Mineralogy 231, Volume 12, pages 1-7, 2009
Quartz Polymorphs - Computer Modeling of Phase Transitions and
Presence in Shatter Cones
ALISTAIR T. HAYDEN, CHRISTINA G. MACHAK
Department of Geological Science, University of Michigan,
ABSTRACT
The accuracy of two functionals, PBE and PW91, was examined in Materials Studio by using
them to model stability under pressure for the SiO2 polymorphs quartz, coesite, and stishovite.
These functionals computed the enthalpy of each polymorph structure, which was used to determine
phase transitions between the polymorphs, which were then compared to empirical values. The
PBE functional was found to do a very poor job modeling the polymorphs under pressure while
PW91 showed proper trends of phase transitions. Additionally, two thin sections were made from a
schist shatter cone, collected from the Santa Fe Impact Structure. Optical and scanning electron
microscopy were used to search for evidence of the high-pressure polymorphs coesite and
stishovite in these thin sections. Though these high-pressure polymorphs were not found, planar
deformation features (PDFs) and shattered quartz were abundant, indicating some pressure-related
alteration.
centimeter to several meters can be observed with their
central axes pointing in the same general direction,
probably towards the impact site. Pressures for shatter cone
formation have been determined empirically to be in the
range of 2-30 Gpa, above that usually associated with
metamorphism. Through a comparison of the shocked
quartz in samples to empirical data Fackelman and
colleagues constrained the pressure for the shatter cone
formation in the Santa Fe structure to a range of 5-10 GPa
(Fackelman et al., 2008).
In addition to macroscopic shock features,
microscopic evidence of the shock is also preserved. These
microscopic features are called Planar Deformation
Features (PDFs) and include shocked quartz and shattered
quartz and are found solely within about 2 mm of the
shatter surface. Shocked quartz can be indentified using
optical microscopy by its parallel laminae, which are
decorated with small fluid inclusions (Fig. 1).
INTRODUCTION
Shatter Cone Geology
The Santa Fe Impact Structure, as described by
Fackelman et al. (2008), is located approximately 8km
northeast of Santa Fe, New Mexico in the southernmost
part of the Sangre de Cristo Mountains. The Sangre de
Cristo Mountains span from southern Colorado to just
southeast of Santa Fe, New Mexico. They are bounded on
the east by the Rio Grande Rift and on the west by the
High Plains province. The sample examined for this paper
was obtained from a road cut exposing the bedrock beneath
the supposed ancient impact site.
The bedrock containing the impact structure is
composed primarily of intrusive igneous and metamorphic
rocks. According to Bauer et al. (1997), the metamorphic
rocks in the formation are layered, alternating between a
quartzofeldspathic unit and an amphibolite unit. The
quartzofeldspathic unit is composed of quartz-rich finegrained schist, quartzite, and quartz-feldspar-muscovite
gneiss. The sample that generated the thin sections
examined in this paper is a dark quartz-rich schist, likely
from the quartzofeldspathic unit.
The presence of shatter cones is considered strong
evidence for a meteorite impact in overlying rock (Wieland
et al., 2006). Shatter cones are macroscopic features
thought to result from the tensile stress produced by a
shock wave propagating through the rock during the early
compressional phase after impact. A shatter cone is a
conical surface produced by the fracturing of the rock
normal to the direction of wave propagation. The
fracturing of the rock to create a cone is believed to
nucleate at areas of existing heterogeneity in rock (Adachi
et al., 2008) and manifests along the surface in a distinct
“horse-tail” outward-curving pattern. Throughout an
outcrop, many shatter cones ranging in length from a
Fig. 1. PDF in Quartz (Fackelman et al., 2008)
1
HAYDEN AND MACHAK: QUARTZ POLYMORPHS AND PHASE TRANSITIONS
2
Computational Modeling
Various functionals can be used in Materials Studio to
model the energy of a crystal. There are two main theories
upon which these functionals operate  Hartree-Fock and
density functional theory (DFT). Both of the functionals
used in this project, PW91 and PBE, are derived from
DFT, which was developed by Hohenberg, Kohn, and
Sham in the 1960s. They determined that the total energy
of a structure can be determined from the density of
electrons and an unknown functional. Approximations of
functionals have been made which produce variable
results. Different functionals produce more accurate results
for different types of calculations and for different
structures, thus the evaluation of functionals is an ongoing
process.
