Chemical weathering indices (one-dimensional/1D index values) and accompanying ternary plots (two-dimensional/2D compositional space) facilitate quantitative comparison of whole-rock and mineral major-element data, and empirical chemical trends with predicted weathering vectors. However, data analysis in ternary plots is restricted by poles grouping elements that are hosted in different minerals or that are influenced selectively by later alteration (e.g., diagenesis/metasomatism). Tetrahedral plots (three-dimensional/3D compositional space) offer enhanced analytical utility of major-element data by shifting elements across four poles and (or) incorporating additional proxy elements. Tetrahedral space can better reveal combined effects on major-element compositions from independent mineralogical controls and post-depositional alteration via curvilinear trends that are otherwise simplified and linear in ternary space. This study focuses on mafic-rock weathering and first reviews applications and limitations of the 1D mafic index of alteration (MIA) and index of lateritization/bauxitization (IOL/IOB) that integrate into molar Al2O3–CaO*–Na2O–K2O–(FeO(T)/Fe2O3(T))–MgO and SiO2–Al2O3–Fe2O3(T) ternary compositional space, respectively. Analysis in tetrahedral space is then demonstrated with Phanerozoic weathering profile and Precambrian paleosol data in two plots of the molar Al2O3–CaO*–Na2O–K2O–(FeO(T)/Fe2O3(T))–MgO system (A–CN–K–FM and AF–CN–K–M plots) and one plot of the molar Al2O3–CaO*–Na2O–K2O–(FeO(T)/Fe2O3(T))–MgO–SiO2 system (A–L–F–S plot). Common chemical weathering indices are integrated into these 3D tetrahedral spaces or onto some of their 2D ternary faces. However, the tetrahedral compositional space is a key to (1) assessing integrative effects from labile element loss while accounting for the variable, redox-dependent behaviour of Fe, (2) better exposing, and correcting for, overprinting effects of diagenesis/metasomatism, and (3) tracking Si loss across all stages of chemical weathering.

The development of major-element chemical weathering indices (one-dimensional/1D data) and their translation into ternary plots (two-dimensional/2D data) constituted a significant leap forward for quantitative siliciclastic sedimentary geochemistry (see overview in Nesbitt 2003). Compositional analysis with ternary plots provides an effective data visualization strategy whereby whole-rock sample compositions can be evaluated relative to mineral compositions and predicted vectors of the compositional changes associated with chemical weathering reactions (e.g., elements lost during hydrolysis) or other sedimentary processes. The chemical index of alteration (CIA) and accompanying Al2O3–CaO*+Na2O–K2O (A–CN–K) plot (or “feldspar” diagram) are the premier examples, with their coupled utility in assessing feldspar weathering across a wide spectrum of rock types, hydrodynamic sorting trends in siliciclastic sediment and sedimentary rocks, and diagenetic/metasomatic enrichment of K in lithified weathering profiles (paleosols), sediment, and sedimentary rocks (Fedo et al. 1995; Nesbitt and Young 1982, 1984, 1989). Two ternary plots adding Fe and Mg, the Al2O3–CaO*+Na2O+K2O–(FeO(T)/Fe2O3(T))+MgO (A–CNK–FM) plot, often referred to as the “mafics” diagram, and the Al2O3–CaO*+Na2O+K2O+MgO–(FeO(T)/Fe2O3(T)) (A–L–F; where L = Ca, Na, Mg, K, the “labile” element component) plot, were introduced subsequently to assess the effects of both feldspar and mafic mineral weathering and extreme weathering effects, respectively (Nesbitt and Young 1989; Nesbitt and Wilson 1992). This development was followed by the introduction of the Al2O3+(FeO(T)/Fe2O3(T))–CaO*+Na2O+K2O–MgO (AF–CNK–M) plot and retrospective integration of the 1D mafic index of alteration (MIA) into all of the aforementioned Fe+Mg-bearing ternary plots (Babechuk et al. 2014). The extended Al2O3–CaO*–Na2O–K2O–(FeO(T)/Fe2O3(T))–MgO (A–C–N–K–F–M) compositional system aids in unravelling processes involving ferromagnesian minerals in siliciclastic petrogenesis, from source to sink. For example, the added Fe+Mg dimension is essential to properly evaluate mafic-rock weathering, which is in turn relevant to (1) modulating atmospheric CO2 levels as part of Earth's C cycle (Dessert et al. 2003; Kent and Muttoni 2013; Goll et al. 2021), (2) examining redox vs. nonredox weathering processes and associated atmosphere–lithosphere interactions captured in Precambrian paleosols (Gall 1992; Rye and Holland 1998), and (3) reconstructing Martian surface processes via basalt-derived sediments and sedimentary rocks (McLennan et al. 2014; Mangold et al. 2019; Thorpe et al. 2021).

The analysis of whole-rock major-element data in ternary plots can expose the mineralogical controls that change 1D weathering index values; however, there are still limitations imposed by the 2D compositional space, especially as more elements are added to a defined compositional system. The MIA and associated ternary plots of the extended A–C–N–K–F–M system, unlike the CIA and A–CN–K system, are significantly influenced by provenance composition. Abundance variations of mafic minerals relative to feldspars across the igneous rock spectrum are associated with variable (Fe+Mg)/(Ca+Na+K) ratios that can significantly shift 1D MIA values and 2D plotting positions independent of sedimentary petrogenetic effects. Beyond this source-rock effect, there are limitations imposed by plot-specific element configurations. The use of ternary space to study extended compositional systems requires more element grouping onto single poles, despite the potential for grouped elements to be hosted in different minerals or exhibit contrasting weathering and (or) post-depositional alteration behaviour. The highly used A–CNK–FM ternary plot, while facilitating the analysis of chemical effects associated with ferromagnesian minerals, comes with new limitations related to the grouping of Ca, Na, and K on one pole and, under some scenarios, also related to the grouping of Fe and Mg on one pole. The CNK grouping comes with the loss of feldspar weathering resolution (i.e., being able to separate plagioclase from K-feldspar effects) and the inability to easily detect and correct for diagenetic/metasomatic K addition back to a pre-diagenesis/metasomatism composition. The FM grouping can make it challenging to fully assess the contrasting chemical weathering behaviour of Fe (i.e., mobile or immobile) under different redox conditions, because different Fe behaviour produces different vector magnitudes for the weathering of mafic minerals. Specifically, for oxidative weathering, there is a restriction on the compositional plotting range due to the contrasting behaviour of Mg loss and Fe retention, whereas reducing weathering opens up more of the plot since the effects of Mg and Fe loss are combined. Babechuk et al. (2014) proposed using different arrangements of Fe on A–C–N–K–F–M ternary plots in combination with the MIA to address contrasting Fe redox behaviour, but all of these plots retain the feldspar resolution penalties associated with the CNK grouping. The CIA, MIA, and most of their associated ternary plots are also restricted to addressing the chemical stages of weathering preceding extensive breakdown of kaolinite/halloysite (i.e., they do not track intense-to-extreme weathering stages). The A–L–F plot does allow for visual tracking of chemical effects at more advanced weathering stages, but this advantage comes with the penalty of losing the resolution of all mineral-specific chemical effects at earlier stages of weathering due to the grouping of all labile elements (Ca, Na, Mg, K) on one pole. Chemically tracking more advanced stages of weathering requires the introduction of Si and use of other 1D proxies such as the index of lateritization/bauxitization (IOL/IOB) (Schellmann 1982; Babechuk et al. 2014).

An effective solution to some of the limitations outlined above is to shift elements across four poles rather than three by extending 2D ternary into three-dimensional/3D tetrahedral space, which maintains a maximum resolution of specific mineral or process effects when evaluating major-element compositions. Using the new A–CN–K–FM tetrahedral plot, Fedo and Babechuk (2023) introduce this 3D analytical approach to study not only chemical weathering, but all processes across the sedimentary petrogenesis continuum. The A–CN–K–FM tetrahedral plot retains the advantages of the A–CNK–FM ternary plot, while regaining feldspar resolution and the ability to reconstruct K-diagenetic/metasomatic effects by having Ca+Na and K separated. However, despite its numerous advantages, the A–CN–K–FM plotting approach retains some limitations related to contrasting Fe redox behaviour by having Fe and Mg grouped (Babechuk et al. 2014).

This contribution is a companion piece to Fedo and Babechuk (2023) that further builds on the demonstrated utility of 3D compositional space to expose chemical weathering trends. Some of the remaining limitations of the A–CN–K–FM plot can be addressed by combining the 3D approach with the rearrangement of Fe across different poles as demonstrated for ternary plots in the A–C–N–K–F–M system (Nesbitt and Wilson 1992; Babechuk et al. 2014). Furthermore, the introduction of Si to tetrahedral configurations can open up 3D compositional analysis as a new strategy to investigate chemical changes during intense to extreme weathering. This work focuses on terrestrial basaltic weathering trends and secondary diagenesis/metasomatism preserved in mafic-rock weathering profiles, starting with a review of the 1D and 2D methods that lay the foundation for extending chemical weathering analysis into the third compositional dimension. Specifically, this work first summarizes the advantages, limitations, and best-practice applications of the MIA (with comparison to the CIA) and the IOL/IOB 1D weathering indices, including a new proposal to use molar oxide proportions for the latter index. From here, an overview is provided of the main ternary plots in the A–C–N–K–F–M system and the SiO2–Al2O3–Fe2O3(T) (S–A–F) plot that integrate the MIA and IOL/IOB weathering indices, respectively. Throughout this review, the plotting positions of minerals, igneous rocks, model weathering vectors, and permissible plot domains associated with specific chemical weathering and (or) alteration processes are used to demonstrate key mineral transformations, element trends of labile/mobile element (Ca, Na, K, Mg±Fe) depletion relative to immobile elements (Al±Fe), and alkali element (K, Na) addition during diagenesis/metasomatism. Stemming from this review, two new tetrahedral plot rearrangements of elements in the A–C–N–K–F–M system and one tetrahedral plot introducing Si on its own pole (i.e., an A–C–N–K–F–M–S system) are introduced. These three example tetrahedral plots are

  • (1) the A–CN–K–FM tetrahedral plot (see also Fedo and Babechuk 2023) to study reducing weathering (no oxidation of Fe2+ to Fe3+, depletion and (or) redistribution of Fe with Mg) trends that separate the effects of feldspar (both plagioclase and K-feldspar) and mafic mineral weathering in tandem with the effects of diagenesis/metasomatism (i.e., an ideal strategy for studying metasomatized Precambrian paleosols formed in reducing weathering environments);

  • (2) the AF–CN–K–M tetrahedral plot to study oxidative weathering (full oxidation of Fe2+ to Fe3+, immobility of Fe) trends that separate the effects of feldspar (both plagioclase and K-feldspar) and mafic mineral weathering in tandem with the effects of diagenesis/metasomatism (i.e., an ideal strategy for studying metasomatized Precambrian paleosols formed in oxidative weathering environments); and

  • (3) the A–CNKM–F–S (A–L–F–S) plot to study a full progression from incipient weathering to extreme weathering, i.e., the transition from weathering reactions (primary hydrolysis) forming kaolinite/halloysite (loss of “labile” elements, minor Si loss), commonly via other intermediary clay minerals (smectites, illite), and beyond into weathering reactions associated with extensive desilication and forming residual concentrations of Al-(oxy)(hydr)oxides (gibbsite, diaspore, boehmite) and Fe-(oxy)(hydr)oxides (hematite, goethite, maghemite).

The 3D tetrahedral analysis approach is demonstrated with previously published data from Phanerozoic mafic-rock weathering profiles spanning from saprolite to laterite/bauxite, and Precambrian mafic paleosols formed prior to and after Earth's Great Oxidation Event (GOE). These profiles record weathering conditions at different points across ca. 2.5 billion years of Earth's chemical weathering history and address the contrasting, redox-dependent weathering behaviour of Fe. More specifically, despite poor constraints on ancient Fe-oxidation kinetics and biological modulation of redox reactions (e.g., Planavsky et al. 2018), the Fe geochemistry of the Precambrian paleosol and siliciclastic sedimentary rock records indicates that reducing weathering conditions were typical in the Archean and early Paleoproterozoic, and that oxidative weathering conditions were typical from ca. 2.3 Ga onwards as the GOE triggered more extensive terrestrial Fe2+ oxidation (Kump and Holland 1992; Rye and Holland 1998; Bekker and Holland 2012; Young 2013).

