The Rise of Proterozoic Diagenetic Spheroids Formed by Chemically Oscillating Reactions and Stimulated by Environmental Redox Changes

Abstract

Diagenetic spheroids are rounded mineralised structures in sedimentary rocks that span several orders of size dimensions. These objects include rosettes spanning tens of micrometres; millimetre-sized granules; and centimetre- to metre-scale botryoids, nodules, and concretions. Connections between diagenetic spheroids and chemically oscillating reactions (COR) have been established based on chemical and pattern similarities. Nevertheless, it is unknown if there are variations in their occurrences throughout geological time, especially during periods of global environmental change. This is because COR are pattern-forming reactions where carboxylic acids are decarboxylated by strong oxidants like sulphuric acid, bromate, or iodate. The hypothesis is that there should be a greater number of diagenetic spheroids at periods of increased atmospheric and oceanic oxygenation levels. Hence, this work presents the first compilation of occurrences of diagenetic spheroids between 0.541 and 1.8 billion years ago (Ga). The compiled patterned objects are those with concentric laminations and radially aligned crystals, which are patterns akin to equidistant circularly concentric waves that radially diffuse in COR. Another characteristic of diagenetic spheroids, similar to that found in botryoidal minerals, is the destructive interference that forms circular twins; this is identical to the COR pattern formed when circular waves meet. The timeline of Proterozoic diagenetic spheroids produced in this work reveals a significant increase in occurrences across the Ediacaran, which is attributed to an increased environmental oxidation state. During this interval, seawater is known to have become richer in sulphate and iodate, which create ideal conditions for the abiotic and diagenetic oxidation of biomass. Therefore, increased occurrences of diagenetic spheroids in the Neoproterozoic possibly represent sedimentological evidence for abiotic decarboxylation reactions and widespread COR in productive environments. The distribution of diagenetic spheroids observed during the Proterozoic may also be more broadly applicable to other epochs of Earth’s history.

1. Introduction

Diagenesis includes all the biological, chemical, and physical processes that alter deposited sedimentary assemblages from sedimentation to erosion or metamorphism [1,2]. Concretions, nodules, botryoids, granules, and rosettes are mineralised spheroidal structures that are prevalent in the sedimentological record and usually relate to diagenesis. These objects can display circularly concentric and radial mineral patterns, a limited dominant mineralogy, and a common association with organic matter. They are also considered as abiotic in origin; hence, they are here grouped as ‘diagenetic spheroids’. Diagenetic spheroids are distinguished according to size ranges. Mega-concretions can have a diameter as large as several metres, and rosettes are the smallest type with diameters < 10⁻⁴ m [3]. Both concretions and nodules have sizes from 10⁻² m to 10⁻¹ m. Whereas the mineralogy of concretions is akin to its host rock, the composition of nodules differs from their surrounding sediments [4]. Granules are irregular spheroids that range between 10⁻² m and 10⁻⁴ m in diameter. Botryoidal minerals include interconnected, or twinned, smooth spheroids, and their globular texture is grape-like, mammillary, or reniform in appearance [5]. Botryoids span a large diameter range from 10⁻¹ m to 10⁻⁶ m.

Despite the array of descriptive terms, these objects commonly exhibit a sub-rounded morphology with circularly concentric and radially aligned geometric patterns [6,7,8]. Occasionally, they exhibit a triaxial ellipsoidal or lenticular morphology. The term diagenetic spheroids groups together those objects with identical ranges of patterns, which may imply a similar sedimentary and diagenetic history [5,6,7,8,9,10]. Typical mineral compositions of diagenetic spheroids include microcrystalline quartz (chert; chalcedony) [11,12], dolomite, pyrite, apatite, and/or organic matter [3,6]. Fossils may also be encapsulated in diagenetic spheroids and usually have a comparable mineral composition. For instance, well-preserved Ediacaran microfossils, like Vendotaenia sp. and Oscillatoriopis obtusa, have been identified within chert concretions in the Shibantan Lagerstätte [13,14,15].

The formation mechanism of diagenetic spheroids has yet to reach consensus. For instance, Dodd et al. (2018) disputed the wave action model for granules in granular iron formation on the basis that the arrangement of fine equidistant, circularly concentric laminations and radially aligned acicular crystals is improbable to form under turbulence. Moreover, shallow marine wave agitation cannot explain the common association of granules with organic matter and well-preserved microfossils. Diagenetic spheroids are considered abiotic precipitates and are therefore possible indicators of physicochemical processes [16,17]. However, nucleation-controlled growth around a central mass [18,19] is more likely to generate irregular clumps, rather than equidistant concentric laminations with density gradients. The Liesegang phenomenon is another abiotic process that is the purported origin of diagenetic spheroids [20], but it is unable to explain regular patterns of circular laminations [7]. Liesegang banding is produced by the precipitation and diffusion of metal cations within silica gels [20,21,22]. Moreover, Liesegang rings have a gravity-driven linear arrangement [23,24], in contrast with concentric rings observed in diagenetic spheroids.

