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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:

[email protected]

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


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.


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


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.


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.


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.


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


STD


Rietveld Refinement (BGMN1)


Rietveld Refinement, illite only (BGMN1)


Rietveld Refinement (BGMN2)


Rietveld Refinement, illite only (BGMN 2)


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


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.).


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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(Received 24 January 2017; revised 12 April 2018;

Ms. 1161; AE: E. Ferrage)


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