Determination of H 2 Densities Over a Wide Range of Temperatures and Pressures Based on the Spectroscopic Characterization of Raman Vibrational Bands

Abstract

Raman spectroscopy is a powerful method for determining the densities of gas species in fluid inclusions, especially for H₂-bearing inclusions in which the microthermometry approach is difficult to apply. The relationships between Raman peak position and H₂ density have been recorded in several previous studies. However, systematic discrepancies exist among these studies. In this study, the Raman spectral parameters (peak position, width, and intensity) of the vibrational bands of H₂ (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) were systematically measured at temperatures from 25 to 400 °C and pressures up to 150 MPa using a high-pressure optical cell. The variation in each parameter as a function of H₂ density was discussed. Several calibration polynomials derived from the measured peak positions and peak widths of these vibrational bands and the peak intensity ratios of Q₁(1) to Q₁(n = 0, 2, 3) were established to determine H₂ densities up to 0.062 g/cm³ at 25 °C. For natural fluid inclusions, the peak position of the Q₁(1) band is the best choice for density determination mainly because (i) Raman spectra derived from fluid inclusions are not always of applicable qualities and the strongest intensity Q₁(1) band could be obtained easier than others, and (ii) the peak position is insensitive to instrumental factors. The relationship between the peak position of Q₁(1) band and density can be represented by ΔQ₁(1) = 90,246.070 × ρ⁴ – 5471.203 × ρ³ + 770.944 × ρ²– 41.038 × ρ (r² = 0.999), where ρ is the density of H₂ in g/cm³; ΔQ₁(1) (cm^–1) is the difference between the obtained peak position of Q₁(1) band of H₂ and the known peak position of Q₁(1) band of H₂ at near-zero density. This polynomial is independent of instrumental factors and can be applied in any laboratory, as long as the peak position of H₂ with a near-zero density is known. The effects of temperature on the relationship between these spectral parameters and H₂ density were also examined.

Keywords

Raman spectroscopy quantitative analysis density

Introduction

Hydrogen is an important component in many geological environments, and its major sources are usually supposed to involve biological and abiotic processes. The mechanisms for biological processes mainly include organic matter fermentation and anaerobic oxidation of carbon monoxide,^1,2 and those for abiotic processes consist of mantle degassing,^3,4 radiolysis,^5–8 the serpentinization reaction,^9,10 the low‐temperature reactions associated with active fault movements,^11,12 and basaltic magma crystallization.^13,14 Although the appearances of H₂ in fluid or melt inclusions are rarely reported, H₂-bearing inclusions have been found in many geological environments, including igneous rocks,^15,16 uranium deposits,^17–19 high‐grade metamorphic rocks,^20,21 fault planes,²² and hydrothermal environments.^23,24 Among these, H₂-rich fluids are commonly found in uranium deposits^5,6,17,18 and hydrothermal environments.^25,26 In addition, hydrogen has also been found in experiments that simulated the water–rock interaction and redox reactions in natural hydrothermal environments.²⁷ H₂ fluid in the earth system plays an important role, and its origin and evolution have attracted more and more attention because of its value to chemosynthetic life and to our understanding of the redox state, and its influence on geochemical evolution.^28–30

Determining densities of H₂ in the H₂-bearing fluid inclusions is important for knowing the physicochemical state and related processes that take place in geological environments. However, the microthermometric analysis of H₂-bearing fluids has long been hampered owing to the extremely low temperature of the triple point of H₂ (–259.2 °C), which prevents freezing H₂ with the frequently used coolant, liquid N₂.³¹ The limitation makes the laser Raman spectroscopy currently the only reliable tool for studying H₂‐bearing inclusions.^16,31

