Thermal modeling of shock melts in Martian meteorites: Implications for preserving

Martian atmospheric signatures and crystallization of high-pressure minerals

from shock melts

Cliff S. J. SHAW1 and Erin WALTON2,3*

1Department of Earth Sciences, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada2Department of Physical Sciences, MacEwan University, City Centre Campus, Edmonton, Alberta T5J 4S2, Canada3Department of Earth and Atmospheric Sciences, University of Alberta, 1-26 Earth Sciences Building, Edmonton,

Alberta T6G 2E3, Canada*Corresponding author. E-mail: ewalton@ualberta.ca/waltone5@macewan.ca

(Received 21 June 2012; revision accepted 30 January 2013)

Abstract–The distribution of shock melts in four shergottites, having both vein and pocketgeometry, has been defined and the conductive cooling time over the range 2500 °C to 900 °Ccalculated. Isolated 1 mm2 pockets cool in 1.17 s and cooling times increase with pocket area.An isolated vein 1 9 7 mm in Northwest Africa (NWA) 4797 cools to 900 °C in 4.5 s.Interference between thermal haloes of closely spaced shock melts decreases the thermalgradient, extending cooling times by a factor of 1.4 to 100. This is long enough to allowdifferential diffusion of Ar and Xe from the melt. Small pockets (1 mm2) lose 2.2% Ar and5.2% Xe during cooling, resulting in a small change in the Ar/Xe ratio of the dissolved gasover that originally trapped. With longer cooling times there is significant fractionation of Xefrom Ar and the Ar/Xe ratio increases rapidly. The largest pockets show less variation of Ar/Xe and likely preserve the original trapped gas composition. Considering all of the modelcalculations, even the smallest isolated pockets have cooling times greater than the durationof the pressure pulse, i.e., >0.01 s. The crystallization products of these shock melts will beunrelated to the peak shock pressure experienced by the meteorite.

INTRODUCTION

Isolated regions of silicate glass containing a varietyof microlites are found heterogeneously distributedthroughout the groundmass of strongly shockedchondrite and achondrite meteorites (Dodd andJarosewich 1979, 1982; Chen et al. 1996; Gillet et al.2000; Malavergne et al. 2001; Xie et al. 2002, 2006; Becket al. 2004). These features are called shock-melt veins orshock-melt pockets to indicate their origin via impact onthe parent body. They are interpreted to have formed inlocal hot spots (up to 2500 K) by shock impedancecontrasts or frictional melting along shear bands as shockwaves traveled through heterogeneous, cracked, and/orporous materials (Langenhorst and Poirier 2000; Becket al. 2004, 2007). The hot spots are distinct from thebulk rock in which the temperature increase, by shockcompression and the nonadiabatic deposition of heat

after decompression, was limited to a few hundreddegrees (Sharp and DeCarli 2006). This study focuses onshock-melt veins and pockets (hereafter referred tosimply as veins and pockets) in shergottites: mafic,permafic, or ultramafic igneous rocks from Mars havingsubophitic, porphyritic, or poikilitic textures (Waltonet al. 2012). Shock melts are ubiquitous amongshergottites, comprising up to 14 vol% of the host rock(Allan Hills [ALH] 77005; Treiman et al. 1994). Shockmelts in shergottites are of particular interest becausethey host a nearly pure sample of the Martianatmosphere, defined by isotopic ratios and abundances ofN2, CO2, and noble gases (Bogard and Johnson 1983;Marti et al. 1995; Walton et al. 2007).

In this study, we present a detailed analysis of thepostshock thermal history of four shergottites usingthe 2D mode of the HEAT model developed byK. Wohletz (Wohletz et al. [1999] and http://geodynamics.

Meteoritics & Planetary Science 48, Nr 5, 758–770 (2013)

doi: 10.1111/maps.12100

758© The Meteoritical Society, 2013.

lanl.gov/Wohletz/Heat.htm). The goals are twofold: (1)to resolve the discrepancy between shock-melt coolingtimes, i.e., the time required for cooling to the solidus ofthe melt, derived from previous calculations of heat flowand those from dynamic crystallization experiments, and(2) to assess the thermal history of natural meteoriteswith a range of shock-melt distributions and abundances.The models in this study provide refined estimates for therate of meteorite cooling after a shock event.

RATIONALE FOR CURRENT STUDY

Shock veins and shock-melt pockets comprisematerial that was locally melted (Fredriksson et al.1963) and then cooled by conduction of heat to thesurrounding host rock (Langenhorst and Poirier 2000;Leroux et al. 2000; Sharp et al. 2003; Xie et al. 2006).Calculations by Beck et al. (2007) indicate cooling ratesfor a 1 mm diameter shock melt of 5000 °C s�1 overthe cooling interval 2500–500 °C, giving a cooling timefor this interval of 0.2 s. This is considerably shorterthan cooling rates of 0.2–0.3 °C s�1 determined byWalton et al. (2006) from dynamic crystallizationexperiments. These longer cooling times correspond to acooling duration of 8�16 min to hours for the largestcm-size shock melts found in shergottites. Reactiontextures between shock melts and host rock minerals areconsistent with cooling times longer than thoseestimated by Beck et al. as indicated by experimentaldata (Walton and Shaw 2009). The cooling times ofshergottite shock melts are of particular importance forsampling of Martian atmosphere. The longer coolingtimes of Walton et al. (2006) support diffusion ofMartian atmosphere to the host rock, which has thepotential to erase or modify that atmospheric signature,especially if the diffusion rates of the gases involved aresignificantly different.

