We use mineral liberation analysis (MLA) to quantify the spatial association of 15,118 grains of accessory apatite, monazite, xenotime, and zircon with essential biotite, and clustered with themselves, in a peraluminous biotite granodiorite from the South Mountain Batholith in Nova Scotia (Canada). A random distribution of accessory minerals demands that the proportion of accessory minerals in contact with biotite is identical to the proportion of biotite in the rock, and the binary touching factor (percentage of accessory mineral touching biotite divided by modal proportion of biotite) would be ~1.00. Instead, the mean binary touching factors for the four accessory minerals in relation to biotite are: apatite (5.06 for 11,168 grains), monazite (4.68 for 857 grains), xenotime (4.36 for 217 grains), and zircon (5.05 for 2876 grains). Shared perimeter factors give similar values. Accessory mineral grains that straddle biotite grain boundaries are larger than completely locked, or completely liberated, accessory grains. Only apatite-monazite clusters are significantly more abundant than expected for random distribution. The high, and statistically significant, binary touching factors and shared perimeter factors suggest a strong physical or chemical control on their spatial association. We evaluate random collisions in magma (synneusis), heterogeneous nucleation processes, induced nucleation in passively enriched boundary layers, and induced nucleation in actively enriched boundary layers to explain the significant touching factors. All processes operate during the crystallization history of the magma, but induced nucleation in passively and actively enriched boundary layers are most likely to explain the strong spatial association of phosphate accessories and zircon with biotite. In addition, at least some of the apatite and zircon may also enter the granitic magma as inclusions in grains of Ostwald-ripened xenocrystic biotite.

Review

In many peraluminous, and even some metaluminous, granitic rocks, biotite is a prominent, macroscopic, major mineral phase. In those same rocks, apatite, monazite, xenotime, and zircon are inconspicuous, microscopic, accessory mineral phases. A casual examination of thin sections, either in plane-polarized light or cross-polarized light, appears to show concentrations of these accessory minerals enclosed in biotite, because their optical properties are strongly contrasted with biotite, but it is not clear what proportions of them occur elsewhere in the granite, because they are fine grained, and many of their optical properties have weak contrast with quartz and feldspars. Are the accessory zircon and phosphate phases randomly distributed in granitic rocks, or is there a spatial correlation between them and biotite in granitic rocks? And, if there is a statistically significant spatial association, what is the reason?

Several researchers have, to varying extents, previously addressed these questions. For example, Chappell (1978) and Chappell et al. (1987) noticed that the concentration of apatite in biotite was 20 times greater than in feldspar, but concluded that because the biotite was assumed to be restitic, the included apatite must also be restitic. In contrast, Bacon (1989) explored the role of boundary-layer enrichment of phosphorus around growing biotite, the subsequent nucleation of magmatic apatite, monazite, and xenotime, and the incorporation of those accessory minerals into the biotite. In addition, Wark and Miller (1993) enhanced the magmatic interpretation for the spatial association by examining compositional variations in the accessory minerals.

Purpose

The principal objective of this investigation is to provide a rigorous quantitative measure of the spatial association of accessory phosphate minerals (apatite, monazite, and xenotime) and zircon with biotite in three granitic rocks from a single outcrop in the South Mountain Batholith (SMB), located in southwestern Nova Scotia. The SMB is a large (7300 km2), post-tectonic, peraluminous (Al2O3/(CaO+Na2O+K2O) = 1.05–1.40) granodiorite-monzogranite-granite complex that intruded the Cambro-Ordovician Meguma Supergroup ~380–370 m.y. ago (MacDonald, 2001; Clarke et al., 2004; Bickerton et al., 2020). We also interpret the spatial association between accessory minerals and biotite in terms of the many contemporaneous physical (nucleation and synneusis) and chemical (Fe-P association and chemical gradients) processes operating in the magma during its crystallization. Other objectives include an investigation of the grain-size distribution of the accessory minerals and the frequency of clustering of accessory minerals in relation to a hypothetical random distribution.

Claim

We demonstrate that there is a statistically significant spatial association of accessory minerals with biotite, and we believe that the phosphate and zircon accessories are best explained by processes of passive and active boundary layer enrichment, and that at least some apatite and zircon occur as inclusions in xenocrystic biotite. We also believe that these spatial associations depend on the specific temperature-pressure-composition conditions of formation of the granite, and that our analytical and statistical approach will lead to a better understanding of the genesis of granitic rocks in the future.

Agenda

To start, we present the spatial association and crystal size distribution for each of the four accessory minerals. Then we compute the touching factors, and shared perimeter factors, with biotite and compare these factors with expected random distributions. Next, we compile and analyze the accessory mineral grain-size data as a prelude to being able to simulate expected clustering of accessory mineral grains. Finally, because many of the observed touching factors, shared perimeter factors, and accessory mineral clustering are significantly non-random, we explore a range of physical and chemical processes to account for their spatial associations.

For this study, we collected three macroscopically similar biotite monzogranite samples (AB1, AB2, and AB3) at intervals of ~10 m along a straight roadside outcrop (44.625° N, 63.627° W) of the South Mountain Batholith. The outcrop is less than 1 km from the contact with the country rock (Jamieson et al., 2012), and it is a moderately contaminated melagranite typical of the marginal facies of the SMB (MacDonald and Clarke, 2017). Although these rocks do not show any strong fabric, to mitigate any possible effect of orientation, we cut each sample into a cube, and we cut polished thin sections from three mutually perpendicular sides of each cube. We then analyzed each of the resulting nine polished thin sections (AB1A, AB1B, AB1C, etc.) in a Mineral Liberation Analyzer (MLA) at the Helmholtz Institute Freiberg for Resource Technology.

The MLA comprises a FEI Quanta 650F field emission scanning electron microscope equipped with two Bruker Quantax X-Flash 5030 EDX detectors and FEIs MLA suite v. 3.1.4.686 for data acquisition. Identification of mineral grains by MLA is based on backscattered electron (BSE) image segmentation and collection of EDX-spectra of the grains distinguished in BSE-imaging mode. Boundaries between two grains of the same mineral are not visible because the BSE intensities are identical.

