Highly retentive core domains in K-feldspar and theirimplications for 40Ar/39Ar thermochronology illustratedby determining the cooling curve for the Capoas Granite,Palawan, The Philippines

M. A. FORSTER1*, R. ARMSTRONG1, B. KOHN2, G. S. LISTER1, M. A. COTTAM3† AND

S. SUGGATE3z

1Research School of Earth Sciences, The Australian National University, Canberra, ACT 2601, Australia2School of Earth Sciences, The University of Melbourne, Parkville, Vic 3010, Australia3SE Asia Research Group, Department of Earth Sciences, Royal Holloway University of London,

Egham TW20 0EX, UK

K-feldspar from the late Miocene Capoas Granite on Palawan in The Philippines appears to contain highlyretentive diffusion domains that are closed to argon diffusion at near-solidus temperatures during coolingof this »7 km-diameter pluton. This is an important result, for K-feldspar is commonly considered notretentive in terms of its ability to retain argon. Closure temperatures for argon diffusion in K-feldspars areroutinely claimed to be in the range »150�400�C but the release of 39Ar from irradiated K-feldspar duringfurnace step-heating experiments in vacuo yields Arrhenius data that imply the existence of highlyretentive core domains, with inferred closure temperatures that can exceed »500�700�C. These highclosure temperatures from the Capoas Granite K-feldspar are consistent with the coincidence of 40Ar/39Arages with U�Pb zircon ages at ca 13.5 § 0.2 Ma. The cooling rate then accelerated, but the rate ofchange had considerably slowed by ca 12 Ma. Low-temperature (U�Th)/He thermochronology showsthat the cooling rate once again accelerated at ca 11 Ma, perhaps owing to renewed tectonic activity.

KEY WORDS: dating emplacement, 40Ar/39Ar geochronology, U�Pb SHRIMP geochronology, (U�Th)/Hethermochronology, K-feldspar geochronology, closure temperature, South China Sea, hydrocarbonmaturity, age of unconformity.

INTRODUCTION

Forster & Lister (2010) demonstrated that, at least in the-ory, K-feldspar might be considerably more retentive interms of argon diffusion than present estimates wouldallow. This is an intriguing result because for two deca-des, in reference works (e.g. McDougall & Harrison 1999),and in research papers, potassium feldspar is generallyconsidered to have variable but relatively low closuretemperatures. Estimates range from: (i) 150 to 300�C (e.g.McLaren et al. 2002; Streepey et al. 2002; Cassata & Renne2013); (ii) 150 to 350�C (Lovera et al. 1989; Karlstrom et al.2010); or even (iii) 200 to 400�C (Harrison & Lovera 2013).Lovera et al. (1997) report activation energies in therange 30�77 kcal/mol, with frequency factor a functionof a correspondence equation determined by Lovera etal. (1997) for slab-shaped diffusion domains. The leastretentive domains in the average K-feldspar (E »46 kcal/

mol; Lovera et al. 1997) are closed to argon diffusion at»250�C, for a cooling rate of 20�C/Ma. Naturally the sizeof a diffusion domain is critical in determining retentiv-ity, and the smaller the domain, the less its retentivity.Even for the most retentive diffusion domains, consid-ered by McDougall & Harrison (1999) to be »100 mm indimension, closure temperature estimates are150�320�C for cooling at 20�C/Ma at zero pressure,assuming a slab-shaped diffusion domain.

In part, these estimates vary because individualresearchers analyse Arrhenius data differently. Forster& Lister (2010) showed that traditional ‘slope-averaging’methods (e.g. using least-squares analysis) invariablyunderestimate the actual values of activation energyand frequency factor used in simulations. Many pub-lished values for the diffusion parameters of K-feldsparcould thereby have inadvertently underestimated itsretentivity.

*Corresponding author: marnie.forster@anu.edu.au†Present address: BP Exploration Operating Company Limited, 1�4 Wellheads Avenue, Dyce, Aberdeen AB217PB, UKzPresent address: RPS Energy, Ashfields Farm, Priors Court Road, Hermitage RG18 9XY, UK� 2015 Geological Society of Australia

Australian Journal of Earth Sciences (2015)

62, 883�902, http://dx.doi.org/10.1080/08120099.2015.1114524

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To test this hypothesis we present a case study dem-onstrating the analysis of 40Ar/39Ar ages from K-feldsparin Miocene granite, based on geochronology using fur-nace step-heating experiments. The results imply theexistence of highly retentive core domains, with closuretemperatures high enough to allow the retention ofargon at temperatures above, or just below, the granitesolidus. Within uncertainty the ages obtained from thesedomains coincide with the results of U�Pb geochronol-ogy using zircon analysed with SHRIMP. Thermochro-nology is still possible, because less retentive diffusiondomains exist, but different methods need to be appliedto interpret the data.

We also simulate the response of a collection of diffu-sion domains with varying activation energy, and to cou-ple the results with those from the low-temperaturethermochronometers provided by (U�Th)/He geochro-nology. Of particular interest is the way we can infer apreviously unrecognised two-stage cooling history basedon K-feldspar alone, and how this could be confirmed by(U�Th)/He geochronology. We back these conclusions bya modelling study that shows that the fundamentalasymmetry principle (FAP) developed by Forster &Lister (2010) can be extended to the analysis of Arrhe-nius plots for a material with two activation energies, aslong as these are very different.

This theoretical model is used to show that minimumestimates for diffusion parameters can be directlyinferred from internal sequences in the Arrhenius plot.Previously, it had been thought that estimates for activa-tion energy could be obtained only from the first few datapoints in the Arrhenius plots, and the value of the activa-tion energy inferred from these points was then routinelyapplied to a set of diffusion domains calculated for the K-feldspar in question (Lovera et al. 1989, 1993, 1997, 2002). Inthese previous studies monotonic cooling curves wereimposed, constrained using multi-domain diffusion(MDD) models. MDD models published prior to 2012 haveextrapolated the activation energy inferred for the leastretentive diffusion domains to the entire MDD model.

We first discuss the data, and thereafter the theoreti-cal considerations that allow analysis of Arrhenius plotsusing the FAP when widely varying activation energiesapply. The paper applies these methods by using the eAr-gon program for iterative forward modelling to con-struct model crystals with specified parameters fordifferent diffusion domains. 39Ar release from these the-oretical constructs produce results that closely mimicArrhenius plots derived from the measured data. Theseanalyses yield complex MDD models that are used by theMacArgon program for iterative forward modelling. Inthis way we were able to constrain the shape of tempera-ture�time (T�t) histories that allow observed 40Ar/39Arage spectra to be approximated, assuming release by dif-fusional processes alone.

GEOCHRONOLOGY

The Capoas Granite (Figure 1) is a fresh equigranular toporphyritic biotite granite well exposed around the baseof Mt Capoas on Palawan in The Philippines. It displaysa textural continuum between K-feldspar phenocryst-rich (Figure 2) and phenocryst-poor varieties, as well as

enclaves of biotite-rich fine-grained granite and K-feld-spar phenocrysts that show magmatic flow alignment(Encarnaci�on & Mukasa 1997). Thin-sections of the K-feldspar mineral separate illustrate a variety of micro-structures typical of fresh unaltered granite (Figure 3);there is no evidence of deformation. The bulk of the sep-arate (>»60% of the volume) consists of relativelyunstructured crystalline material, with occasional sub-grains demonstrating <2�3� misorientation. Microcline,as evidenced by twinning, is a minor component. Occa-sional inclusions of white mica are very small, and volu-metrically insignificant. Maps of atomic densityvariation obtained using Scanning Electron Microscopy(Figure 4) show minor variation in the Na/K ratio fromone microcline twin to another, and the late (very minor)introduction of albite in narrow veins and cracks.

SHRIMP U�Pb geochronology

A SHRIMP U�Pb zircon study of four samples (PAL33,34, 35 and 37) of the Capoas Granite as reported in Sug-gate et al. (2014) yielded dates all within the uncertaintyof each other, and a pooled U�Pb weighted mean206Pb/238U date of 13.5 § 0.2 Ma (95% confidence limit).One of these samples (PAL33, 13.4 § 0.1 Ma), was alsoused for a parallel 40Ar/39Ar study, as described below.The zircons from these samples are generally euhedralto subhedral, clear and lightly coloured with cathodolu-minescence imaging showing magmatic zoning (see Sug-gate et al. 2014) consistent with crystallisation withinfelsic to intermediate igneous rocks. The range of indi-vidual measurements is plotted in Figure 5.

40Ar/39Ar geochronology

PAL33 was utilised for 40Ar/39Ar geochronology. Thesample was dissected so K-feldspar from the groundmasscould be analysed separately to K-feldspar derived fromcrushed phenocrysts. The two K-feldspar aliquots wereanalysed using the step-heating method in a resistancefurnace attached to a VG1200 mass spectrometer. Isother-mal heating steps (cf. Lovera et al. 1997; Forster et al.2014) were included in the step-heating sequence becausethese appear to have some capacity to drive out extrane-ous or ‘excess’ argon (i.e. argon that had not been accu-mulated in the crystal lattice as the result of radiogenicdecay, but was present because it had been incorporatedin fluid inclusions, cracks and other high diffusivitypathways). Since the release of 40Ar and 39Ar is not con-cordant in these steps, one can safely assume such‘excess’ argon to have been present. The age spectra forthe first 30% of gas released (Figure 6a, b) show thegreatest effect of these isothermal steps, with consider-able oscillation in age. The first (generally older) stepappears to be the most contaminated so this step isreferred to as the cleaning step. Age spectra based on therelatively clean second isothermal step rise relativelysmoothly (Figure 6c, d), so the method of asymptotes andlimits (Forster & Lister 2004) can be applied to providethe age estimates shown. All age data obtained duringcleaning steps were therefore systematically eliminated.