Alternatively, Bosak et al. (2010) proposed that diagenetic spheroids associated with microbialites and stromatolites may be mineralised gas bubbles generated by photosynthetic microorganisms. Internal features, such as mineral inclusions and organic matter, are absent within bubbles [25]. The gas bubble theory therefore does not explain the occurrence of microfossils and concentric laminations in some diagenetic spheroids [3]. Occurrences of microfossils, degraded organic matter, or highly variable carbon and sulphur isotope compositions in diagenetic spheroids have been interpreted to suggest a biologically mediated formation [13,26,27,28,29]. For example, organic matter could act as nucleation sites, and mineral precipitation may be actively induced by microbial interaction with its niche [30].

COR have been proposed as an alternative formation model to explain the circularly concentric, radially aligned, and density gradient patterns often found in diagenetic spheroids [3,5,6,7,8,10,11,12,31]. Zaikin and Zhabotinsky (1970) report that “radial circular waves of oxidation were propagated” when phenanthroline ferrous sulphate (ferroin) was added to an aqueous solution of bromate, bromide, malonic acid, and sulphuric acid. Interference occurs when concentric waves from different initiation points intersect, producing ‘interconnected round arcs’ (or circular twins), known as Belousov–Zhabotinsky (B–Z) patterns [32]. B–Z reactions in Petri dishes display regular wave patterns and the effects of chemical turbulence. These circular waves span several size dimensions and are hence fractal patterns. In nature, abiotic carboxylic acids could be central to this reaction; alternatively, there are implications for biosignatures if the carboxylic acids are derived from biomass [3]. The radially propagating circles have been frequently recreated and analysed in experimental settings [6,33,34,35,36,37,38,39,40,41]. Nevertheless, it was only recently proposed [5,7,8] that the patterns and products of COR are analogous with those of diagenetic spheroids. If COR occur naturally in the environment and indeed represent environmental proxies [12], then their occurrences might preserve evidence of global biogeochemical changes. In turn, if diagenetic spheroids form through COR, their occurrence in the rock record would represent direct sedimentological evidence for carbon cycling.

The Proterozoic spans from 2.5 to 0.541 Ga and includes a prolonged biogeochemical stasis between 1.8 and 0.8 Ga, dubbed the ‘Boring Billion’ [42,43], or, perhaps less anthropocentrically, the ‘Balanced Billion’ [44]. This interval is characterised by tectonic and environmental stability, with steady isotopic compositions of carbon, sulphates, and sulphides observed in marine sediments [45]. By contrast, the Neoproterozoic underwent large climatic variations due to major tectonic events like the Rodinian fragmentation and Gondwanan formation [46], as well as major glaciations. Cap carbonates, which are sedimentary sequences that record deglaciations, have calcite and dolomite with strong depletions in ¹³C. These have been variably interpreted as evidence for the oxidation of dissolved or suspended organic matter in the water column [47], local methane seeps [48], anaerobic oxidation of methane [49], or diagenetic oxidation of biomass in sediments [50]. Therefore, a timeline of the abundances of diagenetic spheroids in geological strata between 1.8 Ga (start of the ‘Balanced Billion’) and 0.541 (the Ediacaran–Cambrian boundary) may provide further insight into whether diagenetic spheroids are more likely to form under stable long-term geochemical conditions or dynamic ones, respectively. The emerging hypothesis is that an increased abundance of diagenetic spheroids near the end of the Neoproterozoic would be expected due to increased environmental oxidation because enhanced continental weathering provides an increased supply of dissolved ions in post glacial oceans. Based on a literature review, this work addresses two main scientific questions about diagenetic spheroids:

• (a). Are there secular variations in the abundance of diagenetic spheroids during the Proterozoic?

• (b). Could Proterozoic diagenetic spheroids represent sedimentological signatures of abiotic carbon cycling favoured by environmental oxidation?

2. Approach for a New Compilation

To determine the correlation between the occurrences of diagenetic spheroids during stable conditions and enhanced influxes of environmental oxygen, the abundance of concretions, nodules, botryoids, granules, and rosettes in sedimentological beds between 0.541 and 1.8 Ga was collected (Table 1). Secondary data were collected from widely available search engines like Google Scholar, Web of Science, and JSTOR, using key terms such as ‘Proterozoic concretions’, ‘Proterozoic nodules’, ‘Proterozoic botryoids’, ‘Proterozoic granules’, and Proterozoic rosettes’. Altogether, 72 occurrences of diagenetic spheroids from 33 formations were documented (Figure 1), and this dataset is up to date as of November 2024. Even though this is a comprehensive compilation of Proterozoic diagenetic spheroids, sample and formation bias is inherent within these collated data due to outcrop availability, the variable number of studies for each formation, the analytical approach used in publications, and whether authors reported occurrences of diagenetic spheroids of various sizes when they occurred. While these sampling biases are inherent to the geological and publication records, we argue that this compilation can still serve a useful purpose and show possible first-order trends. In the future, this compilation should be augmented and refined to hopefully create a momentum that stimulates the reporting of the occurrences of many more diagenetic spheroids, including those at microscopic scales.

