Clumped-isotope evidence for the formation of nonplanar dolomite textures at near-surface temperatures—Discussion

Ryan et al. (2023) report an instance of nonplanar dolomite texture in the Paleocene–Eocene Umm er Radhuma Formation (Qatar). Clumped-isotope analyses indicate that this dolomite formed at crystallization temperatures ranging from 38.8° to 54.2°C. On the basis of these data the application of crystal growth theory, specifically crystal surface-roughening and the roughening transition at the atomic level (Jackson 1958a, 1958b,; 2004), as a control on macroscopic dolomite crystal morphology (Gregg and Sibley 1984) is called into question.

In this discussion I will: 1) point out what I believe are flaws in the petrographic analysis of Ryan et al. (2023), 2) defend Gregg and Sibley (1984; also Gregg and Sibley 1986; Sibley and Gregg 1987) in terms of the criticism, made by Ryan et al. (2023), of crystal texture classification, 3) briefly discuss the kinetic theory of crystal growth, including advances made over the past 40 years, and why this can be applied to understanding dolomite crystal morphology.

Ryan et al. (2023) outline in their Methods how petrographic analysis of Umm er Radhuma Formation samples was conducted. They state that their thin sections were prepared by Core Laboratories (Abu Dahbi) and stained with alizarin red-S. I presume that the thin sections were of standard thickness (30 µm) and unpolished, and likely had cover slips. Because of the surface topography on unpolished thin sections, it frequently is difficult to determine crystal-boundary relationships. Etching during staining further increases surface topography. Crystals may also overlap one another in thin sections of standard thickness. Gregg and Sibley (1986) recommended using polished thin sections or even doubly polished ultra-thin sections for more finely crystalline dolomites. Also, Gregg and Sibley (1986) suggested using SEM to qualitatively evaluate crystal-boundary relationships. We should have pointed out that the most reliable way to do this is to use polished etched plugs or thin sections for SEM work.

Figure 2 presented by Ryan et al. (2023) shows thin-section photomicrographs of finely to medium crystalline (size classification of Folk 1959) dolomite. My immediate impression, looking at these, was that they are planer-S dolomite. In fact an abundance of preserved crystal-face junctions, an indicator of planar dolomite, are labeled. Figures 3A and 4A presented by Ryan et al. (2023) similarly appear to me to be planar-S dolomites. I realize that without looking at the actual thin sections (rotating the stage, racking up and down, changing magnification), it is difficult to make an evaluation on a published photomicrograph. In any event, if, as I suspect, the thin sections used in this study are of standard (30 µm) thickness and unpolished, this would tend to invalidate counts of preserved crystal-face junctions. (For the definition of a preserved crystal-face junction see Gregg and Sibley 1984 and/or Sibley and Gregg 1987.)

Here I will try to present an example of how such difficult petrographic evaluations can be made. Figure 1A (this paper) displays an example of planar-S dolomite, at a magnification similar to that shown in Ryan et al. (2023), that could easily be mistaken for nonplanar dolomite. Crystal-boundary relationships are poorly defined, appearing to be nonplanar and few preserved crystal-face junctions can be observed (since all of my thin sections are polished and uncovered, a direct comparison with the photomicrographs in Ryan et al. (2023) is not possible). Figure 1B shows an example of the same dolomite (different section) using a polished ultra-thin section (15 µm) at higher magnification. This photomicrograph clearly shows planar boundary relationships between the dolomite crystals and abundant preserved crystal-face junctions.

The SEM photomicrographs in Ryan et al. (2023) pose greater challenges for interpretation. Figure 3B (Ryan et al. 2023) appears, on close examination, to have abundant planar crystal boundaries. Figure 3C may display irregular boundaries, but it is difficult to tell because the exposed surface has so many irregularities due to fracturing. Figure 4B is clearly a planar-E dolomite with several preserved crystal-face junctions visible, and Figure 4C is more ambiguous with boundary relationships difficult to determine. The same is true for the SEM photomicrographs in Figure 5.

So what should a nonplanar dolomite look like in thin section? Figure 1C in this paper shows a very finely to finely crystalline nonplanar dolomite replacing an aragonite bivalve shell. This sample was synthesized in a hydrothermal autoclave at 300°C (experimental details can be found in Gregg 1982). The boundary relationships between crystals are irregular; there are no preserved crystal-face junctions observable in this field, and the crystals have strongly undulatory extinction. Figure 1D shows a nonplanar dolomite from the Mississippian of the Irish Midlands (left field) grading into a mixed planar-S–nonplanar dolomite (right field). Here the nonplanar crystals display irregular intercrystal boundaries; there are few (if any) observable preserved crystal-face junctions, and the crystals display strongly undulatory extinction. This texture was interpreted by Wright et al. (2003) as a recrystallization transition. Gregg and Sibley (1984) published a number of thin section and SEM photomicrographs of both planar and nonplanar dolomites that may also be consulted.

