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Abstract
The effect of crystal-water contents on the optical properties and dielectric characteristics of calcium sulfate in the THz band is investigated. The complex dielectric constant and conductivity are analyzed using the Drude-Smith model. The refractive index and absorption coefficient are linearly increased with the content of crystal-water, and the corresponding linear fitting lines of R2 over 0.97 are obtained. The dielectric properties of calcium sulfate are significantly affected by the crystal-water content. These results indicate that a new method to quantitative measurement of the crystal-water content in hydrous minerals is provided.
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1. Introduction
Water is the origin of life and plays a very important role in the evolution of the Earth and in the formation of minerals [1–3]. The water content of minerals can be used to infer the mantle water cycle, the stability of the Craton, mantle metamorphism, and other geologic activities in the region [4–6]. In addition, it significantly affects the chemical and physical properties of minerals (e.g. electrical conductivity and dielectric constant) [7,8]. The complex dielectric constant and the complex conductivity both increased with increasing the degree of hydration [9,10]. The relative dielectric constant of laterite is mainly affected by the volumetric water content [11,12]. At present, the methods for quantitative measurement of water moisture content mainly include thermogravimetric method, secondary ion mass spectrometry (SIMS), Raman spectroscopy, and Fourier transform infrared spectrum (FTIR) [13–16]. However, these approaches also face a number of problems. For example, FTIR spectroscopy requires to choose a baseline, but so far there is no rigorous theory to guide how to deduct this baseline. Raman spectroscopy is commonly used to determine the water content of melt inclusion micro-zone, but it overestimates (or underestimates) the water in minerals. Therefore, they face significant challenges to accurately measure water in minerals.
It is well known that the main component of gypsum is calcium sulfate dihydrate (CaSO4·2H2O). The CaSO4·2H2O is mainly used as a modifier in soil, road base materials and cement [17,18], and its application value is low. The hemihydrate and anhydrous calcium sulfate obtained by calcination has advantages of high temperature resistance, good toughness, high strength, non-toxicity and low price, and has a good application prospect in heat-insulating materials, environmental materials, friction materials and so on [19–21]. Until now, the hydrogen bonding in CaSO4·2H2O is studied by X-ray, IR and Raman spectroscopy to explain the phase transition and structural changes of calcium sulfate [22–24]. However, the response frequency of hydrogen bonding is usually below 2.0 THz. The resolution of IR and Raman spectroscopy is not enough in this range.
Terahertz time-domain spectroscopy (THz-TDS) is an optical spectroscopy technique developed in recent years, which has the advantages of non-contact, coherence and rapidity. It can obtain the optical and dielectric properties of materials in the terahertz band [25,26]. It also enables to obtain low-frequency vibrational information such as lattice vibrations [27], hydrogen bond [28]. As the vibration and rotation energy levels of water molecules are in the terahertz band. The THz-TDS can be used to study the water content and the water spatial distribution for Crude Oil, wheat leaf and minerals [29–33].
In this paper, the THz-TDS is used to investigate the terahertz time-domain signals of calcium sulfate (CaSO4) with different crystal-water contents. The absorption coefficients and refractive of the CaSO4 are calculated using the Fourier transform and the electromagnetic wave transfer equation. The complex refractive index and the complex permittivity as well as the complex conductivity have been deduced. The relationship between physical parameters and water content has been established, which provides new insight for the determination of water content in hydrous minerals.
2. Experimental methods
2.1 Sample preparation
Calcium sulfate crystals are available in three phases, calcium sulfate dihydrate (CaSO4·2H2O), calcium sulfate hemihydrate (CaSO4·0.5H2O, α and β types) and anhydrous calcium sulfate (CaSO4). There, α type is dehydrated in saturated steam or pure water solution, and β type is dehydrated in dry air. The dehydration process is carried out in a dry air environment, the CaSO4·2H2O begins to dehydrate at 120 °C and CaSO4·0.5H2O is formed at 140°C. Finally, the crystalline water is completely dehydrated to become calcium sulfate at 300 °C [34,35].
The crystal-water content percent in CaSO4·2H2O is defined as:
The mixture of CaSO4 hydrate and polytetrafluoroethylene (PTFE) with a mass ratio of 1:1 is stirred in an agate mortar for 15 min. The sample powder is dried in a constant temperature oven at 80°C for 30 min to avoid the effect of moisture absorption in air. Then, 250 mg of dry powder is weighed, and pressed for 2 min at a pressure of 6 T. The circular samples with a diameter of 13 mm and thickness range of 0.820-0.850 mm are obtained.
