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Feldspar and orthopyroxene piezometers constrained using quartz–feldspar and olivine–orthopyroxene mineral pairs from natural mylonites

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Feldspar and orthopyroxene piezometers constrained using quartz–feldspar and olivine–orthopyroxene mineral pairs from natural mylonites

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Differential stress magnitude is a fundamental parameter in the study of geodynamic processes in the continental lithosphere, and is typically estimated in quartz- and olivine-dominated lithologies using recrystallized grain size piezometers. Here we evaluate the piezometric relationships in natural mylonites with mineral pairs of quartz–feldspar and olivine–orthopyroxene, which commonly coexist in deformed crustal and mantle rocks, respectively. To analyze mineral pairs, we measured dynamically recrystallized grain sizes in both phases that deformed under approximately isoviscous conditions. Using the experimentally calibrated piezometers for quartz and olivine, we develop piezometric relationships for feldspar and orthopyroxene. These new feldspar and orthopyroxene piezometers reasonably predict grain size relationships observed for mineral pairs from naturally deformed lithospheric shear zones. Combining our naturally constrained datasets with the existing experimental datasets for feldspar and orthopyroxene, we also derive piezometers that are consistent with the wattmeter model and with observations from other studies of mylonitic rocks. Our results provide an alternative for estimating stress in rocks such as granulites and pyroxenites, for which the quartz and olivine piezometers are unsuitable.
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Journal of Structural Geology 154 (2022) 104495
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Feldspar and orthopyroxene piezometers constrained using quartzfeldspar
and olivineorthopyroxene mineral pairs from natural mylonites
P.A. Speciale
a
,
**
, L. Tokle
b
, W.M. Behr
a
,
b
,
*
a
Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, 23 San Jacinto Blvd., Austin, TX, 78712, USA
b
Structural Geology and Tectonics Group, Geological Institute, Department of Earth Sciences, ETH Zürich, Sonneggstrasse 5, 8092, Zürich, Switzerland
ARTICLE INFO
Keywords:
Piezometry
Mylonites
Quartz
Feldspar
Olivine
Orthopyroxene
ABSTRACT
Differential stress magnitude is a fundamental parameter in the study of geodynamic processes in the continental
lithosphere, and is typically estimated in quartz- and olivine-dominated lithologies using recrystallized grain size
piezometers. Here we evaluate the piezometric relationships in natural mylonites with mineral pairs of
quartzfeldspar and olivineorthopyroxene, which commonly coexist in deformed crustal and mantle rocks,
respectively. To analyze mineral pairs, we measured dynamically recrystallized grain sizes in both phases that
deformed under approximately isoviscous conditions. Using the experimentally calibrated piezometers for quartz
and olivine, we develop piezometric relationships for feldspar and orthopyroxene. These new feldspar and
orthopyroxene piezometers reasonably predict grain size relationships observed for mineral pairs from naturally
deformed lithospheric shear zones. Combining our naturally constrained datasets with the existing experimental
datasets for feldspar and orthopyroxene, we also derive piezometers that are consistent with the wattmeter
model and with observations from other studies of mylonitic rocks. Our results provide an alternative for esti-
mating stress in rocks such as granulites and pyroxenites, for which the quartz and olivine piezometers are
unsuitable.
1. Introduction
The magnitude of differential stress in the continental lithosphere is
fundamental to our understanding of continental mechanics, but is un-
certain and frequently debated. Estimates of lithospheric strength pre-
dicted by ow laws for quartz (e.g., Luan and Paterson, 1992; Gleason
and Tullis, 1995; Hirth et al., 2001; Tokle et al., 2019), plagioclase (e.g.,
Dimanov et al., 1999; Xiao et al., 2002; Rybacki et al., 2006) and olivine
(e.g., Mei and Kohlstedt, 2000; Hirth and Kohlstedt, 2003; Keefner et al.,
2011), coupled with inversion of geophysical and geodetic data, form
the basis for models of geodynamic processes such as postseismic
relaxation (e.g., Freed et al., 2012) and global mantle convection (e.g.,
Landuyt et al., 2008). The relative strength of the crust and upper mantle
also has important implications for lithospheric seismicity (Maggi et al.,
2000; Jackson, 2002), the stability of mountain ranges and subducting
slabs (Burov and Diament, 1995; Burov and Watts, 2006), and the
localization of deformation into relatively narrow plate boundary shear
zones (e.g., Bürgmann and Dresen, 2008).
Methods of quantifying static stress state in the frictional regime
include borehole studies (e.g., Zoback et al., 1993) and indirect
geophysical methods such as shear wave splitting (e.g., Holt et al., 2013)
or earthquake focal mechanism inversions (e.g., Hardebeck and
Hauksson, 2001). In the viscous regime, empirically determined piezo-
metric relationships between stress and recrystallized grain size are the
most widely used methods for estimating stress. A recrystallized grain
size paleopiezometer (hereafter referred to simply as a piezometer) is an
inverse relationship between the recrystallized grain size (d) and the
differential stress (
σ
), or ow stress (Twiss, 1977):
d=K
σ
p,(1)
where K and p are empirically or theoretically determined constants.
Piezometers have been experimentally calibrated for a wide range of
earth materials, such as quartz (e.g., Mercier et al., 1977; Stipp and
Tullis, 2003), feldspar (Post and Tullis, 1999), olivine (e.g., Karato et al.,
1980; Ross et al., 1980; van der Wal et al., 1993), orthopyroxene (e.g.,
* Corresponding author.
** Corresponding author. Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, 23 San Jacinto Blvd., Austin, TX,
78712, USA.
E-mail addresses: pamela.speciale@utexas.edu (P.A. Speciale), leif.tokle@erdw.ethz.ch (L. Tokle), wbehr@ethz.ch (W.M. Behr).
Contents lists available at ScienceDirect
Journal of Structural Geology
journal homepage: www.elsevier.com/locate/jsg
https://doi.org/10.1016/j.jsg.2021.104495
Received 21 March 2021; Received in revised form 13 December 2021; Accepted 14 December 2021
Journal of Structural Geology 154 (2022) 104495
2
Ross and Nielsen, 1978; Linckens et al., 2014), halite (e.g., Guillope and
Poirier, 1979; Ter Heege et al., 2005) and calcite (e.g., Schmid et al.,
1980; Rutter, 1995; Barnhoorn et al., 2004).
The two most widely used piezometers are those calibrated for
quartz (Stipp and Tullis, 2003) and olivine (van der Wal et al., 1993),
due to the high abundance of these minerals in the crust and upper
mantle, respectively (Fig. 1). Application of these piezometers to natural
rocks commonly yields results that are consistent with independent es-
timates of crustal and mantle rheology (e.g., Vissers et al., 1997; Dijkstra
et al., 2002; Gueydan et al., 2005; Warren et al., 2008; Katayama et al.,
2009; Behr and Hirth, 2014; Chatzaras et al., 2015; Bernard and Behr,
2017; Bernard et al., 2019; Bose and Mukherjee, 2020; Feng et al., 2020;
Kohli and Warren, 2020). For example, Behr and Hirth (2014) found
that viscosities derived using the olivine piezometer of van der Wal et al.
(1993) and olivine ow laws were consistent with viscosities estimated
using geodetic observations of postseismic relaxation in the Mojave re-
gion of the western USA (e.g., Freed and Bürgmann, 2004; Thatcher and
Pollitz, 2008; Freed et al., 2012). Studies that employ the Stipp and
Tullis (2003) quartz piezometer and quartz ow laws yield geologically
reasonable strain rates and stress estimates for the middle crust that are
independently consistent with upper crustal friction laws (e.g., Behr and
Platt, 2011, 2013, 2014; Kidder et al., 2012). Furthermore, deformation
experiments performed on quartz (e.g., Stipp et al., 2006; Kidder et al.,
2016; Soleymani et al., 2020) and olivine (e.g., Tasaka et al., 2016;
Speciale et al., 2020) have repeatedly demonstrated that the piezome-
ters for these phases are robust and reproducible at experimental
conditions.