An important characteristic of nonplanar-dolomite texture that should be emphasized here is undulatory extinction. Although not used as an essential characteristic, Gregg and Sibley (1984) and Sibley and Gregg (1987) repeatedly state that undulatory extinction is typical of nonplanar dolomite crystals. In fact, in the 40 years that have passed since publication of Gregg and Sibley (1984) I cannot remember observing an undisputable nonplanar dolomite that has not displayed this characteristic. Ryan et al. (2023) do not mention if their dolomites display undulatory extinction, so I presume not.

It also needs to be pointed out that the temperature range, indicated by clumped-isotope analysis, for the Umm er Radhuma Formation (Ryan et al. 2023), overlaps with the temperature at which roughening is theoretically predicted to begin by Gregg and Sibley (1984). The roughening transition is not sharp, as Ryan et al. (2023) incorrectly state, but is transitional (Temkin 1969; Jackson 2004; Sunagawa 2005). It is possible, if not likely, that the textures observed by Ryan et al. (2023), if evidence of nonplanar crystal boundaries can be found to exist, represent a transition from planar to nonplanar as similarly described by Wright et al. (2003) for textures observed in the Mississippian of the Irish Midlands.

Clumped isotopes may not be an entirely reliable indicator of temperature for dolomite that has undergone recrystallization at low water to rock ratios: “…dolomite recrystallization has the potential to affect T(Δ_47dol) at depths shallower than previously demonstrated” (Veillard et al. 2019). For instance, in the Villany Hills of western Hungary, dolomite likely was exposed to higher temperatures, based on burial history, than indicated by clumped isotopes (Lukoczki et al. 2020). This may not be applicable to the Umm er Radhuma Formation if they were never exposed to burial conditions, or may be an indication that that this unit was, in fact, more deeply buried than suspected or possibly exposed to warm fluids emanating from depth. The latter could result in recrystallization modifying the dolomite texture.

In closing this section of the discussion, I should say that it would have been better to have a more clear example of a “nonplanar” dolomite than the crystal textures presented in the figures by Ryan et al. (2023) in the Umm er Radhuma Formation.

In the “Discussion” section of their paper, Ryan et al. (2023) presented a number of criticisms of the Gregg and Sibley (1984) interpretation of dolomite texture. They also suggest a number of alternative geochemical and petrographic reasons for nonplanar dolomite, without ever saying how these would actually result in nonplanar dolomite crystal growth. Space does not permit a detailed response to each of these; however, I will try to address some of the more salient points brought up by Ryan et al. (2023).

Certainly one can envision circumstances where dolomite textures that are technically nonplanar can arise that are not related to kinetic roughening at the atomic level. These might include dissolution surfaces (e.g., Gregg and Hagni 1987, their Fig. 6) and textures that develop during tectonically induced strain recrystallization (Schmidt 1965; Spry 1969). Ryan et al. (2023) correctly point out that dolomite crystals with well-developed faces frequently grow into their own growth solutions at temperatures above predicted roughening. This is true of many materials growing from solution, not just carbonates, and can be attributed to additional impediment that control the development of crystal faces (Dowty 1976). It is not necessarily due to “impurities” as stated by Ryan et al. (2023) although fluid composition can contribute to this. More likely it is related to desolvation or to the adsorption of solvent (Lewis 1975) or mass transfer during crystal growth into solution, and saturation and supersaturation in the diffusion boundary layer (Sunagawa 2005). This was discussed by Gregg and Sibley (1984). As an aside, it should be noted that at elevated temperature faceted dolomite crystals frequently display curvature (resulting in sweeping extinction in thin section) described as “saddle dolomite” (Radke and Mathis 1980). The causes of saddle-dolomite crystal growth have been attributed to temperature (Radke and Mathis 1980; Gregg 1983) and may be related to growth above the roughening transition.

