mechanical properties of quartz at the α‐β phase transition

Article

Volume 14, Number 1

28 January 2013

doi:10.1029/2012GC004482

ISSN: 1525-2027

Mechanical properties of quartz at the a-b phase transition:Implications for tectonic and seismic anomalies

Zhenwei Peng and Simon A. T. RedfernDepartment of Earth Sciences, University of Cambridge, Cambridge, UK ([email protected])

[1] The anelastic response of single-crystal and polycrystalline quartz and quartz-rich sandstones to appliedstress at low frequencies has been investigated by dynamic mechanical analysis and force torsion pendulummeasurements. The dynamic modulus was measured on heating and cooling through the a-b phase transi-tion under shear and bending stress applied at low frequency (~1Hz). Single crystal quartz shows highlyanisotropic properties in both the real and imaginary part of the modulus. Polycrystalline novaculite quartzdisplays the a-b phase transition temperatures (Tc) around 8�C higher than seen in single crystal quartz, dueto the pinning stress effect of grain boundaries. The properties of the sandstone vary with heating and cool-ing cycles as the cementation and microfracturing of the grain structure changes at high temperature. Thephase transition in quartz is ferrobielastic, and as such energy differences between domains in the transfor-mation microstructure arise under conditions of applied shear stress. Pre-transition softening and an increasein anelastic loss above Tc are attributed to ferrobielastic switching of incipient domain microstructures thatarise in the silica microstructure. The influence of temperature on this microstructure is to induce increasedswitching of domains as a response to thermal stress inherent in the anisotropic thermal expansion of thepolycrystalline structure. These results indicate that ferrobielastic switching in quartz is an important mech-anism in controlling changes in mechanical properties. As such, we anticipate that it will induce measurableanomalies in seismic signatures of quartz-rich portions of the Earth’s crust in regions of high thermal flux.The transition may also be responsible for observed seismic velocity reductions and tectonic weakening inwestern North America and in certain parts of Tibetan plateau.

Components: 7,300 words, 9 figures.

Keywords: phase transition; anelasticity; rheology; quartz; Q�1.

Index Terms: 3909 Mineral Physics: Elasticity and anelasticity; 3947 Mineral Physics: Surfaces and interfaces;4465 Nonlinear Geophysics: Phase transitions; 5112 Physical Properties of Rocks: Microstructures; 8159Structural Geology: Rheology: crust and lithosphere (8031).

Received 5 October 2012; Revised 28 November 2012; Accepted 29 November 2012; Published 28 January 2013.

Peng, Z., and S. A. T. Redfern (2013), Mechanical properties of quartz at the a-b phase transition: Implications fortectonic and seismic anomalies, Geochem. Geophys. Geosyst., 14, 18–28, doi:10.1029/2012GC004482.

1. Introduction

[2] The anelastic properties of rock-forming mineralsare a potential cause of seismic wave attenuation[Kern, 1979; Carpenter and Zhang, 2011]: changes

in bulk and shear modulus, as well as energy dissi-pation can all affect seismic wave velocity [Liuet al., 1976]. Low-frequency mechanical responsesin quartz associated with its phase transition are ofinterest to Earth sciences in view of the prevalence

©2013. American Geophysical Union. All Rights Reserved. 18

of this phase in Earth’s crust. Quartz is one of themost common crustal minerals, and it has beensuggested that the transition may also modify themechanical strength of quartz-rich rocks in the deepcrust. Xu et al. [2007] and Nikitin et al. [2007, 2009]identify weakening and seismic velocity reductionsin areas of Tibet which influence the dynamictectonics of the region. A high abundance ofquartz-rich rocks in the lower crust has been pro-posed as a major triggering factor for initiatingdeformation, but the role of the phase transition onincreasing the potential importance of quartz incontrolling such deformation has not been directlyinvestigated. The role of quartz in controllinglarge-scale deformation of continents was brieflydiscussed by Lowry and Pérez-Gussinyé [2011]recently. However, no low-frequency mechanicalspectroscopic investigations of quartz, in the seis-mic frequency regime (i.e., around and below1Hz), have thus far been undertaken.

[3] The a-b phase transition in quartz is, in manyrespects, a model example of a co-elastic displacivephase transition. Its importance in Earth sciences,materials science, and fundamental structural phys-ics is widely recognized. Occurring at Tc= 573�Cin pure crystalline SiO2, the a-b phase transition isvery slightly first order in thermodynamic characterand is accompanied by the existence of an incom-mensurate structure which appears over an intervalof 1.3�C around Tc [Dolino et al., 1983; Peng et al.,2012]. Early observations, by electron microscopy,of triangular domains in the vicinity of the a-b phasetransition, were interpreted as Dauphiné microtwins[Van Tendeloo et al., 1976]. Detailed studies of theincommensurate structure and its influence on thetransition have demonstrated that the transition fromb-quartz to the incommensurate structure is secondorder, whereas the subsequent transition from theincommensurate phase to a-phase is first order[Heaney and Veblen, 1991; Peng et al., 2012].

