Journal of Sedimentary Research, 2020, v.

90, 286–296
Research Article
DOI: http://dx.doi.org/10.2110/jsr.2020.16

QUANTIFICATION OF THE MORPHOLOGY OF GOLD GRAINS IN 3D USING X-RAY MICROSCOPY AND

SEM PHOTOGRAMMETRY

FRANÇOIS-XAVIER MASSON,1,3 GEORGES BEAUDOIN,1,3 AND DENIS LAURENDEAU2,3

1
Département de Géologie et de Génie Géologique, Université Laval, Québec, QC G1V 0A6, Canada
2
Département de Génie Électrique et de Génie Informatique, Université Laval, Québec, QC G1V 0A6, Canada
3
Centre E4m–Centre de Recherche sur la Géologie et l’Ingénierie des Ressources Minérales, Université Laval, Québec, QC G1V 0A6, Canada

ABSTRACT: The shape of gold is widely used in mineral exploration and in sedimentology to estimate the distance of
transport from the source to the site of deposition. However, estimation of the morphology is based on qualitative
observations or on the quantification of shape in 2D. The 3D analysis of grain shape is useful for accurate
morphometric quantification and to evaluate its volume, which is related to particle size. This study compares X-ray
3D microscope and 3D SEM photogrammetry to reconstruct the shape of gold particles. These new methods are
exploited to quantify the shape of gold grains 85 to 300 lm in size. The shape parameters, such as axial lengths, surface
area, volume, diameter of curvature of all corners, and diameter of the largest inscribed sphere and smallest
circumscribed sphere are measured on a particle in order to estimate shape factors such as flatness ratios, shape
indices, sphericity, and roundness. Most shape parameters and shape factors estimated on the same gold grain with
simple geometry are similar between the two approaches. This result validates these methods for the 3D description of
gold particles with simple morphology, while providing a methodology for describing grains with more complex
geometry.

INTRODUCTION Aschenbrenner 1956) or using the volume and surface area of the particle
(Wadell 1932; Aschenbrenner 1956). Other factors such as the Janke
In detrital environments, the shape of a gold grain is commonly used for (1966), Williams (1965), Aschenbrenner (1956), and oblate–prolate
mineral exploration (Giusti 1986; Hérail 1988; Grant et al. 1991; Minter et (Dobkins and Folk 1970) form factors help describe particle morphology.
al. 1993; Averill 2001; Townley et al. 2003), but grain description remains According to Blott and Pye (2008), the most representative value of
qualitative and subjective. It is accepted that the shape of a gold grain roundness and angularity is estimated using the average ratio of the
provides information about the distance of transport relative to the source diameter of curvature of all corners and the diameter of the largest
(Hallbauer and Utter 1977; Hérail et al. 1990; Dilabio 1991; Knight et al. inscribed circle (Wadell 1932).
1999; Averill 2001; Townley et al. 2003; Craw et al. 2017; Kerr et al. The physical characteristics, especially the malleability, of natural gold
2017). The evolution of gold-grain morphology is used to estimate the grains can yield a complex shape, and the quantification of morphology
distance of transport from the primary source in various surficial deposits remains problematic in two dimensions (2D). A 2D characterization of the
(Hérail et al. 1989; Youngson and Craw 1999; McClenaghan 2001; Craw et shape of gold grains can be performed using software tools (Crawford and
al. 2017). Mortensen 2009). The SEM image scale is approximate and overlooks the
In the fluvial environment, some authors have used the flatness index topographic variations at the surface of the grain such that the estimation of
(Wentworth 1922; Cailleux 1945) and the Corey Shape Factor (Corey 2D measurements is not accurate. The thickness of a particle is used in
1949) to quantify the particle flatness as a proxy for the distance of many shape-factor estimates, and this parameter is difficult to quantify on
transport of the gold grain (Giusti 1986; Hérail et al. 1990; Youngson and 2D images with a binocular-microscope or SEM images. Three-
Craw 1999; Townley et al. 2003; Barrios et al. 2015). However, for dimensional (3D) quantification provides a better way to estimate shape
glacial and eolian environments, classification depends on the shape and factors. In addition, the volume of a grain, quantified in 3D, is the only
the surface texture of gold grains determined by scanning electron parameter unaffected by the shape of the grain; unlike the long axis, for
microscope (SEM) observation (DiLabio 1990; Minter et al. 1993; Smith example, it can thus give an accurate estimate of the particle ‘‘size’’
et al. 1993). In sedimentology, additional factors are used to quantify a (Wadell 1932). In addition, 2D characterization covers a particle’s visible
particle shape (Blott and Pye 2008). Sphericity is commonly calculated surface, and the results can differ from one face to another, especially for
using the three principal axes to yield the intercept sphericity (Krumbein malleable gold grains. The 3D methods are therefore necessary to measure
1941), the maximum sphericity (Folk 1955; Sneed and Folk 1958), and the particle dimensions with greater precision, the surface area and the
the working sphericity (Aschenbrenner 1956). Some sphericity factors volume.
are calculated using the ratio of the diameter of the largest inscribed circle This study presents two methods to quantify the shape of gold grains using
to the diameter of the smallest circumscribed circle (Wadell 1933; 3D reconstructions: 1) 3D high-resolution X-ray microscopy (XRM), and 2)

Published Online: March 2020

Copyright Ó 2020, SEPM (Society for Sedimentary Geology) 1527-1404/20/090-286

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TABLE 1.—Common shape factors (after Blott and Pye 2008). Abbreviations: L, long axis; I, intermediate axis; S, short axis; V, volume of the particle;
Vcs, volume of the circumscribed sphere; M, maximum axis length; A, surface area of the particle; Dis, diameter of the largest inscribed sphere; Dcs,
diameter of the smallest circumscribed sphere; Dr, diameter of the curvature of the particle corners; n, number of corners of the particle.