All functionals based on DFT operate using this
general concept, but differ in their exact calculations
(Probert 2009). The calculations involved in determining
energy for a given structure are beyond the scope of this
paper, but a detailed explanation of DFT can be found in a
paper by Professor M.C. Payne published in the Review of
Modern Physics (1992).
data, including enthalpy, for the arrangement. Enthalpies
were normalized for the number of SiO2 molecules in the
unit cell and plotted against their respective pressures.
Trend lines were determined from the enthalpy data of
each polymorph and the phase transitions of SiO2
determined from the intersections of the trend lines.
Thin Section Preparation
From the schist shatter cone, two chips were cut
perpendicular to the plane of the shatter surface, one in the
horizontal direction and one in the vertical (see Fig. 3) to
preserve maximum information about the sample. The thin
sections were prepared from these chips by James
Hinchcliff and were spatter-coated with carbon (to prepare
them for SEM) by Devon Renock.
SiO2 Polymorphs
Quartz is just one of many SiO2 polymorphs (Fig. 2).
Two of the polymorphs, coesite and stishovite, are relevant
to the examination of the Santa Fe Impact Structure shatter
cones in this paper because they occur at the high pressures
and low temperatures of shatter cone formation.
Fig. 3. Thin section cuts relative to shatter cone. The
cuts were made perpendicular to the surface.
Scanning Electron Microscopy
We used the scanning electron microscope (SEM) in
the University of Michigan Department of Geological
Sciences. With help from Devon Renock, the thin sections
were imaged with secondary electrons while compositions
of grains were determined using energy dispersive
spectroscopy.
The online Mineralogy Database
(Barthelmy) was used as a reference to compare the
measured compositions to standard compositions to
identify the minerals.
Fig. 2. Phase diagram of SiO2
METHODS
Computational Analysis
All computer work was done in Materials Studio 4.0
and CASTEP. Unit cells were created using data from the
American Mineralogist Crystal Structure Database (Downs
& Hall-Wallace, 2003) and then subjected to various
pressures at 0 K using the PBE and PW91 functionals. The
functionals calculated the most stable geometric
configuration of the atoms at each pressure and returned
RESULTS
Computational Analysis
A variety of pressures were simulated for each
polymorph structure using the PW91 and PBE functionals.
The enthalpies, a proxy for stability, increased linearly
with pressure for all minerals and functionals. Trend lines
fit the data very well, with R2 values of around 0.995 in all
cases. Refer to Tables 1 and 2 and to Figures 4 and 5 for
data and trends.
Because lower enthalpy is taken to mean higher
stability, phase transitions occur when trend lines intersect,
meaning that one mineral suddenly has lower enthalpy at
HAYDEN AND MACHAK: QUARTZ POLYMORPHS AND PHASE TRANSITIONS
3
that pressure. The data from the two functionals yielded
different approximations of the phase transitions. The
model produced from PW91 placed the quartz-coesite
transition at 5.02 GPa and the coesite-stishovite transition
at 11.97 GPa (Figure 4) while the PBE model placed the
quartz-coesite transition at 8.29 GPa and the coesitestishovite transition at 7.66 GPa (Figure 5).
