Three types of re-equilibration experimental setups (
Figure 8) were described by Doppler et al. [
10], Doppler and Bakker [
11] and Bakker and Doppler [
12]: (1) modifications of H
2O-rich fluid inclusions in a D
2O environment (
Figure 8a); (2) modifications of H
2O-NaCl-rich fluid inclusions in a pure H
2O environment (
Figure 8b). In addition, a series of “blank” re-equilibration experiments was performed (
Figure 8c), i.e., H
2O-rich fluid inclusions were re-equilibrated in a pure H
2O environment. Most of the experiments were performed within the α-quartz stability field (see
Table 1 and
Table 3), whereas
GMR-010 and
GMR-013 were performed within the β-quartz stability field. Modifications of fluid inclusions are evident and recorded by changes in homogenization temperatures, melting (or dissolution) temperatures, inclusion shape, inclusion size and Raman spectra. Gases such as H
2 and CH
2 were not detected in fluid inclusions after re-equilibration experiments. The use of binary fluid mixtures, i.e., H
2O-D
2O and H
2O-NaCl, allows an accurate characterization of processes such as diffusion and total volume changes.
5.1. “Blank” Re-Equilibration Experiments
A series of “blank” re-equilibration experiments was performed to illustrate that the experiment method itself does not cause modifications of the properties of fluid inclusions. These experiments were performed in similar temperature and pressure conditions with the same fluid as in the original synthesis experiments (
GMR-004g,
GMR-009b and
GMR-010b in
Table 3).
Two “blank” re-equilibration experiments were performed in the α-quartz stability field at 600.6 °C-336.3 MPa (
GMR-004g) and 624.8 °C-279.1 MPa (
GMR-009b). Re-equilibrated inclusions from
GMR-004g homogenize at similar temperatures as after the original synthesis (
Figure 3 in Bakker and Doppler [
12]), which confirms the reliability of the experimental method. The experiment
GMR-009b reveals insignificant lower homogenization temperatures after the “blank” re-equilibration experiment (
Figure 6 in Doppler and Bakker [
11]). This minor modification is caused by an unintended internal under-pressure of −11.2 MPa (
Table 4). This relatively low pressure in inclusions (270 MPa) is caused by a minor pressure difference between argon gas in the pressure line and the fluid pressure in the Au-capsule (see
Section 3) during the synthesis. A minor modification to higher fluid densities (i.e., to lower
Th) is expected if the inclusions are adapted to the external fluid properties in the re-equilibration experiment.
The “blank” re-equilibration experiment in the β-quartz stability field at 674.9 °C and 322.6 MPa (
GMR-010b) reveals a significant change in homogenization temperatures (
Figure 6 in Doppler and Bakker [
11]). The original fluid inclusions reveal homogenization temperatures that exceed the expected values by about 5 °C (
Table 2), due to the previously-mentioned pressure differences between argon gas and fluid in the capsule (see
Section 3). Consequently, during the re-equilibration experiments, the inclusions have an internal under-pressure of about −9.6 MPa (
Table 4). Similar to the “blank” experiment in the α-quartz field, modification of the fluid inclusion density would result in lower homogenization temperatures, i.e., towards higher densities. However, the observed modifications are significantly higher homogenization temperatures corresponding to lower densities (
Figure 6 in Doppler and Bakker [
11]). An additional process must have been activated in the β-quartz field experiment, which was absent in the α-quartz field experiment, which is able to modify fluid inclusions even in “blank” experiments. It is most likely that the α-β-quartz phase transition is causing this minor modification in fluid inclusion density, corresponding to a total volume increase of about 1% by the induction of micro-cracks or diffusion of H
2O during the transition.