Methods and data are further outlined in the supple-mentary material (Appendices 1, 2). Note that (followingexisting conventions) all steps on the age spectra are

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shown with an error band that is one standard deviationon either side of the mean age obtained. When an aver-age of the age of a group of steps is taken, the agereported is the mean § two standard deviations of thescatter of the mean age for each step included. No vol-ume weighting of the results is undertaken. This allowsan approximation of the 95% confidence limit, in orderto compare with the SHRIMP ages.

The youngest ages recorded in the initial steps are inthe range ca 11.5�11.2 Ma. Once data from the cleaningsteps are discarded, the age spectra can be seen to risesmoothly (and asymptotically) towards limits defined bysub-plateaux at ca 13.0 and ca 12.7 Ma (Figure 6c, d).These sub-plateaux are attained before »20% gas releasehas taken place, and they imply a distinct stage in thecooling history of the Capoas Granite.

The age spectra, from the phenocrysts, and from thegroundmass, then rise from these sub-plateaux to anaverage of ca 13.5 § 0.2 Ma (95% confidence limit, or CL)for the phenocrysts, and ca 13.6 § 0.4 Ma (95% CL) for

the groundmass. There is more scatter in the data fromthe groundmass, whereas the data from the phenocrystscan be taken to asymptotically rise to a poorly definedplateau at ca 13.5 § 0.2 Ma (95% CL) and thus provides(following the logic outlined by Forster & Lister 2004) aminimum estimate for the age of the Capoas Granite.

Within uncertainty this estimate is the same as pro-vided using U�Pb zircon geochronology.

(U�Th)/He analysis

Low-temperature thermochronology data on samplePAL33 were obtained using fission track and (U�Th)/Hemethods (e.g. Farley 2002; Gleadow et al. 2002). Apatitefission track analysis was unsuccessful, as most crystalscontained abundant crystallographic dislocations thatcould not be confidently distinguished from genuine fis-sion tracks (see also Cottam et al. 2013).

Apatite and zircon (U�Th)/He analyses were thencarried out using the methodologies detailed by Gleadow

Figure 1 Map showing the geology of Palawan, and the location of samples utilised in this study. The Capoas Granite is markedin red on the northwestern coast of the island (modified from Suggate et al. 2014).

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et al. (2015). Six single grain zircon (U�Th)/He analyses(Table 1) yielded a weighted average age of 10.3 § 1.1 Ma(95% CL), and five single grain apatite (U�Th�Sm)/Heanalyses yielded a weighted average age of 8.5 § 1.5 Ma(Table 2). Note this latter age does not include apatiteanalysis no. 8772, which is considered to be an excess Heage that is close to the crystallisation age of the graniteand older than coexisting zircon (U�Th)/He ages, whichrecord a higher closure temperature than apatite (seebelow). Such excess He ages and (U�Th)/He age disper-sion between grains from the same sample are com-monly observed in (U�Th)/He thermochronometry andhave been attributed to a number of possible factorssuch as heterogeneous distribution of U and Th, radia-tion damage, or grain breakage (e.g. Fitzgerald et al.2006; Shuster et al. 2006).

The zircon (U�Th)/He age is interpreted as recordingcooling of the granite through a closure temperature of»170�190�C that is estimated on the basis of the rela-tively young crystallisation age of the granite and its rel-atively low radiation damage (accumulated alpha-doseof »2�6 £ 1016 a/g; Guenthner et al. 2013). The apatite(U�Th�Sm)/He age is considered to record coolingthrough a closure temperature of »70�C (Ehlers & Farley2003).

ANALYSIS OF ARRHENIUS DATA

Forster & Lister (2010) investigated Arrhenius plots pro-duced using 39Ar release data from simulations of step-heating experiments applied to theoretical materialscomprising a multitude of crystalline diffusion domains.These simulations were limited to domains that all hadthe same activation energy, and the same frequency fac-tor, although the domain size varied. In some cases inves-tigated the multi-diffusion domain (MDD) model had avolume-size variation that was fractal, with differenttypes of fractal also investigated. The aim of this investi-gation was to establish procedures that should be fol-lowed when attempting to infer diffusion parametersfrom an Arrhenius plot, taking advantage of the fact thatthe parameters used to construct the MDD simulationwere determined beforehand. Because the input parame-ters were controlled the answer was predetermined, andwe were able to confirmmathematical ‘rules’ establishedby Forster & Lister (2010) that allowed objective analysisof the data and the determination of quantitative (mini-mum) constraints for the values for two of the diffusionparameters (namely, the activation energy and the fre-quency factor).

This led to the formulation of the FAP, which statessimply that any line drawn to estimate diffusion parame-ters on an Arrhenius plot must divide the population ofpoints by rank order. A corollary of the FAP is that anyvalid estimate for the value of the diffusion parameter inquestion is less than or equal to the actual value. Thismeans that, when comparing different estimatesobtained graphically from the Arrhenius plot, the high-est value should always be taken.

These two simple rules allow for expedient analysis,and objective determination of minimum constraints forthe diffusion parameters. In practice, by using the pro-gram eArgon, the analysis can be quite rapid: (i) usingthe graphic interface to eliminate any estimate that doesnot divide the population by rank order; and (ii) sinceany estimate mathematically can be shown to be a mini-mum estimate, adopting the highest estimates for activa-tion energy and normalised frequency factor.

In review of this paper, it became evident that moreexplanation was necessary, in particular the nature ofdecisions that need to be made when dividing the popu-lation by rank order. In the simplest terms, dividing byrank order means a line on the Arrhenius plot wherepoints measured before are on or to the right of the line,and those measured after are on the line or to its left.For isothermal sequences, before the line, the sequencesare entirely to the right, and after, entirely to the left.

Figure 2 Capoas Granite: (a) hand-specimen scale showingphenocrysts of K-feldspar within a K-feldspar-rich ground-mass; (b) outcrop-scale showing flow alignment of phenoc-rysts; and (c) exposed rim of the Capoas Granite onshoreline in north Palawan. The location is 10.774655�N and119.301248�E on a small headland at the end of a beach (acces-sible by foot only).

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Practical issues in application of the FAP

Conventional MDD analysis considers each diffusiondomain to have the same activation energy, with eachdomain differing only in size and thus varying only inits normalised frequency factor, D0/r

2. In such cases,Forster & Lister (2010) showed that it is a mathematicalrequirement that analysis of an Arrhenius plot shouldproceed according to the FAP and that the traditional

‘slope-averaging’ method produces false results,although this is a well-established practice for the analy-sis of Arrhenius data. In many cases slope ‘averaging’will considerably underestimate the activation energyinferred using Arrhenius data derived from furnacestep-heating experiments. Forster & Lister (2010) alsoshowed that a fractal distribution of diffusion domainsize and volume blurred the contribution of individualdomains in the Arrhenius plot so that an end-member

Figure 3 Optical microstructures from a thin-section of an aliquot of the K-feldspar mineral separate used in this analysis:(a�f) from the groundmass; (g�l) from the phenocrysts.

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fractal distribution with domains having an activationenergy of 75 kcal/mol yields an Arrhenius plot with an‘average’ slope estimated as 46 kcal/mol, which is theaverage value reported by Lovera et al. (1997).

Although to apply the FAP certain ‘rules’ need to befollowed, practical requirements mean that some lati-tude needs be given because estimates that are sensustricto compliant with the FAP can be based on twopoints alone resulting in estimates made using the FAPlimited by measurement uncertainty. A pragmatic

solution is to define an estimate by a ‘least-squares bestfit’ for a FAP-compliant line on the Arrhenius plotthrough three or more FAP-compliant points, to adoptonly those estimates that do not include significant out-liers. What constitutes a significant outlier is left to thejudgment of the individual, noting that including toomany points will lead to traditional ‘slope-averaging’and significant underestimates of the diffusionparameters.

The question then arises as to how to proceed whenestimates suggest the existence of domains with widelydifferent diffusion parameters. Is it possible to apply theFAP in aMDDmodel with ‘core’ domains that are consid-erably more retentive than inferred ‘rim’ domains, suchas is the case in the samples from the Capoas Granite onPalawan? To answer this question further analysis wasundertaken, using the step-heating schedule adopted forthe Palawan samples, extending the type of simulationsreported in Forster & Lister (2010) by modelling theeffect of MDD materials with widely differing diffusionparameters (Figure 7). This work demonstrates that it ispossible to apply the FAP when distinct regions in theArrhenius plot can be recognised. The same ‘rules’ areapplicable, but note that these apply for step-heatingexperiments that utilise monotonically increasingsequences of heating steps. However, this exclusion stillallows the FAP to be applied to the analysis of Arrheniusdata obtained from an experiment using sequences oftwo or more isothermal heating steps.