2.2 Experimental setup and data processing methods
The optical path principle in the experiment is shown in Fig. 1. The terahertz setup is composed of a femtosecond laser, a terahertz radiation generation device, a corresponding detection device, and a time-delay control system. The titanium sapphire laser produced a femtosecond laser (wavelength 800 nm, pulse width 100 fs and repetition frequency 80 MHz), which is divided by a beam splitter into a pump beam and a probe beam. The pump light is passed through a time-delay system and then irradiated onto a gallium arsenide photoconductor antenna to excite a terahertz pulse, which is collimated and focused by off-axis parabolic mirror and then passed through the sample. The terahertz pulse with sample information and the probe light are reached to the ZnTe crystal (thickness 2 mm and orientation <110>) at the same time to realize the photodetection. The time-delay system is scanned over a path of 3 mm with a travel step of 0.005 mm, and the system is operated over a time range of 0-20 ps, obtaining a terahertz spectrum in the range of 0-3 THz [36]. The optical path is purged with dry air to reduce the effect of water vapor on the terahertz waves, keeping the relative humidity at 3%. The acquired reference and sample signals are Fourier transformed to acquire the frequency-domain spectrum, and the refractive index n(ω) and absorption coefficient α(ω) are calculated as follows [37]:
In the terahertz band, the complex refractive index of the material is further deduced to obtain the complex permittivity and complex conductivity [38,39]. The complex refractive index $\tilde{n}(\omega )$, complex dielectric constant $\tilde{\varepsilon }(\omega )$ and complex conductivity $\tilde{\sigma }(\omega )$ are expressed as:
In this study, we assume that the velocity of the electrons remains constant after the first collision to describe the dielectric properties of CaSO4 hydrate by using the Drude-Smith model [40,41]. According to the Drude-Smith model, the equations for complex permittivity $\tilde{\varepsilon }(\omega )$ and complex conductivity $\tilde{\sigma }(\omega )$ are expressed as:
3. Results and discussions
3.1 Thermogravimetric and XRD
Thermogravimetric (TG) analysis is a method of measuring the water content of a sample by heating so that the sample is completely dehydrated and a curve of mass versus temperature is obtained. Figure 2(a) shows the detection of CaSO4·2H2O using TG. It shows that mass loss is 20.83% for CaSO4·2H2O in the temperatures range of 80°C-200°C. According to Eq. (3), the water content of CaSO4·2H2O can be obtained. In this process, the status of the calcium sulfate hydrate is characterized by the XRD as shown in Fig. 2(b). It can be seen that the intensity of the diffraction peak at 25.659° (crystal face <301>) increased with the decrease of crystal-water content. And after dehydration, a new diffraction peak at 25.502° (crystal face <020>) appears, which corresponds to the CaSO4.
Fig. 2. Thermogravimetric (TG) curves (a) and XRD patterns (b) of CaSO4 hydrate with different crystal-water contents. See Data File 1 for supporting content.
3.2 Refractive index and absorption coefficient
The CaSO4 hydrate is also analyzed by THz-TDS. Figure 3(a) shows terahertz time-domain signals of CaSO4 hydrate with different crystal-water contents. The peak amplitudes under different water contents are extracted, as shown in Fig. 3(b). The peak amplitude increases linearly from 6.61 to 7.83 with the decreasing of water content. The amplitude of anhydrous CaSO4 is 8.12. It indicates that the time-domain signal is influenced by the crystal-water content in the samples. As CaSO4·2H2O is heated, breaking of the hydrogen bond occurs between H2O and the O2- in [SO4]2-, causing the crystal-water breaking away from the lattice of the CaSO4 hydrate [42]. In order to further investigate the different crystal-water content of CaSO4 hydrate, the frequency-dependent refractive index and absorption coefficient are calculated according to Eqs. (4) and (5), and the results are shown in Fig. 4.
Fig. 3. (a)The time-domain of CaSO4 hydrate with different crystal-water contents. (b)The fitting curve for the peak amplitude in the time domain. See Data File 2 for supporting content.
Fig. 4. The refractive index (a) and absorption coefficient(c) for CaSO4 hydrate. (b) and (d) are the fitting curves at1THz. See Data File 3 for supporting content.
Figure 4(b) shows the relationship between refractive index and water content at 1THz. The refractive index of 1.85 corresponds to the anhydrous CaSO4. The refractive index decays linearly with decreasing crystal-water content in the range of 1.95 to 2.02, and R2 is 0.762. In classical geometrical optics, the time for light to pass through a medium is determined by the optical distance, i.e. the product of the refractive index and thickness of the medium. The difference in thickness of the tested samples of 0.03 mm is expected to have a small effect on the refractive index. The increase in refractive index is mainly attributed to the large proportion of the dielectric constant of the water of crystallization in the sample, and the increase in water content induced the increase the dielectric constant, resulting in a backward shift of the peak-out time in the time domain. Figure 4(c) shows the absorption coefficients of CaSO4 hydrates in the terahertz band, and the absorption coefficient increases with the increase of frequency. The corresponding absorption coefficient intensities of CaSO4 hydrates are extracted at 1 THz, and the fitting curves are shown in Fig. 4(d). The absorption coefficient increases with increasing water content of CaSO4 hydrate, and R2 is up to 0.995. This indicates that the reduction of water crystals requires less energy for the jump of the rotational-vibrational energy levels of water molecules in the terahertz band, and the absorption of terahertz energy by the samples is weakened. On another possibility, the hydrogen bonding in CaSO4·0.5H2O is significantly weaker than in CaSO4·2H2O due to the longer O-H···O bonding distances [23], resulting in a larger terahertz absorption by calcium sulfate dihydrate.