Raman parameters, such as peak position and peak width, can be used to determine the properties of H₂-containing gases. May et al.^32–35 reported the first Raman characteristics of gaseous, liquid, and solid H₂ at temperatures (T) from 85 to 300 K and pressures (P) up to 200 MPa. Bischel and Dyer³⁶ measured the temperature and density dependence of the Raman peak position and peak width of H₂ at temperatures from 77 to 480 K and pressures up to 3.4 MPa. Rahn et al.³⁷ reported the self-broadening coefficients of H₂ Q(0–5) Raman transitions from 295 to 1000 K and 0.2–5 MPa. Li et al.³⁸ studied the density and temperature dependences of the peak position and peak width of hydrogen vibrational Raman bands from 50 to 400 °C and 5–40 MPa. Fang et al.³¹ presented the Raman peak position, peak width, peak height, and peak area of the vibrational bands of H₂ and CH₄ in pure H₂, CH₄ gases, and their mixtures at room temperature and pressures up to 40 MPa. Although these reports have documented density-dependent variations in the Raman spectra of H₂, the relationship between Raman peak position of vibrational bands (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) and H₂ density at room temperature has not been investigated systematically. The results of May et al.³² and Fang et al.³¹ show that different laboratories have their calibration curves for this Raman shift–density relationship, and so cannot be used in other laboratories.

In this study, using a high‐pressure optical cell (HPOC), ^39,40 we systematically collected Raman spectra of pure H₂ at temperatures from 25 to 400 °C and pressures up to 150 MPa. The relationship between the Raman parameter (peak position, peak width, and peak intensity ratio) and H₂ density was established, and the applicability of these spectral parameters was evaluated. The effects of temperature on the relationships were also discussed.

Experimental Method

Apparatus and Procedures

An HPOC was used in this study for the Raman spectroscopic analyses of pure H₂ in isothermal or isobaric experiments, and the apparatus and procedures are similar to those described previously in detail.^31,41 The HPOC is a capillary tube (200 μm inner diameter, 665 μm outer diameter, and ∼25 cm length), which can be connected to a high-pressure system. The pressure was maintained by a pump (HiP # 37-5.75-60) using water as the pressure medium and was monitored from an Omega PX91N0-35KSV digital pressure transducer (241 MPa full scale, accurate to ±0.5% of full scale) with an Omega DP41-8-230 manometer. A Linkam CAP500 heating–cooling stage, with the accuracy of ±0.1 °C from 0 to 100 °C and ±0.5 °C for temperatures near 400 °C,⁴² was used for temperature control. Raman spectra were collected at various pressures and temperatures, and the measured pressures and temperatures were used to calculate H₂ density based on the equation of state of H₂ formulated by Leachman et al.⁴³ from the National Institute of Standards and Technology (NIST) Chemistry WebBook (https://webbook.nist.gov/chemistry/).

Collection and Calibration of Raman Spectra

The Raman vibrational bands of H₂ were obtained on a JY/Horiba LabRAM HR Evolution Raman system equipped with a frequency-doubled neodymium-doped yttrium aluminum garnet (Nd:YAG) laser (532 nm) excitation whose output laser power is approximately 14 mW, a 50× long-work-distance Olympus objective with 0.35 numerical aperture, and an 1800 groove/mm grating with a spectral resolution of about 0.65 cm⁻¹. Three spectra were collected at each P–T condition, and each spectrum was collected with two accumulations.

The spectral resolution can be promoted to 0.03 cm⁻¹ using a curve fitting technique.^44,45 Therefore, the measured spectra for H₂ were fitted by the program PeakFit v.4.12 (AISN Software Inc.) using a summed Gaussian–Lorentz function, which is the best fit function for vibrational bands of H₂ with the highest R² greater than 0.99 for each spectrum. The peak position and full width at half‐maximum (FWHM) were determined using the program PeakFit v.4.12, whereas peak intensities for H₂ were derived from integration using GRAMS AI software (Galactic Industries). Note that here, peak intensity is in terms of the integrated intensity of the peak, not the integrated area. The separation between the Ne lines at 3907.37 cm⁻¹ and 4363.75 cm⁻¹ was used to calibrate the peak positions of H₂. The real Raman peak positions (υ_real) of the vibrational bands of H₂ were obtained from the following relationship:⁴⁶

\frac{υ_{r e a l} - 3907.37}{υ_{m} - N e_{m 1}} = \frac{4363.75 - 3907.37}{N e_{m 2} - N e_{m 1}}

(1)

where υ_real is the real Raman position of the vibrational bands of H₂, υ_m is the measured position of the vibrational bands of H₂, and Ne_m1 and Ne_m2 are the measured lines of the two reference Ne lines.

