Introduction

The Rustenburg Layered Suite (RLS) of the Bushveld Complex, South Africa, is a giant ultramafic-mafic layered complex that contains most of Earth’s viable chromium (Cr) and platinum reserves (Naldrett et al. 2009), suggesting its formation by potentially unique processes. Accounting for the vast amount of Cr in the RLS is a considerable challenge (e.g., Eales 2000). Possibly the most plausible mechanism proposed to date is that the RLS represents cumulates of basaltic-andesitic melts formed by assimilation of Kaapvaal craton crust by komatiite magmas (e.g., Eales and Costin 2012). Recent versions of this model also propose that the suite’s layered rocks formed by multiple injections of crystal-slurry sills (Yao et al. 2021). However, the precipitation of chromite as a direct consequence of assimilation (Yao et al. 2021) means that each magma batch, following appreciable assimilation of the crust, must travel rapidly from the deep crustal site of assimilation to the upper crustal intrusion without losing the denser crystals along the way. Consequently, such a model requires that the high concentration of highly compatible elements in the mantle and in komatiites, which have very low abundances in crustal rocks, should be present in proportions within the average lower RLS that mirror their komatiitic roots. This does not appear to be so for two of the most important elements, Cr and Ni, with most of the common silicate rocks of the Lower- and Critical Zones massively enriched in Cr over typical komatiite compositions and primitive mantle values (Fig. 1). In addition, the Sr-isotopic heterogeneity inherent to the RLS (Kruger 1994) poses an additional challenge to this hybridised magma model. Komatiitic magmas are unlikely to arise through the partial melting of mantle metasomatised by crustally derived fluids or melts because such metasomatised mantle is enriched in pyroxene (e.g., Keleman et al. 1998; Simon et al. 2007). Thus, if derived from hybridised komatiitic magmas, the recorded variable Sr-isotopic composition of the RLS can only be ascribed to assimilating variable amounts of crust, or crust of different compositions. In this study, we consider the Sr-isotopic variations in the RLS to reflect different magma batches sourced from isotopically variable mantle that was metasomatised by the addition of small amounts of crustally derived fluid or melt, possibly as much as 1 Ga prior to the formation of the RLS, during assembly of the craton.

Fig. 1
figure 1

Trace-element compositions of Rustenburg Layered Suite (RLS) Lower- and Critical Zone silicate cumulate rocks (green squares; Maier et al. 2013); average Kaapvaal craton Archaean komatiite (red circles; Robin-Popieul et al. 2012; spinifex analyses removed); upper, middle, and lower continental crust (light to dark blue hexagons; Gao et al. 1998); primitive mantle (orange stars; Lyubetskaya and Korenaga 2007); and proposed quenched primitive RLS magmas (diamonds; Sharpe and Hulbert 1985, dark purple; Barnes 1989, light pink; Wilson 2012, dark pink, spinifex analysis removed; Maier et al. 2016, light purple). The ratios of Cr/Ni and V/Ni in the RLS mafic-ultramafic Lower- and Critical Zones are notably higher than primitive mantle values, and greatly in excess of the Cr/Ni and V/Ni ratios in well characterised Archaean komatiites. They are also higher than minor rock types in the RLS interpreted to possibly represent relatively unhybridised komatiitic parental magmas. Where overlap of these rocks with the Lower- and Critical Zone cumulates do occur, they are either relatively low in Cr and Ni for typical komatiites, or contain considerably more Ni relative to Cr than the cumulates. If hybridised komatiite magmas were responsible for the formation of the RLS and its chromitites, much higher Ni values would be expected for average Lower- and Critical Zone silicate cumulate rocks, particularly considering the fraction of olivine in some of the cumulates and the fact that pyroxene:melt partitioning coefficients for Ni, Cr, and V are considered to overlap for basaltic magmas (e.g. Bédard 2007)

