Introduction

Various climate proxies have been used to estimate the variability of the surface air temperature prior to the existence of instrumental records1. They include global proxies, for instance the isotopic ratio between 18O and 16O in ice cores2,3 or in shell of fossil marine organisms4,5; and local proxies, such as tree rings studies6,7,8, palynological studies9 and fluid inclusions (FIs)10,11,12. FIs are present in virtually all rocks on Earth. A record of the fluid chemistry and environment at the time of rock formation can be kept in FIs for billions of years13. FIs are thus considered to be direct samples of the volatile phases which circulated through the Lithosphere over the course of the Earth’s history. From their study some general rules have emerged, which have led e.g. to a model of fluid distribution in the earth’s crust and upper mantle14,15,16 or to the reconstruction of the composition of sea-water through time17,18,19,20,21. FIs are among the most useful witnesses of many natural processes on Earth in which fluids play a role.

FIs are small cavities (with a typical size from 1 to 100 μm) in minerals. The usual assumption about the path followed in the pressure-temperature plane by the liquid in a FI is schematically illustrated on Fig. 1a. We are interested in FIs that were initially filled with a homogeneous fluid during their formation in the host mineral at the formation temperature Tf and pressure Pf (point A in Fig. 1a). If cooled, the monophasic FI follows a curve (ABCD) that crosses the liquid-vapour equilibrium curve at a temperature TX (point B). Upon further cooling, the liquid often becomes metastable (curve BCD) and, usually, a vapour bubble nucleates (transition from D to E). When a bubble bearing FI is heated in a micro-thermometric study (curve EFB), the bubble shrinks and eventually disappears at the homogenization temperature Th (point B). Here Th = TX. For a rigid host mineral, the density of the liquid along AB is constant. Hence, the isochore starting at TX from the liquid-vapour equilibrium curve is used as the locus of possible formation temperatures (and corresponding pressures)22. To determine Tf, another piece of information is needed, such as the local geothermal gradient, which gives the relation between depth, pressure and temperature. Tf then corresponds to the intersection of the isochore and the geothermal gradient curve. If the pressure is high, TX can be much lower than Tf. But for rocks formed at atmospheric pressure, relevant for paleoclimate, one has Tf = TX. If the equality Th = TX holds, the bubble disappearance temperature Th would thus provide the temperature Tf prevailing during the mineral formation.

Figure 1
figure 1

Schematic path followed by fluid inclusions (FIs).

Note that the axis are not to scale. (a) Commonly assumed path. A monophasic FI is formed at a temperature Tf and pressure Pf (A). During cooling, the pressure of the liquid is reduced along an isochore (curve AB) and the liquid becomes metastable with respect to the vapour phase (curve BCD). This may lead to nucleation of a vapour bubble (transition from D to E), producing a biphasic FI (E). During heating, the FI follows the bulk liquid-vapour equilibrium (LVE) (curve EFB), the bubble shrinks and eventually disappears at Th = TX (B). This assumption is valid for FIs with low fluid density and large volume. (b) Path modified by surface tension effects. Surface tension and the associated Laplace pressure lead to LVE at pressures below the bulk LVE (path EF)33. Eventually the bubble collapses (transition from F to C) at a temperature Th, bringing back the FI on the isochore (curve ABCD). Surface tension thus causes Th to be strictly less than TX. This effect is relevant for FIs with high fluid density and small volume33. In contrast, warming the monophasic FI along the isochore and finding with Brillouin spectroscopy the crossing point B with the bulk LVE curve gives the correct TX.

