The closure temperature(s) of zircon Raman dating

Abstract. We conducted isochronal and isothermal annealing experiments on radiation-damaged zircons between 500 and 1000 °C for durations between ten minutes and five days. We measured the widths (Γ) and positions (ω) of the internal ν1(SiO4), ν2(SiO4), ν3(SiO4), and external rotation Raman bands at ~ 974, 438, 1008, and 356 cm-1. We fitted a Johnson-Mehl-Avrami-Kolmogorov and a distributed activation energy model to the fractional annealing data, calculated from the widths of the ν2(SiO4), ν3(SiO4), and external rotation bands. From the kinetic models, we determined closure temperatures Tc for damage accumulation for each Raman band. Tc range from 330 to 370 °C for the internal ν2(SiO4) and ν3(SiO4) bands; the external rotation band is more sensitive to thermal annealing (Tc ~ 260 to 310 °C). Our estimates are in general agreement with previous ones, but more geological evidence is needed to validate the results. The Tc difference for the different Raman bands offers the prospect of a multi-closure-temperature zircon Raman thermochronometer.


Introduction
Zircon (ZrSiO4) is used with several geochronometers because of the substitution of U and Th for Zr in its lattice. Its occurrence in various types of rocks and high chemical and mechanical resistance make it useful for geochronological applications. The α-disintegration of U and Th creates lattice disorder by the impact of α-particles and the recoil of daughter nuclei. The zircon Raman spectrum is sensitive to lattice damage: the downshift and broadening of the Raman bands provide a quantitative measure for the radiation damage (Nasdala et al., 1995(Nasdala et al., , 1998. Measurements of the radiation damage and of the U and Th content allow to calculate a zircon Raman age (Pidgeon, 2014;Jonckheere et al., 2019).
Radiation damage is annealed at high enough temperatures (Zhang et al., 2000a;Geisler et al., 2001;Nasdala et al., 2001;Pidgeon et al., 2016). Figure 1 shows the Raman spectrum of zircon with progressive annealing. The Raman bands shift to higher wavenumbers, towards the band positions of well-ordered zircon, and become narrower and more intense. This loss of damage with temperature and time is a problem for the interpretation of zircon Raman ages as crystallization ages (Nasdala et al., 2001(Nasdala et al., , 2002 but unlocks the potential for determining cooling ages and analyzing the thermal histories of natural zircon samples (Resentini et al., 2020). Annealing of radiation damage also affects Hediffusion and is thus a process that needs to be taken into account in the interpretation of (U-Th)/He data of zircon (Ginster et al., 2019;Anderson et al., 2020).
A thermochronometer is characterized by its closure temperature Tc, the temperature of the dated sample at the time of its apparent age (Dodson, 1973(Dodson, , 1979. Tc estimates range from ~130 °C for natural samples at isothermal conditions in the KTB borehole (Jonckheere et al., 2019) to ~650 °C for the re-crystallization of metamict zircon based on the retention of Pb in zircons that were heated to these temperatures (Mezger and Krogstad, 1997). Pidgeon (2014)  Previous laboratory annealing experiments distinguished several annealing stages based on the changes of lattice constants measured by XRD (Weber, 1993, Colombo and Chrosch, 1998a, 1998b and on changes in the relationship of Raman shift (ω3) to bandwidth (Γ3) of the ν3(SiO4) Raman band (Geisler et al., 2001, Geisler, 2002, Ginster et al., 2019.  Geisler (2002) and Ginster et al. (2019). The offset and difference in slope between the damage accumulation and annealing trends are evident. Breaks in slope of the annealing trend mark transitions between the annealing stages. A sharp break separates the steep stage I and the flat stage II, but a more gradual transition occurs between stage II and a stage III assumed by Geisler (2002). Stage I is dominated by the elimination of point defects; stage II is ascribed to crystallization of the amorphous domains (Colombo and Chrosch, 1998a, Capitani et al., 2000, Geisler et al., 2001, Geisler, 2002, Ginster et al., 2019; and stage III is related to the diffusion of residual point defects (Geisler, 2002).
