The In Vacuo Release of Ar from Minerals: 4—Polymineralic Samples

Abstract

The in vacuo release of Ar and other noble gases is well understood for single minerals. However, natural samples, even those seemingly pure under the optical microscope, mostly consist of mm-to-µm scale intergrowths of different minerals. Typically, relict phases and retrogression products are contained in minerals that are studied in sufficient detail. Only exceptionally can the number of different mineral generations be as low as two; single-generation gems (diamonds, rubies, emeralds) are not routinely used in geochronology. In polygenetic mixtures, the systematics of temperature-dependent release of artificial Ar isotopes used as compositional indicators (³⁸Ar and ³⁷Ar) can be linked to the ⁴⁰Ar/³⁹Ar ratio and disambiguate the ages of individual mineral generations.

1. Introduction

The ³⁹Ar–⁴⁰Ar dating method is based on in vacuo degassing of selected geochronometer minerals irradiated by fast neutrons, followed by mass spectrometric measurement of ³⁹Ar, the isotope representing the radioactive parent, and of ⁴⁰Ar*, the radiogenic daughter isotope [1]. The daughter/parent ratio, ⁴⁰Ar*/³⁹Ar, can be converted to an apparent age; the geological interpretation, i.e., the translation of the mass spectrometric apparent age into a geological age, requires analytical approaches tailored to the addressed problem and to the studied mineral. A few among hundreds of recent papers on ³⁹Ar–⁴⁰Ar dating are listed here to illustrate its relevance and versatility in addressing a variety of tectonic problems [2,3,4,5].

The most widely used analytical protocol is stepwise heating of the sample in a furnace attached to a mass spectrometer. It has been argued [6,7] that stepwise heating is suitable to deconvolve mixtures of minerals that are intergrown at the (sub-)µm scale, finer than the spatial resolution (≥20–30 µm) of in situ analyses. The physical processes controlling the in vacuo Ar release have been addressed for different kinds of monomineralic samples: dehydroxylation for hydrous samples [8]; second-order phase transitions for nominally anhydrous sanidine [9]; and structural collapse and recrystallization for apatite [10]. The present paper will describe the in vacuo Ar release in the simplest case of polymineralic sample, in which two minerals co-exist in sufficient relative amounts in the analyzed separate.

2. Bond-Breaking

Individual minerals have different interatomic distances and therefore different bond lengths and strengths. It is only to be expected that all macroscopic properties of minerals that depend on bond length/strength should display regular and predictable sequences. Typical examples are weatherability [11], ionic porosity [12], Mohs hardness, etc. Dahl [12] further points out that the retentivity of age information by geochronometer minerals can be controlled by several factors, all of which primarily depend on bond length and strength between the structure-forming ions. These factors also include (but not exclusively) Fick’s Law Diffusion, FLD.

Isolated individual atoms do not exhibit the macroscopic properties of the element. Just as no individual copper atom is an electric conductor, individual argon atoms do not follow the Ideal Gas Law (pV = nRT) and therefore are not a gas. Individual Ar atoms are not noble either, as they do interact with the structure-forming ions. Although stable Ar compounds are not routinely observed, Ar atoms are polarizable and thus cannot avoid electrical interactions with surrounding ions when trapped inside crystal structures. Compounding polarizability with an atomic radius much larger than that of all major ions forming the mineral structure, it is intuitive (and confirmed by the quantum mechanical calculations by ref. [13]) that the transport of Ar atoms through a crystal requires a high activation energy, typically equal to the energy necessary to form Schottky defects [13,14], i.e., around 250–300 kJ/mol.