Collected EDX-spectra are then classified using a list of mineral spectra collected by the user. More detailed information about functionality of the MLA system is detailed in Fandrich et al. (2007) and Bachmann et al. (2017). According to the aim of this study, the extended BSE liberation analysis (XBSE) measurement mode was carried out for all samples. Consistent operating conditions were applied at 25 kV accelerating voltage, a probe current of 2 nA, and an acquisition time of 120 ms. Pixel size was set to 1.5 µm/pixel at a minimum particle and grain size of 5 pixels. Contrast and brightness were calibrated on Cu (252), and the background was set so that minerals were not analyzed when appearing significantly darker than biotite in the BSE (e.g., feldspar and quartz).

The generated data sets were processed in the MLA image processing software. A coincidence threshold of 80% with standard spectra was used for the classification of the XBSE measurements. The standard mineral list contains only biotite, chlorite, ilmenite, apatite, monazite, xenotime, and zircon. Later the biotite and the chlorite were grouped together. All other minerals appearing were classified as unknown and were removed during a touch-up procedure. Also, all pixels classified as background within the biotite and all accessories were turned into the host mineral by using a touch-up function, to achieve appropriate perimeter values. Therefore, a border length of apatite with the other minerals can be calculated for the remaining six phases as well as for the “free surface.” This calculation was performed by using the mineral association and perimeter data of every individual accessory mineral grain analyzed in the sample. Using the perimeter as a proxy for the grain size is possible because the accessory minerals in our sample have idiomorphic to hypidiomorphic shapes.

Touching Parameters

Figure 1 shows five different images of the same section cut from one of the three granite samples. Tables 1–4 contain all the relevant association data for the accessory minerals, apatite, monazite, xenotime, and zircon, respectively, in the nine thin sections from three rocks (AB1, AB2, and AB3). In a purely random distribution, the proportion of accessory minerals in full or partial contact with biotite would be approximately equal to the modal proportion of biotite in the rock ( Appendix 1). In the cases of all accessory minerals, their proportions in full or partial contact with biotite appear to be considerably greater than expected from a random distribution. In very general terms, the modal proportion of biotite is ~15%, but biotite contains ~75% of the accessory minerals.

Crystal Size Distribution

Comparison of Accessory Mineral Grain Sizes

For each of the 15,118 measured accessory grains, the MLA analyzer has provided the perimeter. Figure 2 shows boxplots for the grain sizes of all the accessory minerals. One prominent feature is the number of large grains of apatite and zircon. Pairwise t-tests, adjusted for multiple comparisons using the Bonferoni correction, were used to compare mean log10 crystal size for the four accessory minerals. Monazite was not significantly different from xenotime (P > 0.05), and xenotime was only marginally significantly different from zircon (0.05 < P < 0.01). The other comparisons were all highly significant (P < 0.01).

Locked-Straddled-Liberated Grain Sizes

Figure 3 shows boxplots of the grain sizes of the four accessory minerals, sorted by their spatial association with biotite (locked—completely enclosed in biotite; straddled—partly enclosed in biotite; and liberated—simply not touching biotite, as opposed to being freed from former enclosure in biotite). We used pairwise ANOVAs (analysis of variance) to assess differences in perimeter between the straddled and locked or liberated grains, and for each accessory mineral, the results were highly significant (P < 0.01).

Superficially, it might appear that unusually large accessory mineral grains grow preferentially on the margins of biotite grains. Instead, this grain-size disparity is related to the probability that an accessory grain can straddle the biotite margin: the larger the radius ratio of accessory mineral grain to the biotite grain, the greater is the probability that the accessory grain can lie across the biotite margin ( Appendix 1).

Analysis of Spatial Association between Accessory Minerals and Biotite

We present two possible measures of the spatial association for each accessory mineral and biotite:

  1. the binary touching parameter (BTP), in which an accessory grain that shares at least one adjacent pixel with biotite is considered as touching, and the binary touching factor (BTF) is the percentage of touching accessory grains divided by the modal percentage of biotite—and because apparently non-touching grains in a twodimensional thin section could still be touching in three dimensions, the calculated binary touching factor is a minimum; and

  2. the shared perimeter parameter (SPP), which is the proportion of the perimeter of an accessory grain shared with biotite, and the shared perimeter factor (SPF) in which the percentage of total accessory mineral perimeters adjacent to biotite is divided by the modal percentage of biotite (Tables 14).

If there is a random spatial association between any of the accessory minerals and biotite, the proportion of cases in which a particle of the accessory mineral touches biotite should be approximately the same as the modal (area) proportion of biotite. Thus, our first requirement is to test for a statistically significant spatial correlation between each of the four accessory minerals (zircon, apatite, monazite, and xenotime) and biotite.

Binary Touching Factor (BTF)

Table 5 and Figure 4 report and show the mean binary touching factor for the four accessory minerals. For a purely random distribution of these accessory minerals, the expected touching factors would all lie in the narrow range of 1.00−1.21, provided that the diameters of accessory minerals are less than 10% of the diameter of biotite ( Appendix 1).

The binary touching factors in Figure 4 are all much greater than the random distribution value of ~1. The probability of all 36 BTFs being either above or below 1, if there is no spatial association between biotite and the accessory minerals, is:
graphic
(1)

which is essentially zero; thus there is very strong evidence against the hypothesis of no spatial association.

A one-way analysis of variance (ANOVA) shows that there are statistically significant differences among the mean BTFs for the four accessory minerals (F = 3.71, with 3 and 32 degrees of freedom, and P = 0.02). A subsequent analysis using pairwise t-tests shows that the mean BTF for xenotime is significantly different from the mean BTFs for apatite (t = −2.832, p < 0.01) and zircon (t = 2.811, p < 0.01).