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By modelling the stoichiometries of partial melting reactions in garnet peridotite that may have produced the RLS parental magmas, an alternative hypothesis for the origin of RLS chromitites and its ferromagnesian layering is explored. In mantle source rocks, melting is incongruent; the melt has a composition different to the sum of the reactants. This must result in the formation of new, peritectic, crystalline phases (e.g., Grove et al. 2013; Kinzler 1997), and their production at a variety of melt fractions provides ample opportunity for their entrainment into the magmas on segregation from the source. To this end, thermodynamically constrained petrological modelling was utilised to explore the effects of peritectic crystal entrainment on the chemistry of the resultant magmas (i.e., melt plus crystals) and their subsequent crystallisation in the upper crust. The results suggest a double-peritectic process, involving entrainment of peritectic orthopyroxene in the source and the reaction of this to produce peritectic olivine and chromite in the ascending magma. This process represents a highly efficient mechanism to explain the origin of RLS chromitites, and also fits well with Cr/Ni ratios of the RLS.

Methods

Modelling overview

There are three steps involved in the modelling method designed to investigate the details of melting reactions in mantle source rocks, the magma compositions that would result, and the partial crystallisation of these magmas in the upper crust. Details of each step are described fully in the sections below.

First, we studied the stoichiometry of the partial melting reactions in representative peridotitic mantle sources in a relevant area of pressure-temperature (P-T) space, in constant-composition systems without magma extraction. This allowed the peritectic crystals that increase in abundance with melt to be identified. Second, we investigated sequential magma extraction events that may occur, and the magma compositions produced along two different approximately adiabatic melting paths. Magma extraction was set to occur when melt volume exceeded 5 wt% – within the threshold suggested by Winter (2010) – with peritectic crystal entrainment set to occur when these crystals were produced with the melt. Only the peritectic crystals produced in the preceding step along the P-T path were entrained into the extracted magma, thus representing a minimum estimate of entrained peritectic material. If no peritectic phases were produced, only melt was extracted. Lastly, we modelled magma ascent and fractional crystallisation of selected magma batches emplaced as sills into the crystal mush at the base of a hypothetical 0.3 GPa upper-crustal magma chamber, over the cooling interval down to ~ 1000 ºC. Solids in the magma at emplacement were modelled as undergoing immediate density separation on intrusion.

Modelling details

Thermodynamically constrained petrological calculations were performed using the Rcrust software (Mayne et al. 2016), which emulates open-system behaviour via a path-dependent calculation strategy that allows bulk compositional change via processes of mass transfer. Rcrust version 2020-04-19 was used with the Holland and Powell (2011) thermodynamic dataset and the 2020 revised hp633ver.dat thermodynamic data file from Perple_X in the NKCFMASTCr (Na2O-K2O-CaO-FeO-MgO-Al2O3-SiO2-TiO2-Cr2O3) chemical system. MnO was excluded from the modelling due to the absence of MnO as a component in the igneous melt model. The following phase solution (activity-composition) models were used: Cpx(HGP) for clinopyroxene, Gt(HGP) for garnet, O(HGP) for olivine, Opx(HGP) for orthopyroxene, Sp(HGP) for spinel, and melt(HGP) for melt (Holland et al. 2018); Fsp(C1) for plagioclase and potassium-feldspar (Holland and Powell 2003); and Ilm(WPH) for ilmenite (White et al. 2000). The modelling method applied has been demonstrated to produce a high level of consistency between the modelling and experimental results on peridotite partial melting under upper-mantle conditions (Otto et al. 2023). Adjustments made to solution model parameters are listed in the Supplementary Material.

Identifying peritectic phases in the modelling

To identify areas of peritectic crystal production with high probability of crystal entrainment to the magma, for each of the peridotitic compositions investigated (Table 1), P-T phase diagrams and phase abundance maps were modelled between 1300 ºC and 1600 ºC and 3.0 to 1.5 GPa. P-T areas characterised by an increase in the abundance of a crystalline phase as a function of partial melting were identified as areas of peritectic phase production. It is important to note that such considerations are made in terms of the increase or decrease in abundance of the mineral phase/s as a consequence of the melting reaction, i.e., along decompression paths, phase changes due to pressure-induced mineral stability transitions (e.g., garnet to spinel) are not considered peritectic.

