# New experimental constraints on seismic velocities and densities across the α-β quartz transition at deep crustal conditions

Giulia Mingardi, Julien Gasc, Matteo Ardit, Ross J. Angel, Wilson A.

Crichton, Dmitrii Druzhbin, Alexandre Schubnel, Matteo Alvaro, Jérôme
Aubry

► To cite this version:

Giulia Mingardi, Julien Gasc, Matteo Ardit, Ross J. Angel, Wilson A. Crichton, et al. New experimental constraints on seismic velocities and densities across the α-β quartz transition at deep crustal conditions. Contributions to Mineralogy and Petrology, 2025, 180 (3), pp.21. 10.1007/s00410-025-02206-8. hal-05122145

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https://cnrs.hal.science/hal-05122145v1

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# New experimental constraints on seismic velocities and densities across the α-β quartz transition at deep crustal conditions

Giulia Mingardi<fnref n="1" />,<fnref n="2" />✉ · Julien Gasc<fnref n="1" /> · Matteo Ardit<fnref n="3" /> · Ross J. Angel<fnref n="4" /> · Wilson A. Crichton<fnref n="5" /> · Dmitrii Druzhbin<fnref n="5" /> · Jerome Aubry<fnref n="6" /> · Alexandre Schubnel<fnref n="1" /> · Matteo Alvaro<fnref n="2" />

Received: 22 October 2024 / Accepted: 24 January 2025 / Published online: 25 February 2025
© The Author(s) 2025

## Abstract

At the pressure and temperature conditions of the lower crust, quartz undergoes a displacive phase transition from a tri-gonal (α) to a hexagonal phase (β). At room pressure, the α-β quartz transition occurs at 574.1 °C and it is associated with large changes in the thermodynamic and elastic properties. For that reason, it is interpreted as the cause of significant seismic velocity contrasts in the crust seen by seismic tomography. Existing thermodynamic models and Equations of State (EoS) of quartz are mostly constrained by data collected at room pressure (or at high pressure and room temperature). In this work we characterized the α-β quartz transition experimentally at simultaneous HP-HT conditions using synchrotron X-ray diffraction and acoustic measurements, and derived values of Vp, Vs, the adiabatic bulk modulus (Ks) and the shear modulus (G). The data collected in the α field agree with the models from the literature, so entrapment pressures of α-quartz inclusions calculated via elastic barometry with these EoS should be reliable. However, our measured Vp, Vs, and Ks are significantly lower than those predicted for β-quartz. Whatever the cause of this discrepancy, interpretations of seismic data in terms of the properties of β-quartz in the lower crust and calculations of entrapment conditions of quartz inclusions in the stability field of β-quartz should be treated with caution.

**Keywords** α-β quartz transition · Synchrotron X-ray diffraction data · Acoustic velocity measurements · Lower crust

## Introduction

Quartz is a common rock-forming mineral and characterizing its behaviour at crustal conditions is crucial for understanding its role in geological processes. Difficulties arise because at crustal pressures and temperatures, quartz undergoes a displacive phase transition from a low-symmetry phase (α) to a higher-symmetry phase (β). This phase transition has been extensively studied since its discovery (Le Chatelier 1890) and is now well documented at room pressure. The α-β quartz transition occurs at 574.1 °C (Carpenter et al. 1998) with the presence of an intermediate incommensurate phase that is stable over a small temperature range, from 573 °C to the temperature of the transition (e.g. Bachheimer 1980; Dolino 1990). Because the α to β transition in quartz is thermodynamically continuous, it is non-quenchable, meaning that the transformation occurs immediately after the transition boundary is crossed. There is no volume change at the transition but as the transition is approached the thermal expansion coefficient approaches an infinite value (e.g. Carpenter et al. 1998), the bulk modulus

Communicated by Othmar Müntener.

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Giulia Mingardi
mingardi@geologie.ens.fr

<footnote n="1">¹ Laboratoire de géologie, CNRS UMR 8538, Ecole Normale Supérieure-PSL University, 75005 Paris, France</footnote>

<footnote n="2">² Department of Earth and Environmental Sciences, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy</footnote>

<footnote n="3">³ Department of Geosciences, University of Padova, Via G. Gradenigo 6, 35131 Padua, Italy</footnote>

<footnote n="4">⁴ Istituto di Geoscienze e Georisorse, Consiglio Nazionale delle Ricerche, Corso Stati Uniti 4, 35127 Padua, Italy</footnote>

<footnote n="5">⁵ ESRF-The European Synchrotron Radiation Facility, Grenoble, France</footnote>

<footnote n="6">⁶ Institute of Earth Sciences, Université Savoie Mont-Blanc, Avenue du Lac d'Annecy, 73370 Le Bourget-du-Lac, France</footnote>
drops to zero (e.g. Lakshtanov et al. 2007), and the compres-
sional and shear wave velocities are about 1 km/s slower
than in the α field (e.g. Kern 1978; Lakshtanov et al. 2007).
As a consequence, quartz-bearing rocks show large drops
in both shear and compressional wave velocities (Kern
1978, 1982) as they pass through the transition temperature,
whose pressure dependence is very well constrained by pis-
ton cylinder, high-pressure dilatometry and diamond-anvil-
cell experiments (Shen et al. 1993; Raz et al. 2002).

At a given pressure (P), the effects of the phase transi-
tion on the elasticity of quartz are spread over a wide range
of temperature (T), to the extent that the bulk modulus of
α-quartz at room conditions, more than 500 °C below the
transition, is only 60% of the value that would be expected
without the transition (Carpenter et al. 1998; Lakshtanov
et al. 2007; Abers and Hacker 2016; Angel et al. 2017).
Conventional simple EoS fail to describe the rapid volume
changes and the behaviour of the elastic moduli near the
transition in quartz. To overcome this issue, some authors
have related heat capacity, thermal expansion, and elastic
compliances using Pippard (1956)'s equations, without
explaining precisely the behaviour away from the tran-
sition point (Hughes and Lawson 1962; Garland 1964;
Klement and Cohen 1968; Coe and Paterson 1969; Bach-
heimer and Dolino 1980; Dolino et al. 1983; Hosieni et al.
1985; Dorogokupets 1995). Carpenter et al. (1998) have
successfully modelled all of the details of the α-β quartz
transition as a function of temperature using Landau theory.
Angel et al. (2017) extended this analysis to high pressures
and developed a new P-V-T EoS that fully describes the
volume, density, and bulk modulus of quartz. Apart from
the calculation of phase equilibria for the interpretation of
phase assemblages in terms of metamorphic conditions, this
EoS is used extensively in elastic thermobarometry to infer
the P and T conditions prevailing at the time of entrapment
of quartz inclusions in phases such as garnet during garnet
growth (e.g. Kohn et al. 2023). The EoS of quartz and simi-
lar models (e.g. Hacker and Abers 2004; Abers and Hacker
2016) also show that seismic velocity contrasts in the crust,
such as those observed beneath the Tibetan Plateau, may
be attributed to the drop in velocities and the bulk modu-
lus associated with the α-β quartz transition (Marini and
Manzella 2005; Zappone and Benson 2013; Sheehan et al.
2014). Furthermore, it is suggested that the large changes in
the elastic properties associated with the transition can also
alter the mechanical properties and induce a weakening of
the crust (Johnson et al. 2021; Morana et al. 2023).