Cooling times of shock melts also have implicationsfor the pressure at which shock melts crystallize andcool below the solidus. This is important because themineral assemblages that crystallize within shock melts,when compared with phase diagrams obtained fromstatic high-pressure experiments, can be used toconstrain the pressure conditions of crystallization (seediscussions in Sharp and DeCarli 2006; Gillet et al.2007). How the crystallization pressure relates to theshock history of the meteorite will depend on twofactors: the shock duration, defined as the time lagbetween the arrival of the initial shock wave and theproduction of the release wave, and the quench time ofthe melt (Xie et al. 2006). Constraints on the shockduration in one shergottite, Zagami, have been obtainedby studying trace-element concentrations in liquidusaggregates of K-hollandite in a shock-melt pocket (Beck

et al. 2005). This method assumes that the trace-elementpartitioning took place during the shock pulse so thetime required for a trace element to diffuse from themelt into the K-hollandite can be used to calculate aminimum value for the duration of shock pressure.Based on their measurements of Cs, Ba, and Rb theequilibrium shock pressure duration was found to be ofthe order of 10 ms (0.01 s). Similar time estimates forthe shock duration are derived based on formation andpreservation of high-pressure phases in Chassigny (Fritzand Greshake 2009). If the shock duration exceeds thequench time, crystallization occurs at the peak pressureand the mineral assemblage that crystallizes will bedirectly related to the peak shock pressure experiencedby the meteorite. If the shock duration is shorter thanthe quench time, only part of the cooling path will be athigh pressure with remainder occurring after thepassage of the release wave. Finally, if the quench timeis much longer than the shock duration the shock meltwill remain molten after pressure release to crystallize amineral assemblage whose formation conditions areunrelated to the shock-pressure conditions.

PETROGRAPHY OF SHOCK MELTS IN

SHERGOTTITES

Shock-melt veins are easily observed in polishedsections as black to brown veins cutting across theentire meteorite sample. Their widths vary from 1–2 lmup to several millimeters and they may beinterconnected or occur as single, straight features.Shock-melt pockets are rounded or amoeboid features,varying in size from <1 mm to several cm in apparentdiameter. We have selected four nonbrecciated, igneousMartian meteorites for our models: Los Angeles(Warren et al. 2004), Dar al Gani (DaG) 476 (Zipfelet al. 2000), DaG 1037 (Russell et al. 2004) andNorthwest Africa (NWA) 4797 (Walton et al. 2012).These meteorites were chosen as they cover a widerange of shock-melt distribution and geometry, evenamong paired samples (DaG 476 and DaG 1037). NWA4797 is the least complex in terms of the distribution ofshock melts, as it contains only a single shock-meltvein. Los Angeles lacks veins but has a number ofpockets of different sizes, some of which are isolatedfrom other shock melts while others are within amillimeter or two of adjacent pockets. DaG 476 and1037 are the most complex in terms of the variation insize and distribution of shock melts. DaG 476 containsregularly distributed pockets with a very thin veinwhereas DaG 1037 has one thick and one thin vein, anda range of pockets sizes from less than 1 mm to 4 by8 mm. Detailed microtextures of the shock melts ineach meteorite sample are shown in Fig. 1.

Thermal modeling of shock melts in Martian meteorites 759

ANALYTICAL METHODS

High-resolution images of the polished surface ofeach meteorite were acquired using a Zeiss EVO MALaB6 filament scanning electron microscope (SEM) inbackscattered electron (BSE) mode at the University ofAlberta. BSE images were acquired using a Si diodedetector under conditions of 20 kV (acceleratingvoltage) and 5–8 mm (working distance). ImageJ, animage analysis software program, was used to determinethe modal abundance of shock melts in each sample, aswell as to measure vein and pockets dimensions fromBSE images.

To map the distribution of shock melts theindividual thin sections (Los Angeles, DaG 476, andNWA 4797) or polished tile (DaG 1037) werephotographed in transmitted light (thin sections) orreflected light (tile). This provided a low magnification

overview of the entire sample showing the size, shape,and spatial distribution of shock melts in 2D. Thephotographs were then imported into a commercialimage software program to produce a binary map ofeach section, dividing the samples into shock melt(black) and host rock (white) (Fig. 2). Thecharacteristics of each thin section examined, includingthe width/length ratio of shock melts and their volume%abundance (determined by manual point counts on thethin section + tile photographs) are given in Table 1.

