How to Quantify Heavy Mineral Fertility From Point‐Counting Data

Heavy minerals (HM) are widely used in provenance studies, for example, for reconstructing source areas and quantifying sediment budgets. Source rock mineral fertility influences the composition and concentration of HM in sediments. The resulting bias is of particular interest when interpreting single‐grain data such as detrital age distributions. However, the quantification of fertility is complex and there are no robust data for most HM, which prevents the routine implementation of fertility in many studies. In this study, we test whether mineral fertility can be assessed by quantifying mineral concentrations in detrital samples through point counting and quantitative evaluation of minerals by scanning electron microscopy (QEMSCAN). The challenge is to transform the resulting area percentage into mass percentage, which is a prerequisite for comparing those data with grain size or geochemical data. We suggest overcoming this problem by recording grain‐size and shape metrics of minerals using image analysis, and applying several transformation steps. We test our method by (a) using a series of detrital grain mixtures of known density and mass, and (b) applying it to a natural sediment from the European Alps. Our results agree with existing methods developed for apatite and zircon, that is, the quantification of fertility through geochemistry (with P2O5 and Zr concentrations as proxies for apatite and zircon) and the separation of pure apatite and zircon concentrates using additional separation steps. The advantage of our method is its applicability to all HM (not only apatite and zircon) and the redundancy of additional separation steps, which might create bias.


Introduction
Heavy minerals (HM) are widely used in provenance studies to reconstruct erosion, transport, and deposition in sediment routing systems (e.g., Caracciolo, 2020;Weltje & von Eynatten, 2004).HM contained in sediments or sedimentary rocks may, for example, provide information about the lithologies, metamorphic grades, and crystallization and cooling ages present in the source area (von Eynatten & Dunkl, 2012).Despite the rich information encrypted in heavy mineral grains, numerous processes can influence their occurrence and concentration, potentially leading to bias and erroneous interpretations in provenance studies (Garzanti & Andò, 2019).These processes include (a) varying heavy mineral concentrations in source rocks (fertility), leading to under-or overrepresentation of specific minerals in the detritus derived from certain lithologies (e.g., Moecher & Samson, 2006), (b) hydraulic sorting and selective entrainment that may lead to the enrichment or depletion of minerals of certain densities, sizes or shapes (e.g., Garzanti et al., 2008;Komar, 2007), and (c) weathering or diagenetic effects that may deplete or eliminate less stable mineral species (e.g., Morton & Hallsworth, 1999).
Although fertility-related bias is widely recognized (Chew et al., 2020;Dickinson, 2008;Malusà et al., 2016), mineral fertility is not easily quantified, and fertility data are scarce and therefore challenging to implement routinely in provenance studies.Dickinson (2008) addressed zircon fertility by analyzing zirconium (Zr) contents using bulk rock geochemistry and concluded that zircon fertility varies by a factor of 5 even in similar (in this case, granitic) lithologies.Therefore, quantifying fertility by directly analyzing the heavy mineral contents in source rocks would require extremely dense sampling of all potential source rocks.Especially in large catchments with multiple source lithologies, this is often not feasible due to financial and temporal constraints.Malusà et al. (2016) suggested that the heavy mineral content of detrital fluvial sediment produced in proximal catchments mirrors source rock fertility if the heavy mineral spectrum is not modified during transport or deposition.These authors compared sediment geochemistry (with P 2 O 5 and Zr contents as proxies for apatite and zircon, respectively) with the mass of apatite and zircon grains separated from the bulk sediment through magnetic, hydraulic, and heavy liquid mineral separation techniques.They concluded that the geochemistry approach consistently overestimates the actual apatite and zircon concentrations.This can be explained by other minerals incorporating Zr and P 2 O 5 and/or zircon and apatite occurring as small inclusions detected by geochemistry but not separated using mineral separation approaches.Both the "geochemistry approach" (sensu Dickinson, 2008) and the "separation approach" (sensu Malusà et al., 2016), however, have limits for routine fertility estimation.Firstly, the separation approach favors grains that behave similarly in the different separation steps.However, detrital grains from the same mineral species may behave differently during (a) hydraulic separation using shaking tables due to different grain sizes (Sláma & Košler, 2012) or grain shapes (e.g., rounded vs. prismatic/ elongated grains), (b) magnetic separation due to different magnetic properties (Heaman & Parrish, 1991;Sircombe & Stern, 2002), and (c) heavy liquid separation due to intergrowth with other, lighter or heavier, phases.Secondly, both the geochemistry and separation approaches are not applicable to most other HM because they (a) exhibit larger geochemical variability than zircon and apatite (e.g., the tourmaline or garnet groups), (b) lack a clear geochemical proxy (e.g., the TiO 2 minerals, as Ti also occurs in other dense phases such as titanite and ilmenite), and (c) cannot be separated from other HM through mineral separation techniques because of similar shape, density or magnetic properties.This limited applicability of the existing fertility measures is problematic because other (heavy) minerals are increasingly used in quantitative provenance analysis, for example, for mixing modeling and sediment budgeting (e.g., mica in Gemignani et al., 2017;K-feldspar in Zhang et al., 2014;amphibole in Vezzoli et al., 2016).
In this paper, we explore the quantification of fertility based on the mineral distribution in detrital samples without further separation.We determined the area percentage of different minerals via point counting, image analysis, and automated mineral analysis using QEMSCAN.Although such area percentage data are often collected in heavy mineral studies, the conversion from area percentage to mass percentage needed to quantify fertility is complex.We test the conversion using a series of grain mixtures with known mass and density and record grain shapes and sizes while point counting and via image analysis.Furthermore, we apply the conversion steps to a natural river sand sample from the European Alps and test if the calculated heavy mineral mass percentages match the expected mineral fertility.The data are then compared to the separation and geochemistry approaches of Malusà et al. (2016) and Dickinson (2008) for apatite and zircon.

