3.3 Discussion
3.3.1 Oxygen diffusion
Experimental studies on oxygen diffusion in apatite are scarce. Farver and Giletti (1989) predicted oxygen to diffuse faster than REE (Nd, Sm). They studied oxygen self-diffusion at hydrothermal conditions from 550 to 1200°C and oxygen isotopes were measured by depth profiling using a Cameca ion microprobe. Diffusion of oxygen along the c axis of apatite was found to be 3 orders of magnitude faster than perpendicular to the c axis.
No published study has investigated oxygen diffusion in apatite in a geological setting. In a study on the resetting of various isotopic systems in a prograde metamorphic sequence (Hammerli et al. 2014), oxygen data were acquired (Hammerli, pers comm.). The results showed that for rocks experiencing a maximum of 350°C, the detrital δ18O signature in apatite was preserved, whereas
at ~420°C, apatite that retained its detrital Sm-Nd isotopic signature had a homogenised oxygen isotope composition. The conservation of Sm-Nd isotopic signature shows that this homogenisation was likely not due to recrystallization, but to solid-state diffusion of oxygen.
Closure temperature modelling following the diffusion coefficient from Farver and Giletti (1989) for the C-axis (activation energy = 205 kjmol-1, pre-exponential factor = 9x10-9 m2s-1) using the
formulations of Ganguly and Tirone (1999; 2001) was done in collaboration with Michael Jollands. The model produced for spherical grains of 40 μm diameter (Figure 1 - 5) yields bulk closure temperatures between 340 and 440°C for most geologically relevant cooling rates , which is consistent with the data provided by J. Hammerli (pers. comm.).
Figure 1 - 5 Model of Temperature of Closure of apatites for self-diffusion of oxygen, for a grain diameter of 40 μm according to geologically relevant cooling rates, calculated using data by Farver and Giletti (1989).
Given that closure temperature is an estimate of the bulk closure of a crystal, and we measured δ18O in situ observing microscale contrasts within a grain, a 1D finite difference approximation
to Fick’s second law was also modelled, following, e.g. Crank (1975) and Costa et al. (2008). Inital conditions were assumed to be a step function, the boundary kept constant throughout the model duration (assuming an infinite external reservoir), and with constant diffusion coefficients (isothermal model). This model is created with the assumption that the homogenisation of δ18O
signatures is akin to the diffusion of a trace element into the crystal: the change in lattice created by the introduction of the new atomic species is negligible (here change in permil concentration of a nearly identical atom) and does not cause the diffusivity to change with concentration.
The time taken to homogenise a 1D transect along the c axis of a 40 μm grain, is <1Myr at 500°C (Figure 1 - 6, Table 1 - 4) in both the case where it is standing in a matrix, and if it is surrounded by an overgrowth. In contrast, at 400°C (Table 1 - 4), a >10% zoning can persist for >10 Myr.
Table 1 - 4 Time of δ18O homogenisation for a small apatite crystal . Homogenisation is defined as the time when the central cell reaches 90% of the boundary value.
T (°C) core (40 μm) core + overgrowth (40 μm+40 μm)
550 15 kyr 104 kyr 500 105 kyr 724 kyr 450 949 kyr 6 559 kyr 400 11 943 kyr 82 872 kyr 350 227 000 kyr 1 570 570 kyr 300 320 340 360 380 400 420 440 460 1 10 100 1000 Tc (C)
Figure 1 - 6. Relative concentration profiles along the C axis of modelled apatites, showing the evolution of relative concentration contrasts in the crystal at 500°C. The final time step represent the time required for a 10% contrast to be preserved. This corresponds to the minimal difference analysable by SHRIMP (ca. 1 ‰), in the case of the maximal initial δ18O contrast expected in the Halilbağı unit: ca. 10 ‰, it thus represents a maximum homogenisation time.
Based on these two diffusion models and the preliminary data of Hammerli (pers. comm.), it is expected that small prograde or magmatic apatite cores in the Halilbağı samples (20 µm size) were reset during the time apatite resided at 500°C and above (up to 580°C, see details in Chapters 3&4) during prograde evolution to exhumation of the Halilbağı unit. This result is quite robust since this evolution happens on a heating trajectory so that the maximum temperature controls the diffusion evolution, without much influence of the heating rate.
In contrast to the homogenised small cores, a ca. 5 ‰ core-rim zoning in oxygen isotopic composition is observed in apatite grains from sample SHB12B, which have a diameter of 200- 250 μm. In this sample, the minimum δ18O contrast as sampled by garnet is 6 ‰ (see Chapter 4),
which indicates that single apatite crystals preserve at least 80% of the δ18O heterogeneity. The
working hypothesis for the creation of such contrasts (see Chapter 4) is a metasomatic event occurring at the start of exhumation, altering the initial WR of ca +8 ‰. This fluid event created recrystallization rims in all major rock-forming minerals (garnet, omphacite and phengite) that yield a reactive WR δ18O of ca. 14 ‰, and then the sample reequilibrated during cooling. This,
scenario is different from cooling-only, where δ18O contrast is only created by changes in
fractionation behaviour according to T decrease (e.g. Eiler et al., 1992). δ18O-zoned apatites might
be created by crystallisation of a high δ18O rim around low δ18O cores similarly to garnet, or by
diffusion of surrounding 18O into unzoned low δ18O apatites.