A volatile-free system was modelled because the peridotite solidus is lowered by both H2O and CO2. A consequence of this is that our modelling maps out behaviour in the highest possible temperature range. Introduction of volatiles would lower the solidus temperature and increase the peritectic crystal yield.

Table 1 Compositions of the peridotitic sources used for Rcrust petrological modelling
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Quantifying peritectic phase production and modelling magma extraction

To investigate magma extraction, with the possibility of peritectic phase entrainment, we investigated partial melting and magma extraction for rocks undergoing approximately adiabatic decompression. Lower- and higher-temperature decompression paths were investigated. Where peritectic phase production was identified, the amounts of peritectic phases were quantified by calculating the increase in their abundance for each P-T step along the path.

Adiabatic ascent paths

To simulate adiabatic decompression, modelling was performed using the 502 peridotite composition (Table 1) across 4.5 to 1.5 GPa – thus ensuring that the starting P-T conditions were located below the solidus – with a 0.02 GPa pressure resolution. To accommodate the heat of melting and subsequent departure of the temperature path from the geotherm, the P-T path trajectories above the solidus were modelled to follow a decreasing temperature path that displayed the steadiest values of entropy of the bulk system during decompression. This yielded approximately adiabatic paths with potential temperatures (McKenzie and Bickle 1988) of 1260 ºC and 1450 ºC for paths 1 and 2, respectively. For the three other compositions studied, the adiabatic paths utilised mimic that of the paths applied in the modelling of the 502 source; note that, in reality, they would all vary by a small amount.

During magma extraction events, entropy loss was noted, but was minimal, and the values subsequently return to the entropy of the magma prior to extraction (see the Supplementary Material).

Magma extraction events

Melt formation, and entrainment of peritectic phases into the melt on segregation from the source, will create magmas with chemical compositions that reflect a combination of the mass of segregated melt and the compositions and abundances of the entrained crystals. Sequential magma extraction events were performed along the described adiabatic paths using the 502 peridotite composition. Extraction was set to be triggered whenever melt exceeded 5 wt% in the source. To approximate a degree of melt retention on grain boundaries, an amount of 10% of the original melt was left unextracted. Peritectic phase entrainment was modelled by considering a scenario in which only the peritectic crystals produced in the preceding step along the P-T path were entrained, with peritectic crystals produced in previous steps assumed to have recrystallised into structures too large for entrainment. As the temperature steps used in this modelling were small (~ 0.5 ºC), this represents a minimum estimate of the amount of peritectic material that may be entrained. Note that, due to reaction between the entrained peritectic crystals and the melt on adiabatic ascent, melt proportions grow relative to the crystal fraction and the crystal assemblages and compositions continually change to maintain equilibrium.

Entrainment modelling of peritectic phases

Quantification of the proportion of peritectic phases produced, if any, was calculated using the Rcrust ‘Delta’ function. Since peritectic phases are produced as products of incongruent melting reactions, they must increase in abundance during melting. The Delta function allows the user to specify only the portion of a predicted phase that increases in abundance during melting to be quantified and included in extraction simulations. In other words, for a predicted phase, the Delta function calculates the incremental difference between the point of extraction (point b) and a specified previous point (point a), such that the change in the phase proportion from point a to point b can be incorporated in the extraction simulation. The Delta function can be expressed as:

$$delta\{phase;x\_a;y\_a;unit\}$$
(1)

where phase is the phase intended for extraction, x_a and y_b describe the location of point a, and unit can be measured in mol%, vol%, or wt%. Point a can specified in two ways: (i) ‘prev_ext_X’, where X can be any phase of choice from which the delta change must be calculated, or (ii) ‘prev_ext’, where the name of the extracting phase is the default choice for the delta calculation.

In our modelling, an estimate on the behaviour of peritectic entrainment was modelled using the ‘prev_ext’ specification discussed above, where the delta change in wt% of the peritectic phases to be entrained are calculated from the point of extraction to one P-T point (which is dependent on the adiabat) before the extraction.