Results and Discussion

In this study, only the four vibrational bands of H₂ (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) were systematically investigated because the pure rotational lines of H₂ (from approximately 350 to 1050 cm⁻¹) are usually hindered by the stronger Si–O bands of silicate host minerals (from approximately 300 to 1200 cm⁻¹) when analyzing natural fluid inclusions.³¹ Both Q₁(0) and Q₁(2) and Q₁(1) and Q₁(3) correspond to the vibrational Raman bands of para‐hydrogen and ortho‐hydrogen, respectively.³⁸ Figure S1 (Supplemental Material) shows the four vibrational bands (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) of H₂ at 25 °C and pressures up to 150 MPa.

Variation in the H₂ Peak Position and the Equations for H₂ Density Calculations

Figure 1 shows the peak positions of the vibrational (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) bands of H₂ as a function of density near room temperature based on May et al.,³² Fang et al.,³¹ and this study. Interestingly, the peak positions of the four vibrational bands behave similarly: their wavenumbers decrease first and then increase with increasing gas density. This likeness in behavior indicates that the observed perturbation is due primarily to the variation in vibrational frequency.³² The initial decrease in the frequency with density is associated with the predominance of intermolecular attractive forces in this range, whereas the later increase must be ascribed to repulsive forces at high densities.³⁴ The minimum peak positions for Q₁(0), Q₁(2), and Q₁(3) correspond to the density of ∼ 0.0205 g/cm³ (at 30 MPa), whereas the minimum peak position for Q₁(1) corresponds to the density of ∼ 0.033 g/cm³ (at 55 MPa) (Table S1, Supplemental Material).

As shown in Fig. 1, the Raman shifts–density relationships of the three data sets are almost parallel to each other at room temperature, revealing that systematic difference among these data sets can be eliminated by following the method described for the CH₄ system.^47–49 Here, ΔQ₁, instead of the peak position of H₂, was used as a variable to remove the systematic differences among different Raman laboratories (Fig. 2), where ΔQ₁ = υ_ρ–υ₀, the difference between the peak positions of H₂ at elevated densities (or pressures) (υ_ρ) and a near-zero density (or at near 1 atm P) (υ₀). The peak positions of Q₁ (n = 0, 1, 2, 3) bands of H₂ with near-zero density (or near 1 atm P) and experimental temperatures for our study, May et al.³² and Fang et al.³¹ are listed in Table I. Noting that the study of Fang et al.³¹ was done in our laboratory about three years ago, and the υ₀ has a discrepancy of 0.29 cm^–1 from this study.

Table I.

Peak positions of Q₁(n = 0, 1, 2, 3) bands of H₂ with a near-zero density (or near 1 atm P) (υ₀) and experimental temperatures.

Reference	T(°C)	Q₁(0)	Q₁(1)	Q₁(2)	Q₁(3)
This study	25	4162.68	4156.76	4144.96	4127.36
May et al.³²	∼24	4161.13	4155.20	4143.38	4125.83
Fang et al.³¹	25	4162.39	4156.47	4144.67	4127.07

Our results at 25 °C agree well with those reported by Fang et al.³¹ and most of the data points of May et al.,³² especially for H₂ densities below 0.03 g·cm^–3 (Fig. 2). The relationship between the peak position and density in this study can be simply expressed as the following equation:

Δ Q_{1} (n = 0, 1, 2, 3) = υ_{ρ} - υ_{0} = a \times ρ^{4} + b \times ρ^{3} + c \times ρ^{2} + d \times ρ

(2)

where ρ is the density of pure H₂, and a, b, c, and d are coefficients that depend only on temperature. The results of the least squares fitting with polynomials of different degrees showed that the standard deviations are not improved with polynomials with terms higher than ρ⁴. The values of a, b, c, and d for Q₁ (n = 0, 1, 2, 3) at 25 °C in this study are shown in Table II. Equation 2 can be used to calculate H₂ densities based on the measured Raman shifts of vibrational bands of H₂ at room temperature, as long as υ₀ is known. This can make it possible by direct measurement of the H₂ peak position at pressures near 1 atm (or near-zero density) in an HPOC.