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However, the use of Th for this purpose suffers from two important limitations. The first is simply the absence of bubble; this situation can be due to a weak metastability (i.e. high energy barrier for bubble nucleation and low nucleation rate) that is not sufficient to lead to bubble nucleation. Previous research has concentrated in developing methods to artificially stimulate bubble nucleation23,24,25,26,27,28. The standard procedure consists in cooling the samples below −10 or −20 °C for several days or even weeks10,25,29. But there are fundamental limitations with this method such as the potential stretching of the inclusion and its neck-down during repeated cycles of cooling/heating30,31. A more recent technique consists in focusing femtosecond laser pulses to overcome metastable states at room temperature32. In this case the threshold laser intensity must be controlled because it can damage the mineral and thus change the volume of the inclusion, or cause leakage or stretching11. The above mentioned methods may work if the bubble is absent for kinetic reasons, that is when the bubble does not appear spontaneously in an observable time without stimulation because the nucleation rate in the metastable liquid is too low. However, the bubble can also be absent for thermodynamic reasons, when the free energy of the biphasic FI is always higher than that of the monophasic FI. This situation, due to surface tension effects33,34, occurs for FIs small in size and which contain a fluid at high density. Even if a bubble was created in such a system, it would disappear immediately and the FI would become monophasic again. Even for FIs in which the state with bubble (naturally present or nucleated by one of the above means) can be thermodynamically stable, a second limitation is a possible bias when assuming Th = TX. Because of the small radius of curvature of the bubble, surface tension induces a Laplace pressure difference between the liquid and vapour phase, which modifies the liquid-vapour equilibrium (Fig. 1b). The bubble collapse (transition from F to C) then occurs at Th < TX. A correction based on a detailed thermodynamic model has been derived33. However, as the model requires an accurate formulation for the free energy of the fluid, it was applied only to the case of pure water, for which an accurate equation of state is available. Further sources of uncertainty arise from the need to measure the bubble radius and from the fact that the state with bubble remains metastable in a range of temperatures. All these effects make Th lower than the actual TX, with a larger shift (up to several degrees) for smaller inclusions and/or denser liquids.

We propose to overcome the above limitations using Brillouin spectroscopy to directly determine TX without the need for a bubble and its Th. Brillouin scattering from a liquid results from the inelastic interaction of light with the thermal density fluctuations (acoustic waves) of the liquid35. The frequency of the scattered light is shifted from that of the incoming light by an amount ΔfB proportional to the sound velocity in the liquid. ΔfB thus depends on the liquid, its temperature and density. For the liquid along its liquid-vapour equilibrium (LVE), the Brillouin shift as a function of temperature is known from calculations, or calibration measurements (see Methods). Now, when a monophasic FI is warmed or cooled, the liquid that it contains does not follow the LVE, but an isochore (see Fig. 1). ΔfB along an isochore at density ρ is a function of T uniquely determined by ρ. Therefore, measuring ΔfB(T) for the monophasic FI defines a curve that, by definition, crosses at TX (see Fig. 1). Brillouin spectroscopy thus provides a non-destructive method to directly measure TX in monophasic FIs containing pure or salty water, without the need to nucleate a bubble. Hence it is not biased by surface tension effects.

The aim of this paper is to provide a proof of concept of the method by measuring TX on samples in which Th can also be measured and such that the assumption Th = TX is valid. To this end, we have selected 4 FIs in quartz crystals (see Fig. 2a). Because these FIs where formed at a pressure Pf above atmospheric pressure, they are not directly relevant to paleoclimatic reconstruction. Yet their TX are well defined and can be obtained based on the measured Brillouin shifts. Moreover, because the quartz host is robust, a bubble can be nucleated in the FIs by cooling-heating cycles, without damaging the crystal nor changing the FI volume. The Th of each FI can then be measured by traditional microthermometry. For the fluid density and volume of the selected FIs, surface tension effects are negligible33 and Th = TX. Therefore the comparison between measured Th and TX provides a benchmark for the proposed method.

Figure 2
figure 2

Fluid inclusions studied in this work.

(a) Microphotographs of FIs used in this study (scale bars: 7 μm): one synthetic (FI1) and two natural (FI2 and FI3) FIs containing pure water and one natural FI (FI4) containing dissolved salts. (b) Example of Brillouin spectrum (here recorded for FI3 at 50 °C). Error bars show the shotnoise equal to the square root of the counts. The red curve is a fit with equation (1), which yields the value of ΔfB = 7.746 GHz for this example.

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Results

FIs containing pure water

Three samples (FI1, FI2 and FI3, see Fig. 2a) were chosen among those for which it is possible to nucleate a bubble by cooling-heating cycles. The 3 FIs contained pure water, based on their melting points with a bubble present. A typical Brillouin spectrum is shown on Fig. 2b (see Methods for more details). ΔfB(T) was measured for each monophasic sample, leading essentially to a straight line (Fig. 3a). Two procedures were used to determine the temperature TX at which ΔfB(T) intersects the calculated LVE curve (see Methods). The first one used the full ΔfB(T) expression as a function of ρ based on formulations from the International Association for the Properties of Water and Steam (IAPWS) (see Methods). TX was deduced from a fit to the data with ρ as a free parameter (Fig. 3a). The second, simpler procedure, consists in fitting the difference to a straight line and find where it crosses zero (Fig. 3b). Table 1 shows that this second procedure agrees perfectly with the first one, while being simpler to implement.