Even though it is associated with crustal processes, the
changes in the elastic properties of quartz due to the α-β
transition are mostly constrained by data collected at room
pressure,and at high-temperature(HT). In fact, the only P-T
dataset available is from Raz et al. (2002), which extends

to 0.35 GPa and 700 °C, conditions still too low to con-
strain the elastic behaviour at crustal depths. Recently,
Moarefvand et al. (2024) attempted to assess changes in
compressional wave velocities across the transition at high-
pressure (HP). Although their results suggested a lower
velocity than expected in the β field, they could not fully
characterize the behavior across the transition. Here, we
report the first dataset of elastic wave velocities of quartz
collected at simultaneous *P* and *T* across the phase boundary
and assess whether the existing models for the properties of
quartz at crustal conditions are correct.

Methods

Starting material

The material used for the experiments was novaculite, a
sedimentary rock composed of microcrystalline quartz pres-
ent in the Ouachita Mountains of Arkansas and Oklahoma,
and in the Marathon Uplift and Solitario regions of Texas
(Lowe and Stone 1977). The block of novaculite used for
the experiments consists of 99% extra-fine grained quartz
(3–6 µm) previously tested for ultrasonic measurements
(Moarefvand et al. 2024). Prior to the high pressure experi-
ments we conducted active acoustic tests on the novaculite
block which showed no detectable anisotropy in primary
(P) and secondary (S) wave velocities. Cylindrical samples
(discs) of 1.6 mm × 0.62 mm were then extracted from the
same novaculite block for synchrotron experiments. These
samples were carefully polished on both sides to achieve a
reflective surface suitable for analysis.

X-ray diffraction in the Large Volume Press

Synchrotron X-ray diffraction patterns were collected dur-
ing Large Volume Press (LVP) experiments performed at
the ID06 beamline at the European Synchrotron Radiation
Facility (ESRF) in Grenoble, France. The wavelength of the
monochromatic incident X-ray beam (0.5 mm × 0.5 mm
size) was λ = 0.234818 Å (Crichton et al. 2024). Diffraction
data were collected every 3 s with a PILATUS 3X CdTe
900K-W-ESRF 2D detector (Crichton et al. 2023). Calibra-
tion of the instrumental parameters was performed using
lanthanum hexaboride (LaB₆, SRM660a). In order to obtain
correct estimates of the room pressure unit-cell volume
(V₀), a data collection was also performed at the end of the
experiment at room conditions. The LVP was used in a 6–8
configuration. The octahedral high pressure cell assembly
was compressed via eight cubic anvils with 4 mm trunca-
tions and six second stage anvils. One cylindrical novacu-
lite sample was enclosed in a 10 mm edge MgO octahedron
equipped with an X-ray window of cemented boron-epoxy rods. The sample was situated between two 0.2 mm thick Pt foils, used as strain markers and acoustic wave reflection surfaces. A 1.5 mm long boron nitride (BN) cylinder was placed between the upper foil and the type C thermocouple (see Fig. 1). X-ray images of the sample were collected every minute during the experiment in order to record the length variations during the loading and heating cycles. The heating and pressurisation rates were sufficiently slow (about 270 °C/h and 0.5 GPa/h) that consecutive diffraction patterns are indistinguishable from one another. Therefore only every 100th pattern, corresponding to a time step of 5 min, was refined with the Rietveld method using the TOPAS software (Coelho 2018). Because the X-ray beam illuminated not only the sample but also the entire sample assembly, the diffraction patterns contain peaks belonging to other phases in addition to quartz, such as BN, MgO, Al₂O₃ and Pt which were all included in the Rietveld refinements.

## P and S wave velocity measurements

In our acoustic setup, we employed a LiNbO₃ transducer attached to the first stage anvils. Measurements were conducted using the pulse-echo method (Crichton et al. 2024). Travel times for P- and S-waves were obtained from waveforms collected at frequencies of 30 and 60 MHz respectively by cross-correlating the reflections corresponding to

<figure><img src="image_3.png" /><figcaption>**Fig. 1** Schematic of the assembly used in the synchrotron experiments. The novaculite sample (violet) is enclosed in a 10 mm edge MgO octahedron, which features an X-ray window made of cemented boron-epoxy rods. The sample is positioned between two 0.2 mm thick platinum (Pt) foils (blue). A 1.5 mm long boron nitride (BN) cylinder (white) is placed between the upper Pt foil and the type C thermocouple, placed in a ceramic cement</figcaption></figure>

the alumina rod and the sample itself. This cross-correlation methodology, widely used in seismological studies, results in a substantial reduction of errors in P- and S-wave measurements, often achieving an order of magnitude improvement or more, particularly when waveform similarities are present (Schaff and Waldhauser 2005). In our measurements the initial and most prominent signal observed is the reflection from the cube-buffer rod interface, followed by buffer rod-top of sample and then from the bottom of the sample. There are a number of subsequent internal reflections (all P-waves, see Supplementary materials) followed by S-wave reflections. Arrival times collected during the experiment were stacked in order to observe their evolution with respect to the time of the experiment. Travel times were converted to velocities by using the length of the sample determined by X-ray imaging (see Supplementary materials for details).

## EBSD

Electron Back Scatter Diffraction (EBSD) analysis was performed on the polished sample recovered from the experiment. The assembly was embedded in an epoxy mount and the sample was exposed by successively polishing with 10 µm, 6 µm, 3 µm, 1 µm, and 0.25 µm diamond pastes. The last polishing stage was performed using colloidal silica. Analyses were conducted at the Ecole Normale Superieure (Paris) using a FEG-SEM ZEISS Zigma instrument with an accelerating voltage of 10 kV. The EBSD maps were acquired on half of the sample, with a step-size of 1 µm. We applied a pre-processing operation with a 6 nearest neighbors hole filling algorithm to fill in the pixels that were not indexed after the map acquisition. We processed the collected maps using the MTEX MATLAB toolbox to determine grain boundary misorientations, grain size and shape parameters (Bachmann et al. 2010).

## Calculations for a P–T path

Existing data on the α-β quartz transition were obtained at room pressure and high temperatures (Lakshtanov et al. 2007) or viceversa (Wang et al. 2015). There are only a few in-situ studies on the transformation at simultaneous high-pressure and high-temperature (HP-HT), in which the highest pressure reached is 0.35 GPa (Fielitz 1971; Christensen 1979; Kern 1978; Raz et al. 2002). In this study we were able to cross the transition several times, both in temperature and in pressure at pressures above 2 GPa. The most informative experiment was performed with an initial heating, followed by loading and unloading stages under hydrostatic conditions. This sequence crossed the transition three times, α→β then β→α and finally α → β.
To calculate the pressure and temperature conditions reached during this experiment, we applied a methodology that combines the elastic properties of quartz as a function of *P*, *V*, *T* with the heater-power calibration of the LVP at the ID06 beamline. The initial intention was to obtain temperatures from a type-C thermocouple. These thermocouples are designed for the high temperature conditions that we expected to reach during these experiments. In the assembly, the thermocouple was placed in MgO cement, a few millimeters away from the sample (see Fig. 1). In an early stage of analysis it was determined that the temperature measured by the thermocouple was far from that indicated by the quartz EoS (Angel et al. 2017) and the position of the phase boundary. Therefore, we relied upon a generalised power curve as a zeroth-order estimation of temperature. The effect of pressure on the temperatures (at constant power) was estimated considering the change in temperature recorded by the thermocouple and rescaled appropriately (see Supplementary materials for details).