The cooling history of each meteorite sample wasmodeled using the HEAT program of Wohletz (http://geodynamics.lanl.gov/Wohletz/Heat.htm and Wohletz etal. 1999) in 2D mode. We have also tested a 3D coolingmodel. Since the thermal conductivity is isotropic,cooling times in a 3D model are the same as those inthe 2D models. However, we recognize that in thenatural samples, it is possible for pockets or veins not

Fig. 1. BSE images of the Los Angeles (a, b), DaG 476 (c), DaG 1037 (d) and NWA 4797 (e, f). a) A small shock-melt pocketin Los Angeles (center) has crystallized a high-pressure mineral assemblage of stishovite + glass (Chennaoui Aoudjehane et al.2005). b) A larger mm-size shock-melt pocket in the same thin section as shown in (a) contains a mineral assemblage(olivine + pyroxene + alkali glass + iron sulfide spheres; Walton and Spray 2003). c) The contact between a mm-size shock-meltpocket in DaG 476 and the basaltic host rock is shown. Elemental exchange has occurred between plagioclase in the host rockand neighboring pyroxene as evidenced by the diffuse contact between these two minerals. d) The contact between the mm-sizeshock-melt vein in the DaG 1037 and the basaltic host rock. Reaction textures and diffusive exchange between neighboringigneous minerals are observed within a zone approximately 500 lm from the shock vein/host rock contact. e) The mm-sizeshock-melt vein in the NWA 4797 has crystallized a mineral assemblage of olivine + pyroxene and iron sulfide spheres in alkali-rich glass. f) Plagioclase within the host rock is a highly vesiculated glass with flow textures. SMP = shock-melt pocket,SMV = shock-melt vein, pl-glass = plagioclase glass, ol = olivine, px = pyroxene.

760 C. S. J. Shaw and E. Walton

in the plane of the 2D model to affect cooling rates.The 2D finite element model applied to the meteoritehas a minimum grid size of 0.01 m, which is too largeto model the meteorite samples. However, the results ofthe model are easily scaled to allow us to examineshock-melt pockets with an area as small as 1 mm2. It ispossible to model even smaller pockets, but the requiredincrease in the number of cells in the model increasesthe calculation time by a factor of 1000. A limit of1 mm was reasonable based on the observed pocket andvein size and on the constraints of the model.To accommodate the thinner shock melts in themeteorite samples (100 lm), we applied a linearextrapolation of our data.

For each sample, the distribution of shock meltswas mapped onto a grid (Fig. 2). For the purposes ofmodeling we ignored pockets and veins with length orwidth significantly less than 1 mm. For example thisomits the thin shock vein and several shock-meltpockets from DaG 476. For all four meteorites weassumed a basaltic bulk composition with a rockdensity of 3000 g cm�3, thermal conductivity of1.8 W m�1 K�1 (Murase and McBirney 1973) and heatcapacity of 1000 J kg�1 K�1 at 800 K (Bouhifd et al.2007). The temperature of the host rock was taken tobe 500 °C and assumed to be homogeneous (i.e., thesame conditions as the Beck et al. [2007] calculation).The shock melts are assumed to be of approximately

Table 1. General characteristics of shock melts in the four shergottite samples modeled.

Meteorites

Shock melts Width/length ratio % Abundance High-P Low-P

Pockets Veins Range Average Shock melta Min Min

Los Angeles ✓ ✕ 0.5–1.0 0.8 5.4 ✓ ✓

DaG 476b ✓ ✓ 0.4–1.0 0.7 7.6 ✓ ✓

DaG 1037b ✓ ✓ 0.1–1.1 0.7 13.8 ? ✓

NWA 4797 ✕ ✓ 0.14 n.a. 10.3 ✕ ✓

n.a. = not applicable, NWA 4797 contains a single shock melt vein.a%Abundance of shock melts measured from point counts on thin sections.bDaG 476 and DaG 1037 are possibly paired meteorite specimens (Russell et al. 2004).

Fig. 2. Binary maps showing the size, shape, location, and distribution of shock melts (black) and host rock (white) in fourshergottite meteorites. 1 mm2 grids were then assigned to each black area on the sketches to model the thermal history of thesenatural meteorites during shock.

Thermal modeling of shock melts in Martian meteorites 761

basaltic composition with density of 2725 g cm�3,thermal conductivity of 2 W m�1 K�1, and heatcapacity of 1500 J kg�1 K�1 (Murase and McBirney1973; Bouhifd et al. 2007). Thermal conductivity inmelts varies from 1.3 W m�1 K�1 at 900 °C to2.3 W m�1 K�1 at 1500 °C (Murase and McBirney(1973). Using the minimum experimentally determinedconductivity (1.3 W m�1 K�1) rather than our chosenvalue of 2 W m�1 K�1, results in a 7.5% increase incooling time, whereas using the maximum value gives a1.7% decrease in cooling time. The melt temperaturewas taken as 2500 °C, i.e., just above the solidus ofbasalt at 20–25 GPa (Wang and Takahashi 1999;Hirose and Fei 2002), corresponding to the sameparameters modeled by Beck et al. (2007). This may bean underestimate of the initial temperature as we haveno reliable indicator of the actual peak temperature. Inall models we assumed that there was no convection inthe melt and no P–T dependency of the solidus. Sincemodeled cooling times are small (seconds to minutes)radioactive decay heat is insignificant and is ignored.The latent heat of crystallization was taken into account(see Wohletz et al. [1999] for details on the calculation),as there is some quench crystallization in the pocketsand veins (Walton and Shaw 2009).