The main goal of this study is to articulate the translation of whole-rock major-element data of mafic-rock weathering profiles from 1D (index) values into 2D (ternary plot) and 3D (tetrahedral plot) compositional space. The 3D tetrahedral spaces, or their ternary projections, integrate different iterations of the MIA or the IOL/IOB and provide a novel visualization of whole-rock major-element data that can reveal compositional evolution information not fully decipherable in ternary plots alone. By shifting elements across four poles, the tetrahedral plotting strategy ensures that greater accuracy in process-related conclusions is drawn from the integrative weathering index values preserved in modern and ancient chemical weathering profiles. The extra dimension in tetrahedral plots is key to seeing the competing effects of independent mineral weathering vectors on whole-rock compositions, and in illuminating element-specific diagenesis/metasomatism effects as they influence different precursor mineral assemblages. While the examples herein focus on mafic-rock weathering, the plotting strategy is not restrictive to either mafic source rocks or chemical weathering. Accordingly, this study pairs with Fedo and Babechuk (2023) in laying a strong foundation for how to work with major-element data in 3D compositional space to provide a more comprehensive understanding of source-to-sink siliciclastic sedimentary petrogenesis.

Mineral compositions

A compilation of mineral/mineral group compositions for this work, following the abbreviations of Whitney and Evans (2010), with some exceptions, includes quartz (Qz), albite (Ab), anorthite (An), plagioclase (Pl), K-feldspar (Kfs), calcite (Cal), hornblende (Hbl), olivine (Ol), augite (Aug), vermiculite (Vrm), montmorillonite (Mnt), nontronite (Non), kaolinite (Kln), halloysite (Hal), illite (Ilt), biotite (Bt), muscovite (Ms), and chlorite (Chl; represented by clinochlore/Clc). Also included are grouped Al- (gibbsite/Gbs, diaspore/Dsp; AlOx) and Fe- (goethite/Gth, hematite/Hem, maghemite/Mgh; FeOx) (oxy)(hydr)oxides. When combined as a group, anorthite, albite, and K-feldspar are listed as feldspar (Fsp). In recognition of the range of major-element substitution possible in some aluminosilicate minerals, mineral compositions measured directly from samples would be of ideal use for comparison to whole-rock major-element data. However, for the purpose of this study, all mineral compositions are taken from selected empirical analyses reported in Deer et al. (2013), with the exception of the Fsp, AlOx, and FeOx minerals that are assumed to be pure endmembers (Table 1; CJES-2022-053supplb). The positions of these minerals in selected ternary plots are shown in Figs. 2 and 3. The positions of each mineral in tetrahedral plots are shown in the supplementary figures (CJES-2022-053suppla), whereas the positions of the minerals relevant to specific tetrahedral plot examples are shown in Figs. 46.

Simplified stages of chemical weathering and compiled weathering profile data

Other studies have articulated details of the mineralogical, textural, and geochemical transformations accompanying the chemical weathering of basalt, which are not reviewed in detail here (e.g., Colman 1982; Eggleton et al. 1987; Nesbitt and Wilson 1992; Gislason and Arnórsson 1993; Widdowson 2007; Rasmussen et al. 2010). Instead, summative descriptions of stages of chemical weathering, with accompanying chemical trends and secondary mineral stabilities, are defined here as follows:

  • (1) Incipient

    • early loss of Ca, Na, and Mg (+Fe in reduced environments); minimal Si loss

    • Al and appreciable Mg and K conserved in 2:1 clays such as smectites and vermiculite during early conversion from igneous silicates; Fe conserved in Fe-(oxy)(hydr)oxides in oxidative environments

  • (2) Intermediate

    • moderate to extensive loss of Ca, Na, Mg, and K (+Fe in reduced environments); further Si loss

    • Al conserved in 2:1 clays that dominate mineralogy; appreciable Mg and K retained in 2:1 clays; Fe conserved in Fe-(oxy)(hydr)oxides in oxidative environments

  • (3) Advanced

    • near-complete to complete Ca, Na, Mg, and K loss (+Fe in reduced environments); greater Si loss

    • Al conserved in 1:1 clays such as kaolinite and halloysite that form from breakdown of 2:1 clays; Fe conserved in Fe-(oxy)(hydr)oxides in oxidative environments

    • incipient-to-advanced weathering stages typical of saprolitic profiles with the net process referred to as kaolinitization

  • (4) Intense

    • Si loss dominates; some Fe or Al loss/mobility possible

    • early stages of 1:1 clay weathering with most Al conserved in Al-(oxy)(hydr)oxides; most Fe conserved in Fe-(oxy)(hydr)oxides in oxidative environments

  • (5) Extreme

    • extensive Si loss ± Al > Fe or Fe > Al loss

    • near-complete to complete breakdown of 1:1 clays to Al-(oxy)(hydr)oxides if Al is retained; Fe possibly quantitatively retained in Fe-(oxy)(hydr)oxides.

    • Extreme weathering with Si+Fe loss resulting in Al-enriched residuum is considered bauxitization (producing bauxite), and that with Si+Al loss resulting in Fe-enriched residuum is considered lateritization (producing laterite).

All major-element data for modern and ancient mafic-rock weathering profiles for this work were compiled from previous studies. Weathering profiles selected for this study are summarized below along with relevant contextual information, and the profile major-element data are compiled and reported in the supplementary tables (CJES-2022-053supplb). Figure 1 shows field photos of weathering features from some of these selected profiles.

Pre-GOE mafic paleosol

The ca. 2.45 Ga K-metasomatized Cooper Lake paleosol developed on a mafic dike was selected to represent chemical weathering under a reducing atmosphere that resulted in no Fe2+ oxidation to Fe3+ and coupled loss and (or) internal redistribution of Fe+Mg (Sutton and Maynard 1993; Utsunomiya et al. 2003; Babechuk et al. 2019). The paleosol was divided into chlorite-dominated and mica-dominated portions. The dike was interpreted as an intrusive feeder geologically associated with mafic volcanic rocks of the Thessalon Formation in the Huronian Supergroup (Bennett et al. 1990, 1991; Young et al. 2001; Ketchum et al. 2013). A mean composition (n = 12) of the Thessalon volcanic rocks with the closest geochemical affinity to the dike (based on immobile element geochemistry) was taken as the parent rock composition (Ketchum et al. 2013; Babechuk et al. 2019). Samples of other Thessalon Formation volcanic rocks from drill core in the area of the paleosol outcrop (Sutton and Maynard 1993; Utsunomiya et al. 2003) are plotted for comparison.

Post-GOE mafic paleosol

The ca. 1.85 Ga Na- and K-metasomatized Flin Flon paleosols developed on variably seafloor-altered mafic volcanic “greenstone” were selected to represent chemical weathering under an oxidized atmosphere that resulted in near-complete Fe2+ oxidation to Fe3+ (Goetz 1980; Holland et al. 1989; Pan and Stauffer 2000; Babechuk and Kamber 2013). The paleosols were divided into green-coloured (chlorite-dominated), maroon-coloured (hematite-/mica-dominated), and a colour intermediate between the latter two colours (mixed illite/chlorite with some hematite) portions, as described in the original studies. Of the samples identified in the original studies as least-altered greenstone (n = 8), the mean of a subset (n = 3) with a Ca-Na-Mg budget most comparable to fresh basalt-basaltic andesite was taken here as the parent rock composition. A mean composition of volcanic rocks from the Hidden Formation (n = 41), as reported in Babechuk and Kamber (2013) based on the data of DeWolfe et al. (2009), is plotted for comparison.

Phanerozoic weathering profiles

Four Phanerozoic weathering profiles developed on basalt were selected to represent chemical weathering across different stages of intensity. Incipient to advanced weathering is represented mainly by two saprolitic Pleistocene–Holocene weathering profiles: (1) the Chhindwara profile (upper flow only) from the Deccan Traps, India (Babechuk et al. 2014) and (2) the Baynton profile from SE Australia (Nesbitt and Wilson 1992). Intense weathering is represented by a deep Neogene–Holocene profile from Hainan Island, China (Ma et al. 2007). Extreme weathering is represented by three profiles: (1) Pleistocene–Holocene “ferruginous bauxite” (here: laterite) profiles developed on lava flows of the Koloa Volcanic Series, Hawaii (Patterson 1971); (2) the Cretaceous–Paleogene Bidar laterite profile from the Deccan Traps (Borger and Widdowson 2001); and (3) Late Eocene–Holocene bauxite profiles (Cowlitz and Columbia) developed on the Columbia River basalts, USA (Liu et al. 2013). The sample in the Bidar laterite profile immediately above the parent rock (BB-2) was grouped with saprolite rather than laterite. Parent rocks for each profile were taken as described in the original studies and are identified in the supplementary tables (CJES-2022-053supplb). A mean composition of these parent rocks from all Phanerozoic profiles was taken here as a wider parent-basalt composition.

The weathering profiles in this study were selected to include (1) only those with established mineralogical and textural traceability from parent rock to weathering profile, (2) only those interpreted to have negligible modification to their major-element composition from allochthonous element sources during chemical weathering stages, and (3) in the case of paleosols, only those restricted to passing geological, mineralogical, and geochemical screening criteria to be considered a likely or definite paleosol as per Rye and Holland (1998). The latter screening included immobile-element ratio analysis with an extended suite of high field strength elements beyond Al and Ti (Zr, Hf, Nb, Ta; Maynard 1992; Babechuk et al. 2015). Thus, all chemical trends can be considered to arise primarily from in situ chemical weathering and, when relevant, later diagenetic/metasomatic overprinting of the originally weathered substrate. Applying the ternary and tetrahedral plots in a manner similar to the outlines provided in this study should be contingent on the same type of independent geological assessment. Furthermore, chemostratigraphic elemental analysis (chemical trends vs. depth) should be performed on all weathering profiles to confirm the autochthonous nature of the weathered material and examine for any vertical redistribution trends that aid interpretations of plotting positions in 2D/3D compositional space.

Unweathered igneous rock data and weathering vector models

Unweathered igneous rock compositions were taken from the mean values reported in Le Maitre (1976). The positions of these igneous rock compositions in selected ternary and tetrahedral plots are shown in the supplementary figures (CJES-2022-053suppla). Modeled weathering vector trends, calculated on a molar oxide proportion basis, were generated to demonstrate specific elemental controls on weathering index values and to plot in ternary and tetrahedral space as references. Starting compositions for models were represented by profile-specific parent rock values, unweathered igneous rock values, or a modeled composition already depleted in other selected elements. The model trends for the weathering of igneous rocks are available in the supplementary tables (CJES-2022-053supplc). The model weathering trends from the basalt composition of Le Maitre (1976) are used in figures showing example mafic-rock weathering trends (Figs. 2 and 3).

For weathering vector models, elements or groups of elements were depleted in either 1:1 (e.g., Ca = Na) or 2:1 (e.g., (Ca+Na) > Mg) proportions, reflecting a broad mineralogical control on main elemental trends (e.g., Ca+Na in plagioclase, K in K-feldspar, Fe+Mg in ferromagnesian minerals), in 10% increments with all other elements assumed to behave conservatively. For incipient-to-advanced weathering stages, reference lines of Ca+Na+K+Mg(±Fe) loss (1:1:1:1) or Ca+Na (1:1) loss followed by K+Mg(±Fe) (1:1) loss are typically shown on plots. Equal-proportion depletion vectors (vs. disproportional element depletion) and a two-stage depletion were favoured for two reasons. First, equal-proportion element depletions appear as linear trends in 3D space, and make more apparent the curvilinear nature of empirical data trends caused by disproportionate element loss from different minerals or mineral groups. Second, two-stage evolution reflects the long-standing empirical observations in weathering profiles drawn from A–CNK–FM and A–CN–K ternary plots (e.g., Nesbitt and Young 1989; Nesbitt 2003). Specifically, it is common for Ca+Na loss to begin and reach completion prior to complete Mg±Fe and K depletion. This reflects plagioclase weathering directly to kaolinite, while aluminous ferromagnesian minerals (e.g., pyroxenes, biotite) and K-bearing minerals (e.g., K-feldspar, muscovite) are weathering to intermediate 2:1 clays (with higher cation retention capacity), prior to the latter clays weathering further to kaolinite. However, there are exceptions in natural weathering systems related to factors such as source-rock texture and mineralogy and drainage conditions during weathering. For example, when olivine is a major mineralogical component of a source rock, some empirical observations point to olivine weathering to “iddingsite” during incipient-to-intermediate weathering stages being associated with some whole-rock Mg loss in parallel with or preceding Ca+Na loss (Nesbitt and Wilson 1992; Thorpe and Hurowitz 2020). No attempt at generating reference lines from thermodynamic mineral weathering data were undertaken here; a caution on the challenges associated with doing this for complex multi-mineral systems was outlined in earlier studies (Nesbitt and Young 1989; Nesbitt 1992).