This method is functional but involves some uncertainties. In fact, the highest pressure we obtained for the experiment is 3.25 GPa at 1174 °C. This is slightly above the quartz-coesite equilibrium (Bose and Ganguly 1995), but no coesite was observed in the X-ray diffraction patterns. At this temperature, the coesite stability field was crossed by only 0.1 GPa, hence we have assumed that this value represents the minimum uncertainty on the pressure estimate we obtained with this method. Pressures were then calculated considering the obtained temperatures and the unit-cell volumes from the refinements of the diffraction patterns using the EoS from Angel et al. (2017).

# Results

## X-ray diffraction along the α-β quartz transition

X-ray diffraction data play a crucial role in interpreting the results of this experiment. The Rietveld refinements in Fig. 2 show the phases present and their evolution with respect to pressure and temperature. Unfortunately, neither the diffraction peaks of BN (too weak) nor Pt (too much preferred orientation) provide accurate unit-cell parameters, making them unsuitable as standard materials. Consequently, the most reliable results from the refinements are the unit-cell parameters of quartz (α and/or β), which we used to characterize further the nature of the transition.

Of particular interest is the temporal evolution of the collected diffraction patterns. Figure 2 illustrates the stacked patterns during the initial heating stage, where the transition occurred once. The 2θ angle of the 101 reflection decreases with increasing temperature, reflecting normal thermal

expansion, until some grains in the sample begin to transform into β-quartz. At this point, the intensity associated with the 101 diffraction peak decreases. This corresponds to the transition region related to the coexistence of both α and β-quartz peaks which are close to each to other but do not overlap. The intensity then recovers when the sample is completely transformed into β-quartz.

## Pressure and temperature path evolution, velocity and volume calculations

In this section, we describe the *P*–*T* path calculated for our experiment, highlighting the phase transitions observed at specific points along the path (see Fig. 3). At the beginning of the experiment, the novaculite sample was loaded and pressurised to 0.14 GPa. Subsequently, at a constant applied load, the temperature was gradually increased by increasing power supplied to the heater. At 1258 °C and 2.83 GPa we reached the phase transition boundary as demonstrated by the first appearance of β-quartz in the diffraction patterns. The pressure increase in the sample during the temperature ramp from room temperature corresponds to the thermal pressure of approximately 2.7 GPa predicted from the EoS of quartz for these temperatures and pressures (Angel et al. 2017). The *P*–*T* path of the sample (Heating stage 1, Fig. 3a) therefore lies very close to an α-quartz isochore, thus reflecting the fact that the cell assembly remains in conditions close to constant volume.

The transition is very evident in the large drop in the measured velocities, particularly $V_p$, as shown in Fig. 4. The transition is also marked by the transient coexistence of the 101 reflections from both α and β-quartz. After the transition, despite the continued increase in power up to almost 1400 °C, the calculated pressure records a drop of almost 1 GPa, from 2.83 to 2 GPa (see Fig. 3a). At this point the sample was completely in the β-field and we initiated the loading stage. During this stage we observed a decrease in temperature caused by the lower efficiency of the graphite furnace (see Fig. 3b). The transition from β back to α-phase during the loading was marked by a significant dip in $V_p$, as observed during the heating stage. Upon reaching the transition, and despite the fact that the pressure cell was being loaded, the *P*–*T* path describes a transient drop of pressure along the transition boundary before eventually passing into the α-field. The loading was stopped at high pressure close to the quartz-coesite boundary before any coesite peaks appeared in the diffraction patterns and the unloading was started, crossing the transition for the third time in the α → β direction (Fig. 3c). Finally, a short heating cycle was conducted to stabilize the β phase before quenching the experiment.
<figure><img src="image_4.png" /><figcaption>**Fig. 2** a Rietveld refined X-ray diffraction patterns collected in the α-field (red, room T, 0.14 GPa) and in the β-field (blue, 1380 °C, 2 GPa). The principal reflections of quartz were labeled and tick marks</figcaption></figure>

**Analysis of the microstructure**

The initial length of the sample was 0.62 mm, but at the onset of the heating stage, the radiography showed that it measured 0.55 mm. This length reduction can only partly be explained by elastic loading (2% shortening at 3 GPa).

were used to identify the other phases of the assembly. b Evolution of the 101 reflection of quartz (the most intense one) across the transition. For the full 2θ range please refer to the supplementary materials

Therefore, most of it was caused by some plastic deformation upon cold-compression and subsequent relaxation while the sample sat overnight at high pressure and room temperature. However, no further significant shortening was observed at high temperature conditions. X-ray images collected during the various heating and loading-unloading
<figure><img src="image_5.png" /><figcaption>**Fig. 3** *P*–*T* path calculated for the experiment, with the observed phase transitions. **a** Starting at room temperature and 0.14 GPa, the novacu- lite sample underwent a gradual temperature increase (in orange) while maintaining a constant load. However the sample exhibited a signifi- cant thermal pressure of about 2.7 GPa. The *P*–*T* evolution in this stage follow a nearly-isochoric trend. At 2.83 GPa and 1258 °C, the tran- sition from α to β-quartz was observed. Despite further temperature</figcaption></figure>

increase, pressure dropped to 2 GPa. **b** The loading (green line) caused a temperature decrease due to furnace deformation and the transition was crossed a second time at slightly lower pressure and temperature than during the heating stage. **c** The transition was crossed a third time during the unloading stage (blue line) and this was followed by a short heating stage (in orange) in the β-field before the quenching of the experiment

cycles showed that the length of the sample then remained constant throughout the heating stage. No major cracks were observed in the recovered sample (see supplementary materials). Along with these preliminary observations we acquired EBSD maps on different portions of the sample.