Beck et al. (2007) carried out simple calculationsof cooling rate in which they examined cooling from2500 °C to 500 °C. We have chosen 900 °C as the endpoint of cooling for our models since at thistemperature diffusion of even the fastest movingcomponent (e.g., Na, Zhang et al. 2010), will be tooslow to have any significant effect on the shock meltcomposition, even if cooling is three orders ofmagnitude slower than calculated by Beck et al.(2007).

RESULTS

Idealized Isolated Shock-Melt Pockets and Shock Veins

In the ideal case, i.e., the conditions used by Becket al. (2007) in their model, shock melts will cool byconduction to the background temperature of themeteorite with no thermal interference from the coolingof nearby melt pockets or veins. The times calculatedfor cooling, over the range 2500 to 900 °C, of suchisolated pockets and veins exhibiting different areas anddifferent width/length ratio (Table 2, Fig. 3) representminimum cooling times. In this ideal case the thermalgradient between the shock melt and host rock is at itssteepest, thus yielding the most rapid quench for a givenarea/volume of melt. The minimum cooling time for thesmallest pockets modeled (1 mm2) is 1.2 s and there is alinear increase in cooling time with area (Fig. 3).

Rectangular pockets show marginally faster coolingthan equidimensional pockets because of their largerperimeter/area ratio.

One mm wide shock veins in which the width tolength ratio is less than 1/3 show significantly fastercooling than the square and rectangular pockets(Table 2, Fig. 3). For such veins we find that thecooling time becomes constant at a width/length ratioof 1/15.

Meteorites

Northwest Africa 4797The 1 mm vein in NWA 4797 is the only melt-filled

structure in the sample (Fig. 2). Cooling of this veintherefore shows the same cooling time as the idealsystem for the observed length of 7 mm (Fig. 3). Evenif this is only a fraction of the actual length of the vein,the calculated cooling time of 4.5 s is only 0.8 s lessthan the maximum possible time calculated for an idealisolated vein (Table 2).

Los AngelesThe Los Angeles sample contains two 1 mm2 and

three 3 mm2 shock-melt pockets (Fig. 2). The 1 mm2

pocket give cooling times <0.1 s longer than the idealtime for an isolated pocket (1.24 s versus 1.17 s)indicating that there is no significant effect on coolingtime from the other shock-melt pockets in this part ofthe sample (Fig. 3, Table 2). All three larger pocketsgive cooling times of 5 to 7 s, i.e., 1.8 to 2.6 timeslonger, compared to the cooling time of an isolatedpocket of the same size (Fig. 4, Table 2). The regionbetween two closely spaced 3 mm2 pockets is heatedwell above the solidus and could have sufferedpostshock melting or diffusive modification (Fig. 5).

Dar al Gani 476The model DaG 476 sample contains 11 discrete

shock-melt pockets (Fig. 2). The actual sample also hasa thin shock-melt vein (1–100 lm wide) and severalpockets with areas significantly less than 1 mm2. Asthese are smaller than the minimum grid size in theHEAT model they are ignored here. The consequencesof this are minimal; the additional heat contained inthese pockets would increase cooling times slightly buttheir omission has no significant effect on the resultspresented. Two of the seven 1 mm2 pockets cool to900 °C at nearly the same rate at the idealized isolatedpockets (Fig. 3, Table 2). However, the remaining fivepockets take approximately 20% longer (1.42 versus1.17 s) to reach 900 °C than an ideal (isolated) pocket.These slower cooling regions are within 1–2 mm ofanother pocket so that the temperature gradient during

762 C. S. J. Shaw and E. Walton

cooling is decreased (Fig. 4). The three 2 mm2 pocketsalso show significant variation in cooling time. Themost isolated of these pockets cools in 1.9 s, which isvery close to the ideal cooling time. The remaining two

are near to each other and to a 1 mm2 pocket. Theinterference between the thermal haloes of these closelyspaced pockets extends cooling to 900 °C by 1 and 1.3 s(compared to an isolated pocket of the same size). The

Fig. 3. Ideal cooling times for square and rectangular shock-melt pockets and a 1 mm wide shock-melt vein of variouslengths compared with calculated cooling times for shockmelts in four shergottites, Los Angeles, DaG 476, DaG 1037,and NWA 4797.

Fig. 4. Effect of adjacent melt on cooling of 1 and 3 mm2

pockets in DaG 476 and Los Angeles.

Table 2. Cooling times for shock-melt pockets and shock veins of different areas and geometries.

Area (mm2)

Cooling times (seconds)

DAG 476 LA DAG 1037 NWA 4797Isolatedsquare SMP

Isolatedrectangular SMP

SingleSMV*

1 1.41 1.24 1.40 1.17 1.17 1.171 1.24 2.502 1.94 2.19 1.812 2.83 2.40

2 3.08 2.603 3.27 4.94 3.40 2.683 7.15

3 5.734 3.90 3.37 3.164 3.90

4 4.104 4.604 4.10

6 6.10 5.18 4.086 7.096 44.576 14.08

6 6.307 4.43 4.438 12.10 6.48 4.67

9 10.71 7.9512 12.89 10.2824 32.18

SMP = shock-melt pocket; SMV = shock-melt vein.

LA = Los Angeles.

*Single SMV calculated for a width of 1 mm appropriate for the NWA 4797 and DaG 1037 meteorites.