[4] The mechanical properties of quartz arestrongly modified by the a-b phase transition andare themselves of technological and geophysical[Takeuchi and Nagahama, 2006] interest in viewof the piezoelectric properties of this material. In-deed, the piezoelectric effect in quartz has been rec-ognized since the early studies of the Curie brothers[Curie and Curie, 1880]. The a-b transitioninvolves a symmetry change from the high temper-ature space group P6422 of the b-phase to the lowtemperature a-structure, space group P3221. Assuch, changes in allowed piezoelectric coefficients,dijk, occur. Furthermore, symmetry-dependent twin-ning results from this phase transition, termed

Dauphiné twinning. Under application of externalfield or stress, ferrobielastic switching may occurdue to coupling via the differing piezoelectriccoefficients.

[5] The a-b transition in quartz is usually describedin terms of the critical behavior of the B1 zone-center optic phonon [Carpenter and Salje, 1998],which provides a mechanism for symmetry break-ing. Elastic anomalies also occur due to orderparameter-strain coupling and have been success-fully explained and shown to be energetically dom-inant, within the framework of Landau theory byCarpenter et al. [1998]. Hence, critical softeningof individual elastic moduli at and approaching Tcmay result in a reduction to less than half the valueobserved high into the b-phase.

[6] Quartz displays highly anisotropic characteris-tics, with strongly direction-related physical prop-erties. Elastic constants of quartz across the a-btransition vary with respect to each other [Ohno etal., 2006] and contribute to the elastic and anelasticanisotropy of quartz under stress. The influence ofgrain size and sample self-clamping on this phe-nomenon has been explored by Pertsev and Salje[2000], Ríos et al. [2001] and more recently, usingultrasonic mechanical methods, by McKnight et al.[2008]. It is found that the typical first-order behav-ior seen in single crystal samples is modified to sec-ond order in nanocrystalline natural samples, due tothe effective field induced by grain-grain clamping.

[7] Here, we report the results of high-temperaturemechanical studies on quartz samples of differingmicrostructural scales. We compare results of dy-namic mechanical analysis and forced torsion pen-dulum measurements on single crystal quartz withthose on polycrystalline quartz (novaculite) andmore porous polygrain sandstone samples. Ourresults provide new data on the thermodynamiccharacter of the a-b phase transition as a functionof grain size and reveal the mechanical and anelasticanomalies related to the transition. Finally, we dis-cuss the possible role of this transition on modifyingthe properties of quartz-rich rocks in Earth’s crust.

2. Experimental

[8] Mechanical spectroscopic measurements wereperformed by dynamic mechanical analyzer(DMA) and inverted force torsion pendulum. ThePerkin Elmer DMA 7e three-point bending system(Figure 1) measures the stiffness of a sample underdynamic beam bending as a function of temperature,

GeochemistryGeophysicsGeosystemsG3G3 PENG AND REDFERN: QUARTZ AT THE a-b PHASE TRANSITION 10.1029/2012GC004482

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applied force, and frequency by considering theprobe position as a function of time [Harrisonet al., 2004a]. The Young’s modulus and mechani-cal loss of our samples under periodic force at lowfrequencies were obtained. Temperature scans werecarried out from room temperature to 640�C at fixedfrequencies for sinusoidally modulated stress atfrequencies of 1, 2, 5, and 10Hz. Samples wereprepared as rectangular bars, held between knifeedges spaced 5mm apart, with typical bar widthsaround 3mm and thicknesses of around 0.5mm.The DMA requires samples be subjected to a con-stant (static) bias stress which is then modulatedby a dynamic component. The static force was setto 220mN for single crystal quartz and novaculitesamples and 110mN for sandstone samples. Themodulating dynamic force was 200 and 100mN,respectively. Low static and dynamic force wasapplied to sandstone samples, which have lowerfracture strength, to avoid breakage of samples.The conditions of force and sample displacementlie squarely in the regime of linear elastic behavior,as confirmed in our measurements of sampleresponse as a function of varying stress (Figure 2).Samples were measured under thermal ramps withtemperature ramp rates of 1, 2, 5, and 10�C/min todetermine the influence of thermal heat flow. Threesuccessive heating and cooling runs were operatedwith fixed frequencies and temperature ramp ratefor each measurement.