Presentation of 3D data

All tetrahedral plots were constructed with recast proportions of moles of major-element oxides following similar conventions as for ternary plots. Four proportions of major-element oxides were recast as a fraction of their sum for plotting, with combined element proportions (e.g., CaO*+Na2O) added together before recasting. The CaO* value was designed to reflect the CaO hosted in silicate minerals only (i.e., corrected to remove nonsilicate-hosted Ca); however, exceptions in application exist and commonly not all data are available for full correction of CaO to CaO* (e.g., missing constraints on carbonate abundance). Example calculations are built into the supplementary tables (CJES-2022-053supplb; CJES-2022-053supplc).

Tetrahedral plots were prepared with the freeware CSpace (Torres-Roldan et al. 2000) and are presented in 3D orientations selected to best illustrate specific trends or features of the example tetrahedral system. Tetrahedral information is also presented on an unfolded 2D plane composed of four ternary plot projections, including onto the base of the tetrahedron. For consistency, tetrahedral plots are unfolded from the nadir view of the Al2O3 or Al2O3+Fe2O3(T) pole with the base of the tetrahedron at the centre. In the unfolded view, all sample positions are equivalent to a projection from the missing pole of the 3D system through the sample points in tetrahedral 3D space onto the opposite ternary plane. The latter presentation helps in forming visual links of tetrahedral plots with ternary plots and reveals the integration of 1D weathering indices into some of the ternary plot projections, despite inherently removing the interrelated compositional changes only visible in 3D. For example, projection from the K pole of a tetrahedron results in K-free ternary plots that integrate K-free versions of the MIA and that track weathering progression free from the effects of K-metasomatism (Babechuk et al. 2014). In contrast, some 1D weathering indices are integrated only into the tetrahedral space of the defined systems and not onto projected ternary planes.

MIA layout and equations

The MIA was calculated using proportions of molar oxides and, if appropriate, using corrections to CaO for nonsilicate Ca contributions from one or more of apatite, carbonate, and Ca sulfate (CaO*) as per the CIA (Fedo et al. 1995; Babechuk et al. 2014; Gwizd et al. 2022). The index assumed conservation of Al±Fe in secondary minerals. The contrasting redox behaviour of Fe led to two iterations of the MIA, the MIA(O) and MIA(R), for oxidative or reducing weathering, respectively.

The MIA(O) places total Fe as an immobile element alongside Al, assuming that Fe2+ oxidation to Fe3+ is kinetically rapid and complete, such that Fe is conserved at or very near its igneous mineral source via in situ formation of secondary Fe3+-bearing clays or Fe-(oxy)(hydr)oxides. The MIA(R) places total Fe as a mobile element, assuming that Fe2+ is not oxidized and instead removed in solution alongside Mg during the weathering of mafic minerals. In both iterations, the MIA increases from the value of the starting composition of a rock towards 100, representing complete loss of labile elements (Ca, Na, K, Mg±Fe). However, when applying the MIA(R) to cases of oxidative weathering with quantitative Fe conservation, the index value will have a maximum lower than 100, equivalent to the Al2O3/(Al2O3+FeO(T)) ratio of the parent rock. See Table 1 and the supplementary tables (CJES-2022-053supplc) for calculations of the maximum MIA(R) values for the oxidative weathering of different igneous rock types. In contrast, MIA(O) values of 100 are achievable when applying this iteration of the index to cases of oxidative or reducing weathering.

Note that MIA values are amenable to small changes depending on the choice to express the moles of total Fe as either Fe2O3(T) or FeO(T). In this contribution, FeO(T) was used for the MIA(R) and in the A–CNK–FM and A–CN–K–FM plots, consistent with the original “mafics” plot (Nesbitt and Young 1989), whereas Fe2O3(T) was used for the MIA(O) and in the S–A–F, A–L–F, AF–CNK–M, AF–CN–K–M, and A–CNMK–F–S (A–L–F–S) plots, consistent with the original MIA proposal in Babechuk et al. (2014). Any study comparing MIA values and analyzing trends/vectors on the aforementioned 2D and 3D plots should specify the form of total Fe used and inter-study data should be adjusted for consistency if needed. Weathering index and plotting position calculations using both Fe2O3(T) and FeO(T) are available in the supplementary tables (CJES-2022-053supplb), and an example of the MIA index value differences generated by using these different forms of total Fe is demonstrated with the common mineral and igneous rock data in Table 1.

Advantages and limitations of the MIA compared with the CIA

The CIA is arranged such that intermediate-to-felsic igneous rocks have a CIA value close to that of plagioclase and K-feldspar (50), which are the dominant mineral hosts of Ca, Na, and K in igneous rocks (e.g., andesite/diorite to rhyolite/granite: 46–51; Table 1). Mafic rocks typically have lower CIA values (∼40; Table 1) due to some Ca being hosted in pyroxenes in addition to plagioclase. Intrusive ultramafic rocks containing abundant pyroxene and less plagioclase are typically lower in CIA than mafic rocks (e.g., pyroxenite to harzburgite: 21–30; Table 1). The MIA(O) is lower than the CIA for mafic rocks (typically between ∼30 and 40; Table 1; Babechuk et al. 2014), and values increase gradually from mafic rocks to felsic rocks (∼48–53 for granodiorite to granite; Table 1). The MIA(R) is lower than the MIA(O) for igneous rocks; there is a greater variability across the igneous spectrum because the index is influenced by changes in both Fe and Mg. The MIA(O) and MIA(R) are both significantly lower for ultramafic rocks than other igneous rock types due to the low abundance of Al, Ca, Na, and K, and high abundance of Fe and Mg.

An advantage of the MIA over the CIA, especially when applied to mafic-to-intermediate igneous rock weathering, is that index values approaching 100 (though note the MIA(R) value restriction at values less than 100 when Fe is conserved in oxidative weathering) better represent the full breakdown of igneous silicates to advanced secondary mineral products such as kaolinite and halloysite, commonly via intermediate vermiculite, illite, or smectites, depending on the primary igneous silicates. For example, Ca-, Na-, and K-poor secondary minerals such as chlorite and vermiculite have a CIA of ∼100 despite hosting a significant budget of labile Mg (±Fe); the weathering progression associated with these Fe+Mg-bearing minerals can go uncaptured when using the CIA only. Thus, it is possible to reach inaccurate assumptions regarding total labile element leaching (see further discussion in Fedo and Babechuk 2023). The influence of ferromagnesian aluminosilicate minerals on the MIA increases in proportion with the abundance of these minerals in the source rock. Nevertheless, except for the most silicic source rocks, the MIA can also aid in studying intermediate-to-felsic igneous rock weathering despite the MIA being progressively more controlled by Ca, Na, and K. The MIA can also aid in studying ultramafic rock weathering, but the high sensitivity of the index to parent-rock mineralogical/compositional variations for intrusive ultramafic rocks (e.g., dunite to harzburgite) can make it challenging to track weathering across petrologic contacts. Similarly, for extrusive ultramafic rocks such as komatiite flows, starting values of the MIA will vary from flow base to flow top as a function of intra-flow crystal fractionation.

Due to source-rock effects on the MIA, this index is most powerful when working with a weathering progression from a singular parent rock with a defined starting MIA value (e.g., in weathering profiles developed on a homogeneous igneous parent rock) or with sediment drawn from monolithological catchments. On the same grounds, inter-profile comparisons need to more carefully account for parent rock MIA differences (e.g., by normalizing changes in MIA to the parent rock value) than for the CIA. Applying the MIA to establish the extent of source weathering preserved in sediment and sedimentary rock is possible, but is an exercise that must be undertaken with caution. Independent of source-rock compositional variation (provenance) and source-rock weathering, hydrodynamic mineral mixing/sorting, and authigenesis (e.g., Fe-(oxy)(hydr)oxide precipitation) can all introduce more significant index changes to the MIA than to the CIA. These effects can be difficult to untangle when sediment is sourced from mixed lithology catchments, especially without independent constraints on source-rock contributions (e.g., via insoluble/immobile trace-element ratios) and without firm constraints on mineral mixture/sorting and authigenic effects. Linking effects across the sedimentary petrogenesis spectrum to changes in MIA are argued by Fedo and Babechuk (2023) to be best analyzed in 3D tetrahedral compositional space instead of 2D ternary compositional space.

The MIA(O) and MIA(R) consider end member redox behaviour of Fe being either fully oxidized or fully reduced. Accordingly, applying one of these MIA iterations is less effective for weathering environments with sharp redox gradients where Fe can be mobilized in some areas and fixed in others. The MIA is ideally, even if not required, applied in combination with independent measurement of Fe redox speciation between Fe2+ and Fe3+ and, in the case of weathering profiles, with consideration of chemostratigraphic Fe distribution relative to typically immobile elements such as Al or Ti to evaluate any vertical distribution trends. Tightly coupled Fe and Mg behaviour in weathering profiles, especially with down-profile enrichment, is commonly supporting evidence for Fe having been cycled exclusively, or at least primarily, as Fe2+. Some details of Fe redox variations may be evident on 2D and 3D plots that cast Fe on its own pole despite being difficult to capture with the 1D index value alone.

Effects of diagenesis/metasomatism on CIA and MIA values

Diagenesis/metasomatism adding alkali elements (most commonly K) to weathering profiles or siliciclastic sediment/metasedimentary rock via reactions with existing minerals (Środoń 1999) will produce MIA values lower than reached from preceding chemical weathering. Both iterations of the MIA (oxidative and reducing) can be calculated without K2O, producing the MIA(O) minus K (MIA(O)−K) and MIA(R) minus K (MIA(R)−K), in the same manner as proposed for the CIA−K/CIW (Harnois 1988; Maynard 1992). However, if parent rocks (or sediment/sedimentary rock) contain aluminous potassic phases, the CIA−K/CIW should not be used due to the indices not capturing any compositional changes related to these phases and these indices possibly leading to overestimation of the extent of weathering. For example, unweathered K-feldspar has a CIW of 100, the same as AlOx minerals as a final weathered end product (Table 1). In these cases, the plagioclase index of alteration (PIA) should be used instead (Fedo et al. 1995). When K was added to samples via diagenesis/metasomatism, the molar K2O can also be individually corrected prior to calculating the CIA and (or) plotting samples in the A–CN–K plot to examine predicted pre-metasomatism weathering trends (Panahi et al. 2000). The MIA−K variations suffer from the same limitations as the CIW/CIA−K, albeit to a slightly lesser effect, in that samples with an increasing abundance of aluminous potassic phases produce higher source-rock values. As such, using the MIA to study the weathering (±metasomatism) of intermediate-to-felsic igneous rocks needs to consider (1) the increasingly greater control that K-bearing minerals contribute towards the starting igneous rock MIA value (e.g., MIA(O) vs. MIA(O)−K differ by ∼4 to 10 units for granodiorite to rhyolite; Table 1), (2) that, similar to the CIW/CIA−K, MIA(R)−K and MIA(O)−K values for K-feldspar are 100, the same as AlOx minerals, and (3) that MIA−K values will not capture any effects of K-feldspar weathering. The MIA−K approach is most useful for studying the effects of chemical weathering in mafic-rock weathering profiles or mafic rock-derived sediment/metasedimentary rocks that are influenced by K-diagenesis/metasomatism (e.g., in K-metasomatized mafic paleosols), primarily because there is very little K (no K-feldspar) in the parent rock. With a negligible initial K budget, the MIA(O) and MIA(R) are approximately equal to the MIA(O)−K and MIA(R)−K, respectively (e.g., MIA(O) and MIA(O)−K differing between <1.0 for mafic rocks; Table 1), prior to diagenetic/metasomatic K addition. In such cases, the MIA−K values are an accurate representation of the pre-diagenesis/metasomatism maximum extent of weathering. With the use of A–C–N–K–F–M tetrahedral plots that retain separation of K from Ca+Na, visual correction to pre-diagenesis/metasomatism MIA values is possible for a range of rock types if the preceding weathering trends are known or can be reasonably predicted. The latter approach is demonstrated in this study with the MIA(R) for mafic rocks in the A–CN–K–FM tetrahedron (see also Fedo and Babechuk 2023).