Feldspar and pyroxene are also important minerals in the continental
lithosphere, particularly in quartz- and olivine-poor lithologies such as
lower-crustal granulites and mantle pyroxenites. Reliable piezometric
calibrations for feldspar- and pyroxene-rich aggregates are necessary to
estimate stress from a wider variety of rock types and provide further
constraints on lithospheric rheology. However, extrapolations of the
feldspar (Post and Tullis, 1999) and orthopyroxene (Linckens et al.,
2014) piezometers to relevant geologic conditions yield stress-grain size
relationships that are inconsistent with the rock record (Fig. 1). For
example, the piezometric relationship developed by Post and Tullis
(1999) for feldspar predicts recrystallized grain sizes up to two orders of
magnitude smaller than quartz for a given stress (Fig. 1a), yet
observations of crustal mylonites commonly indicate a more modest
grain size difference between these phases (e.g., Schulmann et al., 1996;
Svahnberg and Piazolo, 2010). The viscosities of olivine and orthopyr-
oxene are thought to be similar in the mantle lithosphere (Bystricky
et al., 2016; Raterron et al., 2016); however, extrapolating the ortho-
pyroxene piezometer (Linckens et al., 2014) to grain sizes commonly
observed in moderate- to high-temperature mantle xenoliths (110 mm
for both olivine and orthopyroxene; e.g., Douglas et al., 1987) would
suggest that orthopyroxene is up to two orders of magnitude weaker
than olivine at lithospheric mantle conditions (Fig. 1b). This relation-
ship would predict that strain should strongly localize into orthopyr-
oxene, but this is inconsistent with observations of peridotite mylonite
microstructures (e.g., Skemer et al., 2010; Falus et al., 2011; Johanesen
and Platt, 2015; Dygert et al., 2019) and with several experimentally
calibrated ow laws (e.g., Mackwell, 1991; Bystricky et al., 2016).
The goal of this study is to use quartzfeldspar and olivine-
orthopyroxene mineral pairs from natural mylonites and
ultramylonites, along with the well established piezometers for quartz
(Stipp and Tullis, 2003) and olivine (van der Wal et al., 1993), to
calibrate new feldspar and orthopyroxene piezometers that are consis-
tent with observations from the rock record and laboratory experiments.
Our approach is to:
1) identify rocks from a wide range of locations and pressure-
temperature conditions in which both mineral phases are inter-
preted to have deformed under similar stress conditions;
2) measure the dynamically recrystallized grain sizes of both phases;
3) estimate the stress from the existing quartz or olivine piezometer;
and
4) derive a piezometer for feldspar or orthopyroxene.
In the following sections we outline these steps in greater detail,
compare the stress-grain size relationships observed in our samples to
those predicted by the existing empirical piezometers for feldspar and
orthopyroxene, and discuss the implications for estimating stress in
naturally deformed rocks.
2. Existing piezometric relationships
Below we provide a brief overview of the empirically derived
piezometric relationships for quartz, feldspar, olivine, and orthopyrox-
ene. The experimental conditions (e.g., temperature, conning pressure,
differential stress, conning media), recrystallized grain sizes, and
resulting piezometric parameters are listed in Table 1.
2.1. Quartz
Stipp and Tullis (2003) performed deformation experiments on as-is
(no water added and no drying prior to deformation) Black Hills
quartzite (~100
μ
m) in axial compression using a Griggs apparatus.
They observed microstructures consistent with dynamic recrystalliza-
tion via subgrain rotation and grain boundary migration (Regimes 2 and
3 of Hirth and Tullis, 1992), and found no temperature dependence on
their stress-grain size relationship over a wide range of experimental
temperatures. Additionally, Stipp et al. (2006) deformed Black Hills
quartzite in a Griggs apparatus in axial compression to investigate the
effect of water content on the Stipp and Tullis (2003) piezometer. They
found varying the water content did not affect the stress-grain size
relationship over their measured range of stress (34268 MPa) and grain
size (3.219.9
μ
m). The samples deformed by Stipp et al. (2006) exhibit
microstructures characteristic of recrystallization by bulge nucleation,
subgrain rotation, and grain boundary migration (Regimes 1, 2 and 3 of
Hirth and Tullis, 1992).
Fig. 1. Existing empirical piezometers for a) quartz (ST03: Stipp and Tullis,
2003; C17: Cross et al., 2017) and feldspar (PT99: Post and Tullis, 1999), and b)
olivine (VDW93: van der Wal et al., 1993; KTF80: Karato et al., 1980) and
orthopyroxene (L14: Linckens et al., 2014). Solid lines represent the range of
stress and grain size used to quantify the piezometric relationships. Dashed
lines represent the extrapolation of the piezometers.
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
3
2.2. Feldspar
Post and Tullis (1999) deformed ne-grained, hot-pressed (110
μ
m)
and natural albitic feldspar (~150
μ
m) from the Hale (Connecticut) and
Tanco (Ontario) pegmatites, respectively, in a Griggs apparatus in both
axial compression and general shear geometries to calibrate a piezo-
metric relationship for feldspar. They achieved similar mechanical re-
sults in both deformation geometries, and observed microstructures
indicative of recrystallization by bulge nucleation (Regime 1 of Hirth
and Tullis, 1992).
2.3. Olivine
van der Wal (1993, doctoral dissertation) investigated the stress-
grain size relationships in samples from axial compression experi-
ments on natural olivine aggregates, the Åheim and Anita Bay dunites
(900 and 100
μ
m, respectively), which were conducted by Chopra and
Paterson (1981, 1984) using a Paterson apparatus. van der Wal (1993)
demonstrated that the recrystallized grain size is largely independent of
temperature and water content over the range of measured conditions.
The olivine piezometer (van der Wal et al., 1993) combines the results of
moderate-stress (30300 MPa) experiments performed by Chopra and
Paterson (1981, 1984) and lower-stress (25120 MPa) creep experi-
ments reported by Karato et al. (1980). In addition, higher-stress
(120800 MPa) axial compression experiments performed on natural
olivine aggregates (Balsam Gap dunite) yielded stress-grain size re-
lationships consistent with the olivine piezometer (Speciale et al., 2020).
Thus, the olivine piezometer is constrained over a broad range of
experimental conditions.
2.4. Orthopyroxene
Linckens et al. (2014) dened a piezometric relationship for ortho-
pyroxene by combining measurements from experimental samples and
naturally deformed lherzolite xenoliths (Boullier and Gueguen, 1975;
Jin, 1995; Skemer and Karato, 2008). They conducted axial compression
deformation experiments in a Griggs apparatus on coarse-grained
(0.52 mm) olivine and orthopyroxene from San Carlos peridotite xe-
noliths, embedded in a ne-grained (~10
μ
m) matrix of olivine. Olivine
stresses were calculated using the olivine piezometer (van der Wal et al.,
1993). Assuming the stresses in olivine and orthopyroxene were similar,
the same stress was assigned to coexisting orthopyroxene in each
sample.