Figure 1

Distribution of various beds of diagenetic spheroids in Proterozoic strata and specifically between 1.8 and 0.541 Ga. The centre of the diagenetic structures’ symbols is aligned to the median age of the formation, with age ranges and further mineralogical information simplified in Table 1. The dark grey outline indicates δ¹³C_carb values across the Neoproterozoic and Mesoproterozoic interval obtained from Shields et al. (2019) and Li et al. (2022), respectively [51,52]. Numbers correspond to geological units: 1 = Dengying Formation; 2 = Omkyk Member, Northern Nama Group; 3 = Stáhpogieddi Formation; 4 = Ediacara Member; 5 = Tindir Creek; 6 = Ambed Formation; 7 = Bhander Limestone; 8 = Doushantuo Formation; 9 = Pioneer Sandstone; 10 = Wollogorang Formation; 11 = Backlundtoppen Formation; 12 = Beck Spring Dolomite; 13 = Bitter Springs Formation; 14 = Roan Group; 15 = Callanna Beds; 16 = Little Dal Group; 17 = Diabaig Formation; 18 = Nama Group; 19 = Apache Group; 20 = Bass limestone; 21 = Milbeena Bore; 22 = Independence Fjord Group; 23 = Newland Formation; 24 = Xiamaling Formation; 25 = Helena Formation; 26 = Amelia Dolomite and Mallapunyah Formation; 27 = Jixian System; 28 = Mount Isa Mine; 29 = Gaoyuzhuang Formation; 30 = Espinhaço Supergroup; 31 = Barney Creek Formation; 32 = Frere Formation; 33 = Athabasca Group; see Table 1 for more information.

[Figure omitted. See PDF]

Table 1

Proterozoic Diagenetic Spheroids.

	Geological and Geographical Location	Age Range (Ga)	Type of Diagenetic Spheroid	Mineralogy of Structures	Host Rock Facies and Associated Sediments	References
1	Dengying Formation,Yangtze Craton,South China	0.545 to 0.551	Botryoids,nodules,concretions	Dolomite, chert unspecified carbonate mineral	Dolomitelaminated micritic and bituminous limestone with abundant fossils	[7,15,53,54]
2	Omkyk Member, Northern Nama Group, Namibia, Africa	ca. 0.5488	Nodules,botryoids	Calcite with dolomitized stromatolite crust	Fossiliferous carbonate, siliclastic rocks	[55]
3	Stáhpogieddi Formation, Digermulen Peninsula, Arctic Norway	ca. 0.563	Concretions	Calcite	Siliclastic sedimentary rocks	[56]
4	Ediacara Member, Rawnsley Quartzite, Flinders Ranges, South Australia	0.541 to 0.635	Concretions,concretionary structures,rosettes, granules	Silica,quartz, andclay coating	Feldspathic sandstone	[57]
5	Tindir Creek,Yukon Territory, Canada	0.541 to 0.635	Nodules,botryoids,granules	Chert withorganic coating	Limestone,shale	[58]
6	Ambed Formation,Bou Azzer mining district, Anti-Atlas, Morocco	0.58 to 0.615	Nodules,concretions	Unspecified silicate mineral with cobalt loellingite accessory crystals and red clays (smectites, talc, chlorite)	Interlaminated siliceous and carbonaceous facies	[59]
7	Bhander Limestone, Thoman River, Maihar, central India	0.544 to 0.65	Nodules, concretions, concretionary structures, granules	Calcic spar, K-feldspar nuclei, glauconite, unspecified carbonate mineral	Limestone	[60,61]
8	Doushantuo Formation, central South China	0.551 to 0.632	Concretions, nodules, granules, rosettes,botryoids	Chert, apatitepyriteorganic matter	Algal and siliceous dolomite, black shale, limestone and phosphorite	[62,63]
9	Pioneer Sandstone, Northeastern Amadeus Basin, Australia	0.58 to 0.709	Granules, rosettes	Quartz, feldspars, barite	Feldspathic sandstonephosphorite	[64,65]
10	Wollogorang Formation, McArthur Basin, northern Australia	ca. 0.705	Concretions, rosettes, granules	Dolomite, quartz,pyrite	Black shales, mudstone, siltstone, sandstone conglomerates	[66]
11	Backlundtoppen Formation, Spitsbergen, Svalbard	0.7 to 0.8	Nodules	Chert, chalcedony	Oolitic, pisolitic,cherty limestone,dolomite	[67,68]
12	Beck Spring Dolomite, eastern California	0.73 to 0.78	Botryoids	Acicular dolomite, aragonite or calcite,strontium rich	Dolomitelimestone	[69,70]
13	Bitter Springs Formation, Australia	ca. 0.8	Concretions, nodules, rosettes	Chert, carbonate, silicaanhydrite, bipyramidal quartz	Biostromal stromatolites, mudstone,dolomite and red beds	[71,72]
14	Roan Group, Katangan Basin, Zambia, Africa	0.735 to 0.883	Concretionary structures, nodules	Anhydrite,dolomite	Arkose with siltstone and clastic carbonate interbeds	[73]
15	Callanna Beds,Willouran Ranges,South Australia	0.802 to 0.827	Nodules, rosettes	Chert, sulphate (barite, anhydrite, or gypsum)	Cherty pyritic, carbonaceous dolomite with siltstone	[74,75]
16	Little Dal Group,Mackenzie Mountains,Canada	0.8 to 1.1	Nodules,botryoids	Calcite, quartz	Limestone,carbonate shale	[76,77]
17	Diabaig Formation, Torridonian Succession, northwest Scotland	0.994 to 1.09	Nodules	Apatite, organic matter	Rhythmically alternating mudstone and sandstones, micro-fossiliferous	[78]
18	Nama Group, Damara Supergroup, Namibia, Africa	1 to 1.2	Botryoids	Carbonate, calcite, iron-rich clays and hematite	Siliclastic sedimentary rocks	[79,80]
19	Mescal Limestone and Troy Quartzite,Apache group,Arizona, North America	1.1 to 1.4	Nodules, rosettes,botryoids, granules	Chert, dolomite,gypsum, chalcedony, quartz	Alternating, thinly laminated dolomite and chert-rich dolomite, sandstones	[81]
20	Bass limestone, Bright Angel Canyon, Arizona, USA	1.1 to 1.255	Rosettes	Chert	Limestone	[82,83]
21	Milbeena Bore,Manganese Group,Western Australia	1.05 to 1.317	Nodules	Braunite, clay, apatite, unspecified carbonate mineral	Well bedded micaceous to sandy shale and siltstone	[84,85,86]
22	Independence Fjord Group, North Greenland	1.23 to 1.38	Concretions	Silica-cemented, carbonate, dolomite, quartz	Sandstonesiltstone	[87]
23	Newland Formation,Belt Supergroup, USA	1.325 to 1.4	Concretions,rosettes	Pyrite,barite, gypsum	Shale	[88]
24	Xiamaling Formation, North China	1.35 to 1.4	Concretions	Calcite, clay (illite, chamosite),ankerite, or siderite	Green silty shale(mainly glauconite and silty quartz)	[89,90,91]
25	Helena Formation, Central Cordillera, North America	1.44 to 1.5	Nodules,rosettes	Dolomite,quartz	Mudstone,sandy grainstone, stromatolites	[92]
26	Amelia Dolomite and Mallapunyah Formation, McArthur Basin, Northern Territory, Australia	1.4 to 1.6	Botryoids,nodules	Chalcedonyanhydrite chert	Dolomite,sandstones,quartz arenite	[93]
27	Jixian System, Yanliao basin, North China Craton	1.4 to 1.6	Concretions	Chert	Stomatolitic and bituminous very finely crystalline dolomite	[94]
28	Mount Isa mine, Queensland, Australia	1.5 to 1.6	Rosettes,nodules	Chert	Dolomite	[95]
29	Gaoyuzhuang Formation, Yanshan area, North China	1.54 to 1.6	Concretions	Unspecified carbonate mineral	Calcareous mudstone dolomite	[96]
30	Espinhaço Supergroup, Minas Gerais, Brazil	1.5 to 1.73	Botryoids	Thin titanium oxide coating, hematite, hongshiite	Quartzite,conglomerate	[97]
31	Barney Creek Formation, McArthur Basin,Northern Territory, Australia	ca. 1.639	Concretions	Unspecified carbonate mineralorganic matter	Shale	[98]
32	Frere Formation, Nabberu Basin, Western Australia	ca. 1.7	Granules,rosettes	Chert, hematite, greenalite, organic matter, stilpnomelane	Stromatolites,granular iron formation	[10,99]
33	Athabasca Group, Athabasca Basin, Canada	1.7 to 1.75	Rosettes	Trioctahedral chlorite (clinochlore)	Quartz-rich sandstone, conglomerate	[100]

