in lherzolites. • Chromium, Al and V distribution in many olivines is highly heterogeneous and it is recommended that multiple points are analysed on each diamond-hosted olivine inclusion to check for heterogeneity and to achieve a reliable average composition. Although the origin of the heterogeneity is unclear, the most likely cause is a latestage process, possibly hydrogen loss during diamond exhumation, resulting in oxidation of Cr 2+ to Cr 3+ and oversaturation of chromite. • Olivine inclusions in diamonds can provide similar information about equilibration temperature, diamond paragenesis and mantle processes as is commonly derived from diamond-hosted garnet inclusions. To fully utilise the potential of olivine in mantle studies, it is recommended that at least the following suite of trace elements is analysed: Na, Al, Ca, Sc, Ti, V, Cr, Mn, Ni.