Shared Perimeter Factor (SPF)

Table 6 and Figure 5 report and show the shared perimeter factors for the four accessory minerals. For a purely random distribution of these accessory minerals, the expected shared perimeter factors would all be 1.00 ( Appendix 1).

The shared perimeter factors in Figure 5 are all much greater than the purely random distribution value of 1. The probability of all 36 SPFs being either above or below 1, if there is no spatial association between biotite and the accessory minerals, is:
graphic
(2)

which is essentially zero; thus there is very strong evidence against the hypothesis of no spatial association.

A one-way analysis of variance shows that there are statistically significant differences among the mean SPFs for the four accessory minerals (F = 5.40, with 3 and 32 degrees of freedom, and P = 0.0040). A subsequent analysis using pairwise t-tests shows that the mean SPF for xenotime is significantly different from apatite (t = −3.711, p = 0.0008), monazite (t = −2.305, p = 0.0278), and zircon (t = −3.202, p = 0.0031).

As for the BTF above, we proceed on the basis that the quantitatively measured spatial association of accessory minerals and biotite is highly significant and in need of an explanation.

Clustered Accessory Grains

The MLA measures the lengths of the perimeter of each accessory grain (apatite—A; monazite—M; xenotime—X; zircon—Z) against all other grains. In most cases, those accessory grain perimeters are simply shared with biotite (locked or straddled) or are shared with quartz or feldspar (liberated). However, a small percentage of accessory grains share part, or all, of their perimeters with other accessory grains, and we refer to these mutually touching accessories as clustered. To investigate such clustering, we made a detailed examination of Section AB1B (only). The sample was chosen randomly. This sample contains 1260 apatite grains, 99 monazite grains, 32 xenotime grains, and 322 zircon grains, but only 80 of the apatite grains (6.3%) are spatially associated (clustered) with other accessories, at least in the observable two-dimensional sections. Specifically, we detected 27 apatite-monazite (AM) clusters, six apatite-xenotime (AX) clusters, 40 apatite-zircon (AZ) clusters, four apatite-monazite-zircon (AMZ) clusters, two apatite-xenotime-zircon (AXZ) clusters, and one apatite-monazite-xenotime-zircon (AMXZ) cluster.

Thus, of the 80 apatites touching other accessories, 40 of them (50%) are against zircon, well below what might be expected because these two minerals represent ~92% of all accessory grains in Section AB1B. The next most abundant accessory mineral clustering involves apatite-monazite constituting 33.75% of the clusters. What would a purely random clustering relationship be?

We realistically simulated 1000 sections by randomly positioning accessory grains on a background consisting of 15.90% biotite, using the same numbers and sizes of accessory grains as measured in Section AB1B, taking into account their association with biotite ( Appendix 2), and Table 7 shows the results. Comparing our observed Section AB1B to the simulation samples shows that observed apatite-monazite clustering was at the very high end of the simulation range. The other observed pairings are not unexpected under random positioning of the accessory grains.

Table 7 compares the observed accessory mineral clustering in Section AB1B with the simulated pairwise clustering ( Appendix 2). We make the following observations and deductions:

  1. Any accessory mineral pairing with itself is a combined function of its abundance and grain size, thus AA clusters are highly likely, and MM, XX, and ZZ clusters are highly unlikely, but no such clusters are detectable using the MLA technique because any cluster, or twin, would be detected as one large grain.

  2. The observed AM and AX clustering in Section AB1B is greater than the median expected from a random distribution, and it may have some physical or chemical cause.

  3. The observed clustering of zircon with the three individual phosphate minerals in Section AB1B (AZ, MZ, and XZ) is close to being random, i.e., there is no physical or chemical explanation needed for their observed clustering.

  4. Judging from their morphologies (euhedral shapes and general lack of re-entrant angles), the large zircon grains in Section AB1B are not likely to be clustered small ones. The same is true for apatite, monazite, and xenotime ( Appendix 3).

  5. Of the 27 AM clusters in Section AB1B, seven of the monazites were completely enclosed in apatite. Because those seven monazite grains had no shared perimeter with biotite, they were considered as liberated for the purposes of Table 2. But because most apatite grains are locked in biotite, these monazite grains were probably locked in biotite also, and might well have also been classified as locked. As a consequence of such a reclassification of accessories in Section AB1B, the BTF for monazite would increase from 4.00 to 4.45. Similarly, the BTF for xenotime would increase from 4.91 to 5.11, and that for zircon would increase from 4.98 to 5.06.

In conclusion, we deduce that clustering among the three phosphate minerals in Section AB1B (AM, AX, and MX) is generally greater than that expected for a random distribution, and therefore may have some physical or chemical cause: for example, they all depend on high concentrations of phosphorus, and might therefore form, and cluster, in such chemical environments. In contrast, the observed clustering of zircon with the three individual phosphate minerals in Section AB1B (AZ, MZ, and XZ) is close to being random, i.e., there is no physical or chemical explanation needed for their observed clustering.

Origin of Biotite in the South Mountain Batholith

The South Mountain Batholith consists exclusively of peraluminous granitoid rocks, with A/CNK values ranging from ~1.05–1.40 (Clarke et al., 2004; Clarke, 2019), and biotite is the most common, and most abundant, mineralogical expression of the peraluminous whole-rock bulk chemical compositions. The maximum solubility of FeO in granite melts is ~2 wt% (Johannes and Holtz, 1996), yielding ~6 vol% of biotite; however, the modal proportions of biotite in our samples range from 12 to 18 vol%. Three possible explanations for these high modal proportions of biotite include:

  1. two to three times the concentration of cumulate magmatic grains;

  2. a combination of magmatic and xenocrystic grains; or

  3. a combination of magmatic and peritectic grains resulting from a melting reaction involving chlorite (unlikely, because the Bt-in isograd in the contact aureole would have been at a temperature of 450–475 °C, up to 1300 m from the actual contact; Hilchie and Jamieson, 2014).