Table II.

Temperature-dependent coefficients (a, b, c, and d) and correlation coefficient (r) of the Raman wavenumber for Q₁(n) according to Eq. 2.

n	a	b	c	d	r ²
0	144,637.328	–12,500.752	1124.653	–34.939	0.998
1	90,246.070	–5471.203	770.944	–41.038	0.999
2	101,632.946	–7081.142	974.851	–29.494	0.999
3	121,180.687	–8945.333	1043.747	–29.222	0.999

Variation in the H₂ Peak Width and the Equations for H₂ Density Calculations

The peak width values of the Q₁ (n = 0, 1, 2, 3) bands of H₂ are represented by the FWHM. The Doppler effect and collisional broadening play substantial roles in controlling the FWHM as the density increases.^36,37 At very low pressures, the Doppler effect dominates, and the collisional effect can be neglected. With increasing pressure, collisional broadening plays the dominant role in the FWHM changes as the density varies. According to the diffusion model,³⁶ the relationship between the FWHM and density can be expressed by the simple equation:

Δ Q_{F W H M} = \frac{A}{ρ} + B \times ρ

(3)

where ΔQ_FWHM is the difference between the FWHM at increasing densities and that at near-zero density in cm⁻¹, A is a coefficient proportional to the self-diffusion coefficient, ρ is the density, and B is the temperature dependence of the collision‐broadening coefficient. Under high-density conditions, the self‐diffusion width, A/ρ, can be neglected.³⁸

In this study, at 25 °C and from 2 to 150 MPa, the FWHM values range from 1.55 to 2.95 cm^–1 for the Q₁(0) band, 1.54 to 2.52 cm^–1 for the Q₁(1) band, 1.55 to 3.75 cm^–1 for the Q₁(2) band, and 1.55 to 4.96 cm^–1 for the Q₁(3) band (Table S2, Supplemental Material). Only collisional broadening was observed in the FWHM trend as the density varied. We obtained the following polynomial equation to calculate the density of pure H₂ with the FWHM:

Δ Q_{F W H M} = a \times ρ^{3} + b \times ρ^{2} + c \times ρ

(4)

where ΔQ_FWHM is the difference between the FWHM at increasing densities and that at 0.0016 g/cm³ (2 MPa) in cm⁻¹. The fitted coefficients for Eq. 4 are listed in Table III. Figure 3 shows that the dependence of the FWHM on density has three main characteristics: (i) the FWHM has a positive correlation with the density of gaseous H₂; (ii) the differences in the FWHMs of the four vibrational bands are very small at low densities but become more obvious as the density increases; and (iii) the effect of density on the FWHM is largest for Q₁(3) but smallest for Q₁(1).

Table III.

Fitting parameters for the Q₁(n = 0, 1, 2, 3) band of H₂ according to Eq. 4.

n	a	b	c	r ²
0	0	0	22.092	0.999
1	0	0	14.825	0.998
2	3542.442	–59.918	25.226	0.999
3	2651.155	171.424	33.680	0.999