[9] A low-frequency inverted force torsion pendu-lum [Gutiérrez-Urrutia et al., 2004] was used formeasuring shear modulus and mechanical loss. Thesuspension arrangement provides high-resolutiondata as a function of temperature and frequency withparticular sensitivity in tan d, the anelastic mechan-ical loss (equivalent toQ�1). The sample was placedin a furnace under high vacuum of around 10�3 Pa

to ensure that no air friction was involved in pendu-lum damping. Experiments were conducted at fixedfrequencies of 1, 5, and 0.5Hz, with temperaturescans performed by heating up to 640�C and thencooled down to 400�C. The stress is controlled viavoltage applied to Helmoltz coils, which couplemagnetically to the pendulum. The voltage was se-lected such that the maximum mechanical shearstress produced a strain of less than 10�4. The tem-perature ramp rate was set to either 1 or 2�C/min.

[10] A natural single crystal of optically transparent,defect-free, Brazil quartz was used. It displayedstrong prismatic habit. Parallelepiped pieces werecut from the optically clear center to avoid anymicrocracks. A white-opaque homogeneous novac-ulite from Arkansas, USA, was composed of99.898% pure silica and only trace amounts of otherelements. Scanning electron microscopy reveals acrystallite size of 1–5mm [McKnight et al., 2008].The third sample was a Permian aolian sandstonecollected from the Corrie shore of the Isle of Arran,Scotland. It features obvious banding, indicating thebedding direction, along which the parallelepipedwas cut. It comprises about 58% quartz, with addi-tional K-feldspar, quartzose and volcanic lithicgrains, and minor opaques, with a porosity of 17%[Van Panhuys-Sigler and Trewin, 1990].

[11] In each case, the sample was prepared bymounting on a glass block and then cut by a fine an-nular diamond saw, lubricated with paraffin. Thesingle crystal quartz parallelepiped samples, dimen-sion 10mm� 3mm� 0.3mm, were cut from themiddle part of the large single crystal, with edgesoriented parallel to the [001], [100], and [120]directions, respectively. Additional samples were

Figure 1. A schematic illustration of the three-pointbending geometry of the DMA.

Figure 2. Stress-strain response of quartz over therange of conditions measured in our experiments. Datahere correspond to single crystal quartz measured byDMA in three point bending geometry, and show theliner response of the material for the strains of interest.


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cut length parallel [100]. Polycrystalline novaculiteand sandstone samples were cut to a similar size asthe single crystal quartz. All samples used for thetorsion pendulum were cut with dimension approx-imately 55mm� 10mm� 1.3mm.

[12] Due to the rigorous sample requirement oftorsion pendulum, we only obtained valid experi-mental data from the (relatively tough) novaculitesamples. The high porous sandstone samples arevery brittle and fragile, especially when cut to verythin strips (<2mm), and they are inevitably brokenduring the experimental set up, let alone their furtherweakening at higher temperature.

3. Results

3.1. DMA Measurements of Single CrystalQuartz and Polycrystalline Novaculite

[13] Measurements of Young’s modulus and inter-nal friction were taken for single crystal quartz sam-ples and novaculite (Figure 3). The same samplewas used during each set of repeated experiments.

[14] The dynamic Young’s modulus E*(o) is re-lated to the deflection of the sample Vd in three-pointbending geometry via the expression:

E* oð Þ ¼ l3

4t3w

Fd

Vdexp idð Þ ¼ E′ oð Þ þ iE′′ oð Þ

where the dynamic force is Fd, the angular fre-quency is o, the phase lag between applied stressand resultant strain is d, and l, w and t are thelength, width and thickness of the sample, respec-tively. From this the storage modulus (real partof Young’s modulus) E′ may be obtained, where

E′= s0cosd/e0 with s= stress, e= strain. The imagi-nary part of the complex dynamic modulus is E00 =s0sind/e0. From this the mechanical loss, or inter-nal friction, is given by E00/E′= tan d which isequivalent to the inverse quality factor, Q�1 [Penget al., 2012]. The absolute accuracy of values formodulus from DMA is affected by systematicerrors in quantities such as sample dimensions,force motor calibration, and probe position, result-ing in absolute errors of around 10%. The preci-sion, however, is far superior, of the order of 1%or better. Thus the relative variation of mechanicalproperties can be measured to high sensitivity, anddata are then calibrated using well-establishedelastic constants [Carpenter et al., 1998].

