Available online at www.sciencedirect.com R Earth and Planetary Science Letters 217 (2003) 1^17 www.elsevier.com/locate/epsl 4He/3He thermochronometry David L. Shuster Ã, Kenneth A. Farley Division of Geological and Planetary Sciences, MC 100-23, California Institute of Technology, Pasadena, CA91125, USA Received 25 April 2003; received in revised form 18 June 2003; accepted 7 October 2003 Abstract Using classical diffusion theory, we present a mathematical technique for the determination of 4He concentration profiles in minerals. This approach should prove useful for constraining the low-temperature cooling histories of individual samples and for correcting (U^Th)/He ages for partial diffusive loss. The calculation assumes that the mineral of interest contains an artificially produced and uniform distribution of 3He obtained by proton irradiation [Shuster et al., Earth Planet. Sci. Lett. 217 (2004) 19^32]. In minerals devoid of natural helium, this isotope allows measurement of He diffusion coefficients; in minerals with measurable radiogenic He, it permits determination of 4He profiles arising during ingrowth and diffusion in nature. The 4He profile can be extracted from stepwise degassing experiments in which the 4He/3He ratio is measured. The evolution of the 4He/3He ratio as a function of cumulative 3He released can be compared with forward models to constrain the shape of the profile. Alternatively, we present a linear inversion that can be used to directly solve for the unknown 4He distribution. The inversion incorporates a standard regularization technique to filter the influence of random measurement errors on the solution. Using either approach we show that stepwise degassing data can yield robust and high-resolution information on the 4He profile. Profiles of radiogenic He are a sensitive function of the time^Temperate (t^T) path that a cooling sample experienced. Thus, by step heating a proton-irradiated sample it is possible to restrict the sample’s acceptable t^T paths. The sensitivity of this approach was explored by forward-modeling 4He profiles resulting from a range of realistic t^T paths, using apatite as an example. Results indicate that 4He profiles provide rich information on t^T paths, especially when the profiles are coupled with (U^Th)/He cooling ages on the same sample. Samples that experienced only moderate diffusive loss have 4He concentration profiles that are rounded at the edge but uniform in the core of the diffusion domain. Such profiles can be identified by nearly invariant 4He/3He ratios after the first few to few tens of percent of 3He have been extracted by stepheating. We show how such data can be used to correct (U^Th)/He ages for partial diffusive loss. ß 2003 Elsevier B.V. All rights reserved. Keywords: helium; di¡usion; thermochronometry; isotope; proton beam; (U^Th)/He 1. Introduction Helium isotopes are used extensively as chro- nometers in terrestrial and extraterrestrial materi- * Corresponding author. Tel.: +1-626-395-2190; 4 Fax: +1-626-683-0621. als. He produced from radioactive decay of U 147 E-mail addresses: [email protected] (D.L. Shuster), and Th series nuclides and Sm forms the basis [email protected] (K.A. Farley). of (U^Th)/He chronometry (e.g., [2^5]), while 3He 0012-821X / 03 / $ ^ see front matter ß 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0012-821X(03)00595-8 EPSL 6893 3-12-03 Cyaan Magenta Geel Zwart 2 D.L. Shuster, K.A. Farley / Earth and Planetary Science Letters 217 (2003) 1^17 produced by cosmic ray spallation is used to esti- loss depends on both the di¡usivity and the con- mate surface exposure ages and erosion rates [6,7]. centration gradient, so converting stepwise release The main attraction of He for these applications data to di¡usivity requires speci¢cation of the is that its production rates are high compared to concentration distribution, Co(x,y,z), where x, y other isotope systems, coupled with the fact that and z are spatial coordinates [12]. An initially uni- high-precision, high-sensitivity He analyses are form concentration across a spherical di¡usion comparatively easy. A critical consideration for domain, Co(r) = constant, is typically assumed, these uses is that He di¡usion in most minerals where r is radius. This assumption is violated occurs at moderate temperatures (250‡C^20‡C) for samples that have experienced He loss either [5]; failure to consider di¡usive loss can lead to by di¡usion or by ejection of K-particles from erroneously young He-based age constraints. In- mineral surfaces following decay. Failure to incor- deed, this is the primary reason that (U^Th)/He porate such pro¢le rounding in the computation and terrestrial cosmogenic 3He dating have seen will yield di¡usivities that