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QUANTITATIVE X-RAY POWDER DIFFRACTION AND THE ILLITE POLYTYPE
ANALYSIS METHOD FOR DIRECT FAULT ROCK DATING: A COMPARISON OF
ANALYTICAL TECHNIQUES
AUSTIN BOLES1 ,*, ANJA M. SCHLEICHER
2, JOHN SOLUM3, AND BEN VAN DER PLUIJM
1
1 Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI, USA2 Helmholtz Center Potsdam, GFZ German Research Center for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
3 Shell International Exploration and Production, Inc., Shell Technology Center Houston, 3333 Hwy 6, Houston, TX 77082,USA
Abstract—Illite polytypes are used to elucidate the geological record of formations, such as the timing andprovenance of deformations in geological structures and fluids, so the ability to characterize and identifythem quantitatively is key. The purpose of the present study was to compare three X-ray powder diffraction(Q-XRPD) methods for illite polytype quantification for practical application to directly date clay-richfault rocks and constrain the provenance of deformation-related fluids in clay-rich brittle rocks of the uppercrust. The methods compared were WILDFIRE# (WF) modeling, End-member Standards Matching(STD), and Rietveld whole-pattern matching (BGMN1). Each technique was applied to a suite of syntheticmixtures of known composition as well as to a sample of natural clay gouge (i.e. the soft material between avein wall and the solid vein). The analytical uncertainties achieved for these synthetic samples using WFmodeling, STD, and Rietveld methods were �4�5%, �1%, and �6%, respectively, with the caveat that theend-member clay mineral used for matching was the same mineral sample used in the test mixture. Variousparticle size fractions of the gouge were additionally investigated using transmission electron microscopy(TEM) to determine polytypes and laser particle size analysis to determine grain size distributions. Thethree analytical techniques produced similar 40Ar/39Ar authigenesis ages after unmixing, which indicatedthat any of the methods can be used to directly date the formation of fault-related authigenic illite.Descriptions were included for pre-calculated WF illite polytype diffractogram libraries, model end-members were fitted to experimental data using a least-squares algorithm, and mixing spreadsheetprograms were used to match end-member natural reference samples.
Key Words—Fault Gouge Dating, Illite, Illite Polytypes, Quantitative X-ray Powder Diffraction,Rietveld Method, Transmission Electron Microscopy.
INTRODUCTION
Illite polytype analysis remains a central method to
constrain the timing of the deformation of low-tempera-
ture structures in the upper crust (see recent review by
van der Pluijm and Hall, 2015). In addition, it is used to
elucidate the provenance of deformation-related fluids in
clay-rich fault rocks (Boles et al., 2015). A key step that
underpins this method is the accurate identification and
quantification of illite polytypes. Various techniques and
tools have been used in the quantification process and
three common approaches were compared in the present
study.
The term illite, sensu stricto, does not refer to a
single mineral, but rather to a family of K- and Al-
bearing mica-like, 1.0 nm dioctahedral minerals. For this
reason, some workers prefer the term ‘‘white mica’’ toemphasize the diversity within the species (Merriman et
al., 1990). Illite is non-expanding and has a 2:1 mica
structure with a tetrahedral-octahedral-tetrahedral (TOT)
sheet sequence. Polytypism is common to clay minerals
and mica and is expressed as a fixed TOT silicate layer
structure with a variable layer stacking sequence. In
illite, five polytypes can be distinguished, denoted as
1M, 1Md, 2M1, 2M2, and 3T. The 3T polytype is
uncommon in nature and is often confused with the 1M
variety (Reynolds and Thomson, 1993). Whereas the
2M1 polytype sheet stacking sequence is characterized
by regular 120-degree rotations, the 1Md polytype is
characterized by rotations in random multiples of 120
degrees with different proportions of cis-vacant (cv) and
trans-vacant (tv) sites and expandable layers, which
increase turbostratic disorder (Grathoff and Moore,
1996). Model X-ray diffractograms were compared
using WILDFIRE# (WF) generated end-members
(Reynolds, 1993) of the three most common illite
polytypes and illustrate the rationale for using X-ray
diffraction as a diagnostic tool to quantify the relative
proportions of illite polytypes in natural samples
(Figure 1). The patterns emphasize that the hkl reflec-
tions of each polytype are quite distinct. Indeed, using
illite polytypism as a proxy for population provenance is
the basis of the method. In practice, most of the observed
natural shale samples and clay-rich fault rocks have two
* E-mail address of corresponding author:
DOI: 10.1346/CCMN.2018.064093
Clays and Clay Minerals, Vol. 66, No. 3, 220–232, 2018.
polytypes, 1Md and 2M1 (van der Pluijm and Hall,
2015). The justification for a two end-member system
lies in the observation that 1M illite formation requires
compositional anomalies that do not occur in a normal
prograde diagenetic/low-grade metamorphic sequence
from 1Md to 2M1 (Peacor et al., 2002). This is further
supported by the argument of Moore and Reynolds
(1997) that 1M and 1Md polytypes likely have separate
diagenetic paths to 2M1 instead of the 1Md ? 1M ?2M1 path proposed by others (Lonker and Fitz Gerald,
1990; Drits et al. 1993). Observations from fault zones
of various types have shown that the disordered polytype
prograde series 1Md ? 2M1 is the predominant one in
low-temperature (i.e. <300ºC), open system, near-sur-
face environments (Solum et al., 2005; Haines and van
der Pluijm, 2012; Hnat and van der Pluijm, 2014).