MacDonald and Clarke (2017) dealt extensively with the melagranites of the SMB, containing high modal abundances of biotite, cordierite, and garnet. They showed that most of these melagranites are spatially related to the contact of the SMB with metagraywacke and metapelite country rocks, suggesting that process (2) above is likely. To a large extent, biotite grains in the country rocks, and even xenoliths, are finer-grained, more anhedral, and essentially free of inclusions relative to biotite grains in the granite. Exceptions to this generalization occur at or near the contact of the country rocks and the granite, whether in situ or as xenoliths, where biotite in the country rocks is coarser grained, and it may even contain zircon inclusions (Fig. 6). Evidence from these melagranites shows that textural and chemical equilibration of xenocrystic and magmatic biotite is rapid (Figs. 6C and 6D) and that there are no easy textural or chemical ways to distinguish between biotites of these two different origins.

If biotite in the SMB granite has two origins, there might be two identifiable populations of inclusions in those biotites. A systematic and detailed investigation of biotite and its inclusions across the margins of xenoliths, such as SLX-1 (Figs. 6E and 6F), might resolve this issue. We do, however, know that the xenocrystic and magmatic biotite become homogenized and/or equilibrated chemically (Fig. 6F), and that those chemical cation exchange processes should not change the inclusion population.

Because the SMB biotite nucleated from, or chemically equilibrated by diffusion through, and texturally equilibrated by recrystallization and Ostwald ripening in, a silicate melt, the biotite in the SMB is de facto magmatic (Fig. 6F), and thus its spatial relationship to all the accessory minerals (apatite, monazite, xenotime, and zircon) must be considered accordingly. As the xenocrystic biotite recrystallized and Ostwald ripened in the silicate melt, it could have acquired inclusions in much the same way that magmatic biotite did. We proceed from this deduction that biotite in our granite samples is a combination of magmatic and xenocrystic biotite, now equilibrated in a granitic melt. Nevertheless, we suspect that there may be differences in the inclusion contents of fine-grained clusters of biotite and the large isolated grains of biotite. Our measurements of BTF and SPF values for the accessory minerals do not, and technically cannot, discriminate between measurements in the two morphological types of biotite. To resolve this question, further refinement of our work would be necessary.

Interpreting the Spatial Association between Accessory Minerals and Biotite

Having established a statistically significant spatial association between the accessory minerals and biotite, we need to understand the reason(s) for this association. Is it physical or chemical, or a combination of both? At no time in its history was the SMB magma likely ever above its liquidus temperature, so it probably always contained crystals of some of its most refractory and insoluble phases, including biotite and probably some of the accessory phases under discussion here. If we follow the above described magmatic-xenocrystic formation model of the biotite in the South Mountain Batholith, we must first examine whether it could also apply to the accessory minerals.

In the absence of quantitative mineralogical data on the modal content of apatite, zircon, monazite, and xenotime in the country rocks, fundamental considerations can be made about the stability of these minerals in metapelites and metagraywacke, as summarized by Yakymchuk et al. (2017). The country rocks consist mainly of greenschist-facies Meguma turbidites (Douma, 1988; Ham et al., 1990). The mineral assemblage is more or less identical to the peraluminous granites of the SMB, but the modal abundances, mineral compositions, and textures can be markedly different.

In the subsolidus region, there are no metamorphic mineral reactions that lead to the breakdown of apatite, monazite, or zircon (Rapp et al., 1987; Ayers et al., 1999; Yakymchuk, 2017; Yakymchuk et al., 2017). Only the stability of xenotime can be negatively influenced by the prograde growth of garnet (Pyle and Spear, 1999; Pyle and Spear, 2000; Spear and Pyle, 2002). In the suprasolidus region, the stability of all minerals we investigate is determined by their solubility in the anatectic melts.

Applied to the case under consideration here, and taking into account that garnet-rich rocks in the exocontact and garnet-rich xenoliths are not common (Douma, 1988; Erdmann et al., 2009; MacDonald and Clarke, 2017), we can therefore assume that we can use a comparable model for the origin of the accessory minerals as for the biotite. The solubility of apatite, monazite, xenotime, and zircon in the granitic melts of the SMB is critical for their respective behavior.

If the solubilities of all four accessory minerals were exceeded at any stage of the evolution of the SMB, all xenocrystic crystals would be preserved. They would then be subject only to effects of recrystallization and overgrowth. Consequently, at each stage of biotite crystal development, xenocrystic crystals of apatite, monazite, xenotime, and zircon would also have been available for inclusion by synneusis in the growing biotite crystals. Crystallization of purely magmatic accessory minerals could have occurred at any stage of SMB development.

If the concentrations of the essential structural components for the four accessory minerals were less than saturation in the SMB magma, kinetically regulated partial dissolution of xenocrystic minerals would have occurred (Watson and Harrison, 1983; Harrison and Watson, 1984; Montel, 1986, 1993; Rapp and Watson, 1986; Pichavant et al., 1992; Wolf and London, 1994; Boehnke et al., 2013; Duc-Tin and Keppler, 2015; Gervasoni et al., 2016), and eventual processes of Ostwald ripening and magmatic crystallization would have been coupled to an exceedance of solubility and renewed nucleation during SMB development. The available data from experimental petrology (Supplemental Material1) are complex and cannot be applied to the case of the SMB without broad generalizations. In any case, these experimental data suggest that the substantial portion of the accessory mineral population must be considered magmatic.

Structural Modifications of Silicate Melts

In physical terms, it is well known that the addition of small amounts of phosphorus to different silicate melts has a large effect on the structure of these melts (Mysen et al., 1981; Dupree et al., 1988; Gan and Hess, 1992; Mysen 1992). This observation has led to many experimental and theoretical studies on this topic. At the same time, our granitic system is much more complex than the model systems of experimental petrology or materials science. For this reason, we can draw only qualitative conclusions by extrapolating these data.