3. Observations from the Compilation of Proterozoic Spheroids

3.1. Geometric Patterns of Diagenetic Spheroids

Concentric lamination patterns are displayed when multiple circles share the same centre. Within Proterozoic diagenetic spheroids, these are the most common type of geometric pattern, with 43% of the total collated diagenetic spheroids displaying circular laminations. However, this value is likely underestimated because the internal geometry of 36 compiled spheroids remains undetermined. Figure 2b shows an example of a calcite concretion with circularly concentric layers and coloured mineral gradients. Botryoidal dolomite from the Dengying Formation (Figure 2c,d) demonstrates the formation of circular twins at the junctions where concentric laminations meet and destructively interfere. This arrangement can be considered as an example of crystal twinning within botryoidal minerals, which vary in size across several orders of magnitude. Irregularly shaped cavity structures also form upon the destructive interference of circularly concentric laminations (Figure 2a). Variations in geometric patterns are dependent on the extent of the convergence of individual concentric circles. Therefore, fractal geometry occurs, since self-similar and circularly concentric patterns are observed at regular intervals over several orders of size magnitudes in Proterozoic diagenetic spheroids.

Centred radial patterns are also commonly exhibited geometric patterns in diagenetic spheroids, with five instances recorded during the Proterozoic (Figure 1). These are self-similar with circularly concentric patterns, but with the addition of radial fibrous crystals that have darker coloured banded zones emanating from a singular centre point. The laminations observed in Figure 2d have rhythmically oscillating thin dark and thick brighter laminae with sharp boundaries. The dark and bright laminae are syntaxial, with the lighter laminae containing larger dolomite crystals [54]. Lenticular and triaxial ellipsoids are infrequent patterns and are typically demonstrated by nodules and concretions. Ellipsoidal shapes in diagenetic spheroids may be due to the original morphology of decomposing clumps of biomass [101].