[15] We observe, from our heating measurements,that in the low-quartz a-phase the real part of theYoung’s modulus of the single crystal measuredparallel to [100] does not vary significantly (from77GPa at 20�C to 72GPa at 500�C) on heatinguntil approaching within 100�C or so of the transi-tion temperature from below (black solid circles inFigure 3). The sample of single crystal quartz cutparallel to [001] (red solid circles in Figure 3),however, softened by more than 15% from97GPa at room temperature to 81GPa at 500�C.A rather abrupt decrease (to 43GPa) followed byan immediate recovery within 10�C is exhibitedon passing through the phase transition, character-ized by a very large elastic softening, followed bya more steady increase on heating above the tran-sition until 600�C. At Tc, the mechanical lossreaches a maximum value of up to 0.28 (emptycircles in Figure 3). The absolute value of Young’smodulus of quartz measured parallel to [001] isabout 25% higher than that measured along [100],with a correspondingly higher mechanical loss. Thisreflects the anisotropy of elastic and anelastic prop-erties, with quartz much softer along the [100] axis.The novaculite sample (blue circles in Figure 3)exhibits a more gradual decrease of Young’s modu-lus on heating, reaching a minimum at 582�C,followed by an increase on further heating. Duringcooling, the Young’s modulus follows a similarpathway, with Tc slightly depressed. The internalfriction of novaculite does not vary greatly, exceptthat near Tc there is a peak, which is significantlybroader than the sharp feature seen in the singlecrystal samples. Novaculite is slightly softer(92GPa at 20�C) than single crystal samples whenmeasured parallel to [001].

[16] The pattern of modulus and tan d during heat-ing is generally the same as observed during

Figure 3. Comparison of Young’s modulus and tan dfor single crystal quartz cut parallel to [001] (red), singlecrystal quartz cut parallel to [100] (black) and polycrys-talline novaculite (blue) at 1Hz with ramp rate _T = 10�Cmin�1 on heating.


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cooling. However, there is a 1�C difference be-tween heating and cooling through Tc, which ispartly due to the thermal hysteresis of the experi-ment and have dependence of heat transfer duringtemperature ramping (higher ramp rates result inlarger thermal hysteresis) and partly a fine reflec-tion of the hysteresis expected by the first-orderthermodynamic character of the phase transition.To correct for thermal heat transfer effects, wecollected data at varying ramp rate and extrapolatedresults to zero ramp rate. Hence we are able to ac-curately calibrate the influence of varying tempera-ture ramp rate in the experiment. The transitiontemperature (corrected in this manner) for singlecrystal quartz was measured as 574�C duringheating and 573�C during cooling, and Tc for no-vaculite was found to be ~582�C on heating and581�C on cooling, respectively.

[17] We note that the DMA data collected agreewell with our previous experiments of incommen-surate phase in single crystal quartz and novaculite[Peng et al., 2012]. However, due to the high cool-ing rate _T = 10�Cmin�1 used in this study, we didnot observe the incommensurate phase during theexperiments. All data are repeatable, indicating thatthe thermal history has no influence on the mechan-ical properties of quartz.

[18] In order to confirm whether or not Tc changesas a function of force, we performed temperaturescans with different static force, which demonstratethat Tc is independent of force within the resolutionof our measurements. We also confirmed that tran-sition temperature is independent of the frequencyof applied stress (Figure 4).

3.2. DMA Measurements of New RedSandstone

[19] The DMA data were collected for Permiansandstone during three successive heating and cool-ing cycles from 500 to 640�C (Figure 5). The samesample was used throughout. On heating, themodulus exhibits a minimum at Tc, followed by arecovery up to ~600�C and then decreases as thetemperature increases to 635�C. During cooling,the modulus does not vary significantly above590�C but shows a sudden decrease at Tc. TheYoung’s modulus measured on cooling cycles isgenerally lower compared to that measured on heat-ing. When cooling, a deep drop of Young’s modu-lus is observed at Tc. Below Tc, Young’s modulusdoes not vary much on cooling. The tan d behaviorreveals an obvious peak at Tc (Figure 5b).

[20] Compared with the reversible changes in mod-ulus and tan d of single crystal and novaculite sam-ples, the modulus of sandstone softens upon furtherthermal cycles, whereas tan d increases. This islikely due to the development of fractures,

Figure 4. Comparison of Young’s modulus of singlecrystal quartz cut parallel to [001] through the a-b phasetransition at different frequencies. Measurements wereconducted at the same ramp rate _T = 10�Cmin�1 oncooling.

Figure 5. (a) Comparison of Young’s modulus duringthree successive heating and cooling cycles for the Perm-ian new red sandstone. (b) Young’s modulus (solid) andtan d (empty) as a function of temperature for Permiannew red sandstone on first heating. Measurements wereconducted at 1Hz with ramp rate _T = 10�Cmin�1.