The addition of phosphorus to pure silicate glasses increases the polymerization of these glasses (Kushiro, 1975; Mysen et al., 1981; Dupree et al., 1988). In aluminosilicate melts, P also increases polymerization, and the formation of an AlPO4 complex occurs (Kosinski et al., 1988; Gan and Hess, 1992). The investigation of the behavior of phosphorus in calcium-rich silicate melts showed that phosphorus is located in Ca-PO4 domains, surrounded by SiO4 tetrahedra. The CaO content decreases the degree of polymerization in the melt, whereas the PO4 units remain unchanged (Galliano et al., 1994). This behavior would not explain a close link between the formation of accessory phosphate minerals and biotite, but rather would exclude it. However, there is an explanation for the well-known and common formation of PO4-rich feldspar phases in the course of fractionation of phosphate-rich granitic melts (London, 1992; London et al., 1995), if there is no longer sufficient Ca for the formation of apatite.

This condition changes when the proportion of non-bridging oxygen (NBO) increases significantly through the addition of positively charged cations, which corresponds to a depolymerization of the silicate melts. In biotite-bearing granitic melts, Fe3+ and Fe2+ are the most commonly occurring cations of this type. Mysen (1992) has described the consequences for Fe- and Ca-bearing silicate melts. A formation of Fe-PO4 complexes occurs, among other effects. A similar behavior has been demonstrated for other cations. Of particular interest for our problem is the behavior of light rare-earth elements (LREEs), heavy rare-earth elements (HREEs), and yttrium. Investigations of the influence of Ce in silicophosphate glasses (Gambuzzi and Pedone, 2014) essentially confirm experimental data in aluminophosphates and silicophoshate glasses of Rygel et al. (2011) and molecular simulations of Du et al. (2011). These investigations showed that polymerized SiO2-rich regions are separated from depolymerized phosphate-rich regions, and that the PO4 tetrahedra act as a “Ce-solvation shell” (Ishii et al., 1987; Gambuzzi and Pedone, 2014). Similar behavior could be shown for lanthanum (Rashid et al., 2000), gadolinium (Ilieva et al., 2001), and yttrium (Martin et al., 2008; Fu and Christie, 2017).

Processes Leading to Spatial Association of Accessory Minerals with Biotite

We can identify the following potential causes for the spatial association between the four accessory minerals and biotite, and we present them in order of increasing complexity of interacting physical and chemical processes.

1. Synneusis

General process. Synneusis (Vance and Gilreath, 1967) is the process of purely physical, random collision of dissimilar grains in a dynamically flowing magma, and subsequent adherence to reduce surface free energy. It might explain the spatial association of accessory minerals with biotite without having to address problems of nucleation or supersaturation of the magma in relation to those accessory phases.

The adherence of an accessory phase and biotite may result in glomeroporphyritic textures. If so, during the early stages of crystallization of the magma, during which time the melt fraction is large and only the low solubility minerals have begun to crystallize, synneusis may be the mechanism that accounts for their close spatial association. During the more advanced states of crystallization of the magma, when the melt fraction is lower and the fluid mechanical behavior completely different (Vigneresse and Tikoff, 1999), accessory minerals and biotite grains are no longer free to move and adhere. Thus, rock-forming minerals (RFMs) and accessory minerals can also come together in a compacting mush (Beane and Wiebe, 2012; Graeter et al., 2015), and inevitably, there will be late-stage accessory minerals associated with other, felsic, phases.

Application to accessory phosphates. The synneusis process can explain the observed strong spatial association between biotite and the accessory minerals, only if biotite and the phosphate accessories dominated the solid fraction of the magma in the early stages of crystallization, or if there is some unknown preferential “adherence” of the phosphates to biotite at higher degrees of crystallization when quartz and feldspar are present in amounts greater than 20%. We cannot exclude synneusis as a contributing factor to the observed strong spatial association between the phosphate accessories and biotite; however, we are certain that it is not the only factor, and its effectiveness probably remains subordinate.

Application to accessory zircon. Similarly, only if the strong spatial association of zircon with biotite occurred at an early stage of crystallization of the magma when biotite and insoluble accessories were the principal phases, or if for some unknown reason, zircon grains preferentially adhere to biotite compared to the other rock-forming minerals (RFMs) at later stages of crystallization, might synneusis explain our observed BTF and SPF values for zircon and biotite.

2. Heterogeneous Nucleation

General process. Heterogeneous nucleation refers to nucleation on the surface of a preexisting, usually crystalline, solid material, rather than spontaneously nucleating out of a melt or a solution (Hammer et al., 2010; Špillar and Dolejs, 2015). In the ideal case, there is some compatibility between crystalline structure of the nucleating phase and that of the solid substrate. In the context of our work, we consider whether our four accessory minerals could nucleate preferentially on biotite.

Application to accessory phosphates. Because of the known solubility of P and REE in granite melts, and the saturation of phosphate accessory minerals, these are among the earliest phases to saturate and crystallize from the granite magma. Likewise, Fe has limited solubility in granite melts (Johannes and Holtz, 1996), so biotite also saturates early. From a kinetics and energetics point of view, it makes sense that the phosphate accessories might nucleate heterogeneously on early-crystallized biotite, rather than nucleate spontaneously in the unstructured melt. Conversely, the biotite might nucleate heterogeneously on early-crystallized phosphate accessories. We cannot rule out, or in, mutual heterogeneous nucleation conditions to explain the close association of accessory minerals with biotite. There are ways to test such a crystallographic relationship by detailed EBSD studies on both host and inclusions, but such investigations go well beyond our current capabilities.

Application to accessory zircon. As with the phosphate accessories, unless there is a compatible crystallographic match between biotite and zircon, heterogeneous nucleation is not likely to be a significant process, and EBSD investigations would be needed to test this hypothesis.

3. Induced Nucleation in Passively Enriched Boundary Layers

General process. The concept of passively enriched boundary layers can be traced back to the fundamental work of Green and Watson (1982) and Bacon (1989). The main principles they defined, and which lead to the formation of such boundary layers, are: (1) a crystal of another mineral grows more rapidly in the boundary layer than diffusion can transport incorporated and rejected elements to and from this crystal; and (2) diffusion must dominate over convection as a mode of mass transfer near the advancing crystal-liquid interface. Major and trace elements incompatible with the growing RFM, and with low diffusivities, concentrate in the boundary layers (Fig. 7).