Fractional crystallisation

The sequential magma extraction simulations described above resulted in a number of extraction events, each producing a model melt or magma. To simulate intrusion and fractional crystallisation in an upper-crustal sill or magma chamber, magma emplacement was modelled to follow isobaric cooling paths at 0.3 GPa, starting at a temperature determined by the relevant ascent path of selected model magmas.

The crystallisation of emplaced magma batches was modelled assuming immediate density separation of the phases at each cooling step. To simulate this segregation of the crystals, the ‘any_phase’ expression in Rcrust was used and allows generic arguments for all phases that may be predicted to be set, given that the phase does not have a phase extraction proportion already specified. Subsequently, for each P-T point along the cooling path, the melt phase extraction proportion was specified as 0%, and for all other predicted phases (any_phase), the extraction proportion was set to 100%. This results in a scenario in which the continued crystallisation of the evolving magma can be simulated, with already crystallised phases ‘leaving’ the magma system as they settle onto the chamber floor, immediately excluding these phases from contributing to the reactive bulk composition in future steps. The abundance and density (amongst numerous other calculated parameters) of the crystallising phases for each P-T step can thus be gathered and quantified in a thermodynamically evolving system, allowing predictions of the possible cumulates that could form as a result of gravity settling.

Results

The resulting pseudosections and phase abundance maps produced from the first step of the modelling are displayed in Fig. 2, allowing the partial melting behaviour of four representative peridotites (Table 1) to be investigated. The volatile-free solidi range from 1300 ºC at ~ 1.3–1.7 GPa to ~ 1470–1550 ºC at 3.0 GPa, as shown by the pseudosections in Fig. 2a-d. Analysis of the phase abundance maps (Fig. 2e-h) show, in the P-T region of interest, the existence of subdomains where spinel and orthopyroxene were identified as peritectic products of partial melting that increased in abundance as melting progressed. For much of the supersolidus space, for all four compositions, the only peritectic phase to form is orthopyroxene, which is produced within a wedge-shaped band that narrows with increasing pressure. Peritectic spinel is present at low pressure for three of the four peridotites studied and is superimposed on the orthopyroxene fields in Fig. 2. Detailed annotations for the interpretation of the phase abundance maps and the melting reactions are indicated for the 502 peridotite in Fig. 2e, as the 502 composition was utilised throughout all modelling routines: With increasing degrees of melting, both orthopyroxene and spinel (where applicable) become reactants in the partial melting reactions. In the case of orthopyroxene, this transition from peritectic product to reactant in the incongruent melting reaction is triggered by the disappearance of clinopyroxene. In the case of peritectic spinel, the trigger is the disappearance of garnet.

Fig. 2
figure 2

The results of petrological modelling to investigate and identify peritectic phase formation during partial melting of representative mantle peridotite sources in the upper subcratonic mantle. a-d Constant-composition P-T sections (pseudosections) for four different peridotite compositions that feature prominently in the literature (a – 502; b – KLB-1; c – MM3; d – HK66), within the P-T range of 1300 to 1600 ºC and 1.5 to 3.0 GPa. 1: Cpx Grt Opx Ol Spl Melt; 2: Cpx Grt Opx Ol; 3: Opx Ol Spl Melt; 4: Cpx Opx Ol Spl Melt; 5: Cpx Grt Opx Ol Spl; 6: Ol Melt; 7: Cpx Opx Ol; 8: Ol Melt. e-h The abundance of orthopyroxene (green) and spinel (pink) for each of the compositions, where applicable. Analysis of phase abundance changes are described here for the 502 peridotite source (e) and is generally applicable to the other sources. The yellow to green field (1) to the left of the heavy black dashed line represents the area of peritectic orthopyroxene production, where orthopyroxene abundance increases with melt volume (in wt%, displayed as red, short-dash contour lines). In this area, orthopyroxene abundance increases from 0 to > 25 wt% (colour change from white to dark green). The cross-hatched, green to yellow field (2) to the right of the black dashed line indicates the area where orthopyroxene is consumed by melting, as is evident by the orthopyroxene abundance change from 25 to < 10 wt% (colour change from dark green to yellow). Two small areas of P-T space (3), superimposed on the orthopyroxene fields, indicate peritectic spinel formation, followed by its consumption (4; cross-hatched) at higher temperature and/or lower pressure. Thus, the production of peritectic crystals, the nature of these crystals, and their abundance, is strongly controlled by pressure, temperature, and the degree of melting. Within the modelled area there are two broad regions where melting of the 502 peridotite produces no new mineral phases and the proportion of all crystal phases in the source decreases as a function of increasing melt volume. The first is the white area above the solidus, and the second is area 2. These areas hold no potential for the entrainment of peritectic crystals. Cpx: clinopyroxene; Grt: garnet; Ol: olivine; Opx: orthopyroxene; Spl: spinel