Table 1 Comparison of the Th values obtain by direct observation of the bubble disappearance, with the TX values obtained with the Brillouin method, using two types of fitting procedures.
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Figure 3
figure 3

Determination of TX with Brillouin spectroscopy for FIs containing pure water.

(a) Brillouin shift ΔfB as a function of temperature for pure water. The solid black curve is along the liquid vapour equilibrium. The data points show ΔfB for FI1 (red diamonds), FI2 (green squares) and FI3 (blue circles). The dotted curves show fits of the data with ΔfB(T) calculated with formulations from the International Association for the Properties of Water and Steam (IAPWS) (see Methods) and treating the density ρ as a free parameter. The crossing point with the LVE curve gives for each FI TX and its uncertainty (see Table 1). (b) The difference is shown for each FI (same symbols as in panel (a)). A linear fit is performed on each data set (solid lines) to give TX as the temperature at which it crosses zero and its uncertainty (see Table 1).

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FIs containing salty water

Next we turn to the more general case of a FI containing an aqueous solution. As an example, we have chosen a FI from the Mont-Blanc (FI4, see Fig. 2a). For this location, the most abundant anion is by far chlorine and the dominant cation is Na+ (around 80% in molality), as determined by several techniques36. Therefore, to calculate the reference Brillouin shift , we have used data for pure NaCl solutions (see Methods). To obtain the total Cl− molality, we used Raman spectroscopy37 (see Methods). Molality is defined as the number of moles of Cl− per kilogram of water in the solution. We find it better to work with molality rather than molarity (number of moles of solute per volume of solution), because molality does not depend on temperature and pressure for a system of fixed mass such as a fluid inclusion. We checked that the Raman spectra at 20 °C were identical whether a bubble was present or not. We obtained a total Cl− molality mRaman = 1.25 ± 0.05 mol kg−1. For comparison, the spectra from pure water and a bulk solution of NaCl with m = 1.25 mol kg−1 are displayed on Fig. 4a: the latter spectrum is identical to the FI spectrum. As a further check, we also used Brillouin spectroscopy to measure the total Cl− molality. First, we calculate the reference Brillouin curve at temperature T and NaCl molality m from literature data (see Methods). We checked that our calculation agrees well with measurements on reference NaCl solutions (Fig. 4b). Then we took advantage of being able to nucleate a bubble in FI4. We measured ΔfB in the biphasic FI4 from 0 °C to Th (Fig. 4c). We then treat m in as a fitting parameter to reproduce the experimental values for ΔfB in the range 0–100 °C. The fit gives mBrillouin = 1.20 ± 0.03 mol kg−1, in excellent agreement with mRaman. This confirms the validity of our procedure. Moreover, Fig. 4c shows that our formula for (see Methods) agrees with the FI data even outside the range of available measurements for the sound velocity. We now have all the ingredients needed to define a general procedure to determine TX for a monophasic, salty FI. The total Cl− molality mRaman is measured by Raman spectroscopy and used to compute the reference Brillouin shift . Then, the Brillouin shift ΔfB(T) is measured on the monophasic FI. A linear fit to gives TX as the point where it crosses zero. We have shown above for pure water that this procedure was as accurate as using a full fitting of ΔfB(T). The result for TX for FI4 obtained in this way (Fig. 4c) matches well the Th value obtained by direct observation of the bubble disappearance (see Table 1), thus validating the procedure for salty FIs.

Figure 4
figure 4

Determination of TX with Brillouin spectroscopy for salt bearing FIs.

(a) Comparison of Raman spectra at 20 °C (all normalized to unit area). The blue curve shows the OH stretching band of pure water. The spectrum from FI4 (red) exhibits a decrease at low shift and increase at high shift, typical of dissolved salt. A standard procedure37 yields an equivalent NaCl molality mRaman = 1.25 ± 0.05 mol kg−1. The spectrum from a bulk aqueous solution of 1.25 molal NaCl is also shown (black) for direct comparison. (b) Brillouin shift ΔfB as a function of temperature for reference NaCl solutions. The curves designated by the solution molality m (in mol kg−1) were calculated from literature data (see Methods). They agree well with the corresponding experimental data (symbols). (c) ΔfB(T) for FI4, with (open symbols) or without (closed symbols) bubble. The thin black curve is the calculated for a NaCl solution with molality 1.20 mol kg−1. The thick red curve is the result of the linear fitting procedure on ; it intersects at TX. (d) Uncertainty δTX (± 1 standard deviation) on TX determined with Brillouin spectroscopy, as a function of TX. The solid curves were calculated with equation (4) (see Methods) for pure water and NaCl solutions with designated molalities (in mol kg−1). The marker shows the error on TX from the linear fitting procedure for FI3, as given in Table 1.