Converting Area Percentage to Mass Percentage
Heavy mineral concentrates are usually embedded in resins to produce grain mounts, thin sections, or strewn slides (Andò, 2020).Point-counting is a standard method to quantify the relative proportions of different mineral species (Galehouse, 1971).Point-counting using the Glagolev-Chayes method provides area percentage (area%) because the probability of a grain being hit by the point-counting grid is proportional to its area in the thin section (Chayes, 1954).Traditional heavy mineral counting often uses the Fleet, ribbon, or line methods instead, which provide number percentages (Galehouse, 1971).To calculate the concentration of HM in the bulk sediment, however, two key figures are needed that are usually provided in mass percentage (mass%).Firstly, due to their higher density and the resulting size shift with respect to the less dense framework grains (Garzanti et al., 2008), HM tend to be enriched in the finer tail of the sediment.Accordingly, most researchers extract HM from one or several grain-size fractions ranging from medium and fine sand to silt (Garzanti & Andò, 2019).The proportion of the used grain-size fraction from the bulk sediment is usually quantified by sieving the sediment and weighing each grain-size fraction, which provides the mass percentage.Secondly, HM are typically separated from less dense grains using gravimetric separation techniques (Andò, 2020).The separated "light" (less dense) and "heavy" (dense) fractions are then weighed to calculate the heavy mineral concentration in the sample in mass percent (Garzanti & Andò, 2007).Given these different units, converting the point-counting results (in area or number percentage) to mass percentage seems preferable.Area percentage may be assumed to be equivalent to volume percentage (vol%) in rock-thin sections where mineral axes are cut randomly (Chayes, 1954).However, samples used for heavy mineral counting are usually produced from loose material, and grains tend to fall on their shortest grain axis (termed c-axis from here on) during the embedding process.Grains with a very short c-axis compared to their a-and b-axis (i.e., platy grains such as mica) may therefore have a considerably higher area percentage than volume percentage compared to isometric or prismatic grains.Thus, additional grain size and shape information is needed to convert area percentage to volume percentage, which must be determined individually for each sample.After compiling such information (Section 2.5), we convert volume percentage to mass percentage using heavy mineral densities compiled by Resentini et al. (2013).The concentration of each heavy mineral (now in mass percentage) in the bulk sediment (Figure 1) is calculated by multiplying with the heavy mineral concentration (in mass percentage) and the fraction of the used grain size window from the bulk sediment (in mass percentage from sieving).

Samples and Sample Preparation
We tested the proposed method by creating a series of artificial sediments from detrital mineral species of known size, shape, and density.The first series consisted of a three-component sand produced from magnetite, bluecolored quartz, and red-colored quartz grains.The quartz was produced from commercially available natural quartz sand (>90% SiO 2 ) that was further purified using magnetic separation at 1.8 A. The non-magnetic fraction was split into two fractions, and these were dyed with commercially available acrylic blue and red paint.After airdrying for 2 days, the quartz was dry-sieved to 125-250 μm.The magnetite portion was produced from an almost pure (∼99%) magnetite placer deposit from Klima beach (Milos, Greece) that was further purified using a hand magnet and then sieved to 63-125 μm to simulate the natural size shift between quartz and magnetite (Garzanti et al., 2009;Resentini et al., 2013).All grains had similar, rounded, and slightly irregular shapes.The magnetite and blue and red quartz were then mixed to achieve mass proportions of approximately 50, 10, 5, and 1 mass% magnetite (Table 1) by weighing the grains with a high-precision scale.The second artificial sample was produced from biotite and the same red quartz described above.The biotite was separated from beach sand collected at  Platja Sant Pol (Catalonian mountain range, NW Spain) using gravimetric separation (Andò, 2020) of the 250-500 μm grain-size fraction.The resulting heavy mineral concentrate consisted almost entirely of biotite (∼95%), and the few other grains were removed by hand-picking under a microscope.Grains were mixed to a proportion of 10 mass% biotite and 90 mass% red quartz using a high-precision scale.
The artificial grain mixtures were shaken thoroughly, and all grains were poured onto glass slides with Canada balsam to prepare strewn slides.The strewn slides were not ground or polished.From all artificial mixtures, highresolution scans were obtained using a Keyence VHX 7000 digital microscope at the University of Münster.The initial mass of mineral fractions can not only be expressed in terms of mass% but also in vol% using calculated densities based on molecular masses and volumes (via webmineral.com;we used 2.65 g/cm³ for quartz, 5.2 g/cm³ for magnetite, and 2.9 g/cm³ for biotite).
Furthermore, we used one natural river sediment collected along a sand bar of the river Ziller in the Austrian Alps.
The Ziller sand sample was sieved into individual grain-size fractions (<63, 63-125, 125-250, 250-500, 500-1,000, 1,000-2,000 μm).The material of each size window was dried and weighed.HM were separated using gravimetric separation of the 63-125, 125-250, and 250-500 μm fractions.First, a representative aliquot was obtained using a riffle box.The samples were then separated using sodium polytungstate at a 2.9 g/cm³ density in separation funnels.The obtained heavy mineral concentrates were rinsed with water, dried, and weighed.We calculated the heavy mineral concentration by dividing the mass of the heavy mineral concentrate by the total sample mass before separation (HM% after Garzanti & Andò, 2007).Split fractions of the concentrates were mounted on double-sided sticky tape and embedded in epoxy resin to produce grain mounts.The grain mounts were subsequently ground and polished to expose the contained grains.