3.2. Mineralogy and Palaeontology of Diagenetic Spheroids

Chert (microcrystalline quartz) is the most common mineral observed in diagenetic spheroids, with 12 out of 72 occurrences of diagenetic spheroids exhibiting a chert mineralogy. Nine carbonate spheroids and one silicate spheroid are recorded, but both lack specificity since these terms represent unspecified mineral groups. For example, the typical anhydrous carbonate minerals are calcite, aragonite, and dolomite. Quartz and feldspars are common types of diagenetic silicates, but further petrographic analyses of thin sections should be conducted more commonly on diagenetic spheroids to further determine their mineralogy. Quartz occurrences (8), dolomite occurrences (7), and calcite (6) are the next most common major minerals (see Table 1). Moreover, phosphorite nodules in siliceous dolomite and micritic limestone are abundant in the Doushantuo Formation in China [62]. Botryoidal apatite occurs among granules in black organic-rich phosphorite of the Doushantuo Formation [63]. Pyritic concretions also occur in the Mesoproterozoic Newland Formation in North America [88].

Seven recorded Proterozoic diagenetic spheroids occur in shallow marine deposits associated with stromatolites or microbialites. In the Namibian Omkyk Member near the end of the Ediacaran, nodules are encrusted by a rim of dolomitised microbial laminates and contain various microfossils (Figure 3a–c) [55]. These purported metazoans are biomineralised and are oriented perpendicular to a fissure wall [55]. Ediacaran microfossils can also be observed within diagenetic spheroids from China’s Shibantan Lagerstätte [15]. Chert nodules from the Shibantan Member of the Dengying Formation also contain well- preserved microfossils such as Oscillatoriopsis obtusa (Figure 3d) [14]. Although the phylogenetic affinities of these microfossils are undetermined, due to their morphological similarity to photoautotrophs, they have been interpreted as benthic cyanobacteria [15]. These observations and inferences have also been made in the Doushantuo Formation where apatite granules commonly contain a range of microfossils [63]. There are also well-preserved microfossils inside concretions of bitumen and chert from the Mesoproterozoic Xiamaling Formation in northern China [89]. In chert granules from the Late Paleoproterozoic Frere Formation, subspherical and filamentous microfossils are clustered together and exhibit varying degrees of mineralisation, whereas most are encrusted with a relatively thick layer of iron oxides [99].

3.3. Distribution Trend of Diagenetic Spheroids

A greater number of occurrences of diagenetic spheroids during the Neoproterozoic, especially in the Ediacaran, can be observed compared to the Mesoproterozoic (Figure 1). The highest frequency of diagenetic spheroids thus coincides with positive excursions of δ¹³C_carb values [51,102], which is a major proxy for increased atmospheric oxygen. By contrast, a limited number of spheroids occur in the 0.8–1.8 Ga interval, which coincides with the ‘Balanced Billion’. For instance, a significant decrease in diagenetic spheroids occurs during the early Tonian because only two diagenetic spheroid occurrences from the Mackenzie Mountains in northwestern Canada have been recorded. There also appears to be no considerable changes in the number of diagenetic spheroids within the Mesoproterozoic, with a roughly similar amount across the Stenian, Ectasian, and Calymmian (Figure 1).

4. Discussion

4.1. Geometric Patterns in Proterozoic Diagenetic Spheroids Compared to Those of COR

Under standard conditions, an unperturbed B–Z reaction produces random oxidation spots that propagate as a series of equidistant concentric rings [32]. Once a significant number of chemical waves have accumulated, destructive interference between waves occur (Figure 4b,c). At late reaction stages, linearly elongated cavities and twinned patterns occur at sites where chemical waves are mutually annihilated, causing the erasure of wave traces [6,7].

The geometric patterns produced by COR are self-similar to the circularly concentric patterns found in diagenetic spheroids. Figure 4a shows an example of equidistant concentric laminations with no interference, perfectly recreating some of the COR patterns. Moreover, sub-parallel wavy layers caused by circular twins can be recreated by B–Z reactions due to destructive interference (Figure 4b). This effect appears related to surface tension in botryoids where the layers usually follow the cavity inside lining, whereas in a Petri dish, the sub-parallel layers follow the glass wall. Circularly concentric waves can also have imperfect equidistant or non-equidistant laminations [5,39], which is akin to the variable spacing distance displayed by laminations in some diagenetic spheroids. Mineral colour density gradients are also apparent in Figure 4b. Asymmetric irregular ellipses of concentric chemical waves are due to a higher concentration of nucleation spots and the resulting twins between chemical waves during radial diffusion (Figure 4c). Other diagenetic spheroids with these kinds of self-similar patterns that have previously been attributed an origin influenced by COR include rosettes of quartz ± apatite ± haematite ± carbonate ± organic matter [10,31]; botryoids of malachite, quartz, and dolomite + organic matter [3,5,7,11,12]; granules of quartz ± apatite ± haematite ± magnetite ± organic matter ± dolomite ± pyrite [6,10]; and concretions or nodules of quartz ± haematite ± carbonate ± organic matter ± pyrite [7,8].