The FAP states that an estimate for the diffusionparameters can be obtained by extrapolation of a linedefined by joining points on an Arrhenius plot, if andonly if, that line defines the population of Arrheniuspoints by rank order. In other words, the line must besuch that measurements made earlier in the step-heat-ing sequence plot on or to its right, whereas measure-ments made later in the step-heating sequence must ploton the line, or to its left. This statement of the FAPapplies at any point in the collection of Arrhenius pointsused to define the dividing line. Such estimates for thediffusion parameters yield minimum values, that is theestimates made are less than or equal to the actual val-ues of the activation energy and/or the (normalised)

Figure 4 SEM images of the K-feldspars from PAL33, showingthe regions of high potassium (high-K) compared with theregions of high sodium (high-Na). High-Na regions are latein most grains and can be associated with twinning inothers. Analysis was done with both quantitative spot analy-sis and area mapping (see Appendix 3 for details).

Figure 5 Cumulative Gaussian and histogram plot of all206Pb/238U ages measured on zircons from the CapoasGranite.

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Figure 6 Apparent 40Ar/39Ar age spectra for the K-feldspar phenocrysts (a) and the groundmass (b). In (c, d) the same spectraare shown, but excluding data from the first of the two isothermal steps that appear to act as cleaning steps. The method ofasymptotes and limits (Forster & Lister 2004) is then applied to provide the age estimates shown (with the steps used in obtain-ing the estimates coloured dark green). In (e, f), the FAP is used to define diffusion parameters for the highly retentive coredomains (red points) as well as for the least retentive domains (turquoise points). The normalised frequency factor shown iscalculated assuming 100% of the volume is occupied by the domain in question, and a correction must be applied when usingthese data for forward modelling.

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frequency factor (i.e. Do/a2) used in the simulation,

where ‘a’ is the diffusion domain radius, and ‘Do’ is thefrequency factor (or maximum diffusivity that couldever be measured).

The first step in the application of FAP (Figure 7a)involves two points on the Arrhenius plot chosen to obeythe rule that they locally divide the measurementsequence by rank order. What can then be seen is asequence of lines that asymptotically increase (ordecrease) in slope as we progress across the plot. Each ofthe lines drawn locally divides the population by rankorder, either by joining a step (e.g. 25) at the end of oneisothermal sequence (e.g. 23�25) to the step (e.g. 26) atthe start of the very next isothermal sequence (e.g.26�28), or by joining steps (e.g. 9 and 11) at the start of asuccession of isothermal sequences (e.g. 9�10 and11�12), or by joining steps at the end of a succession ofisothermal sequences (e.g. 10 and 12). As it turns out, thefirst three steps (1�3) accurately define the activationenergy for the 20% volume of the least retentivedomains, and the last three steps (29�31) accuratelydefine the activation energy for the 80% volume of thehighly retentive ‘core’ domains. However, these divisorsby rank order are so far of local import only. To deter-mine whether they comply with the FAP they must beextrapolated (Figure 7b) and because the two domainsutilised in the simulations have such widely differingdiffusion parameters, this allows the application of the

FAP within specified regions, as shown. The Arrheniusplot can then be divided into a region affected domi-nantly by retentive core domains, and a region domi-nantly affected by the unretentive rim domains(Figure 7b).

Considering estimates for the unretentive rimdomains (Figure 7b), it is evident that linking points16�17 and 14�15 causes clear FAP violations, so thesecan be eliminated leaving other divisors to producenumerically more acceptable estimates (Figure 7c). Thisleads to a least-squares best fit using points 1, 2, 3, 5, 7, 9and 11 to estimate the diffusion parameters for the leastretentive domains. Again the values obtained (e.g.45.5 kcal/mol for the activation energy) underestimatethe values utilised in the actual simulations, in this case,an activation energy of 46 kcal/mol for the least reten-tive domains. Figure 7c also shows that the join 20�21produces a noticeable FAP violation, whereas the join22�23 (Figure 7d) and the join 25�26 (Figure 7e) producenumerically ‘acceptable’ divisions by rank order. Sincethese estimates are minimum estimates, the more reten-tive values of the two estimates should be the one used.This leads to a least-squares best fit using points 25, 26,29, 30 and 31 for the highly retentive core domains, not-ing that the data obtained (e.g. 149 kcal/mol for the acti-vation energy; Figure 7f) still underestimates the actualvalues utilised in the simulations (150 kcal/mol for theactivation energy of the highly retentive core domains).

Table 1 Single grain zircon (U�Th)/He data.

SampleLab.no. He no.

4He(ncc)

Mass(mg)

MeanFT

aU

ppmThppm

Th/U [eU]b

ppmAge(Ma)

Error(§1s)

Grainradius (mm)

Grain length(mm)

Pal-33 8962 27043 7.075 0.0103 0.79 585.6 68.9 0.12 601.8 9.4 0.6 44.6 343.4

Pal-33 8963 27041 5.772 0.0075 0.80 536.0 103.7 0.19 560.3 11.3 0.7 52.8 221.0

Pal-33 8964 27051 4.127 0.0137 0.83 221.4 48.7 0.22 232.8 10.6 0.7 58.6 300.8

Pal-33 8965 27181 11.828 0.0134 0.84 563.7 172.0 0.31 604.1 12.0 0.7 70.6 247.4

Pal-33 9223 27703 3.989 0.0051 0.78 676.0 114.0 0.17 702.8 9.1 0.6 51.0 193.6

Pal-33 9255 27965 7.690 0.0045 0.78 1310.0 154.6 0.12 1346.3 10.4 0.6 43.6 261.5

Weighted average age D 10.3 § 1.1 Ma (at the 95% confidence level)

a FT is the a-ejection correction after Farley et al. (1996).b Effective uranium content D (U ppm C 0.235�Th ppm).

Table 2 Single grain apatite (U�Th�Sm)/He data.

SampleLab.No. He#

4He(ncc)

Mass(mg)

MeanFT

aU

ppmThppm

Smppm Th/U

[eU]b

ppmAge(Ma)

Error(§1s)

Grainradius(mm)

Grainlength(mm)

Pal-33 8754 26362 0.106 0.0078 0.78 13.8 9.9 240.0 0.72 16.1 8.8 0.4 58.6 224.9

Pal-33 8756 26354 0.123 0.0072 0.77 19.3 12.3 226.3 0.64 22.2 8.2 0.4 56.2 225.4

Pal-33 8772 26413 0.355 0.0147 0.83 16.3 8.9 213.3 0.55 18.4 12.8c 0.2 44.0 189.0

Pal-33 9221 27692 0.098 0.0046 0.75 19.8 9.6 241.4 0.48 22.1 9.9 0.6 54.1 157.1

Pal-33 9257 27909 0.047 0.0025 0.64 28.3 16.8 392.0 0.60 32.2 7.3 0.5 33.7 203.2

Weighted average age D 8.5 § 1.5 Ma (at the 95% confidence level)

a FT is the a-ejection correction after Farley et al. (1996).b Effective uranium content D (U ppm C 0.235�Th ppm).cAnalysis not included in weighted average age calculation.

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Application of the FAP is not constrained to usingthe few data points at the beginning of a step-heatingsequence. The FAP allows Arrhenius data to bedivided by rank order at any point in the datasequence, and estimates of activation energy may bemade with FAP-compliant estimates that rely on threeor more data points.

Diffusion parameters based on fractionalloss of 39Ar

Diffusion parameters can be inferred from the percent-age volume of 39Ar released during step-heating experi-ments, using methods pioneered by Lovera et al. (1989,1993, 1997, 2002). Note that although the age data from

Figure 7 Illustration of the application of the FAP with Program eArgon used to simulate an Arrhenius plot, using a modelcrystal with known diffusion parameters and volume ratios as shown (a). Two regions are delineated on the Arrhenius plot.Many local divisors by rank order (a) fail when extrapolated (b�c). Other extrapolations are numerically acceptable withinthe defined regions (c�e). When application of the FAP leads to two divisors by rank order (d, e), the maximum slope shouldbe chosen.

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the first isothermal cleaning step are discarded, diffu-sion data obtained using 39Ar are internally consistentthroughout the entire step-heating sequence and therelease of 39Ar from all heating steps is included. Itsrelease depends only on the kinetics of the diffusion thatallow its migration.

Neutron irradiation is required to produce 39Ar sothis isotope is sourced only in consequence of its diffu-sion and escape from the lattice. In contrast, released40Ar can include extraneous argon, for example, derivedfrom fluid inclusions, or 40Ar caught in relative fast dif-fusion pathways as it attempted to diffuse back into thecrystal lattice from the ambient pore fluid. Conse-quently, the release of 40Ar can include both argon fromthe lattice as well as from these extraneous sources, andage data based on the 40Ar/39Ar ratio can show both con-cordant as well as discordant trends.

Note that plots of the Arrhenius data have been pre-pared assuming a spherical geometry (Figure 6c, f) to

allow comparisons between different datasets. Parame-ters inferred using spherical geometry should not beexchanged with parameters inferred using other geome-tries (see Forster et al. 2014).