Shape factors Formula Range Application

Wentworth flatness index LþI

2S
1 to þ‘ Flatness index:
Wentworth (1922) 1 ¼ cubic or spherical particle
þ‘ ¼ flat particle
Corey shape factor pSffiffiffiffi 0 to 1 Flatness index:
LI
Corey (1949) 0 ¼ flat particle
1 ¼ cubic or spherical particle
Janke form factor pffiffiffiffiffiffiffiffiffiffiffiffi
S
2 2 2
0 to 1 Flatness index:
L þI þS
Janke (1966) 3 0 ¼ flat particle
1 ¼ cubic or spherical particle
Aschenbrenner shape factor LS
I2
0 to þ‘ Oblate-Prolate index:
Aschenbrenner (1956) 0 to 1 ¼ oblate particle
1 ¼ spherical particle
1 to þ‘ ¼ prolate particle
2 I2 2
Williams shape factor 1  LS
I 2 , when I . LS, LS  1, when I  LS -1 to þ1 Oblate-Prolate index:
Williams (1965) 0 to þ1 ¼ oblate particle
0 to -1 ¼ prolate particle
Oblate-Prolate Index 10ðLS
LI
0:5Þ -‘ to þ‘ Oblate-Prolate index:
S
Dobkins and Folk (1970) L 0 to þ‘ ¼ prolate particle
0 to -‘ ¼ oblate particle
qffiffiffiffi
Krumbein intercept sphericity 3 IS 0 to 1 Sphericity index:
L2
Krumbein (1941) 0 ¼ non-spherical particle
1 ¼ spherical particle
qffiffiffiffi
Maximum projection sphericity 3 S2 0 to 1 Sphericity index:
LI
Folk (1955) 0 ¼ non-spherical particle
1 ¼ spherical particle
pffiffiffiffiffiffi
Aschenbrenner working sphericity 12:83 P2 Q
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 to 1 Sphericity index:
, where P ¼ SI and Q ¼ LI
Aschenbrenner (1956) 1þPð1þQÞþ6 2
1þP ð1þQ Þ 2
0 ¼ non-spherical particle
1 ¼ spherical particle
pffiffiffiffiffiffiffiffiffiffi
3
Degree of true sphericity s
¼ 36pV 2 0 to 1 Sphericity index:
A A
Wadell (1932) 0 ¼ non-spherical particle
1 ¼ spherical particle
qffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffi
Operational sphericity 3 V
¼ 3 V 0 to 1 Sphericity index:
Vcs 4 M 3
Wadell (1933), Aschenbrenner (1956) 3pð 2 Þ 0 ¼ non-spherical particle
1 ¼ spherical particle
qffiffiffiffiffiffi
Inscribed circle sphericity Dis 0 to 1 Sphericity index:
Dcs
Riley (1941) 0 ¼ non-spherical particle
1 ¼ spherical particle
P 
Wadell roundness Dr 0 to 1 Roundness index:
n
Wadell (1932) first formula 0 ¼ angular particle
Di
1 ¼ rounded particle

SEM photogrammetry to produce a 3D mesh of the grain shape. Both Janke form factor (Janke 1966) is related to a flatness ratio and yields
methods yield measurements such as triaxial lengths, surface area, and volume results similar to those of the Corey shape factor. The Aschenbrenner
that can be used to quantify particle shape factors, which are compared to four (Aschenbrenner 1956) and the Williams (Williams 1965) shape factors are
gold grains recovered from fluvial, glacial, and aeolian sediments. based on the degree of flatness (S/I) and elongation (I/L) to describe disk-
like or rod-like particles, while the Oblate-Prolate index proposed by
METHODS Dobkins and Folk (1970) is based on the degree of equancy (S/L), to
Shape Factors describe platy and elongate particle. The Krumbein intercept sphericity
(Krumbein 1941), the Folk maximum projection sphericity (Folk 1955),
In sedimentary environments, morphological factors are used to and the Aschenbrenner working sphericity (Aschenbrenner 1956) are
characterize and classify particle shape (Table 1). These morphological generally used to quantify sphericity using the dimensions of the particle.
features were defined in 2D and were applied in 3D through the
The degree of true sphericity proposed by Wadell (1932) is based on the
development of image processing, but it remains complicated to evaluate
particle volume (V) and the surface area (A). This factor is considered the
them accurately (Blott and Pye 2008). Many shape factors are based on the
most accurate estimate of sphericity (Wadell 1932). Wadell (1933)
long (L), intermediate (I), and short (S) axes, considering L . I . S, where
each is orthogonal to the other two axes. The Wentworth flatness index suggested a formula for operational sphericity using the volumes as
(Wentworth 1922), also called Cailleux flatness index (Cailleux 1945), is described by Aschenbrenner (1956). Riley (1941) suggested to measure the
commonly used for the characterization and classification of particle diameters of the largest inscribed and the smallest circumscribed circles to
flatness in fluvial environments. The Corey shape factor is also used to yield a circularity value in 2D, which can be used in 3D as a proxy for
describe flatness in alluvial particles (Giusti 1986; Barrios et al. 2015). The sphericity (Blott and Pye 2008). The roundness value of Wadell (1932) is

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 288 F.-X. MASSON ET AL. JSR

based on the diameter of the largest inscribed circle and the diameter of MeshLab (Cignoni et al. 2008) is used to obtain the surface area, the
curvature at all corners of the particle. volume, and the long, intermediate, and short axes of the grain. A minimal
bounding box that contains the particle is acquired by rotation and
Gold Grains translation, and the dimensions of this box are correlated to the axes of the
grain. To estimate the maximum length axis, the mesh is imported into the
Various shapes of gold grains from various sedimentary deposits were PolyWorks inspection software (InnovMetric), which is used to compare
compared in this study: 1) gold grain 1 is an elongated block and has a the normal direction for each point of the polygonal mesh. The software
simple geometry. It comes from fluvial sediments and was collected with a produces a thickness map along the whole grain. The length is calculated
prospecting pan; 2) gold grain 2 is well rounded and has a cavity on its according to the maximum distance between two surfaces of opposite
surface. It was collected in glacial sediments and extracted by mineral orientations. The MATLAB package entitled A suite of minimal bounding
separation; 3) gold grain 3 has complex geometry and is curled up. It was objects (D’Errico 2014) is used to measure the diameter of the largest
collected under the same conditions as grain 2; 4) gold grain 4 is a flat inscribed sphere, and the package entitled Exact minimum bounding
particle with a smooth surface texture; it was collected in eolian sediments spheres and circles (Semechko 2019) is used to obtain the diameter of the
and extracted by mineral separation. Grain 1 is considered as a reference smallest circumscribed sphere. The MATLAB package entitled Particle
gold grain, and the methodology is described for this one. The guideline is roundness and sphericity computation (Zheng and Hryciw 2015) is used
consistent for the analysis of other grains; however, some software to fit circles on the particle corners and yields a value for roundness on
parameters may vary depending on the nature and positioning of the particle. mesh projections in 2D, based on Wadell’s formula. The script parameters
(tol ¼ 0.3, factor ¼ 0.98, span ¼ 0.07) were kept constant as well as XRM
3D X-Ray Microscope mesh outlines so as not to influence the measurements.