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microcracks, and degradation of the calcareouscement on heating and imposition of dynamicstress. The patterns of behavior during successiveheating and cooling are very different to those seenduring the first run, and the structure has changedirrecoverably. The sandstone is more than 10 timessofter than single crystal quartz, due to its highporosity, and its modulus shows a much less pro-nounced softening, characterized by a rather con-tinuous variation of properties through the phasetransition. The transition temperature for sandstoneis about 5�C higher than that of single crystal quartz.Tc does not vary as a function of number of thermalcycles, demonstrating that the behavior observedin the sandstone samples reflects only the quartzcontent. The sandstone sample became fragileand friable after several heating and cooling runs,even under very small external stress.

3.3. Torsion Pendulum Measurementsof Polycrystalline Novaculite

[21] The inverted force torsion pendulum measuresthe shear modulus and tan d of a sample as a func-tion of temperature. In Figure 6, it is apparent thatthe novaculite sample shows a minimum of shearmodulus and a broad peak of tan d at Tc. The tran-sition temperature is about 581�C, in agreementwith our DMA results, and is independent of fre-quency. The mechanical loss, tan d, measured at0.5Hz is larger, with a broader peak at Tc, due tothe background response of the instrument.

[22] Figure 7 shows the differences of torsion pen-dulum and DMA measurements of shear andYoung’s modulus, and tan d for novaculite at 1Hz

with the same ramp rate of _T = 1�Cmin�1 on cool-ing. The changes in the elastic and anelastic proper-ties of quartz under shear stress are significantlysmaller than those seen in the dilatational and com-pressive stresses of the DMA measurements. Theoverall shear modulus of novaculite is significantlylower than the Young’s modulus, and tan d ishigher under shear stress. Near the phase transitiontemperate Tc, the sample displays a much more sub-tle change both in shear modulus and tan d: shearmodulus only varies by about 3%, compared witha sudden softening from ~85GPa at 400�C to~60GPa at Tc in the three-point bending geometry.

4. Discussion

[23] The most obvious mechanical effect of thephase transition in single crystal quartz is the verylarge critical softening of elastic moduli close toTc. This is clearly seen in data for the modulus ofsingle crystal quartz. The small hysteresis (~1�C)between heating and cooling is characteristic of thefirst-order nature of this phase transition. Further-more, our low-frequency high-temperature DMAand torsion pendulum measurements reveal a sharppeak in mechanical loss at Tc, again characteristicof first-order phase transitions measured at low-frequency, in which the phase interface dominates

Figure 6. Comparison of Shear modulus (solid) andtan d (empty) of novaculite through the a-b phase transi-tion at different frequencies (black 0.5Hz, red 1Hz, blue5Hz) with ramp rate _T = 1�Cmin�1 on cooling near thephase transition temperature Tc.

Figure 7. Comparison of DMA (red) and torsionpendulum (black) measurements of Young’s and shearmodulus (solid) and tan d (empty) for novaculite at 1Hzwith ramp rate _T = 1�Cmin�1 on cooling.


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anelasticity [Jakeways et al., 2006; Walsh et al.,2006; Harrison et al., 2003, 2004b].

[24] The a-phase single crystal quartz shows typicalanisotropic properties between the samples withlength parallel to [001] and [100]. Such directional-dependent divergence can be explained in terms ofthe symmetry-related elastic constants. In thethree-point bending symmetry, a trigonal crystalwith length parallel to [001] under a uniaxial stressthe elastic constant C33 dominates the Young’smodulus. From the theoretical calculations andBrillouin scattering experiments, C33 softenedaround 17% from 20 to 500�C [Ohno, 1995], whichis in agreement with our experimental observationof Young’s modulus in the a-phase for samplewith length parallel to [001]. For the sample mea-sured length parallel to [100], the dominant elasticconstant is C11 in the three-point bending geome-try. Our data are inconsistent with previousobservations.

[25] Quartz is a ferrobielastic with ferrobielasticdomains with opposite axes, the Dauphiné twins.As such the motion of twin walls in response toapplied stress in appropriate orientations can occurwith an accompanying increase in tan d and soften-ing of the effective measured elastic modulus[Guzzo et al., 2006]. However, twin wall motioncan only explain the softening below Tc, because itdisappears in the high-temperature b-phase. Anearly study by Kern [1979] explained that the rapidreduction of elastic constants in the low-tempera-ture a-phase of quartz is correlated to the atomic-force-constant softening due to the increasinganharmonic vibrational character resulting from amovement of the atomic equilibrium positions.However, in the high-temperature b-phase, theincrease in elastic constants is due to the hardeningof the atomic-force-constant as a consequence ofdisappearance of anharmonic vibrational character.Subsequently, elastic constants soften from aboveTc as described by Carpenter et al. [1998], withcoupling between the fluctuating strain and the softoptic mode providing a possible mechanism [Walshet al., 2006]. The transition is frequency and stress-independent, as expected for its thermodynamiccharacter.