When metasomatism involves the addition of elements other than K in the MIA formula (e.g., Mg; Nesbitt and Young 1989), the MIA value will also decrease, but in a way that is not as easily correctable for the 1D index value. However, such metasomatic trends can commonly be visually identified and evaluated on different A–C–N–K–F–M ternary plots (Fig. 2) and tetrahedral plots (Figs. 4 and 5) as deviations from predicted/observed weathering trends. The latter approach is demonstrated for the case of Na-metasomatism (in addition to K-metasomatism) with the MIA(O) for mafic rocks in the AF–CN–K–M tetrahedron.

A–CNK–FM plot and integration with the MIA(R)

The A–CNK–FM plot, or “mafics” diagram, (Fig. 2a) is applied extensively in investigations of terrestrial and Martian weathering and siliciclastic sedimentary processes. Example applications beyond the investigation of chemical weathering include physical processes such as hydrodynamic sorting and tracking authigenic oxide formation or carbonate and sulfate alteration (see some example pathways in Fig. 2). Details of these extended A–CNK–FM plot applications are outlined in more detail elsewhere (e.g., for applications to Martian sedimentary systems, see McGlynn et al. 2012; McLennan et al. 2014). Here, emphasis is on use of the A–CNK–FM plot to study mafic rock weathering. A summary of oxidative weathering trends is provided (see Fedo and Babechuk 2023 for more details), but focus is instead on reducing weathering trends as one of the best applications of this A–C–N–K–F–M arrangement.

The MIA(R) can be integrated into the A–CNK–FM plot as horizontal tie lines between the A–CNK and A–FM joins, increasing upwards towards the A pole. The MIA(R) is equivalent to the recast A value in this ternary system. Oxidative weathering trends that conserve Fe result in a maximum achievable MIA(R) value (after full depletion of Ca, Na, and K) in the A–CNK–FM plot that is equivalent to the parent rock Al2O3/(Al2O3+FeO(T)) ratio, whereas reducing weathering trends can reach an MIA(R) value of 100 that is equivalent to the A pole of the ternary plot. The grouping of Fe and Mg on the same pole does not permit the integration of the MIA(O) into the A–CNK–FM plot.

Oxidative weathering results in vectors in the A–CNK–FM plot away from the CNK (feldspar weathering) and FM (mafic mineral weathering) poles through the position of the parent rock (Fig. 2a, left). Incongruent element release during mineral weathering generates a two-stage vector evolution, typically with an initial trend dominantly away from the CNK pole (yellow arrow) followed by a trend away from the FM pole (blue arrow). Early loss of Mg from olivine could produce a trend away from the FM pole (dashed light blue arrow) through the parent rock prior to the aforementioned two-stage evolution. The CNK and M vectors can also be summative despite CNK loss still dominating, producing a steeper net vector trending towards a point on the A–FM join closer to the A pole (green arrow) than a line from the CNK pole through the parent rock. Such cases indicate combined mafic mineral and feldspar weathering, with increasingly steeper slopes corresponding to an increasingly greater relative rate of element loss from mafic minerals. After full loss of CNK, a vector inversion occurs with more advanced weathering being direct towards the A pole along the A–FM join. For oxidative weathering where Fe is conserved, the grouping of Mg and Fe on the same pole results in a limited overall magnitude of the Mg-loss vector from this FM pole (i.e., samples will not plot in ternary space corresponding to Al2O3/FeO(T) ratios above that of the parent rock). This compositional space restriction is reflective in a low range of MIA(R) values from parent rock to derivative weathered material depleted of all Ca, Na, K, and Mg. Greater ferromagnesian mineral abundance corresponds to lower maximum achievable plotting positions towards the A pole and thus a lower maximum MIA(R) value.

Reducing weathering results in vectors in the A–CNK–FM plot away from the CNK and FM poles, as described above, but with the loss of Fe and Mg being summative and producing a vector with greater magnitude away from the FM pole (Fig. 2a, right). The loss of Fe alongside Mg opens up a greater area in the upper space of the ternary plot, with sample plotting positions as far as to the A pole achievable. This reducing weathering scenario is more appropriate for applying the MIA(R) index and corresponds to the wider range of values from parent rock to weathered material fully depleted in Ca, Na, K, Mg, and Fe (i.e., MIA(R) of 100). Congruent to near-congruent weathering of mafic minerals and feldspar(s) produces a near-vertical trend from the position of the parent rock towards the A pole (brown arrow). In contrast, incongruent element loss from feldspars relative to mafic minerals and (or) a greater relative retention of Fe and Mg in clay minerals produces a first vector with a shallower slope, dominantly from the CNK pole towards the A–FM join (yellow arrow), followed by a second vector with a steeper slope directed away from the FM pole towards the A pole (purple arrow). After full depletion of Ca and Na, more advanced weathering progresses along the A–FM join until complete loss of Fe and Mg (and K) at the A pole. The localized addition of Fe+Mg (e.g., via intra-profile redistribution) above parent rock values can potentially be examined via samples plotting below a modeled vector of Ca+Na loss closer to the FM pole (Fig. 2a). However, any Fe+Mg addition occurring after some Ca+Na+Fe+Mg depletion can be more difficult to detect because whole-rock compositions may still plot within compositional space generated only by elemental losses during chemical weathering.

Depending on the mineral host(s) of K, loss of K can occur at different stages of the previously mentioned oxidative and reducing weathering trends, and thus slightly deflect the described vectors in the A–CNK–FM plot. Nevertheless, the low initial budget of K in mafic rocks results in a limited influence from K in this ternary compositional space. This same low-K property of mafic rocks, however, makes post-depositional K addition more apparent than for cases affecting more felsic rocks. The influence of K addition to weathering profiles via diagenesis/metasomatism is evident in the A–CNK–FM plot via weathering trends being deflected towards the CNK pole. Commonly this occurs after Ca+Na and variable Mg (±Fe) and K loss such that the net result is a bulk sample trend between the A–CNK join and the A–FM join. The ultimate mineralogical residence of K in metasomatized and metamorphosed rocks is typically illite (and mixed-layer clays) and (or) muscovite (or other micas). Chlorite (after smectite) is also stable under the conditions producing micas such that samples tend to fall close to a tie line between chlorite and muscovite/illite on the A–CNK–FM plot (Fig. 2a).

AF–CNK–M plot and integration with the MIA(O)

The AF–CNK–M plot (Fig. 2b) provides an alternative ternary space to examine combined effects of feldspar and oxidative mafic mineral weathering. The key advantage of the plot is the separation of Mg from Fe, which alleviates the limited compositional space variation in the A–CNK–FM plot generated from Fe-retentive oxidative weathering (Fig. 2a). When using the AF–CNK–M plot, Fe is assumed, but ideally confirmed, to be immobile along with Al. However, the plot itself does not readily expose oxidative vs. reducing Fe behaviour due to the combination of Al and Fe on one pole. This Fe behaviour should instead be established independently prior to interpreting trends. A related limitation of the AF–CNK–M plot is the inability to clearly decipher Fe-mineral addition/mixing effects since labile element-free 1:1 clays, such as kaolinite, and Al-/Fe-(oxy)(hydr)oxides plot together as collective alteration products at the AF pole.

The arrangement of Al2O3 and Fe2O3(T) as immobile elements on the same pole of the AF–CNK–M plot allows integration of the MIA(O) as horizontal tie lines between the AF–CNK and AF–M joins, increasing upwards towards the AF pole. The MIA(O) is equivalent to the recast AF value in this ternary system. The element arrangement of this ternary plot does not integrate the MIA(R) nor is it particularly useful for reducing weathering trends since the AF pole then collects two elements with contrasting weathering behaviour.

The breakdown of feldspars and associated loss of Ca+Na+K and the breakdown of mafic minerals and the associated loss of Mg produce vectors from the corresponding poles at the base of the AF–CNK–M ternary plot through the position of the parent rock. The weathering vectors associated with these two mineral groups shift the composition of increasingly weathered materials upwards towards AF pole. The value of the plot, however, is the ability to more readily decipher whether feldspar and mafic mineral weathering and (or) the release of their budget of Ca+Na and Mg proceeds congruently or incongruently. An empirical trend from the parent rock directly towards the AF pole (green arrow) is indicative of a net vector arising from equal losses of Ca, Na, K, and Mg. In contrast, greater relative loss of Ca+Na+K (light green, yellow arrows) or Mg (dashed gray arrow) can produce net vectors that are shallower (towards either the AF–CNK or AF–M joins) until one of the mineral groups is depleted of its labile element budget. After the labile element budget from one mineral/mineral group is fully depleted, the net vector shifts to a steeper slope directed towards the AF pole away from only the pole linked to the mineral/mineral group with remaining labile element budget. Commonly, Ca+Na will be depleted during incipient-to-intermediate weathering stages, alongside some Mg and K, whereas the complete loss of Mg and K occurs subsequently during intermediate-to-advanced weathering stages. The addition of Mg to samples at levels exceeding parent rock values (via intra-profile redistribution or Mg-metasomatism) can potentially be detected from plotting positions below a modeled vector of Ca+Na loss closer to the Mg pole (Fig. 2b), as per Fe+Mg in the A–CNK–FM plot (Fig. 2a). However, effects from redistributed Mg or post-depositional Mg addition that occur after an earlier Ca+Na+Mg depletion can be more difficult to detect because whole-rock compositions may still plot within a compositional space generated by only element losses during chemical weathering.

The effects of K-metasomatism are recorded in the AF–CNK–M plot in a similar way as described for the A–CNK–FM plot, but the deviation from original mineral weathering vectors generated by K addition is more limited in comparison since the combination of Al and Fe results in less relative movement towards the CNK pole.

A–CNKM–F (A–L–F) plot, integration with the MIA(O), and intense to extreme weathering

The A–L–F plot (Fig. 2c) has a versatile arrangement of elements in the A–C–N–K–F–M system. Data arrays in this ternary space may reveal the magnitude of total labile element depletion, assess for reducing vs. oxidative weathering trends (in terms of Fe behaviour), and reveal trends associated with relative Fe- or Al-(oxy)(hydr)oxide enrichment during intense-to-extreme weathering. However, the grouping of all redox-insensitive, labile elements (Ca, Na, K, Mg) onto one pole removes the resolution of all mineral-specific effects.

The position of Al2O3 and Fe2O3(T) on their own poles opposite that of the pole grouping all labile elements allows the MIA(O) to be integrated into the A–L–F plot as diagonal tie lines connecting the L–A and L–F joins such that the index increases from the L pole towards the A–F join (Fig. 2c). Advanced-to-extreme weathering trends occur along the A–F join and are undetectable with the 1D MIA(O) value (i.e., they all occur at or near an index value of 100). This A–L–F ternary arrangement conceivably could be used with an incorporation of the MIA(R), with Fe2O3(T) instead of FeO(T) in the formula, as horizontal tie lines connecting the A–L and A–F joins such that index values increase upwards towards the A apex. However, this arrangement of elements on the poles is less useful for assessing reducing weathering trends since the trends linked to labile element loss from mafic minerals would be split across two poles.