Early workers recognized a positive correlation
between age and grain size in illite-bearing rocks
(Hower et al., 1963) and this observation precipitated
attempts to use these K-bearing micas as a geochron-
ometer in natural systems (e.g. Hoffman et al., 1976;
Covey et al., 1994). Separating the clay size fraction into
a range of subfractions yields a positive correlation
between grain size and age, which through the use of
unmixing can be extrapolated to end-member values and
facilitate the main application of illite dating. The illite
polytype analysis method has been used to date low-
temperature, diagenetic illite in sedimentary basins or
synkinematic illite growth associated with localized
deformation in the brittle crust (Pevear, 1992; Dong et
al., 2000; van der Pluijm et al., 2001). In the illite
polytype analysis method, the inability to physically
isolate diagenetic/authigenic illite from detrital illite is
an obstacle that can be circumvented to obtain the
crystallization ages of the secondary illite population.
Advanced applications of the illite polytype analysis
method have facilitated dates for the more distributed
deformation of low metamorphic grade folds (Fitz-Diaz
and van der Pluijm, 2013) and constrained the dates for
paleo-hydrologic reservoirs and pathways by the use of
hydrogen isotopes (Boles et al., 2015; Haines et al.,
2016). Additionally, Warr et al. (2016) proposed a
similar age analysis technique to date smectite forma-
tion. Clauer et al. (2013) compared the K/Ar and40Ar/39Ar geochronologic methods used in illite age
analysis and concluded that 40Ar/39Ar dating has a
greater potential ability to date tectono-thermal activities
and to deal with mixtures of multiple population illitic
materials due to the fine grain sizes and limited sample
quantities that are inherent to such studies. The
conditions in shallow crustal settings are ideal for illite
polytype analysis because the mineralization tempera-
tures for authigenic or diagenetic illite formation were
likely the highest temperatures experienced by the rocks
before exhumation. Constraining the temperature-time
history of a natural sample is critical to first ensure that a
temperature sufficient for neoformation was reached and
second because the Ar geothermometer in mica is
thermally reset at temperatures >300ºC (Wijbrans and
McDougall, 1986; Verdel et al., 2012) and illite is
resistant to stable isotopic re-equilibration at P-T
conditions lower than the formation conditions (Savin
and Epstein, 1970; Morad et al., 2003).
Various quantitative X-ray powder diffraction
(Q-XRPD) methods constrain the proportions of illite
polytypes and follow the tradition of Velde and Hower
(1963) and Maxwell and Hower (1967). Some techni-
ques directly compare the characteristic peaks
(Tettenhorst and Corbato, 1993; Dalla Torre et al.,
1994; Grathoff and Moore, 1996; Zwingmann and
Mancktelow, 2004), while others compared natural
samples to synthetic diffraction patterns using forward
model algorithms, such as WILDFIRE# (Reynolds,
1993; Grathoff and Moore, 1996; Ylagan et al., 2002;
Figure 1. X-ray diffraction patterns of 1Md, 1M, and 2M1 illites.
Vol. 66, No. 3, 2018 Direct fault rock dating: Analytical techniques 221
Solum and van de Pluijm, 2007; Haines and van der
Pluijm, 2008). These efforts have used both mathema-
tical and graphical methods to optimize the fits between
the model and natural samples. Similar to the graphical
matches of simulated patterns, workers have mixed end-
member polytype standards with good success (Boles et
al., 2015). Others still have proposed crystal thickness
distribution analyses using high resolution transmission
electron microscopy (TEM) or X-ray diffraction (XRD)
(Uhlik et al., 2000; Dukek et al., 2002). Whole-pattern
matching Rietveld analysis has been developed for
decades, but has only been recently applied to illite
polytype analysis and represents a more inclusive
approach to quantification that also allows more diverse
compositions (Rietveld, 1967, 1969).
The purpose of the present study was to compare the
utility of three Q-XRPD techniques as used in practical
applications of illite polytype quantification. The ratios
of 1Md/2M1 polytypes for synthetic mixtures were
quantified using i) models in a WILDFIRE# generated
library, ii) end-member standards, and iii) Rietveld
analysis and then to confirm the polytypes using TEM.
METHODS
Sample description and grain size separation
Synthetic mixtures of 1Md and 2M1 illite that were
spiked with kaolinite as an interference phase were used
to illustrate the illite polytype analysis method. Mineral
reference samples were used to create synthetic mixtures
and for end-member matching. Several particle-size
fractions of different reference samples obtained from
the Source Clays Repository of The Clay Minerals
Society were tested for use as end-members, which
included IMt-1, IMt-2, and ISCz-1. The sample used as a
reference for the 1Md polytype was the 0.05�0.2 mmsize fraction of sample IMt-1 from Silver Hill, Montana,
USA. The 0.05�0.2 mm size fraction was chosen
because it is free of peak overlap from non-illite phases.