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By utilising the pseudosections and phase abundance maps, plots of phase abundances along a nearly adiabatic decompression path (which is indicated on Fig. 2a & e) can be produced and are displayed for each of the four peridotites in Fig. 3. The production of peritectic orthopyroxene in a constant-composition scenario (no magma extraction) due to reactions that consume garnet and clinopyroxene, is observed for all compositions investigated. Figure 4 displays the abundance of Cr2O3 in all of the relevant phases along the same path as in Fig. 3, for each peridotite. These plots indicate that the Cr2O3 content of garnet increases as garnet mode decreases, and once garnet is consumed, the most Cr2O3-rich phase is peritectic orthopyroxene.

Fig. 3
figure 3

Phase abundances along an approximately adiabatic decompression path from below the solidus to 1.5 GPa, showing peritectic orthopyroxene production in a constant-composition scenario (no magma extraction) for four different peridotite compositions that feature prominently in the literature (Table 1). The adiabatic path followed is illustrated in yellow dash-dot on the P-T and phase abundance diagrams of the 502 composition (Fig. 2a & e), The paths followed for the three other compositions approximate this path (see Methodology). The formation of melt and peritectic orthopyroxene by reactions that consume garnet and clinopyroxene are observed in all four compositions

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Fig. 4
figure 4

The abundance of the Cr2O3 in the relevant Cr-bearing phases along the modelled decompression path (illustrated in yellow dash-dot on the P-T diagram of the 502 composition (Fig. 2a)) for the peridotite compositions studied. Note that, for all the peridotite sources, as the garnet mode decreases, the Cr2O3 content of garnet increases and on garnet disappearance, peritectic orthopyroxene becomes the most Cr2O3-rich phase. When considering the Cr2O3 abundance in the relevant phases in relation to partitioning data from Davis et al. (2013), the partitioning coefficient for Cr between melt and orthopyroxene are well within the range reported (see the Supplementary Material)

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Having identified peritectic orthopyroxene production during partial melting as a result of decompression in a constant-composition scenario, the results from the modelling of sequential magma extraction along the two adiabatic paths using the 502 peridotite source is summarised in Fig. 5; the extraction conditions and weight fractions of melt and entrained peritectic phases are displayed. Note that the melt production along the cold path was sufficient only to trigger one extraction event. Two extractions are crystal-free (magmas B2 and B6), and despite generally low peritectic crystal to melt ratios, extraction event B4 produces a crystal-rich magma with > 40% entrained peritectic orthopyroxene.

Fig. 5
figure 5

The results of thermodynamic modelling of the melting reactions and magma extraction events in a representative garnet peridotite (502, Table 1) during decompression. a Plot displaying the P-T conditions of the magma extraction events along the two approximately adiabatic ascent paths. b The components of the magma batches on extraction from the source, discussed in-text