3. Methods
3.1. Sample selection criteria
To examine the relationships between recrystallized grain sizes in
quartzfeldspar- and olivineorthopyroxene-bearing samples for use in
calibrating new piezometers for feldspar and orthopyroxene, we iden-
tied natural samples (or regions within them) that satised four basic
criteria. Firstly, we sought out samples in which both phases of interest
(i.e., quartzfeldspar, olivineorthopyroxene) could be interpreted as
having dynamically recrystallized at approximately the same stress. This
required selecting regions that exhibited a) planar banding between the
two phases at the thin section scale (Fig. 2a and b); b) both phases in
contact, with unmixed bands of recrystallized grains between them
(Fig. 2c and d); and/or c) both phases locally banded in the recrystal-
lized tails of porphyroclasts (Fig. 2e and f). We specically avoided
conducting grain size measurements near pressure shadows or strain
caps around porphyroclasts (Kenkmann and Dresen, 1998; Passchier
and Trouw, 2005; Stipp and Kunze, 2008). Secondly, we only included
samples in which there was no evidence for post-deformational grain
growth (e.g., 120triple junctions, annealing of grain substructures;
Smith, 1948). Thirdly, we avoided samples/regions with mixed recrys-
tallized phases that may have experienced grain pinning (Evans et al.,
2001). Fourth, because grain growth may contribute to the steady-state
grain size during recrystallization (e.g., De Bresser et al., 1998, 2001;
Shimizu 1998, 2008; Austin and Evans, 2007, 2009), we measured
recrystallized grain sizes only in recrystallized clusters with thicknesses
at least three times the recrystallized grain size and avoided newly
nucleated grains on porphyroclast margins.
3.2. Sample suite
3.2.1. QuartzFeldspar mylonites
We examined eight thin sections of quartzfeldspar mylonites
(Table 2). Samples from the Betic Cordillera of southern Spain, and the
Whipple Mountains and Eastern Peninsular Ranges of the western USA
were collected by Whitney M. Behr. The other thin sections were ob-
tained from archived collections at The University of Texas at Austin,
with their source regions given in Table 2. Temperatures from studies
other than the authors are regional estimates.
The exhumed subduction complex of the southern Sierra Alhamilla
in the Betic Cordillera is associated with Miocene deformation at tem-
peratures of 350550 C (Behr and Platt, 2012). In the western USA,
metamorphic core complexes in the Whipple Mountains, NE Harquahala
Mountains, and Santa Catalina-Rincon Mountains record Late Creta-
ceous to Miocene extension at 300600 C (Perry, 2005; Behr and Platt,
2011; Pollard, 2014). The mylonitic zone along the transpressional
M´
erens Fault near the Ari`
ege valley in the Central Pyrenees records late
Variscan-Alpine deformation at 450600 C (Denѐle et al., 2008). Late
Cretaceous deformation during thrust faulting in the Eastern Peninsular
Ranges of California occurred at temperatures of 500600 C (Anderson,
1983).
Our quartzfeldspar samples are porphyroclastic mylonites and
ultramylonites (Fig. 3). Quartz commonly occurs either as lenticular
aggregates with grain aspect ratios up to 3:1, or undulating bands with
attened recrystallized grains oblique to the foliation. In all samples,
feldspar porphyroclasts are sub-round to moderately attened and are
plastically deformed; they are cut by zones of dynamically recrystallized
grains or have extended tails of recrystallized feldspar. However, in one
sample (WM3), some of the larger feldspar porphyroclasts are somewhat
blocky and exhibit domino-style fracturing (Fig. 3a, top-center). Ultra-
mylonite samples form well-segregated bands of quartz and feldspar
Table 1
Existing empirical piezometers for mineral pairs examined in this study.
Phase Media d (
μ
m)
σ
(MPa) P (GPa) T (C) log
10
K p RGS Measurement
a
Reference
Quartz MSC 346 36268 1.5 8001100 3.56 ±0.27 1.26 ±0.13 Root Mean Square Stipp and Tullis (2003)
Quartz MSC 561 34189 1.5 8001100 3.91 ±0.41 1.41 ±0.21 Root Mean Square Cross et al. (2017) (1
μ
m)
Quartz MSC 426 34189 1.5 8001100 4.22 ±0.51 1.59 ±0.26 Root Mean Square Cross et al. (2017) (0.21
μ
m)
Quartz NaCl 12 3501050 1.5 700850 1.89 ± 0.61 ± Linear Intercept Bishop (1996) (unpublished)
Feldspar NaCl 12.5 130480 1.5 900 1.74 ±0.04 0.66 ±0.07 Linear Intercept Post and Tullis (1999)
Olivine atm 25200 25120 0 15001700 3.92 ±0.20 1.18 ±0.11 Linear Intercept Karato et al. (1980)
Olivine gas 357 30300 0.3 11001650 4.18 ±0.01 1.33 ±0.09 Linear Intercept van der Wal et al. (1993)
OPx MgO 354 100500 1.0 11271277 2.65 ±0.15 0.76 ±0.001 Linear Intercept Linckens et al. (2014)
a
RGS Measurement: method of recrystallized grain size measurement. K and p are constants; OPx: orthopyroxene; MSC: molten salt cell.
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
4
oriented sub-parallel to the foliation (Fig. 3b).
3.2.2. Peridotite mylonites
We examined seven thin sections of variably deformed peridotites
(Table 2). Samples from the Navajo volcanic eld were sourced from
Douglas Smith (Behr and Smith, 2016). The other peridotite thin sec-
tions were obtained from archived collections at The University of Texas
at Austin, with their source regions given in Table 2.
Mantle xenoliths from the Navajo volcanic eld in the Colorado
Plateau of the western USA are associated with erosion of lithospheric
mantle during Laramide at-slab subduction of the Farallon plate at
temperatures of 550750 C (Behr and Smith, 2016). Massifs in the
western Alps (Ivrea and Lanzo zones) and French Pyrenees record Late
Paleozoic to Jurassic lithospheric extension at 600850 C (e.g., Skrotzki
et al., 1990; Newman et al., 1999; Kaczmarek and Müntener, 2008).
Our peridotite samples range from weakly deformed tectonites to
Fig. 2. Criteria for sample selection and examples. Sketches and micrographs: a-b) ultramylonite with planar banding between two phases at the thin section scale
(PW53, Whipple Mountains); c-d) weakly deformed tectonite with unmixed bands of recrystallized grains between porphyroclasts (I7, Ivrea Zone); e-f) porphyro-
clastic mylonite with well-segregated, unmixed bands in the recrystallized tail (red box; WM3, NE Harquahalas). Qtz: quartz; Fsp: feldspar; Ol: olivine; OPx:
orthopyroxene. (For interpretation of the references to colour in this gure legend, the reader is referred to the Web version of this article.)
Table 2
Source regions, grain sizes, differential stresses, and inferred temperatures of samples in this study.
Sample Source d (
μ
m) SD (
μ
m) N grains d (
μ
m) SD (
μ
m) N grains
σ
(MPa) T (C) ±(C) Temperature References
Quartz Feldspar
C Rincons 13.5 4.2 81 3.4 0.9 67 85 400 100 Perry (2005)
WB70 Betic 27.2 8.5 35 5.7 1.1 150 49 400 50 Behr and Platt (2012)
D3S4A C. Pyrenees 33.6 8.2 63 8.3 1.8 61 41 450 50 Den`
ele et al. (2008)
WM3 Harquahalas 43.0 13.0 100 11.7 3.3 100 34 450 50 Pollard (2014)
PW53 Whipples 50.6 21.7 50 14.0 4.1 75 30 450 100 Behr and Platt (2011)
PW24 Whipples 55.2 19.3 62 10.5 2.3 62 28 450 100 Behr and Platt (2011)
TPC02 EPR 71.8 28.6 100 23.2 5.8 90 23 550 50 Anderson (1983)
PW25b Whipples 75.3 21.5 60 26.9 6.2 60 22 550 50 Behr and Platt (2011)
Olivine Orthopyroxene
N170 Navajo VF 18.0 2.9 61 5.6 0.7 38 157 600 50 Behr and Smith (2016)
I7 Ivrea Zone 34.4 11.1 77 9.5 2.8 83 96 650 50 Skrotzki et al. (1990)
82-S-16A Lanzo-Sesia 43.2 11.6 80 26.8 10.9 66 81
196GN Navajo VF 47.5 12.3 240 19.0 5.9 240 76 700 50 Behr and Smith (2016)
I9 Ivrea Zone 53.9 24.9 90 24.5 6.2 90 69 650 50 Skrotzki et al. (1990)
LAN9 Lanzo 96.4 36.0 179 67.7 32.0 149 44 800 50 Kaczmarek and Müntener (2008)
990913B Fr. Pyrenees 153.5 38.6 80 115.0 31.6 91 31 800 50 Newman et al. (1999)
Differential stresses were calculated with the quartz (Stipp and Tullis, 2003) or olivine (van der Wal et al., 1993) piezometer. SD: One standard deviation of the grain
size distribution. See Supplementary Table S1 for the geometric mean, median, arithmetic mean, and root mean square grain sizes.