underestimate the true only limited application over the last several de- values, potentially by many orders of magnitude. cades [8] despite considerable analytical advance- In some cases, an unrecognized rounded pro¢le ment [5]. However, if properly characterized, dif- can yield a remarkably linear Arrhenius array 2 fusive loss can be used to study low-temperature that implies incorrect Ea and Do/a , particularly geologic processes through (U^Th)/He thermo- in the earliest steps. chronometry. The goal of previous He di¡usion experiments Knowledge of He di¡usion kinetics is therefore has been to verify He retention in a given material critical for materials in which He measurements under given conditions (e.g., is cosmogenic 3He are made, particularly for chronometry. Although quantitatively retained in quartz at 20‡C? [11]), other methods are sometimes used [9,10], stepwise or to determine the temperature dependence of vacuum outgassing is the most common technique di¡usivity (D(T)/a2) for thermochronological in- for determining the apparent He di¡usivity, D/a2 terpretation [13,14]. As demonstrated by 40Ar/ (D is the di¡usion coe⁄cient, a is the character- 39Ar dating [15], the spatial distribution of a uni- istic length scale of the di¡usion domain). By formly produced radiogenic noble gas re£ects a measuring the temperature dependence of di¡u- sample’s thermal history. If known, the distribu- sivity, it is possible to determine the two param- tion: (i) permits correction of ages for di¡usive 40 39 eters (activation energy, Ea, and frequency factor, loss (i.e., identi¢cation of a Ar/ Ar age plateau) 2 Do/a ) which de¢ne the Arrhenius function D(T)/ and (ii) with knowledge of D(T) and the parent 2 2 a = Do/a exp(3Ea/RT) required to extrapolate nuclide distribution, constrains the thermal histo- He di¡usion coe⁄cients to low temperatures and ry (geologic t^T path) of a sample. Quantitative long time scales over which direct laboratory mea- use of the (U^Th)/He system for these purposes surements are impossible. should also be possible. If we determine the shape Vacuum di¡usion experiments have several lim- of a 4He concentration pro¢le, the function D(T)/ itations. First, they require su⁄cient 4He or 3He a2 and the U and Th distribution within a sample, ( v 1010 and v 106 atoms, respectively) for accu- we can constrain its t^T path. If we determine the rate detection, and so are presently limited to ei- quantity of ‘missing’ He, we can in some cases ther U-rich phases, old samples, samples that ex- correct a He age for di¡usive 4He loss and/or perienced appreciable surface exposure [11] or K-ejection. samples in which He has been introduced by sorp- Direct measurement of a He distribution is not tion [10]. Current detection limits usually require usually possible. Nuclear reaction analysis and either large or multiple grains to be analyzed si- secondary ionization and laser microprobe mass multaneously, whereas for many applications sin- spectrometry lack su⁄cient sensitivity and/or spa- gle-crystal experiments are preferable. A more tial resolution to measure He concentrations at subtle problem is caused by the initial He distri- levels found in most minerals. While ultraviolet bution within a sample. The rate of di¡usive He laser extraction can be used to measure 40Ar/ EPSL 6893 3-12-03 Cyaan Magenta Geel Zwart D.L. Shuster, K.A. Farley / Earth and Planetary Science Letters 217 (2003) 1^17 3 39Ar pro¢les [16], high He di¡usivities in most two isotopes, a ‘trapped’ He component cannot minerals make He susceptible to even a small be identi¢ed as it sometimes can in the Ar system thermal aureole around the ablation pit. Cur- [15]. Therefore, this approach is most e¡ectively rently the only way to assess the shape of a He applied to samples free of excess He in the matrix concentration pro¢le Co(r) is to use the indirect or inclusions. approach of stepwise degassing. To determine Co(r) from stepwise release fractions requires ei- 2.2. Constraining an initial pro¢le with a stepwise ther independent knowledge of D(T)/a2 or a sec- degassing experiment ond, uniformly distributed isotope from which D(T)/a2 can be determined [17]. For reasons discussed below and in [1],itis Here we describe how a laboratory-induced, usually su⁄cient and simpler to represent a natu- 3 4 uniform He distribution coupled with an isotope ral He distribution, Co(x,y,z) by a model radial ratio step-heating experiment can be used to de- distribution, Co(r) within a spherical di¡usion do- termine He di¡usivities in any mineral and to con- main of equivalent surface area to volume ratio. strain an unknown natural 4He distribution using For a di¡using substance having an initial radial either forward or inverse models.