In this study, a Xradia 520 Versa X-ray microscope (Carl Zeiss AG) was 3D SEM and Photogrammetry
used to scan gold grains to quantitatively reconstruct their shape in 3D. X-
ray tomography is non-destructive and splices the grain perpendicular to Photogrammetry was used to reconstruct the 3D shape of nanoscale
the spinning axis. The gold grain is placed in a plastic tube filled with silica particles from SEM images (Gontard et al. 2016). The same process is used
powder to maintain it in the middle part of the tube and enable the grain to to reconstruct the morphology of microscopic gold grains (Fig. 2). A SEM
be recovered after analysis. The matrix supporting the gold grain must be Quanta-3D-FEG (FEI) was used to capture secondary-electron images of
stable and strong enough so that the grain remains immobile in order to gold grains. Grain 1 surface texture is captured with SEM using a secondary-
reduce noise during scanning. For this study, an X-ray energy of 140.1 keV, electron detector and a magnification of a striated surface (Fig. 2A). Sample
a current of 68.9 lA, and a LE6 filter placed between the sample and the preparation consists in placing the grain at the top of a wood stick on carbon
source are used in order to penetrate the dense gold grain. A total of 3,201 tape, in order to have a conductive setup for high-quality secondary-electron
projections are required to obtain high-contrast images. The exposure time images. For this study, the energy is set at 3 keV to yield highest resolution
is set at 2 seconds to minimize processing time. The grain is turned for surface texture, at constant magnification of 3500. In order to document the
surface close to the stage for efficient 3D representation of each face of the
3608 and the detector measures X-ray absorption. A 43 optical
grain, the stage is tilted at 708. The grain is rotated for 3608 with 188 steps,
magnification yields a spatial resolution of 0.73 lm. A set of 1,983
which yields 20 images, the minimum required for volume reconstruction.
grayscale density-contrast images are produced, which represent the image
Overlap is necessary between image pairs for photogrammetric reconstruc-
of the grain slices. Dragonfly (Object Research Systems), a quantitative
tion. With more matching points, the software stitches the mesh object with
visualization software, was used to create a model of the particle in 3D,
better precision and increased textural details. We tested photogrammetry
according to the grayscale apparent-density images.
software tools, such as VisualSFM (Wu 2011) and COLMAP (Schönberger
The apparent density of gold grain 1 ranges from 0 to 60,076. These
et al. 2016), but those software packages could not reconstruct the grain
values change according to experimental conditions in addition to target
from SEM images and the results were not replicable. ReCap Photo
density. The dataset consists of three classes (Fig. 1A): 1) the background
(Autodesk) was able to achieve efficient reconstruction of the particle
noise, composed of air, forms 4.72% of the dataset and has a density value volume with surface textures. ReCap Photo proceeds to the 3D
ranging from 0 to 10,279; 2) the silica matrix that holds the gold grain is reconstruction using 19 camera views from SEM images. After reconstruc-
represented by 71.89% of the dataset, with a density value ranging from tion, a 3D mesh is produced with surface textures (Fig. 2B). However, SEM
10,279 to 37,770; 3) the gold grain forms 23.39% of the dataset with a images do not contain information on focal length, and this results in the loss
density value ranging from 37,770 to 60,076. In order to define the of absolute scale on the mesh produced by ReCap Photo. To recover
boundary of the object, it is necessary to set a minimum density value as absolute scale, the model is calibrated from a SEM reference image.
the transition between silica and gold (Fig. 1A). The minimal density of Measurements are taken on this reference image, for which the scale is
gold for this dataset is set to 37,770, such that higher density values are known, and then applied in the grain model. The magnification of the SEM
assumed to belong to the gold particle (Fig. 1A). Dragonfly ORS striated surface image of gold grain 1 can be observed easily on the
reconstructs the grain in 3D with a gold boundary at apparent density of reconstruction (Fig. 2A). To calibrate the model, we took five measurements,
37,770 and up to 60,076 (Fig. 1B). The background noise and the silica and the average value is used for scale calibration with standard deviations of
matrix are thus removed from this 3D model to yield the particle shape 1) 2.1% for the axial length; 2) 6.2% for the volume; 3) 4.1% for the surface
(Fig. 1B). The grain can be sliced in planes to analyze cross sections and area (Fig. 2B). ReCap Photo offers tools that enable the sample stage to be
generate a density profile through the grain (Fig. 1C). The profile shows removed from the model by deleting mesh triangles (Fig. 2C). However, this
the apparent-density values across the boundary between silica and gold creates a hole in the mesh. To fill this hole, we added a flat mesh at the base
(Fig. 1D). The gold density values are roughly of 50,000, and a drop of of the model to enable estimation of the volume of the particle. Finally, the
apparent density inside the grain indicates a void or heterogeneity in the mesh is aligned with the origin (Fig. 2D).
particle (Fig. 1D). Finally, a region of interest is determined by the The same data processing used for microtomography is used to obtain
apparent density of the gold grain, and a normal mesh is produced. A the axial lengths, the surface area, the volume, the diameter of the largest
Laplacian smoothing filter (one iteration) is used to remove the noise on inscribed sphere, the diameter of the smallest circumscribed sphere, and
this mesh while maintaining its roughness. the computation of the roundness value of the gold grain.