Our aim is to investigate the change of the major Raman bands on annealing and to estimate Tc. We track the changes of ω and Γ of the ν1(SiO4), ν2(SiO4), ν3(SiO4) internal Raman bands, and the external rotation band at ~ 974, 438, 1008, and 356 cm -1 (Kolesov et al., 2001) for isochronal annealing runs at different temperatures. We fit two kinetic models to the widths of the three most intense Raman bands for isothermal annealing for different time intervals and temperatures and consider their extrapolation to geological timescales. We discuss the closure temperatures calculated from the models in comparison to previous Tc estimates.

Zircon samples
We separated zircons from a Late Carboniferous volcanic rock from the Flöha Basin in Saxony, Germany (Löcse et al., 2019). This sample was selected because the zircons are assumed to have retained the radiation damage accumulated since their formation. They have moderate to high radiation-damage densities. Zircon separation was carried out as described in Sperner et al. (2014). The zircon grains for the annealing experiments were hand-picked under a binocular microscope. We discarded grains with cracks that might fall apart upon heating or cooling. For comparison, we measured a zircon synthesized as pure ZrSiO4 by Guillong et al. (2015).

Raman spectrometry
We measured the Raman spectra using a TriVista Spectrometer (Princeton Instruments) in single mode. The power of the 488 nm incident laser light on the sample is ~12 mW. Repeat measurements show that the laser power does not affect the lattice damage. The wavenumber calibration used the 219.2, 520.7, and 1001.4 cm -1 bands of sulfur, silicon, and polystyrene. The spectral resolution is ~0.8 cm -1 and the pixel resolution on the detector is ~0.2 cm -1 . We acquired zircon spectra in step-and-glue mode with three steps spanning 170 to 1100 cm -1 . We cut the spectra into three regions and fitted the bands with Lorentz functions using a 3 rd order polynomial for background subtraction. We corrected the bandwidth for the instrumental function following Tanabe and Hiraishi (1980).

Annealing experiments
We performed isothermal and isochronal annealing runs in a Linn LM111.06 and a Nabertherm LT3/11 muffle oven.
For each run, we prepared a set of zircon grains showing different radiation damage to be annealed together. The zircon grains were individually wrapped in Monel 400 foil (a nickel/copper alloy) and inserted in the pre-heated oven in a ceramic crucible. The temperatures of the isothermal annealing runs ranged from 500 to 1000 °C for cumulative annealing times of 10 minutes, 30 minutes, 5 hours, 24 hours, and 5 days. The experiments followed the approach of Geisler et al. (2001) with each zircon being annealed in consecutive steps at a constant temperature and cooled for measurement between the steps.
In the isochronal experiments, we annealed the zircons for one hour runs at 600 to 1000 °C with a 100 °C interval. The Raman spectrum was measured at room temperature after each run. The locations of measurement spots on the zircon grains were recorded before each annealing step to assure measurements at the same locations. Grains that disintegrated during annealing were discarded.

Changes in band position and width
The change in band position, bandwidth, and intensity is different for each Raman band (Figure 1), as reported in earlier studies (Zhang et al., 2000a;Geisler, 2002). Figure 3 shows plots of ω vs. Γ for the isochronal annealing runs. The different bands exhibit a common trend of decreasing Γ and increasing ω with increasing temperature, but trace distinct lines through the ω-Γ space. Overall, the ω-Γ trajectories for the ν1(SiO4), ν3(SiO4), and external rotation bands resemble that of ν3(SiO4) in Figure 2 with a steep segment at the beginning, followed by a break in slope towards a flatter trend. ω3 and ΓER show the largest changes. The breaks in slope between 700 and 800 °C for the 1h annealing runs are interpreted as the transition from stage I to stage II annealing (Geisler et al., 2001). The slopes of the stage I and stage II segments are different for each band. A striking difference exists between the ν 2(SiO4) band near 438 cm -1 and the other bands. During stage I, ω2 decreases, whereas the other three bands shift to higher wavenumbers. The decrease of ω2 reverses at higher temperatures at the onset of stage II of the other bands. Γ2 values decrease throughout the annealing process like the other bandwidths. The scatter of the ω-Γ data around each common trend is limited, producing a well-defined trend for all Raman bands for stage II, irrespective of the different radiation-damage densities in the unannealed zircons. Our data do not show the gradual steepening between the stages II and III as in Figure 2. Figure 4 traces the ω-Γ trends for two zircon grains with similar initial radiation damage through isothermal annealing at 600 and 1000 °C. As expected, annealing proceeds faster at 1000 °C. The ω-Γ trends follow the same trajectories as in Figure 3. The stage I sections of the 1000 °C trajectories must be assumed because the first annealing step already reached stage II.  up to 800 °C and a flat annealing trend at higher temperatures. This reflects the trends for stage I and II (Figures 2, 3, 4).