Application to accessory phosphates. The nucleation and growth of biotite would passively enrich the adjacent boundary melt in all chemical components not consumed by the biotite, including the essential structural constituents (ESCs) of the phosphate accessory minerals (P, Ca, Ce, and Y). The width and composition of this boundary layer are functions of the growth rate of the RFM, the diffusivities of the elements excluded from the RFM, and the stripping effects of the dynamic flow of the surrounding melt. If the ESCs do not readily diffuse away from the growing biotite, they might concentrate to saturation levels and result in nucleation of the three phosphate accessory minerals (Fig. 7). If so, these accessory minerals ideally might lie in concentric zones in the biotite, in an oscillatory pattern such as Liesegang bands, but this is certainly not the case. Conversely, the depletion zones around growing accessory minerals might induce the nucleation of biotite. If so, we might ideally expect there to be many small biotite grains with central inclusions of accessory minerals in the granitic rock, but this is not the case either. Nevertheless, passive enrichment of P, Ca, Ce, and Y in boundary layers surrounding all the major minerals (biotite, quartz, and feldspars) should take place.

Another consequence is the fact that the bulk chemical compositions of the boundary layers are different around each RFM. In particular, the boundary layers around biotite are richer in SiO2 than around quartz or feldspar, and they are therefore more “differentiated.” Green and Watson (1982) have shown that the solubility of phosphate minerals is lower in more siliceous melts; therefore, this chemical change in the boundary layer may be sufficient to induce nucleation of the phosphate accessories.

Alternatively, the boundary layer around a crystallizing biotite is characterized by an enhanced activity of Fe2+ and/or Fe3+. As a result, that melt forms clusters of depolymerized areas of PO4-Me complexes. In these areas, the saturation limit of minerals such as apatite, monazite, and xenotime can now be exceeded more easily than in areas around felsic (Al-Si–rich) minerals, which are more strongly polymerized at the same PO4 content and do not form such clusters.

Application to accessory zircon. The compositional changes in the boundary layers around biotite are different from the boundary layers around other RFMs. In particular, those biotite boundary layers are depleted in Fe, Mg, Ti, and K, and they are enriched in Si and P, i.e., the melt is more differentiated (Green and Watson, 1982), and probably also more peraluminous because of the depleted K. These more peraluminous differentiated melt compositions reduce the solubility of zircon (Green and Watson, 1982), so that it nucleates preferentially in the biotite boundary layers, and these new, locally formed, zircon grains can become incorporated into the growing biotite. This preferential nucleation of zircon around biotite cannot occur around other RFMs because the compositions of their boundary layers are unsuitable.

4. Induced Nucleation in Actively Enriched Boundary Layers

General process. In actively enriched boundary layers, not only are the ESCs of the accessory minerals passively enriched, but also they are preferentially entrained to the surface of the RFM.

Application to accessory phosphates. Chemical affinity is the property by which unalike elements can form chemical compounds. Such a chemical affinity exists between iron, a multivalent transition element metal, and phosphorus, a multivalent non-metal. In the synthetic Fe-P binary system, the Fe-P chemical affinity is manifest as solid solutions, and as several discrete iron phosphide compounds (e.g., Fe3P, Fe2P, and FeP) (Okamoto, 1990; Nowacki, 2007).

In natural minerals, the Fe-P chemical affinity is manifest as the low-fO2 meteoritic iron-nickel phosphide schreibersite ((FeNi)3P), as well as a wide variety of higher-fO2 iron phosphate compounds, including potentially the anhydrous Fe-II phosphate (Fe3(PO4)2). Normally in the terrestrial environment, additional cations are needed for stabilization of minerals such as graftonite ((Fe2+,Mn,Ca)3(PO4)2) (Hawthorne and Pieczka, 2018) and sarcopside ((Fe2+,Mn,Mg)3(PO4)2) (Hatert et al., 2016). Even higher oxygen fugacities are required to form Fe-(III) phosphates, such as heterosite (Fe3+PO4), which is essentially only known as a secondary mineral and weathering product of triphylite (Włodek et al., 2015). Only high Li concentrations lead to a stabilization of anhydrous Fe-III-phosphates up to the range of magmatic temperatures by solid solution formation (Delacourt et al., 2005; Dodd et al., 2006).

In natural rocks, the Fe-P chemical affinity is clearly manifest in the common strong association of iron oxides and apatite in iron-rich ore deposits (Kiruna—Jonsson et al., 2013; El Laco—Nyström et al., 2008) and in nelsonites (Philpotts, 1967; Kolker, 1982).

In industrial processes, the Fe-P chemical affinity is applied in the use of Fe compounds to remove phosphorus from waste-water systems (Gutierrez et al., 2010; Wilfert et al., 2016), or the use of phosphorus to remove iron impurities from silicon semi-conductor wafers (Bentzen and Holt, 2009; Schön et al., 2014). This use of one element to attract and entrain another is known as “gettering” (Madelung et al., 2002). The concept of gettering may be relevant to the association of phosphate accessory minerals with biotite.

Our observations concerning the spatial relations between accessory minerals and biotite show that all four accessory minerals are significantly more abundant (Tables 1–4) in biotite than in other silicate phases. These observations support the model of an active boundary layer formation for the phosphate accessories, because it appears that phosphorus concentrates more at the margin of biotite than it does at the margins of other, more abundant, rock-forming silicates such as quartz and feldspars. We believe it is possible that, because of the chemical affinity between iron and phosphorus, P was preferentially gettered by Fe migrating to the sites of growing biotite grains. Thus, in actively enriched boundary layers, it is not only rejection from the growing biotite that enriches the boundary layer in phosphorus, but it is also the preferential gettering of phosphorus by iron, escorting it to the surface of the growing biotite. That process leads to a greater concentration of phosphorus against biotite than against other growing silicates where only passive boundary layer enrichment can occur.