The reference material for the the 2M1 polytype was the
<2 mm fraction of a pure muscovite from the State of
Minas Gerais, Brazil. The kaolinite reference material
was the <2 mm fraction of the American Petroleum
Institute (API) reference series H-1 from Murfreesboro,
Arkansas, USA (Keller and Haenni, 1978). Three
synthetic mixtures were created using various propor-
tions of these reference samples. Synthetic mixture 1
(hereafter referred to as SM1) contained 25% kaolinite,
25% 1Md illite, and 50% 2M1 illite by weight. Synthetic
mixture 2 (hereafter referred to as SM2) contained 25%
kaolinite, 50% 1Md illite, and 25% 2M1 illite by weight.
Synthetic mixture 3 (hereafter referred to as SM3)
contained 10% kaolinite, 80% 1Md illite, and 10% 2M1
illite by weight. A natural-fault gouge sample was
chosen to illustrate the impact of the application of the
methods on 40Ar/39Ar geochronology. The fault gouge
sample was collected from the surface trace of the North
Anatolian Fault Zone near Gerede, Turkey and is
designated as sample G2. This sample was thoroughly
characterized and stable isotopic analyses and 40Ar/39Ar
dates were reported in Boles et al. (2015). In order to
avoid surface alteration, the G2 sample was collected
0.5 m beneath the surface and it was hand-crushed by
percussion in an agate mortar and pestle to prevent
crystal comminution or induced strain. The sample was
then dispersed in deionized water using an ultrasonic
bath for 5�15 minutes and washed to remove salts.
Sodium pyrophosphate was added to neutralize surface
charge and inhibit flocculation. The clay-size particle
fraction was extracted from the bulk clay materials by
sedimentation using Stoke’s Law calculations and four
such fractions were separated from sample G2, namely,
2.0�1.0 mm (coarse) , 1 .0�0.2 mm (medium),
0.2�0.05 mm (fine), and <0.05 mm (very fine), to create
a robust mixing line for later multivariate regression
analysis. Samples were dried under a fume hood at
<50ºC.
Transmission electron microscopy (TEM) and particle-
size analysis
In order to confirm a 1Md-2M1 illite polytype end-
member system and to understand the illite population
distributions across the different grain size fractions, the
natural fault gouge sample G2 was investigated using
TEM and laser particle-size analysis. For TEM sample
preparation, small vessels were filled with the powdered
samples and carefully taped on the side to orient the clay
minerals. After a sample was impregnated, it was cut
using a focused ion beam (FIB) device (FEI
FIB200TEM; for more information see Wirth, 2009).
Both the high and low resolution TEM work was
conducted at the GFZ Potsdam facility using a FEI
Tecnai G2 F20 X-Twin transmission electron micro-
scope (TEM/AEM) equipped with a Gatan Tridiem
energy filter, a Fischione high-angle annular dark field
detector (HAADF), and a JEOL energy dispersive X-ray
ana lyzer (EDS) (JEOL USA, Inc . , Peabody,
Massachusetts, USA).
Laser particle-size analysis of the four G2 size
fractions was conducted at the University of Potsdam
using a Sympatec HELOS BR laser diffraction analyzer
(Sympatec GmbH, Clausthal-Zellerfeld, Germany) using
a measuring zone to insert dry/wet dispersers or sample
couplers in order to determine particle sizes between 0.1
and 875 mm.
X-ray diffraction analysis
X-ray analyses were conducted using a Rigaku
Ultima IV diffractometer (Rigaku Corporation, Tokyo,
Japan) used in Bragg-Brentano geometry with CuKaradiation at 40 kV and 44 mA in the Electron Microbeam
Analysis Laboratory (EMAL) at the University of
Michigan. Testing of the Rietveld results was conducted
by analysis of the same samples using a PANalytical
222 Boles, Schleicher, Solum, and van der Pluijm Clays and Clay Minerals
Empyrean diffractometer (Malvern Panalytical,
Westborough, Massachusetts, USA) at the Helmholtz-
Center Potsdam, GeoForschungsZentrum (GFZ) with
CuKa radiation at 40 kV and 40 mA and various slits
were used on both machines.
Qualitative analysis
Oriented slides for qualitative analysis were made by
air drying aqueous suspensions with an average sample
density of 5 mg/cm2. Qualitative measurements were
obtained over the range 2�80º2y with a step size of
0.05º2y and a 1º2y/minute scan rate.
Quantitative analysis (Q-XRPD)
Three Q-XRPD methods were compared in this study
and graphical matching was performed using WF for
natural end-member standards and whole-pattern
Rietveld analysis using BGMN1. In order to gain a
sufficiently random distribution of the powdered sam-
ples, the top-loading method was used at the University
of Michigan and the surface was retouched using a sharp
edge to induce roughness. The back-loading method was
u s e d a t t h e H e l m h o l t z - C e n t e r P o t s d a m ,
GeoForschungsZentrum (GFZ).