The indexed quartz grains are often separated by Dauphiné twin boundaries (see Fig. 5) which is the result of a 60° rotation around the *c*-axis. This is also clear in the histogram in Fig. 5 which illustrates grain misorientations across grain boundaries, the correlated misorientations (between two adjacent grains) and uncorrelated misorientations (between grains that are not directly in contact). The

measured distribution of grain boundary misorientations closely follows the theoretical trends (lines in Fig. 5) for randomly oriented grains for every angle except for 60°. This specific angle is where Dauphiné twins form, and the high frequency of this angle distribution observed in the histogram confirms the presence of numerous twins within the sample. By considering the ratio between the length of the twin boundaries and the length of quartz boundaries, we can estimate that 22% of grain boundaries are twins, which is far higher than the 0.5% in the starting material (Moarefvand et al. 2024). This means that passing our sample through the α-β transition has resulted in the formation of Dauphiné
<figure><img src="image_6.png" /></figure>

**Fig. 4** Variations of $V_p$, $V_s$ and unit cell volumes during the experiment, with the different stages of the experiment identified with different colors. Note the large variations of $V_p$. The minima show that the α-β quartz boundary was crossed three times during the experiment. Estimated uncertainties for $V_p$ and $V_s$ are ±0.07 and ±0.04 km/s, respectively. The transition is less evident in the volume data because of gradients in P and/or T across the sample. The detailed values of velocities and volumes are reported in Table 1 S of the supplementary materials

twins as reported previously (Heaney and Veblen 1991; Wenk et al. 2009; Moarefvand et al. 2024).

Discussion

$V_p, V_s$ and adiabatic bulk modulus ($K_S$) compared
with EoS models

In order to place our new results in a proper context, we first review in more detail the constraints on the velocity and elasticity changes across the α-β quartz transition from previous studies (see Fig. 6). The models of Abers and Hacker (2016) (AH16) and Angel et al. (2017) are both based on several assumptions regarding the pressure and temperature dependencies of the elastic properties of quartz. Both models assume that in the α-field the bulk modulus increases with pressure, i.e. that $K'$ is positive as indicated by experiments (Angel et al. 1997; Calderon et al. 2007; Kimizuka et al. 2007; Wang et al. 2015). In the absence of data, both Abers and Hacker (2016) (AH16) and Angel et al. (2017) assume that the excess properties of α-quartz, and the magnitude of the resulting elastic softening do not change with pressure. However, while both models reproduce the variation

<figure><img src="image_7.png" /></figure>

**Fig. 5** Electron Back Scattered Diffraction (EBSD) map of the recovered novaculite sample showing the presence of Dauphiné twins, marked by the white lines. The grains were colored according to their crystallographic orientation. The histogram represents the frequency of misorientation angles across the grain boundaries. The measured

orientations closely follow the theoretical distributions (overlapping red and yellow lines) for correlated and uncorrelated grains in a material with random distribution of grain orientations, except for 60°, which indicates the high frequency of grain boundaries corresponding to Dauphiné twins
<figure><img src="image_8.png" /></figure>

**Fig. 6** a Densities from Raz et al. (2002), the EoS from Angel et al. (2017), and the thermodynamic model by Abers and Hacker (2016) at room pressure. The three curves agree both in α-field and at the transition point, but diverge slightly in the β-field. b A comparison of densities calculated at different pressures. With increasing pressure,

the AH16 model shows a density behavior at the transition that does not align with the EoS. This discrepancy is due to erroneous assumptions regarding the pressure and temperature dependencies of the elastic properties of quartz

**Fig. 7** $V_p$, $V_s$, $K_s$ and $\mu$ from AH16 model and EoS of quartz (Angel et al. 2017) compared with our data, during the heating and the loading cycles. The experimental data are reported with their standard deviation calculated over 25 points. In the case of $\mu$, the uncertainty is smaller than the symbol size. In the α-field, experimental values align well with model predictions during heating and loading, reflecting negligible changes in the sample length. The model by AH16 predicts the phase transition at 1175 °C, differing from the experimental data and EoS which place it around 1260 °C. The cause for this discrepancy is detailed in section 4.2. In the β-field, $V_p$ and $K_s$ are 14% lower than model and EoS predictions. See detailed values in Tables 1 and 2

<figure><img src="image_9.png" /><figcaption>Loading</figcaption></figure>

of density (Fig. 6a) and bulk modulus at room pressure, the AH16 model predicts negative thermal expansion as the α-β transition is approached at high pressures (Fig. 6b), which is incompatible with the well documented behavior of α quartz (Müser and Binder 2001). In the β-field, the AH16 model assumes that $K'$ remains constant and equal to 4. This latter assumption is not correct because with increasing pressure in the β-field, the bulk modulus must first increase and then decrease as the transition is approached, regardless of the temperature (Angel et al. 2017). Furthermore, the model does not consider the influence of the transition on

the elastic properties of β-quartz, despite the evidence of in-situ elasticity measurements (e.g. Lakshtanov et al. 2007).

In the AH16 model, this density is then used to calculate $V_p$, $V_s$ and $K_s$. These values were compared to the experimental results obtained in the different cycles of the experiment and the EoS of Angel et al. (2017), with particular focus on the first heating stage and the subsequent loading performed in the β-field (see Fig. 3). Accordingly, we juxtaposed the predicted $V_p$, $V_s$ and $K_s$ values from the model and the EoS against the collected data for the initial heating stage and the first loading of the experiment (Fig. 7). Since
<table><caption>**Table 1** Temperature, pressures, and elastic moduli over the first temperature ramp of the experiment</caption><thead><tr><th>T (°C)</th><th>P (GPa)</th><th>K<sub>s</sub> (GPa)</th><th>G (GPa)</th><th>Phase (α/β)</th></tr></thead><tbody><tr><td>22</td><td>0.14</td><td>—</td><td>40.18</td><td>α</td></tr><tr><td>127</td><td>0.28</td><td>—</td><td>40.16</td><td>α</td></tr><tr><td>251</td><td>0.46</td><td>—</td><td>40.73</td><td>α</td></tr><tr><td>314</td><td>0.56</td><td>—</td><td>40.92</td><td>α</td></tr><tr><td>439</td><td>0.78</td><td>35.25</td><td>41.3</td><td>α</td></tr><tr><td>563</td><td>1.02</td><td>35.25</td><td>41.29</td><td>α</td></tr><tr><td>688</td><td>1.28</td><td>35.5</td><td>41.09</td><td>α</td></tr><tr><td>750</td><td>1.41</td><td>34.55</td><td>40.87</td><td>α</td></tr><tr><td>856</td><td>1.65</td><td>33.86</td><td>40.45</td><td>α</td></tr><tr><td>987</td><td>1.97</td><td>31.98</td><td>40.01</td><td>α</td></tr><tr><td>1024</td><td>2.07</td><td>31.38</td><td>39.98</td><td>α</td></tr><tr><td>1118</td><td>2.33</td><td>30.11</td><td>39.53</td><td>α</td></tr><tr><td>1212</td><td>2.65</td><td>27.97</td><td>38.86</td><td>αβ</td></tr><tr><td>1258</td><td>2.83</td><td>25.35</td><td>38.23</td><td>αβ</td></tr><tr><td>1260</td><td>2.55</td><td>23.29</td><td>37.81</td><td>αβ</td></tr><tr><td>1273</td><td>2.25</td><td>41.19</td><td>37.31</td><td>αβ</td></tr><tr><td>1292</td><td>2.29</td><td>45.77</td><td>37.51</td><td>β</td></tr><tr><td>1311</td><td>2.26</td><td>49.45</td><td>37.49</td><td>β</td></tr><tr><td>1349</td><td>2.18</td><td>54.33</td><td>38.01</td><td>β</td></tr><tr><td>1350</td><td>2.12</td><td>55.57</td><td>37.98</td><td>β</td></tr><tr><td>1380</td><td>1.99</td><td>—</td><td>—</td><td>β</td></tr></tbody></table>

$K_s$ and $G$ are obtained from $V_p$ and $V_s$ as shown in Fig. 4. Pressures are calculated from Angel et al. (2017). Note that missing values of $K_s$ and $G$ are indicated by a dash (-), due to errors in the cross-correlation

the EoS from Angel et al. (2017) does not allow direct calculation of the $V_p$ and $V_s$, these values were calculated by combining the EoS volume (i.e., density) predictions with the $\mu$ obtained from the present experiments.