[26] By comparing the Young’s modulus measuredby DMA and shear modulus measured by torsionpendulum, it is clear that the shear modulus variesby only about 3% through the phase transition,while the Young’s modulus drops more than 30%(Figure 7). The dynamic modulus is determinedby the individual elastic constants, and it has been

demonstrated by Ohno [2006] that the linearincompressibility K1 = (C11 +C12 +C13)/3 and K3 =(C33 + 2C13)/3 for isotropic dilatation in directionsperpendicular and parallel to c axis and the trigonalconstant C14 decrease rapidly toward Tc, whereasthe shear moduli C44, Cs1 = (C11 +C33� 2C13)/4andCs3 = (C11�C12)/2 =C66 decrease only slightly.Here Cs1 and Cs3 are shear moduli in the directionsperpendicular and parallel to the c axis, respectively.

[27] Natural polycrystalline novaculite with grainsize 1–5mm has Tc 8�C higher than single crystalquartz, which is attributed to the influence of inter-nal stress, induced by self-pinning and grain bound-ary effects. Formed of randomly oriented grains,the novaculite sample is subjected to increasinginternal pressure on heating because of anisotropicthermal expansion. Unlike the three-dimensionalelastic clamping of nanocrystal systems [Pertsevand Salje, 2000], the natural polycrystalline sampleshave grain boundaries equilibrated within the low-temperature phase, since this corresponds to theirtemperature of formation. Nevertheless, the phasetransition in novaculite does show some continuouscharacter, compared with the behaviors seen in sin-gle crystal quartz. This is obvious most especially inthe broad tan d peak associated with the phase tran-sition. Calorimetric and dilatometric studies indicatethat the first-order transition in quartz becomessmoother in fine-ground quartz or natural quartzite.This smearing of the transition is caused by particlesize effects [Moore and Rose, 1973] as well as theability of fine-grained quartz to release the internalstress by displacement of grain boundaries [Sorrellet al., 1974].

[28] The natural sandstone sample shows mechani-cal response allied to the structural phase transitionin the same general way as seen in quartz and novac-ulite, but with important and significant differences.McKnight et al. [2008] divided three different grain-size-dependent regimes, within which elastic prop-erties show different features. For larger grain sizes,represented by quartzite with grain size >0.1mm,the sample may undergo self-cataclasis due to stressaround the transition because of the formation ofmicrocracks, allowing individual grains to pull apart.The sandstone sample has much bigger grains withvery high porosity. It is certain that the softeningin the vicinity of 580�C is caused by the majorityquartz content of the rock. The initial behavior ofthe sample is similar to that of single crystal quartz,except with substantially lower modulus, due tothe porous structure. It is interesting to note themodulus behavior above 600�C on heating. The


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anomalous decrease indicates the softening of thesample in the high-temperature b-phase. This canbe attributed to the decomposition of the CaCO3-rich cement that pervades the rock. This breaksdown around these temperatures via the reactionCaCO3 ! CaO+CO2. On cooling, the dramaticdifference of modulus, and accompanying tan dvalue, is enhanced in the sandstone sample, causedby the density variation between low-temperaturea-phase and high-temperature b-phase. Defectsand clamping effects lead to the 4�C increase in Tccompared to single crystal quartz. The decrease inmodulus as a function of heating and cooling cyclesis likely linked to the combined effects of cementdegradation and sample self-cataclasis.

5. Geophysical Implications of the a-bQuartz Transition

[29] As the commonest mineral in continental crust,quartz and quartz-bearing rocks dominate crustalseismic wave velocity structures and have signifi-cant potential influence on the tectonics, rheology,and dynamics of the crust.

[30] The a-b phase transition in quartz drasticallymodifies the physical properties of quartz-bearingrocks. In the vicinity of Tc, the thermal expansioncoefficients increase rapidly, elastic constants changeabruptly, especially C12 and C13 which become neg-ative, and accordingly the Poisson’s ratio changessign from positive to negative. Poisson’s ratio issometimes used as an indicator for determiningcrustal mineral and chemical composition, so thefact that it is so variable as a function of temperaturein quartz may result in skewed conclusions if this isnot taken into account. A linear negative correlation

between Poisson’s ratio and increasing SiO2 contentwas inferred for rocks with 55–75wt.% SiO2

[Christensen, 1996], for example, but it is easy tosee that similar results might be obtained in rocksof constant quartz content but varying temperatures,close to the phase transition.