Thermal modeling of shock melts in Martian meteorites 763

cooling time of the single 3 mm2 pocket is also extendeddue to interference of its thermal halo with those ofnearby pockets.

Dar al Gani 1037DaG 1037 shows the most complex distribution of

shock-melt pockets and veins, and consequently the mostcomplex cooling history (Fig. 2). This meteorite samplecontains abundant pockets that vary in size and spatialdistribution, in addition to a 1 mm wide vein cuttingacross the entire sample. The three 1 mm2 pockets coolto the basalt solidus in slightly longer than the time foran ideal pocket; 1.4 s compared to 1.2 s. All remainingpockets take significantly longer to cool than isolatedpockets of the same size. The main retarding influence oncooling is the large shock vein that runs through thecenter of the sample; the hottest part of which takesapproximately 1.75 min to reach 900 °C. For example,cooling times for the six 6 mm2 pockets take from 6 to44 s depending on proximity to the shock-melt veincompared to an ideal time of 4–5 s for isolated pockets.

In both DaG samples (476/1037) the smallestshock-melt pockets experience some reheating (e.g.,Fig. 6), although this does not extend back above thesolidus (900 °C). The interference effects of adjacentpockets in DaG 1037 are illustrated in Fig. 7. Evenafter 1 s there is some interference between the thermalaureole of the vein and largest pocket. By 1.8 s, evensmall adjacent pockets show overlapping thermalaureoles and by 9.5 s only two areas are unaffected byheat from the adjacent pockets and veins. By 22 s thereis a single thermal aureole within the model meteorite.

DISCUSSION

Summary of Results

We have defined the distribution and coolinghistory of shock melt with both vein and pocketgeometry in four shergottite samples: Los Angeles, DaG476, DaG 1037, and NWA 4797 using the HEAT modelof Wohletz et al. (1999). Although the temperaturedifference between the shock melt and the host rock isan important factor in determining the rate at which theshock melt cools, our study demonstrates that otherparameters are also important in governing the coolingrate, specifically the size, shape (equidimensional,rectangular and vein geometry), and spatial distributionof the pockets and veins. All shock melts coolconductively to the background temperature of the hostrock. However, the thermal gradient is largest in thecase where shock melts are not influenced by thethermal haloes of other nearby veins or pockets. Theseisolated shock melts therefore undergo the most rapidquench. This behavior is seen in NWA 4797, whichcontains a 7 mm long, 1 mm wide vein. This veincooled to 900 °C in 4.5 s. The other three samples havecooling times from 1.4 to 100 times longer than in theideal (isolated) system. This deviation is the result ofinterference between the thermal haloes of nearbypockets, and in the case of DaG 1037, a large vein,which decreases the thermal gradient.

Previous Estimates of Cooling Times

Beck et al. (2007) modeled the cooling history ofshock-melt pockets for the same melt and host rock

Fig. 5. Effect of adjacent shock-melt pockets on the igneoushost rock. A small patch of initially solid material betweentwo large, closely spaced pockets in the Los Angeles sample(red shaded area in Fig. 2) would be heated above the solidus.The region remained above the solidus temperature forapproximately 5.5 s.

Fig. 6. Cooling history of the shock vein and two smallshock-melt pockets in DaG 1037 (see Fig. 2 for locations).The veins show a regular cooling path. The veins cool to thesolidus along the same path but show different degrees ofreheating as the thermal halo from the cooling vein migratesoutward.

764 C. S. J. Shaw and E. Walton

temperatures used in this study. In their study, coolingtimes were derived using a single thermal diffusivity forthe host rock and shock melt. Calculations from this1-D model predict that a 1 mm shock-melt pocket willcool to 900 °C in 0.2 s. Additional estimates of coolingtimes for shergottite shock melts by Walton et al. (2006)were based on comparisons of crystal shape betweennatural samples and experimental charges produced bycontrolled cooling. The rates predicted from theseexperiments are significantly slower. A 1 mm shock-meltpocket took 8–12 min to cool to approximately 990 °C;we attribute this to the nature of the starting material.The crystallization experiments were performed usingsynthetic glasses whose composition was based onnatural shock-melt pockets in shergottites. These glasseswere prepared by two fusions of decarbonated oxide—carbonate mixtures at 1600 °C. This method produceshomogeneous, crystal-free glass. The use of such

homogeneous starting material extends cooling timesbecause of the necessity of developing nuclei in the melt(e.g., Lofgren [1980] and references therein). Thus, moretime is required to produce particular textures (skeletalversus equant, euhedral crystal shapes) than would bethe case in nuclei-rich natural shock melt.

The thermal models developed in this study areconsidered to more closely approximate the time neededfor cooling and partial crystallization of shock melts innatural meteorite samples. This is because we take intoconsideration the size, geometry, and spatialdistribution of shock melts in heavily shocked naturalmeteorite samples. The calculations by Beck et al.(2007) were for a very simplified system which did nottake into account differences in density, heat capacity,and thermal conductivity between the melt and host,and therefore led to cooling times for shock melts thatwere too short. We calculate a cooling time for a shock-

Time = 0 sec Time = 1.8 secTime = 0.9 sec

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Fig. 7. Cooling of DaG 1037 showing how the central shock vein affects the cooling of the adjacent melt pockets. Units on theX and Y scale are in cm.