To calculate density and $K_s$ from both the AH16 model and the EoS, it is first necessary to determine whether the P-T conditions correspond to $\alpha$ or $\beta$-quartz. This was done considering two different descriptions that are separated by 10°C at a various pressures (Shen et al. 1993; Angel et al. 2017). In the case of the present experiment, the P-T path obtained intercepts these two boundaries with a very low angle (see supplementary materials), yielding an 85°C difference for the transition point (Fig. 3). This explains the occurrence of the transition at lower T in the AH16 model with respect to the data (see Fig. 7a). However, our data are in agreement with the EoS transition point. This is explained by the fact that the unit-cell volumes obtained with the refinements of the XRD patterns were then used with the EoS to calculate pressures and temperatures. For the loading stage, the two boundaries are intercepted by a nearly isothermal path, resulting in comparable transition temperatures and pressures separated by only 60 MPa. Hence, the model predictions and our data are in better agreement during the loading stage with respect to the $V_p$ minimum corresponding to the transition (see Fig. 7).

<table><caption>**Table 2** Temperature, pressures and elastic moduli over the loading stage</caption><thead><tr><th>T (°C)</th><th>P (GPa)</th><th>K<sub>s</sub> (GPa)</th><th>G (GPa)</th><th>Phase (α/β)</th></tr></thead><tbody><tr><td>1382</td><td>1.92</td><td>57.00</td><td>38.64</td><td>β</td></tr><tr><td>1377</td><td>1.85</td><td>57.36</td><td>38.80</td><td>β</td></tr><tr><td>1360</td><td>1.69</td><td>57.01</td><td>38.92</td><td>β</td></tr><tr><td>1342</td><td>1.66</td><td>56.99</td><td>38.91</td><td>β</td></tr><tr><td>1337</td><td>1.67</td><td>57.00</td><td>38.91</td><td>β</td></tr><tr><td>1319</td><td>1.84</td><td>57.36</td><td>38.80</td><td>β</td></tr><tr><td>1302</td><td>2.12</td><td>56.74</td><td>38.55</td><td>β</td></tr><tr><td>1290</td><td>2.37</td><td>—</td><td>—</td><td>β</td></tr><tr><td>1279</td><td>2.64</td><td>50.92</td><td>38.59</td><td>β</td></tr><tr><td>1261</td><td>2.84</td><td>36.69</td><td>38.53</td><td>β</td></tr><tr><td>1250</td><td>2.78</td><td>36.41</td><td>38.69</td><td>β</td></tr><tr><td>1232</td><td>2.71</td><td>25.36</td><td>38.87</td><td>αβ</td></tr><tr><td>1221</td><td>2.86</td><td>27.32</td><td>40.79</td><td>αβ</td></tr><tr><td>1209</td><td>2.97</td><td>31.12</td><td>42.18</td><td>α</td></tr><tr><td>1192</td><td>3.12</td><td>34.46</td><td>43.25</td><td>α</td></tr><tr><td>1186</td><td>3.22</td><td>35.87</td><td>43.80</td><td>α</td></tr><tr><td>1174</td><td>3.25</td><td>36.62</td><td>43.87</td><td>α</td></tr></tbody></table>

The first dipping of $K_s$ do not represent the transition (see Fig. 7)

Shear-wave velocities and densities (derived from XRD unit-cell data) were used to calculate the shear modulus during both the heating and loading phases (see Fig. 7). The shear modulus, along with $V_s$, exhibits less variation compared to the bulk modulus. During the heating stage, it decreases from 41 GPa in the $\alpha$-phase to 38 GPa in the $\beta$-phase. The shear modulus obtained for the experiment was used to calculate velocities from the EoS of Angel et al. (2017), where this elastic parameter is not given. All the calculated elastic moduli ($K_s$ and $G$) for a given P-T are reported in Table 1 (heating stage) and Table 2 (loading stage).

**The α field** In the $\alpha$-field, the $V_p$ data are close to the values predicted by the AH16 model and the EoS. This consistency is observed during both the heating and loading stages. However, a slight difference of approximately 0.1 km/s is observed, mostly in the heating stage. This may be due to the fine-grained nature of the novaculite sample used for the experiment, which can affect the effective elastic properties (Kern 1978). Velocity measurements conducted under room conditions at the laboratory on the novaculite sample yield a $V_p$ of 5.94 km/s. In the ESRF experiment, due to large errors in the cross-correlation in the low-temperature region, it was not possible to obtain a precise value of $V_p$ (and therefore $V_s$ and $K_s$) below 400 °C. To compare the $V_p$ obtained at 400 °C at ESRF with that obtained at the lab under room conditions, we first extrapolated the former to room temperature by using the value of $\frac{dV_p}{dT} = -0.0002\text{km s}^{-1}\text{K}^{-1}$ (Abers and Hacker 2016). It is noteworthy that the value of $V_p$ at 400 °C was collected at the initial experimental pressure of 0.14 GPa. According to the AH16 model, the
<figure><img src="image_10.png" /><figcaption>**Fig. 8** **a** Evolution of the 100 reflection from α to β-phase. The coexistence of the two phases is highlighted with different colors. **b** A schematic representation of the assembly during the α-β quartz transition showing the inferred distribution of phases inside the sample and how</figcaption></figure>

velocity at 0.14 GPa is increased by 0.02 km/s with respect to room pressure. Consequently, the velocity obtained by extrapolation of the ESRF data from 400 °C and 0.14 GPa to room conditions is 5.89 ± 0.07 km/s. This value matches the measured data at room conditions at the laboratory (5.94 km/s) within the uncertainties, validating the reliability of the experimental $V_p$ values. Therefore, the observed difference of ~ 0.1 km/s between our measurements and the predicted values of AH16 strongly suggest that grain boundaries do soften the elastic properties of the bulk material (Moarefvand et al. 2024).