Ryan et al. (2023) propose that supersaturation may be a control on dolomite texture. This is true. In fact, Gregg and Sibley (1986) state: “It is theoretically possible and has been experimentally verified (Human et al. 1981,; Jetten et at. 1984) that crystals grown at low temperatures undergo a roughening transition due to an increase in supersaturation. In other words, the transition from a smooth to a rough interface can be brought about by an increase in temperature to a critical roughening temperature or by an increase in supersaturation to a critical saturation. Therefore, it is theoretically possible for xenotopic dolomite to form, under conditions of high supersaturation, at low temperature (25°C).” The kinetic effect of supersaturation on crystal faces growing from solution will be treated in detail in the next section. In another example, Sibley and Gregg (1987, their Fig. 11) detail how saturation state might theoretically affect dolomite crystal texture during replacement of limestone. (Note: The terms “idiotopic” and “xenotopic” (Friedman 1965) were replaced by planar and nonplanar (Sibley and Gregg 1987) at the suggestion of Robin Bathurst (personal and written communication 1985)).

Ryan et al. (2023) infer that Gregg and Sibley (1984) attribute all dolomite textures to temperature, “…data presented here suggest that it is unlikely that temperature alone influences dolomite texture, but rather that a variety of physiochemical factors work in concert.” This is simply untrue and was not stated by Gregg and Sibley (1984) or Sibley and Gregg (1987). In fact, in their classification paper, Sibley and Gregg (1987) detail many physiochemical factors that influence dolomite crystal textures, temperature being just one of them. Many of the physiochemical factors discussed (Sibley and Gregg 1987) are the very ones cited by Ryan et al. (2023). The difference is that Ryan et al. (2023) offer no examples or explanation about how these factors might affect textures whereas Sibley and Gregg (1987) do. Ryan et al. (2023) also state “…dolomite texture may not be a reliable temperature proxy.” I do not dispute this. However, the temperature range of 50° to 100°C suggested by Gregg and Sibley (1984) and Sibley and Gregg (1987) was never meant as a “proxy” for diagenetic temperature. It is far too broad a range and blunt an instrument to be considered for that. Rather it is an indicator, in much the same way that the observation of saddle-dolomite cement is an indicator (Radke and Mathis 1980), of burial and/or hydrothermal diagenetic conditions. Once nonplanar dolomite is observed, proxies for diagenetic temperatures, such as fluid-inclusion microthermometry (Goldstein and Reynolds 1994) or, less reliably, clumped-isotope geochemistry (Bonifacie et al. 2017) can be applied. See, for instance, studies by Lukoczki et al. (2019) using petrography and clumped isotopes and Dunseith et al. (2021) using petrography and fluid-inclusion microthermometry to infer diagenetic temperatures.

Regardless of the influence of all of the physiochemical factors that act on a dolomite, the texture that develops is fundamentally due to nucleation and growth of dolomite crystals (Sibley and Gregg 1987). Intentionally or unintentionally, Ryan et al. (2023) appear rather dismissive of Jackson’s (1958a) kinetic model of crystal growth, citing only this single paper. This ignores the broad applicability of this work to materials science and engineering as well as to mineralogy and petrology. Here I will provide some context and explain how it applies to dolomite textures.

k Boltzmann’s constant

T_e equilibrium temperature (degrees Kelvin)

η₁ number of nearest neighbors at the site of attachment of an atom

υ total possible number of nearest neighbors so η₁/υ is the fraction of the total number of nearest neighbors in a plane parallel to the crystal face under consideration.

Note that the temperature of the reaction is inversely proportional to the value of α and as temperature increases, α decreases. The relationship of α to the free energy of a growing crystal surface and the occupancy of sites (at the atomic level) on a growing crystal surface is shown in Figure 2. Curves represent various values for α. At high values of α, filling almost all or none of the surface sites results in the lowest free energy and the crystal face will remain smooth. As α drops below a value of “2,” filling half the sites results in the lowest free energy and the surface becomes rough.

The derivation of Jackson’s alpha-factor and its importance to the macroscopic morphology of crystals is explained in detail by Jackson (2004, Chapter 21). For a less mathematically dense explanation see Sunagawa (2005, Chapter 3). This relationship will vary depending on the crystal face under consideration. For instance, for an ice crystal growing at a few degrees below freezing, the α value of the hexagonal prisms {} will be below “2” and α for the basal pinacoid {0001} remains above “2.” Thus the hexagonal prism faces roughen, undergo rapid growth, and develop dendrites whereas the basal faces undergo slower growth and remain flat. This results in the familiar “snowflake morphology” of ice at the macroscopic level. The enthalpy factor, L_o in Equation 1 will be different for different crystal faces. Higher-energy faces will have lower roughening temperatures. Surface energy for a crystal face is dependent on the internal structure of the crystal (Dowty 1976).

ΔH ^fus molar enthalpy of precipitation (or dissolution) for growth from solution of the crystal face under consideration

R gas constant

T ^fus temperature of precipitation or dissolution (degrees Kelvin)

ln x natural log of the molecular fraction of solute.