The measured Arrhenius data allow classification ofthree distinct domains (Figure 8). The initial stepsinvolve relatively low activation energies, estimated as»54�55 kcal/mol. Thereafter there is a zone of transitionthat may involve a range of diffusion radii. Finally, inthe highest temperature steps, slopes estimated bylocally applying the FAP, activation energies are in therange 92�110 kcal/mol, about twice as large as those thatapply in the initial steps. Figure 6 (e, f) shows estimatednormalised frequency factors for these domains, withclosure temperatures calculated for zero pressure and a20�C/Ma cooling rate. The least retentive domains closeat 304�309�C according to this simple calculation, whilethe retentive core domains close at 547�588�C. However,there is a problem with estimating closure temperatures

Figure 8 Classification of the steps in the age spectra (a, c) based on domains discerned in the Arrhenius plots (b, d) for thephenocrysts and the groundmass, showing the mean age of the dark green steps based on the dark green coloured circles onthe Arrhenius plots. These represent the release of gas from the most retentive domains.

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in this way since the calculation assumes that 100% ofthe volume is occupied by the domain in question. Forthe least retentive domains, to correct for the volumetriceffect, the normalised frequency factor must beincreased, and less retentive values assumed (Table 3)reducing the closure temperature for the least retentivedomains to 273�278�C.

Figure 8 provides a useful classification. The leastretentive domains can be seen to be responsible forthe steps with the greatest oscillation in age data.The sub-plateaux ages at ca 13.0�12.7 Ma are recordedby the median retentivity domains. The age data fromthe highly retentive core domains is more scatteredin the groundmass K-feldspar but the average age forboth phenocrysts and groundmass is the same. Theseretentive core domains account for >70�75% of thevolume of gas released and the points (correspondingthe age steps coloured dark green in Figure 8) definethe alignments on the Arrhenius plot from which esti-mates for extraordinarily high activation energy canbe obtained.

Simulation and modelling

The final step in this process was to undertake a model-ling and simulation study. The Arrhenius data were firstused to produce r/r0 plots (Lovera et al. 1989) that allow aready correspondence between parts of the Arrheniusplot and parts of the apparent age spectrum (Figure 9).This correspondence suggests that the bulk of the gasmeasured was derived from the highly retentive coredomains. Using these steps, the timing of the onset ofrapid cooling after granite emplacement can beestimated.

With the volumetric ratios established we used equa-tions for fractional loss based on specific geometries toforward model the pattern of 39Ar gas release, applyingthe same step-heating schedule used during the in vacuoexperiments that produced the measured age spectra(Figure 9). These methods (including code, and equationsused in the modified version of the eArgon program uti-lised) are summarised by Forster et al. (2014).

The eArgon program was used to forward model theArrhenius plot and the r/r0 plot that would result basedon model crystals comprising collections of diffusiondomains with a specified activation energy and a nor-malised frequency factor (Figure 9). Fractal size-volumerelations were imposed for the two domains with an

activation energy of 55 kcal/mol. In terms of numericalanalysis, this assumption implies these less retentivedomains are not perfectly spherical, but quite rough intheir geometry, with fractal outlines. In terms of thehighly retentive core domains, surprisingly, the fit wasmarkedly improved by considering at least two domains,with approximately the same retentivity and similar vol-umetric ratios. The data used in the final model illus-trated in Figure 10 are shown in Table 4; the fit is greatlyimproved by the addition of this complexity.

Manually iterating volumetric ratios is tedious so theeArgon program was improved by incorporating itera-tive forward modelling based on Monte Carlo simula-tions. Interestingly, there were two valid applications ofthe FAP (Figure 9a, c), both of which divide the popula-tion of Arrhenius points by rank order, one yielding anactivation energy of 92 kcal/mol and the other yieldingan activation energy of 134 kcal/mol. Both choices ofactivation energy allowed accurate approximation of theArrhenius data, but it was not possible to replicate ther/r0 plot with the less retentive value for the activationenergy of 92 kcal/mol (Figure 9b). The higher value ofthe activation energy (134 kcal/mol) did allow an accu-rate replication of the r/r0 plot, however (Figure 9d).This value was therefore assumed in constructing themodel crystal used in the MacArgon program to itera-tively forward model the effects of arbitrary pressur-e�temperature (P�T) histories.

The MacArgon program (modified from codedescribed by Lister & Baldwin 1996) was further devel-oped to allow interactive modelling of the effect ofparametric variation of an arbitrary P�T history. Thevariation of T�t curves is shown in Figure 10. An initialambient pressure of 3 kbar was assumed, consistentwith estimates of the depth of emplacement of the Pala-wan granitoids (cf. Zulauf et al. 1997). The calculation isnot particularly sensitive to the assumed ambient pres-sure, but note that the activation volume used was 15cm3, and this accentuates the increase in retentivitywith increasing pressure (cf. Forster & Lister 2013). Theinteractive use of MacArgon is particularly efficient interms of effort, for the effect on the age spectrum of anychange in the T�t history is interactively provided. Onecan first model the effect of the earlier part of the tem-perature history, obtain the best fit (Figure 10a, b) andthen move to lower temperature segments of the historyto repeat the exercise (Figure 10c, d). In this way an esti-mate for the complete cooling history is obtained

Table 3 Diffusion parameters for a collection of three domains, obtained by selecting representative domains from the classified data(Figure 8).

Simulation data Spherical domains

E 55 55 92 kcal/mol

D0/a2 1.0EC07 2.1EC04 3.1EC09 cm2/s

Volume occupied by base domain 17% 12% 71%

Closure temperature for 10�C/Ma at 2 kbar 273�C

Closure temperature for 80�C/Ma at 2 kbar 374�C

Closure temperature for 200�C/Ma at 2 kbar 586�C

Closure temperature for 400�C/Ma at 2 kbar 597�C Activation volume 18 cm3

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(Figure 10e) and the fit compared with the measured agespectrum (Figure 10f).

T�t points have been added that show the estimatedclosure temperature for helium diffusion in conjunctionwith the ages obtained using (U�Th)/He thermochron-ometry for zircon and apatite. A two-stage cooling curveis therefore confirmed (Figure 10e). Note that this two-stage cooling curve is not dependent on the assumptionof highly retentive core domains but is required by thevariation in the K-feldspar data itself. To demonstratethat this is correct we carried out a traditional analysisof the Arrhenius plot based on ‘averaging’ the slope ofthe least retentive part of the dataset (Figure 11a), andthen extrapolated the activation energy obtained to allother domains. This analysis yielded a simple modelcrystal based on two diffusion domains, but (see smalldots in Figure 11a) is incapable of accurately modellingdiffusional release at the high-temperature end of theArrhenius sequence. This model for inverse modellingyielded reasonable fits at the start and end of the age

spectrum (Figure 11b) but it did not allow a fit to its over-all form, particularly in respect to intermediate seg-ments of the age spectrum. The T�t variation implied bythis traditional analysis (Figure 11c) again requires atwo-stage cooling history, with the detail of the secondstage constrained by the (U�Th)/He thermochronologi-cal data.

The two-stage cooling history is required by the inter-dependence of retentivity estimates for the different dif-fusion domains in K-feldspar. This can be furtherdemonstrated using a simple model based on estimatesfor three diffusion domains (Figure 12). This methodrequires closure temperatures to be iteratively esti-mated based on the assumed form of the cooling curve,and since these depend on cooling rate, several itera-tions may be required. Again, once points are added thatshow the estimated closure temperature for helium dif-fusion in conjunction with the ages obtained using(U�Th)/He thermochronometry for zircon and apatite, atwo-stage cooling curve is required.

Figure 9 Full inversion of the Arrhenius data (a, c). The open circles show the Arrhenius data inferred from measurement,and the smaller (dark blue) dots plot the result of forward modelling the heating schedule imposed during the experiment.Two choices can be made for a divisor by rank order, both compliant with the FAP. Points used are shown in dark green.Although a reasonable match is obtained in terms of the Arrhenius plot (a), the r/r0 plot (b) is not well matched using the(lower) »92 kcal/mol estimate of the activation energy. Assuming an activation energy of 134 kcal/mol for the most retentivedomains (c) allows a considerably better match of the r/r0 plot (d). Note that the calculated closure temperature will increaseby »30�35�C, for each tenfold increase in the cooling rate, for the activation energies used here.

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Figure 10 Forward modelling and simulation using diffusion parameters inferred using the eArgon program, as listed in Table 4.The MacArgon program was used to forward model the effect of cooling curves (a) considering the range shown. The optimal fitto the higher temperature part of the age spectrum (b) is the thicker path. The cooling curve (c) was then adjusted until an opti-mal fit was obtained for the lower temperature part of the age spectrum (d). The optimal fit to the temperature�time path(e) produces a reasonable match to the age spectrum (f) from the groundmass K-feldspar.

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Although this method approximates the cooling curveby considering ‘representative’ domains, it requires theform of the cooling curve to be known. Newtonian cool-ing of the granite body was assumed, i.e. an exponentialdecrease with time in respect to the difference betweenthe temperature in the body in comparison with thatdetermined by an ambient geotherm.

DISCUSSION

The cooling curve presented here is based on twoassumptions, namely that: (i) microstructure remainsconstant during the evolution of the sample in the

natural environment; and (ii) diffusion is the only mech-anism releasing argon into the mass spectrometer.