**The transition point** The evolution of the diffraction patterns with *T* and *P* shows the coexistence of the two phases, α and β-quartz in the sample (see Fig. 8a). At the predicted temperature of the transition, a small shoulder on the 100 reflection of the α-phase appears. This shoulder grows until it is clearly the 100 reflection of β quartz. This evolution passes through a transient stage where a bimodal shape results from the convolution of both α and β 100 reflections with increasing temperature. During the coexistence of the two phases, $V_p$ drops as a result of part of the sample being very close to the transition and thus having very low velocities. At the transition, the first derivatives of Gibbs's free energy are continuous (e.g. the volumes of α and β-quartz are the same). Therefore the transition is thermodynamically continuous and α and β-quartz cannot coexist at a given *P* and *T*, so their coexistence in the experimental sample indicates that the sample is subject to gradients in pressure or temperature or both. If we assume that the gradient is only in temperature, it can be estimated considering

<figure><img src="image_11.png" /><figcaption>(b)</figcaption></figure>

acoustic waves and X-rays cross the sample. Due to the simultaneous presence of both quartz phases a temperature gradient and a more moderate slope of $V_p$ is present at the transition

the Δ*T* between the first observation of the shoulder appearing on the β-quartz main peak (1175 °C), to the complete disappearance of α-quartz peaks (1292 °C), at a slightly higher temperature than the lowest $V_p$ recorded. The same appears to be valid also for the loading stage. The temperature gradient across the sample is therefore estimated to be around 120°C. In Moarefvand et al. (2024), the temperature gradient in the sample is evident from the shape of the $V_p$ curve at the transition. Rather than a sharp change in velocities from the α to the β-field, the authors demonstrate that the velocities exhibit a smoother excursion due to the temperature gradient. In the heating stage of our experiment this behaviour is not observed but can be explained by an experimental artifact. At the transition, the heating power was kept constant and then increased again to fully cross the transition, resulting in a sharper transition than would occur with a constant rate of temperature increase. A smoother transition is, however, observed in the loading stage (Fig. 7). Even though the temperature decreases during loading due to the deformation of the furnace, the thermal gradient is probably lower than during the heating cycle because of the extended time the sample remained at high temperatures in the β field. Between the first appearance of α-quartz peaks in the loading (1291 °C) and the disappearance of β-quartz peaks (1264°C), the temperature gradient is only about 30 °C. The fact that the velocity data reflect the temperature gradient is a result of the geometry of the experiment. During the coexistence of the two phases, the high-temperature β-quartz, must be present in parts of the sample that are hotter and therefore closer to the furnace walls. The present
data reveal that the ultrasonic waves used for the pulse-echo
technique traverse the entire sample, thus sampling both
phases present (Fig. 8b). Similarly, the beam-size used for
XRD is almost as large as the sample and therefore irradi-
ates the entire novaculite disc, producing a powder pattern
with peaks from both phases (see Fig. 8a) which exist in the
hotter (β) and cooler (α) regions of the sample. The dip in
$V_p$ observed in the experimental dataset is smaller than pre-
dicted from the EoS models because the β-quartz regions
reduce the arrival time, acting as a faster medium for acous-
tic wave propagation, while the un-transformed α regions in
the sample have a lower velocity. In other words, the ultra-
sonic measurement method used here yields velocities that
are between those of the fast and slow phases when both are
present. From room temperature to the transition point, the
model shows a $\Delta V_p$ of 0.81 km s$^{-1}$, whereas the experi-
mental value is only 0.58 km s$^{-1}$. The lowest $V_p$ value is
recorded when the transition is nearly complete. Therefore,
as the transition progresses in either direction, the velocities
reflect both the softening due to the transition and the evolv-
ing proportions of the α and β-phases.

At the transition, we observe a pressure drop, both in
the heating and in the loading stage (see Fig. 4). Since this
is asymmetric across the transition, it is unlikely to be the
result of a volume change or a discontinuity of the EoS from
Angel et al. (2017) in the β field. Rather, the pressure drop
could result from a partial stress-release related to the soft-
ening of quartz at the transition, undetectable because of the
fixed azimuth angle during X-ray diffraction patterns col-
lection. This effect might have implications on the mechan-
ics and stress-bearing capabilities of the crust at the α-β
quartz transition. **The β field** In contrast to the results in the
α-field, the velocity (and the adiabatic bulk modulus) mea-
surements within the β-field deviate significantly from the
AH16’s model predictions and the EoS (as shown in Fig. 7).
While AH16 and the EoS from Angel et al. (2017) predict
a peak velocity of 7.45 km/s, our data are approximately
14% slower, reaching a constant value of 6.49(7) km/s. This
difference cannot be attributed to errors in the calculation of
the sample length because the same error would have been
evident in the α-field, which is not the case. Due to the tem-
perature gradient evaluated in the sample, the discrepancy
in $V_p$ might be attributed to an averaging effect between the
values at the transition and those of the β-field, which would
only be possible if the considered P–T conditions were too
close to the transition boundary. In the first heating stage,
after crossing the phase boundary line, we observed a clear
pressure drop, as shown in Fig. 3, and reached a pressure
of 2 GPa in the β field. According to the boundary equa-
tion outlined in Angel et al. (2017), at this pressure, the
transition temperature is predicted to be 1050 °C, while our
experiment recorded 1380 °C. This difference is more than

twice the temperature gradient we have inferred in the sam-
ple assembly (see above), so no part of the sample would
have been near to the boundary conditions, and therefore the
sample did not exhibit transition-induced softening. Neither
can this softer bulk modulus be attributed to a reaction or
breakdown of quartz, because no new phases were detected
in the diffraction patterns.

The EoS employed in this study (Angel et al. 2017) and
the AH16’s model agree on the values of velocities and bulk
modulus for β-quartz at high pressure. Both predict that at
2 GPa and around 1380 °C (Fig. 7), the bulk modulus is
about 82 GPa whereas the lower velocities measured in this
experiment correspond to $K_s = 57(6)$ GPa. This discrepancy
may be simply a consequence of the lack of high P-T data
available to constrain the EoS of Angel et al. (2017) and
AH16. The fact that the high pressure value of $K_s = 57(6)$
GPa is lower than the value of around 70 GPa measured at
room pressure by Lakshtanov et al. (2007) at 900 °C sug-
gests that the intrinsic value of $K'$ of the β-phase may be
negative over the entire pressure range from room pressure
to 2 GPa. Another explanation could be that the softening
effects of the transition at high pressure extend far further
from the transition than the small interval of around 50 K
observed at room P (Lakshtanov et al. 2007). However, this
seems unlikely since a plateau is observed in $V_p$ (and there-
fore in $K_s$) when moving away from the transition and into
the β-field, thus suggesting that these data are not affected
by the transition softening. Our results demonstrate that fur-
ther precise measurements of the in-situ density and wave
velocities of β-quartz are needed around 1300 °C over the
0–3 GPa pressure range, ideally on a quartz single crystal
without temperature gradients across it, to avoid grain-grain
stresses and to ensure that the transition occurs simultane-
ously throughout the sample.