Thermal modeling of shock melts in Martian meteorites 765

melt pocket identical to that of Beck et al. (2007) that isbetween six and seven times longer. The experimentalconditions used to constrain shock-melt cooling timesby Walton et al. (2006) were also too simple, yieldingunrealistically long cooling times. The most significantresult from our models is the long cooling times wecalculate due to thermal interference between adjacentpockets and veins. These longer cooling times call theconclusion of prohibition of chemical diffusion ofatmospheric gas phases in pockets made by Beck et al.(2007) into question. If diffusion carried on for longerthan calculated in their model, there may indeed bemodification of the composition of the pocket duringcooling. This is addressed in the following section.

Ar and Xe Diffusion

Shock recovery experiments have demonstrated thathypervelocity impact provides a viable mechanism forimplanting a sample of ambient gases in melts producedduring shock, without elemental or isotopicfractionation (Wiens and Pepin 1988; Bogard et al.1989). This results from diffusion in a high-pressureenvironment. The high-pressure gas would diffuse intothe locally molten regions of the meteorite (shockmelts). If this meteorite then cools from its postshocktemperature in a low-pressure environment, it would beexpected to lose some of its radiogenic gas (Davis 1977).Here, we assess the potential for shock melts to losesome of their noble gases implanted during shock dueto the extended cooling times predicted by this study.These calculations assume that all the Ar and Xe areinitially contained within the shock melt. Thisassumption is validated by spatially resolved argonisotope measurements performed on neutron-irradiatedsamples of several shergottites including Los Angeles,Zagami, ALHA77005, and NWA 1950 (Walton et al.2007, 2008). These studies show that Martianatmosphere, traced using 40Ar/36Ar as an isotopicfingerprint (as measured by Viking landers; Owen et al.1977), is specifically sited within the shock melts withlittle or no atmospheric component in host rockminerals.

There are good data for Ar diffusion in a range ofmelts (Nowak et al. 2004). These authors show that at1623 K, Ar diffusivity can be related to the degree ofpolymerization of the melt. Walton et al. (2006) givebulk compositions of three shock-melt pockets whoseNBO/T (ratio of nonbridging to tetrahedral oxygens inthe melt; a measure of polymerization calculated usingMysen et al. 1985) is 1.2–3.7. Using the relationshipdetermined by Nowak et al. (2004) and an NBO/T of1.8 we calculate DAr to be 2.15 9 10�10 m2 s�1 at1623 K.

The diffusivity of xenon is less well defined andthere are no data for Xe in basalt. However, Roseliebet al. (1995) and Spickenbom et al. (2010) present dataon both Ar and Xe diffusion in jadeite melts.Extrapolation between the two data sets indicates thatXe diffusion is approximately 5 times faster than that ofAr. If the same relation holds for basalt then thediffusivity of Xe is 1.1 9 10�9 m2 s�1 at 1623 K.

The percentage of each gas remaining in shock-meltpockets of various sizes can be calculated using thespherical diffusion couple solution (Zhang 2008) and thecooling times calculated from the HEAT models.Calculations were made for isolated shock-melt pocketswith a diameter of 1, 2, and 3 mm in a hypotheticalmeteorite. For these models the diffusivity was taken tobe that at 1350 °C rather than at the peak temperatureof 2500 °C. The pockets are at this peak temperaturefor only a fraction of the cooling period; using thediffusivity at this temperature would give unrealisticallylong diffusion profiles. The value at 1350 °C is acompromise, which recognizes that we can only averagethe diffusivity over the cooling time. The jadeite data ofRoselieb et al. (1995) suggest that as temperatureincreases, the diffusivity difference between Ar and Xeincreases by an order of magnitude between 1350 and1600 °C and a further factor of 20 from 1600 to2200 °C, assuming that the experimental data can bereliably extrapolated to such high temperatures. Ourestimates of diffusivity are conservative and will give aminimum amount of fractionation. In all the models theconcentration at the center of the spherical region is notsignificantly altered from the initial concentration(Fig. 8).

The results of the calculations show that for smallpockets (1 mm wide) 2.2% Ar and 5.2% Xe would belost from the pocket over the 1.5 s cooling time. Thiswould result in a small increase in the Ar/Xe ratio, toapproximately 1.02, of the glass over that originallytrapped (Fig. 8). However, if the cooling time isincreased to 5 s due to the effects of nearby veins orpockets, the longer diffusion time leads to significantfractionation of Xe from Ar and the Ar/Xe ratioincreases rapidly to 1.08. The behavior of Ar and Xe ina 1 mm wide 7 mm long vein, which cooled over 4.5 s(NWA 4797), is different. In this case, diffusion ismodeled using a 1 dimensional solution and theresulting loses in Ar and Xe are 7 and 15.6%,respectively, leading to an Ar/Xe ratio of 1.1.