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
5
porphyroclastic mylonites and ultramylonites (Fig. 4). Samples I7 and I9
exhibit relatively low strain, where olivine and orthopyroxene por-
phyroclasts are surrounded by narrow zones (several grain thicknesses)
of recrystallized grains (Fig. 4a). The low strain in these two samples
makes it difcult to validate our assumption of approximately isoviscous
deformation. However, the viscosities of olivine and orthopyroxene are
thought to be similar in the lithosphere (Bystricky et al., 2016; Raterron
et al., 2016). The observation that both phases in these low-strain
samples show dynamic recrystallization supports the hypothesis that
their viscosities are similar (e.g., if one phase were substantially weaker,
strain would likely localize into that phase such that signicantly more
recrystallization would occur in it). Additionally, as we show in Section
4.2.2, the olivineorthopyroxene grain size relationships in these sam-
ples are consistent with the log-linear relationship exhibited by all of our
other samples, suggesting that both phases likely deformed at approxi-
mately the same stress. In porphyroclastic sample LAN9, most of the
olivine is recrystallized and forms lenses oblique to the foliation; some
orthopyroxenes form ribbon grains approximately parallel to the folia-
tion, whereas grains in less favorable orientations for dislocation glide
dynamically recrystallize on their margins (Fig. 4b). Sample LAN9 is
transected by zones of nely recrystallized olivine and orthopyroxene
grains cross-cutting earlier deformation fabrics (white arrows, Fig. 4b)
that we interpret to represent a later deformation event at higher stress;
we do not include these grains in our orthopyroxene calibration.
3.3. Recrystallized grain size measurements
Recrystallized grain sizes were measured optically in cross-polarized
light in thin sections with Zeiss Zen Pro software connected to a Zeiss
Axio Imager M2m petrographic microscope (Table 2). Because our
samples are archival, slip covers prevented electron backscatter
diffraction (EBSD) analyses. However, we found that by rotating the
polarizing stage and adjusting the z-direction, we were able to con-
dently identify grain boundaries. In the mylonites, recrystallized grains
were easily distinguished from porphyroclasts by their much smaller
size. In the ultramylonites, porphyroclasts are rare but were identiable
based on their higher degree of undulose extinction. To analyze
recrystallized grain sizes, we measured the length of a line across the
intermediate axis (representing the average of the long and short axes)
of each grain. For quartz and feldspar, we quantied the average
recrystallized grain size by calculating the root mean square (RMS) of
the grain size distribution and applied no geometric correction factor,
following Stipp and Tullis (2003). For olivine and orthopyroxene, the
geometric mean of the grain size distribution was multiplied by a geo-
metric correction factor of 1.75, following van der Wal (1993). We did
not use the linear intercept method employed by van der Wal (1993);
however, we did apply both methods (intermediate axis and linear
intercept) to two samples and the grain sizes were the same within error.
We measured 35240 grains per sample (Table 2), which is consistent
with the van der Wal et al. (1993) olivine and Schmid et al. (1980)
Fig. 3. Representative micrographs of quartzfeldspar mylonites. a) Por-
phyroclastic mylonite: Harquahala Mountains, USA (WM3), note domino-style
fracturing in a large feldspar porphyroclast (top-center); and b) ultramylonite:
Whipple Mountains, USA (PW24), quartz and feldspar fabrics are composi-
tionally banded. See the supplementary materials for detailed micrographs.
Fig. 4. Representative micrographs of deformed peridotites. a) Weakly
deformed tectonite: Ivrea Zone (I9), with narrow zones of recrystallization
around porphyroclasts; and b) porphyroclastic mylonite: Lanzo massif (LAN9),
olivine is almost completely recrystallized, most orthopyroxene forms ribbon
grains. Fine-grained zones that cross-cut earlier deformation fabrics (white ar-
rows) are interpreted to represent a later deformation event at higher stress. See
the supplementary materials for detailed micrographs.
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
6
calcite piezometers.
Several studies suggest a minimum number of grains are needed to
accurately calculate the average recrystallized grain size (e.g., Hum-
phreys, 2001; Stipp, 2018); however, as highlighted by Lopez-Sanchez
(2020), there is no universal minimum sample size. For example, the
olivine piezometer developed by van der Wal et al. (1993) is based on 23
samples, but only one sample has an average recrystallized grain size
based on more than 200 grains (sample 4272 with 202 grains). The
average recrystallized grain sizes for six samples are based on 20 grains
per sample, with the remaining samples measuring 48194 grains per
sample (see Table on p. 104 in van der Wal, 1993, doctoral dissertation).
Karato et al. (1980) calculated the average recrystallized grain sizes in
their deformed olivine samples by measuring 2050 grains per sample,
and their stress-grain size results are within error of the van der Wal
et al. (1993) piezometer. Speciale et al. (2020) conducted EBSD analyses
on a series of experimentally deformed olivine aggregates, measuring
~1000 recrystallized grains per sample, and found that the stress-grain
size results were within error of the olivine piezometer (van der Wal
et al., 1993). Likewise, Schmid et al. (1980) quantied a piezometric
relationship for calcite measuring 50 recrystallized grains per sample.
Additional experimental studies on calcite by Rutter (1995) and Barn-
hoorn et al. (2004) show stress-grain size relationships within error of
the calcite piezometer (Schmid et al., 1980), demonstrating strong
reproducibility. These experimental observations show that a large grain
size population (>200 grains) is not always necessary to accurately es-
timate the average recrystallized grain size.
3.4. Flow stress calculations and piezometer uncertainties
Differential stresses are calculated in the quartzfeldspar mylonites
using the Stipp and Tullis (2003) quartz piezometer, hereafter referred
to as the quartz piezometer, and those in the peridotite mylonites using
the van der Wal et al. (1993) olivine piezometer, hereafter referred to as
the olivine piezometer. We use these piezometers as reference frames for
our feldspar and orthopyroxene calibrations, respectively. We make the
assumption that the stresses in quartz and olivine are determined by the
respective piezometer, and assign the same stress to coexisting feldspar
and orthopyroxene in each sample, respectively. Our assumption is
supported by the observed consistency of the quartz and olivine pie-
zometers with independent estimates of crustal and mantle rheology (e.
g., Vissers et al., 1997; Dijkstra et al., 2002; Gueydan et al., 2005;
Warren et al., 2008; Katayama et al., 2009; Behr and Hirth, 2014;
Chatzaras et al., 2015; Bernard and Behr, 2017; Bernard et al., 2019;
Bose and Mukherjee, 2020; Feng et al., 2020; Kohli and Warren, 2020),
as well as their experimental reproducibility (e.g., Stipp et al., 2006;
Kidder et al., 2016; Tasaka et al., 2016; Soleymani et al., 2020; Speciale
et al., 2020). We note, however, that our mineral-pair recrystallized
grain size results do not depend on the accuracy of the quartz and olivine
piezometers. The grain size relationships we observed in the mineral
pairs would not change if the quartz and olivine piezometers are reca-
librated in the future; only the associated stress would change, enabling
our feldspar and orthopyroxene piezometers to be recalibrated.