Each of these two assumptions has significant draw-backs, and caveats related to the limitations posed bythese assumptions need to be considered when attempt-ing to draw geological inferences based on the results, asdiscussed below.

Effect of microstructural change

It is unlikely that any microstructure remains constantthroughout the history of a rock, and this is true even ingranite that has cooled rapidly without deformation (e.g.Villa 2006; Parsons & Lee 2009; Putnis 2009; Putnis &

Table 4 Diffusion parameters for a full collection of domains, obtained by inverting the Arrhenius data and the r/r0 plots (Figure 10).

Simulation data

E 55 55 134 134 kcal/mol

D0/a2 5.5EC06 2.1EC04 4.6EC15 9.0EC14 cm2/s

Volume occupied by base domain 9.7% 7% 41.3% 32.5%

Closure temperature for 20�C/Ma at 0 kbar 278�C 344�C 680�C 702�C

Fractal Yes Yes No No

n iterations 10 5

/ radius iterator 2 2 Per iteration� volume iterator 0.2 0.5 Per iteration

Total volume occupied by fractal 12.2% 14.0% Spherical domains

Figure 11 Forward modelling and simulation using diffusion parameters inferred using traditional ‘slope-averaging’methods,extrapolating the low activation energy that can be inferred using the first few points on the Arrhenius plot to all otherdomains (a). The MacArgon program was used to forward model the effect of cooling curves (b) until a fit was obtained. Eventhough the fit was poor, the inferred cooling curve (c) still required two stages. Note that, for the activation energy used here,increasing the cooling rate by a factor of 10 will lead to elevation of the calculated closure temperature by merely »40�C. How-ever, this model cannot explain the coincidence of the U-Pb and the 40Ar/39Ar ages.

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John 2010). This has led to controversy, noting contrast-ing views expressed in Villa (2013) and Harrison & Lov-era (2013). Nevertheless, we must conclude that MDDmodelling limits itself by the assumption that micro-structure remains constant, at least in MDD models asthey are currently applied.

Does microstructure matter? It is not at all certainthat microstructural change prevents systematic analy-sis of an age spectrum, since in the final microstructureit is typically the less retentive parts that have been cre-ated and/or modified on the cooling path by processessuch as (fluid-assisted) recrystallisation and grainboundary migration. Therefore, the modification of amicrostructure need make relatively little difference interms of the P�T�t history that can be inferred.

Consider the effect of argon release as the result ofgrain boundary migration in the natural environment.This will lead to an abrupt age transition in the age spec-trum that cannot be effectively simulated. Yet the relictmicrostructure continued to be subject to the sameP�T�t history, and thus coexisted with the newly cre-ated/modified microstructure. For this reason, in con-straining the range of possible P�T�t histories, themost important part of the age spectrum to match is theearly part of the release from the least- and median-retentive domains. Ensuring coincidence with the ear-lier released parts of younger age sub-spectra ensuresthat the model reflects the effect of diffusional releasefrom these modified or newly created aspects of themicrostructure.

Thus, we arrive at an important qualification of thestatement above. While MDD models need not exactlyreplicate the abrupt transition to the oldest part of the

age spectra, they must not neglect the match with theearlier part of the age spectrum, i.e. it is important tomatch that part that results from release of argon fromless retentive domains. We thus disagree with thereviewer who asserted that an ‘intermediate solutionbetween A and B (in Figure 10a) … produces a model agespectra that is apparently as good as any in (Figure 10c).’This is not correct. None of the single-stage cooling pathsoffers a good match to the early part of the age spectrum.

Significantly, the lower T parts of the age spectrumcould be matched only once the option of a two-stagecooling history had been introduced (Figure 10d, e). Inother words, the K-feldspar data alone require a two-stage cooling history.

The 40Ar/39Ar age spectra provide no information onthe precise form of the cooling curve past ca 12 Ma. Tofurther constrain the two-stage cooling path (U�Th)/Hedata are then necessary. Consistent with the above obser-vations, these data require the onset of renewed coolingat ca 11 Ma, and an acceleration of cooling rates as wouldbe expected in the footwall of large normal faults thatare inferred to exist along the coast of Palawan (Frankeet al. 2011; Walia et al. 2012; Hall 2013). Cooling of theCapoas Granite appears to have considerably slowed byca 12 Ma, suggesting that the rim of the granite plug hadreached temperatures expected in consequence of theambient geotherm by that time. An ambient geothermin the range 25�30�C/km implies a depth of emplace-ment at 7�9 km.

We note that this two-stage history makes sense in thecontext of independent geological data. Renewed tecto-nism readily explains the Late Miocene unconformity inthe adjacent basin, and the influx of sediment that depos-ited on the unconformity from ca 10 Ma (personal com-munication, Prof. Robert Hall). Steuer et al. (2013) notethe oldest sediments that lie on this unconformity depos-ited at 9.2 Ma. The initial asymptotic decrease in temper-ature towards »220�C allows an inference of ambientconditions, implying (as above) a depth of emplacementof 7�9 km, and ample latitude in terms of the require-ment for large volumes of material to have subsequentlybeen made available for erosional denudation.

Break-down reactions in the mass spectrometer

A reviewer was concerned that the minerals were break-ing down (or melting). Indeed, it is true that the Arrhe-nius data reported in this paper have been calculated byapplying fractional loss equations on the basis of the per-centage release of 39Ar from temperature controlled step-heating experiments in vacuo by diffusion alone.

These data have been taken as constraining the diffu-sion of 39Ar from the crystal lattice but only if thisassumption were correct can we infer the existence ofhighly retentive core domains in K-feldspar. Perhaps weshould also consider the option that some other processis mimicking (or complicating the kinetics of) diffu-sional release, e.g., the advance of sub-microscopic melt-ing fronts in the K-feldspar at high temperatures duringthe step-heating experiment, or the effects of non-Fick-ian diffusion. The advance of sub-microscopic meltingfronts does not prevent diffusive loss, although it may

Figure 12 Cooling curve based on three domains selected onthe basis of the classification of the Arrhenius plot intothree regions (Figure 8). Diffusion data used are shown inTable 3. The cooling curve is based on monotonicallydecreasing temperature. Closure temperature was itera-tively computed based on the values estimated from thiscurve. This method allows a semi-quantitative constraintwithout full inversion of the Arrhenius data (as perFigure 11). Combined with the (U�Th)/He data the coolingcurve requires two stages.

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modify the release path. It is likely that argon would belost by diffusion before melting occurred.

Non-Fickian diffusion says nothing more than thatsimple equations do not apply, to which claim we canoffer no comment except that Fickian diffusion does notneed to be limited to a single species model (cf. Villa2013). All that numerical models need is reasonablenumerical accuracy, and from this viewpoint it is inter-esting that we seem to be able to reasonably approximatethese experiments using only simple diffusion equa-tions. Since we can predict the percentage of argonreleased during a heating step of known duration, thenperhaps it is reasonable to assume that diffusion alsooccurs in nature.

We note that argon diffusion inferred in natureappears to coincide with the onset of dislocation climb,as implied by microstructures that suggest dynamicrecovery (Forster & Lister 2013). However, exceptionallyhigh values for the frequency factor can be inferred forthe retentive core domains and Forster & Lister (2013)demonstrate compression of the temperature intervalduring which such materials degas. Argon release fromthe retentive core domains is thus likely to precede thefinal disintegration of the lattice that occurs duringmelting. We emphasise that the advance of sub-micro-scopic melting fronts during heating in an ultra-high-vacuum will thus not prevent diffusional release ofargon from within the (almost ready to disintegrate)lattice.

Comparing data from K-feldspar with zircon

In the natural environment the same argument as aboveholds, in reverse. The highly retentive diffusion parame-ters mean that K-feldspar should be expected to retainsome argon even in a magmatic environment, after K-feldspar mineral grains crystallise. In this case not onlywill K-feldspar core domain ages record the earlieststages of the cooling history, but occasionally (dependingon the relative roles of cooling vs depressurisation intriggering zircon growth) K-feldspar ages may predateages obtained using U�Pb measurements. There arethus limitations on the conclusions that can be drawnbased on coincidence with ages obtained using U�Pbzircon geochronology, as well as limitations on theconclusions that can be drawn based on any lack ofcoincidence.

It can be difficult to interpret zircon data as requiringa single magma emplacement age, e.g. Schoene et al.(2012) showed that crystallisation in a ballooning pluton(in Adamello, Italy) endured for ca 0.3 Ma. There is a nat-ural spread of U�Pb zircon ages that reflects the timetaken to inflate and construct a magmatic edifice.

Another difficulty is caused when fluid-catalysedrecrystallisation leads to grain boundary migrationwithin the newly formed K-feldspar crystal, leading to insitu replacement and regrowth. This means that, inde-pendent of any coeval diffusion process, regrowth of K-feldspar core domains can reset ages to be younger thanthe time at which the original K-feldspar crystals grew.S�anchez-Mu~noz et al. (2012) described microstructures ingranitic pegmatite that formed during cooling. Suchmicrostructural evolution may destroy or modify

retentive core domains. The median-retentive domainsmight thus record the time of such resetting, and thusbecome useful indicators of progress.