WILDFIRE# (WF) Model End-member library
The computer program WILDFIRE# generates 3D
diffraction forward models for pure and interlayered clay
minerals (Reynolds, 1993). Along with inputs of
machine geometric parameters, a user can vary layer
rotational disorder, octahedral cation occupancy, chemi-
cal substitutions, crystallographic orientation, and crys-
tallite thickness. Polytype quantification using
WILDFIRE# was illustrated by Grathoff and Moore
(1996), Ylagan et al. (2002), Solum and van der Pluijm,
2007, Haines and van der Pluijm (2008), and others.
Similar to the just cited authors, 695 variations of 1Md
illite and 20 variations of 2M1 illite were generated in
the present study as candidate end-member polytype
matches to natural samples. The parameters used to
generate the patterns in the libraries are shown in
Tables 1 and 2. These libraries are included in Figure S1
and Table S1 (available in the Supplemental Materials
section, deposited with the Editor-in-Chief and available
a t h t t p : / / www . c l a y s . o r g / J OURNAL / J o u r n a l
Deposits.html) of this manuscript as a reference for new
users with the caveat that the curves should be
regenerated using geometric parameters that are specific
to their diffractometer for the best results. The
diffractometer values used to generate the patterns in
the libraries were based on a divergence slit of 2º, a
goniometer radius of 25 cm, Soller slits of 4º and 1º, a
sample length of 4.5 cm, and a quartz reference intensity
of 1000 counts per second.
A simple approach to quantify polytypes in a natural
sample using WF generated libraries is to graphically
compare a natural sample diffractogram to a composite
diffractogram produced by combining 1Md and 2M1
patterns in various proportions using the equation:
Wp = Ax + By + Cz (1)
where Wp is the resultant sum of the 1Md and 2M1
combined WF patterns and a linear background, A is the
intensity of the 2M1 WF-generated pattern for a single
step in º2y, x is the proportion of 2M1, B is the intensity
of the 1Md WF-generated pattern for a single step in º2y,
Table 1. Parameters used for 1Md illite pattern generation (695 patterns).
Parameter Explanation Values
Water Layer Water in expandable interlayers 0, 1, 2Pex Fraction of expandable interlayers 0.1, 0.3%CV Percentage of cis-vacant layers (describes octahedral occupancy) 0, 50, 100DFD Defect free distance, mean and maximum 1-5, 4-20Dol Dollase Factor 0.7, 0.8, 0.9, 1.0P0 Probability of zero degree rotation 0.33, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0
Table 2. Parameters for 2M1 illite pattern generation (20 patterns).
Parameter Explanation Values
K Number of K atoms per SiO4 0.7Fe Number of Fe atoms per SiO4 0.1N1 Number of unit cells along X 60N2 Number of unit cells along Y 30Del Minimum number of continuous interlayers 5N3 Number of unit cells along Z 10, 15, 20, 25, 30Dollase Dollase Factor 0.8, 0.85, 0.9, 0.95, 1.0
Vol. 66, No. 3, 2018 Direct fault rock dating: Analytical techniques 223
y is the proportion of 1Md, and C is an arbitrary linear
background constant scaled using z to account for
background variations between modeled and measured
patterns. An example spreadsheet of such a mixing
procedure is included in Table S2 (available in the
Supplemental Materials section) of this manuscript.
A more robust alternative to manually selecting end-
members for graphical matching, which is cumbersome
and has so many end member options (around 14,000
possible combinations), is to run a least squares
algorithm for first pass identification. The MATLAB
least-squares algorithm is included in Table S3 (avail-
able in the Supplemental Materials section) performs a
search of the WILDFIRE#-generated end-member
libraries that are included in Figure S1 and Table S1
and returns best fit end-members and their relative
proportions. Peaks chosen for fitting should be selected
judiciously in order to avoid peak overlap of non-illite
peaks with an emphasis on polytype differentiation (i.e.
hkl reflections). Non-illite peaks invalidate the least
squares calculation (the routine minimizes w2, which can
yield graphically nonsensical results in the presence of
extraneous peaks). In practice, this often means match-
ing the polytype specific hkl reflections in the 16�44º2yrange while excluding any chlorite, calcite, or feldspar
that may occur. Empirical uncertainty estimates were on
the order of �7�8% for our synthetic sample set using
this method.
Figure 2 illustrates the use of the least-squares
algorithm on synthetic sample mixture SM1, but
excludes the º2y ranges 20.25�22.5, 24.5�25.3, and
30.5�34 to avoid the non-clay phases discussed above.
The SM1 synthetic mixture has a 1Md/2M1 ratio of 1:3
and the algorithm predicts a 1Md abundance of
1Md/(1Md+2M1) = 30%. An iterative approach can be
applied with a least-squares calculation that suggests
possible end-members and is followed by graphical
fitting using a mixing spreadsheet. This approach was
applied in the present study. A distinct advantage of the
WILDFIRE# libraries is the relative ease of calculating
patterns with different structural parameters. The
breadth of an end-member library will be limited by
the source clays, preparation time, etc.