Accounting for Selective Entrainment
Selective entrainment processes may influence the absolute concentration of HM in a natural river sediment (Garzanti et al., 2008(Garzanti et al., , 2009;;Komar, 2007).Less dense minerals like quartz and feldspar tend to be larger than the HM they were deposited with (settling-equivalence principle, Garzanti et al., 2008;Rubey, 1933).Larger, less dense minerals are, in turn, easier to be entrained by the current (Komar, 2007;Komar & Li, 1988), which can lead to the enrichment of HM and eventually to the formation of placer deposits (Reid & Frostick, 1985).For the heavy mineral concentration to faithfully reflect source rock fertility, selective entrainment processes should either be absent or corrected (Malusà et al., 2016).Bulk densities for modern sediments commonly range between 2.65 and 2.8 g/cm³ (Garzanti & Andò, 2007), depending on the provenance and selective entrainment, which can lead to notably higher values.Garzanti et al. (2012) suggested identifying samples affected by selective entrainment by measuring the bulk sediment density using a hydrostatic balance.However, the method is time-consuming and prone to erroneous results due to the incomplete elimination of interstitial air (Garzanti et al., 2012).Therefore, we used a Micromeritics® helium pycnometer which yields quicker and more reproducible results.30 g of the sample material was filled in a chamber of known volume and placed in the gas pycnometer.The pycnometer introduces a known volume of gas into the chamber and measures the pressure building up.The pressure is released by letting the gas flow into an expansion chamber of known volume.The sample volume is calculated using the difference between the known volume of the chamber and the expansion chamber divided by the pressure measurements.
The density of the sample material is then calculated by dividing the sample mass by the sample volume attained by the pycnometer.Given the axial belt provenance of the Ziller, we assumed a density between 2.7 and 2.8 g/cm³ for the Ziller sand (Garzanti & Andò, 2007;Garzanti et al., 2010;Malusà et al., 2016).Lower or higher values suggest hydraulic sorting bias.Finally, the composition of the Ziller sample was compared with available geochemical and mineralogical compositions of its main source rock, the Zentralgneis of the Tauern window (Finger et al., 1993;Melcher et al., 1996;Raith, 1970;Wyss, 1993) to evaluate if the sand composition deviates from the source rock composition.

QEMSCAN Analysis
Point-counting results may be biased by operator experience (Dunkl et al., 2020) and may have relatively high uncertainties depending on the number of total counts and the percentage of the mineral in question (van der Plas & Tobi, 1965).Therefore, we analyzed the heavy mineral spectra of the Ziller sediment using QEMSCAN, which analyses more grains per sample and generally has higher analytical accuracy than manual point-counting (Dunkl et al., 2020).A Quanta 650-F QEMSCAN© (FEI/Thermo Fisher) scanning electron microscope (SEM) was used at the Institute of Applied Mineralogy and Economic Geology, RWTH-Aachen University.The polished epoxy mounts bearing the sample material (fractions 250-500 μm, 125-250 μm, and 63-125 μm) were analyzed after carbon coating.The SEM measurements were performed with an acceleration voltage of 15 kV and a fixed sample current of 10 nA while operating in particle mineralogical analysis mode (PMA mode).In contrast to the field scan mode which is used for the measurement of non-particulate samples, the PMA mode is used for measuring samples containing individual particles.Prior to the measurement itself, the QEMSCAN system automatically identifies particles and their extents.Conducting the measurement in PMA mode then produces an individual image and corresponding spectral data for each particle.The spatial surface resolution of the measurement was set to 5 μm.The backscattered electron (BSE) intensities for each 5 × 5-μm pixel were recorded with a 4-quadrant BSE detector, while the individual X-ray spectra were recorded with two DualXFlash 5030 SDD energy dispersive x-ray detectors manufactured by Bruker AXS (Karlsruhe, Germany).The mineral phases were identified by comparing measured spectral data for each 5 × 5-μm pixel with library data.The library data were provided by the SEM device-specific iDiscover software suite (Version 5.3.2.501, FEI/Thermo Fisher, Hillsboro, OR, USA).The identification of the mineral phases was then carried out after a comparison of the measured spectra with the mineral phases listed in a species identification protocol created by the operator.
Mineral phase identification follows a first-match and best-fit procedure.After the mineral phase identification, images of the sample material were created, and each sample's modal composition in area percentage was calculated.In addition, the QEMSCAN software calculates mineral associations by identifying all neighboring pixels to each pixel.Minerals that are predominantly associated with "background" pixels (i.e., epoxy resin) or unidentified, "low-confidence" pixels (that occur frequently along cracks or on the rim due to poor and/or mixed BSE signal) can be assumed to occur as individual particles, whereas minerals associated with other minerals occur either in polymineralic grains or as inclusions.