Other difficulties arise when excess argon is present(i.e. 40Ar incorporated into the lattice from the pore fluidin the natural environment, and released into the massspectrometer during the highest temperature part of thestep-heating experiment) (Foster et al. 1990). Such effectsare routinely evident when calcic plagioclase is mea-sured; potassium concentrations in such minerals arelow and the accuracy of an age determination can beoverwhelmed. Calcium produces both 39Ar and 36Ar inthe reactor during fast neutron irradiation. Caution isneeded in respect to ages with high Ca/K ratios, sincethese may reflect the influence of gas released fromminor plagioclase at the end of the step-heatingexperiment.

A need for further comparative analysis

The inferred cooling rate for the 7 km-diameter stockthat defines the Capoas Granite was initially very muchfaster than expected. The outcrop of the Capoas Graniteis similar to the granite body exposed in Mt Kinabalu,»600 km to the southwest. There is a rapid increase insurface elevation, rising from sea-level to >»960 mwithin less than »4 km distance. The cooling rate duringexhumation and cooling of the Kinabalu Granite is esti-mated at 120�C/Ma (Cottam et al. 2013). More rapid rateswere estimated for initial cooling of the Shivling leucog-ranite in the High Himalaya immediately beneath theSouth Tibetan Detachment (175�350�C/Ma; Searle et al.1999). This 1�2 km-thick laccolith had cooled below400�C in about one million years from the time of its ini-tial crystallisation. In comparison, for a 9 km-thick sill-like body, the Falkenberg Granite (Oberpfalz, Germany)required ca 6 Ma before it cooled below 400�C (Zulauf etal. 1997).

Cooling rates can be very rapid for samples near therim of a pluton. Nabelek et al. (2012) showed that thesolidification time can be prolonged because ‘wall rocksbecome more insulating as temperature rises’ but theseauthors also showed that temperatures near the rim ofthe batholith drop below 400�C within 0.1�0.2 Ma of thetime when the pluton crystallised. Modelling the coolingof a high-level granite body (5 km-diameter, 2 km thick,with its top level 3 km from the surface) produced cool-ing rates initially as high as »1500�C/Ma, but largergranite bodies deeper in the crust would cool moreslowly. The Capoas Granite has a typical granitic tex-ture, and does not exhibit characteristics of a hypabyssalintrusion such as that above. Yet cooling rates inferredfrom the K-feldspar data are high, and perhaps arehigher than should have been expected. This raises ques-tions as to the effect of mechanical forcing of the stockupwards immediately after emplacement, since this pro-cess would explain the odd nature of the start of the cool-ing path implied by the simulation illustrated inFigure 10e. Nabelek et al. (2012) found that the thermalconductivity of rock decreased at temperatures aroundthe solidus, so at those temperatures the wall rock of theCapoas Granite will have hindered cooling. Graniteemplacement thus appears to be self-insulating.

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Continual episodes of intrusion as noted by Schoene etal. (2012) would also slow overall cooling for the first ca0.5 Ma there after cooling would accelerate towards ratesas inferred in this study if the stock were then ‘punched’upward through the adjacent cooler country rock.

The rapid cooling rates inferred for the Capoas Gran-ite suggest further experiments are needed, along a tra-verse from its core to its rim. Only if initial cooling rateswere slower will it be possible to readily discriminatewhen in the cooling curve K-feldspar core domains haveindividually closed, and to provide independent proof asto the inferred high retentivity of the core domains.The uncertainty in the age determinations based on theU�Pb zircon data mean that there is overlap withthe uncertainty in the age determinations based on thehigh-temperature 40Ar/39Ar data, and this preclude useof these data to independently choose between: (i) coinci-dence with the SHRIMP ages because the K-feldspar coredomains are highly retentive (see inverted Arrheniusmodel in Figure 9c, d and forward modelling inFigure 10); or (ii) coincidence with the SHRIMP agesbecause of the effect of very rapid cooling (see invertedArrhenius model in Figure 11a and the forward model-ling in Figure 11b, c).

Figure 11 was constructed using a ‘classic’ averagingapproach to the analysis of the Arrhenius data, extrapo-lating the relatively unretentive diffusion parametersinferred from the initial data points. The inferred clo-sure temperature for the retentive core domains thenbecomes a mere »370�C for a cooling rate of 700�C/Maallowing closure 0.2 Ma after the time of initial emplace-ment. Taking the initial cooling rate as 1400�C/Maimplies crystallisation at 13.9 Ma, which is outside thelimit of uncertainty of the estimated age of 13.5 § 0.2 Ma.While the uncertainty mentioned above, means that thisalternative scenario cannot be completely dismissed, wefurther note the relatively poor fit between the modelsimulation and the observed age spectrum. As demon-strated, even with a two-stage cooling history, it was notpossible to match the detail in the observed age spec-trum. The observed age spectrum cannot be moreexactly matched unless highly retentive core domainsare assumed (Figure 10).

K-feldspar can retain argon above the solidus

K-feldspar has been shown to be able to retain argonwhile immersed in a magma. Gillespie et al. (1983, 1984)noted this phenomenon, while Renne et al. (2012) usedbarium diffusion fronts to quantify the period of immer-sion. This paper in turn demonstrates the highly reten-tive diffusion parameters that make this phenomenonpossible.

The implication is that sanidine such as that in theFish Canyon Tuff (Renne et al. 2010; Phillips & Matchen2013) would be capable of recording ages relict from thetime of K-feldspar growth, as well timing the rapid cool-ing that occurs after eruption (Renne et al. 2012). A simi-lar comment can be made in respect to sanidine from theYounger Toba Tephra (Mark et al. 2013).

The diffusion parameters for K-feldspar recorded inthis paper mean that highly retentive core domains alsoimpact on the question of inheritance, e.g. the age of 20 §

1 Ma (Copeland et al. 1990) for the Manaslu Granite whileother work (Deniel et al. 1987; Guillot et al. 1994; Harrisonet al. 1999) suggest it intruded as sills in magmatic pulsesstarting at 25�22 Ma and continuing for 6�9 millionyears thereafter. K-feldspar grown during earlier mag-matic pulses may well be able to retain vestiges of itsoriginal age, a phenomenon which is well possible if coredomains are as retentive as some of the diffusion datareported here can be taken to imply. This is not excessargon sensu stricto, although it has been referred to assuch. It is argon relict from decay in the minerals grownat an earlier stage of the rock’s history.

Practical implications of this work for argongeochronology

This paper demonstrates that estimates of activationenergy can be made internally within an Arrheniusdata sequence, and that such an analysis can yield esti-mated values for the activation energy and frequencyfactor that are well beyond the range documented byprevious workers (e.g. Lovera et al. 1997, 2002). This isimportant for many previously published furnacestep-heating 40Ar/39Ar geochronology experimentsusing K-feldspar that also contain internal sequencesin Arrhenius data, which can similarly be taken toimply the existence of highly retentive ‘core’ domains,e.g. Knapp & Heizler (1990) in K-feldspar from theMaria Fold and Thrust Belt, Lovera et al. (1993) for theclassic MH10 K-feldspar, or Warnock & Zeitler (1998)for K-feldspar from the German KTB deep drill hole.Such internal analysis of an Arrhenius sequenceshould therefore become routine.

On the practical side, this paper demonstrates K-feld-spar can be sufficiently retentive so as to allow directdating of processes that reduce the dimensions of diffu-sion domains, e.g., cataclased and/or recrystallised K-feldspar in fault rock and/or mylonite. Forster & Lister(2009) were thereby able to date the formation of crushedfeldspar in 25 Ma north-sense shear zones that over-printed the south-sense 35�30 Ma South Cyclades ShearZone (Ios, Cyclades, Greece). Forster et al. (2014) dupli-cated this success, dating the timing of crushing of K-feldspar in greenschist facies ductile shear zonesexposed in the Wyangala Batholith, NSW, Australia.Analysis of the latter dataset showed that deformation ofK-feldspar in a shear zone is capable of pervasively modi-fying the diffusion parameters, and that it is this processthat makes it possible to directly date the timing ofmovement.

These are important developments in the methodol-ogy of 40Ar/39Ar geochronology, but we need to clarifythe nature of these highly retentive core domains. In par-ticular, we need to better understand how microstruc-tural processes modify the core domains duringdeformation and metamorphism. In our future researchit is now key that we determine the role of fluid ingressin triggering grain boundary migration, since we knowcases that involved in situ recrystallisation, and whenthis occurs, this process appears to be able to eliminateand regrow the core domains, leading to relativelyyouthful ages.

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CONCLUSIONS

The Capoas Granite on the northwest coast of the islandof Palawan in The Philippines, was dated with U�Pb zir-con using SHRIMP and by 40Ar/39Ar K-feldspar geochro-nology using temperature controlled step-heatingexperiments involving isothermal cleaning steps. The40Ar/39Ar age spectra show considerable scatter when allsteps are included, but if the data for the (contaminated)cleaning steps were omitted, the age spectrum simplifies,and allows application of the method of asymptotes andlimits as described by Forster & Lister (2004). The agesobtained are within uncertainty of those obtained usingU�Pb dating of the timing of zircon crystallisation.This is consistent with the interpretation of the Arrhe-nius data that K-feldspar from the Capoas Granite con-tains diffusion domains that close at temperatures»500�700�C for rapid cooling rates, allowing direct dat-ing of mineral growth and/or the timing of magmaemplacement.