Table 1. PW91-calculated enthalpies
Quartz
Coesite
Pressure
Enthalpy
Enthalpy
(GPa)
(eV)
(eV)
0
-991.127
1
-990.887
2
-990.644
-990.6
3
-990.404
4
-989.966
5
-991.127
-990.0
6
-989.8
7
7.5
8
-989.4
9
-989.117
10
-989.0
11
12
failed
15
failed
-
Table 2. PBE-calculated enthalpies
Quartz
Coesite
Pressure
Enthalpy (eV)
(GPa)
Enthalpy (eV)
0
-985.20
1
-984.95
2
-984.72
3
-984.48
4
-984.24
5
-984.01
6
-983.79
7
-983.57
8
-983.35
9
-983.14
10
-982.93
-983.002
11
-982.73
-982.801
12
-982.53
-982.602
13
-982.33
-982.405
14
-982.13
-982.208
15
-981.94
-982.014
Stishovite
Enthalpy
(eV)
-990.3
-989.8
-989.6
-989.4
-989.3
-989.2
-989.1
-989
-988.6
-988.2
Stishovite
Enthalpy
(eV)
-983.841
-983.548
-983.106
-982.825
-982.37
Scanning Electron Microscopy
From the SEM images (Figures 6-8), nine
representative grains were selected that then had their
compositions analyzed (Table 3).
One grain that
resembled much of the sample was determined to be
quartz. Four grains representing the other abundant
mineral were determined to be muscovite. One apatite
grain was analyzed and others were visible in all of the
images as small grains. Albite was found in one sizeable
grain, but others could not be located. The last two grains
analyzed, visible as bright white flecks in the image, were
indentified as monazite because of they contained an
abundance of rare heavy elements.
Table 3. Measured and expected compositions
Mineral
webmineral.com
Measured
Composition
Composition
Quartz
Muscovite
Apatite
Albite
Monazite
Si
O
K
Al
Si
H
O
F
Fe
Ca
P
O
F
Na
Ca
Al
Si
O
La
Ce
Th
P
Nd
O
46.74 %
53.26 %
9.81 %
20.30 %
21.13 %
0.46 %
47.35 %
0.95 %
39.74 %
18.43 %
38.07 %
3.77 %
8.30 %
0.76 %
10.77 %
31.50 %
48.66 %
14.46 %
29.17 %
4.83 %
12.89 %
12.01 %
26.64 %
49.63 %
50.37 %
5.06 %
13.48 %
16.54 %
52.48 %
3.25 %
40.42 %
20.18 %
26.63 %
2.76 %
7.25 %
3.11 %
13.02 %
33.26 %
43.36 %
13.05 %
28.56 %
6.34 %
18.32 %
31.58 %
HAYDEN AND MACHAK: QUARTZ POLYMORPHS AND PHASE TRANSITIONS
4
Fig. 4. Stability graph using PW91 functional
Fig. 5. Stability graph using PBE functional
HAYDEN AND MACHAK: QUARTZ POLYMORPHS AND PHASE TRANSITIONS
5
Optical Microscopy
Quartz, biotite, and muscovite are by far the most
prevalent minerals and the only easily-identifiable ones.
Quartz was identified by transparence in plane-polarized
light (ppl), low-order birefringence in cross-polarized light
(xpl), and some conchoidal fracturing. The micas were
identified by their lamellar nature and their second-order
birefringence in xpl.
Biotite, which is brown and
pleochroic in ppl, stood apart from the transparent
muscovite mica and quartz.
Coesite and stishovite were not identified despite
much searching, though planar deformation features
(PDFs) and shattered quartz were found to be common
near shatter cone surfaces.
Fig. 6. Micrograph showing albite, quartz, muscovite
and monazite.
Fig. 9. Ppl image of bulk of sample. Quartz is clear
and muscovite is clear but with lamellae.
Fig. 7. Micrograph showing shatter surface with
quartz, muscovite, apatite, and monazite
Fig. 10. Xpl image of same bulk of sample. Quartz
exhibits first order birefringence while muscovite exhibits
the more-colorful second-order birefringence.
Fig. 8. Micrograph of quartz, muscovite, and apatite
HAYDEN AND MACHAK: QUARTZ POLYMORPHS AND PHASE TRANSITIONS
6
Fig. 11. Xpl image of PDFs along shatter surface
both elevated temperatures that would require elevated
pressures to form coesite and attenuated shock waves that
would not reach these requisite pressures.