Grain-Size and Shape Metrics
Both the Ziller sample QEMSCAN phase maps and the artificial sand scans were analyzed with the Fiji derivation of ImageJ (Schindelin et al., 2012;Schneider et al., 2012) to describe and quantify grain shapes and sizes.Each grain was defined by the operator instead of using a grain-separation algorithm, because the algorithms were unable to separate touching or overlapping grains, mis-identified air bubbles as grains in the artificial samples, and did not perform well with composite grains in the Ziller sample.Composite grains in the Ziller sample were considered as individual minerals only if they were mostly monomineralic, that is, consisting of over 80 area% of one single mineral phase (Figure 2a; not including unidentified pixels, which are often found on the grain rims or along cracks).Composite grains consisting of two or more individual, clearly separated minerals larger than 40 μm were counted as individual phases (Figure 2b), whereas composite grains consisting of multiple smaller or strongly intergrown phases were treated as rock fragments (Figure 2c).
We measured the longest and shortest visible axes, which we term "a-axis" and "b-axis," respectively, from here on, of all defined individual grains in the samples.In order to calculate the area of each grain using the grain diameters, the shape of the particles has to be approximated.Because all grains in the artificial samples have the same shapes, we assumed simple circular shapes for quartz and magnetite.In contrast, the Ziller sample consists of a range of minerals with different shapes, and we tested the best-fitting area approximation by comparing the true and calculated areas of selected grains.We measured the a-and b-axes of 160 mostly monomineralic, differently shaped grains of apatite, biotite, epidote, feldspar, garnet, hematite, hornblende, ilmenite, pyrite, titanite and zircon and calculated their areas using circles, squares, ellipses and rectangles.The same grains were measured using the wand-tool in ImageJ, which selects all pixels of the same color within a grain and calculates their true area.The best fit between calculated and true area was determined using the least square method (Stutenbecker, 2024a), and we accordingly assumed elliptic shapes for all grains except for the phyllosilicates, which were best approximated using rectangular shapes: The (presumably shortest) axis that is not visible in the two-dimensional maps or scans, the "c-axis," was examined and measured by turning >20 loose grains of the most abundant and easily identifiable mineral species (apatite, biotite, epidote group, garnet, hornblende, zircon) of the 63-125 and 125-250 μm fractions under a Keyence VHX 7000 digital microscope.Both the baxis and the c-axis of a total of 158 grains were measured.The mean b-to caxis ratio of each mineral group was subsequently used to calculate the c-axis of all grains in the sample using the b-axis measured from the 2D phase maps.
If the b-to c-axis ratio was not quantifiable (e.g., because the mineral had low abundance or was not identifiable in a reliable way under transmitted light), we made b-to c-axis ratio assumptions based on microscope observations and typical crystal shapes.For white mica and chlorite, we assumed the same ratios as for biotite.For ankerite, pyrite, quartz-feldspar rock fragments and the TiO 2 phase, we assumed a c-axis equal to the b-axis.For ilmenite, hematite, and titanite, we assumed the same ratio as for epidote.Based on the (detrital) crystal shapes observed during microscopy, we then calculated the volume of all grains as follows: V Because the Ziller samples were prepared as polished grain mounts for QEMSCAN analysis (Section 2.2), the grain diameter measured in 2D phase maps is an apparent one and not the true diameter.Due to the range of grain sizes within a sieved fraction, grains may be cut at a random diameter that is not necessarily equal to but potentially smaller than their true (equatorial) diameter.The mismatch between measured (apparent) and true diameter is larger for large grains than for small grains and pronounced for spherical and ellipsoid grains, whereas it is absent for cubic and cuboid grains (Figure 3a).This effect is negligible for samples prepared as strewn slides because the entire area of a grain is usually visible under transmitted light, even if a large proportion of the grain is below the surface of the strewn slide.Natural samples usually contain a range of grain sizes and shapes.If they are prepared as polished grain mounts, a correction procedure is therefore necessary (Figure 3b).If the thickness of the material h that is removed by grinding and polishing (i.e., the difference between the original surface S O and the exposed surface S E ) is known or can be estimated in a reliable way, and the apparent diameter D m is measured, the true diameter D t can be calculated as the chord length for spheric or ellipsoid grains as follows: The thickness h can be determined by placing a few commercially available glass beads of known diameter on the sticky tape along with the sample material before casting the epoxy resin, measuring their diameter after grinding and polishing and applying Equation 6.In the case of ellipsoid grains, the ratio between the a-axis and b-axis does not change due to grinding the sample by a thickness h.Therefore, the diameter of the true a-axis D t(a) calculated through Equation 7 can be used to calculate the true b-axis based on the known ratio of the apparent a-axis and baxis.The ratio of a-axis to c-axis, however, changes due to the grinding process.In our case, this correction process works anyway because we can assume that the c-axis is roughly equal to the b-axis for ellipsoid grains such as apatite, garnet, and zircon (see Section 3.2).

Point Counting
The artificial sand samples were point-counted using the Glagolev-Chayes method to obtain area percentage values (Chayes, 1954).The samples were counted three times each with at least 200 counts each time.The uncertainty of point-counting results depends on the overall number of grains counted and the proportion of the counted phase, where phases with low proportions have higher uncertainty than phases with high proportions (van der Plas & Tobi, 1965).We estimated the uncertainty of the point-counting results applying the method proposed by van der Plas and Tobi (1965) using the standard deviation.

Image Analysis Using a Color Threshold
The artificial grain mixture scans were processed in ImageJ to obtain an additional estimate for area percentage.
Because of the simple and homogenous grain colors, we used the "color deconvolution" tool to define and split the colors (red, blue, and black for the quartz/magnetite mixtures; red and dark brown for the quartz/biotite mixture).Afterward, the "color threshold" and "analyze particles" tools were used to transform all red, blue, black, and brown pixels into separate black-and-white grain maps and measure each grain's area (Figure 4).The resulting pixel count for each color class was divided by the total pixel count to get area%.Furthermore, image data allowed total grain counting and determination of grain or number% values (i.e., Fleet method).