The uncertainties in our naturally constrained piezometers are larger
than those of the experimentally constrained piezometers. The uncer-
tainty in our feldspar and orthopyroxene piezometers (see Section 4.2,
Eqs. (2) and (3)) accounts for error propagation of the uncertainties
reported by Stipp and Tullis (2003) and van der Wal et al. (1993) for the
quartz and olivine piezometers, respectively. The uncertainty in our
single-t feldspar and orthopyroxene piezometers (see Section 5.5, Eqs.
(4) and (5)) accounts for error propagation of the uncertainties reported
for the quartz and olivine piezometers, respectively, as well as those
reported by Post and Tullis (1999) and Linckens et al. (2014) for the
existing feldspar and orthopyroxene piezometers, respectively. Un-
certainties in our grain size measurements are listed in Table 2 and
represent one standard deviation of the grain size distribution.
4. Results
4.1. Microstructural observations
The microstructures of our quartzfeldspar and peridotite mylonites
are described below. Microstructural descriptions, recrystallized grain
size histograms, and micrographs of each individual sample are given in
the supplementary materials (Figs. S1S15).
4.1.1. QuartzFeldspar
Quartz has sweeping undulose extinction, serrated grain boundaries
and, in some samples, recrystallized grain sizes that are similar to the
subgrain size, consistent with bulge nucleation and subgrain rotation
recrystallization mechanisms (Regimes 1 and 2 of Hirth and Tullis,
1992). All of our samples exhibit feldspar microstructures consistent
with bulge nucleation (Regime 1). In samples that deformed at the
highest stresses, quartz grain boundaries are highly irregular and have
ne recrystallized grains on their margins; feldspar grain sizes are
similar to the width of bulges in the porphyroclasts. In some samples
that deformed at moderate stress, quartz forms undulating bands or
lenticular aggregates; recrystallized grains are smaller than the sub-
grains (Fig. 5a). Recrystallized feldspar grains are equant to tabular with
aspect ratios up to 2:1, and appear to dismember some porphyroclasts
almost entirely (Fig. 5b). In other moderate-stress samples, quartz grains
are attened and oblique to the foliation (Fig. 5c); recrystallized feldspar
grains are tabular with aspect ratios up to 3:1, and are also oblique to the
foliation (Fig. 5d). In samples that record the lowest stresses, quartz
grain sizes are similar to the subgrain size, consistent with subgrain
rotation recrystallization (Fig. 5e). Feldspar subgrains are only rarely
observed in porphyroclasts, but are larger than recrystallized grains,
which are similar to the width of porphyroclast bulges (Fig. 5f).
4.1.2. OlivineOrthopyroxene
Ultramylonite samples are compositionally banded, either locally or
at the thin section scale. Both olivine and orthopyroxene appear some-
what round, but some grains are attened with aspect ratios of 2:1; the
grains have gently curved grain boundaries and patchy undulose
extinction (Fig. 6a and b). In porphyroclastic sample LAN9, olivine is
almost completely recrystallized and the recrystallized grains have
gently curved grain boundaries; recrystallized orthopyroxene is
observed along the margins of porphyroclasts and the interiors of ribbon
grains (Fig. 6c and d). In another sample that exhibits a lesser degree of
recrystallization (990913B, ~30%), olivine, orthopyroxene, and garnet
porphyroclasts are somewhat attened and dene a weak foliation.
Olivine porphyroclasts have highly irregular, lobate grain boundaries
and patchy to sweeping undulose extinction; recrystallized grains on
their margins have gently curved boundaries and lower degrees of
undulose extinction (Fig. 6e). Recrystallized orthopyroxene grains form
either on the margins or transect the porphyroclasts and have gently
curved grain boundaries (Fig. 6f).
4.2. Stress-grain size relationships
4.2.1. QuartzFeldspar mineral pairs
The recrystallized grain sizes and calculated differential stresses of
quartz and feldspar are given in Table 2. By denition, our quartz grain
sizes plot on the quartz piezometer (Fig. 7a). With the assumption of
homogeneous stress, as outlined in Section 3.1, we plot our feldspar
grain sizes at the same stress as quartz for each sample. A least-squares
t to our feldspar data yields the stress-grain size relationship:
d=103.30 ±0.69
σ
1.47 ±0.43 R2=0.93,(2)
where d is in
μ
m and
σ
is in MPa. We plot the feldspar piezometer re-
ported by Post and Tullis (1999), hereafter referred to as the Post/Tullis
piezometer, for comparison with the stress-grain size relationships in
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
7
our quartzfeldspar samples. We also plot the high-stress quartz
piezometer (Bishop, 1996), hereafter referred to as the Bishop piezom-
eter, which was reported in Stipp and Tullis (2003).
4.2.2. OlivineOrthopyroxene mineral pairs
The recrystallized grain sizes and calculated differential stresses of
olivine and orthopyroxene are given in Table 2. Again, by denition, our
olivine grain sizes plot on the olivine piezometer (Fig. 7b). We plot the
corresponding orthopyroxene grain sizes at the same stress as olivine for
each sample. A least-squares t to our orthopyroxene data gives the
stress-grain size relationship:
d=105.01 ±0.89
σ
1.96 ±0.49 R2=0.96,(3)
where d is in
μ
m and
σ
is in MPa. We note that the stress-grain size re-
lationships in samples I7 and I9 (hollow squares, Fig. 7b) follow the
same log-linear pattern as all of our other samples, providing support for
our interpretation that both phases in these samples deformed at
approximately the same stress even though they are weakly deformed
tectonites with limited dynamic recrystallization (Figs. 2d and 4a). We
also plot the orthopyroxene piezometer of Linckens et al. (2014), here-
after referred to as the Linckens piezometer, for comparison with the
stress-grain size relationships observed in our peridotite samples.
5. Discussion
5.1. On the temperature dependence of the piezometric relationships
Some theoretical models for recrystallized grain size explicitly pre-
dict temperature-dependent piezometric relationships when the acti-
vation enthalpy for grain growth is different from that of creep (e.g., De
Bresser et al., 1998, 2001; Shimizu, 1998, 2008; Austin and Evans, 2007,
2009). Recent studies investigating grain growth in both quartz and
olivine, however, suggest that activation enthalpies between grain
growth and dislocation creep are similar. Speciale et al. (2020), for
example, found that the experimentally determined activation enthalpy
for grain growth of olivine during and after deformation is similar to that
for dislocation creep of wet olivine (Hirth and Kohlstedt, 2003),
providing a possible explanation for the lack of temperature dependence
in the olivine piezometer. Similarly, Tokle and Hirth (2021), in a reex-
amination of existing deformation and grain growth experiments,
determined that the activation enthalpy for grain growth of wet quartz is
within error of that for dislocation creep, consistent with the experi-
mental observations by Stipp and Tullis (2003). Although grain growth
kinetics and dislocation creep parameters are less well constrained for
various feldspar compositions, we note that activation enthalpies for
grain growth (365 ±25 kJ mol
1
, Dresen et al., 1996) and dislocation
creep (345 kJ mol
1
, Rybacki et al., 2006) in anorthite are within error
Fig. 5. Cross-polarized micrographs of representative quartzfeldspar mylonites. a-b) D3S4A (Central Pyrenees); c-d) WM3 (Harquahala Mountains, USA); e-f)
PW25b (Whipple Mountains, USA).
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
8
Fig. 6. Cross-polarized micrographs of representative deformed peridotites. a-b) 196GN (Navajo volcanic eld, USA); c-d) LAN9 (Lanzo Massif, Italian Alps); e-f)
990913B (French Pyrenees).
Fig. 7. Empirical piezometers for a) quartz and
feldspar, and b) olivine and orthopyroxene. Our
feldspar and orthopyroxene piezometers are from
Eqs. (2) and (3), respectively. Grain size uncertainties
in our data (squares) are one standard deviation of
the grain size distribution. In b), samples I7 and I9 are
represented by hollow squares (see Section 4.2.2 for
details). Solid lines represent the range of calibration
for each piezometer; dashed lines are extrapolations.