For ω3, most of our data are slightly lower than those of Ginster et al. (2019), consistent with the values of Geisler (2002), but more strongly annealed than those of Zhang et al. (2000a). We also observed more annealing of ω compared with Zhang et al. (2000a) for the other three bands. The small difference between our isochronal runs for 1h and the 90 min runs of Ginster et al. (2019) can be attributed to the difference in annealing time.
The main difference between our results and those of Zhang et al. (2000a), Geisler (2000), and Ginster et al. (2019) relates to ω2, for which Geisler (2002) reported a constant value through stage I and II that only begins to increase in stage III. Our data show an initial drop of ω2, followed by a shift to higher wavenumbers at the onset of stage II. Zhang et al. (2000a) show a similar decrease of ω2 which was only reversed during stage III.
The differences between ν2(SiO4) and the other Raman bands are interpreted as due to the different Raman modes. The vibrational frequencies of the stretching bands ν1(SiO4) and ν3(SiO4) depend most on the bond lengths. In contrast, ν2(SiO4) is a bending mode, depending on the angle between the Si-O bonds in the SiO4 tetrahedron (Geisler, 2002). The O-Si-O angle is related to the ratio of the unit cell parameters a and c (Tokuda et al., 2019). Figure 6 plots c vs. a for the XRD data for the annealing experiments of Colombo and Chrosch (1998a) and Geisler et al. (2001). Due to damage accumulation, c increases more than a (Salje et al., 1999;Zhang et al., 2000b). The increased ratio c/a reduces the O-Si-O angle between the oxygen atoms shared by Si and Zr (Tokuda et al., 2019), shifting the ν2(SiO4) Raman band to lower wavenumbers. During stage I annealing, the unit cell shrinks anisotropically, reducing a more than c, causing a further increase of c/a and lowering of the O-Si-O angle. The anisotropic shrinkage is thought to be due to the preferential diffusion of point defects in the basal plane of zircon during recovery Colombo and Chrosch, 1998a).  convergence towards a common stage II is also apparent for the other Raman bands (Figures 3 and 4), as well as for the XRD unit cell data ( Figure 6). Stage II is interpreted as representing a state of the zircon lattice that is independent of the damage accumulation history. We assume, based on the interpretation of the successive annealing stages of Colombo and Chrosch (1998a), Ríos et al. (2000), and Geisler et al. (2001), that stage II describes zircons in which the lattice has lost most of its point defects and is predominantly strained by the amorphous domains caused by α-recoils. In this case, the position of a zircon along the stage II trend represents the remaining amorphous fraction.