Note that as the mole fraction of solute increases (saturation increases) α decreases. Therefore, increasing saturation would lead to the kinetical roughening of Jetten et al. (1984). This equation has been shown to work experimentally for a number of laboratory-constrained solvent–solute systems (Bennema 1993).

A large body of theoretical modeling and experimental work summarized by Jackson (2004) and Sunagawa (2005) verify the application of Jackson’s (1958a) work to both the internal structure and composition of crystals as well as the external morphology of crystals grown from vapors, melts, and solution. This research has been of particular importance to the manufacture of materials used in the electronics industry and elsewhere (Jackson 2004; Sunagawa 2005). The theory also has been applied to understanding morphology of silicate minerals in igneous and metamorphic rocks (e.g., Dowty 1976; Kirkpatrick 1981; Carstens 1983; Sunagawa 2005).

Here I will present an example of how the roughening transition, due to temperature, can affect the morphology of natural dolomite crystals replacing a limestone. Figure 3A is a cathodoluminescence photomicrograph of planar dolomite crystals, replacing calcite micrite, in the Cochrane Formation (Silurian) Oklahoma, USA (Silva et al. 2020). Compositional zoning (Fig. 3A) indicates that these crystals maintained planar rhombohedral {} faces throughout their growth history. Stable-oxygen-isotope data further indicate that this dolomite likely formed in equilibrium with Silurian seawater at near surface temperatures. By contrast, Figure 3B is a cathodoluminescence photomicrograph of nonplanar dolomite crystals, similarly replacing calcite micrite, in the Bonneterre Dolomite (Cambrian) Missouri, USA (Gregg and Shelton 1990). Compositional zoning indicates that these crystals underwent nonplanar growth (approaching a dendritic morphology) throughout their growth history. The macroscopic morphology displayed is clearly indicative of surface-roughening at the atomic scale during growth (see illustrations in Jackson 2004; Sunagawa 2005). Fluid-inclusion microthermometry indicates that these crystals were exposed to temperatures up to 120°C during growth (Gregg and Shelton 1990). Although kinetical roughening, due to possible higher supersaturation, cannot be entirely ruled out and may be a contributing factor, I think it is much more likely that the nonplanar growth (Fig. 3B) in the Cambrian example is controlled by the higher temperature during growth.

As shown above, Ryan et al. (2023) failed on several levels to demonstrate that nonplanar dolomite cannot be used as an indicator of elevated diagenetic temperatures. The Umm er Radhuma Formation likely does not display nonplanar dolomite texture, but displays planar-S texture that was mistakenly identified as nonplanar. Even if on a closer look evidence for nonplanar dolomite or a transitional texture is observed, the range of temperatures indicated by clumped isotope analysis for the Umm er Radhuma Formation overlaps with the lower range of temperatures that are predicted to result in nonplanar dolomite. Clumped isotope analysis, under some circumstances, may underestimate diagenetic temperatures. Most of the criticisms made by Ryan et al. (2023) of Gregg and Sibley (1984) and Sibley and Gregg (1987) are without merit as the reasons for these criticisms were adequately addressed by Gregg and Sibley (1984) and Sibley and Gregg (1987). Regardless of whether Ryan et al. (2023) observed planar or nonplanar dolomite, the criticism of the kinetic theory of crystal growth (Jackson 1958a, 2004) is baseless. Roughening, at the atomic level, and its effect on crystal morphology, has been repeatedly demonstrated, through modeling and laboratory experiments, for simple as well as complex crystal structures growing from vapor, melt, and solution. Finally, nonplanar texture has been repeatedly observed in dolomite that can be demonstrated to have formed under burial and/or hydrothermal conditions through isotope geochemistry, fluid inclusion microthermometry, or other associations (e.g., Kupecz et al. 1993; Melim and Scholle 2002; Hitzman et al. 2002; Lonnee and Machel 2006; Davies and Smith 2006; Cruset et al. 2021; and many others). By contrast, observation of nonplanar dolomite formed in verified low-temperature diagenetic settings is rare.

This discussion profited from discussions with Hans Machel, Jeff Lonnee, and Duncan Sibley. Maurice Tucker provided a valuable review and edit of this manuscript. I also wish to thank the late Kenneth A. Jackson (1931–2022), Professor of Materials Science and Engineering, University of Arizona, and Fellow of the National Academy of Engineering. In 1981 he took the time to discuss and explain to me the possible role of crystal surface-roughening to dolomite crystal textures.