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FIG. 1.—A) Histogram of apparent density values for the dataset of gold grain 1. The apparent-density boundary between the background and the silica matrix is at 10,279,
whereas the apparent density of the gold grain is set at 37,770. B) Gold grain 1 mesh in orthographic projection with three axial planes (X, Y, Z) at apparent density above
37,770. C) X, Y, and Z planes that compose the dataset, with a longitudinal transect representation on the X plane. D) Apparent density on the 300 lm of the longitudinal
transect in the gold grain with a drop of apparent density that corresponds to an inclusion or a void inside the gold grain.

RESULTS 3C), based on the convex hull of the particle. The Wadell roundness was
calculated with the MATLAB algorithm on six projection planes (X, -X, Y,
Estimates of Shape Parameters -Y, Z, -Z) of the particle (Fig. 3D). The 3D SEM particle reconstruction of
grain 1 was imported in MeshLab in order to measure the minimal
The 3D XRM mesh of grain 1 was imported in MeshLab to measure the
bounding-box dimensions, the surface area, and the volume (Fig. 4A).
minimal bounding-box dimensions (L, I, S), the surface area, and the volume
PolyWorks yields measurement of the maximum axis length and the volume
(Fig. 3A). PolyWorks yields a maximum axis length and the volume of the
of the circumscribed sphere (Fig. 4B). The MATLAB packages are used to
circumscribed sphere (Fig. 3B). The thickness map indicates an anomaly in provide the diameter of the largest inscribed sphere and the smallest
the particle with variations of the thickness detected on the surface. This circumscribed sphere on the convex hull of the grain (Fig. 4C). The Wadell
anomaly suggests the presence of a void or an inclusion at 0 to 25 lm depth roundness was calculated on the six projection planes of the particle (Fig.
(Fig. 3B). The MATLAB packages produce the diameter of the largest 4D). Average shape parameters and standard deviation on grain 1 show that
inscribed sphere and the diameter of the smallest circumscribed sphere (Fig. the difference between both methods is less than 6% (Table 2).

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 290 F.-X. MASSON ET AL. JSR

FIG. 2.—A) SEM image of gold grain 1 and magnification of small features for calibration using five measurements (Mi). B) Gold grain reconstruction with the sample
stage covered by carbon tape and magnification of the same area as in (Part A) to calibrate the model with the same five measurements (Mi). C) Gold grain after removing
base mesh elements and calibration processing. D) The model is transformed and closed to fit with the origin of the mesh represented by the grid.

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FIG. 3.—Morphological parameters obtained with the 3D X-ray microscope method on gold grain 1. A) MeshLab representation with the minimal bounding box (green)
that contains the grain. The software provides measurements of the long axis (L), the intermediate axis (I), the short axis (S), the surface area (A), and the volume (V).
B) Thickness map representation of the grain obtained with the 3D X-ray microscope (produced by PolyWorks). The red line shows the maximum length axis (M), and the
indigo area shows the same inclusion or void as the transect at 0 to 25 lm depth (Fig.1). C) Representation of the particle convex hull with the largest inscribed sphere and the
smallest circumscribed sphere. The diameter of the smallest circumscribed sphere (Dcs) and the diameter of the largest inscribed sphere (Dis) are measured. D) Illustration of
six plane sections with the values of the Wadell roundness. The green circles show the curvature of all corners of the particle and the red circle shows the diameter of the
largest inscribed circle.

The shape parameters were computed for the other gold grains with of the XRM mesh is smaller than the long-axis measurement, so the volume
different geometry (Fig. 5). The reconstruction models for grain 2 yield of the smallest circumscribed sphere is estimated with the value of the long
similar results, but the heterogeneity on the surface reconstructed by the SEM axis. The surface area and the volume of grain 3 vary significantly (Table 2).
mesh was not captured on the XRM mesh (Fig. 5A). Shape parameters Grain 4 is flat, and the part in contact with the carbon tape cannot be
affected by the particle geometry lead to differences between the two methods measured by SEM photogrammetry such that it is not represented well on the
of 10.2% to 24.2% (Table 2). The grain 3 reconstruction models show SEM model (Fig. 5C). Similar to grain 3, the maximum length of the SEM
slightly different results. The complexity of the grain geometry adds volume mesh is smaller than the long-axis measurement. Shape parameters affected
at the base of the SEM mesh reconstruction (Fig. 5B). The maximum length by flat particle have differences range between 10.2% and 22.5% (Table 2).

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FIG. 4.—Morphological parameters obtained with the 3D SEM method on gold grain 1. A) MeshLab representation with the minimal bounding box (green) and the
measurements of the long axis (L), the intermediate axis (I), the short axis (S), the surface area (A), and the volume (V). B) Thickness map of the mesh with the red line
showing the maximum axial length (M). C) Representation of the convex hull with the largest inscribed sphere and the smallest circumscribed sphere. The diameter of the
smallest circumscribed sphere (Dcs) and the diameter of the largest inscribed sphere (Dis) are measured. D) Illustration of six plane sections with the values of the Wadell
roundness. The green circles show the curvature of all corners of the particle and the red circle shows the diameter of the largest inscribed circle.

Estimates of Shape Factors degree of equancy, indicates that grain 1 is slightly flat, moderately
elongated, and moderately non-equant for SEM results. XRM results show
The shape factors are estimated from the shape parameters according to a slightly flat, slightly elongated, and moderately non-equant particle. The
XRM and SEM photogrammetry results (Table 3). The Wadell roundness flatness indices are generally similar for the two methods and illustrate a
corresponds to the average value of the six projection planes. For grain 1, moderately to slightly flat particle. The Aschenbrenner, the Williams, and
the two methods show a difference on the computed shape factors less than the oblate-prolate factors indicate that the particle is prolate (rod-like). The
6%, with the exception of the Williams shape factor, the Oblate-Prolate Krumbein intercept sphericity, the maximum projection sphericity, the
index, and the Wadell roundness, with a difference of 23.1%, 20.1%, and degree of true sphericity, and the inscribed circle sphericity indicate that
8.5%, respectively (Table 3). The classification proposed by Blott and Pye the particle is moderately spherical. However, the operational sphericity
(2008), based on the degree of flatness, the degree of elongation, and the has lower values and corresponds to a low-sphericity particle. The

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TABLE 2.—Average shape parameters measured and standard deviations for gold grain 1. These results are based on five meshes produced with the five
measurements in Figure 2, for the SEM method, and on three meshes produced with different apparent density, for the XRM method. The differences
between the estimates with the two methods are expressed for gold grains 1 to 4.