Variation in Peak Intensity Ratios and the Equations for H₂ Density Calculations

The Raman peak positions and FWHM values of Q₁ (n = 0, 1, 2, 3) bands of H₂, both of which are sensitive to density, have been reported as density indicators.^32–38 However, Fang et al.³¹ found that in H₂‐dominated fluids with mixed CH₄, the peak intensity ratios of the Q₁(1) band to Q₁(3) band are sensitive to pressure and insensitive to composition, indicating that the relative peak intensity of Q₁(1) and Q₁(3) of H₂ is a better alternative for pressure determination. In this study, the peak intensity ratios of the Q₁(1) band to Q₁(n = 0, 2, 3) bands were investigated. Over the entire density range from 0 to 0.0623 g/cm³, the peak intensity ratios are from 5.55 to 16.73 for Q₁(1)/Q₁(0), 5.63 to 7.48 for Q₁(1)/Q₁(2), and 7.19 to 14.13 for Q₁(1)/Q₁(3), corresponding to the variation in the peak intensity ratios with 11.18 for Q₁(1)/Q₁(0), 1.85 for Q₁(1)/Q₁(2), and 6.94 for Q₁(1)/Q₁(3) (Table S3, Supplemental Material). Therefore, the effect of density on the peak intensity ratios of Q₁(1) to Q₁(2) is small compared to those of Q₁(1) to Q₁(0) and Q₁(1) to Q₁(3). The differences in the peak intensity ratios of Q₁(1) to Q₁(0) and Q₁(1) to Q₁(2) are very small at low density (<0.01 g/cm³) and then increase with density.

The relationship between the peak intensity ratios and density obtained in this study can be expressed as the following equation (Fig. 4):

Δ P I R (\frac{Q_{1} (1)}{Q_{1} (n = 0, 2, 3)}) = a \times ρ^{3} + b \times ρ^{2} + c \times ρ

(5)

where ΔPIR (Q₁(1)/Q₁(n = 0, 2, 3)) represents the difference between the peak intensity ratios at elevated densities and near-zero density. The coefficients a, b, c, and r² for Q₁(1)/Q₁(n = 0, 2, 3) are listed in Table IV.

Table IV.

Fitting parameters according to Eq. 5.

ΔPIR (Q₁(1)/Q₁(n))	a	b	c	r ²
n = 0	24 282.046	362.277	60.962	0.999
n = 2	0	–14.954	30.705	0.997
n = 3	0	–305.501	128.181	0.999

Error Analysis

The accuracy of the H₂ density derived from Raman parameters (peak position, peak width, and peak intensity ratio) of vibrational bands of H₂ with Eqs. 2, 4, and 5 are primarily affected by Eq. 1, the accuracy of the measured Raman spectral parameters of H₂ and Eq. 2 the accuracy of the calculated values using Eqs. 2, 4, and 5. To realize the maximum accuracy, a high-resolution grating and a narrow slit were used during the measurement, and the spectra were collected with a single spectral window. Additionally, each spectrum had two accumulations. The vibrational bands of H₂ were collected three times at each density and their average value was presented as the measured value. The uncertainties of spectral parameters (peak position, peak width, and peak intensity ratio) are estimated based on the standard deviation of the three consecutive measurements of spectra at each density (Tables S1, S2, and S3, Supplemental Material). In addition, peak positions and peak widths were obtained by fitting the summed Gaussian–Lorentzian curve for each H₂ Raman spectrum and corrected with two neon emission lines. The fitting curve was found to be the best fit curve for the H₂ peak in this study with the highest r² greater than 0.99 for each spectrum. Therefore, the maximum uncertainty of H₂ peak positions coming from the peak position fitting (±0.01 cm^–1) and calibration (±0.01 cm^–1) is estimated to be about ±0.02 cm^–1, the uncertainty of H₂ peak widths resulting from peak fitting is about ±0.01 cm^–1, and the error of peak intensity ratio arising from integration is about 0.1.

The uncertainty of the H₂ density derived from Eq. 2 can be estimated by using the following relations:⁴⁹

d υ / d ρ = 4 \times a \times ρ^{3} + 3 \times b \times ρ^{2} + 2 \times c \times ρ + d

(6a)

d ρ / d υ = \frac{1}{(4 \times a \times ρ^{3} + 3 \times b \times ρ^{2} + 2 \times c \times ρ + d)}

(6b)

where a, b, c, and d are the parameters in Table II. The accuracy of the H₂ density calculated from peak width and peak intensity ratio can also be estimated by the same procedure.