Our analysis of the Arrhenius data confirms that K-feldspar can be considerably more retentive of argonthan previous estimates would allow, and in consequencethat there need be little difference between U�Pb agesmeasured from zircon, and 40Ar/39Ar ages measuredfrom highly retentive ‘core’ diffusion domains in K-feld-spar. In these circumstances, direct estimates of graniteemplacement ages are possible, especially if rapid cool-ing then follows. The remaining part of the cooling curvecan also be determined using data from other less reten-tive domains in the same mineral grains.

Forward modelling based on MDD inferred from sys-tematic and self-consistent analysis of Arrhenius dataderived from release of 39Ar from K-feldspar during step-heating require a two-stage curve for cooling of theCapoas Granite. After some time, very rapid coolingtook place, but with an asymptotic decrease in coolingrate implying the depth of emplacement was 7�9 km.The granite had thus cooled towards ambient tempera-tures by ca 12 Ma, and we can infer a period of tectonicquiescence thereafter. The (U�Th)/He data allow infer-ence that exhumation then once again commenced, lead-ing to an acceleration of the cooling rate. Coolingcontinued at an averaged rate of »70�75�C/Ma foranother 4.2 million years until 8.5 § 0.4 Ma, by whichtime ambient temperatures had declined to »70 § 5�C.

ACKNOWLEDGEMENTS

Geoff Fraser, Fred Jourdan and an anonymousreviewer are thanked for their efforts during review.MAF acknowledges the support of an AustralianResearch Council Australian Research Fellowship andDiscovery Projects DP0877274 and DP120103554. Min-eral separation was undertaken by Shane Paxton atRSES, ANU. 40Ar/39Ar analysis was undertaken onthe VG1200 in the RSES Argon Facility, ANU, whereDavood Vasegh provided technical support and under-took data reduction. Data were analysed using theeArgon and MacArgon computer program written byGSL. Scanning Electron Microprobe analysis (SEM)was undertaken at the Centre for Advanced

Microscopy at ANU with Dr Frank Brink. Fieldworkwas supported by Professor Robert Hall at the SEAsia Research Group, Department of Earth Sciences,Royal Holloway University of London, who also pro-vided invaluable discussion as to the tectonic signifi-cance of the two-stage cooling history as these resultsemerged. The University of Melbourne thermochro-nology laboratory received infrastructure supportunder the AuScope Program of NCRIS. Roland deJesus at the Mines and Geosciences Bureau gave per-mission to conduct fieldwork. Edwin Mojares was ourgeological guide in Palawan.

SUPPLEMENTARY PAPERS

Appendix 1 40Ar/39Ar Geochronology analytical proce-dures (Capoas Granite).Appendix 2 40Ar/39Ar geochronology data: Sample 11,PAL33a, K-feldspar.Appendix 3 SEM data: on the Hitachi 4300 FESEM.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by theauthors.

REFERENCES

CASSATAW. S. & RENNE P. R. 2013. Systematic variations of argon diffu-sion in feldspars and implications for thermochronometry. Geo-chimica et Cosmochimica Acta 112, 251�287.

COPELAND P., HARRISON T. M. & LE FORT P. 1990. Age and coolinghistory of the Manaslu granite: implications for Himalayantectonics. Journal of Volcanology and Geothermal Research44, 33�50.

COTTAM M. A., HALL R., SPERBER C., KOHN B., FORSTER M. A. & BATT G. E.2013. Rapid Neogene uplift of northern Borneo constrained bythermochronology from Mt Kinabalu. Journal Geological Society,London 170, 805�816, doi:10.1144/jgs2011-130.

DENIEL C., VIDAL P., FERNANDEZ A., LE FORT P. & PEUCAT J.-J. 1987. Isoto-pic study of the Manaslu granite (Himalaya, Nepal): inferenceson the age and source of Himalayan leucogranites. Contributionsto Mineralogy and Petrology 96, 78�92.

EHLERS T. A. & FARLEY K. A. 2003. Apatite (U�Th)/He thermochronom-etry: methods and applications to problems in tectonic and sur-face processes. Earth & Planetary Science Letters 206, 1�14.

ENCARNACI�ON J. & MUKASA S. B. 1997. Age and geochemistry of an“anorogenic” crustal melt and implications for I-type granite pet-rogenesis. Lithos 42, 1�13.

FARLEY K. A. 2002. (U�Th)/He dating: Techniques, calibrations andapplications. In: Porcelli C., Ballentine C. & Wieler R. eds.Reviews in Mineralogy and Geochemistry Vol. 47: Noble Gases inGeochemistry and Cosmochemistry, pp. 819�844. MineralogicalSociety of America and Geochemical Society, Washington D.C.

FARLEY K. A., WOLF R. A. & SILVER L. T. 1996. The effects of long alpha-stopping distances on (U�Th)/He ages. Geochimica et Cosmochi-mica Acta 60, 4223�4229.

FITZGERALD P. G., BALDWIN S. L., WEBB L. E. & O’SULLIVAN P. B. 2006.Interpretation of (U�Th)/He single grain ages from slowlycooled crustal terranes: A case study from the TransantarcticMountains of southern Victoria Land. Chemical Geology 225,91�120.

FORSTER M. A. & LISTER G. S. 2004. The interpretation of 40Ar/39Arapparent age spectra produced by mixing: application of themethod of asymptotes and limits. Journal of Structural Geology26, 287�305.

FORSTER M. A. & LISTER G. S. 2009. Core complex related extension ofthe Aegean lithosphere initiated at the Eocene�Oligocene

900 M. A. Forster et al.

Dow

nloa

ded

by [

Roy

al H

ollo

way

, Uni

vers

ity o

f L

ondo

n] a

t 03:

10 2

6 Fe

brua

ry 2

016

transition. Journal of Geophysical Research (Solid Earth) 114,B02401, doi:10.1029/2007JB005382.

FORSTER M. A. & LISTER G. S. 2010. Argon enters the retentive zone:reassessment of diffusion parameters for K-feldspar in the SouthCyclades Shear Zone, Ios, Greece. Geological Society, London, Spe-cial Publications 332,17�34, doi:10.1144/SP332.2

FORSTER M. A. & LISTER G. S. 2013. 40Ar/39Ar geochronology and thediffusion of 39Ar in phengite�muscovite intergrowths duringstep-heating experiments in vacuo. Geological Society, London,Special Publications 378, 107�135, doi 10.1144/SP378.16

FOSTER D. A., HARRISON T. M., COPELAND P. & HEIZLER M. T. 1990. Effectsof excess argon within large diffusion domains on K-feldspar agespectra. Geochimica et Cosmochimica Acta 54, 699�1708.

FORSTER M. A., LISTER G. S. & LENNOX P. G. 2014. Dating deformationusing crushed alkali feldspar: 40Ar/39Ar geochronology of shearzones in the Wyangala Batholith, NSW, Australia. Australian Jour-nal of Earth Sciences 61, 619�629, doi: 10.1080/08120099.2014.916751

FRANKE D., BARCKHAUSEN U., BARISTEAS N., ENGELS M., LADAGE S., LUTZ R.,MONTANO J., PELLEJERA N., RAMOS E. G. & SCHNABEL M. 2011. The con-tinent�ocean transition at the southeastern margin of the SouthChina Sea.Marine and Petroleum Geology 28, 1187�1204.

GILLESPIE A. R., HUNEKE J. C. & WASSERBURG G. J. 1983. Eruption age of aPleistocene basalt from 40Ar¡39Ar analysis of partially degassedxenoliths. Journal of Geophysical Research 88, 2156�2202, doi:10.1029/JB088iB06p04997

GILLESPIE A.R., HUNEKE J.C. & WASSERBURG G.J. 1984. Eruption age ofa »100,000 year-old basalt from 40Ar�39Ar analysis of partiallydegassed xenoliths. Journal of Geophysical Research 89,1033�1048.

GLEADOW A. J. W., BELTON D. X., KOHN B. P. & BROWN R. W. 2002. Fissiontrack dating of phosphate minerals and the thermochronology ofapatite. In: Kohn M. J., Rakovan J. & Hughes M. J. eds. Reviews inMineralogy and Geochemistry Vol. 48: Phosphates; Geochemical,Geobological, and Materials Importance, pp. 579�630. Mineralogi-cal Society of America and Geochemical Society, Washington D.C.

GLEADOW A., HARRISON M., KOHN B., LUGO-ZAZUETA R. & PHILLIPS D. 2015.The Fish Canyon Tuff: A new look at an old low-temperaturethermochronology standard. Earth and Planetary Science Letters424, 95�108.

GUENTHNER W. R., REINERS P. W., KETCHAM R. A., NASDALA L. & GIESTER G.2013. Helium diffusion in natural zircon: Radiation damage,anisotropy, and the interpretation of zircon (U�Th)/He thermo-chronology. American Journal of Science 313, 145�198.

GUILLOT S., HODGES K., LE FORT P. & PECHER A. 1994. New constraints onthe age of the Manaslu leucogranite: Evidence for episodic tec-tonic denudation in the central Himalayas. Geology 22, 559�563.