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The results from the simulation of the emplacement of selected magma batches from the extraction modelling (Fig. 5) into an upper-crustal magma chamber, and subsequent crystallisation, is shown in Fig. 6, which displays the resulting variation in phase abundances as a function of decreasing temperature, and the igneous stratigraphy that would be produced by selected magma batches, if intruded as sills. The amounts of melt remaining in the sill at the end of the cooling temperature interval are also displayed. From Fig. 6, the crystallisation behaviour of magma B2, which involves no peritectic phase entrainment (b), shows less cumulate formation along the cooling path, and no chromite (b(i)). As displayed in (c) and (d), magmas with entrained peritectic orthopyroxene (magmas B4 and B5, respectively) intrude as chromite- and olivine-bearing slurries (c(i)) or show chromite crystallising at lower temperature (d(i)). Crystallisation due to cooling of the B4 magma in the sill results in the formation of a chromitite layer, followed by pyroxenite and then norite, or, as illustrated, if plagioclase segregates by density, an anorthosite layer will result following loss of the residual melt. Note that the removal of orthopyroxene on the ascent path is important to chromite formation. As a result of the lower intrusion temperature of magma A1 (a), the magma is predicted to intrude the crustal chamber as an olivine-bearing slurry. The magma is Cr2O3-bearing, but this Cr is contained in orthopyroxene and therefore cannot undergo density segregation from the silicate minerals, thus resulting in no chromite formation.

Fig. 6
figure 6

The results of thermodynamic modelling from the emplacement of the resulting model magmas at 0.3 GPa, displayed as plots of cumulative phase abundance, and the igneous stratigraphy predicted for cooling from emplacement temperature, assuming that the crystals present at emplacement undergo perfect density-driven segregation (as outlined in Fig. 7). The plots are labelled according to the extraction event in Fig. 5 that produced the model magma. The cumulative phase abundance displayed at each point along the temperature interval reflects the sum of all of the phases produced during the crystallisation sequence up until that point. Note that the stratigraphy is illustrative of that which would be produced by significant cooling in the sill. If the magma drained out of the structure following settling of the chromite from the slurry, a chromitite layer would be the only marker of intrusion. If the magma did not inject as a sill but mixed with resident magma in a chamber, then a Cr-enriched and chromite saturated magma may result. Ilm: ilmenite; Pl: plagioclase

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Using the phase abundance and density data collected during crystallisation modelling routines, the plot in Fig. 7 shows the variation in density for the different crystallising phases during cooling in a magma chamber in the upper crust. This data was utilised to produce the igneous stratigraphy (example cumulates) plotted in Fig. 6. Note that ferromagnesian silicate and oxide minerals that crystallised together, as a function of cooling in a sill, were not modelled as undergoing density segregation from another, but were regarded as separating from the near-neutral-buoyancy plagioclase by this mechanism. Melt remaining at the end of the crystallisation sequence was modelled as draining off by filter pressing due to compaction (Connolly and Schmidt 2022) from layers deposited by overlying sills, or other deformation processes.

Fig. 7
figure 7

A plot of the modelled phases in the magma during fractional crystallisation and the thermodynamically calculated density values as a function of temperature along the 0.3 GPa isobaric crystallisation path for extraction event B4 (solid lines), as numbered in Fig. 5a-b. Density estimates for typical basaltic (dark grey dashed) and andesitic magmas (light grey dashed) at 1 bar and 1.0 GPa (Lesher and Spera 2015) are displayed as references for comparison with the modelled melt density values. Vectors on the right indicate the calculated effects of the density differences between the crystalline phases and the melt. Chr: chromite

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Discussion

The double-peritectic model for silicate & chromite layering

Our results show that during partial melting of a garnet peridotite in the upper mantle, peritectic orthopyroxene is produced over a wedge-shaped P-T domain that is closer to the solidus at low pressure and separates from the solidus and narrows at higher pressure (Fig. 2). Orthopyroxene has a crystal-chemical affinity for Cr (Jean and Shervais 2017; Fig. 4) and the entrainment of peritectic orthopyroxene fundamentally changes the magma chemistry to be enriched in Cr. This has profound consequences for the assemblage of crystals in the magma (Fig. 5) and crystallisation behaviour (Fig. 6). Our modelling demonstrates that, during magma ascent, melt volume grows by the incongruent melting of the orthopyroxene cargo (Fig. 8), producing new peritectic chromite and olivine.