As shown in Fig. 5, the accuracy of density was drawn with increasing density in the range of 0∼0.062 g/cm³. The error of H₂ density derived from measured peak position with Eq. 2 is quite small in the range of 0∼0.011 g/cm³ and 0.035∼0.062 g/cm³ for Q₁(0) band, 0∼0.020 g/cm³ and 0.043∼0.062 g/cm³ for Q₁(1) band, 0∼0.008 g/cm³ and 0.031∼0.062 g/cm³ for Q₁(2) band, and 0∼0.008 g/cm³ and 0.031∼0.062 g/cm³ for Q₁(3) band, respectively. However, out of these ranges, the error is quite large, and the accuracy of H₂ density obtained from Eq. 2 is much lower (Fig. 5a). Fortunately, the error of H₂ density determined with measured peak width is pretty small (<0.0007 g/cm³) for four vibrational bands of H₂, especially for the Q₁(3) band (<0.0003 g/cm³) (Fig. 5b). The error of H₂ density obtained with measured peak intensity ratio is relatively small, mainly the Q₁(1)/ Q₁(0) at densities higher than 0.023 g/cm³ and the Q₁(1)/ Q₁(3) at densities lower than 0.023 g/cm³ (Fig. 5c).

To test the reliability of the calibration polynomials derived from the measured Raman spectral parameters (peak position, peak width, and peak intensity ratio) for H₂ density determination, several samples were prepared in the HPOC with known densities of 0.00910∼0.03173 g/cm³. The calculated ρ values from measured peak position, peak width, and peak intensity ratio, according to Eqs. 2, 4, and 5, are listed in Table S4 (Supplemental Material), and they agree well with the sample densities with the average absolute deviations of less than ±7%.

Temperature Effect on the Relationship Between the H₂ Raman Spectrum and Density

To investigate their temperature dependence, Raman spectra of H₂ (in an HPOC) were collected at temperatures from 25 to 400 °C and pressures up to 150 MPa, and the neon lines were collected concurrently throughout the analysis. Noting that the sample chamber is very easy to crack when the experimental conditions are above 200 °C and 100 MPa. Therefore, for safety reason, the data under these conditions were not acquired, except for those obtained accidentally. Fig. S2 (Supplemental Material) shows the Raman spectra of the four vibrational bands (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) of H₂ at 80 MPa from 25 to 400 °C, and two additional vibrational bands (Q₁(4) and Q₁(5)) at ∼4104 and ∼4075 cm^–1, respectively, appeared at high temperatures (>100 °C). It also shows that the intensity of the Q₁(0) band becomes weaker with increasing temperature, resulting in large uncertainties for the peak fitting procedure. In contrast, the intensity of the Q₁(3) band becomes stronger at higher temperatures.

Peak positions of the four vibrational bands of gaseous H₂ as a function of density at different temperatures (25∼400 °C) are shown in Fig. 6. The results show that the peak positions of the four vibrational bands of H₂ shift to lower wavenumber and then shift to higher wavenumber as density increases at 25, 100, and 200 ^oC, and always shift to higher wavenumber at 300 and 400 °C. When the temperature increases at a constant density (>0.01 g/cm³), they shift to higher wavenumbers. The higher the density, the greater the temperature effect, which is consistent with previous observations.³⁸ This result indicates that the temperature strongly perturbs the vibrational motion of H₂; thus, the temperature dependence of hydrogen Raman wavenumbers is stronger than those of other gases, such as H₂S and CH₄.^41,48 The temperature-dependence coefficients (a, b, c, and d) of the Raman wavenumber are connected with vibrational coupling, isotropic intermolecular force, and the population of the initial rotational level. The values of a, b, c, and d for Q₁ (n) (n = 0, 1, 2, and 3) over a temperature range of 100∼400 °C are shown in Table S5 (Supplemental Material). Therefore, to obtain an accurate H₂ density from Raman peak positions at higher temperatures, the temperature effect should be considered.

The dependence of the FWHM on density at different temperatures is shown in Fig. S3 (Supplemental Material). At higher temperatures, the influence of the density on the FWHM is more obvious. This is because increasing the temperature accelerates the molecular thermal motion and the collision frequency. Compared to the Q₁(0), Q₁(1) and Q₁(2) bands, the changes in the Q₁(3) bandwidth show a weaker temperature dependence. The FWHMs of the Q₁(0) band have large uncertainties due to their intensity being very weak, especially at high temperatures (Fig. S3).