Gold Grain 1 Gold Grain 2 Gold Grain 3 Gold Grain 4

Shape Parameters 3D XRM 3D SEM Difference Difference Difference Difference

L (lm) 283.5 6 0.9 297.0 6 6.2 4.8 % 11.6 % 1.9 % 2.1 %

I (lm) 175.7 6 0.2 174.9 6 3.8 0.5 % 16.6 % 0.2 % 2.8 %
S (lm) 124.7 6 0.6 123.3 6 2.6 1.1 % 6.9 % 0.8 % 21.8 %
M (lm) 300.4 6 0.6 301.6 6 6.3 0.4 % 3.7 % 9.2 % 2.6 %
Dis (lm) 123.4 6 0.7 123.3 6 2.8 0.1 % 3.3 % 1.8 % 22.2 %
Dcs (lm) 301.1 6 0.8 305.2 6 6.4 1.4 % 10.2 % 1.9 % 2.8 %
A (lm2) 1.4Eþ05 6 6.8Eþ02 1.3Eþ05 6 5.6Eþ03 1.7 % 7.5 % 27.2 % 10.2 %
V (lm3) 2.9Eþ06 6 6.2Eþ04 3.1Eþ06 6 1.9Eþ05 5.9 % 24.2 % 42.9 % 22.5 %
Vcs (lm3) 1.4Eþ07 6 7.9Eþ04 1.4Eþ07 6 8.9Eþ05 1.3 % 11.5 % 1.9 % 6.9 %

FIG. 5.—SEM images, 3D meshes, and shape parameters for SEM and XRM methods: A) gold grain 2. The dashed red square shows the heterogeneity on the SEM images
and the 3D SEM mesh. B) Gold grain 3. C) Gold grain 4.

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TABLE 3.—Average shape factors computed for grain 1 and the differences between the two methods expressed for gold grains 1 to 4.

Gold Grain 1 Gold Grain 2 Gold Grain 3 Gold Grain 4

Shape Factors 3D XRM 3D SEM Difference Difference Difference Difference

Degree of flatness (S/I) 0.71 0.70 1.4 % 9.2 % 0.0 % 23.5 %

Degree of elongation (I/L) 0.62 0.59 4.8 % 5.1 % 1.3 % 5.1 %
Degree of equancy (S/L) 0.44 0.42 4.5 % 5.0 % 2.0 % 20.0 %
Wentworth flatness index 1.84 1.91 3.8 % 6.0 % 0.0 % 27.5 %
Corey shape factor 0.56 0.54 3.6 % 6.0 % 0.0 % 23.1 %
Janke form factor 0.61 0.58 4.9 % 5.4 % 0.0 % 23.3 %
Aschenbrenner shape factor 1.15 1.20 4.3 % 11.6 % 3.3 % 27.6 %
Williams shape factor -0.13 -0.16 23.1 % 220.0 % 30.0 % 38.1 %
Oblate-Prolate index 4.07 4.89 20.1 % 675.9 % 294.4 % 562.5 %
Krumbein intercept sphericity 0.65 0.63 3.1 % 0.0 % 1.4 % 6.1 %
Maximum projection sphericity 0.68 0.66 2.9 % 3.9 % 0.0 % 14.6 %
Aschenbrenner working sphericity 0.87 0.86 1.1 % 1.1 % 0.0 % 10.8 %
Degree of true sphericity 0.72 0.76 5.6 % 6.7 % 75.0 % 5.7 %
Operational sphericity 0.59 0.60 1.7 % 2.9 % 13.7 % 4.7 %
Inscribed circle sphericity 0.64 0.64 0.0 % 4.1 % 0.0 % 11.1 %
Wadell roundness 0.47 0.43 8.5 % 19.6 % 100.0 % 100.0 %