Fig. 8
figure 8

A physical model for the generation of chromitite and silicate layering through entrainment of peritectic crystals in the upper mantle source during magma extraction. a Under specific mantle conditions, incongruent partial melting reactions produce new peritectic crystals at the melting sites. A proportion of these crystals may be entrained to the melt on segregation from the source. Changing P-T conditions during approximately adiabatic ascent consume the entrained peritectic crystals, and recrystallisation at mid- to shallow crustal conditions produces a melt-dominated magma with new crystal phases in suspension. Emplacement of sills within or below magma chambers of this crystal-mush can produce layering similar to that found in the lower portions of the RLS, assuming effective density separation of crystals in the magma chamber as the magma cools. The upward migration of the remaining melt is achieved by filter pressing due to compaction, or due to the decreasing density of melt as the crystalline phases settle out. b (i) The consumption of the entrained peritectic orthopyroxene during ascent is displayed by its decrease in abundance as magma travels along the adiabat. The reaction of this Cr-rich, ferromagnesian phase with the melt results in the crystallisation of peritectic olivine and ultimately, the formation of peritectic chromite at low pressure. (ii) As the amount of orthopyroxene decreases due to the melting reaction, its Cr2O3 content increases until saturation. At this point, Cr-spinel appears, and becomes more Cr2O3-rich as decompression continues

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The formation of peritectic chromite depends on both the amount of orthopyroxene entrained to the magma, and the amount of orthopyroxene that undergoes incongruent melting on magma ascent, which is a function of temperature and amount of decompression (Fig. 8b). Magmas leaving their sources as melt only (extraction B2, Fig. 6b) cannot form chromite crystals as the Cr dissolved in melt (0.16 wt%; see the Supplementary Material) is easily accommodated in pyroxene which crystalises prior to chromite saturation. Similarly, magmas entraining peritectic crystals that originate at relatively low pressure and temperature (extraction A1; 0.23 wt% Cr2O3) do not melt enough pyroxene on ascent to produce peritectic chromite. In contrast, extracted magmas bearing peritectic orthopyroxene that originate at high temperature, produce peritectic chromite crystals on ascent (extraction B4; Cr2O3 in the magma is increased from 0.26 wt% to 0.81 wt% due to the presence of peritectic orthopyroxene), or crystalise chromite during cooling after emplacement (extraction B5; 0.26 wt% to 0.47 wt% Cr2O3 increase). Chromitite layers will most readily be produced by magma batches such as B4, where the magma injects as an olivine- and chromite-bearing slurry, with the density contrast between these phases ensuring efficient separation, at least on scale of meters, forming a chromitite layer at the base of the sill (Fig. 6c). Further cooling can produce layers of dunite, pyroxenite, norite, and possibly anorthosite, whereas inefficient crystal separation can produce layers of dunite, gabbro, and norite, with interstitial chromite. Should magma drainage occur shortly after intrusion of the sill, potentially only a chromitite or a chromitite plus a dunite layer would result (Fig. 6c(i)).

Peritectic crystal entrainment depends on peritectic crystals nucleating as independent crystals in the melt, as well as channelised, sufficiently rapid melt flow to remove these crystals from the source and incorporate them into the magma. Experiments using glass starting materials have confirmed peritectic orthopyroxene formation during mantle melting (e.g., Grove et al. 2013; Kinzler 1997). In the case of the mantle peridotites we have studied, peritectic orthopyroxene would be the most common and abundant phase produced with melt in the subcratonic upper mantle, and the first orthopyroxene phase to appear (Figs. 3 and 4). Experiments on crustal compositions using mineral mixtures (Stevens et al. 1997), where the kinetics of mineral dissolution, intra-crystalline diffusion and nucleation control the distribution of phases, commonly show that peritectic orthopyroxene nucleates easily and abundantly (Zellmer et al. 2016) in melt pools (Zhang et al. 2010). Thus, with no prior orthopyroxene on which to nucleate, the peritectic orthopyroxene is likely to form as small, discrete crystals suspended in the melts (Erdmann et al. 2012).