The labile element grouping produces a single predictable weathering vector in cases where Al and Fe are quantitatively retained: a line from the L pole through the position of a parent rock towards the A–F join (Fig. 2c). The magnitude of this vector represents cumulative loss of the labile elements until reaching the A–F join (representing a substrate of only Fe-(oxy)(hydr)oxides and advanced clay minerals like kaolinite/halloysite). This cumulative vector will commonly involve Ca+Na loss first (from plagioclase; yellow arrow) alongside some Mg loss (with greater early Mg loss when olivine is weathered), followed by continued loss of Mg (from mafic minerals and secondary clays; blue arrow) and loss of K (from K-feldspars and clay minerals; magenta arrow). The advantage of the single predictable vector for oxidative weathering (Fe retained) is that the contrasting case of reducing weathering (Fe lost) can be detected by data plotting above this weathering vector, i.e., closer to the A pole and shifting away from the F pole (brown and purple arrows). This is possible because Fe loss during the incipient to advanced stages of reducing weathering will commonly occur while Al is retained. Such weathering conditions may also produce local zones in a weathering profile where Fe(+Mg) are enriched relative to the parent rock abundances, which can be detected by samples plotting slightly lower than the primary modeled oxidative weathering vector (i.e., closer to the F pole). This Fe+Mg addition would commonly occur deeper in a weathering profile in areas where these elements were scavenged after leaching from higher in the profile.

The A–L–F plot is unique relative to other ternary diagrams in the A–C–N–K–F–M system in its capacity to decipher some of the trends associated with intense and extreme weathering reactions (Nesbitt and Wilson 1992). These weathering conditions, typically occurring at or near complete labile element loss, can generate residual enrichment of Al or Fe that is tracked via trends plotting along the A–F join towards the A (bauxitization; gray arrow) or F (lateritization; red arrow) poles, respectively. These intense-to-extreme weathering stages are associated with 1:1 clay (kaolinite, halloysite) breakdown into Al-(oxy)(hydr)oxides, but can involve different Fe behaviour that includes loss of Fe2+ under localized reducing conditions at depth or by ligand-aided transport of Fe3+. The details of these latter processes are not readily decipherable from the A–L–F ternary plot. The primary compositional change occurring during intense to extreme weathering is controlled by Si loss, which is not directly apparent on the A–L–F, or any other ternary plot in the A–C–N–K–F–M system.

IOL/IOB layout and equations, traditional (wt.%) and new (molar)

Incipient-to-advanced weathering reactions are dominated by labile-element loss relative to Al (±Fe) with 1:1 clays (kaolinite, halloysite) as stable weathering products, whereas advanced-to-extreme weathering reactions are dominated by Si loss (desilication) to form Al- and (or) Fe-(oxy)(hydr)oxides. The IOL/IOB was developed as a 1D strategy to quantify the loss of Si primarily during these intense-to-extreme weathering stages. The index is arranged such that progressive loss of Si generates increasingly higher IOL/IOB values until complete Si loss at a value of 100. However, the index does not itself distinguish between weathering leading towards lateritic or bauxitic residues (i.e., whether Si loss is accompanied by Al > Fe loss or Fe > Al loss).

The traditional calculation of the IOL/IOB (see Babechuk et al. 2014, and references therein) uses proportions of wt.% oxides. The starting index value of mafic rocks is relatively limited (∼35–36; Table 1), and the values decrease for progressively more felsic igneous rocks (e.g., ∼18–20 for granite/rhyolite) due to the increasing proportion of Si and decreasing proportion of Fe during igneous fractionation.

Here, we propose that future applications of the IOL/IOB use molar oxide proportions, i.e., using the same calculation as above with molar proportions of SiO2, Al2O3, and Fe2O3(T), following convention with the original CIA calculation and derivative weathering index products. The same relative trends are preserved for the starting IOL/IOB values of igneous rocks as noted above, but the use of molar proportions shifts the absolute index values lower (e.g., mafic rocks at ∼21–22).

Both the wt.% (traditional; Fig. 3a) and molar (new; Fig. 3b) versions of the IOL/IOB are susceptible to changes in absolute value if total Fe is expressed as either FeO(T) or Fe2O3(T), similar to the MIA. For this study, all applications of the IOL/IOB and accompanying plots use Fe2O3(T).

IOL/IOB integration with the S–A–F plot and the “limit of kaolinitization”

The traditional IOL/IOB was designed to integrate into the S–A–F plot because both use recast proportions of SiO2, Al2O3, and Fe2O3(T) in wt.% (Schellmann 1981, 1982, 1986; Babechuk et al. 2014) (Fig. 3a). When the S–A–F ternary plot is oriented with the S pole at the top, the IOL/IOB index values are equivalent to horizontal tie lines connecting the S–A and S–F joins, increasing downwards in the ternary away from the S pole (0) towards the A–F join at the base (100). The plot separates a field of kaolinitization from a field of lateritization/bauxitization at a calculated “limit of kaolinitization”. This limit varies by parent rock type and corresponds to the amount of SiO2 wt.% loss needed for a specific parent rock composition to reach the SiO2/Al2O3 (mass/mass) ratio of kaolinite. In this traditional use of the S–A–F plot, the “limit of kaolinitization” is shown as a horizontal line at the recast SiO2 wt.% value where the latter SiO2/Al2O3 ratio is reached (IOL = 60 in example in Fig. 3a). The field of lower SiO2 below the “limit of kaolinitization” is divided by horizontal lines (specific relative SiO2 values) into three equal proportions, to define progressive stages (weak, moderate, strong) of lateritization/bauxitization (Fig. 3a).

In accordance with the proposed changes to the IOL/IOB, we propose that the S–A–F plot also use molar oxide proportions (Fig. 3b). In this molar version of the S–A–F plot, we recommend placing a fixed line starting from the position of kaolinite (/halloysite) along the S–A join (2/3 S and 1/3 A) connected to the F pole, forming a boundary that corresponds to the constant molar SiO2/Al2O3 of 2 for kaolinite. In terms of relative Si and Al proportions, on or above the line are igneous silicates and all 2:1 and 1:1 clay minerals, and below are Al-(oxy)(hydr)oxides. When whole-rock major-element compositions plot below the boundary, they have lower Si than can be readily attributed to retention in kaolinite/halloysite, the end product of advanced weathering (kaolinitization). Having this fixed kaolinite/halloysite line on the plot makes it easier to visually determine the “limit of kaolinitization” for the weathering of different parent rocks, but also to divide the remaining SiO2 below into three parent rock-specific proportions of weak, moderate, and strong lateritization/bauxitization, as per the traditional (wt.% oxide) use of the plot (CJES-2022-053supplc). For simplicity, the kaolinite/halloysite line is labelled as the “limit of kaolinitization” in the S–A–F ternary plot (Fig. 3b), despite the recognition that the specific limit for the weathering of different rock types will correspond to different SiO2 values in the plot. A trend from the S pole through the position of a parent rock (brown arrow) can be extended to its intersection with the kaolinite/halloysite line, which represents the “limit of kaolinitization” for the specific parent rock type. The recast molar SiO2 value/molar IOL value (horizontal tie line between S–A and S–F joins) at this intersection point starts the division of the remaining field below into the three equal stages of lateritization/bauxitization (example shown for basalt in Fig. 3b).

The plotting regions above the aforementioned intersection point but still below the “limit of kaolinitization” line in the S–A–F plot (light red shaded area) can only be reached by samples that experienced Fe loss near the transition from advanced to intense weathering. If it is unknown whether a ferruginous or aluminous alteration zone was developed predominantly in situ and from a specific identified parent rock, it is not recommended to include the subdivisions into different stages of lateritization/bauxitization. In quartz-undersaturated mafic rocks, Si is hosted in aluminosilicates and identifying the “limit of kaolinitization” and stages of lateritization/bauxitization as described above is straightforward. However, intermediate-to-felsic igneous rocks can contain an increasing abundance of Si from quartz. Quartz is more resistant to the effects of chemical weathering than aluminosilicates (Nesbitt et al. 1997), such that aluminosilicates can possibly weather beyond the “limit of kaolinitization” (i.e., starting to form Al-(oxy)(hydr)oxides), while whole-rock plotting positions remain above the “limit of kaolinitization” line due to Si in residual quartz.

Key applications and limitations

During incipient-to-advanced stages of oxidative weathering (assuming Al and Fe are immobile), the absence of other labile elements on the S–A–F plot reduces chemical weathering trends to one of a Si loss line from the S pole through the position of the parent rock. This line shows the extent of Si depletion across these early stages of weathering prior to reaching the “limit of kaolinitization”, which correspond to more limited changes to IOL/IOB values compared with the subsequent intense-to-extreme weathering stages. The latter stages are where the IOL/IOB values and accompanying S–A–F plot are most useful, and in combination with each other because the 1D index value alone does not distinguish between relative enrichment of Al > Fe or Fe > Al during the more advanced stages of Si loss. Samples clustering close to a vector of Si loss only (gray arrow) in the S–A–F plot (Fig. 3b) represent intense to extreme weathering where Al and Fe was retained close to their proportions in the parent rock. Samples deviating left towards the Al pole or right towards the Fe pole can be considered to be evolving towards bauxite or laterite, respectively.

The application of the S–A–F plot described above is as proposed in the original studies introducing this approach (Schellmann 1981, 1982, 1986), in a manner that assumes profiles developed by residual enrichment of elements from a parent rock (autochthonous development) and considering weathering products to be bauxite or laterite sensu stricto (Aleva and Creutzberg 1994; Widdowson 2007). Applying the S–A–F plot and IOL/IOB in this manner is understood to be an oversimplification of the complex processes potentially leading to the development of extremely weathered surface materials enriched in Al- and Fe-(oxy)(hydr)oxides, which can include ferricretes. For example, neglected are the potential for (1) Si redistribution leading to amorphous Si precipitation in profiles, (2) mixed autochthonous vs. allochthonous (lateral transport, airborne dust addition) controls on element additions and distributions, (3) physical translocation of weathered materials, and (4) complex redox-dependent and (or) ligand-dependent behaviour of Fe (Bourman 1993). The environmental conditions leading to either bauxite or laterite formation also differ (e.g., Schellman 1994), making the use of only relative chemical proportions of Si, Al, and Fe insufficient to extract all key information needed for robust paleo-environmental reconstruction. In part for these reasons, and also due to unclear and inconsistent nomenclature usage of “laterite,” there has been criticism and debate regarding potential misuse of the S–A–F plot to infer processes based on plotting positions (Bourman and Ollier 2002; Schellmann 2003). This limitation is reemphasized here as a cautionary reminder; we stress that best-practice application of the IOL/IOB and S–A–F plot requires independent establishment of geological field relationships and textural and mineralogical evolution of extremely weathered surface materials before integrating geochemistry-based interpretation. With these factors taken into consideration, the S–A–F plot is a useful tool to decipher intense-to-extreme weathering processes.

The S–A–F plot can also be useful in examining Fe vs. Si trends during reducing weathering (Fe mobile and Al immobile). In such cases, the loss of Fe during incipient-to-advanced weathering stages is tracked with a vector away from the F pole. When combined with the redox-independent Si-loss vector away from the S pole, reducing weathering would produce a net vector from the position of the parent rock towards the S–A join (ultimately evolving towards the position of kaolinite), which could be accompanied by a (possibly misleading) decrease in the IOL/IOB index value. After full Fe depletion, near the transition from advanced to intense weathering (i.e., near the “limit of kaolinitization”), further Si loss during chemical weathering would then be tracked by a vector extending along the S–A join below the position of kaolinite towards the A pole. In this way, the S–A–F plot can be useful as an accompaniment in assessing reducing (e.g., pre-GOE) chemical weathering, with an advantage of tracking Fe and Si loss across all major stages of weathering.

A–CN–K–FM tetrahedral plot

Overview and integration of 1D weathering indices

The A–CN–K–FM tetrahedral plot (Fig. 4; Fedo and Babechuk 2023) retains the advantages of the A–CNK–FM ternary plot (i.e., separating feldspar from mafic mineral weathering trends), but offers new potential to further distinguish K-feldspar (and other aluminous potassic phases) from plagioclase weathering effects and to reconstruct K-diagenesis/metasomatism trends while considering a more complete picture of preceding labile element depletion. The latter builds on the useful capacity of the A–CN–K plot for K-diagenesis/metasomatism corrections to now also decipher transformations of Fe+Mg-bearing clay minerals such as smectites to K-bearing mixed-layer clays or illite.