Implications of the new data of the α-β quartz
transition

Given the prevalence of quartz in continental crust, its phase
transitions hold significant potential to shape the tectonics,
rheology, and dynamics of the crust. The α-β quartz phase
transition, in particular, may significantly impact the elastic
properties of rocks, potentially leading to their weakening.
This mechanism has been proposed by Johnson et al. (2021)
on the basis of numerical modeling. Their simulations dem-
onstrate that the elastic stresses generated by the α-β quartz
transition can exceed the brittle tensile and shear strengths
of common crustal rocks, potentially causing brittle failure
and/or damage. In-situ heating experiments on quartz inclu-
sions in garnets (Morana et al. 2023; Gilio et al. 2023) show
similar results. As the α-β transition in the quartz inclusions
is approached, the stress in the inclusions greatly increases
because the inclusions are constrained by their garnet host. It is observed that this stress causes fracturing or explosive shattering of the surrounding garnet. These models and experiments carried out in the last few years illustrate the importance of the α-β quartz transition as a potential weakening and fracturing mechanism in both host-inclusion systems and rocks containing quartz. The new evaluation of bulk modulus, shear modulus and velocities that we have reported at *HP-HT* conditions should help to better constrain these mechanisms, especially at the real conditions of the lower crust.

Moreover, the significance of the α-β quartz transition extends to the interpretation of variations in crustal temperatures. As an example, in the Tibetan region the temperature of the crust was characterized through seismic detection of the transition (Mechie et al. 2004), using the variation of *V*<sub>p</sub> at the transition. Consequently, in some subsequent studies, the α-β quartz transition has been widely used as a crustal thermometer and applied to interpret seismic tomography data. For instance, in the Himalayan region, the observed increase in the *V*<sub>p</sub>*V*<sub>s</sub> ratio within the crust is attributed to the transition in felsic rocks (Sheehan et al. 2014). However, our new data imply that the assumption of constant transition properties at crustal pressures built into the model (Abers and Hacker 2016) used to interpret seismic data may not be correct. In particular, our data demonstrate a smaller contrast in the velocities of the α and β phases, thus providing a better fit to the tomography data (Mechie et al. 2004; Sheehan et al. 2014), and would imply a larger portion of α-quartz in the lower crust. Similarly, Jagoutz and Behn (2013) interpreted the relatively low seismic velocities of the lower-crust as the predominance of α over β quartz, therefore constraining the PT conditions of these rocks, which is challenged by the lower-than-expected velocities obtained here in the β field. Furthermore, at the conditions of the lower crust, velocity variations could also be influenced by plastic deformation and recrystallization of quartz, which is not considered in this work. For these reasons, we suggest a careful use of the α-β quartz transition in interpreting tomography data at *HP-HT* and for crustal temperature calculations.

## Conclusions

This work represents the first experimental study of the elastic properties of the α-β quartz transition at simultaneous *HP* (over 1 GPa) and *HT*. Our experimental data in the α-quartz phase generally agree with models from literature, indicating that these are reliable for predicting the properties of α-quartz, at least in the *P*-*T* range of our experiments. Therefore, metamorphic P-T conditions calculated

using the EoS for quartz inclusions trapped as α-quartz are reliable, provided the EoS of the host is correct.

In the β-quartz stability field, our measured *V*<sub>p</sub>, *V*<sub>s</sub> and *K*<sub>s</sub> values are significantly lower than those predicted by both the AH16 model and the EoS of quartz, suggesting that they do not fully predict the real behavior of β-quartz under *HP-HT* conditions. Therefore interpretations of seismic data across the α-β quartz transition in terms of crustal temperature gradients and processes, particularly in tectonically active regions such as the Tibetan Plateau, should be treated with caution. The same is true for calculations of entrapment conditions of quartz inclusions within the stability field of the β-phase. At low entrapment pressures, perhaps under 0.5 GPa at high temperatures, the EoS must still be dominated by the elastic properties of β-quartz measured at room pressure, so entrapment conditions may still be correct. But calculated entrapment pressures of β-quartz inclusions above 0.5 GPa and at temperatures far from the α-β phase transition boundary are unreliable. Resolving these issues for β-quartz requires further precise measurements of elasticity and wave velocities at the extreme conditions of the β-field.

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/s00410-0-25-02206-8.

**Acknowledgements** This work was financially supported by Vinci-Chapitre II grant from Université Franco-Italienne to G. Mingardi, Fondazione Cariplo grant agreement #2023-2431 to M. Alvaro, PRIN-MIUR projects n. 2020WPMFE9 to G. Pennacchioni and n. 2022AL5MSN to M. Cremonesi. We thank M. Gilio for discussions, suggestions and comments on this work and Damien Deldicque for his support and technical assistance during EBSD analysis. We thank Othmar Müntener, Evangelos Moulas and an anonymous reviewer for improving the quality of this work.

**Funding** Open access funding provided by Università degli Studi di Pavia within the CRUI-CARE Agreement.

**Data availability** All data utilized in this study is comprehensively presented within this published article and its supplementary files.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
## References

Abers GA, Hacker BR (2016) A MatLab toolbox and Excel workbook for calculating the densities, seismic wave speeds, and major element composition of minerals and rocks at pressure and temperature. *Geochem Geophys Geosyst* 17(2):616–624

Angel RJ, Allan D, Miletich R, Finger L (1997) The use of quartz as an internal pressure standard in high-pressure crystallography. *J Appl Crystallogr* 30(4):461–466

Angel RJ, Alvaro M, Miletich R, Nestola F (2017) A simple and generalised P-V-T EoS for continuous phase transitions, implemented in EosFit and applied to quartz. *Contrib Miner Petrol* 172:1–15

Bachheimer J (1980) An anomaly in the $\beta$ phase near the $\alpha-\beta$ transition of quartz. *J Phys Lett* 41(23):559–561

Bachheimer J-P, Dolino G (1980) Study of thermal expansion of quartz near the $\alpha-\beta$ phase transition under uniaxial stresses. *Ferroelectrics* 25(1):423–426

Bachmann F, Hielscher R, Schaeben H (2010) Texture analysis with MTEX-free and open source software toolbox. *Solid State Phenom* 160:63–68

Bose K, Ganguly J (1995) Quartz-coesite transition revisited: reversed experimental determination at 500 – 1200°C and retrieved thermochemical properties. *Am Miner* 80(3–4):231–238

Calderon E, Gauthier M, Decremps F, Hamel G, Syfosse G, Polian A (2007) Complete determination of the elastic moduli of $\alpha$-quartz under hydrostatic pressure up to 1 GPa: an ultrasonic study. *J Phys Condens Matter* 19(43):436228

Carpenter MA, Salje EK, Graeme-Barber A, Wruck B, Dove MT, Knight KS (1998) Calibration of excess thermodynamic properties and elastic constant variations associated with the alpha $\leftrightarrow$ beta phase transition in quartz. *Am Miner* 83(1–2):2–22

Christensen NI (1979) Compressional wave velocities in rocks at high temperatures and pressures, critical thermal gradients, and crustal low-velocity zones. *J Geophys Res Solid Earth* 84(B12):6849–6857

Coe RS, Paterson MS (1969) The $\alpha-\beta$ inversion in quartz: a coherent phase transition under nonhydrostatic stress. *J Geophys Res* 74(20):4921–4948

Coelho AA (2018) TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++. *J Appl Crystallogr* 51(1):210–218

Crichton WA, Kieffer J, Wattecamps P, Valls V, Berruyer G, Ruat M, Favre-Nicolin V (2023) Correction and integration of solid-angle data from the azimuthally resolving 2D detector at ID06-LVP. *ESRF J Synchrotr Radiat* 30(6):1149–1155. https://doi.org/10.1071/S1600577523008020