Plots of the peak intensity ratios Q₁(1)/Q₁(n = 0, 2, 3) as a function of density are shown in Fig. S4 (Supplemental Material). When the density is low, the peak intensity ratios of Q₁(1)/Q₁(0) are very similar at different temperatures; then, the value of this ratio increases with density, and for a given density, it increases with temperature. However, the peak intensity ratios between Q₁(1) and Q₁(2) and between Q₁(1) and Q₁(3) decrease with increasing temperature at constant density. More interestingly, the slope of the plot of the peak intensity ratio of Q₁(1) to Q₁(2) versus density is very similar at different temperatures. For the peak intensity ratio of Q₁(1) to Q₁(3), the value changes greatly with the density at 25 °C, and then hardly changes with the density as the temperatures increase up to 400 °C. In other words, at high temperatures, the peak intensity ratio between Q₁(1) and Q₁(3) is independent of density and cannot be used as an indicator of density.

Density Determination of H₂-Dominated Fluids

As mentioned above, the peak position and peak width (FWHM) of the four vibrational bands (Q₁(0), Q₁(1), Q₁(2), and Q₁(3)) of gaseous H₂ and the peak intensity ratios Q₁(1)/Q₁(n = 0, 3) are sensitive to density. Although several quantitative equations for the determination of H₂ density have been established at 25 °C, their applications to natural fluid inclusions remain optional because Raman spectra obtained from natural inclusions are not always of applicable qualities.

Even though the peak intensity ratios Q₁(1)/Q₁(0) and Q₁(1)/Q₁(3) of H₂ are very sensitive to density (Fig. 4), they are highly dependent on the instrumental setting and sample quality. Similarly, even though the accuracy of density calculated with FWHM is very high, it is also worth noting that the FWHM not only changes with the instrumental setting, such as the wavelength of the laser, the groove density of grating, the slit width, and so on⁴⁹ but also is largely dependent on the type of fitting distribution curve and the baseline of the spectrum. The deviation of FWHM of H₂ between the fitting Gaussian–Lorentzian curve and Gaussian curve can be up to 10%. However, the peak position of a pure Raman active species is independent of the instrumental factors.⁵⁰ It varies with the change of pressure and temperature since the nearest neighbor environment of the molecule changes with the change of density.⁴⁷ Absolute peak positions may be determined with an accuracy of better than ±0.02 cm^–1 by reference to some standard; in our case, a neon lamp is used. Therefore, although the accuracy of density derived from peak position is much lower than those obtained with peak widths and peak intensity ratios, the peak position is most suitable for density determination.

According to this study, once the peak position of the vibrational bands of H₂ in fluid inclusion is obtained in a laboratory, the value of D in Eq. 2 could be determined as long as the peak position at near-zero density υ₀ was known, then the density of H₂ in the fluid inclusion can be expediently obtained from Fig. 2 and Eq. 2. Among the four vibrational bands, the Q₁(1) band has the strongest intensity and could be obtained easier than others, indicating that it is a better alternative for density determination. It is important to note that, for a given D, there may be two possible density values in the range of 0∼0.055 g/cm³ for the Q₁(1) band. This trend is extraordinarily alike to that observed in simple fluids such as methane⁴⁹ that the peak position of H₂ first shifts to lower wavenumber until it reaches a minimum, and then shifts to higher wavenumber with increasing density at constant temperature.⁵¹ Noting that the density of H₂ in the range of 0∼0.033 g/cm³ (corresponding to 0∼55 MPa) meets most of the geological environment.

Natural H₂-bearing fluid inclusions commonly contain other volatile components, such as CH₄, CO₂, H₂S, N₂, O₂, He, and H₂O.^5,29,46 Unfortunately, Raman spectroscopic studies of these mixtures remain quite limited. Fang et al.³¹ found that the effect of the addition of CH₄ on the peak position and peak width of Q₁(1) band of H₂ was quite small when the molar ratio of H₂ to CH₄ was ≥5, indicating that our calibration polynomial based on the peak position of Q₁(1) band is reliable in H₂‐dominated fluid with H₂–CH₄ gaseous mixtures. To study a wider range of mixtures of H₂ with geologically important volatile components, additional experiments should be carried out.