Orienting the A–CN–K–FM tetrahedral plot with A at the top of the tetrahedron best illustrates that the MIA(R) weathering index is integrated as horizontal planes connecting the A–FM, A–CN, and A–K joins, with the index increasing upwards in the tetrahedron towards the A pole (100). The MIA(R) is equivalent to the recast A value in this tetrahedral system. Of the four unfolded ternary faces of the A–CN–K–FM tetrahedron (Fig. 4, top), one ternary projection represents the A–CN–K plot (Fedo and Babechuk 2023, discusses this projection in detail), integrating the CIA as tie lines between the A–K and A–CN joins. Another projection is the A–CN–FM plot, integrating the MIA(R)−K weathering index as horizontal tie lines between the A–CN and A–FM joins. For mafic rocks with negligible initial K, the latter is equivalent to showing the projection of samples from the K pole to a ternary plane that reveals weathering trends prior to K addition via diagenesis/metasomatism.

Of several potential ways to apply the A–CN–K–FM plot (see Fedo and Babechuk 2023, for others), this study focuses on reducing mafic-rock weathering where predicted weathering vectors result in the coupled loss (and (or) potential redistribution) of Fe and Mg.

Primary (reducing) weathering trends

Ancient reducing weathering trends are illustrated here using the example of the ca. 2.45 Ga Cooper Lake paleosol (Sutton and Maynard 1993; Utsunomiya et al. 2003; Babechuk et al. 2019). Under reducing conditions, igneous aluminosilicate mineral weathering forming Al-bearing secondary minerals produces vectors of different slopes directed towards the A pole of the A–CN–K–FM plot (Fig. 4). In a similar manner to using the A–CNK–FM ternary plot (Fig. 2a), whether plagioclase and mafic minerals released their labile element budgets congruently or incongruently can be determined in the A–CN–K–FM plot (Fig. 4) with comparison to model vectors representing the endmember cases of Ca+Na (1:1) depletion only (yellow arrow) followed by Fe+Mg+K (1:1:1) depletion (purple arrow) and Ca+Na+Fe+Mg+K (1:1:1:1:1) depletion (brown arrow) from the parent rock composition. The Cooper Lake paleosol samples recording incipient-to-intermediate weathering stages plot closer to the modeled line of only Ca+Na loss from the parent rock. The samples could then be predicted to follow a modeled weathering vector of Fe+Mg+K loss away from the FM and K poles (purple arrow; note that the parent rock K budget is minimal) towards the A pole starting from the modeled Ca+Na-depleted composition. Indeed, the samples corresponding to intermediate-to-advanced weathering stages follow a steeper trend towards the A pole after Ca+Na depletion, consistent with coupled Fe+Mg loss, but are directed more towards the A–K join than the A pole (due to the K-metasomatism discussed below). Thus, the data array in the A–CN–K–FM plot reveals that samples broadly follow a two-stage trend with a dominant vector from the CN pole and then from the FM pole. This observation indicates that element loss during mineral weathering was incongruent, with depletion of Ca+Na from plagioclase dominant during early weathering stages and essentially complete prior to significant depletion of Fe+Mg from mafic minerals. During these early weathering stages, most Fe+Mg was retained in 2:1 clays (smectites) until these clays weathered to 1:1 clays (e.g., kaolinite) at more advanced weathering stages. The two-stage primary chemical weathering and Fe+Mg redistribution trends are also apparent in the unfolded A–CN–FM ternary projection (Fig. 4) in a manner similar to that described for the A–CNK–FM plot (Fig. 2a).

In more detail, many Cooper Lake paleosol samples showing Ca+Na depletion during early weathering stages plot slightly above the modeled line from the CN pole in the A–CN–K–FM tetrahedron, in a direction slightly away from the FM pole that reveals a minor component of Fe+Mg loss in parallel with Ca+Na loss. In other words, many samples follow a more curvilinear trend from combined plagioclase and mafic mineral weathering effects. Furthermore, some samples plot closer to the FM pole, below the model Ca+Na depletion line; these samples correspond to areas of the profile where Fe+Mg was accumulated via scavenging by and incorporation into 2:1 clay minerals (Babechuk et al. 2019). The Fe+Mg was lost from areas of more advanced weathering and redistributed within the profile. In the case of the Cooper Lake paleosol, the Ca+Na+Fe+Mg(+K) loss proceeded preferentially both in areas closer to the unconformity (i.e., closer to the paleo-surface) and along edges of the dike hosting the paleosol, with Fe+Mg redistributed preferentially into the dike centre and at greater depth below the unconformity.

The intermediate-to-advanced weathering products of the Cooper Lake paleosol reach plotting positions in the A–CN–K–FM tetrahedron close enough to the A pole (corresponding to MIA(R) values reaching up to ∼62) that are only possible if Fe was mobile and removed from the system. If Fe was fully retained alongside Al, the magnitude of the vector from the FM pole would be limited by the Al2O3/FeO(T) ratio of the Cooper Lake paleosol parent rock, which corresponds to an MIA(R) of 45.5. This maximum MIA(R) for oxidative weathering is marked as a horizontal plane approximately halfway up the tetrahedron, and the limit is equivalent to the same value of MIA(R)−K as evident in the A–CN–FM ternary projection (Fig. 4). Note that this plane projects to a shaded ternary “area”, where samples in the shaded area correspond to those exceeding the Al2O3/FeO(T) ratio of the parent rock in the recast ternary compositional space. The latter area is shown only for the two unfolded ternary projections that contain both an A and FM poles (the A–CN–FM and A–FM–K projections). The maximum MIA(R) values recorded by the Cooper Lake samples are a minimum indicator of total labile element leaching due to the MIA(R) being influenced by later K addition via diagenesis/metasomatism.

Diagenesis/metasomatism trends

The paleosol samples recording intermediate-to-advanced weathering stages are offset from the modeled vector of Fe+Mg+K loss (after Ca+Na loss) towards the K pole in the A–CN–K–FM plot due to the later addition of K to the profile. This offset exposes the advantage of placing K on its own pole (rather than coupled with Ca+Na) as a means to track and reverse the effects of K-metasomatism. The greatest K addition occurred in the most highly weathered (most Al-enriched) areas of the profile and decreased progressively in samples that retained more Fe+Mg in clays prior to K addition. Reversing the effect of this K addition to a pre-metasomatism composition can be achieved in the A–CN–K–FM tetrahedral space with a line projected from the K pole through the position of the paleosol sample onto the original modeled weathering vector of Fe+Mg+K loss (shown in Fig. 4 with three example trends, magenta arrows, representing different extents of weathering prior to K addition). The A–CN–FM ternary projection also shows that the maximum extent of weathering recorded by the paleosol as a MIA(R)−K value is ∼80, which, due to the negligible K in the mafic parent material, can be considered approximately equivalent to a pre-metasomatism MIA(R) value. The projection approach in the tetrahedron confirms the close correspondence of the pre-metasomatism MIA(R) values and the MIA(R)−K values.

The K-diagenesis/metasomatism reversal steps above are performed in a manner similar as achieved in the ternary space of the A–CN–K plot (Fedo et al. 1995), as illustrated on the A–CN–K ternary projection (the inverse of the well-known CIA plot) of the A–CN–K–FM tetrahedral plot in Fig. 4. The latter projection reveals that pre-metasomatism CIA values were ∼100. However, the perspective offered from the more limited A–CN–K system neglects the compositional effects associated with mafic mineral-derived clays before and after metasomatism (e.g., smectites, now preserved as chlorite and mixed-layer illite-chlorite). The neglect of this mafic component can produce misleading interpretations if the high pre-metasomatism CIA value is taken as indicative of a substrate that was dominated by kaolinite (or halloysite) and that K addition is assumed to have been accommodated only by reaction of K with kaolinite to produce micas/illite. Chlorite and vermiculite are not advanced weathering products but have a negligible CNK component, and thus a CIA of ∼100 similar to kaolinite (Fedo and Babechuk 2023); the weathering of these minerals (associated with loss of Mg ± Fe) is not captured in the A–CN–K ternary space, occurring entirely at the CIA value of 100. In contrast, the A–CN–K–FM tetrahedral space reveals that K addition also modified less-weathered materials with varying proportions of remaining Fe+Mg. In other words, the plot captures that K addition is accommodated by a full spectrum of mixed illite-chlorite phases (Sutton and Maynard 1993; Babechuk et al. 2019). Thus, while the chemical effect of K-metasomatism is illustrated well in some ternary plots (Fig. 4), none of the ternary plots capture all of the primary mineral weathering trends (i.e., mafic mineral and feldspar weathering effects) prior to the overprinting effect of K-metasomatism, while also allowing the reversal of K addition to a pre-metasomatism composition. This can only be accomplished in a single composition space with the A–CN–K–FM tetrahedron.

Summary of the paleosol mineral-chemical evolution

In A–CN–K–FM compositional space, the Cooper Lake paleosol samples follow trends similar to a two-stage model of initial Ca+Na loss and then Fe+Mg loss, but with samples also showing a minor component of combined Ca+Na+Fe+Mg loss and some showing evidence for Fe+Mg addition. The second stage of the weathering reaches labile element loss beyond the maximum level achievable if Fe was quantitatively retained in the profile. While some of these trends are evident in an A–CNK–FM ternary plot, the A–CN–K–FM tetrahedral plot makes the combined compositional effects of Ca+Na+Fe+Mg-leaching and redistribution of Fe+Mg more apparent via curvilinear trends in 3D space and deviations from modeled vectors. Mineralogically, the maximum extent of weathering was significantly advanced with most 2:1 clay minerals converted to 1:1 clays such as kaolinite and halloysite, whereas less weathered areas were dominated by 2:1 layer clays (Fe2+-/Mg-bearing smectites), some of which scavenged Fe+Mg leached from elsewhere in the profile. The intermediate-to-advanced weathering trend in the A–CN–K–FM plot points to a position along the A–K join rather than the A pole, reflecting the increasing abundance of K in the most weathered samples, a component added during diagenesis/metasomatism. A projection-based approach in the A–CN–K–FM tetrahedral plot similar to the one used in the A–CN–K ternary (see Fedo et al. 1995) plot allows a visual reversal back to the state of Ca, Na, Mg, Fe (and K) depletion prior to K addition (i.e., considers preceding composition change from both feldspar and mafic mineral weathering), more accurately identifying the pre-metasomatism maximum extent of weathering. In the tetrahedron, the positions of chlorite-dominated and mica-dominated samples of Cooper Lake paleosol are close to a tie line between the mineral compositions of chlorite-illite and illite-muscovite, respectively, the metasomatized and metamorphosed products of the smectites and kaolinite inferred to originally be in the profile prior to burial and K addition.

AF–CN–K–M tetrahedral plot

Overview and integration of 1D weathering indices

The AF–CN–K–M tetrahedral plot (Fig. 5) retains the advantages of the AF–CNK–M ternary plot (i.e., separating feldspar from mafic mineral weathering trends), but offers new potential to further distinguish K-feldspar (and other aluminous potassic phases) from plagioclase weathering effects and to reconstruct K-diagenesis/metasomatism trends while considering a more complete picture of preceding labile element depletion. The latter builds on the useful capacity of the A–CN–K plot for K-diagenesis/metasomatism corrections to now also decipher transformations of Fe+Mg-bearing clay minerals such as smectites to K-bearing mixed-layer clays or illite. Like the AF–CNK–M plot (Fig. 2b), the positioning of Al and Fe together on one pole of the AF–CN–K–M plot (Fig. 5) makes this tetrahedral arrangement useful primarily to cases of oxidative weathering where Fe is retained alongside Al across all stages of incipient to advanced weathering. This behaviour of Fe should be independently established before plotting and interpretation.

Orienting the AF–CN–K–M tetrahedral plot with AF at the top of the tetrahedron allows visual demonstration that the MIA(O) weathering index is integrated as horizontal planes connecting the AF–M, AF–CN, and AF–K joins, with the index increasing upwards in the tetrahedron towards the AF pole (100). The MIA(O) is equivalent to the recast AF value in this tetrahedral system. Of the four unfolded ternary projections of the AF–CN–K–M tetrahedral plot (Fig. 5), one ternary projection is the AF–CN–M plot that integrates the MIA(O)−K weathering index as horizontal tie lines between the AF–CN and AF–M joins. For mafic rocks with negligible initial K, the latter is equivalent to showing the projection of samples from the K pole to a ternary plane that reveals weathering trends prior to K addition via diagenesis/metasomatism.