End-member Natural Standards (STD)
The technique for End-member Standards Matching
(STD) is similar to the WF technique except that natural
as opposed to synthetic diffractograms are used as input.
The motivation to use natural 1Md and 2M1 illite
polytype standards instead of patterns calculated using
a diffractogram generator is two-fold: i) the use of
natural end-members with a similar origin and grain size
as the sample under investigation allows a good fit to
many of the structural parameters inherent to the
mineral, and ii) by measuring the end-members and the
sample using the same diffractometer and optical setup,
the geometric characteristics, X-ray intensity, and back-
ground subtleties unique to a particular diffractometer
can be matched. When the end-member standards are
measured, the diffractograms are mixed to create a
composite diffractogram (using equation 1) and are
graphically fitted to the unknown sample to estimate the
relative proportions of 1Md and 2M1. Uncertainty
estimates were less than 5% for our synthetic sample
set using this method. The mixing spreadsheet in
Table S2 (in the Supplementary Materials section) can
be used for end-member mixing in addition to
WILDFIRE# pattern mixing.
Rietveld Refinement using BGMN1
The third method used for polytype quantification
was developed for structure refinement and structure
Figure 2. Illustrated use of least-squares algorithm on synthetic sample SM1.
224 Boles, Schleicher, Solum, and van der Pluijm Clays and Clay Minerals
solution in the absence of single crystal specimens
(Rietveld, 1967, 1969). BGMN1 is a powerful quanti-
tative powder diffraction modeling system that was
introduced to separate the influences of the experimental
setup from the contribution of the measured sample to
the diffraction pattern and is similar to other programs,
such as Topas, Profex, or AutoQuan (e.g. Cheary and
Coelho, 1992), and BGMN1 allows users to quantita-
tively assess the proportions of known mineral phases in
an unknown mixture (Bergmann et al., 1998). Control
files that define the mineral structure include various
parameters that can be constrained to known values or
allowed to vary in order to maximize the potential for
achieving a good fit. Parameters that were allowed to be
optimized (in the same way for each synthetic mixture)
by the software in the present study included variables
that control peak broadening due to crystallite size and
microstrain (B1, K1, and K2), an isotropic or anisotropic
scaling factor (GEWICHT), and the parameter that
controls the background fit (RU). The structure files
that were used in the present study are included in
Table S4; a structure file for a 1Md illite with a tv site
yielded robust and stable results and was, therefore,
preferentially utilized here, although cv-illite could also
be incorporated into such a test (available in the
Supplemental Materials section). The kaolinite and
1M-illite models used here utilize an empirical peak
broadening approach to model disorder that is a BGMN-
specific technique (Bergmann and Kleeberg, 1998).
Uncertainty estimates are also important assessment
tools. BGMN1 returns a number of uncertainty esti-
mates, which can help understand the validity of a model
fit. These estimates include various R-factors (reliability
factors) and the Durban-Watson statistic. Low R-factors
do not mean that the quantification is accurate but R
factors >5% are a good indication that the fit is of poor
quality (Toby, 2006). The estimated accuracy of the
phase content measurements can be as great as ~2% for
each phase, but such accuracy depends on a number of
factors such as the number of phases, kinds of phases,
quality of models, and user training (Ufer et al., 2008;
Kleeberg, 2009; Kaufhold et al., 2012; Dietel, 2015).
Uncertainty estimates based on errors between the
calculated and real 2M1 to 1Md illite ratios from a
series of standards are discussed below.
40Ar/39Ar geochronology
Ar-dating was conducted at the Noble Gas Laboratory
at the University of Michigan using the encapsulation
method (van der Pluijm and Hall, 2015). The Scherrer
thicknesses were calculated from the full-width at half
maximum (FWHM) of the illite 001 peak of each G2
size fraction to differentiate between the use of the recoil
and retention ages (Fitz-Dıaz et al., 2013) and the recoil
(i.e. total gas) ages.
RESULTS AND DISCUSSION
TEM and grain size distribution analysis
TEM investigation of the coarse size fraction of
sample G2 provided direct imagery of both 1Md and 2M1
illite polytypes (Figure 3). Light- and dark-field images
show the plate-like morphology of the illite crystallites,
which taper toward the edges as well as accessory
phases, such as quartz. Lattice-fringe images and
Selected Area Electron Diffraction (SAED) patterns
clearly distinguish between well-ordered 2M1 and
disordered 1Md and the poorly-ordered illite exhibits
the streaking of non-001 reflections.
The grain size abundance histograms for coarse and
medium size fractions of sample G2 show a local
maximum near 3 mm in the coarse fraction histogram as
well as positively skewed tails in both histograms that
likely indicate the presence of coarser, non-clay minerals
(Figure 4). This is corroborated by TEM imagery and
Q-XRPD patterns. A significant maximum between
1�2 mm likely represents coarse, detrital clay minerals
with a more subtle peak at ~1 mm in the medium grain
size fraction that represents the authigenic mineral
population. Indeed, the TEM light- and dark-field
images of sample G2 show 1Md crystallites with a
length of ~1 mm. The finest size fractions were outside
the instrument resolution and, therefore, could not be
compared. Most likely, the grain size separates are not
continuous grain size arrays with Gaussian distributions,
but rather contain two dominant grain sizes with one size
composed of detrital grains and the other size composed
of authigenic grains mixed in various proportions in the
different grain size fractions.