The lack of coesite could also be explained by the
difficulty in its identification. Coesite looks very similar to
quartz under the microscope because it lacks color, is
transparent, displays conchoidal fracturing, and has a low
birefringence. It seems the only way to tell the difference
between the two is by determining the indicatrix because
quartz is unixial (+) while coesite is biaxial (+). In the
many interference figures generated for quartz-like grains,
none identified definitively as biaxial (+).
Stishovite would have been obvious because its optical
characteristics, including second-order birefringence, are
very different from quartz. Therefore, not finding it
probably means it is not present which is to be expected
because stishovite requires very high pressures to form.
CONCLUDING REMARKS
Fig. 12. Xpl image of shattered quartz along shatter
surface
DISCUSSION
Extrapolating from empirically-derived equations
down to the 0 K used in the computer simulations, the
quartz-coesite transition should occur around 2-3 GPa
(Bose & Ganguly, 1995) and the coesite-stishovite
transition should occur near 6-8 GPa (Zhang, Li, Utsumi,
& Liebermann, 1996). The phase boundary equations for
pressure are linear with respect to temperature so this
extrapolation is probably fairly accurate.
The PW91 functional gave data that predicted the
order of phase transitions successfully, though its actual
values for the phase transitions were too high by 3-4 GPa.
The PBE functional predicted the transitions poorly
because
it
predicted
that
coesite
is
never
thermodynamically favorable, though the model does have
an accurate coesite-stishovite transition at about 8 GPa.
Therefore, PW91 might be considered fairly accurate at
evaluating SiO2 polymorphs, but PBE is probably not.
The lack of high-pressure polymorphs of SiO2 could
be due to many things. The presence of shattered and
shocked quartz indicates that this sample did indeed
undergo a stress event, but the pressure might not have
been high enough to create even coesite, especially if the
sample was buried deep below the impact site meaning
Because all computations were done at 0 K, both sets
of data might be made more comparable to experimental
data by running the calculations for more realistic
temperatures like the elevated temperatures (600 K) used
in the empirical experiments. Other work with the
functionals of course includes the ongoing search for better
functionals and evaluation of existing ones.
Samples from this shatter cone outcrop should be
searched more thoroughly to see if high-pressure
polymorphs exist elsewhere. If they are found to be
absent, then this can help to constrain the pressures
experienced at this site. If high-pressure polymorphs are
found to be lacking at other shatter cones sites as well, this
can help guide our hypotheses about their formation.
The detection of monazite throughout much of the
sample is exciting because the radioactive elements it
contains could perhaps be used as a geochronometer to
constrain the dates of the impact event.
ACKNOWLEDGMENTS
Thanks to Rod Ewing for assigning a research project, for
without that assignment this would never have happened. A lot
of thanks to Devon Renock for helping with every step of the
process from beginning to end. Also, thanks to the mystery
source of money that allowed us to get thin sections and time on
the SEM.
REFERENCES CITED
Adachi T, Kletetschka G. (2008) Impact-pressure
controlled orientation of shatter cone magnetizations in
Sierra Madera, Texas, USA. Studia Geophysica Et
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Barthelmy, D. (2009). Mineralogy Database.
Retrieved from http://webmineral.com/
Bose, K., & Ganguly, J. (1995). Quartz-coesite
transition revisited: Reversed experimental determination
at 500-1200 °C and retrieved thermochemical properties.
American Mineralogist, 80, 231-238.
Downs, R., & Hall-Wallace, M. (2003). American
Mineralogist Crystal Structure Database. Retrieved from
http://rruff.geo.arizona.edu/AMS/amcsd.php
HAYDEN AND MACHAK: QUARTZ POLYMORPHS AND PHASE TRANSITIONS
7
Payne, M. C., M. P. Teter, D. C. Allen, and T. A.
Arias. (1992) Iterative minimization techniques for ab
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Wieland, F., W. U. Reimold, and R. L. Gibson. (2006)
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Zhang, J., Li, B., Utsumi, W., & Liebermann, R. C.
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