[31] The a-b phase transition in quartz-rich rockscan lead to the formation and concentration ofmechanical stresses at the same time as a decreasein elastic stiffness. The temperature dependence ofthe strength of quartz was examined by Westbrook[1958], who reported a minimum in strength at thephase transition. This agrees with the general rela-tionship between elastic modulus and yield strengthfor ceramics [Ashby, 1999] and our measurementsof elastic modulus, which indicate the likelihoodof mechanical weakening near the phase transitionin quartz-rich crustal materials.

[32] Phase transitions in minerals are recognized asa potentially important mechanism for weakeningin the Earth’s crust and mantle. Christian et al.[2003] provide indirect experimental evidence ofphase transition induced weakening by observingthe deformation of fluid inclusions in a quartz crys-tal through the a-b phase transition. They demon-strate that at the phase transition, the creep strengthof the quartz sample reaches a minimum, and theonly possible mechanism is plastic deformation in-duced by the phase transition itself (transformationplasticity). In the crust, transformation plasticity ofquartz could give rise to plastic deformation in shearzones. Figure 8 displays the plastic strain of our no-vaculite measured by torsion pendulum, from whichit is seen that a drastic increase of plastic strainoccurs at Tc and reaches a maximum near 600�C.Early experiments demonstrated that the strengthof a quartz crystal at 600�C is around 100-fold lowerthan at 300�C, due to the hydrolization of the Si-Obond, and hence large plastic deformations can beproduced without fracture [Griggs and Blacic,1965]. This feature can be expected to give rise toweakening in Earth’s quartz-rich lower crust. Evenwithout the participation of water, the dramaticchange of plastic strain due to the phase transitionhas the potential to cause tectonic weakening overa narrow temperature range. The plastic strain inthe b-phase is substantially higher than that in thea-phase. In areas where high thermal flux occurs,the weaker high-temperature phase of quartz couldallow significant tectonic strain to develop.

[33] In the lower crust or tectonically active zones,the a-b phase transition of quartz intersects the geo-thermal gradient, potentially resulting in discrete

Figure 8. Plastic strain of novaculite measured bytorsion pendulum near the a-b phase transition at1Hz with ramp rate _T= 1�Cmin-1 on cooling.


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zones of much weaker crust. Nikitin et al. [2009]suggested the phenomenon may occur in the centralTibetan Plateau. Some argue that weak zones in thecrust caused by the a-b phase transition in quartzwould only be narrow in terms of depth or tempera-ture range. Gibert and Mainprice [2009] discoveredthat the thermal conductivity of quartz reaches aminimum at the a-b phase transition. This sharpdecrease of thermal conductivity extends over30�C around Tc, which corresponds to a depth rangeof around 1 km along the geotherm. The reductionof conductivity and the associated latent heat ofthe transition near Ttr can therefore stabilize thegeotherm at the phase transition and increase its po-tential influence.

[34] A recent study [Menegon et al., 2011] investi-gated the relationship between Dauphiné twinningand plastic strain in quartz and found that stress-induced twinning occurring at the a-b phasetransition has an influence on the partitioning andlocalization of plastic strain. An increase in plastic-ity is therefore expected near the phase transitionand transformation-induced superplasticity canoccur in discrete zones of high microplasticity, sur-rounded by an elastically deformed medium. Thephase transition can also facilitate failure of quartzrich rocks, which would be expected to promotethe formation of shear zones or regions of highdeformation [Nikitin et al., 2007]. Kern [1979]conducted a series of experiments with differentsamples containing various percentages of quartzcrystals and found that the amount of softening nearthe a-b phase transition seems to be independent ofcontent of the constituent quartz crystals, althoughsoftening occurs over a narrower temperature rangein quartzite (100 vol.% quartz) than granite and

granulite (21.6 vol.% and 28.2 vol.% quartz, respec-tively). Furthermore, quartz and other silicateminerals are well developed on many seismic faults,even when the surrounding rocks are not quartz-bearing, suggesting that the high-temperature prop-erties of quartz may be important at earthquakes inmany rock types [Power and Tullis, 1989].