X-ray diffraction analysis
X-ray diffraction patterns of the air dried and the
ethylene glycolated <2.0 mm fraction of the G2 fault
gouge sample revealed minor swelling of the chlorite
phase (in the glycolated sample). The sample also likely
had an R0 chlorite (0.8�0.9)/smectite ordered structure
(as identified using the 002/002 chl/sm peak listed in
table 8.4 of Moore and Reynolds, 1997) and discrete
chlorite (Figure 5). Similar chlorite mixtures were
identified in the Punchbowl Fault (Solum, 2003) and
the SAFOD borehole (Schleicher et al., 2008). These
studies concluded that such clays can occur at depth and,
therefore, do not necessarily indicate exhumation-related
processes or near-surface weathering. No mixed-layer
illite-smectite was observed. Illite and chlorite were the
major clay minerals in the sample. Further qualitative
assessment of sample G2 identified quartz and calcite.
Using the three quantitative methods described above
and qualitative characterizations of sample G2, the total
content of each mineral was calculated and listed in
Table 3. As mentioned above, the WF and STD methods
reported polytype abundance as a proportion of total
illite, whereas the Rietveld method reported the
Vol. 66, No. 3, 2018 Direct fault rock dating: Analytical techniques 225
abundance of each individual mineral phase as a
proportion of the total mixture. The proportions of
polytypes in the total illite sample was also reported
using the Rietveld method.
The fit of the models (Figure 6) to the SM1, SM2, and
SM3 sample patterns using each Q-XRPD technique (in
gray) were compared to the measured sample patterns (in
black) and graphically illustrated the various uncertainty
estimates associated with each method. The contribution
of 1Md in the Rietveld models to the diffraction pattern
(Figure 6) is displayed as a dashed line. The WF models
successfully fit the background as well as the key peaks
at 20, 27, and 35º2y, but matching all of the hkl peaks
remains a challenge. STD provided a satisfactory fit for
the illite polytypes and effectively ‘‘sees through’’ the
contaminant phases. The errors calculated for the STD
technique were very low, but this was a best-case
scenario because the same reference clays used to match
the patterns were used to create the synthetic mixtures.
Rietveld refinement is the most successful method to
replicate pattern data, yields accurate results, and
provides robust error estimates; however, some
Rietveld matches were poor and the calculated errors
from the standard matches indicated that the Rietveld
refinement errors were about 6%. The results for each
synthetic model fit are reported in Table 4. Even though
the most extensive laboratory preparations were
required, the BGMN_1 (based on patterns collected at
the University of Michigan) and BGMN_2 (based on
patterns collected at GFZ Potsdam) results in Table 3
Figure 3. Light- and dark-field transmission electron micrographs of sample G2 coarse fraction to indicate the morphology of illite
crystallites: (a) illite and quartz particles; (b) illite particles; lattice-fringe images and selected area diffraction patterns of (c) 1Md
illite, and (d) 2M1 illite.
226 Boles, Schleicher, Solum, and van der Pluijm Clays and Clay Minerals
were repeatable for different experimental setups with
minor variations. The interlaboratory variations may be
accounted for by the different sample preparation
techniques (i.e. different roughness and preferred
orientation characteristics). The use of a spray dryer to
prepare samples would likely minimize these differ-
ences. Appendix S5 (available in the Supplemental
Materials section) includes the model fits used in the
present study. A visual comparison of the model fits to
the synthetic samples for each Q-XRPD technique
highlights the various uncertainties associated with
each approach.
The calculated illite patterns used for matching with
WF were as follows: columns 9 and 74 in the 2M1 and
1Md libraries were used, respectively, for all synthetic
mixtures; 2M1 column 5 and 1Md column 88 were used
for G2-C; 2M1 column 5 and 1Mdd column 33 were used
for G2-M; and 2M1 column 5 and 1Md column 27 were
used for G2-F and G2-VF (parameters reported in
Table 5). The chosen calculated end-member was
allowed to vary between grain sizes for a single sample
because grain size can induce peak broadening at very
small grain sizes.
Error estimates
Quantification of the errors associated with each of
the three Q-XRPD techniques is essential in order to
estimate the errors in the ages that are calculated using
illite age analysis (e.g. Pevear, 1992). To calculate these
errors, the difference between the 1Md and 2M1 illite
concentrations from the best matches of each technique
were compared to the actual phase concentrations in the
three synthetic mixtures (Table 6). Quantification errors
using the WF technique ranged from 0 to 9% with an
average of approximately 5%. Errors from the STD
technique ranged from 0 to 2% with an average of 1%.
Rietveld refinement errors ranged from 5 to 7% with an
average of 6%. The errors for the STD technique
represent a best-case scenario because the same refer-
ence materials used to create the synthetic mixtures were
used in the matching process.