Kinetic modeling and closure temperature
For estimating the temperatures at which annealing takes place on geological timescales, we fitted kinetic models to the Raman bandwidth data for the isothermal annealing runs. We fitted Γ2, Γ3, and ΓER, but not Γ1 which shows lower bandwidths than the other bands, implying lower sensitivity to radiation damage. We quantified the fractional lattice repair Φ(t, T) following isothermal annealing for a time t and a temperature T equivalent to the parameter α of Geisler et al. (2001): Γi is the bandwidth of the unannealed sample, Γ(t,T) that after annealing for a (cumulative) time t at temperature T. Γ0 is the bandwidth of undamaged zircon; we assumed 5.0, 1.9, and 3.6 cm -1 for the ν2(SiO4), ν3(SiO4), and external rotation bands, based on the values of the synthetic zircon, we measured. Φ = 0 indicates no annealing, Φ = 1 complete annealing. A Pearson correlation test with Bonferroni correction for multiple testing (Abdi, 2007) showed that none of the co-annealed zircons exhibited a significant dependence of Φ on the initial damage Γi. We fitted the arithmetic mean  (2019), who worked with samples of different age and provenance so that we assume that the annealing kinetics of our samples are applicable to a broader range of zircons. We fitted two models: a Johnson-Mehl-Avrami-Kolmogorov (JMAK) model (Kolmogorov, 1937;Avrami, 1939;Johnson and Mehl, 1939) and a distributed activation energy (DAE) model (Lakshmanan et al., 1991;Lakshmanan and White, 1994). The JMAK model is described by: where n is the Avrami exponent and k is a temperature-dependent rate factor that follows an Arrhenius law: k0 is a frequency factor, EA an activation energy, and κ the Boltzmann constant. JMAK models are used for describing crystallization processes (Avrami, 1939;Johnson and Mehl, 1939). Since crystallization of amorphous domains takes place during radiation-damage annealing, Geisler et al. (2001) and Geisler (2002) used this model for estimating the activation energies of the radiation-damage annealing stages II and III of zircon. The DAE model assumes that the annealing process draws from a distribution of activation energies. It is applied to processes involving sub-reactions with different activation energies and has been used for describing hydrocarbon decomposition and fission-track annealing (Lakshmanan et al., 1991;Lakshmanan and White, 1994). The fractional repair is expressed as follows: k0 is a frequency factor and G(E) a Gaussian distribution of activation energies E with mean E0 and standard deviation σ.
We fitted both models by minimizing the sum squared Φ-residuals (SSR). Table 1 lists and Figure 9 shows the results.
The (mean) activation energies are between 2.7 and 3.0 eV for the three bands and both models. In contrast, the k0 values span three orders of magnitude. The Avrami exponent is similar for Γ2 and Γ3 (n = 0.11) and lower for ΓER (n = 0.08). The standard deviations of G(E) are ~1 eV for the three Raman bands. The best-fit SSR are comparable for all models with the lowest values for ΓER. The overall agreement of predicted and measured Φ values is close to 1:1 for all experimental conditions (Figure 9). The SSR surfaces plotted against log k0 and mean EA show a distinct trough of low SSR that includes the best-fit parameters. We estimate the closure temperatures Tc with the approach of Dodson (1979) for fission-tracks: The equation considers cooling through the closure temperature following a linear increase of 1/T with time; t50 is the time at which half the damage is retained. E is the activation energy (EA; JMAK) or its distribution (G(E); DAE).
Equation (5) is equated to the model Eqs.
(2), (3), and (4), rearranging and substituting 0.5 for Φ(t, T) (Appendix A): for the JMAK model and for the DAE model. Equations (6) and (7) are solved iteratively for Tc. The results for cooling rates of 10 K/Myr and 30 K/Myr are given in Table 1. As expected, Tc is higher for the faster cooling; the difference is ~12 °C. Values for Tc at 10 K/Myr cooling rate range from 260 to 370 °C. The Tc values for all Raman bands are higher for the JMAK than for the DAE models. For both, Tc is highest for Γ2 and lowest for ΓER; Tc for Γ3 is slightly lower than for Γ2. We interpret the more sensitive response of the external rotation band to annealing compared with ν2(SiO4) and ν3(SiO4) to the stronger Si-O bonds within the SiO4 tetrahedra and weaker Zr-O bonds between the tetrahedra (Dawson et al., 1971).