HALL R. 2013. Contraction and extension in northern Borneo drivenby subduction rollback. Journal of Asian Earth Sciences 76,399�411, doi: 10.1016/j.jseaes.2013.04.010

HARRISON T. M. & LOVERA O. M. 2013. The multi-diffusion domainmodel: past, present and future. Geological Society, London, Spe-cial Publications 378, 91�106, doi 10.1144/SP378.9

HARRISON T. M., GROVE M., MCKEEGAN K. D. & COATH C. D., LOVERA O. M. &LE FORT P. 1999. Origin and episodic emplacement of the Manasluintrusive complex, Central Himalaya. Journal of Petrology 40,3�19.

KARLSTROM K. E., HEIZLER M. & QUIGLEY M. C. 2010. Structure and40Ar/39Ar K-feldspar thermal history of the Gold Butte block: Re-evaluation of the tilted crustal section model. In: Umhoefer P. J.,Beard L. S., Lamb M. A. eds. Miocene Tectonics of the Lake MeadRegion, Central Basin and Range, pp. 331�352. Geological Societyof America Special Paper 463, doi: 10.1130/2010.2463(15)

KNAPP J. H. & HEIZLER M. T. 1990. Thermal history of crystallinenappes of the Maria fold and thrust belt, West Central Arizona.Journal of Geophysical Research 95, 20049�20073.

LISTER G. S. & BALDWIN S. L. 1996. Modelling the effect of arbitraryP�T�t histories on argon diffusion in minerals using the MacAr-gon program for the Apple Macintosh. Tectonophysics 253, 83�109.

LOVERA O. M., GROVE M., HARRISON T. M. & MAHON K. I. 1997. Systematicanalysis of K-feldspar 40Ar/ 39Ar step-heating experiments I: sig-nificance of activation energy determinations. Geochimica et Cos-mochimica Acta 61, 3171�3192.

LOVERA O. M., GROVE M. & HARRISON T. M. 2002. Systematic analysis ofK-feldspar 40Ar/39Ar step-heating experiments II: relevance oflaboratory K-feldspar argon diffusion properties to Nature. Geo-chimica et Cosmochimica Acta 66,1237�1255.

LOVERA O. M., HEIZLER M. T. & HARRISON T. M. 1993. Argon diffusiondomains in K-feldspar II: kinetic properties of MH-10. Contribu-tions to Mineralogy and Petrology 113, 381�393.

LOVERA O. M., RICHTER F. M. & HARRISON T. M. 1989. 40Ar/39Ar geother-mometry for slowly cooled samples having a distribution of diffu-sion domain sizes. Journal of Geophysical Research 94,17917�17935.

MARK D. F., PETRAGLIA M., SMITH V. C. B, MORGAN L. E., BARFOD D. N.,ELLIS B. S., PEARCE N. J., PAL J. N. & KORISETTAR R. 2013. Multipleinterpretive errors? Indeed. Reply to: Climate effects of the 74 kaToba super-eruption: Multiple interpretive errors in ‘A high- pre-cision 40Ar/39Ar age for the Young Toba Tuff and dating of ultra-distal tephra’ by Michael Haslam. Quaternary Geochronology 18,173�175.

MCDOUGALL I. & HARRISON T. M. 1999. Geochronology and thermochro-nology by the 40Ar/39Ar method, 2nd edition. Oxford UniversityPress, Oxford UK, 288 p.

MCLAREN S., DUNLAP W. J., SANDIFORD M. & MCDOUGALL I. 2002. Thermo-chronology of high heat-producing crust at Mount Painter, SouthAustralia: implications for tectonic reactivation of continentalinteriors. Tectonics 21, 1�18, doi:10.1029/2000TC001275

NABELEK P. I., HOFMEISTER A. M. & WHITTINGTON A. G. 2012. The influ-ence of temperature-dependent thermal diffusivity on the con-ductive cooling rates of plutons and temperature�time paths incontact aureoles. Earth and Planetary Science Letters 317�318,157�164, doi:10.1016/j.epsl.2011.11.009.

PARSONS I. & LEE M. R. 2009. Mutual replacement reactions in alkalifeldspars I: microtextures and mechanisms. Contributions to Min-eralogy and Petrology 157, 641�661, doi:10.1007/s00410-008-0355-4

PHILLIPS D. & MATCHAN E. L. 2013. Ultra-high precision 40Ar/39Ar agesfor Fish Canyon Tuff and Alder Creek Rhyolite sanidine: new dat-ing standards required? Geochimica et Cosmochimica Acta 121,229�239.

PUTNIS A. 2009. Mineral Replacement Reactions. Reviews in Mineral-ogy and Geochemistry 70, 87�124, doi:10.2138/rmg.2009.70.3

PUTNIS A. & JOHN T. 2010. Replacement processes in the Earth’s crust.Elements 6, 159�164, doi:10.2113/gselements.6.3.159

RENNE P. R., MUNDIL R., BALCO G., MIN K. W. & LUDWIG K. R. 2010. Jointdetermination of 40K decay constants and 40Ar�/40K for the FishCanyon sanidine standard, and improved accuracy for 40Ar/39Argeochronology. Geochimica et Cosmochimica Acta 74, 5349�5367.

RENNE P. R., MULCAHY S. R., CASSATA W. S., MORGAN L. E., KELLEY S. P.,HLUSKO L. & NJAU J. 2012. Retention of inherited Ar by alkali feld-spar xenocrysts in a magma: Kinetic constraints from Ba zoningprofiles. Geochimica et Cosmochimica Acta 93, 129�142.

S�ANCHEZ-MU ~NOZ L., GARC�IA-GUINEA J., ZAGORSKY V. Y., JUWONO T., MODRE-

SKI P. J., CREMADES A., VAN TENDELOO G. & DE MOURA O. J. M. 2012.The evolution of twin patterns in perthitic K-feldspar from gra-nitic pegmatites. The Canadian Mineralogist 50, 989�1024,doi:10.3749/canmin.50.4.989.

SCHOENE B., SCHALTEGGER U., BRACK P., LATKOCZY C., STRACKE A. &G€UNTHER D. 2012. Rates of magma differentiation and emplace-ment in a ballooning pluton recorded by U�Pb TIMS-TEA, Ada-mello batholith, Italy. Earth and Planetary Science Letters355�356, 162�173, doi:10.1016/j.epsl.2012.08.019

SEARLE M. P., NOBLE S. R., HURFORD A. J. & REX D. C. 1999. Age of crustalmelting, emplacement and exhumation history of the Shivlingleucogranite, Garhwal Himalaya. Geological Magazine 136,513�525.

SHUSTER D. L., FLOWERS R. M. & FARLEY K. A. 2006. The influence of nat-ural radiation damage on helium diffusion kinetics in apatite.Earth and Planetary Science Letters 249, 148�161.

STEUER S., FRANKE D., MERESSE F., SAVVA D., PUBELLIER M., AUXIETRE J.-L.& AURELIO M. 2013. Time constraints on the evolution of southernPalawan Island, Philippines from onshore and offshore correla-tion of Miocene limestones. Journal of Asian Earth Sciences 76,412�427.

STREEPEY M. M., HALL C. M. & VAN DER PLUIJM B. A. 2002. The 40Ar�39Arlaser analysis of K-feldspar: constraints on the uplift history ofthe Grenville Province in Ontario and New York. Journal of Geo-physical Research 107 (B11), 2296, doi:10.1029/2001JB001094

SUGGATE S., COTTAM M., HALL R., SEVASTJANOVA I., FORSTER M. A., WHITE

L., ARMSTRONG R., CARTER A. & MOJARES E. 2014. South China conti-nental margin signature for sandstones and granites from Pala-wan, Philippines. Gondwana Research 26, 699�718, doi:10.1016/j.gr.2013.07.006

Highly retentive domains in K-feldspar 901

Dow

nloa

ded

by [

Roy

al H

ollo

way

, Uni

vers

ity o

f L

ondo

n] a

t 03:

10 2

6 Fe

brua

ry 2

016

WALIA M., KNITTEL U., SUZUKI S., CHUNG S.-L., PENA R. E. & YANG T. F. 2012.No Paleozoic metamorphics in Palawan (the Philippines)? Evi-dence from single grain U�Pb dating of detrital zircons. Journal ofAsian Earth Sciences 52, 134�145, doi:10.1016/j.jseaes.2012.03.005.

WARNOCK A. C. & ZEITLER P. K. 1998. 40Ar/39Ar thermochronometry ofK-feldspar from the KTB borehole, Germany. Earth and PlanetaryScience Letters 158, 67�79.

VILLA I. M. 2006. From nanometer to megameter: Isotopes, atomic-scale processes, and continent-scale tectonic models. Lithos 87,155�173.

VILLA I. M. 2013. Diffusion of Ar in K-Feldspar: Present and Absent.Geological Society of London Special Publications 378, 107�116,doi:10.1144/SP378.4.

ZULAUF G., MAIER M. & ST €OCKHERT B. 1997. Depth of intrusion and ther-mal modeling of the Falkenberg granite (Oberpfalz, Germany).Geologische Rundschau 86, S87�S92.

Received 16 November 2014; accepted 26 October 2015

902 M. A. Forster et al.

Dow

nloa

ded

by [

Roy

al H

ollo

way

, Uni

vers

ity o

f L

ondo

n] a

t 03:

10 2

6 Fe

brua

ry 2

016