40Ar/39Ar geochronology
The sample G2 size fractions decrease in age with
decreasing grain size, as expected, and the 1Md illite
concentration increases. Radiometric ages for the four
measured G2 samples were 90.33 � 0.84 Ma for the
coarse fraction, 89.43 � 0.49 Ma for the medium
fraction, 73.55 � 0.31 Ma for the fine fraction, and
68.4 � 0.37 Ma for the very fine fraction. Multivariate
linear regression was used for the age analyses and the
other unmixing procedures (Boles et al., 2015). The
correlations between isotopic composition and 1Md/2M1
abundance ratios were calculated using both a modified
York-type regression analysis (Mahon, 1996) and a
Bayesian-type regression analysis (Staisch, 2014) and
yielded unmixing lines that were used to extrapolate to
the end-member 1Md and 2M1 illite population values.
In the York least-squares linear regression, the following
assumptions were made about the slope and intercept
Figure 4. Grain-size abundance histograms for coarse and
medium sample G2 size fractions.
Figure 5. X-ray diffraction patterns of the <2 mm size fraction of sample G2 fault gouge air dried and glycolated.
Vol. 66, No. 3, 2018 Direct fault rock dating: Analytical techniques 227
values: the values represent a Gaussian distribution, are
independent, and are uncorrelated. If this approach is
utilized, despite the high accuracy of the independent
errors of each of the x and y datasets and the excellent
correlations (high R2), the unochron error can lead to a
large uncertainty in the age if the range in 1Md/2M1
abundance ratios is small (Pana and van der Pluijm,
2015). Samples that exhibit a large range in 1Md/2M1
Table 3. The Q-XRPD results for WILDFIRE# (WF), End-member Standards Matching (STD), and Rietveld (BGMN)methods for each size fraction of sample G2, where C is coarse (2.0�1.0 mm), M is medium (1.0�0.2 mm), F is fine(0.2�0.05 mm), and VF is very fine (<0.05 mm). Two columns are shown for each Rietveld refinement, one with all phasesand the other shows only the concentrations of 2M1 and 1Md illite.
Sample Phase ————————— Wt.% by Q-XRPD Method ————————WF STD — BGMN_1 — – BGMN_2 –
G2_C
2M1 illite 91 95 67.5 97 69 961Md illite 9 5 2.4 3 3 4Chlorite – – 8.2 – 4 –Quartz – – 19.7 – 21.7 –Calcite – – 2.2 – 2.3 –
G2_M
2M1 illite 79 85 54.2 90 47.1 711Md illite 21 15 6.1 10 19.4 29Chlorite – - 35.7 – 32.2 –Quartz – - 3.3 – 3.2 –Calcite – - 0.7 – 0.4 –
G2_F
2M1 illite 62 65 58.5 61 58 601Md illite 38 35 36.9 39 38 40Chlorite – – 4.3 – 2.5 –Quartz – – 0 – 0 –Calcite – – 0.3 – 1.5 –
G2_VF
2M1 illite 41 45 48 49 50.6 521Md illite 59 55 50.5 51 47.3 48Chlorite – – 0 – 0 –Quartz – – 0 – 0 –Calcite – – 1.5 – 2 –
Figure 6. Model (WF, STD, BGMN) fits (in gray) to SM1, SM2, and SM3 sample X-ray diffraction patterns (in black) using Q-XRPD
techniques to graphically indicate the estimated uncertainties of each technique.
228 Boles, Schleicher, Solum, and van der Pluijm Clays and Clay Minerals
abundance ratios across the grain size separates should,
therefore, be selected to limit this problem. Hence, the
York-type multivariate regression analysis was used in
this study.
The uncertainties associated with each technique
(Figure 6) contributed to the uncertainty estimates of
individual data points (brackets) and of the York-type
regression line (and corresponding fields) of the mixing
Table 4. The Q-XRPD results for synthetic mixtures.
Q-XRPD Method Phase Weight fraction, Synthetic MixtureSM1 SM2 SM3
Measured Weight Fraction
1Md illite 0.25 0.5 0.82M1 illite 0.5 0.25 0.1Kaolinite 0.25 0.25 0.1
Measured Weight Fraction, illite only
1Md illite 0.33 0.67 0.892M1 illite 0.67 0.33 0.11Kaolinite – – –
WF
1Md illite 0.4 0.67 0.842M1 illite 0.6 0.33 0.16Kaolinite – – –
STD
1Md illite 0.33 0.65 0.892M1 illite 0.67 0.35 0.11Kaolinite – – –
Rietveld Refinement (BGMN1)
1Md illite 0.29 0.53 0.812M1 illite 0.45 0.19 0.05Kaolinite 0.25 0.28 0.13
Rietveld Refinement, illite only (BGMN1)
1Md illite 0.39 0.74 0.942M1 illite 0.61 0.26 0.06Kaolinite – – –
Rietveld Refinement (BGMN2)
1Md illite 0.30 0.53 0.772M1 illite 0.47 0.16 0.15Kaolinite 0.23 0.29 0.07
Rietveld Refinement, illite only (BGMN 2)
1Md illite 0.39 0.73 0.842M1 illite 0.61 0.27 0.16Kaolinite – – –
Table 5. WILDFIRE parameters used for model parameters in this study.