In order to export the results of laboratory measurements using the ³⁹Ar–⁴⁰Ar dating method to make inferences about the geological evolution of rocks it is necessary to understand and compare the physical processes that control the laboratory degassing of Ar from geochronometer minerals with the physical processes that control isotope transport in rocks at the metric scale (e.g., [15]). It is well established that different minerals are outgassed in vacuo at different furnace temperatures (e.g., [16]). The observations on hydrous minerals are that a massive structural reshuffle, such as caused by dehydroxylation [8,17], causes a highly enhanced in vacuo noble gas release over a narrow temperature interval, quantified by a cusp-shaped curve of the differential degassing rate. An example from the literature is shown in Figure 1. For anhydrous minerals such as K-feldspar and apatite, the Ar release occurs more gradually, during a subtle sequence of both reversible (rotation and deformation of SiO₂ tetrahedra: [9,18]) and irreversible (Al,Si disordering: [9,19]) transformations, vaguely resembling FLD, but not identical to it. The quantitative observations of reversible structural transformations are based on the Raman microprobe study of feldspar structures [20], and are not readily visible by optical microscopy performed at room temperature, as reversible transformations do not irreversibly modify optical parameters such as birefringence. The fact that the structure of the mineral matrix is not inert forbids downslope extrapolation of high temperature laboratory data; this prudence is common practice for He diffusion experiments in apatite, whose low-temperature thermochronometric properties should only be modeled based on data from laboratory degassing performed below 400–450 °C [21,22].

Figure 1. Differential ³⁹Ar release plot of two different white mica varieties from retrogressed eclogites from Naxos (Greece). The muscovite (solid violet line) has a similar, but well distinct, Ar degassing pattern to the phengite (dashed green line); the peak of degassing rate is visibly different both in width and in position. The data were manually scanned from ref. [23], their Figure 5, as the original publication does not provide the complete data.

3. Mono and Polymineralic Samples

The quantitative interpretation of the chronometric behavior of mineral mixtures adds a serious complication to the above paragraph. Single-generation gems (diamonds, rubies, emeralds) are rare, costly, K-free, and are not routinely used in geochronology. All other minerals (mostly terrestrial ones, due to the pervasive influence of liquid water) reveal the co-existence of several mineral phases when petrographically studied in sufficient detail. The phase inventory can include the following three kinds of heterochemical minerals, in addition to the geochonometer targeted for dating: minerals belonging to the same paragenesis, formed simultaneously and in isotopic equilibrium with it; relicts of pre-existing minerals that were incorporated when the “target mineral” was formed; and patches of retrograde reaction products, which were formed during the exhumation of the “target mineral”. Both the latter kinds of inclusions are in isotopic and chronological disequilibrium with the target mineral. Because of the difficulty of precisely identifying all of the mineral phases present in a natural sample, the isotope systematics of mixtures are best and more clearly studied by comparing artificial, controlled mixtures of approximately monomineralic materials with the separate starting components of the mixture (e.g., [23,24,25,26] and references therein). One additional example is presented here to illustrate additional diagnostic plots to constrain the effects of polymineralic mixtures. The insight gained from controlled, artificial mixtures can then be exported to natural samples whose polymineralic nature is suspected but not yet documented. This enables dedicated petrographical searches (typically, element maps with a 1 µm resolution obtained by electron microprobe), which so far have always confirmed the isotopic indications. This emphasizes the indispensable necessity to acquire high-resolution element maps on each and every analyzed sample. This practice is routinely applied to U–Pb dating (e.g., [27]), and has only recently become common in ³⁹Ar–⁴⁰Ar dating (e.g., [28,29,30,31]).

4. Materials and Methods

The two approximately monomineralic samples chosen as comparison paragons are a K-feldspar (the Fish Canyon Tuff sanidine: [32,33]), FCs, and unpublished sericite G-13 from the same outcrop as that studied by ref. [34] on Elba Island, Italy. Sericite is a dioctahedral mica produced by alteration of feldspars [35,36,37,38,39]. The choice of artificially mixing sanidine and sericite is designed to simulate the Ar isotopic pattern that is developed during natural alteration of K-feldspar. The present sericite and K-feldspar samples are totally unrelated; they were chosen because they have different ages and different Cl/K ratios. Note carefully that it is not necessary for the two starting paragons to be strictly monomineralic (in this case they are not, but this is not the issue discussed here). What the present experiment focuses on is the comparison between the different degassing characteristics of the artificial mixture relative to the starting material in the employed diagrams.