5.2. Synthesis in H2O and Re-Equilibration in D2O
A series of re-equilibration experiments was performed with
GMR-004 and
GMR-002 at about 600 °C and 336 MPa in a pure D
2O environment (
Table 3). The induced gradients include only H
2O-fugacities and D
2O-fugacities, whereas the pressure difference between fluid inclusions and the Au-capsule can be neglected (
Table 4). The expected diffusion of H
2O out of inclusions and D
2O into inclusions was tested with a variety of run-times (29.8, 125, 450.7 and 960 h,
Figure 9a,b) and temperatures (~300, 400, 500 and 600 °C,
Figure 9c). Complete re-equilibration at 600 °C, i.e., when the internal H
2O is completely replaced by D
2O, must result in a decrease of
Th (down to 288 °C) (
Table 5) and an increase of
Tm (up to +3.8 °C). Incomplete re-equilibration would result in intermediate values, according to the ideal mixing behavior of H
2O and D
2O. The completeness of diffusion is, however, dependent on the parameters in a classical diffusion model [
7,
8], such as duration, temperature, fluid inclusion size and distance to surface. A fluid inclusion assemblage will be modified according to these parameters and may therefore contain a large variety of
Th and
Tm values (
Figure 9), corresponding to a large variety in D
2O content in one single experiment. Up to 10 mole% D
2O (
Tm = 0.4 °C,
Figure 9a) is detected in fluid inclusions after the 29.8-h re-equilibration experiment, with similar
Th (slightly increased values) as in the original synthesis experiment. The 125.0-h re-equilibration experiment resulted in both significantly higher
Th and
Tm values (
Figure 9a), up to 298.1 °C and +2.7 °C, respectively. These temperatures do not correspond to the expected ideal mixing behavior of H
2O and D
2O (dashed lines in
Figure 9) and were caused by the difference in the diffusion constant of H
2O and D
2O. For this specific run-time, relatively “slow” diffusion of D
2O into the inclusion compared to “fast” H
2O diffusion out of the inclusion results in a temporary density loss [
10]. For longer run-times (450.7 h,
Figure 9a; and 960 h,
Figure 9b), modifications of
Th and
Tm (D
2O concentration) approach the ideal mixing line between pure H
2O and pure D
2O inclusions.
The application of a classical diffusion theory [
8] predicts a variation in fluid inclusion modifications according to depth (distance inclusion-quartz surface) (
Figure 10) and fluid inclusion size (
Figure 11).
Figure 10 illustrates that deep inclusions reveal less modifications than shallow inclusions, but these modifications are not uniform at specific depths. The variation in fluid inclusion size is causing this spread at specific depths (
Figure 11). For example, large inclusions that are located close to the surface are less modified than small inclusions at similar depths (
Figure 12a). At deeper levels, the large inclusions may show only minor modifications, whereas smaller inclusions are considerably modified. The distance between the quartz surface and fluid inclusions may be overestimated if the remaining open crack space, in which the fluid inclusions were formed, is neglected (
Figure 12b). These types of fluid inclusions are marked with red symbols in
Figure 10 and
Figure 11 and contain more D
2O than expected from their distance to the surface. For example, the inclusions that contain 26–32 mole% D
2O in
Figure 11c (red symbols) correspond to a distance of 46–56 µm (
Figure 11b) to the remaining open crack, whereas they were classified to a larger distance quartz surface-inclusion (125–135 µm).
The factor temperature in diffusion coefficients from classical diffusion theories was also investigated by Doppler et al. [
10]. The experiment at 400.6 °C-336.7 MPa did not reveal any D
2O in re-equilibrated fluid inclusions after 460 h of experimentation (
Figure 9c). Up to 26 mole% D
2O was detected in small inclusions close to the surface in the experiment at 499.7 °C-337.3 MPa (
Figure 9c). The efficiency of diffusion is, therefore, limited to temperatures between 400 and 500 °C in our experimental setup, which may correspond to the previously mentioned “closure temperature” at about 336 MPa (see also
Figure 7 in Doppler et al. [
10]). D
2O was not detected in synthetic fluid inclusions after similar re-equilibration experiments at lower temperatures (
GMR-006a).
One specific H
2O molar volume (27.5 cm
3/mol) in fluid inclusion assemblages was selected to re-equilibrate in both the α-quartz and the β-quartz stability field (
Figure 13). The re-equilibration was performed in a D
2O environment (
GMR-009a,
GMR-010a,
GMR-013a in
Table 3). Detailed results of these experiments are given in Doppler and Bakker [
10]. The expected modifications of fluid inclusion properties correspond to modifications observed in the previously-described experiments at about 600 °C and 336 MPa in the α-quartz stability field. Complete replacement of H
2O by D
2O (diffusion) in fluid inclusions would result in lower
Th: 316.9 °C (Δ
Th = −3.7) for
GMR-009a and 312.0 °C (Δ
Th = −5.5) for
GMR-010a, with ice melting temperatures of +3.8 °C. Incomplete re-equilibration results in mixtures of H
2O-D
2O with
Th and
Tm values according to ideal mixing behavior (dashed lines in
Figure 14).
The modifications of fluid inclusions in experiment
GMR-010a (β-quartz) are more pronounced than in
GMR-009a (α-quartz), due to the differences in the experimental temperatures. Most inclusions in
GMR010a reveal a nearly complete replacement of H
2O by D
2O, whereas
GMR-009a has only D
2O contents up to 68 mole%. Similar to the “blank” experiment with
GMR-009,
Th values are insignificantly lower (red symbols in
Figure 14) than the expected values (red dashed line in
Figure 14), due to lower fluid pressures inside the Au-capsule than the argon pressure in the pressure line (see
Section 3). Although the modifications of fluid inclusions in
GMR-010a result in lower
Th values (green symbols in
Figure 14), they are significantly higher than the expected values (green dashed line in
Figure 14). Again, a similar result was observed in the “blank” experiment, corresponding to the interpreted increase of inclusion total volume due to the α-β-quartz phase transition. Enhanced permanent modifications in total inclusion volume at this phase transition were also identified by Schmidt et al. [
9] with extremely short experimental run times (less than 400 s).