Shaded regions represent the uncertainties in our pi-
ezometers. Black circle in a) indicates the observed
feldspar recrystallized grain size in a lower-crustal
xenolith (~0.5 mm; Bernard and Behr, 2017)
plotted at the stress predicted by our feldspar
piezometer (~23 MPa; see Section 5.3). ST03: Stipp
and Tullis (2003); B96: Bishop (1996); PT99: Post and
Tullis (1999). Black circle in b) is the stress-grain size
relationship observed in naturally deformed ortho-
pyroxene (20 MPa, 250
μ
m, Skemer et al., 2010, but
here adjusted to ~290
μ
m; see Section 5.4). VDW93:
van der Wal et al. (1993); L14: Linckens et al. (2014).
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
9
of each other. For orthopyroxene, the activation enthalpies for grain
growth (720 ±80 kJ mol
1
, Skemer and Karato, 2007) and dislocation
creep (600720 kJ mol
1
, Bystricky et al., 2016) are also within error of
each other. The log-linear relationships we observe in our feldspar and
orthopyroxene data, from samples that deformed over a range of infer-
red temperatures, are consistent with the experimental observations that
the steady-state recrystallized grain sizes in feldspar and orthopyroxene
are not signicantly temperature dependent.
5.2. Stress exponents associated with piezometers
The slope of a piezometer is dened by the stress exponent (p) in Eq.
(1). Many theoretical models developed to characterize a materials
piezometric relationship relate p to the stress exponent for creep from
ow laws as well as the grain growth exponent from static grain growth
laws (e.g., Hall and Parmentier, 2003; Austin and Evans, 2007, 2009).
These theoretical models estimate p can range from 0.75 to 2.5; how-
ever, based on experimental observations, p ranges from ~0.6 to ~2.0,
with the majority of p values ranging from ~1.0 to ~1.6 (see Fig. 6a and
Table 2 in Shimizu, 2008). The stress exponents of our naturally con-
strained feldspar (p =1.47) and orthopyroxene (p =1.96) piezometers
fall within the observed experimental range. In contrast, only a few
studies report p <1, including the Bishop quartz piezometer, the
Post/Tullis feldspar piezometer, and the Linckens orthopyroxene
piezometer. The remaining studies that report p <1 did not correct for
friction in the Griggs apparatus, which inuences their stress measure-
ments (Ave Lallemant, 1978; Ross and Nielsen, 1978; Ross et al., 1980).
The Bishop, Post/Tullis, and Linckens piezometers are based on exper-
iments conducted with solid conning media, thus raising the question
as to whether the conning medium inuenced the stress measurements
and calculated piezometric relationships. The theoretical analysis by
Shimizu (2008), for example, omits data from studies that use solid
conning media, cautioning that stress resolution is compromised by
friction. However, Post and Tullis (1999) argue that the use of solid salt
did not contribute to sample strength at their experimental conditions,
and Gleason and Tullis (1993) observed little difference between stress
determined using talc or solid salt compared to the molten salt cell in
high-temperature experiments. Additionally, Linckens et al. (2014)
calculated stress using the olivine piezometer such that their stresses
represent stresses internal to the sample and are thus independent of
frictional effects in the Griggs apparatus. The stress-grain size relation-
ships observed in solid salt cell experiments on quartz (Kidder et al.,
2016) are consistent with the quartz piezometer calibrated using the
molten salt cell (Stipp and Tullis, 2003). Furthermore, stress-grain size
data from olivine deformation experiments performed by Speciale et al.
(2020) using the molten salt cell are consistent with the olivine
piezometer, which was quantied with stress-grain size data from ex-
periments using gas media (van der Wal, 1993) combined with data
from creep experiments at atmospheric pressure (Karato et al., 1980).
These observations provide evidence that conning media has little ef-
fect on the stress-grain size relationship in high-temperature experi-
ments. Therefore, it is unlikely that the low p values constrained in the
Bishop, Post/Tullis and Linckens piezometers result from the use of solid
conning media. We discuss other potential explanations for the dif-
ferences in the experimental versus naturally constrained feldspar and
orthopyroxene piezometers below.
5.3. Feldspar piezometer
The Post/Tullis calibration is based on a limited range of grain sizes
(1.02.5
μ
m) with relatively large uncertainties, and feldspar recrys-
tallization via bulge nucleation (Regime 1 of Hirth and Tullis, 1992).
The transition in the slope of the Post/Tullis piezometer and our feldspar
piezometer (Eq. (2)) is remarkably similar to the transition in slope
observed in the quartz piezometers (Fig. 7a), which Stipp and Tullis
(2003) attributed to a transition in recrystallization mechanism from
Regime 1 to Regime 2 of Hirth and Tullis (1992). However, because our
feldspar also records deformation in Regime 1, we do not interpret the
different slope of our feldspar piezometer as a transition in recrystalli-
zation mechanism, as proposed by Post and Tullis (1999). Subgrain
rotation recrystallization (Regime 2 of Hirth and Tullis, 1992) in feld-
spar has been observed in nature, but only at higher temperatures
(>650 C) than we infer for our samples (Tullis, 2002). Instead, the
slopes of our feldspar piezometer and the Post/Tullis piezometer may
result from different deformation mechanisms as predicted by the
wattmeter model, wherein a change in the stress exponent for creep
leads to a change in the slope of the piezometric relationship (Austin and
Evans 2007, 2009). Tokle and Hirth (2021) show evidence for a change
in the piezometric slope correlating with a change in stress exponent for
creep in experimentally deformed wet quartzite, providing support for
this interpretation.
The feldspar grain sizes measured in this study and those predicted
by the Post/Tullis piezometer are similar at ~100 MPa but diverge
signicantly at lower stress, suggesting that the Post/Tullis piezometer
is inconsistent with both the quartz piezometer (i.e., it predicts a
different stress than the quartz piezometer for a given quartzfeldspar
sample) and the plagioclase ow law (Rybacki et al., 2006). For
example, Bernard and Behr (2017) estimated the stress of a
plagioclase-rich, lower-crustal xenolith from the Mojave region of
Southern California, USA, with a recrystallized grain size of 0.51 mm
using the Post/Tullis piezometer (0.010.04 MPa). Our feldspar
piezometer predicts a stress approximately two orders of magnitude
higher (23 MPa) for a grain size of 0.5 mm (black circle, Fig. 7a). Based
on the geothermal gradient in this region and the depth from which the
lower-crustal xenolith was derived, the plagioclase ow law of Rybacki
et al. (2006) predicts a minimum stress of ~4 MPa (Behr and Hirth,
2014), which is within uncertainty of the stress derived from our feld-
spar piezometer but inconsistent with the Post/Tullis calibration. At 4
MPa, the Post/Tullis piezometer predicts a grain size of ~22
μ
m, more
than an order of magnitude smaller than that observed by Bernard and
Behr (2017). We emphasize that these stress estimates are outside the
range of calibration for both piezometers; however, this example dem-
onstrates the signicantly different interpretation of stress that would
result from the use of these piezometers on naturally deformed rocks.
5.4. Orthopyroxene piezometer
The Linckens piezometer is based on data from four experimental
samples and six lherzolite xenoliths (see Fig. 4 in Linckens et al., 2014);
it predicts orthopyroxene grain sizes to be smaller than olivine at
stresses up to ~500 MPa, but larger than olivine at higher stresses. The
orthopyroxene grain sizes measured in this study and those predicted by
the Linckens piezometer are similar at ~100 MPa; however, the Linck-
ens piezometer predicts an increasingly signicant grain size contrast
between olivine and orthopyroxene at lower stresses (Fig. 7b). This is at
odds with our observations of naturally deformed peridotites, and pre-
viously published work (e.g., Douglas et al., 1987; Skemer et al., 2006;
Skemer et al., 2010; Behr and Hirth, 2014). For example, Skemer et al.