There is continuous debate about how rapidly melt can be extracted from mantle source rocks (Rees Jones and Rudge 2020). Some studies of melt production and extraction from the mantle regard both as slow processes (e.g., Bulau et al. 1979; McKenzie 1984). However, as in the crust, mantle melting occurs in different tectonic settings and, in some situations, the rates of P-T change or activities of volatile components are likely sufficient to allow rapid melting and melt extraction. This is supported by several lines of evidence. For many alkali-rich mafic magmas, flow through the mantle must be channelised and fast, as such compositions are strongly out of equilibrium with typical mantle rocks (Keleman et al. 1997). Additionally, information on rates of basalt accumulation and on the required minimum rates of ascent of a variety of magma types that exhume mantle xenoliths demonstrate clearly that mantle melts are produced, segregate and ascend rapidly enough to transport even decimetre-sized mantle xenoliths and peritectic products from deep staging chambers to the surface (Li et al. 2012; O’Reilly and Griffin 2010; Sun et al. 2018). As such, it is rather apparent that an accelerated, chemically isolated mechanism of melt production and transport is unavoidable (Keleman et al. 1997; Spiegelman and Kenyon 1992).

Melt extraction from partially molten mantle regions has been widely attributed to the formation of high-permeability pathways through reactive-infiltration instability (e.g., Chadam et al. 1986; Daines and Kohlstedt 1994), defined as the positive feedback between melt flow and reaction. Sandwich experiments of partially molten rock between a porous sink and a melt source (Pec et al. 2017) indicated that melt fractions as low as 0.04 show the development of channels in the partially molten rock, with increased melting (greater than 0.2) forming multiple channels, and considerable melt pooling at melt fractions at or greater than 0.05 (Miller et al. 2014). Importantly, peritectic olivine phenocrysts of various sizes that were initially randomly distributed in the melt source, collect in large numbers during infiltration (Pec et al. 2017). This requires the olivine crystals to be advected toward major channel entrances by focused melt flow, where crystals become locally entrained in the melt-rich channels forming due to pyroxene consumption. In Fig. 3, olivine is the slowest consumed reactant, suggesting a similar reaction-induced channelisation mechanism is likely, given that the permeability is increased by the reaction. Since intracratonic plume and rift settings are characterised by high rates of mantle melting (Van Wijk et al. 2001; White 1993) and evidence for short magma transport times is well-established (Connolly et al. 2009; O’Reilly and Griffin 2010; Rees Jones and Rudge 2020), the likelihood of strong melt channelling and rapid magma extraction will favour peritectic phase entrainment into the magma in the source if it is produced by the melting reaction, without its presence having a significant effect on magma viscosity (Costa et al. 2009).

There are two important aspects in the findings of this study. Considering that the crystallisation of the RLS occurred within 1.02 ± 0.63 Ma and required large magma volumes (> 5 km3/year) with rapid accretion over < 100 ka (Zeh et al. 2015), the likelihood of rapid melting, magma extraction and magma ascent suggests the entrainment of peritectic orthopyroxene. Second, hotter magmas that formed at higher pressure will undergo more decompression, and this results in a greater yield of chromite in the sill. As such, the chromitite layers of the RLS would represent magma production events that favoured both peritectic orthopyroxene entrainment and derivation from sufficient depth to produce hot, chromite-crystal laden magmas that were delivered into the sill or a crustal chamber, or that produced chromite during cooling. In this way, some of the proposed processes for the formation of RLS chromitites, such as the growth of chromite crystals on a cold lower contact surface (Latypov et al. 2018) or gravity-driven fractional crystallisation (e.g., Naldrett et al. 2012), may be equally applicable to our proposed sills, but these would represent second-order processes. The double-peritectic model thus provides a simple, first-order, chemically and thermodynamically constrained process in which the entrainment of peritectic orthopyroxene in the source and its digestion by the ascending magma can explain the formation of the RLS chromitites.