Aschenbrenner working sphericity suggests a greater value associated with Estimates of Morphological Parameters and Factors
high-sphericity grain. The Wadell roundness suggests that grain 1 is
subrounded for both methods. Nevertheless, for gold grains with simple geometry, such as gold grain
The other grains, having a complex geometry, show larger differences 1, each method enables estimation of the parameters with less than 6%
between the two methods (Table 3). For these grains, the Williams shape difference of shape parameters (Table 2). For the 3D SEM method, the
factor and the Oblate-Prolate index have differences up to 30.0% and estimates vary according to the surface placed on the carbon tape and the
294.4%, respectively. The Wadell roundness has a difference up to 19.6%. geometry of the grain, such that errors in the measurement of shape
The MATLAB algorithm was not applied on grains 3 and 4 for two parameters can be greater (Table 2). Grain 1 has a small contact area with
projection planes because of their uncertain boundaries. Other shape factors the carbon tape, so the error on the volume and the surface area is minimal.
that have difference in values larger than 10% are i) the Aschenbrenner For flat and complex geometry grains, the particle should be placed on a tip
shape factor, for grain 2, ii) the operational sphericity and the degree of true or a slice, to minimize this area. However, the matching points can be more
sphericity, for grain 3, and iii) the majority of shape factors, for grain 4. difficult for the photogrammetric software to reconstruct the particle
volume. The difference between the long axis is generally greater than the
difference for the intermediate and the short axes. That is because to find
DISCUSSION
the minimal bounding box, the short axis was found first, followed by the
Comparison Between the Two 3D Methods intermediate axis, and the long axis is orthogonal to the two above axes.
Although the difference in the maximum length is less than 10% for all
This study presents two 3D methods to quantify the morphology of gold grains, this measurement remains problematic when it is smaller than the
grains. Four particles were used to compare shape parameters in 3D, and long-axis value, especially when the grain is curved or has a complex
grain 1 is considered as a reference for the methodology. The Xradia 520 geometry. This term affects the volume of the circumscribed sphere
Versa generates X-rays with high energy that penetrate gold and produces a parameter and, therefore, the operational sphericity shape factor. In the case
full 3D reconstruction of grains approximately 85 to 300 lm in size. The of a comparative study with multiple grains, it is recommended to use the
model represents the surface morphology and gives information about the diameter of the smallest circumscribed sphere, measured with the convex
core of the grain by detecting voids or inclusions. The disadvantages of this hull, although it is less accurate than the maximum length axis.
method are: 1) the apparent-density contrast must be adjusted to Most of the shape factors of grain 1 have less than 6% difference
circumscribe the grain, and the boundary between the silica matrix and between the two methods, which confirms their use for grains with simple
the gold grain is subtle even if this transition zone is not significant, geometry (Table 3). However, this is not the case for other grains with more
considering the standard deviation of the axial lengths, surface area, and complex geometries (Table 3), where the Oblate-Prolate index and the
volume measurements obtained in the experiments; 2) some artifacts may Williams shape factors have a higher difference up to 294.4% and 30.0%,
distort the scan quality, such as the blurry borders produced by movement respectively. The large error between the two methods show that the
of the grain on the rotating base; 3) the resolution of the device is adequate Oblate-Prolate index is not recommended to estimate the shape of gold
to reconstruct a gold grain greater than 85 lm in long axis. 3D SEM particles. The Williams shape factor is efficient to approximate an oblate or
photogrammetry reconstructs the shape of gold grains greater than 20 lm prolate particle shape and, except for grain 2, the results are similar
in size with high resolution. The 3 keV energy provides a better surface considering the range of values expected for the factor (Table 1). The same
texture information, which is useful for the reconstruction. The acquisition applies for the Aschenbrenner-shape-factor estimates on grains 2 and 4.
time (~ 1 h) is faster than the 3D XRM scan (~ 4 h). The disadvantages of The Wadell roundness is calculated on six projection planes in 2D. The
this method are: 1) the acquisition of a partial reconstruction mesh, because estimation in 3D is determined by the average result of the sections. This
the base of the grain must be replaced by a flat mesh; 2) the scale parameter is highly dependent on mesh smoothness, and the results vary
calibration needs to be performed with an average accuracy 6 6.2% and according to the projection plane orientations. The meshes are obtained
depends on the magnification of a small feature of the object; 3) the with two different software packages and different degrees of smoothing.
observer has no control on the mesh produced by ReCap Photo, on the In this study, we decided to work with the original mesh, but there is
production of the mesh, or on the smoothing process after reconstruction. residual roughness at the boundaries. SEM images with high resolution

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 JSR QUANTIFICATION OF THE MORPHOLOGY OF GOLD GRAINS IN 3D USING XRM AND SEM 295

TABLE 4.—Comparison of shape parameters and computed shape factors shape parameters cannot be measured on a 2D image, which limits the
between 2D SEM and 3D SEM, for gold grain 1. Dis and Dcs are amount of computed shape factors that may be relevant to particle-shape
estimated in 2D based on the diameter of the largest inscribed circle and quantification (Table 4). The computed shape factors show significant
the smallest circumscribed circle, respectively. differences between 2D and 3D quantification (Table 4), which are
greater than differences of shape factors computed for the two 3D
Shape Parameters and Factors 2D SEM 3D SEM Difference
methods (Table 3), except for the Wadell roundness, which is based on
L (lm) 289 297.0 2.7 % 2D projections. 3D analysis provides a more accurate quantification of
I (lm) 135 174.9 22.8 % the commonly used shape factors and of the non-quantifiable factors in
S (lm) 54 123.3 56.2 % 2D, based on the volume, the surface area, and the maximum axis of the
M (lm) Non-measurable 301.6 Non-measurable particle.
Dis (lm) 171 123.3 38.7 %
Dcs (lm) 295 305.2 3.3 %
A (lm2) Non-measurable 134386 Non-measurable
Impact of the Proposed Approaches for Mineral Exploration and
V (lm3) Non-measurable 3071205 Non-measurable Sedimentology
Vcs (lm3) Non-measurable 14376811 Non-measurable
Degree of flatness (S/I) 0.40 0.70 43.9 %
On one hand, 3D XRM is not a common tool for mineral exploration.
Degree of elongation (I/L) 0.47 0.59 20.3 % On the other hand, the estimates based on 3D SEM presented in this paper
Degree of equancy (S/L) 0.19 0.42 54.8 % are promising for the characterization of particles with simple geometry.
Wentworth flatness index 3.93 1.91 105.8 % Using 3D SEM for the quantification of complex and flat geometries
Corey shape factor 0.27 0.54 50.0 % depends on how the grain is placed on the carbon tape. This method can be
Janke form factor 0.29 0.58 50.0 % used to evaluate in 3D the shape of gold grains smaller than 63 lm in size,
Aschenbrenner shape factor 0.86 1.20 28.3 % which typically form 80 to 90% of gold grains in glacial sediments (Averill
Williams shape factor 0.14 -0.16 187.5 %
2001). The comparison of morphological factors quantified in 3D on
Oblate-Prolate index 8.31 4.89 69.9 %
Krumbein intercept sphericity 0.44 0.63 30.2 % detrital gold grains coupled with textural observations is useful to classify
Maximum projection sphericity 0.42 0.66 36.4 % the evolution of a malleable gold particle, during transport from the source,
Aschenbrenner working sphericity 0.66 0.86 23.3 % in a sedimentary system.
Degree of true sphericity Non-estimated 0.76 Non-estimated In sedimentology, characterizations of detrital fragments and heavy
Operational sphericity Non-estimated 0.60 Non-estimated minerals are used to estimate the distance of transport and provide
Inscribed circle sphericity 0.76 0.64 18.8 % information about the source of particles (Wadell 1935). The two methods
Wadell roundness 0.41 0.43 4.7 %
can provide a quantification of 3D morphology of sedimentary particles
and minerals other than gold grains. The 3D estimates can be used to refine
degrees of roundness, sphericity, and flatness in order to estimate the
provide a detailed mesh based on surface texture, which corresponds to the
distance of transport.
surface roughness, while the resolution of the 3D XRM produces a smooth
surface with less detail on the roughness. The MATLAB algorithm is not
CONCLUSION
efficient for complex grain shapes, especially when the boundaries are
rough. The roundness differences are influenced by smoothing and the The 3D XRM and the SEM coupled with photogrammetry enable the
orientation of the projection planes, such that the shape factor is not 3D morphology of a gold grain to be reconstructed. For a gold grain with
recommended to estimate the roundness. simple geometry, both methods provide similar results on axial lengths,
The operational sphericity and the degree of true sphericity depend on surface area, volume, diameter of the largest inscribed sphere, and diameter
the volume of the particle. This is a major factor, and the difference is of the smallest circumscribed sphere, and most of the shape factors
higher than 10%, except for grain 1 (Table 2). This difference can be estimated have less than 6% difference. Quantification of gold grains with
correlated with the grain manipulation during the setup change between a complex geometry, such as flat or curved grains, yield differences
XRM and SEM. However, the SEM setup can be used for analysis with 3D between shape parameters and shape factors that are greater than for grains
XRM, which will reduce the number of manipulations and shape with simple geometry, and it varies mainly depending on how the grain is
modification. The volume, estimated by SEM photogrammetry, is also positioned, especially for the SEM method. However, the XRM method
highly dependent on the surface area placed on the carbon tape, and the produces relevant results to reconstruct the morphology in 3D of a complex
estimation remains delicate. It is essential to limit the contact with the gold grain regardless of its orientation. On one hand, the 3D XRM is more
carbon tape or to use the XRM method for large complex or flat particles to suitable to quantify gold-grain sizes greater than 85 lm and produces full
guarantee an accurate volume measurement. 3D reconstruction. On the other hand, the resolution of the 3D SEM-based
method provides a partial reconstruction but allows reconstruction of the
Comparison of 2D and 3D Analyses 3D shape of particles smaller than 85 lm in size.
Shape parameters and computed shape factors are estimated in 2D, for
gold grain 1, using a SEM image (Fig. 2A) and compared to the 3D SEM ACKNOWLEDGMENTS