Due to the stronger linear relationship of the absorption coefficient than the refractive index, it is feasible to establish a relationship between the absorption coefficient and crystal-water content. The relationship is expressed as follows:
where ɛ is the linear molar absorption coefficient (in L·mol-1·cm-1), x is the concentration (in ppm), and b is the absorption coefficient in the absence of water. The quantitative content of crystal-water of CaSO4·2H2O at 1 THz is:It shows that crystal-water content can be quantitatively characterized by the absorption coefficient in terahertz band.
3.3 Dielectric properties
The optical dielectric constant of a material describes the response to electromagnetic waves, with the real part indicating the refractive properties of the material and the imaginary part indicating the ability of the material to absorb electromagnetic waves. The dielectric constants of CaSO4 hydrate with different crystal-water contents are obtained from Eq. (7) as shown in Fig. 5. The waveform of the real part of the dielectric constant presents a similar trend to the refractive index, and the magnitude of the value of the real part is insensitive to the extinction coefficient. Furthermore, the imaginary part of the dielectric constant that is also a similar tendency with the absorption coefficient. Compared to the real part, the imaginary part of the dielectric constant is more sensitive to the frequency, and this is attribute to the imaginary part of the dielectric constant determined by the extinction coefficient. During the phase transition from calcium sulfate dihydrate to calcium sulfate, the dielectric constant increases as the dipole moment of the hydrogen bond decreases, and it is affected by the orientation of the hydrogen bond [22].
Fig. 5. The real part (a) and imaginary part (b) of dielectric constant of CaSO4 hydrate with different crystal-water contents. The measured data (dots) and the model fitting (solid line) show a good agreement. See Data File 4 for supporting content.
The parameters ${\omega _p}$, τ and c in Table 1 are extracted from the experimental data by fitting the Drude-Smith complex permittivity model for CaSO4 hydrate. It can be seen that the plasma frequency increases from 108.01 to 205.17 THz, and τ decreases from 2.58 to 1.20 fs with the crystal-water decreasing. This means that the crystalline water in the CaSO4 enhances the electric scattering time. The hydrogen bond in the crystalline water is more sensitive to the THz wave than the Ca2+ and [SO4]2-, and the former is easily absorption the THz.
Table 1. The parameters ${{\omega }_{p}}$, τ and c in permittivity fitting
The conductivity is the other important physical parameter in geophysics, and the conductivity of water-bearing minerals is sensitive to in water changes. Figure 6 shows the complex conductivity of CaSO4 hydrate with different crystal-water contents. Both the real part and the imaginary part of the conductivity present a good agreement of the measurement data with model fitting. The value of the imaginary part of the conductivity linearly decreases with frequency. From those results, it is seen that the fitting is reasonable and the parameters are shown in Table 2.
Fig. 6. The real part (a) and imaginary part (b) of conductivity of CaSO4 hydrate with different crystal-water contents. The measured data (dots) and the model fitting (solid line) show good agreement. See Data File 5 for supporting content.
Table 2. The parameters ${{\omega }_{p}}$, τ and c in conductivity fitting
During the dehydration of calcium sulfate dihydrate to calcium sulfate, the plasma frequency is increased and τ is decreased with the decrease of water content. This result is in agreement with that in complex permittivity fitting.
In order to assess the effect of water content on dielectric constant and conductivity in the CaSO4 hydrate, the imaginary part of the dielectric constant and the real part of conductivity are selected to fit the results at 1 THz. The relationship is shown in Fig. 7. A high R2 of 0.982 and 0.956 are obtained for the imaginary part of the dielectric constant and the real part of conductivity respectively. Those results indicate that it is possible to quantitatively assess the water content in hydrate minerals.
Fig. 7. The imaginary part of the dielectric constant (a) and the real part of conductivity (b) fitting at 1 THz of CaSO4 hydrate with different crystal-water contents. See Data File 6 for supporting content.
4. Conclusion
In this study, the optical parameters and dielectric properties of CaSO4·2H2O with different crystal-water contents are investigated by THz-TDS. Those results will help to study the spectral properties of hydrous minerals and provide a new guidance for THz-TDS measurements of the content of crystal-water in minerals. The main conclusions are presented below.
- (1) The different crystalline water contents of CaSO4·2H2O are investigated by XRD, and the diffraction peak intensities of CaSO4 hydrate relate to the crystal-water content.
- (2) As the crystal-water content increases, the absorption coefficient increases linearly, which can be applied to quantitatively assess the crystal-water content.
- (3) The dielectric characteristics of CaSO4 hydrate are obtained by THz-TDS, which is provided a new means to study the dielectric characteristics of minerals.
Funding
National Natural Science Foundation of China (61805214); Open Fund of State Key Laboratory of Infrared Physics (SITP-NLIST-YB-2022-12); Piesat Information Technology remote sensing interdisciplinary research project (HTHT202202); Fundamental Research Funds for the Central Universities (2-9-2022-203); Young Elite Scientists Sponsorship Program by Bast (BYESS2020037).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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