Primary (oxidative) weathering trends

Post-GOE oxidative weathering trends are illustrated here using deep profiles of the ca. 1.85 Ga Flin Flon paleosol (Goetz 1980; Holland et al. 1989; Pan and Stauffer 2000; Babechuk and Kamber 2013). Under oxidative conditions, igneous aluminosilicate mineral weathering to Al- and Fe-bearing secondary minerals, produces vectors of different slopes directed towards the AF pole of the AF–CN–K–M plot. In a similar manner to using the AF–CNK–M ternary plot (Fig. 2b), whether plagioclase and mafic minerals released their labile element budget congruently or incongruently can be deciphered in the AF–CN–K–M plot (Fig. 5) with comparison to model vectors representing the endmember cases of Ca+Na (1:1) depletion only (yellow arrow) followed by Mg depletion (blue arrow) vs. Ca+Na+Mg+K (1:1:1:1) depletion (green arrow) from the parent-rock composition. The Flin Flon paleosol samples (Fig. 5) indicate that element loss during mineral weathering was largely incongruent, with depletion of Ca+Na dominating at incipient-to-intermediate weathering stages (trend shown primarily by the green-coloured/chlorite-dominated paleosol) followed by depletion of Mg dominating at intermediate-to-advanced weathering stages (trend starting with the intermediate-coloured/mixed-layer clay-dominated paleosol and continuing into the maroon-coloured/mica/hematite-dominated paleosol). In other words, the paleosol samples follow a two-stage trend with a dominant trend first away from the CN pole and then away from the M pole. The green- and intermediate-coloured paleosol samples also have Mg abundances that commonly exceed that of the parent greenstone, suggesting that some of the Mg lost from more weathered (i.e., maroon-coloured) horizons of the paleosol was scavenged in deeper, less weathered horizons. The latter Mg redistribution is evident by plotting positions offset towards the M pole, below the modeled Ca+Na vector (yellow arrow).

Throughout the previously documented two-stage weathering progression captured in the Flin Flon paleosol, Fe is retained and the maroon colouration of the samples recording more advanced weathering (greatest Mg depletion) is, in large part, due to the increasing abundance of hematite (Holland et al. 1989; Babechuk and Kamber 2013). The most-weathered samples extend high into the AF–CN–K–M tetrahedron, corresponding to maximum MIA(O) values of ∼80, indicating extensive leaching of the labile elements while Fe was retained via (oxy)(hydr)oxide development. However, these MIA(O) values mark only a minimum indicator of the full extent of element leaching during chemical weathering due to the influence of both Na and K addition during diagenesis/metasomatism, as discussed further below.

In the case of the Flin Flon paleosol there were different mineralogical controls on the weathering trends than encountered during chemical weathering of “fresh” basalt, due to the parent rock being seafloor-altered greenstone. Specifically, some of the Ca was depleted from minerals other than plagioclase and pyroxenes, such as epidote and calcite, and most of the Mg was depleted from chlorite, actinolite, and some from relict pyroxenes—the seafloor hydrothermal alteration products of fresh igneous aluminosilicates. The seafloor hydrothermal alteration also generated some chemical variability across the parent greenstone prior to subaerial weathering profile development, which is evident through (1) the higher degree of Ca+Na depletion in samples significantly below the unconformity and identified texturally as least-weathered greenstone in original studies; (2) the high levels of K in some samples capturing the incipient-to-intermediate stages of weathering that are better explained by earlier seafloor-alteration effects than by later K addition via diagenesis/metasomatism (Babechuk and Kamber 2013); and (3) possibly some of the Mg addition in samples capturing the incipient to intermediate stages of weathering.

In addition to the carbonate interpreted to have formed during seafloor hydrothermal alteration, chemostratigraphic Ca trends are partly controlled by pedogenic carbonate that incorporated Ca leached from higher in the profile. As per Babechuk and Kamber (2013), the CaO* is corrected for apatite but not carbonate due to the CaO* corrections otherwise resulting in overestimates of the extent of weathering preserved in deeper areas of the profile (chlorite-dominated paleosol) and disruptions to the internal chemostratigraphic distribution trends of Ca. The upper part of the profile retains a small amount of Ca in apatite, but this is accounted for in the CaO* correction, which is ∼0 for these areas of the paleosol. As such, the samples from higher in the profile (mica/hematite-dominate paleosol) that do not show full Ca+Na depletion are due entirely to Na addition via diagenesis/metasomatism rather than from remnant carbonate or Ca-hosting silicates (Babechuk and Kamber 2013).

Diagenesis/metasomatism trends

The intermediate-to-advanced weathering trend of the Flin Flon paleosol (intermediate- to maroon-coloured) is offset from the modeled vector of Mg+K loss (after Ca+Na loss) towards both K and Na and thus pointing towards the AF–CN–K face, rather than offset towards just K and thus pointing towards the AF–K join (as per the case of K-diagenesis/metasomatism described with the A–CN–K–FM plot; Fig. 4). In the AF–CN–K–M tetrahedron, samples follow a more complex, rotated curvilinear trend due to the pull towards K on its own pole and partly back to the CN pole (noting that Ca has no influence here) across the preceding chemical weathering stages where Mg loss dominated. The greatest rotation is evident in the most highly weathered, maroon-coloured samples (closest to the A pole), consistent with the upwards chemostratigraphic enrichment of Na and K (Babechuk and Kamber 2013).

The combined effects of both K- and Na-metasomatism are exposed readily in the AF–CN–K–M tetrahedron, in a way not easily captured in the A–CN–K plot or A–C–N–K–F–M ternary plots. The A–CN–K plot is useful in examining the K-addition component of diagenesis/metasomatism and relating the preserved maximum CIA (∼80) to a pre-K-metasomatism CIA (∼90) of the Flin Flon paleosol via projection from the K pole to the A–CN join (not shown here, but see Babechuk and Kamber 2013); however, the addition of Na is not clear from this plot because Na addition tracks back along the initial weathering trend away from the CN pole. Correspondingly, even the pre-K-metasomatism CIA underestimates the maximum extent of weathering reached in the profile before later addition of Na. The grouping of Na and K on a single pole results in any diagenetic/metasomatic addition of both elements falling on the same vector such that individual alkali element effects are not decipherable. The individual effect of K-metasomatism is evident on the AF–M–K projection (free of Ca+Na) of the AF–CN–K–M tetrahedron as a deflected sample trend towards the AF–K join from a predicted initial Mg+K loss trend close to the AF–M join (Fig. 5). Similarly, the individual effect of Na-metasomatism is evident on the AF–CN–M projection (free of K) of the AF–CN–K–M tetrahedron as an offset of the full weathering trend towards the CN pole away from the modeled Mg+K loss line (after full Ca+Na depletion) and a greater rotated deflection towards CN in the most highly weathered maroon-coloured samples (Fig. 5). The latter AF–CN–M projection is also useful in two other ways, when applied with knowledge of the profile mineralogy and negligible initial K budget of the parent greenstone. First, this plot incorporates the MIA(O)−K and provides a visual means to track the combined effects of Ca+Na and Mg loss and Mg addition in some areas of the paleosol, and reveals the maximum MIA(O)−K of ∼90 reached during weathering. However, like the pre-K-metasomatism CIA value, the maximum MIA(O)−K is still a minimum estimate of the full extent of weathering reached. Recognizing that CaO* in the upper paleosol is ∼0 (all minimal remaining Ca is phosphate-hosted), the AF–CN–M plot can also be used similarly to the A–CN–K plot to project back to a pre-Na-metasomatism MIA(O) value of ∼100 (a line from the CN pole through the samples that ends near the AF pole).

From the analysis above, it is apparent that chemical weathering had originally depleted the entire budget of Ca and Na, such that the CIA (and other A–C–N–K-based proxies like the PIA; Fedo et al. 1995) were initially ∼100, and that advanced weathering depleted nearly all of the original Mg budget in the upper profile such that the MIA(O) reached as high as ∼100. These chemical weathering effects were obscured by the combined addition of Na and K during burial and diagenesis/metasomatism of the profile, but several of these details could be lost when analyzing trends with only the CIA or a limited set of A–C–N–K–F–M ternary plots. The AF–CN–K–M tetrahedron provides a singular compositional space that exposes the combined addition of Na and K across the full range of Mg depletion that developed during preceding stages of chemical weathering. However, correcting back to pre-metasomatism compositions in the AF–CN–K–M plot in a manner that accounts for both Na and K addition is not as easily achieved as for K addition only.

Summary of the paleosol mineral-chemical evolution

The pre-metasomatism position of the most weathered Flin Flon paleosol samples can be reconstructed to have been at the AF pole of the AF–CN–K–M tetrahedron, indicating that the extent of weathering was highly advanced with nearly all 2:1 clay minerals weathered to 1:1 clays such as kaolinite and halloysite. In the process, nearly all of the Ca, Na, and Mg budget of the parent greenstone was lost from the upper profile. Less weathered horizons of the profile were dominated by 2:1 layer clays (Mg-/Fe2+-/Fe3+-bearing smectites) that likely scavenged Mg lost from elsewhere in the profile, and pedogenic carbonate that likely scavenged Ca (and lesser Mg) lost from elsewhere in the profile. Across these stages of weathering Fe was near-quantitatively retained in Fe3+-bearing clays and Fe-(oxy)(hydr)oxides (now hematite), although, at the decimeter scale of corestones, mobility of Fe is apparent in some exposures of the paleosol (Sindol et al. 2020). In the lower horizons of the paleosol, the chemical effects of seafloor hydrothermal alteration in the greenstone are still apparent despite the subaerial weathering overprint (and the signatures from both processes can be difficult to separate from each other), but the more advanced weathering removed relict signatures of the seafloor alteration and homogenized the composition of the subaerially weathered substrate. The addition of both Na and K via diagenesis/metasomatism are apparent in the paleosol, but do not disrupt the trend of Fe retention throughout the subaerial weathering progression of the greenstone. The position of Flin Flon paleosol samples in ternary and tetrahedral plots is close to a tie line between the mineral compositions of chlorite and illite/muscovite, the latter being the metasomatized and metamorphosed products of the kaolinite/halloysite inferred to originally be in the upper horizons of the profile prior to burial and Na and K addition.

A–CNKM(L)–F–S tetrahedral plot

Overview and integration of 1D weathering indices

The A–L–F–S tetrahedral plot (Fig. 6) bridges two traditionally separated ternary plots, the A–L–F (Fig. 2c) and S–A–F plots (Fig. 3b), and is enabled by our recommended use of molar proportions in the S–A–F plot rather than wt.% oxide proportions. The loss of Si during incipient to advanced stages of weathering is not included in most 1D weathering indices, such as the CIA and MIA, nor is it visualized in A–C–N–K(–F–M) ternary plots. However, Si loss (commonly as silicic acid) starts from early stages of chemical weathering alongside other mobile elements (Ca, Na, Mg, K) as igneous aluminosilicates convert to 2:1 clays and these to 1:1 clays (kaolinite/halloysite) and later becomes the dominant chemical weathering trend during intense-to-extreme weathering stages as weathering products become dominated by Al- and Fe-(oxy)(hydroxides). Accordingly, the primary advantages of the A–L–F–S plot are its ability to track chemical changes across all stages of chemical weathering, from incipient to extreme, in a single 3D compositional space. The tetrahedron tracks whole-rock compositions as they evolve from plotting positions in 3D space (at incipient-to-advanced weathering stages) to plotting positions in 2D S–A–F space at the point of full Ca, Na, K, and Mg depletion and the remaining weathering tracked with Si loss. In this way, the A–L–F–S plot addresses the limitation of the A–L–F plot where Si loss accompanying incipient to extreme weathering is not tracked, and the limitation of the S–A–F plot where the loss of other labile elements during incipient to advanced weathering is not apparent.

Two of the four ternary projections on the unfolded A–L–F–S tetrahedral plot (Fig. 6) plot are the A–L–F plot that incorporates the MIA(O) (Fig. 2c) and the S–A–F plot that incorporates the IOL/IOB (Fig. 3b). It is via these two key ternary projections (A–L–F and S–A–F) that the 3D compositional space of the A–L–F–S tetrahedral plot bridges the two traditionally separated 1D index values across different stages of chemical weathering by visually monitoring combined Si and labile element (Ca, Na, K, Mg) loss.