(2010) studied the microstructural evolution of a mantle shear zone in
the Fresno Bench section of the Josephine Peridotite, SW Oregon, USA,
and estimated stress using the olivine piezometer (1320 MPa). Two
microstructural domains were observed in the highly deformed core of
the shear zone: coarse-grained olivine (~550
μ
m) and ne-grained,
well-mixed olivine and orthopyroxene, both with a grain size of ~250
μ
m (Skemer et al., 2010). They assumed that the coarse-grained domain
represents the lower stress limit (13 MPa using the olivine piezometer)
to account for possible grain growth. Because the presence of secondary
phases inhibits grain growth (Smith, 1948), they interpreted the
ne-grained domain to represent the upper stress limit during dynamic
recrystallization (20 MPa using the olivine piezometer). They also infer
similar strengths between olivine and orthopyroxene in the ne-grained
zone. Accounting for the change in geometric correction factor from 1.5
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
10
(used by Skemer et al., 2010) to 1.75, the grain size for both phases is
~290
μ
m. At 290
μ
m, our orthopyroxene piezometer (Eq. (3)) and the
olivine piezometer predict approximately the same stress (black circle,
Fig. 7b), which is consistent with the independent analysis of Skemer
et al. (2010). In contrast, for a grain size of ~250
μ
m (using a geometric
correction factor of 1.5), the Linckens piezometer predicts a stress of ~2
MPa, about one order of magnitude lower than that estimated for this
shear zone (Skemer et al., 2010). We acknowledge that phase pinning
prevented the ne-grained domain from achieving a steady-state
recrystallized grain size, but even the pinned grain size is still much
larger than predicted by the Linckens piezometer.
In the stress range of 1857 MPa, the Linckens piezometer is con-
strained by sheared lherzolite xenoliths erupted from ~200 km depth
(Boullier and Gueguen, 1975; Jin, 1995; Skemer and Karato, 2008), and
the large contrast in grain size between olivine and orthopyroxene at
low stress is attributed to slow pyroxene grain growth kinetics. Skemer
and Karato (2008) concluded that dynamic recrystallization was fol-
lowed by a transition from deformation by dislocation creep to a grain
size-sensitive creep mechanism, such as diffusion creep or
dislocation-accommodated grain boundary sliding (disGBS), based on
progressive fabric randomization. Therefore, the mantle xenoliths may
not record steady-state recrystallized grain sizes.
The experiments reported by Linckens et al. (2014) all record stresses
greater than ~100 MPa and are interpreted to have deformed by disGBS,
whereas the microstructures of our natural mylonites indicate defor-
mation by dislocation creep. A reassessment of the experimental data of
Linckens et al. (2014) indicates that the slope of their data is similar to
that of their combined dataset (experiments and mantle xenoliths), with
a stress exponent (p) of ~0.8. The uncertainties in our orthopyroxene
piezometer and the Linckens piezometer overlap near a stress of 100
MPa, and it is plausible that the transition in slope between these pie-
zometers results from a transition in deformation mechanism, as pro-
posed by grain size evolution models such as the wattmeter (Austin and
Evans, 2007, 2009).
5.5. Piezometers constrained using both natural and experimental
datasets
Another possible interpretation for the feldspar and orthopyroxene
piezometers is a piezometric relationship based on combining our
naturally constrained datasets with the experimental datasets of Post
and Tullis (1999) and Linckens et al. (2014), respectively. Given the
uncertainties in each of the piezometers, a single t can be made to both
datasets with good agreement (Fig. 8). These single-t relationships
benet from the fact that they are t over a larger range of grain sizes
(and therefore stresses) than the natural or experimental datasets alone.
For the feldspar piezometer, a single t decreases the stress exponent
(p) from 1.47 to 1.01, which is still within the range of commonly
observed p values based on experimentally calibrated relationships (p ~
1.01.6). The single-t feldspar piezometer follows the relationship:
d=102.59 ±0.37
σ
1.01 ±0.19 R2=0.96,(4)
where d is in
μ
m and
σ
is in MPa. The p value of 1.01 is also close to the
value predicted by the wattmeter model (Austin and Evans 2007, 2009),
where p =(n +1)/(k +1), n is the stress exponent for creep and k is the
grain growth exponent. For anorthite, n =3.0 (Rybacki et al., 2006) and
k =2.52.7 (Dresen et al., 1996); based on the wattmeter model p
~1.081.14. We plot the single-t piezometer (Eq. (4)) along with our
naturally constrained feldspar piezometer (Eq. (2)) in Fig. 8a; the un-
certainties in these piezometers overlap somewhat at stresses less than
~30 MPa. We also plot our feldspar data (squares) and the experimental
data of Post and Tullis (1999; diamonds). The range of feldspar recrys-
tallized grain sizes reported in other studies of naturally deformed
quartzfeldspar mylonites are plotted at the range of stresses estimated
by the quartz piezometer, based on the recrystallized grain sizes of
coexisting quartz (Schulmann et al., 1996; Svahnberg and Piazolo, 2010;
Wex et al., 2019); these studies interpreted that both phases deformed at
nearly isoviscous conditions. The range of quartz and feldspar recrys-
tallized grain sizes reported by Schulmann et al. (1996) result in
stress-grain size relationships that t well with our naturally constrained
feldspar piezometer (Fig. 8a). We note that although Wex et al. (2019)
interpreted that their feldspar underwent grain size reduction by
dissolution-precipitation, their quartz deformed by dislocation creep,
and their feldspar grain sizes are reasonably consistent with both our
feldspar piezometer and the single-t piezometer. Svahnberg and Pia-
zolo (2010) measured a range of quartz recrystallized grain sizes but
reported only one feldspar recrystallized grain size. Over the range of
stress indicated by the quartz piezometer, the feldspar grain size is more
consistent with the single-t feldspar piezometer, although the
higher-stress estimate is within uncertainty of our naturally constrained
feldspar piezometer. We also highlight that the single-t piezometer
predicts a stress of <1 MPa for the plagioclase-rich xenolith reported by
Bernard and Behr (2017), which is inconsistent with the lower stress
limit in the Mojave region based on the ow law of Rybacki et al. (2006),
as discussed in Section 5.3.
For the orthopyroxene piezometer, we combine our naturally con-
strained data with only the experimental data of Linckens et al. (2014);
specically, the three samples for which they provided the recrystallized
grain sizes of both olivine and orthopyroxene (see Table 2 in Linckens
et al., 2014). We normalized the Linckens et al. (2014) grain size data for
both phases to a geometric correction factor of 1.75, following van der
Wal (1993). A single t to these data decreases the stress exponent (p)
Fig. 8. Plots of recrystallized grain size versus dif-
ferential stress showing piezometric relationships
based on a single t combining our datasets for
feldspar and orthopyroxene with the experimental
datasets of a) Post and Tullis (1999) and b) Linckens
et al. (2014). The single-t relationships for feldspar
and orthopyroxene are from Eqs. (4) and (5),
respectively. We note that Linckens et al. (2014)
provided grain size data on both olivine and ortho-
pyroxene for only three experimental samples. Our
naturally constrained piezometers are shown for
comparison (Eqs. (2) and (3)). Data from this study
(squares), experiments (diamonds), and other studies
of naturally deformed rocks are also shown. PT99:
Post and Tullis (1999); BB17: Bernard and Behr
(2017); S96: Schulmann et al. (1996); W19: Wex et al.
(2019); SP10: Svahnberg and Piazolo (2010); L14:
Linckens et al. (2014); S06: Skemer et al. (2006); S10:
Skemer et al. (2010); D87: Douglas et al. (1987); H75:
Harte et al. (1975); BH14: Behr and Hirth (2014).