In order to explore conditions that would allow the preservation of 80% of the initial δ18O contrast
in single apatite crystals, oxygen diffusion was also modelled in a cooling system, starting at the T of metasomatism (450-500°C, see Chapter 4 for more details) and cooling assuming the relationship between 1/T as time is linear (Figure 1 - 7c, as commonly done in conductively cooling systems, e.g. Ito and Ganguly, 2006). This assumption is likely only crudely modelling the cooling rate, as the dynamics of the top of the subduction plate would allow more complicated temperature trajectories by juxtaposition of cooler or warmer units (e.g. Whitney et al., 2014). One-dimensional profiles along the C axis were again modelled using the finite difference approximation for an initially homogenous grain of 240 μm across with constant boundary conditions, with T and thus diffusion coefficients changing at each time step. A typical diffusion profile is shown in Figure 1 - 7b, and the core concentration x is tracked trough time following different cooling rates in Figure 1 - 7a, showing much more homogenisation at lower cooling rates (cooling parameter: log eta= -17.8), and virtually no homogenisation at high cooling rates (log eta= -16.5). Tables showing how residence times above a certain temperature and maximum x change according to cooling rate (Tmax is constant, x max changes) and Tmax (x max is kept constant and the cooling rate changes) are also presented in Figure 1 - 7.
In order to retain isotopic heterogeneities of the order of 80% of the initial step, the apatites need to have cooled to 400°C within ca 3.3 My for a starting temperature of 500°C (log eta= -17.3). The time increases for lower Tmax: if metasomatism happened at 475°C, a contrast of 80% can be retained for 7.4 My on a conductive cooling trajectory (log eta= -17.7).
Figure 1 - 7. a. Evolution of the apatite core concentration (x) according to time. b. Example of a relative concentration profile along the C axis corresponding to the conditions symbolised by the star (log eta = -17.8, t = 832 kyr). c. Evolution of temperature according to time for different log eta values. The tables correspond to the set of time and concentration values corresponding to different models (one line per model), first for a constant Tmax and different cooling rates, then for varying Tmax,, with x max set to 0.2.
However, at temperatures above 500°C, this time is greatly reduced, e.g. 708 ky for a Tmax of 550°C (log eta = -16.15). This is also the case if the apatite stays at 500°C on a slow cooling trajectory (e.g. log eta= -17.8), in which case 80% contrast is lost within 832 ky and with further cooling results in an end contrast of 40% only. It is thus likely that the WR change in δ18O
occurred shortly before the apatites were cooled and exhumed quickly, or during a slower exhumation but at temperatures lower than 500°C (more details given in Chapter 4). The cooling rate modelled here for a starting temperature of 500°C is compatible with a plate-motion speed of exhumation or faster, as proposed by previous authors for the Halilbağı unit (Whitney and Davis 2006; Whitney et al. 2014; Fornash et al. 2016).
It is to note that the hypothesis of an infinite exchanging reservoir providing constant boundary conditions could not apply to these minerals, similarly to a cooling only scenario explored by Eiler et al., (1992). Indeed, at ca. 450°C or even 500°C, most rock-forming minerals are closed for diffusion (e.g. garnet, omphacite), which would restrict the exchanging reservoir for the equilibrating apatites, if a fluid phase is absent. Moreover, the studied apatites are small (200-250 μm) compared to rock-forming minerals and thus might have been included in closed phases. This could explain some of the grain-to-grain variability observed in SHB12B: small grains can preserve core-like signatures (inclusion in the core of closed phases), and large grains can preserve rim-like signatures (new growth only). This shows that the interpretation of δ18O signatures on
the exhumation path is much less robust than on the prograde path, especially when T is nearing the closure temperature of the investigated minerals. As such, the population of measured apatites may or may not record metasomatic oxygen contrasts, according to their textural position. Nevertheless, the models yield more robust information about the homogenisation within single apatite crystals, which indicates that the temperature of metasomatism is likely lower than 500°C, and/or the exhumation relatively quick (less than 1.5 Ma spent >450°C) in order to preserve the observed contrasts.
The oxygen isotopic composition of apatite and garnet was measured together in 8 samples: SHS3, SIB50B, SHB53, SHB45, SHS44A, SHB12B and SHB05. In samples that yield homogenous garnet and apatite δ18O (SHS44A, SHS44B, SHB05), Δ18O
garnet-apatite is around 2 ‰, a bit higher
for SIB50B (3 ‰), where garnets are tiny, Mn-rich and likely crystallised earlier on the prograde path at lower temperature. According to the increment method calculations of Zheng (1991, 1993), this would correspond to apparent equilibrium temperatures of 500 and 300°C respectively (Figure 1 - 8). SHS44A and SHS44B record temperatures ≥500°C, which indicates that diffusion played a limited role on the retrograde path for these samples, as significant re-equilibration would lead to a higher δ18O in apatite, a higher Δ18O
garnet-apatite and thus lower apparent equilibration
Figure 1 - 8. Relation between apatite and garnet δ18O measured in the same sample, where apatite shows REE depletion indicating garnet presence. Lines indicate fractionation behaviour at varying temperatures as modelled by (Zheng 1993a; Zheng 1996).
The results of diffusion modelling and comparison with garnet thus indicate that prograde δ18O
zoning of apatites is lost during a short residence at peak temperature (550-580°C), but that δ18O
zoning created on the retrograde path from ca. 500°C can be preserved in the Halilbağı apatites.
4 Monazite
Oxygen isotopes in monazite were explored for the study of the timing of fluid circulation in the Dora Maira whiteschists. The results of this work were published in Chemical Geology (Rubatto et al. 2014, Appendix A1) as part of the development of matrix effect calibration, the context of the case study is found in Chapter 2 (Gauthiez-Putallaz et al. 2016, Appendix A2). Here, the main results are summarized and discussed in light of a recent study proposing a new correction scheme for oxygen isotope analysis in monazite (Didier et al. 2017).