results (Table 4). The 2D shape parameters such that the diameter of the We thank Stéphane Gagnon for the data-acquisition analyses with the SEM at
largest inscribed circle, the intermediate axis, and the short axis show Université Laval and Rui Tahara for the data-acquisition analyses with the
large differences with the 3D SEM results (Table 4). The short-axis Xradia 520 Versa at McGill University. Tomographic acquisition was performed
measurement yields the largest difference because it is difficult to using the infrastructure of the Integrated Quantitative Biology Initiative,
measure on a 2D image, even with the large depth of field of the Canadian Foundation for Innovation Project 33122. The research presented in
secondary-electron SEM image. The short axis can be estimated using this paper was funded by the Natural Sciences and Engineering Research
other SEM images from different orientations, to improve the accuracy of Council of Canada (NSERC) collaborative Research and Development grant in
measurement of this parameter. The size of the minimal bounding box is partnership with Agnico Eagle Mines Ltd and the Ministère de l’Énergie et des
highly dependent on the observer’s position relative to the sample. Some Ressources Naturelles du Québec (MERN).

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 296 F.-X. MASSON ET AL. JSR

REFERENCES HÉRAIL, G., FORNARI, M., VISCARRA, G., AND MIRANDA, V., 1990, Morphological and
chemical evolution of gold grains during the formation of a polygenic fluviatile placer:
ASCHENBRENNER, B.C., 1956, A new method of expressing particle sphericity: Journal of the Mio-Pleistocene Tipuani placer example (Andes, Bolivia): Chronique de la
Sedimentary Petrology, v. 26, p. 15–31. Recherche Miniere, p. 41–49.
AUTODESK, 2019, ReCap Photo, https://www.autodesk.com. JANKE, N., 1966, Effect of shape upon the settling velocity of regular convex geometric
AVERILL, S.A., 2001, The application of heavy indicator mineralogy in mineral exploration particles: Journal of Sedimentary Petrology, v. 36, p. 370–376.
with emphasis on base metal indicators in glaciated metamorphic and plutonic terrains, KERR, G., FALCONER, D., REITH, F., AND CRAW, D., 2017, Transport-related mylonitic ductile
in McClenaghan, M.B., Bobrowsky, P.T., Hall, G.E.M., and Cook, S.J., eds., Drift deformation and shape change of alluvial gold, southern New Zealand: Sedimentary
Exploration in Glaciated Terrain: Geological Society of London, Special Publication Geology, v. 361, p. 52–63.
185, p. 69–81. KNIGHT, J., MORISON, S., AND MORTENSEN, J., 1999, The relationship between placer gold
BARRIOS, S., MERINERO, R., LOZANO, R., AND OREA, I., 2015, Morphogenesis and grain size particle shape, rimming, and distance of fluvial transport as exemplified by gold from the
variation of alluvial gold recovered in auriferous sediments of the Tormes Basin (Iberian Klondike District, Yukon Territory, Canada: Economic Geology, v. 94, p. 635–648.
Peninsula) using a simple correspondence analysis: Mineralogy and Petrology, v. 109, p. KRUMBEIN, W.C., 1941, Measurement and geological significance of shape and roundness
679–691. of sedimentary particles: Journal of Sedimentary Petrology, v. 11, p. 64–72.
BLOTT, S.J., AND PYE, K., 2008, Particle shape: a review and new methods of MCCLENAGHAN, M.B., 2001, Regional and local-scale gold grain and till geochemical
characterization and classification: Sedimentology, v. 55, p. 31–63. signatures of lode Au deposits in the western Abitibi Greenstone Belt, central Canada, in
CAILLEUX, A., 1945, Distinction des galets marins et fluviatiles: Société Géologique de McClenaghan, M.B., Bobrowsky, P.T., Hall, G.E.M., and Cook, S.J., eds., Drift
France, Bulletin, v. 5, p. 375–404. Exploration in Glaciated Terrain: Geological Society of London, Special Publication
CIGNONI, P., CALLIERI, M., CORSINI, M., DELLEPIANE, M., GANOVELLI, F., AND RANZUGLIA, G., 185, p. 201–224.
2008, Meshlab: an open-source mesh processing tool: Eurographics, Italian Chapter MINTER, W., GOEDHART, M., KNIGHT, J., AND FRIMMEL, H., 1993, Morphology of
Conference, p. 129–136. Witwatersrand gold grains from the Basal Reef: evidence for their detrital origin:
COREY, A., 1949, Influence of shape on the fall velocity of sand grains [MS Thesis]: Economic Geology, v. 88, p. 237–248.
Colorado A&M College, Fort Collins, Colorado, U.S.A., 102 p. POLYWORKS, 2018, InnovMetric, https://www.innovmetric.com.
CRAW, D., HESSON, M., AND KERR, G., 2017, Morphological evolution of gold nuggets in RILEY, N.A., 1941, Projection Sphericity: Journal of Sedimentary Petrology, v. 11, p. 94–
proximal sedimentary environments, southern New Zealand: Ore Geology Reviews, v. 97.