The linear troughs in Figure 9 reflect a trade-off between EA (E0 for DAE models) and k0. Different parameter pairs fit the data equally well due to the limited range of laboratory annealing times and temperatures (Mialhe et al., 1988;Lakshmanan et al., 1991). The trade-off is a problem for the extrapolation of the experimental data to geological timescales, since Tc varies along the trough.  (2002) JMAK models for stage II and III annealing. Their Avrami exponent (n = 0.11) agrees with ours for Γ3. Their activation energy is ~3.8 eV for stage II and ranges from 6.4 to 6.9 eV in stage III; their log k0 is 9.3 for stage II and >15 in stage III. The differences result mainly from the trade-off between EA (E0) and log k0 and do not necessarily reflect different kinetics. Moreover, most of our data are from annealing stages I and II, whereas those of Geisler et al. (2001) and Geisler (2002) are from stage II and stage III. Their results and those of Ginster et al. (2019) suggest that stage I annealing requires a lower activation energy than stages II and III which could also in part account for the lower activation energies obtained from our models. The variation of Tc along the SSR troughs in Figure 9 is also the probable reason for the different Tc estimates for the JMAK and DAE models. There is no independent physical evidence for either model, and both models fit our experimental data equally well (Table 1). Therefore, we assume the DAE value as the lower limit and the JMAK value as the upper limit of the Tc range for each Raman band. of Tc (160 to 650 °C) is in part due to the different approaches. That of Deliens et al. (1977) resulted from comparing radiation-damage ages of Precambrian zircons, calculated from an internal bending IR band, with the ages determined with established geochronometers. The IR ages tended to be higher than the corresponding titanite U-Pb ages (Tc ≳ 650 °C, Stearns et al., 2015) and whole-rock Rb-Sr ages, but were mostly higher than mica and feldspar Rb-Sr ages (Tc ~ 320 to 575 °C, Harrison and McDougall, 1980;Giletti, 1991). The zircon radiation-damage Tc estimate of Mezger and Krogstad (1997) is based on their observation that zircons that remained below 600 to 650 °C during parts of their geological history experienced Pb-loss by Pb-leaching from metamict zones. ages (Tc ~ 320 °C, Harrison and McDougall, 1980) for the same units. Pidgeon (2014) (2014) and Deliens et al. (1977). Figure 10b shows the partial annealing zones for the JMAK models for Γ2, Γ3, and ΓER. The partial annealing zone temperatures are highest for Γ2 and lowest for ΓER. Under isothermal holding for >1 Ma, partial annealing occurs at temperatures as low as 200 °C, and full annealing requires temperatures above 450 °C. The low-temperature boundary is in agreement with the stage I annealing temperature of Pidgeon (2014) but higher than that of Jonckheere et al. (2019); the upper boundary is consistent with full annealing at 600-650 °C assumed by Mezger and Krogstad (1997).

Conclusions
The results of our isochronal and isothermal annealing experiments indicate that the ν1(SiO4), ν2(SiO4), ν3(SiO4), and external rotation Raman bands at 974, 438, 1008, and 356 cm -1 of radiation-damaged zircon anneal differently with respect to the bandwidth (Γ) and band position (ω). Γ decreases for all Raman bands during annealing while ω increases, but ω2 drops to lower wavenumbers during the first annealing stage, increasing again from the second annealing stage onwards. The different annealing trajectories can help to detect partial annealing in natural zircons.
Our ν3 annealing data on volcanic zircons are consistent with those of Ginster et al. (2019) Dodson (1973) defined the closure temperature Tc as the temperature of a parent-daughter system at the apparent age of a rock. For fission tracks, Dodson (1979) equates the time for 50 % annealing at the closure temperature to the cooling time constant defined for a cooling following a linear increase of 1/T: κ is the Boltzmann constant and EA is the activation energy of the annealing process at 50% annealing. For the Johnson-Mehl-Avrami-Kolmogorov model, the fraction of annealing Φ(t, T) is given by: k0 is a frequency factor, EA the activation energy and n the Avrami exponent.
Rearranging (A2): (A5) is solved iteratively for Tc, given the model parameters EA, k0, and n in Table 1, and assuming a cooling rate dT/dt.
For the distributed activation energy model, Φ(t, T) is given by: G(E0, σ) is the Gaussian distribution of activation energies with mean E0 and standard deviation σ; k0 is a frequency factor.