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The details of the above procedure are valid for FIs containing NaCl solutions. Different dissolved salts affect the properties of the solution in different ways. However, these differences remain small for Raman37, refractive index38 and sound velocity39, which are the ingredients needed to apply the procedure we propose. Therefore, the equations for NaCl solutions will provide a good approximation for other solutes. If a better accuracy is needed, the composition of salts in the FI must be known for the studied location, or determined. This can be done for example by measuring the eutectic point of the aqueous solution, by Raman analysis of the solution37,40 and of frozen salt hydrates41, or using other (destructive) techniques such as LIBS (laser-induced breakdown spectroscopy)36 or LA-ICP-MS (laser-ablation inductively coupled plasma mass spectrometry)42,43. Then reference solutions can be prepared in the laboratory to record a series of Raman and Brillouin spectra for calibration, as was done in the present work for NaCl solutions. The reference Brillouin shift may also be calculated from refractive index and sound velocity data of the given solution if available (see Methods).

Uncertainty on TX

The constant finite uncertainty on ΔfB translates into an increasing uncertainty on TX at lower temperatures (Table 1). This is due to the fact that, whereas the slope of ΔfB(T) along isochores remains nearly constant, the slope of increases with decreasing temperature. For pure water, the two slopes eventually become equal at the temperature of maximum density around 4 °C. This effect defines the only limitation of our method, for FIs made of pure water and having the lowest TX. As dissolved salts suppress the anomalies in water and in particular decrease its temperature of maximum density44, a better accuracy is obtained for FIs containing salt than for pure water. Literature data is available to calculate the uncertainty on TX in the range 5–40 °C and for molalities up to 1 mol kg−1 (see Methods). The result is shown on Fig. 4d. For pure water, the calculation agrees well with the error from the fit for FI3. The calculated uncertainty increases at low temperatures, but it is significantly reduced for salt solutions. For instance, at 12 °C, we expect an uncertainty of 5.8 °C for pure water and 2.5 °C for a 1 mol kg−1 NaCl solution. Molalities higher than 1 mol kg−1 would lead to an even lower uncertainty.

Discussion

Using FIs in quartz crystals, we have demonstrated the potential of our technique to uncover the value of TX for a monophasic FI, with an initially unknown salt concentration. This provides an alternative approach to the laser-induced nucleation of bubbles in monophasic FI32, with the following advantages: (i) the method does not risk damaging the inclusion, (ii) TX values measured with Brillouin spectroscopy do not have to be corrected for surface tension effects11,33, a correction that is available at present only for pure water. The application of the proposed technique to samples actually used in paleoclimate reconstruction (such as speleothems and evaporites) remains to be evaluated; this will be the subject of future work. If confirmed, the proposed paleothermometer would be particularly suitable for evaporitic deposits. Evaporites sediments in contact with water and air at the surface of Earth are able, by their rapid growth, to trap the fluids from which they precipitate (average precipitation rate in evaporitic basin is ca. 1 to 2 mm/year). The high salt concentrations in the trapped fluids are toxic for most organisms, preventing classical paleoclimatic reconstruction based on paleoecological and sedimentological analysis. The Brillouin paleothermometer, which becomes more accurate at higher salt concentrations, thus appears as a promising method to access seasonal temperature variations on Earth and sea surfaces.

Methods

Samples

We have studied one synthetic (FI1)45 and three natural (FI2, FI3 and FI4 from the Mont Blanc massif in the Alps) FIs in pieces of quartz, cut perpendicular to the c axis (to avoid birefringence effects46 in Raman spectroscopy), 300 and 200 μm thick, respectively and polished on both sides. The FIs had a rounded shape, with a diameter around 4 to 8 μm (see Fig. 2a). They were observed with an upright microscope (Zeiss Axio Imager.Z2 Vario), equipped with a temperature stage (Linkam THMS 600) with 0.1 °C resolution and a long-working distance ×100 objective (Mitutoyo Plan-Apo, N.A. 0.7). Values of Th for each FI were obtained by direct observation of the bubble disappearance, with at least 5 independent determinations. For Brillouin and Raman calibration, reference NaCl solutions were prepared by dissolving anhydrous NaCl (Sigma, purity= 99.8%) in ultrapure water (Millipore, Direct Q3 UV), obtaining the desired molality by weighting.