2M1
Column in end-memberlibrary
K Fe N1 N2 N3 Del Dollase
9 0.7 0.1 60 30 10 5 0.95 0.7 0.1 60 30 30 5 0.85 0.7 0.1 60 30 30 5 0.85 0.7 0.1 60 30 30 5 0.8
1Md
Column in end-memberlibrary
Waterlayer
% expandable %CV DFD Dollase P0
74 2 0.1 0 43210 0.7 0.488 2 0.1 50 43210 0.7 133 0 0.1 50 43210 0.7 0.3327 0 0.1 0 43210 0.7 0.5
Vol. 66, No. 3, 2018 Direct fault rock dating: Analytical techniques 229
lines (Figure 7). Significantly, all the methods produced
statistically identical results for the ages of end-members
(approximately 42.5 to 43.5 Ma), but the uncertainty
estimate was most robust using the STD method and
least robust using the WF models. One should re-
emphasize, however, that the small errors associated
with the End Member Standard Method used in this
study represent a best-case scenario. In addition, note
that all methods significantly and effectively model illite
polytypism in the presence of non-illite peaks. As long
as the isotopic signal being investigated is not sig-
nificantly influenced by the presence of other phases,
WF and STD methods remain effective analytical
techniques for the illite polytype analysis method. If
other phases influence the isotopic signal, the Rietveld
method should be used.
CONCLUSIONS
The three analytical techniques of WILDFIRE# (WF)
modeling, End-member Standards Matching (STD), and
Rietveld refinement using BGMN1 offer effective
approaches to quantify the proportions of illite polytypes
for use in illite polytype and illite age analyses for
application to clay-rich fault gouges. Each method can
accurately model illite polytypes in the presence of non-
illite peaks as long as sample preparation and X-ray
diffraction best practices are followed. In order of
increased statistical certainty and robustness, the
approaches rank as follows: WF modeling < Rietveld
refinement using BGMN1 < STD. The question,
however, is not which method is the best for rock
dating, but that all three techniques lead to similar
results.
In summary, the STD method is recommended as the
simplest method for new practitioners of the illite
polytype analysis method to use for dating or stable
isotopic fingerprinting of authigenic illite, provided that
the type of 1Md illite used as a reference material is
sufficiently similar to the illite in the natural samples. If
multiple 1Md illite types are present in a set of samples,
then the WF approach will likely be the most appropriate
because of the larger number of 1Md patterns in the WF
library. If significant concentrations of non-clay and/or
non-illite phases are present, then Rietveld refinement is
recommended for its improved statistical robustness,
although simple fitting approaches can also incorporate
the X-ray patterns of other minerals. If other mineral
Table 6. Calculated errors from quantification of synthetic mixtures.
Q-XRPD Method Phase ——————— Measured error ———————SM1 SM2 SM3 AVE
WF1Md illite 0.07 0.00 0.09 0.052M1 illite 0.07 0.00 0.05 0.04
STD1Md illite 0.00 0.02 0.00 0.012M1 illite 0.00 0.02 0.00 0.01
Rietveld Refinement, illite only1Md illite 0.06 0.07 0.05 0.062M1 illite 0.06 0.07 0.05 0.06
Figure 7. Plots of e(lt�1) vs. % 2M1 illite with York-type
regression lines and corresponding mixing line fields for total
gas ages using WF, STD, and Rietveld methods (e(lt�1) is a
fundamental expression in the Ar/Ar age equation that relates
the decay constant, l, to time, t. See van der Pluijm and Hall,
2015, for more detail about the age equation.).
230 Boles, Schleicher, Solum, and van der Pluijm Clays and Clay Minerals
populations contribute to the isotopic signal under
investigation, then quantifying all of the phases is
perhaps most important. BGMN1 provides excellent
model fits in addition to a decreased user dependency
and provides interlaboratory repeatability (although a
much greater learning curve is required). Further
improvements to the illite polytype analysis method,
such as the use of methods from other isotopic systems
(e.g. O, H, Hg, B, or Sr), to trace diagenetic or
deformation-related fluids in deformed upper crust is
anticipated.
ACKNOWLEDGMENTS
The authors thank Jasmaria Wojatschke for developingthe Rietveld capabilities at the University of Michigan andRoss Maguire and Trevor Hines for developing the Matlabcoding for the least-squares fitting algorithm. A MATLABscript for generating Bayesian-type linear regressions for xand y data with the respective uncertainties can berequested from Eric Hetland at the University of Michigan([email protected]). Heide Kraudelt is thanked for thelaser particle size analysis data and Richard Wirth for theTEM analyses. The research was supported by the NationalScience Foundation, most recently under grant EAR-1629805. This manuscript was greatly improved by thecomments of Joseph W. Stucki, Eric Ferrage, Steve Hillier,and two anonymous reviewers.
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Ms. 1161; AE: E. Ferrage)
232 Boles, Schleicher, Solum, and van der Pluijm Clays and Clay Minerals