Separation Approach
From the Ziller sample, apatite and zircon grains were separated using established mineral separation protocols at the University of Tübingen that are similar to those reported by Malusà et al. (2016).We used MinSorting ( Resentini et al., 2013) to identify the grain-size fractions that should contain most apatite and zircon according to the expected size shift of these minerals.The grain size fractions of 63-125 μm, 125-250 μm, 250-500 μm, and 500-1,000 μm were separated using magnetic separation at 1.75 A. The non-magnetic fractions expected to host most of the apatite and zircon grains were separated twice using sodium polytungstate (at 2.8 g/cm³) and methylene iodide (at 3.32 g/cm³).Apatite (density of ca.3.2 g/cm³) should be contained in the concentrate between 2.8 g/cm³ and 3.32 g/cm³, whereas zircon (density of ca.4.65 g/cm³) was expected in the concentrate >3.32 g/cm³.However, the produced concentrates were rarely entirely pure, so the content of the two targeted minerals was determined by point counting of the individual separates (Malusà et al., 2016).

Geochemistry
The concentrations of phosphorus oxide (P 2 O 5 ) and zirconium (Zr) may be used as proxies for apatite and zircon concentrations, respectively (Dickinson, 2008;Malusà et al., 2016).Accordingly, we measured P 2 O 5 and Zr concentrations within the narrow grain size fractions and the bulk sample of the Ziller sediment.The samples were milled in an agate jar at 750 cycles per second for 2 minutes.The major element oxides and a suite of common trace elements, including Zr, were analyzed via lithium borate fusion coupled with ICP-MS at Bureau Veritas ACME laboratories in Vancouver, Canada.The detection limits for P 2 O 5 and Zr were 0.01wt% and 5 ppm, respectively.We applied atomic/molecular mass factors to account for the amount of P 2 O 5 in apatite (Ca 5 (PO 4 ) 3 F, factor 0.454) and the amount of Zr in zircon (ZrSiO 4 , factor 0.497).To account for the complex Example image analysis of the artificial grain mixtures (here, the 50 mass% magnetite sample).First, the three colors are split into three separate channels and then processed using a color threshold that transforms the image into simple black-and-white grain maps, which can then be analyzed using the "analyze particles" tool of ImageJ.
character of the multielement data set, and to visualize, characterize, and compare the results with literature data, concentration values were log-ratio transformed and further processed by principal component analysis.For multivariate data analysis, we used the software package CoDaPack (Thió-Henestrosa & Martín-Fernandez, 2006).

Artificial Grain Mixtures
The measurements of the a-and b-axes (Stutenbecker, 2024b) of all grains via image analysis provide mean grain sizes for magnetite (a: 168 μm, b: 117 μm), red quartz (a: 235 μm, b: 170 μm), blue quartz (a: 263 μm, b: 186 μm), and biotite (a: 512 μm, b: 348 μm).Based on the microscope observations, the quartz and magnetite grains were assumed to have c-axis similar to their b-axis.In contrast, we measured a mean c-axis of 90 μm (±12 μm) based on 30 individual grains for the platy biotite.Overall, the area percentages derived through (a) point-counting, (b) image analysis using a color threshold, and (c) grain-size analysis (calculating areas using mean b-axis as sphere radii) yield identical results within the error of manual point-counting (Figure 5, see Stutenbecker, 2024bStutenbecker, , 2024cStutenbecker, , 2024d)).The largest deviation occurs for the 1 mass% magnetite sample, where the magnetite area percentage derived from point counting is almost twice as high as the value derived from image analysis.When converting area percentages to volume percentage (using the assumed/measured c-axis values) and finally to mass percentage (using density estimates), the result falls within 95% of the initial mass percentage determined by highprecision weighing (Figure 5).Number and mass percentages are considerably higher than area percentage, and area percentage is higher than volume percentage for all magnetite-quartz mixtures.In the case of biotite, the volume percentage is similar to the mass percentage, the area percentage is considerably higher, and the number percentage is lower than the mass percentage.