80, p. 784–799. SCHÖNBERGER, J.L., ZHENG, E., FRAHM, J.-M., AND POLLEFEYS, M., 2016, Pixelwise view
CRAWFORD, E.C., AND MORTENSEN, J.K., 2009, An ImageJ plugin for the rapid selection for unstructured multi-view stereo: European Conference on Computer Vision,
morphological characterization of separated particles and an initial application to placer p. 501–518.
gold analysis: Computers & Geosciences, v. 35, p. 347–359. SEMECHKO, A., 2019, MathWorks: exact minimum bounding spheres and circles, https://
D’ERRICO, J., 2014, MathWorks: a suite of minimal bounding objects. www.github.com/AntonSemechko/Bounding-Spheres-And-Circles.
DILABIO, R., 1990, Classification and interpretation of the shapes and surface textures of SMITH, D.B., THEOBALD, P.K., SHIQUAN, S., TIANXIANG, R., AND ZHIHUI, H., 1993, The Hatu
gold grains from till on the Canadian Shield: Geological Survey of Canada, Papers, v. 88, gold anomaly, Xinjiang–Uygur Autonomous Region, China: testing the hypothesis of
Current Research, Part C, p. 61–65. aeolian transport of gold: Journal of Geochemical Exploration, v. 47, p. 201–216.
DILABIO, R., 1991, Classification and interpretation of the shapes and surface textures of SNEED, E.D., AND FOLK, R.L., 1958, Pebbles in the lower Colorado River, Texas, a study in
gold grains from till, in Hérail, G., and Fornari, M., eds., Gisements Alluviaux d’Or, p. particle morphogenesis: The Journal of Geology, v. 66, p. 114–150.
297–313. TOWNLEY, B.K., HÉRAIL, G., MAKSAEV, V., PALACIOS, C., DE PARSEVAL, P., SEPULVEDA, F.,
DOBKINS, J.E., AND FOLK, R.L., 1970, Shape development on Tahiti-nui: Journal of ORELLANA, R., RIVAS, P., AND ULLOA, C., 2003, Gold grain morphology and composition
Sedimentary Petrology, v. 40, p. 1167–1203. as an exploration tool: application to gold exploration in covered areas: Geochemistry:
DRAGONFLY, 2019, Computer software version 4.0, Object Research Systems (ORS), Inc., Exploration, Environment, Analysis, v. 3, p. 29–38.
Montreal, Canada, available at http://www.theobjects.com/dragonfly. WADELL, H., 1932, Volume, shape, and roundness of rock particles: The Journal of
FOLK, R.L., 1955, Student operator error in determination of roundness, sphericity, and Geology, v. 40, p. 443–451.
grain size: Journal of Sedimentary Petrology, v. 25. WADELL, H., 1933, Sphericity and roundness of rock particles: The Journal of Geology, v.
GIUSTI, L., 1986, The morphology, mineralogy, and behavior of ‘‘fine-grained’’ gold from 41, p. 310–331.
placer deposits of Alberta: sampling and implications for mineral exploration: Canadian WADELL, H., 1935, Volume, shape, and roundness of quartz particles: The Journal of
Journal of Earth Sciences, v. 23, p. 1662–1672. Geology, v. 43, p. 250–280.
GONTARD, L.C., SCHIERHOLZ, R., YU, S., CINTAS, J., AND DUNIN-BORKOWSKI, R.E., 2016, WENTWORTH, C.K., 1922, The shapes of beach pebbles: U.S. Geologocal Survey,
Photogrammetry of the three-dimensional shape and texture of a nanoscale particle using Professional Paper 131–C, p. 75–83.
scanning electron microscopy and free software: Ultramicroscopy, v. 169, p. 80–88. WILLIAMS, E.M., 1965, A method of indicating pebble shape with one parameter: Journal of
GRANT, A., LAVIN, O., AND NICHOL, I., 1991, The morphology and chemistry of transported Sedimentary Petrology, v. 35, p. 993–996.
gold grains as an exploration tool: Journal of Geochemical Exploration, v. 40, p. 73–94. WU, C., 2011, VisualSFM: a visual structure from motion system: http://ccwu.me/vsfm/.
HALLBAUER, D., AND UTTER, T., 1977, Geochemical and morphological characteristics of YOUNGSON, J.H., AND CRAW, D., 1999, Variation in placer style, gold morphology, and gold
gold particles from recent river deposits and the fossil placers of the Witwatersrand: particle behavior down gravel bed-load rivers: an example from the Shotover/Arrow–
Mineralium Deposita, v. 12, p. 293–306. Kawarau–Clutha River system, Otago, New Zealand: Economic Geology, v. 94, p. 615–
HÉRAIL, G., 1988, Morphological evolution of supergenetic gold particles: geological 633.
significance and interest for mining exploration: Paris, Académie des Sciences, Compte ZHENG, J., AND HRYCIW, R., 2015, Traditional soil particle sphericity, roundness and surface
Rendus, v. 307, p. 63–69. roughness by computational geometry: Géotechnique, v. 65, p. 494–506.
HÉRAIL, G., FORNARI, M., AND ROUHIER, M., 1989, Geomorphological control of gold
distribution and gold particle evolution in glacial and fluvioglacial placers of the
Ancocala–Ananea basin: southeastern Andes of Peru: Geomorphology, v. 2, p. 369–383. Received 6 August 2019; accepted 5 December 2019.

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