Both FCs and G-13 were wrapped separately and irradiated with fast and thermal neutrons at the McMaster nuclear reactor, and analyzed by stepwise heating following the protocol in ref. [28]. In addition, the gas released from the two paragons was digitally added, multiplying the respective Ar amounts by the mass fractions of a synthetic mixture (15 mg FCs, 0.45 mg G-13) designed to mimic a natural analog, namely a slightly altered (sericitized) K-feldspar. A 3% mass fraction of feldspar alteration forming sericite is usually overlooked unless a dedicated high-resolution search is undertaken.

5. Results

Age spectra (Figure 2) for the two pure paragons and the virtual artificial mixture are presented first, even if the information that they provide is quite limited; the comparison between the flat spectra of the two paragons and the step-like shape of the mixture merely underscore the point extensively made by ref. [26], namely that discordant age spectra are produced by polymineralic mixtures.

Figure 2. Age spectra of K-feldspar (solid violet line), sericite (dashed green line), and K-feldspar + sericite mixture (gray dotted line). CR39 is the cumulative release of ³⁹Ar, in percent. Apparent step ages are shown as boxes with 2 sigma uncertainty height.

Equally predictable is Figure 3a, which highlights that the differential release of ³⁹Ar, DR₃₉, normalized to the temperature interval of the relevant heating step, ΔT, has its maximum at a low furnace temperature for sericite and a well distinct one at a high furnace temperature for K-feldspar. The normalized differential release for the artificial mixture has a telltale broad, bimodal distribution, which denounces immediately the diachronous degassing of two different phases. Figure 3b displays the normalized differential release of ³⁸Ar_Cl, DR_38C, which shows a totally different behavior from Figure 3a. The discrepant shapes of the release patterns can only be explained if K and Cl reside in different minerals; the behavior of DR_38C denounces sericite as the main carrier phase of artificial ³⁸Ar_Cl, even if its mass fraction is only 3% of that of sanidine.

Figure 3. Differential release rates for (a) DR₃₉/ΔT and (b) DR_38C/ΔT. K-feldspar, solid violet line; sericite, dashed green line; K-feldspar + sericite mixture, thick gray dotted line. The prominent ³⁸Ar_Cl release peak at 750 °C is entirely due to the first step of FCs, which probably can be attributed to saline fluid inclusions.

The most useful diagrams to diagnose, and unravel, the ³⁹Ar–⁴⁰Ar systematics of mineral mixtures are the common-denominator three-isotope correlation diagrams [25,40,41]. In such plots, binary mixtures define linear alignments [42]. One such diagram is shown in Figure 4. The pure Kfs, which is stoichiometrically Cl-free, plots very close to the ordinate axis. The sericite has vastly variable Cl/K ratios, which might indicate that it actually consists of successively grown generations. As mentioned above, the point of the experiment was not to test the natural sericite for homogeneity but to reveal the effect of adding 3% sericite to K-feldspar. The sericite steps that contributed Ar in the temperature interval in which both minerals release Ar, ca. 750–950 °C (Figure 3), are marked as “mid-T Src” in the bottom-right corner of Figure 4. The gray triangles along the dashed line marked “mixing trend” are not present when pure Kfs is analyzed and are only observed when 3% sericite is admixed. Their ~10% age reduction is small because the amount of sericite was kept intentionally small.

Figure 4. Common-denominator correlation diagram ⁴⁰Ar*/³⁹Ar vs. ³⁸Ar_Cl/³⁹Ar. The ordinate is equivalent to the step age (which, for the young ages of the present samples, is almost a linear function of ⁴⁰Ar*/³⁹Ar); the abscissa is directly proportional to the molar Cl/K ratio. K-feldspar, violet circles; sericite, green circles; Kfs + Src mixture, open gray triangles. The square enclosing two points at the lower right, labeled “mid-T Src”, corresponds to Ar released by sericite at mid-temperature, ca. 750–950 °C, i.e., the T range where the Ar releases of both minerals overlap.