Ziller Sample
The Ziller sample is a unimodal sand with a mean grain size of 365 μm (M G ; Folk & Ward, 1957) and poor sorting (σ G of 2.24, Folk & Ward, 1957).Its bulk sediment density is 2.725 g/cm³, with the highest density measured in the finest fraction (<63 μm: 2.776 g/cm³) and the lowest density in the coarsest fraction (1,000-2,000 μm: 2.693 g/cm³).According to MinSorting modeling, 71% of apatite and 82% of zircon should be contained in the 63-500 μm fraction, but significant amounts should also be present in the 500-1,000 μm fraction (Table 2).
Mean grain sizes were measured via image analysis within the 63-125 and 125-250 μm fractions (Figure 8) because the coarser grain-size fractions comprise mainly phyllosilicates and complex composite grains rather than individual minerals.The raw data can be found in Stutenbecker (2024f).Mean grain axes were 196 ± 64 μm for the a-axis and 120 ± 39 μm for the b-axis in the 125-250 μm fraction, and 111 ± 12 μm (a-axis) and 61 ± 4 μm (b-axis) in the 63-125 μm fraction.Overall, the range of grain sizes, expressed as the relative standard deviation, was considerably smaller (11% and 6% for the a-and b-axes, respectively) in the 63-125 μm fraction than in the Note.Note that the MinSorting model assumes that all mineral species may be present in each grain size fraction.
125-250 μm fraction (32% for both the a-and b-axes).In the 125-250 μm fraction, the larger standard deviation is caused by the minerals zircon, ankerite, chlorite, and the TiO 2 phase (Figure 8), which all tend to occur as smaller minerals in composite grains.
After applying these metrics in our stepwise scheme (Figure 1) to transform area percent to mass percent (for a stepwise example see Stutenbecker, 2024h), we observe changes in the resulting heavy mineral spectra (Figure 10).The most extreme changes occur for those minerals that are abundant and have large density contrasts, for example, the opaque phases and the phyllosilicates.Compared to their area percentage, the mass percentage of apatites deviates by up to 22%, of ankerite by up to 49%, of epidote group minerals by up to 25%, of garnet by up to 32%, of hornblende by up to 34%, of light minerals by up to 15%, of monazite by 104%, of opaque phases by up to 217%, of phyllosilicates by up to 71%, of the TiO 2 phase by up to 41%, of titanite by up to 98%, and of zircon by up to 78%.We used the achieved mass percentage of apatite and zircon in the heavy mineral concentrate to calculate the apatite and zircon concentrations in the entire sieve fraction (Figure 1) by multiplying with the heavy mineral content (Table 2).This transformation yielded 2,415 ppm and 2,453 ppm of apatite (or Figure 6.QEMSCAN-derived heavy mineral spectra of the 63-125, 125-250, and 250-500 μm fractions of the Ziller sample (in area %).Mineral abbreviations according to Whitney and Evans (2010); bt = biotite, ms = muscovite, chl = chlorite, qz = quartz, fsp = feldspar, py = pyrite, ilm = ilmenite, hem = hematite.As indicated in the figure, the group of phyllosilicates comprises biotite, muscovite, and chlorite; light minerals comprise quartz and feldspar (often intergrown in rock fragments); and opaques summarize pyrite, ilmenite, and hematite.1,096 ppm and 1,114 ppm of P 2 O 5 ) and 826 and 31 ppm of zircon (or 410 and 15 ppm of Zr) in the 63-125 and 125-250 μm fractions, respectively (Figure 11).
The separation approach yields higher apatite than zircon concentrations and shows that both apatite and zircon contents increase with decreasing grain size (Table 3).The analysis yielded 2,424 ppm apatite and 557 ppm zircon in the 63-125 μm fraction, 1,923 ppm apatite and 129 ppm zircon in the 125-250 μm fraction, and 567 ppm apatite and 67 ppm zircon in the 250-500 μm fraction.These mineral contents would translate to concentrations of 1,048 ppm P 2 O 5 and 277 ppm Zr in the 63-125 μm fraction, 873 ppm P 2 O 5 and 64 ppm Zr in the 125-250 μm fraction, and 257 ppm P 2 O 5 and 33 ppm Zr in the 250-500 μm fraction (Figure 11).Measured P 2 O 5 and Zr contents in the Ziller fractions are 800-3,300 ppm and 104-856 ppm, respectively (Table 4).P 2 O 5 and Zr contents increase with decreasing grain size, and the highest concentrations were measured in the <63 μm fraction.Measured P 2 O 5 contents are around 1.25 times higher, and Zr contents are approximately two times higher than the values derived from the separation and point-counting approaches (Figure 11).