P.A. Speciale et al.
Journal of Structural Geology 154 (2022) 104495
11
from 1.96 to 1.28, which is well within the range of commonly observed
experimental p values (p ~ 1.01.6). The single-t orthopyroxene
piezometer follows the relationship:
d=103.80 ±0.90
σ
1.28 ±0.45 R2=0.85,(5)
where d is in
μ
m and
σ
is in MPa. The p value of 1.28 is also consistent
with the value predicted by the wattmeter model, where n =3.0
(Bystricky et al., 2016) and k =1.73.1 (Skemer and Karato, 2007);
based on the wattmeter model p ~0.981.52. We plot the single-t
piezometer (Eq. (5)) along with our naturally constrained orthopyrox-
ene piezometer (Eq. (3)) in Fig. 8b; the uncertainties in these piezome-
ters overlap signicantly at stresses less than ~80 MPa. We also plot our
orthopyroxene data (squares) and the experimental data of Linckens
et al. (2014; diamonds). The range of orthopyroxene recrystallized grain
sizes reported in other studies of naturally deformed peridotite mylon-
ites are plotted at the range of stresses predicted by the olivine
piezometer, based on the recrystallized grain sizes of coexisting olivine
(Harte et al., 1975; Behr and Hirth, 2014; Douglas et al., 1987; Skemer
et al., 2006, 2010). For these studies, we normalized the reported grain
sizes of olivine and orthopyroxene to a geometric correction factor of
1.75, following van der Wal (1993). Although these studies do not
specically discuss whether olivine and orthopyroxene deformed under
isoviscous conditions, the two phases likely have similar viscosities
under natural conditions (Bystricky et al., 2016). However, we
acknowledge that the assumption of isoviscous deformation may be
limited to lithospheric depths, below which pressure effects signicantly
increase the viscosity of orthopyroxene (Raterron et al., 2016). The
stress-grain size relationship reported by Skemer et al. (2010) is
consistent with our orthopyroxene piezometer, as discussed in Section
5.4. Douglas et al. (1987) and Skemer et al. (2006) reported orthopyr-
oxene grain sizes that are within uncertainty of both our orthopyroxene
piezometer and the single-t piezometer. However, the single-t
orthopyroxene piezometer provides a better t to the range of ortho-
pyroxene grain sizes reported by Harte et al. (1975) and Behr and Hirth
(2014). Indeed, almost all of the naturally deformed samples (including
our samples, below a stress of ~80 MPa), are within uncertainty of the
single-t orthopyroxene piezometer. Additional experimental work is
needed to further constrain the piezometric relationships for feldspar
and orthopyroxene, especially at low-stress conditions; however, our
piezometers provide an improvement on estimating stress in feldspar-
and pyroxene-rich lithologies at geologic conditions.
6. Summary and future work
We estimate stress magnitudes in naturally deformed quartz-
feldspar and peridotite mylonites from a diverse range of tectonic
settings and pressure-temperature conditions, and derive piezometers
for feldspar (Eq. (2)) and orthopyroxene (Eq. (3)) that reasonably pre-
dict the grain size relationships observed for quartzfeldspar and olivi-
neorthopyroxene mineral pairs from naturally deformed lithospheric
shear zones. Our piezometers differ signicantly from the existing
feldspar and orthopyroxene piezometers, especially at geologically
reasonable stresses. The stress exponents of our feldspar (p =1.47) and
orthopyroxene (p =1.96) piezometers are within the range of observed
experimental values (p ~ 0.62.0). In addition, we t existing experi-
mental data and our naturally constrained data to develop a set of single-
t piezometric relationships for feldspar (Eq. (4)) and orthopyroxene
(Eq. (5)). The stress exponents for feldspar (p =1.01) and orthopyroxene
(p =1.28) are consistent with the piezometric slope (p) predicted by the
wattmeter model (Austin and Evans, 2007, 2009) based on existing ow
laws and grain growth laws. Both sets of piezometric relationships
provide a good t to the grain size relationships of the mineral pairs
(quartzfeldspar and olivineorthopyroxene) reported in previous
studies on natural mylonites. These new piezometers offer an alternative
for estimating stress in lower-crustal and lithospheric mantle rocks, such
as granulites and pyroxenites, which lack signicant quartz and olivine.
Although the grain size relationships we observed do not depend on
the accuracy of the quartz and olivine piezometers, our calibrations are
based on our assumption that they are robust. This assumption is sup-
ported by the reproducibility of stress-grain size relationships observed
in deformation experiments on quartz (e.g., Stipp et al., 2006; Kidder
et al., 2016) and olivine (e.g., Tasaka et al., 2016; Speciale et al., 2020),
and the consistency of the quartz and olivine piezometers with
numerous investigations of crustal and mantle rheology (e.g., Vissers
et al., 1997; Dijkstra et al., 2002; Gueydan et al., 2005; Warren et al.,
2008; Katayama et al., 2009; Behr and Hirth, 2014; Chatzaras et al.,
2015; Bernard and Behr, 2017; Bernard et al., 2019; Bose and
Mukherjee, 2020; Feng et al., 2020; Kohli and Warren, 2020). Although
challenging, experiments that constrain the lower-stress domains of
these piezometers would demonstrate the efcacy of their extrapolation
to natural conditions, and/or facilitate the development of more accu-
rate piezometers. The calibrations we report here can be systematically
scaled to any revised piezometer for quartz or olivine. Similarly, eld
studies that report the recrystallized grain sizes of multiple phases (e.g.,
olivine and orthopyroxene) could be used to test the applicability of
piezometers to naturally deformed rocks and enhance our understand-
ing of stress in the lithosphere.
Author statement
All authors listed on this manuscript contributed to its production. P.
A. Speciale conducted work on this project from 2014 to 2019 under W.
M. Behrs supervision, while pursuing her Ph.D. at UT Austin. All
microstructural observations and analytical work were conducted by
Speciale at UT Austin. Behr and Tokle assisted in interpreting micro-
structural data and analyses, and contributed to several drafts of the
original manuscript.
Data availability statement
Datasets related to recrystallized grain size measurements for
quartzfeldspar (https://doi.org/10.18738/T8/GORIZE) and olivine-
orthopyroxene (https://doi.org/10.18738/T8/Q3RWEQ) can be
accessed through the Texas Data Repository (https://data.tdl.org).
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgments
This research was funded by NSF grant 1249737 awarded to W.M.
Behr. We thank Douglas Smith and The University of Texas at Austin for
providing thin sections. We also thank two anonymous reviewers for
constructive suggestions that greatly improved the manuscript.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.jsg.2021.104495.
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P.A. Speciale et al.
... Feldspar grains in our samples appear disaggregated during deformation, and we used the geometric mean of recrystallized grains for grain-size piezometry. We considered three feldspar piezometers, including from Post and Tullis (1999) and two calibrations from Speciale et al. (2022). Evaluation of these different piezometer calibrations is beyond the scope of this study, but our recrystallized grain-size observations translate to generally similar flow stress estimates for these piezometers because the three piezometers nearly intercept in grain-size vs stress space. ...
... In the ultramylonite part of sample 19SNV23, plagioclase and Kfeldspar define aggregate bands that are distributed across the shear Table S1). This suggests flow stresses near ~50 MPa (Post and Tullis, 1999;Speciale et al., 2022). There is no discernible CPO for the feldspar grains ( Table S1). ...
... Feldspar grain-size is ~6-8 μm and ~7-11 μm for plagioclase and K-feldspar, respectively, depending on the analyzed location within the sample (Supplemental Table S1). These recrystallized grain sizes are consistent with stresses of ~50 MPa (Post and Tullis, 1999;Speciale et al., 2022). There is weak-to-no discernible CPO, and M and R indices are 0.01-0.03 ...
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