Oxidation spots in COR are chaotically distributed [103], which is akin to the random locations of diagenetic spheroids within sedimentary layers. Hastings et al. (2003) argued against random initiation by attributing microscopic fluctuations in the concentration of reactants to the initial nucleation of chemical activity [104]. Despite the unpredictability of COR, these reactions produce self-similar patterns such as circularly concentric equidistant laminations, twinned circles, cavity structures, radial diffusion, and colour gradients in laminations. All these self-similar patterns closely resemble those found in Proterozoic diagenetic spheroids (Figure 4). Oxidation spots with circularly concentric laminations in COR experiments have diameters that span sub-millimetre to decimetre sizes [32,41]. Therefore, COR display fractal patterns, akin to the fractal nature of patterns displayed by diagenetic spheroids.

Furthermore, radially aligned crystals in diagenetic spheroids are often displayed (Figure 2d and Figure 4b), and they are similar to the radial diffusion observed in COR. There are also strong colour gradients produced during COR, which are analogous to alternating light and dark mineral laminations of iron oxide and organic matter within circularly concentric spheroids (Figure 2d and Figure 4b,c). The characteristic red and blue seen in COR experiments is produced via ferroin reduction and oxidation, respectively [41]. The oscillatory patterns displayed in Figure 4 are initiated inside a ten-centimetre diameter glass Petri dish and require a film of COR solution [7]. Less distinguished chemical waves and cavity structures become apparent when some of the reactants are exhausted after around 30 min [35]. During diagenesis, COR must occur three-dimensionally and at much larger scales, which is a limitation not yet demonstrated by COR experiments. Furthermore, COR experiments in Petri dishes can be restarted when the solution is shaken, which suggests that COR in nature would occur during the early stages of burial diagenesis, under calm conditions and within relatively short time scales. Nevertheless, it likely took longer in environmental settings than in COR experiments due to the expected lower concentration of reactants. Despite these limitations, patterns of circularly concentric laminations, colour gradients, radial geometry, twins, and cavities are found both in COR and in diagenetic spheroids (Figure 4), which constitutes a solid basis to argue for COR as a model for the formation of diagenetic spheroids.

4.2. Comparison of Substances in COR and Proterozoic Diagenetic Spheroids

Experimental COR begin when a redox-sensitive metal-based catalyst is added to a solution with a strongly oxidising halogen, its complementary halide salt, malonic acid, and sulphuric acid [32,39]. Variable concentrations can be utilised to initiate COR, and there are various reactants that can produce B–Z patterns [36,39]. Although many chemical reactions can occur during COR formation, two equations are particularly important:

2Fe²⁺ + BrO₃⁻ + HBrO₂ + 3H⁺ ↔ 2Fe³⁺ + 2HBrO₂ + H₂O + 2e⁻(1)

3CH₂(COOH)₂ + 4BrO₃⁻ → 4Br⁻ + 9CO₂ + 6H₂O(2)

In Equation (1), iron in phenanthroline ferrous sulphate (ferroin) is oxidised from Fe²⁺ to Fe³⁺, which causes the observed colour change. In Equation (2), the reaction involves decarboxylation of malonic acid (or other carboxylic acids), the production of carbon dioxide (seen as bubbles in COR experiments), and a change in the oxidation state of bromine from +5 to −1. In COR, the chemical composition of products and intermediates remains undetermined, yet it can be predicted that the chemical waves are composed of variably oxidised ferroin and halogenated carboxylic acids [7].

The concentration of bromide ions (Br⁻) has been argued to control the oscillating nature of the B–Z reaction (Orbán et al., 2001) [40]. When Br⁻ exceeds the critical level, the oxidation of iron in ferroin is favoured, which generates a colour change in the diffusing circular waves from red (Fe²⁺) to blue (Fe³⁺). Other metals can also act as possible catalysts in COR [39]. The reaction is thought to terminate when electron donor molecules like carboxylic acids or electron acceptors like bromate are exhausted or become too low in concentration [5]. Therefore, diagenetic environments that can concentrate reactants are ideal, such as evaporitic environments where halogens, sulphate, and biomass can accumulate.