Conclusion

This work provides the Raman spectral parameters, including peak position, width, and intensity, of the vibrational bands of H₂ from 25 to 400 °C and pressures up to 150 MPa. We have discussed the variation in each parameter as a function of fluid density. Several calibration polynomials based on our experimental results were established to determine H₂ densities up to 0.062 g/cm³ at 25 °C. Our data on the peak positions are independent of instrumental factors and are generally applicable to other laboratories, as long as the near-zero density peak position is obtained. Notably, the temperature has a great influence on these parameters and cannot be ignored. Thus, when using our method for the determination of the H₂ density in H₂-bearing fluid inclusions, the fluid inclusions should not be appreciably heated. In the application to natural inclusions, the peak position of the strongest intensity Q₁(1) band is a better alternative for density determinations mainly because (i) Raman spectra obtained from natural inclusions are not always of applicable qualities and the strongest intensity Q₁(1) band could be obtained easier than others and (ii) the peak position is insensitive to instrumental factors. Future experiments should be performed to determine how the peak position, peak width, and peak intensity ratio of H₂ bands are affected by additional components in fluid inclusions.

Supplemental Material

sj-pdf-1-asp-10.1177_00037028221080489 - Supplemental material for Determination of H₂ Densities Over a Wide Range of Temperatures and Pressures Based on the Spectroscopic Characterization of Raman Vibrational Bands

Supplemental material, sj-pdf-1-asp-10.1177_00037028221080489 for Determination of H₂ Densities Over a Wide Range of Temperatures and Pressures Based on the Spectroscopic Characterization of Raman Vibrational Bands by Ying Chen and I-Ming Chou in Applied Spectroscopy

Footnotes

Acknowledgments

We thank Dr Nanfei Cheng of the Institute of Deep‐Sea Science and Engineering, Chinese Academy of Sciences for English editing.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by the Key Frontier Science Program (QYZDY‐SSW‐DQC008) of Chinese Academy of Sciences and the National Natural Science Foundation of China (No. 41973055).

ORCID iD

I-Ming Chou

Supplemental Material

All supplemental material mentioned in the text is available in the online version of the journal.

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Supplementary Material

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Determination of H 2 Densities Over a Wide Range of Temperatures and Pressures Based on the Spectroscopic Characterization of Raman Vibrational Bands

Abstract

Keywords

Introduction

Experimental Method

Apparatus and Procedures

Collection and Calibration of Raman Spectra

Results and Discussion

Variation in the H2 Peak Position and the Equations for H2 Density Calculations

Variation in the H2 Peak Width and the Equations for H2 Density Calculations

Variation in Peak Intensity Ratios and the Equations for H2 Density Calculations

Error Analysis

Temperature Effect on the Relationship Between the H2 Raman Spectrum and Density

Density Determination of H2-Dominated Fluids

Conclusion

Supplemental Material

sj-pdf-1-asp-10.1177_00037028221080489 - Supplemental material for Determination of H2 Densities Over a Wide Range of Temperatures and Pressures Based on the Spectroscopic Characterization of Raman Vibrational Bands

Footnotes

Acknowledgments

Declaration of Conflicting Interests

Funding

ORCID iD

Supplemental Material

References

Supplementary Material

Variation in the H₂ Peak Position and the Equations for H₂ Density Calculations

Variation in the H₂ Peak Width and the Equations for H₂ Density Calculations

Variation in Peak Intensity Ratios and the Equations for H₂ Density Calculations

Temperature Effect on the Relationship Between the H₂ Raman Spectrum and Density

Density Determination of H₂-Dominated Fluids

sj-pdf-1-asp-10.1177_00037028221080489 - Supplemental material for Determination of H₂ Densities Over a Wide Range of Temperatures and Pressures Based on the Spectroscopic Characterization of Raman Vibrational Bands