[35] Lowry and Pérez-Gussinyé [2011] investigatedthe role of crustal quartz in controlling Cordillerandeformation in western North America. The ratioof compressional (Vp) to shear (Vs) seismic wavevelocity was interpreted in terms of compositionalvariations, in particular of variations in quartz con-tent. Taking the Clausius-Clapeyron slope of thea-b phase transition and laboratory measure-ments of rock properties into consideration, low-temperature quartz is expected to be the stable phasein the lower crust of the weakened zones in westernNorth America. Bürgmann and Audet [2011] con-cluded that the lower value of Vp/Vs is uniquelyassociated with high concentrations of quartz inthe crust, which is invoked to be responsible fortectonic weakening in specific zones. The ratioof Vp/Vs for quartz is, however, highly temperature-dependent [Kern, 1979]. The ratio of Vp/Vs in no-vaculite was calculated and is illustrated in Figure 9.The seismic frequency data obtained in this studyare good agreement with the ultrasonic measure-ments of Kammer et al. [1948] and Zubov andFirsova [1962]. The lowest value is associatedwith the phase transition at relative high temperature(>500�C) and Vp is mainly controlled by theYoung’s modulus, whereas Vs is dominated byshear modulus. The Young’s modulus varies morethan 30% with temperature (Figure 7), while shearmodulus is almost temperature-independent. Hencethe Vp/Vs variation is mainly related to the depen-dence of Vp on temperature. According to thesurface heat flow distribution [see Lowry andPérez-Gussinyé, 2011, Figure 4a], it is clear thatthe tectonically weak zones have high thermal fluxin the crust and below. Hence, rather than invokinga high concentration of quartz and variations in min-eral content, their observations may be explained interms of temperature variations and the associatedphase transition in quartz. This also greatly weakensthe mechanical strength of lithologies in which itresides and may be a trigger for plastic deformation.

[36] The existence of the a-b transition in rocks ofCentral Tibet at depths of 18–32 km may lead toone such zone of quartz-dominated mechanicalweakening. In the southeastern Tibetan Plateau,pre-melting has been proposed as the cause ofintra-crustal low velocity zones [Xu et al., 2007],

Figure 9. Comparison of the ratio of Vp/Vs from thepolycrystalline novaculite sample and that obtained fromprevious studies of the elastic constants of single crystalquartz.


26

but the quartz phase transition would lead to similarphenomena. Seismologic observation of the northernLhasa block by Min and Wu [1987] and Zhang andKlemperer [2005] revealed an anomalously low ve-locity zone at the upper crust. In this area [see Zhangand Klemperer, 2005, Figure 1], Vp reduced to5.1 km/s at depths of 20 km, but at shallowerregions Vp ranged from 5.6 to 6.2 km/s. This low-velocity zone has a thickness of around 5 km, overly-ing a thick middle-lower crust of velocity 6.5 km/s.The ratio of Vp/Vs also decreases to 1.65 from 1.75or higher. High-temperature/pressure experiments[Kern, 1982] showed that basic rocks below andclose to the solidus have a Vp/Vs ratio of 1.75, whichonly quartz-rich rocks at high-temperature/pressureconditions can produce such low Vp/Vs ratios. Minand Wu [1987] demonstrated that a granitic orquartz-rich upper crust with a relatively high tem-perature gradient of 50�C/km at the surface and18�C/km at a depth of 20 km is consistent with theseismic data. However, they attributed the lowVp/Vs ratio to high volumetric thermal expansionand the development of microcracks at grain bound-aries. According to our experiment (Figure 9), thea-b phase transition in quartz is the major cause ofthe decreasing of the Vp/Vs ratio. Other physicalproperties also change at the a-b transition, includinglower thermal conductivities, to enhance the effect ofthe seismic velocity reduction, and potentially ex-pand this region to 5 km in thickness.

[37] In conclusion, the phase transition of quartzwill occur in areas of the crust with high magmaticand thermal activity: the base of the lithosphere andtop of the asthenosphere, and in subduction zones.Indeed, the a-b phase transition in quartz acts as ageothermometer and has been used to constrainthermal structure at depth [Mechie et al., 2004].However, the phase transition in quartz is not irrel-evant to the stable continental crust: granitizationoccurs at temperatures close to or exceeding Tc, sothe a-b is expected in such areas [Nikitin et al.,2009]. Despite well over a century of study, it isclear that this phase transition retains features thatdemand further investigation and considerationand that may have wider implications for thegeneral behavior of geomaterials in the Earth.

Acknowledgments

[38] The authors are grateful to Dr. M. Daraktchiev for assist-ing with torsion pendulum experiments. Z. Peng acknowledgesfinancial support from the Gates Cambridge Trust. We thankProf. J. Tyburczy, Prof. I. Jackson and two anonymousreviewers for valuable comments of our original manuscript.

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mechanical properties of quartz at the α‐β phase transition

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