Carboxylic acids and ketones are examples of other organic acids that can initiate COR [6,39,40]. In nature, carboxylic acids are abundant because they are natural constituents of biomass, which decays in part through decarboxylation reactions [105,106,107]. Spheroidal microfossils such as Oscillatoriopsis obtusa and Namapoikia rietoogensis occur in Proterozoic diagenetic spheroids (Figure 3a–d [15,55]), and other Proterozoic microfossils commonly occur in diagenetic spheroids [63,89]. Subspherical and filamentous microfossils occur in granules from the late Palaeoproterozoic Frere Formation in the Nabberu Basin, and they often exhibit iron oxide encrustation [99]. The association of organic matter with iron oxides and pyrite could be because these minerals can be products of microbial sulphate reduction [108,109]. However, disseminations of iron oxides, pyrite, carbonate, and organic matter in diagenetic spheroids composed of quartz can also be interpreted to arise from abiotic COR because these can constitute the self-similar patterns [7,8,12]. In addition, some diagenetic spheroids also contain both sulphides like pyrite and sulphates like gypsum, anhydrite, or barite. All these mineral substances are like those in COR because they involve iron, carbon, and sulphur compounds with variable oxidation states, which is an important phenomenon in COR. The common occurrence of authigenic quartz in diagenetic spheroids can be interpreted to represent alkalinity generated during early diagenetic decomposition of biomass. Silica and high pH are different from the usually acidic conditions of COR, but they do not impede on pattern formation in COR [7]. Other approaches are needed to distinguish contributions from biological sulphate reduction and abiotic sulphate reduction in diagenetic spheroids, such as through large ranges of sulphur isotope ratios. However, COR have not yet been investigated for stable isotope fractionation on sulphur, carbon, iron, or halogens. Therefore, the abiotic putrefaction of microbial biomass in diagenetic environments is a likely process that uses organic acid reactants for COR [7]. The COR model can thus elegantly explain why Proterozoic diagenetic spheroids are often associated with fossils and organic matter.

For COR to occur naturally, productive, oxidising, and evaporitic diagenetic environments are well-suited to decompose microbial biomass. Table 1 displays the variety of environments considered in this study and shows that limestone, phosphorite, chert, and quartzitic sandstone most commonly contain diagenetic spheroids. The preservation of perfectly equidistant circularly concentric laminations, radially aligned crystals, and a limited range of chemical composition is not immediately compatible with the wave action model for the formation of diagenetic spheroids like botryoids and granules [110,111,112,113]. Hence, while wave action cannot be excluded to play a role in rounding granules for instance [10], it should be considered an insufficient model to explain the occurrence of specific geometric patterns within. The gas bubble model [25] can also be ruled out based on its inability to explain why microfossils are commonly inside diagenetic spheroids. Considering their circular concentricity, mineralogy, and inclusions of organic matter and common microfossils, the COR model is the most convincing model for the formation of diagenetic spheroids [3,5,6,7,8,10,11,12,31].

During early diagenesis, the oxidation of organic acids through the decarboxylation of organic matter was likely needed to initiate COR and produce spheroidal objects [6,7]. Originally, colloidal silica is present under alkaline conditions. However, when carboxylic acids undergo decarboxylation, acid is produced, and the pH is lowered [7]. If this occurs under alkaline conditions, it results in the precipitation of minerals, such as quartz, apatite, carbonate, and pyrite [8]. Microcrystalline quartz, cryptocrystalline apatite, micritic carbonate, nanoscopic pyrite and hematite, and finely disseminated organic matter are all commonly found within diagenetic spheroids (Table 1). Hence, these minerals are consistent with the COR model of diffusing reaction products and intermediates in colloidal gels with its consequent permineralisation under pH gradients. Therefore, in addition to the variety of geometric patterns, the mineralogy and chemical substances of diagenetic spheroids can also be explained by the COR model.

4.3. Influences of Atmospheric Oxygenation on Occurrences of Diagenetic Spheroids

Most diagenetic spheroids occur during the Neoproterozoic era (Figure 1). The increase in occurrences coincides with intense variations in δ¹³C_carb, ranging from −10 to +10‰ [51], which is a well-known proxy for atmospheric oxygenation. Therefore, this is an indication that major perturbations in the carbon cycle are linked to increased occurrences of diagenetic spheroids and thus of COR naturally occurring in environmental settings. This observation also supports the COR model for the formation of circularly concentric laminations in diagenetic spheroids and for the preservation of microfossils in diagenetic spheroids. This is further supported by the smaller number of diagenetic spheroid occurrences during the ‘Balanced Billion’, when perturbations in δ¹³C_carb were significantly smaller, stagnating mostly near 0‰ [51].

Under increased environmental oxygen, higher chemical weathering rates, and intense greenhouse conditions, more cations and anions are delivered into sea water [114]. Hence during the Ediacaran, iodate, bromate, and sulphate levels in seawater increased [114], thereby providing an increased availability of COR reactants. Post-glacial Neoproterozoic rocks of marine sedimentary origin also show increased variations in δ³⁴S_sulphate and δ³⁴S_sulphide, which imply increased availability of seawater sulphate [115,116]. Oxidised sulphur species can act as electron acceptors in the remineralisation of organic carbon by sulphate-reducing bacteria, or abiotically as in the case of COR in the environment. Primary productivity of organic matter also increased during the Neoproterozoic and promoted a profound expansion of ecosystems because sulphate and phosphate play central roles in biochemistry [117]. This biosphere expansion would enable an increased availability of biomass and carboxylic acids, which again are key reactants in COR. Lastly, environmental oxygenation during the Neoproterozoic would also have contributed to create redox gradients and thermodynamic disequilibria in sedimentary marine environments, thereby further stimulating COR.