A shock-melt pocket with a width of 2 mm and acooling time of 4 to 6 s loses 1.7–2.2% Ar and 4.1–5%Ar, respectively. The Ar/Xe ratio increases slightly to1.02–1.03 during cooling. For pockets with a protractedcooling history (e.g., the 2 by 3 mm pocket in DaG1037), which takes approximately 45 s to cool to 900 °C

766 C. S. J. Shaw and E. Walton

(7–11 times the minimum rate), the amount of Ar andXe lost increases to 6.6 and 13.9%, respectively, and theAr/Xe ratio increases to 1.08 (extrapolated from the fitto the 2 mm pocket curve in Fig. 8). Pockets withwidths of 3 mm giving cooling times of 10–12 s loseapproximately 2% Ar and 4.4 to 4.9% Xe and show asimilar increase in Ar/Xe ratio to the 2 mm widepocket.

For the larger pocket (3 mm) there is less variationof the Ar/Xe ratio over the cooling time (Fig. 8b). Thissuggests that even though the cooling time is longer,larger, isolated pockets are more likely to preserve theoriginal trapped gas composition than smaller pocketsthat have elevated cooling times due to thermal effectsof nearby shock melts.

Implications for the Crystallization Pressure of Shock

Melts

Minerals stable at high temperatures and pressuresare found within or adjacent to shock melt veins andpockets in shergottites, e.g., omphacite, jadeite, stishovite,akimotoite, tuite, hollandite, amorphized (Mg,Fe)SiO3

pervoskite, magnesiow€ustite, wadsleyite, ringwoodite, andCa,Na-hexaluminosilicate (Langenhorst and Poirier 2000;Beck et al. 2004; Fritz and Greshake 2009; Imae andIkeda 2010; Miyahara et al. 2011). These minerals formby crystallization from a silicate liquid during shock or bysolid-state phase transformation. High-pressure mineralassemblages that crystallize during the shock pressure

pulse can be used to constrain shock conditions anddurations, by combining the crystallization assemblageswithin the shock vein with their phase equilibriadetermined from static high-pressure experiments (seediscussions in Sharp and DeCarli 2006; Gillet et al. 2007).In contrast, high-pressure minerals formed by solid-statemechanisms are less reliable as indicators for shockconditions compared with shock-melt crystallizationproducts because their formation requires over-steppingof the phase boundary (in pressure) for nucleation tooccur (Sharp and DeCarli 2006).

The mineral assemblage that crystallizes within theshock melts, and which can be used to constrain shockP–T conditions experienced by the meteorite, isdependent on the shock duration and quench time (seediscussion in the Rationale for Current Study section).Based on the cooling times modeled in this study usingHEAT (see the Results section), and a 0.01 s shockpulse duration (Beck et al. 2005; Fritz and Greshake2009) the following observations can be made of shockmelts in shergottites:(1) The mm-size pockets and veins, ubiquitous among

the modeled shergottites, cool in timeframesgreater than 1 s, even in those shock meltscompletely isolated from the thermal effects ofnearby shock melts. The crystallization assemblageof these shock melts will be unrelated to the peakshock pressure experienced by the meteorite.

(2) Scaling our models to examine 100 lm wideshock-melt pockets observed in DaG 476 and DaG1037 samples, but not included in our modelcalculations, decreases cooling times by a factor of102 which is sufficient to allow cooling from 2500to 900 °C over approximately 0.01 s. The pressurestability of the crystallization products within thesesmaller 100 lm size melts, when compared withtheir experimentally determined pressure stability,can be used to place constraints on the peak shockpressure experienced by the meteorite. The quenchwill be faster for 100 lm vein with a width/lengthratio of less than 1/5, as this geometry cools morequickly compared with equidimensional pockets.

(3) When shock-melt regions are close together, eventhose that are submillimeter-sized will have coolingtimes that are longer than that required forcrystallization of high-pressure phases during theshock pressure pulse.

(4) The search for a pristine sample of Martianatmosphere should focus on the center of largeshock-melt pockets whereas only the smallestshock-melt regions will crystallize high-pressurephases related to the peak shock pressureexperienced by the meteorite.

Fig. 8. Evolution of the Ar/Xe ratio in shock-melt pockets ofradius 1, 2, and 3 mm over the modeled cooling times (seetext for details). Note that the Ar/Xe ratio in a 1 mm widevein is significantly higher after cooling than in a sphericalshock-melt pocket of the same radius. The inset shows thecalculated compositional profile for Xe in a 1 mm radiusshock-melt pocket.