Brillouin light scattering

More details about the setup and procedure are given in Ref. 47. We just give here a brief summary. For Brillouin scattering experiments, the light from a single longitudinal mode laser at λ = 532 nm (Coherent Verdi 6) was coupled to the microscope and focused to a 1 μm spot in the FI. The intensity was kept below 150 mW at the sample. The light backscattered into the objective was analysed with a 6-pass tandem Fabry-Perot interferometer (Sandercock TFP-1) to record its Brillouin spectrum; entrance and exit pinholes were 300 and 450 μm in diameter, respectively. A spectrum reached typically 300 counts at the Brillouin peak. The intensity as a function of the frequency shift Δf was fitted with the following function48:

convoluted with the instrumental response. I0 is an intensity factor and ΔfB and ΓB are the Brillouin frequency and half-width, respectively. Based on repeated measurements on the same FI, performed for several FIs and on the measurement of pure water from 0 to 120 °C along its liquid-vapour equilibrium, the total (1 standard deviation) uncertainty on ΔfB is 30 MHz. More details can be found in Ref. 47. The Brillouin shift measured in the backscattering geometry is given by:

where λ is the wavelength of light and n and w are the refractive index and sound velocity of the liquid, respectively.

Raman spectroscopy

Raman spectra were also recorded with the same microscope setup from the backscattered light with a Raman spectrometer (Horiba Jobin-Yvon iHR 550, 300 lines mm−1 grating, 50 μm entrance slit). For FIs, the resolution of the setup was high enough to remove the quartz signal by a simple parabolic baseline correction. For solutions, a two-point linear baseline correction was sufficient. Spectra in the region of the OH stretching band were analysed as in Ref. 37, to give the total Cl− molality.

Reference Brillouin shift

For pure water, was calculated with equation (2) along the LVE using the IAPWS formulations for n49 and w50,51, valid over the whole range of temperatures of interest. For salty water, similarly to Raman, depends essentially on the total Cl− molality in the FI, with only a weak dependence on the cation. We used data for NaCl solutions. Equation (2) requires the sound velocity w and refractive index n as a function of temperature T and molality m. Whereas w is available in the range 0–100 °C and 0–6 mol kg−1 (Ref. 39), n is available in the range 0–6 mol kg−1 but only at 20 °C (Ref. 38). To calculate n at other temperatures, we assumed the validity of the Gladstone-Dale relation (GDR): n(T, m) = 1 + Kρ(T, m), where ρ(T, m) is the solution density (available in the range 25–200 °C and 0–6 mol kg−1 (Ref. 52) and K is calculated from n and ρ at 20 °C and molality m (Ref. 38). GDR is known to be accurate for pure water53. Measurements on calibrated NaCl solutions in the range 20–60 °C and 0–2 mol kg−1 (Fig. 4b) confirmed that calculated via the GDR is accurate. Moreover, based on the FI4 data (Fig. 4c), the calculation at m = 1.20 was also found to be reliable in the whole range 0–120°.

Calculation of the uncertainty on TX

The finite uncertainty on the Brillouin shift, δΔfB = 30 MHz (± 1 standard deviation)47, translates into an uncertainty δTX on TX. It can be calculated as follows. For a salt solution with molality m, let Δs(TX, m) be the difference in slope between the isochore and the LVE that cross at TX. To calculate the uncertainty on TX, we treat Δs(TX, m) as a constant Δs, an assumption justified by the good results obtained with the linear fitting procedure described above. A measurement run generates N pairs of temperature and difference in shift (i = 1 to N). This data set is fitted by the method of least squares with the linear function Δs(T−TX). TX is thus obtained by minimizing the sum of squared residuals . It follows that:

The dominant uncertainty is that on ΔfB, so that the uncertainty on TX writes:

We have explained above how to compute . ΔfB(T, m) along an isochore requires the knowledge of the sound velocity under pressure. It is available in a wide temperature range for pure water50, but in a reduced range for NaCl solutions. We used sound velocity data for the ranges 5–40 °C, 0–100 MPa and 0–1 mol kg−1 (Ref. 54). Combined with the density data52 and the GDR (see above), we computed Δs(TX, m). The uncertainty calculated with equation (4) for a typical set of N = 5 Brillouin measurements is plotted on Fig. 4d.

Additional Information

How to cite this article: El Mekki-Azouzi, M. et al. Brillouin spectroscopy of fluid inclusions proposed as a paleothermometer for subsurface rocks. Sci. Rep. 5, 13168; doi: 10.1038/srep13168 (2015).