A natural progression of this study includes the expansion of the considered age range to encompass the Phanerozoic eon (0.541 Ga until modern times) as well as the Paleoproterozoic era and Archean eon. This study provides valuable new insights on the influence of intense variations in δ¹³C_carb on the prevalence of diagenetic spheroids in sedimentary rocks, and it is likely also applicable to the Paleoproterozoic. An almost symmetrical distribution of the occurrences of diagenetic spheroids, with greater amounts at both ends of the Proterozoic, would therefore further support the newly proposed COR model. Since the connection between COR and diagenetic spheroids is still in its infancy, broader documentation of these spheroidal structures is needed to search for additional occurrences. This may eventually confirm that the COR model applies to most types of diagenetic spheroids throughout Earth’s history. Diagenetic spheroids should thus be regarded as sedimentological patterns produced abiotically from carbon cycling with carboxylic acid reactants and CO₂ products. While carboxylic acids are most likely of biological origin in most environments (on Earth), they may also be abiotic in origin, for instance in hydrothermal vent systems where Fischer–Tropsch type synthesis takes place [118]. Hence, this study may even apply more broadly to oceanography, planetary sciences, and exobiology.

5. Conclusions

The classical COR is the B–Z reaction, which produces characteristic fractal patterns and CO₂ bubbles from reactants such as malonic acid, bromate-bromide, sulphuric acid, and ferroin. Self-similar fractal patterns, such as circularly concentric laminations, radial geometries, twins, and linearly elongated cavities occur in diagenetic spheroids and are identical to those produced by COR. These diagenetic spheroids include concretions, nodules, botryoids, granules, and rosettes. Similarities between chemical reactants and products of COR and diagenetic spheroids have also been elucidated based on chemical substances. Hence, diagenetic spheroids are interpreted to be formed by COR based on their patterns and substances, and they can thus be considered as evidence of abiotic carbon cycling.

Because biomass is enriched in carboxylic acids, organic matter in sediments is affected by decarboxylation during the formation of diagenetic spheroids; hence, the COR model explains why fossils and microfossils are common in these mineralised objects. In this first compilation of occurrences of diagenetic spheroids over geological history between 0.541 and 1.8 Ga, a secular peak in the frequency of their occurrences is documented during the late Neoproterozoic. This observation is consistent with the COR model because the Neoproterozoic oxygenation event resulted in high levels of biomass, increased oxidative weathering, and greater amounts of oxidants, such as iodate and sulphate, all of which are linked to reactants in COR. These conditions during the Neoproterozoic were favourable to COR and resulted in increased occurrences of diagenetic spheroids in sedimentary rocks from this era. This study is a prelude to others that will cover the rest of Earth’s history.

Author Contributions

Conceptualization, D.P.; methodology, D.P. and P.A.B.-a.; formal analysis, D.P. and P.A.B.-a.; investigation, P.A.B.-a.; writing—original draft preparation, P.A.B.-a.; writing—review and editing, D.P. and P.A.B.-a.; visualization, P.A.B.-a.; supervision, D.P.; project administration, D.P. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

No new data were created in this study. All data can be found in the cited references.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 2. A selection of common geometric patterns observed within diagenetic spheroids. (a) Botryoidal gypsum forms filled with quartz and acicular pseudomorphs from the 1.1 to 1.4 Ga basal Troy Quartzite in Arizona [81]. (b) Calcite concretion with concentric ring structures from the Xiamaling Formation, 1.35 to 1.4 Ga [90]. The “D” marks displacive growth, whilst “R” displays the areas of replacive growth [90]. (c) Cathodoluminescence photomicrograph displaying a cavity structure of botryoidal dolomite from the Dengying Formation [53]. Crystalline dolomite (CD) cements and fascicular slow dolomite (FSD) cements are indicated, as well as micritic dolomite (MD) and microcrystalline dolomite (MCD). (d) Botryoidal laminations from the Dengying Formation (0.545 to 0.551 Ga) in the Gaojiashan outcrop [54]. Blue arrows showcase dark lamina (DL), whereas red arrows point towards brighter lamina (BL) [54]. All figures reproduced with permission.

Figure 3. Microfossil occurrences in Proterozoic diagenetic spheroids. (a) Outcrop image of nodules containing Namapoikia rietoogensis from the Omkyk Member, Nama Group, southern Namibia [55]; (b) Longitudinal holotype [55]; and (c) Transverse section [55]. (d) Oscillatoriopsis obtusa from the Shibantan Lagerstätte [15]. Figures reproduced with permission.

Figure 4. Summative grid to compare the self-similar geometric patterns of diagenetic spheroids, shown in plane-polarised light, with those produced by COR. The COR experimental images are from Papineau et al. (2021), and Petri dishes are 10 cm in diameter [7]. (a) Carbonate–apatite concretion with a circularly concentric lamination pattern in phosphorite, Doushantuo Formation in China (Papineau et al., in review). (b) Botryoids composed of fascicular slow dolomite (FSD) cements with chemical growth zonations, radial geometry, and circular twins that grew from a microbialite substrate found in the Dengying Formation, Yangtze Craton [53]. The abbreviation MD stands for micritic dolomite [53]. (c) Apatite granule from the Doushantuo Formation that shows concentric gradients of brown-coloured organic matter along with white arrows indicating linearly elongated cavity structures [63]. Figures reproduced with permission.

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