Discussion
The artificial grain mixture experiments show that relative mineral proportions of the same sample, given in mass, number, volume, and area percentage are different.The quartz-magnetite experiment shows that large grain size differences (as simulated by smaller magnetite and larger quartz grains) can cause considerable differences between number percentage and mass percentages.The data further show that area percentage does not necessarily equal volume percentage, which Chayes (1954) showed for rock thin sections but not for unconsolidated grain mixtures.The quartz-biotite sample shows that mass percentage equals volume percentage if the density difference between the grains is not pronounced.Still, the platy shape of mica causes a mismatch of area and volume percentage.Although the grains have complex shapes due to their detrital nature, our approximation of spherical shapes for magnetite and quartz yielded realistic results that matched the known (initial) mass percentages.Depending on the scope of the study, transformations between these units can be made by measuring or assuming grain-size and shape metrics as well as grain density.Our point-counting results generally faithfully reflect area percentage, as shown by comparing point-counting, image, and grain-size analyses.However, the 1:1:98 quartz-magnetite mixture also shows that point-counting of minerals with very low percentages is associated with high errors (van der Plas & Tobi, 1965), which can influence the calculations.In our case, the minerals were very easy to identify based on color alone, but in natural sediment samples, the error associated with misidentification might be much higher (Dunkl et al., 2020).
Most natural heavy mineral concentrates are a mixture of grains with different densities (from "light" amphibole to "heavy" zircon) and shapes (from nearisometric pyrite to platy micas).This results in potentially significant differences between number, volume, and area percentages.The example of the Ziller sand shows a typical Alpine heavy mineral spectrum with abundant epidote group minerals, amphibole, and mica (Garzanti & Andò, 2007b).The apatite and zircon proportions calculated using the proposed method generally align with the fertility values for granitoid rocks in axial belts measured by Malusà et al. (2016).A comparison between the measured grain sizes and the grain size range expected from the size shift (Resentini et al., 2013, Table 2) shows that the size shift only partially mirrors actual grain size distributions in the heavy mineral concentrate.The MinSorting model, which takes into account hydraulic behavior and not the crystal size distribution in the source rock, predicts significant amounts of zircon (>40%) and apatite (>50%) to occur in the grain-size fractions 250-500 and 500-1,000 μm.However, both QEMSCAN analyses and the separation approach yielded no individual apatite or zircon grains in the 500-1,000 μm fraction and few apatite grains in the 250-500 μm fraction.Instead, P 2 O 5 and Zr concentrations are highest in the <63 μm fraction, which, according to the MinSorting model, should contain less than 5% of all apatite and zircon.Microscopic and QEMSCAN observations confirm that zircon especially does not occur as large individual grains in the grain-size fractions >125 μm.This illustrates that mineral size distributions may not be predominantly controlled by the size shift but rather by the original crystal size in the source rock, and thus should be measured (e.g., through QEMSCAN analysis) to yield reliable mineral distribution data, especially for poorly sorted sediments.
While the geochemistry data of the Ziller sand may scatter depending on the analyzed grain-size fraction, all fractions are chemically similar to more felsic source rock compositions (Figure 12) measured at different locations in or near the Ziller catchment (Finger et al., 1993;Melcher et al., 1996;Wyss, 1993).This supports the idea that felsic granitoid rocks are the dominant source rock in the catchment and that sediment chemistry reflects source rock chemistry in settings with limited chemical weathering (Stutenbecker et al., 2023;von Eynatten et al., 2012).Mineralogical compositions of rocks in the Ziller catchment (Raith, 1970) show that the dominance of epidote and mica can be explained by source rock composition.Thus, the chemical and mineralogical similarity  Malusà et al., 2016), the QEMSCAN results (recalculated to mass percent using the proposed method), and the geochemistry approach (sensu Dickinson, 2008).Apatite and zircon contents were recalculated to P 2 O 5 and Zr contents by applying atomic/molecular mass factors (see Section 2.9). between source rock and sand underlines that mineral fertility can be quantified from detrital heavy mineral spectra (Malusà et al., 2016) if changes to the spectrum due to hydraulic sorting can be excluded or corrected.Malusà et al. (2016) showed that P 2 O 5 and Zr contents overestimate the actual apatite and zircon contents in similar sediments because Zr and P may be contained in other phases.In the Ziller case, a similar pattern emerges where geochemical analysis generally yields higher P 2 O 5 and Zr contents than the separation and QEMSCAN approaches (Figure 11).Due to the 5-μm-step size in the QEMSCAN analysis, smaller apatite and zircon inclusions could not be detected, but could be additional P 2 O 5 and Zr hosts.P 2 O 5 could also be hosted in monazite, which was found in low abundances (0.03 and 0.51 area%) in the Ziller sediment.Besides in small zircon inclusions, Zr could be contained in trace amounts in other minerals such as amphibole (Lee et al., 2003), mica (Tischendorf et al., 2001), and ilmenite (Jang & Naslund, 2003;Jia et al., 2022), which are abundant in the Ziller sediment.The P 2 O 5 contents calculated via the QEMSCAN approach are generally similar to those calculated via the separation approach (Figure 11).For the 63-125 μm fraction, the fit is almost perfect.This testifies to an effective separation process as supported by the fact that most apatites occur as pure apatite grains and are not frequently intergrown with other phases in this fraction (Figure 7).In the 125-250 μm fraction, there is a mismatch of ca.300 ppm, which can be explained by the higher proportion of apatites being associated with other phases in this fraction (e.g., epidote group minerals and hornblende, see Stutenbecker (2024e) and a less effective separation.In the 63-125 μm fraction, Zr contents calculated via the QEMSCAN approach are ca.60 ppm lower  Wyss (1993), Finger et al. (1993), and Melcher et al. (1996).
than the values from geochemical analysis (Figure 11), suggesting that this amount is hosted in other mineral phases or small zircon inclusions.Zr contents derived from the QEMSCAN approach are about 130 ppm higher than the Zr content calculated via the separation approach.This could be explained by the association of zircons with other phases since only 70% of zircons are present as individual grains (Figure 7), and the separation approach may not separate zircon grains intergrown with other (lighter) phases.In contrast, the Zr contents in the 125-250 μm fraction yielded by the separation approach are higher than those calculated via the QEMSCAN approach.This is somewhat surprising because zircons in this fraction are dominantly associated with other minerals (Figure 7), which would make the separation process less effective.On closer inspection, the zircon concentrate produced through the separation approach contained almost exclusively zircons smaller than 130 μm (Figure 9), which should not be present in this sieve fraction.It is possible that the zircon grains separated from their neighboring minerals during the separation process, and the distribution of zircon grains in the grain size fractions is therefore different compared to the samples prepared for QEMSCAN analysis.Despite these differences, the results from the separation and QEMSCAN approaches are generally within the same order of magnitude, and deviations can be explained considering the detailed information generated through QEMSCAN analysis.

Conclusions
This study illustrates that quantitative measures of heavy mineral fertility can be obtained from point-counting detrital minerals in strewn slides, thin sections, or grain mounts.We show that number, area, volume, and mass percentages may vary considerably and that the different grain sizes, shapes, and densities cause these differences.When recording grain sizes and shapes during or after point counting, mineral proportions can be transformed from, for example, area percentage to mass percentage using simplified assumptions and thus can be compared to other "traditional" counting as well as geochemical data sets.The method applied here adds another time-consuming step to heavy mineral studies.However, it works without further magnetic, hydraulic, and chemical separation steps, which may introduce bias (e.g., Sircombe & Stern, 2002), and it works on all mineral species encountered in a sample, not only apatite and zircon.With the advancement of automated mineral identification and quantification techniques, for example, automated mineralogy such as QEMSCAN (Vermeesch et al., 2017) or Raman mapping (Lünsdorf et al., 2019), grain-size and shape metrics will be more readily available.Furthermore, grain-size and shape metrics may add valuable provenance information, such as transport processes and source rocks, as illustrated, for example, in some zircon-based studies (e.g., Augustsson et al., 2018;Gärtner et al., 2013).preparation, and David Chew, one anonymous reviewer and guest editor Alberto Resentini for their constructive and helpful comments.This work was funded through the German Research Foundation (DFG), project number 442580342 within the priority program "4D-MB: Mountain building processes in 4D." Open Access funding enabled and organized by Projekt DEAL.
A rectangle = a * b for the phyllosilicates, (1) where a = diameter of a-axis, b = diameter of b-axis.A ellipse = π * a/2 * b/2 for all other grains, (2) where a = diameter of a-axis, b = diameter of b-axis.