The degassing rate shown in Figure 3 allows the calculation of an Arrhenius diagram, in which the logarithm of a rate constant is plotted against the inverse temperature (e.g., [43]). It is very important to note that the rate constant of any temperature-dependent process can follow the Arrhenius equation. In a study associating the Ar degassing rate constant (sometimes mistakenly identified as the Fick’s Law diffusivity) with mineralogical heterogeneities, Chafe et al. [44] hypothesized that heterochemical alteration minerals were producing kinked Arrhenius trajectories. The present artificial mixture demonstrates (Figure 5) the behavior exactly matching the hypothesis by ref. [44]. Since in the intermediate furnace temperature range between 622 and 998 °C both Kfs and Src simultaneously contribute ³⁹Ar, the degassing rate is the sum of two separate release mechanisms from two different mineral structures. The segment of the Arrhenius trajectory marked by gray triangles is meaningless, as it is neither controlled by the Ar release rate of pure K-feldspar nor by that of pure sericite.

Figure 5. Arrhenius diagram quantifying the ³⁹Ar degassing rate constant in an artificial mixture mimicking a slightly sericitized K-feldspar. The kinked Arrhenius trajectory consists of three sections: for T < 571 °C, the ³⁹Ar is only released from sericite (green circles); for T > 1102 °C, the ³⁹Ar is only released from K-feldspar (violet circles); in the intermediate temperature range, when both Kfs and Src simultaneously contribute ³⁹Ar, the degassing rate is the sum of two separate release mechanisms from two different mineral structures, and is geologically meaningless (open gray triangles).

6. Precision vs. Accuracy

Looking in detail at the step ages of the Kfs reveals an additional effect. The admixture of 3% sericite with a different age shifts the Kfs age by 0.36% (Figure 6). This difference is resolvable at the 1 sigma level. Taking the step age at face value is evidently an inaccuracy, due to neglecting the indication provided by the Cl/K of that step, the compositional fingerprint of alteration. Such a systematic inaccuracy is “small” or “large”, according to the precision that the experimenter is aiming for: if the intended precision is 0.1%, then a 0.36% bias is unacceptable.

Figure 6. Enlarged detail of the age spectrum of Figure 2. The heating step yielding the highest Ar amount has a slightly higher age in pure Kfs (solid violet box) than in the Kfs–sericite mixture (dotted gray box).

Over half a century ago, ref. [45] had introduced the practice of Cd-shielding the samples subject to neutron irradiation to block the thermal neutrons, one of whose effects was the artificial production of ⁴⁰Ar in the reaction ⁴⁰K(n,p)⁴⁰Ar. The rationale for Cd-shielding was apparently a gain in precision, as the correction for the undesirable ⁴⁰Ar addition due to thermal neutrons was typically (⁴⁰Ar/³⁹Ar)_thermal ≈ 0.04 ± 0.0004, increasing the overall uncertainty of the age determination; in contrast, the reaction ⁴⁰K(n,p)⁴⁰Ar due to fast neutrons is over two orders of magnitude smaller, (⁴⁰Ar/³⁹Ar)_fast ≈ 0.0002 ± 0.0002. The increase in uncertainty is thus halved by Cd-shielding. However, the improvement in apparent precision has a potential cost in terms of accuracy: since ³⁸Ar_Cl is also produced by thermal neutrons, the possibility to detect alteration phases in the analyzed separated is forgone, and the accuracy control is made impossible.

7. Conclusions

Real-world mineral separates analyzed for dating overwhelminlgy contain (sub-)µm-sized relict phases and retrogression products. The recognition of such admixtures is essential to ensure accurate corrections for mineral phases unrelated to the geological process that one is endeavoring to date. Useful criteria to diagnose the presence of unwanted mineral phases are provided by the signatures of in vacuo Ar degassing. The differential release rates of mineral mixtures, coupled to the independent indications provided by three-isotope isotope correlation diagrams, can identify with near certainty the number, and often the identity, of the mineral phases in the studied separate. This sets the stage for element mapping by electron microprobe, as required for accurate dating by petrochronology.