Incipient-to-advanced oxidative weathering trends and the MIA(O) ternary projection

The chemical trends associated with a full spectrum of mafic-rock weathering stages are illustrated here using a compilation of basaltic weathering profiles spanning from Pleistocene–Holocene saprolite to older and deeper laterite and bauxite profiles (Patterson 1971; Nesbitt and Wilson 1992; Borger and Widdowson 2001; Ma et al. 2007; Liu et al. 2013; Babechuk et al. 2014). Under oxidative conditions, igneous aluminosilicate mineral weathering forming Al- and Fe-bearing secondary minerals produces a net vector controlled by both the loss of Si (away from the S pole through the parent rock) and other mobile elements (away from the L pole through the parent rock) in the A–L–F–S plot (Fig. 6). The samples from two different saprolitic weathering profiles (Baynton and Chhindwara; Nesbitt and Wilson 1992; Babechuk et al. 2014) define similar empirical trends from their respective parent basalt compositions (slight differences exist due to minor variations in original igneous mineral abundances). For comparison to the empirical trends, a model of labile element (Ca, Na, K, Mg) loss only, starting from the mean composition of all parent basalt samples, is added in Fig. 6. From this comparison, it is immediately apparent that across the stages of incipient-to-advanced weathering where 2:1 clays form, compositional change is dominated by the loss of Ca, Na, Mg, and K over Si, but Si loss has a clear influence (i.e., the empirical trend requires a vector contribution away from the S pole). As samples reach more advanced chemical weathering stages, there is a progressively more curvilinear empirical trend with a change towards a different slope marking greater relative Si loss. The slope change reflects the increasing formation of 1:1 clays (kaolinite, halloysite) during intermediate to advanced stages of weathering. At the point of reaching full labile element depletion, there is a loss of the 3D compositional component of the A–L–F–S plot with samples reaching the S–A–F projection. Subsequent chemical weathering trends are all captured on the S–A–F ternary projection (Fig. 6). Without considering Si, as per the A–L–F ternary projection of the unfolded A–L–F–S plot, the loss of labile elements prior to this stage is tracked with the MIA(O).

The chemical trends described above are premised on the quantitative retention of Fe across incipient-to-advanced weathering stages, such that the net weathering vector is controlled only by Si and labile element (Ca, Na, K, Mg) loss. The A–L–F–S plot does not resolve the relative losses of specific mobile elements/element groups and thus does not reveal mafic mineral vs. feldspar weathering effects; this analysis requires combining the use of the A–L–F–S plot with tetrahedral plots in the A–C–N–K–F–M system. The combination of Ca, Na, K, and Mg on one pole, without K isolated on its own pole, makes the A–L–F–S plot useful mainly for weathering profiles free of influence from K-metasomatism.

Intense-to-extreme weathering trends, the limit of kaolinitization plane, and the IOL/IOB ternary projection

The 3D compositional space of the A–L–F–S plot shifts the line marking the “limit of kaolinitization” into a plane of equivalent Al2O3/SiO2 ratio marking the “limit of kaolinitization” (Fig. 6). However, complete loss of Ca, Na, K, and Mg typically precedes or occurs concurrently with loss of Si from 2:1 clays such that the transition from advanced-to-intense stages of chemical weathering (marked by start of Si loss from 1:1 clays) commonly occurs near to where the plane of the “limit of kaolinitization” intersects as a line on the S–A–F ternary projection. The subsequent intense-to-extreme weathering stages are recorded on or very near to the face of the S–A–F ternary projection that integrates the IOL/IOB.

The selected profile recording predominantly the intense stage of chemical weathering (Hainan Island; Ma et al. 2007) plots near and just below the kaolinitization line in the division of “weak” lateritization/bauxitization with IOL/IOB values between ∼40 and 62. Most of these samples cluster near the model vector of Si loss only (with quantitative retention of Fe and Al), but some shift away from this line towards the A pole showing that some Fe loss occurred across the stage of intense weathering. The selected profiles recording the extreme stage of chemical weathering extend from plotting positions near the “limit of kaolinitization” on the S–A–F ternary projection towards the A–F join. Collectively, all of these span the defined divisions of weak to strong lateritization/bauxitization, with IOL/IOB values reaching up to ∼97. However, the samples can also be separated based on where they fall relative to the model Si loss only line, into those where Fe loss typically accompanies Si loss (i.e., the Columbia River bauxite; Liu et al. 2013) and where Al loss typically accompanies Si loss (i.e., the Bidar laterite profile and the Koloa Volcanic Series profiles; Patterson 1971; Borger and Widdowson 2001). In other words, the strictly chemical perspective of intense-to-extreme weathering trends can be recorded on the S–A–F ternary projection, as part of the expanded A–L–F–S tetrahedral plot that also records the earlier incipient-to-advanced weathering trends.

The tetrahedral plots outlined in this study are examples with element configurations targeted to integrate with the MIA or IOL/IOB and provide better analysis of the whole-rock major-element compositional changes associated with different stages of chemical weathering and, where relevant to paleosols, also the chemical influence of K(±Na)-diagenesis/metasomatism. However, the 3D approach is clearly not restrictive and has utility beyond the selected examples for analyzing other chemical weathering trends, as well as analyzing other geochemical changes across a more expanded realm of source-to-sink siliciclastic sedimentary petrogenesis.

An A–CNFM–K–S plot can assess the magnitude of Si loss relative to labile element loss accompanying reducing chemical weathering, while retaining the ability to evaluate and reverse the effects of K-diagenesis/metasomatism. Similarly, an AF–CNM–K–S plot can assess the magnitude of Si loss relative to labile element loss accompanying ancient oxidative chemical weathering, while retaining the ability to evaluate and reverse the effects of K-metasomatism. However, the last two configurations, like the A–L–F–S plot, come at the penalty of losing resolution of feldspar vs. mafic-mineral weathering trends.

As per the extended list of ternary plot applications in sedimentary petrogenesis (see Nesbitt 2003 for a summary), tetrahedral plots offer potential to examine processes beyond in situ chemical weathering in the siliciclastic sedimentary continuum. Such applications benefit from independent measurements of mineral-chemical compositions to develop mixing lines within the plotting space. For example, the plots incorporating Si introduced here are also useful in assessing hydrodynamic sorting and (or) quartz dilution effects, which is a task typically otherwise examined on scatter plots with SiO2 wt.%. In such cases, the positioning of Si on its own pole can be advantageous in that quartz dilution would produce a singular vector from the position of aluminous clays (and (or) unweathered aluminous silicates) towards the S pole (position of quartz). It is well beyond the scope of this contribution to detail extended sedimentary petrogenesis applications with the tetrahedral plots introduced here, but several examples using the A–CN–K–FM plot are presented in Fedo and Babechuk (2023).

Quantitative chemical weathering indices (1D values) and accompanying ternary (2D) plots have aided the study of chemical weathering and siliciclastic sedimentary petrogenesis for decades, as illustrated here with a selective review on mafic-rock weathering trends, the MIA and IOL/IOB indices, and ternary plots in the A–C–N–K–F–M and S–A–F systems. However, ternary plotting approaches are inherently limited by the grouping of elements on individual poles, which influences their ability to fully capture distinct mineral weathering and (or) secondary alteration effects. Many of these limitations can be overcome with the use of a tetrahedral (3D) plotting approach where elements can be shifted or newly added to a fourth pole.

Tetrahedral plots retain the same advantages of ternary plots, including the ability to compare whole-rock and mineral-chemical compositions, compare empirical data with model/predicted weathering vectors, and integrate widely applied chemical weathering indices. However, the tetrahedral plots provide a single compositional space with enhanced visual and predictive/comparative control on more of the individual processes that collectively contribute to whole-rock compositional change and exert control on weathering index values. Competing vectors related to elements on different poles of tetrahedral plots can manifest as curvilinear net-vector trends that can expose more process/mineralogical effects when compared with ternary plots. The same trends in ternary plots are inherently linear, leaving less resolving power when interpreting whole-rock geochemical data.

This study demonstrates the utility of specific tetrahedral plot arrangements in the A–C–N–K–F–M and extended A–C–N–K–F–M–S systems with a compilation of major-element data from common minerals and modern and ancient mafic-rock weathering profiles that formed under oxidative or reducing surface conditions. These tetrahedral plots build from several ternary plots applied in sedimentary geochemistry to date (Nesbitt and Young 1989; Nesbitt and Wilson 1992; Babechuk et al. 2014), but offer extra resolution in examining K-feldspar and plagioclase vs. mafic mineral weathering that accounts for Fe redox behaviour, the ability to visualize and track the behaviour of Si loss alongside labile elements (i.e., Ca, Na, K, Mg ± Fe), and greater ability to detect and reverse post-depositional alteration effects. With regard to the latter, the fourth pole of a tetrahedron allows separation of K from Ca and Na, alleviating the limitation of all three being on a single pole in ternary plots. The isolation of K allows a projection-based correction for diagenetic/metasomatic K addition back to a pre-metasomatism composition and MIA value, as per the technique widely used in the A–CN–K plot to determine pre-metasomatism CIA values (Fedo et al. 1995).

The A–CN–K–FM tetrahedral plot is ideal for analysis of reducing weathering (loss of both Fe and Mg from mafic minerals), integrates the MIA(R) weathering index, and allows the effects of K-metasomatism to be visualized and corrected for (to a pre-metasomatism MIA(R) value) via projection from the K pole to predicted pre-metasomatism weathering vectors.

The AF–CN–K–M tetrahedral plot is ideal for analysis of oxidative weathering (loss of Mg only from mafic minerals with Fe retention in (oxy)(hydr)oxides), integrates the MIA(O) weathering index, and allows the effects of K-metasomatism to be visualized and corrected for (to a pre-metasomatism MIA(O) value) via projection from the K pole to predicted pre-metasomatism weathering vectors (or K- and Na-metasomatism effects to be visualized).

The A–L–F–S tetrahedral plot allows a full spectrum of chemical weathering stages to be visualized in a single plot and bridges two traditionally separated ternary plots, the A–L–F plot, and the S–A–F plot, via the addition of Si. This plot allows the traceability of labile element and Si loss during incipient to advanced stages of weathering in 3D compositional space, followed by further Si loss in 2D compositional space of the S–A–F plot that integrates the IOL/IOB.

Analysis of data using a 3D plotting approach is best combined with geological context (e.g., mineralogical and textural observations) and chemostratigraphic analysis of 1D weathering index values and, if relevant, also element mass-balance trends associated with individual minerals/mineral groups. The latter is essential for accurate interpretation of plotting positions in tetrahedral space being related to case-specific trends/processes such as intra-profile element redistribution (as demonstrated here for the Cooper Lake and Flin Flon paleosols). The 3D tetrahedral plotting approach illustrated here for chemical weathering processes, and in a companion study by Fedo and Babechuk (2023) for additional siliciclastic sedimentary processes, holds significant potential to better expose and unravel provenance reconstructions, chemical weathering, hydrodynamic sorting and mixing, and diagenetic/metasomatic effects across ca. 3.8 billion years of Earth's sedimentary record.

Support during the development of this work was provided by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2017-05028) to MGB. The ideas herein benefitted from discussions with numerous colleagues while MGB was in Canada, Germany, and Ireland. CMF thanks continued discussions about the 3D plots with H.W. Nesbitt and G.M. Young. N. Suhr is thanked for providing field photographs and M. Widdowson is thanked for providing permission to appear in photographs. Insightful reviews were provided by M.T. Thorpe and A. Bekker. We thank D.G.F. Long for support during editorial handling of this work and contributing to the organization of this volume celebrating G.M. Young.

No new data were collected for this study. All data used are taken as reported from previous studies, all of which are cited in the text. All of these compiled data are provided in full within the published article and its supplementary materials.

Conceptualization: MGB, CMF

Data curation: MGB

Formal analysis: MGB

Funding acquisition: MGB

Investigation: MGB, CMF

Methodology: MGB, CMF

Writing – original draft: MGB

Writing – review & editing: CMF

Supplementary data are available with the article at

This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Competing Interests

The authors declare that there are no competing interests.

Supplementary data