Application to accessory zircon. In the graKrmíčnite magma, biotite is clearly a sink for Ti (Fig. 6F); thus, a strong Ti-depletion zone develops in the boundary layer, and a concentration gradient of Ti develops from relatively higher concentrations in the main melt down into that Ti-depletion zone. Just as P might be entrained by Fe toward the growing biotite to explain its spatial association with the phosphate accessories, so cations of Zr4+ (ionic radius 80 picometers [pm]) may be entrained with cations of Ti4+ (ionic radius 75 pm) and become actively enriched in the boundary layer around biotite to explain its spatial association with zircon. If Ti4+ and Zr4+ diffuse together at approximately the same rate through the silicate melt toward the growing biotite (Mungall et al., 1999), to answer its demand for small quadrivalent cations, and if KDTi >1 (LaTourrette et al., 1995; Krmíček et al., 2014) and KDZr <1 for biotite (Ewart and Griffin, 1994; Schmidt et al., 1999), Zr and Si will concentrate in the boundary layer, eventually reaching saturation in ZrSiO4. These new, locally formed, zircon grains can easily become incorporated in the growing biotite. This preferential enrichment of Zr around biotite does not occur around other RFMs because Zr is only passively, not actively, enriched in those boundary layers.

In summary, biotite is the only ferromagnesian rock-forming silicate mineral in these peraluminous granites. If the Fe diffusing toward growing biotite getters P into the boundary layer, and if the Ti diffusing toward growing biotite entrains Zr into the boundary layer, but only the Fe and Ti are taken into the biotite, the boundary layer around biotite (only) might become simultaneously enriched in Zr and substantially reduced in zircon solubility. This combination of active enrichment of Zr and P with reduced solubility of all four accessory minerals might account for their strong spatial association with biotite. So, to nucleate the phosphate accessories, is it passive “differentiation” in the boundary layer to decrease the solubility of AMX, or is it active gettering of P to raise the P content in the boundary layer; or is it a combination of both? This is still an open question.

5. Xenocrystic Phosphates and Zircon

General process. We have already established that the melagranites of the SMB are contaminated rocks (MacDonald and Clarke, 2017), and because the mineral assemblages of the country rocks and granites are essentially identical, every mineral grain in the granite can be suspect xenocrystic, including all the accessory minerals. The question becomes: how much of the spatial association between accessory minerals and biotite occurred before their being introduced into the magma?

Application to accessory phosphates. There has been no systematic study of phosphate minerals in the country rocks of the South Mountain Batholith, but Jähkel (2010) did investigate the occurrence of apatite, monazite, and xenotime in xenoliths and the adjacent contact rocks. Very fine-grained concentrations of apatite occur patchily in the country rocks, and partial melting and disaggregation of these rocks in the granite magma has released xenocrystic apatite. Figure 8 illustrates the progression from fine-grained anhedral xenocrystic apatite to coarser grained euhedral “magmatic” apatite.

Thus, our observation that apatite is strongly associated with biotite could have the following origins: metamorphic apatite still intact in xenocrystic biotite, xenocrystic apatite in magmatic biotite, or magmatic apatite in magmatic biotite. Again, because both apatite and biotite appear to readily equilibrate chemically and texturally with the granite magma (Figs. 6E, 6F, and 8), we cannot easily distinguish among these cases. If xenocrystic phosphate accessories were not growing at the time of being introduced into the magma, they could not have been undergoing heterogeneous nucleation or forming in boundary layers, and, therefore, their current spatial association with biotite can only be explained by synneusis or by an original metamorphic relationship.

Application to accessory zircon. Many of the Ostwald-ripened biotites in the wall rocks and xenoliths contain abundant zircon inclusions (Figs. 6C and 8); therefore, at least some of the spatial association of zircon with biotite occurs before their incorporation into the granite magma. The high modal abundances of biotite in our granite samples suggests that much of it probably has a xenocrystic origin and that, although its chemical composition may have equilibrated with the magmatic biotite through the medium of the silicate melt, the inclusion assemblage has not. A test for this hypothesis would be to use cathodoluminescence to determine the morphological differences, or laser ablation–inductively coupled plasma mass spectrometry (LA-ICP MS), to determine the age differences, of zircons in biotite compared with those in the granite matrix. If those included in biotite are predominantly old detrital zircons from the country rock, compared with young, granite-age, zircons from elsewhere in the rock, this result would support the xenocrystic interpretation.

Thus, our observation that zircon is strongly associated with biotite could have the same explanations as for apatite above. Some of the zircon must be metamorphic in xenocrystic biotite (Figs. 6C and 8), but xenocrystic zircon can otherwise associate with biotite by synneusis.

In summary, all five processes (synneusis, heterogeneous nucleation, passive boundary layer enrichment, active boundary layer enrichment, and xenocrysts) have probably variously contributed to the spatial association of accessory minerals with biotite. Synneusis and xenocrystic origins were most likely important during the early stages of crystallization of the granite magma, heterogeneous nucleation could occur throughout the entire crystallization range, and passive and active boundary layer enrichments were probably most important when the granite magma was no longer dynamically convecting. If true, and if passive and active boundary layer enrichments best explain the high and statistically significant BTFs and SPFs, the implication is that most of the accessories must have saturated late in the crystallization history of the granite magma. This deduction is, however, at variance with the observation that biotite saturates early in the magma, indicating that more detailed work must be done to reconcile these apparent contradictions.