Figure 2 .
Figure 2. Composite grains in the Ziller samples were considered individual grains only if they were largely monomineralic (>80%, not counting unidentified pixels often found along the grain rims) (a), or, if polymineralic, if the individual grains were larger than 40 μm (b).Composite fragments consisting of smaller intergrown phases (c) were treated as rock fragments.

Figure 3 .
Figure 3. (a) Measured (apparent) diameter, D m , vs. true diameter, D t , of spheric, ellipsoid and cuboid grains of different sizes if prepared as polished grain mounts.In this sample preparation technique, the original surface S O is ground down to an exposed surface S E by an amount h.(b) Chord lengths for spheric and ellipsoid grains with r = radius, r a = radius of a-axis, r c = radius of c-axis.

Figure 4 .
Figure 4. Example image analysis of the artificial grain mixtures (here, the 50 mass% magnetite sample).First, the three colors are split into three separate channels and then processed using a color threshold that transforms the image into simple black-and-white grain maps, which can then be analyzed using the "analyze particles" tool of ImageJ.

Figure 5 .
Figure5.Comparison of magnetite contents of the four artificial quartz-magnetite sands and the biotite content in the quartzbiotite sample in mass%, vol%, area%, and number%.(a) Initial (weighted) mass% based on the mass of magnetite, quartz, and biotite grains.See Table1for data.(b) Mass% calculated based on grain radii measured by image analysis and approximated mineral shapes.SeeStutenbecker (2024b).(c) Initial vol%: calculated based on the initial weighted mineral proportions (a) and literature values of molecular masses and volumes.(d) Vol% calculated based on grain radii from image analysis (b) and c-axis values.(e) Area% determined by point-counting using the Glagolev-Chayes method; the uncertainty of the point-counting results (error bar) was calculated following van derPlas and Tobi (1965).SeeStutenbecker (2024c) for data.(f) Area% calculated based on grain radii from image analysis (b) and b-axis values.(g) Area% of values extracted from color-deconvoluted high-resolution scans (image analysis).SeeStutenbecker (2024d) for data (h) Number% obtained after grain counting in image data.SeeStutenbecker (2024b) for data.

Figure 7 .
Figure 7. Mineral associations of apatite and zircon in the three considered grain-size fractions show that the frequency of individual apatite and zircon grains decreases with increasing grain size.See Stutenbecker (2024e) for raw data.

Figure 8 .
Figure 8. Grain-size metrics from the 63-125 and 125-250 μm fractions of the Ziller sample, derived from measuring the aand b-axes of all grains contained in the sample.

Figure 10 .
Figure10.Comparison of area, number, volume, and mass percentage for the different grain-size fractions of the Ziller sample.See Figure4for further details.On the right panel, the deviation (in %) of number%, vol%, and mass% from area% is displayed for each mineral.Note that for the 125-250 μm fraction, the y-axis is broken to display a wider range of values.

Figure 9 .
Figure 9. Relationship between the measured b-axis and c-axes of 158 individual grains from the most abundant and easily identifiable minerals apatite (n = 21), biotite (n = 25), epidote (n = 39), garnet (n = 24), hornblende (n = 27) and zircon (n = 22) in the Ziller sediment sample.Note that minerals of both grain-size fractions 63-125 and 125-250 μm were measured, but in the case of zircon, even the coarser grain size fraction did not contain zircon grains larger than ca.130 μm.

Figure 11 .
Figure 11.Comparison of P 2 O 5 and Zr contents derived from the separation approach (sensuMalusà et al., 2016), the QEMSCAN results (recalculated to mass percent using the proposed method), and the geochemistry approach (sensuDickinson, 2008).Apatite and zircon contents were recalculated to P 2 O 5 and Zr contents by applying atomic/molecular mass factors (see Section 2.9).

Table 1
Weighed Proportions of Red Quartz, Blue Quartz, and Magnetite for the Four Artificial Sand Samples

Table 2
Grain-Size Distribution, Sediment Density, Heavy Mineral Concentration, and MinSorting-Modeled Apatite and Zircon Percentages of the Ziller Sand (Sample Site N  47.158026, E 11.876757)

Table 3
Results of the Separation Approach Using the Ziller SampleGrain-size fraction Magnetic fraction [g] Light fraction [g] Heavy fraction[g] STUTENBECKER ET AL.

Table 4
Results From Lithium Borate Fusion Coupled With ICP-MS of the Individual Grain-Size Fractions of the Ziller SampleGrain size fraction (μm) SiO 2 Al 2 O 3 Fe 2 O 3 MgO CaO Na 2 O K 2 O TiO 2 P 2 O 5 MnO Cr 2 O 3Note.The major element oxides are given in wt%, the trace elements in ppm.Bold values highlight the P 2 O 5 and Zr concentrations, which are subsequently used to quantify apatite and zircon concentrations.LOI = loss of ignition, bdl = below detection limit.Biplot of principal component analysis showing the similarity of the Ziller sand samples with exposed source rocks in the drainage basin.Major element source rock geochemistry from