The size of fluid inclusions defines the variation in the amount of the modification for both experiments (
Figure 15). Relatively large inclusions (≈600 µm
2) contain maximally 15 mole% D
2O, whereas relative small inclusions (≈60 µm
2) in
GMR-0009a contain up to 70 mole% D
2O. The large variation for a specific size is defined by the distance between inclusion and quartz surface. A similar effect is observed in
GMR-010a, where small inclusions contain up to 100 mole% D
2O and large inclusions only up to 45 mole% D
2O.
5.3. Synthesis in H2O-NaCl and Re-Equilibration in H2O
The original synthesis of H
2O-NaCl-rich fluid inclusions [
12] resulted in a relative unexpected broad span of densities (
Table 2,
GMR-005,
GMR-011 and
GMR-014). Consequently, the re-equilibration conditions in a pure H
2O environment and a constant pressure of about 337 MPa resulted in a variety of minor pressure gradients between inclusions and the Au-capsule, in addition to H
2O-fugacity gradients (
Table 4). The average pressure gradients are negative, corresponding to internal under-pressures.
The application of a classical diffusion model [
8] for
GMR-005 would finally result in a minor dilution of the aqueous solution in fluid inclusions, from 19.8 down to 19.4 mass% NaCl, a minor decrease in molar volume (−1.23%) and an increase in internal pressure (from 336 to 359.5 MPa) in the experimental conditions. These minor modifications correspond to higher
Tm values (−16.0 °C) and lower
Th values (321.5 °C), which is in contrast to our observations (
Figure 16). Only a few of the re-equilibrated fluid inclusions from the short run-time experiment (
GMR-005c, open symbols in
Figure 16) reveal modifications according to a classical diffusion model. However, most inclusions reveal preferential loss of H
2O, resulting in higher salinities, corresponding to lower
Tm values and higher
Th values. The longer run-time experiments (
GMR-005a, green symbols in
Figure 16; and
GMR-005b, red symbols in
Figure 16) illustrate fluid inclusion modifications of
Th and
Tm that are completely in contrast to the diffusion model, but reveal a linear trend away from the expected values.
The combination of homogenization temperatures and dissolution temperatures of fluids in the binary H
2O-NaCl system can be used to calculate modifications in composition, molar volume and total volume of fluid inclusions [
12]. The relative amount of H
2O loss can be calculated from modifications of
Tm, assuming that H
2O is the only mobile component. The loss of certain amounts of a component must lead to an increase of molar volume in fluid inclusions with a constant total volume. Small amounts of H
2O loss would already result in intensive modifications of
Th (see Table 6 in Bakker and Doppler [
12]). The observed
Th values do not correspond to these calculated modifications and are much lower than expected (i.e., lower molar volumes). Consequently, these lower molar volumes can only be obtained by the reduction of the total volume of fluid inclusions. The experimental data from
GMR-005a,
GMR-005b,
GMR-005c,
GMR-011a and
GMR-0014a have been used to calculate the amount of preferential H
2O loss and the amount of total volume loss, according to these considerations (
Figure 17). The fluid inclusions from the relative short run-time experiment
GMR-005c (120.4 h) revealed an average preferential H
2O loss of 3.0% and a total volume decrease of 3.4 vol %. The intermediate run-time experiment
GMR-005a (458.9 h) revealed an average 10.3% preferential H
2O loss and 9.7 vol % total volume decrease and the long run-time experiment
GMR-005b (961.9 h), a 17.5% preferential H
2O loss and a 16.2 vol % total volume decrease. The re-equilibration experiments
GMR-011a and
GMR-014a were consistent with these results. In summary, the replacement of one mole H
2O from the fluid inclusion with approximately one mole quartz from the host crystal resulted in the observed modifications of
Th and
Th. The molar volume of quartz and H
2O were nearly equal in these experiments conditions, which resulted in a one-to-one mole alteration. This process is not triggered by fugacity coefficients, but is most likely caused by the internal under-pressure in fluid inclusions. This quartz-fluid exchange is a time- and temperature-dependent process, similar to their significance in diffusion processes, but this is a much stronger process to modify fluid inclusion properties than simple diffusion according to fugacity gradients.