We have assumed that apatite, monazite, and zircon have always been at saturated concentrations in the granite magma, whereas xenotime might only have reached saturation only after extensive (fractional) crystallization, perhaps in a late interstitial melt. That interstitial melt is enriched in phosphorus, and not only is the solubility of xenotime lower than that of monazite, but it also decreases with increasing phosphorus content in the melt (Duc-Tin and Keppler, 2015). This condition leads to the possibility that xenotime may be below saturation level initially, which may explain that the BTF and SPF values of xenotime are lower than for the other three accessory minerals. Apatite, monazite, and zircon became included in biotite by a combination of synneusis, heterogeneous nucleation, passive grain boundary layer enrichment, and active boundary layer enrichment, whereas late-crystallizing xenotime may have principally become included in biotite by Fe-P gettering-enhanced boundary layer enrichment. However, if so, and if active boundary layer enrichment is the most efficient process, some other factor, such as decreased diffusion rates of yttrium through an increasingly viscous melt, might account for the lower BTF and SPF values for xenotime. We note, however, that this interpretation does not account for the single large grain of xenotime (Fig. A3-1 in  Appendix 3).

We have quantified the spatial associations of four accessory minerals (apatite, monazite, xenotime, and zircon) with biotite in peraluminous granites from one small part of the South Mountain Batholith, and we have shown that they are ~4–5 times more abundant in biotite than expected by purely random distribution. We have shown that these spatial associations are statistically significant, and we believe that they are also petrogenetically significant. We conclude that the strong spatial association of accessory minerals with biotite is primarily magmatic in origin, and that it is the product mainly of passive and active boundary layer enrichment during the growth of biotite. However, at least some of the biotite in these rocks is Ostwald-ripened xenocrystic, and, although the chemical composition of the biotite may have equilibrated with the magmatic biotite, its inclusion assemblage of phosphates and zircon has probably not. Thus, not all of the observed spatial association of accessories with biotite is magmatic.

We are aware that our three samples come from one outcrop in one batholith, that this granite is probably highly contaminated, and therefore that our conclusions may not apply to all other biotite-bearing granites. It remains for others to test our findings in other geological settings.

We wish to acknowledge Saskia Erdmann for Figure 6A and for analyzing the biotites in our sample SLX-1 (Fig. 6F), Rebecca Jamieson for providing samples and discussing the origin of biotite in the country rocks and granites, Yana Fedortchouk for photographing Figures 6B–6D and providing three photomicrographs for Figure 6, and David London for permission to use Figure 7. In addition, we thank Charles Bacon, Ryan Currier, an anonymous reviewer, and editor Guil Gualda for their many helpful recommendations to improve our manuscript.

1Supplemental Material. Compilation of available experimental petrological data on the solubility of accessory minerals in granitic melts. Please visit https://doi.org/10.1130/GEOS.S.16840708 to access the supplemental material, and contact editing@geosociety.org with any questions.
Science Editor: Shanaka de Silva
Guest Associate Editor: Guilherme Gualda

APPENDIX 1. SIMULATION OF BTF AND SPF

The values for binary touching factor (BTF) and shared perimeter factor (SPF) are calculated for simulated samples where accessory grains are randomly scattered on a background containing one region of biotite. The biotite region is circular with radius R and its center chosen in advance. The accessory grains are also circular with radius r, and their centers are chosen randomly from a uniform distribution over the rectangular background. Accessory grains touch biotite if the distance between the centers of the grain and the biotite is equal to or less than the sum of the two radii R+r.

Given a sample, the BTF is calculated as the proportion of accessory grains touching biotite divided by the area of the biotite region. Accessory grains are completely contained in the biotite region if the distance between the centers of the accessory grain and the biotite is less than R-r, and the perimeter shared with biotite is the circumference 2πr. Accessory grains partially intersect with the biotite region if the distance between the centers of the grain and biotite regions is between R-r and R+r. The shared perimeter is calculated from the angle between the two radii that join the center of the accessory grain to the two points of intersection of the accessory grain and biotite circles.

Figure A1-1 shows simulation results for samples of size 50,000 for various choices of the radii R and r. The vertical axis is the value of BTF or SPF and the horizontal axis is the ratio of the accessory grain radius to the biotite radius, r/R. Where r/R is small, both BTF and SPF are close to one. As r/R increases, however, the two factors diverge. SPF remains close to one, whereas BTF increases gradually. Probability theory can be used to explain this increase. With a uniform probability distribution over the rectangle, the probability that an accessory grain touches the biotite region is the area of the circle with radius R+r divided by the area of the rectangle, A, or π(R+r)2/A. The area proportion of the biotite region is πR2/A, and the expected BTF is the ratio (R+r)2/R2 = (1+r/R)2. So BTF increases as a quadratic in r/R as shown in Figure A1-1. In our data, the apatite grains are generally <0.1 as big as the biotite regions, and the other accessory grains are even smaller. Thus, the possible value for BTF under the assumption of random scattering of the accessory grains is 1.12 = 1.21, as shown in Figure A1-1.

APPENDIX 2. SIMULATION OF CLUSTERING

To investigate whether the observed pattern of clustering in Section AB1B could have arisen by chance, 1000 samples were randomly generated, and the extent of clustering between all possible pairs of accessories was recorded. The observed numbers and sizes of each type of accessory grain in Section AB1B were used in each random sample. The grains were assumed to be circular, and their approximated sizes were obtained by converting their perimeters to radii. The locations of the accessory grains were randomly generated from a uniform distribution. A realistic approach was used to account for the association of the accessory grains with biotite. For example, in Section AB1B, there are 1260 apatite grains, of which 947 are touching biotite and 313 are not. Biotite comprised 0.159 of the ~6 cm2 area of Section AB1B. The simulation randomly positioned the 947 apatite grains in an area of 0.954 cm2 and 313 grains in an area of 5.046 cm2, and the same approach was used with the other accessory minerals. Pairwise distances between grains were calculated, and the grains were determined to be clustered if this distance was less than the sum of radii of the two grains.

APPENDIX 3. ACCESSORY GRAIN SIZES AND SHAPES OF SAMPLE AB1B

Sample AB1B was also used for comparison between simulated values of clustering of the respective accessory minerals and real measured values. Here we show the output of the MLA measurements for the accessory minerals, apatite, monazite, xenotime, and zircon for this sample, sorted according to size (Fig. A3-1).

Gold Open Access: This paper is published under the terms of the CC-BY license.