Crichton W, Thomson A, Rosenthal A, Spektor K, Druzhbin D, Winkler B, Schwarz M, Wattecamps P, Kieffer J, Hino R, Brussel D, Garlet R, Watier Y, Roth T, Berruyer G, Valls V, Mauro A, Ruat M, Favre-Nicolin V, Verbeni R (2024) EBS status of the large-volume press at beamline ID06-LVP. *High Pressure Res* 44:1–31. https://doi.org/10.1080/08957959.2024.2379354

Dolino G (1990) The $\alpha$-inc-$\beta$ transitions of quartz: a century of research on displacive phase transitions. *Phase Trans* 21(1):59–72

Dolino G, Bachheimer J, Zeyen C (1983) Observation of an intermediate phase near the $\alpha-\beta$ transition of quartz by heat capacity and neutron scattering measurements. *Solid State Commun* 45(3):295–299

Dorogokupets PI (1995) Equation of state for lambda transition in quartz. *J Geophys Res Solid Earth* 100(B5):8489–8499

Fielitz K (1971) Untersuchungen von kompressions-und scherwellengeschwindigkeiten in gesteinen unter erhöhtem druck. *Z Geophys* 37:943–956

Garland CW (1964) Generalized Pippard equations. *J Chem Phys* 41(4):1005–1008

Gilio M, Morana M, Angel R, Mihailova B, Alvaro M (2023) Does the polymorphic transition in quartz trigger lower crustal earthquakes? In: EGU general assembly conference abstracts, p 13491

Hacker BR, Abers GA (2004) Subduction Factory 3: an Excel worksheet and macro for calculating the densities, seismic wave speeds, and $H_2O$ contents of minerals and rocks at pressure and temperature. *Geochem Geophys Geosyst* 5(1)

Heaney PJ, Veblen DR (1991) Observations of the $\alpha-\beta$ phase transition in quartz: a review of imaging and diffraction studies and some new results. *Am Miner* 76(5–6):1018–1032

Hosieni KR, Howald RA, Scanlon MW (1985) Thermodynamics of the lambda transition and the equation of state of quartz. *Am Miner* 70(7–8):782–793

Hughes A, Lawson A (1962) Cylindrical approximation and the $\alpha-\beta$ quartz transition. *J Chem Phys* 36(8):2098–2100

Jagoutz O, Behn MD (2013) Foundering of lower island-arc crust as an explanation for the origin of the continental moho. *Nature* 504(7478):131–134

Johnson SE, Song WJ, Cook AC, Vel SS, Gerbi CC (2021) The quartz $\alpha\beta$ phase transition: does it drive damage and reaction in continental crust? *Earth Planet Sci Lett* 553:116622

Kern H (1978) The effect of high temperature and high confining pressure on compressional wave velocities in quartz-bearing and quartz-free igneous and metamorphic rocks. *Tectonophysics* 44(1–4):185–203

Kern H (1982) Elastic-wave velocity in crustal and mantle rocks at high pressure and temperature: the role of the high-low quartz transition and of dehydration reactions. *Phys Earth Planet Inter* 29(1):12–23

Kimizuka H, Ogata S, Li J, Shibutani Y (2007) Complete set of elastic constants of $\alpha$-quartz at high pressure: a first-principles study. *Phys Rev B-Condens Matter Mater Phys* 75(5):054109

Klement W Jr, Cohen LH (1968) High-low quartz inversion: thermodynamics of the lambda transition. *J Geophys Res* 73(6):2249–2259

Kohn MJ, Mazzucchelli ML, Alvaro M (2023) Elastic thermobarometry. *Annu Rev Earth Planet Sci* 51:331–366. https://doi.org/10.146/annurev-earth-031621-112720

Lakshtanov DL, Sinogeikin SV, Bass JD (2007) High-temperature phase transitions and elasticity of silica polymorphs. *Phys Chem Miner* 34:11–22

Le Chatelier H (1890) Sur la dilatation du quartz. *Bull Minér* 13(3):112–118

Lowe DR, Stone C (1977) The arkansas novaculite: some aspects of its physical sedimentation. In: Symposium on the Geology of the Ouachita Mountains, vol 1, pp 132–138

Marini L, Manzella A (2005) Possible seismic signature of the $\alpha-\beta$ quartz transition in the lithosphere of Southern Tuscany (Italy). *J Volcanol Geoth Res* 148(1–2):81–97

Mechie J, Sobolev SV, Ratschbacher L, Babeyko AY, Bock G, Jones A, Nelson K, Solon K, Brown L, Zhao W (2004) Precise temperature estimation in the Tibetan crust from seismic detection of the $\alpha-\beta$ quartz transition. *Geology* 32(7):601–604

Moarefvand A, Gasc J, Deldicque D, Labrousse L, Schubnel A (2024) P-wave velocities across the $\alpha\beta$ quartz transition at lower continental crust pressure and temperature conditions. *J Geophys Res Solid Earth* 129(3):2023–207850

Morana M, Angel RJ, Alvaro M, Mihailova B (2023) High-temperature behavior of quartz-in-garnet system revealed by in situ Raman spectroscopy. *Phys Chem Miner* 50(3):21

Müser M, Binder K (2001) Molecular dynamics study of the $\alpha-\beta$ transition in quartz: elastic properties, finite size effects, and hysteresis in the local structure. *Phys Chem Miner* 28:746–755

Pippard A (1956) XLVIII. Thermodynamic relations applicable near a lambda-transition. *Phil Mag* 1(5):473–476

Raz U, Girsperger S, Thompson AB (2002) Thermal expansion, compressibility and volumetric changes of quartz obtained by single
crystal dilatometry to 700°C and 3.5 kilobars (0.35 GPa). Technical report, ETH Zurich

Schaff DP, Waldhauser F (2005) Waveform cross-correlation-based differential travel-time measurements at the Northern California Seismic Network. Bull Seismol Soc Am 95(6):2446-2461

Sheehan AF, Torre TL, Monsalve G, Abers GA, Hacker BR (2014) Physical state of Himalayan crust and uppermost mantle: constraints from seismic attenuation and velocity tomography. J Geophys Res Solid Earth 119(1):567-580

Shen A, Bassett W, Chou I-M (1993) The α-β quartz transition at high temperatures and pressures in a diamond-anvil cell by laser interferometry. Am Miner 78(7-8):694-698

Wang J, Mao Z, Jiang F, Duffy TS (2015) Elasticity of single-crystal quartz to 10 GPa. Phys Chem Miner 42:203-212

Wenk H-R, Barton N, Bortolotti M, Vogel S, Voltolini M, Lloyd G, Gonzalez G (2009) Dauphiné twinning and texture memory in polycrystalline quartz. Part 3: texture memory during phase transformation. Phys Chem Miner 36:567-583

Zappone AS, Benson PM (2013) Effect of phase transitions on seismic properties of metapelites: a new high-temperature laboratory calibration. Geology 41(4):463-466

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