Thermal modeling of shock melts in Martian meteorites 767

Application to Shock Melts in Shergottites

Our models make testable predictions regarding thedistribution, size, and shape of shock melts in shergottitesthat will represent true high-pressure melts (i.e., crystallizein <0.01 seconds). Although a detailed study on thedistribution of high-pressure minerals in the modeledshergottites is out of the context of this study, severalearlier-published works, while not focussing specificallyon the distribution of high-pressure phases versus shock-melt size, do support our predictions. Walton and Spray(2003) investigated shock-melt pockets in the same LosAngeles stone 1 thin section modeled in this study(Fig. 2). The mm-size shock-melt pockets containschlieren-rich glass with Fe-sulfide spheres, and dendriticolivine, merrillite, titanomagnetite, and plagioclase.No high-pressure compositional equivalents such aswadsleyite, ringwoodite, lingunite, or tuite wereencountered. The mm-size melt pockets are also vesicle-rich indicating low confining pressures, consistent withtheir crystallization during or after pressure release(Walton and Spray 2003). One smaller shock-melt pocketin the Los Angles thin section (approximately 300 lmthick) was devoid of vesicles and contained needle-shapedstishovite that crystallized from the melt (Fig. 1a; see alsoWalton and Spray 2003; Chennaoui Aoudjehane et al.2005). Similarly, the mineralogy and composition of theminerals that crystallized within the 1 mm thick vein inthe NWA 4797 thin section record a lower pressuremineral assemblage of olivine + pyroxene + alkali glass +Fe-sulfide spheres (Walton et al. 2012). Transmissionelectron microscopic investigation of thin (1–100 lmthick), black shock veins in the Zagami shergottite byLangenhorst and Poirier (2000) discovered a number ofhigh-pressure minerals such as stishovite, lingunite,akimotoite, and amorphous silicate perovskite. AlthoughZagami was not specifically modeled in this study, theresults of Langenhorst and Poirier (2000) do show thathigh-pressure phases occur exclusively in thin veins insome shergottites.

Cooling History of Shock Melts in Shergottites Versus

Chondrites

Shock metamorphism is ubiquitous among allmeteorites (e.g., St€offler et al. 1991). However, the shockhistory of Martian meteorites is very different from thosemeteorites (e.g., chondrites) derived from small planetarybodies. Most chondrites are breccias, reflecting multiple-impact processing within the asteroid belt early in thehistory of the solar system (Bogard 1995). Laser probe40Ar-39Ar dating of shock veins in the Peace River L6chondrite (containing minerals stable at high pressure)yielded an age of 450 � 30 Ma (McConville et al. 1988),

and therefore tied vein formation to disruption of theL-chondrite parent body in a major collision event atapproximately 400–500 Ma (Anders 1964). In contrast,most Martian meteorites are coherent igneous rocks thathave been strongly shock metamorphosed but notbrecciated (with the exception of monomict breccia ALH84001, a ~4.5 Ga ungrouped Martian orthopyroxenite;Treiman 1995). Shergottites have been ejected from thenear surface of Mars in five discrete impact events overthe past 0.7 to 20 Ma (Nyquist et al. 2001). Studies ofshock duration have shown that the pressure pulse inchondrites (approximately 1 s) is much greater than inMartian meteorites (10 ms) (Beck et al. 2005; Fritz andGreshake 2009). This will strongly affect the mineralassemblages that crystallize from shock melts. If theduration of the shock pulse is longer (e.g., 1 s), as it is forchondrites, then the shock melt is more likely to crystallizeduring shock compression, forming minerals that record acrystallization pressure directly related to the shock P–Thistory of the host rock. Indeed this is the case for severalchondrites including L6 chondrite Yamato 791384, inwhich shock veins up to 2 mm thick have crystallized amajorite-pyrope solid solution indicative of shockpressures 18–23 GPa (Ohtani et al. 2004).

CONCLUSION

Propagating shock waves causes melting at localhot spots. These melts quench crystallize to glass +crystals that preserve high- or low-pressure mineralassemblages depending on the cooling times of the meltsand the shock duration. We have defined thedistribution of shock-melt veins and pockets in Martianmeteorites NWA 4797, Los Angeles, DaG 476, andDaG 1037, and we use a finite element model tocalculate their cooling history. The thermal modelsdeveloped in this study are considered to more closelyapproximate the time needed for cooling and partialcrystallization of shock melts in natural meteoritesamples. This is because we take into consideration thesize, geometry, and spatial distribution of shock meltsin heavily shocked natural meteorite samples. Ourresults demonstrate that the quench process is morecomplex than simple conductive cooling to a cooler hostrock. Other parameters are also important in governingthe rate of shock-melt quench, specifically the size,geometry, and spatial arrangement of these hot spotswithin the host rock. We draw the followingconclusions from the results of our thermal models:(1) Cooling times of shock melts may be extended 1.4

to 100 times by the interfering thermal haloes ofnearby shock melts. This decreases the thermalgradient between shock melt and host rock whichincreases the overall cooling time.

768 C. S. J. Shaw and E. Walton

(2) Shock-melt veins having the same area as shock-melt pockets cool more quickly due to theirincreased surface area with the cooler host rock.

(3) There may be diffusive loss of atmospheric gasesduring extended cooling times from high postshocktemperatures; however, the center of larger,isolated shock-melt pockets are more likely topreserve the original trapped gas composition thansmaller pockets that have elevated cooling timesdue to thermal effects of nearby veins and pockets.

(4) Only smaller pockets and veins (approximately100 lm thick) that are isolated from the thermaleffects of other hot spots within the host rock willquench before pressure release. In these, sincecrystallization occurs at the peak pressure andtemperature, the pressure stability of the mineralassemblage within the shock melt is related to thepressure conditions of the impact event. This isespecially relevant to those meteorites experiencinga short shock duration such as the shergottites.

Acknowledgments—This work has been funded byNSERC Discovery Grant RES0007057 awarded toE. W. and NSERC Discovery Grant 249939 awarded toC. S. Helpful comments provided by Zhidong Xie andan anonymous reviewer, as well as those of theassociate editor, Ed Scott, improved the quality ofthe final manuscript.

Editorial Handling—Dr. Edward Scott

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