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We introduce a sample cell that can be used for pressure-dependent terahertz time-domain spectroscopy. Compared with traditional far-IR spectroscopy with a diamond anvil cell, the larger aperture permits measurements down to much lower frequencies as low as 3.3 cm−1 (0.1 THz), giving access to new spectroscopic results. The pressure tuning range reaches up to 34.4 MPa, while the temperature range is from 100 to 473 K. With this large range of tuning parameters, we are able to map out phase diagrams of materials based on their THz spectrum, as well as to track the changing of the THz spectrum within a single phase as a function of temperature and pressure. Pressure-dependent THz-TDS results for nitrogen and R-camphor are shown as an example.
© 2017 Optical Society of America
1. Introduction
Terahertz time-domain spectroscopy (THz-TDS) is a useful tool to probe the materials that have dynamics in millielectronvolt (meV) energy range, such as phonons in crystals [1], collision-induced dipolar absorption in non-polar liquids [2] and conformational changes in large molecules [3]. With changing temperature or applied external fields, the properties of many materials can change significantly. As a result, researchers have combined cryogenic equipment and high-field magnets with THz-TDS, opening new windows on the dynamics and properties of materials [1,4].
Hydrostatic pressure is another degree of freedom that can influence a sample’s properties. Pressure-dependent spectroscopy can help elucidate the relationship between structure and dynamics, and has been commonly employed in many spectroscopic contexts [5]. Moreover, many materials form new phases that only exist at high pressure. However, the use of hydrostatic pressure as an external control variable in THz experiments is relatively uncommon, due to the experimental challenges. Diamond anvil cell (DAC) techniques have occasionally been used in high pressure optical studies for solids and liquids at far infrared frequencies [6–16]. However, due to the small aperture size, it is extremely challenging to use a DAC in the lower range of the THz spectrum, i.e., below about 3 THz. With the help of devices such as a Winston cone to facilitate tight focusing, there have been a few high pressure far infrared studies which extended their lower frequency limit into this regime [17–19]. But the strong interferences caused by the phase response of the Winston cone [20] and the small sample thickness can both introduce strong frequency-dependent distortions on the measured low-frequency spectra, which can often render interpretation difficult.
The value of measuring pressure-dependent spectra in the THz range has been recognized by numerous researchers. Many studies of gas-phase systems have been reported, e.g., refs [21–23]. In addition, some theoretical work has predicted the pressure-dependent spectra of a few molecular solids using density functional theory (DFT) [24,25]. Earlier work on the development of pressure cells for THz measurements has also been reported [26,27]. This research group has demonstrated several novel studies of THz spectra of molecules solvated in supercritical fluoroform (CHF3) at pressures ranging up to 15 MPa. However, the field of THz spectroscopy contains few pressure-dependent studies, and the overwhelming majority of pressure-dependent spectroscopy measurements in the far infrared have relied on a DAC and therefore do not reach to frequencies below 3 THz. As a result, many important material systems remain unaddressed, particularly soft condensed matter systems such as molecular crystals where vibrational modes are often present in the THz range [1,28,29].
Here, we introduce a high pressure cell that is designed for THz-TDS. In order to reach down to the very low frequency range (~3 cm−1), we design our cell to have a relatively large aperture of 8 mm. This necessitates that we sacrifice the ability to access the high pressure range of a diamond anvil cell, since the large cell window can withstand only a limited pressure range. The pressure tuning range of our cell is up to 34.4 MPa; temperature control is also possible, in the range from 100 to 473 K. With this large range of tuning parameters, we are able to map out phase diagrams of materials based on their THz spectrum, as well as to track the variation of the THz spectrum within a single phase as a function of temperature and pressure. The measurable frequencies are from 0.1 to 3 THz, limited at the upper end by the thickness of the ZnTe crystal used for free-space electro-optic detection of the THz signal. We illustrate the capabilities of this cell by studying the THz refractive index of nitrogen near its gas-liquid phase transition, where we observe the non-supercritical and supercritical transition behavior, and pressure-dependent THz absorption spectra of R-camphor, where we observe a new spectroscopic result: the pressure tuning of terahertz molecular vibrations.
2. Experimental setup
Figure 1 illustrates a diagram of the experimental setup. A mode-locked Ti:sapphire laser, with a repetition rate of ~80 MHz, a central wavelength of ~810 nm, pulse duration of ~30 fs, and an average power of ~0.85 W, is used as the femtosecond laser source to generate and detect the THz pulses. The THz radiation is generated from a large-aperture GaAs photoconductive antenna with a 340 V bias modulated with a square wave at 56 kHz. The radiation transmits through a silicon beam splitter (8 mm thickness) and then is focused into the pressure cell by a parabolic mirror. In the pressure cell, a CVD single crystal diamond window with a diameter of 13 mm (clear aperture 8 mm) and a thickness of 3 mm and a platinum-coated sample spacer form a well-sealed sample chamber where solid or liquid samples can be placed. The THz radiation transmits through the window and the sample and then is reflected by the sample spacer, so that the measured time-domain signals contain both a normal-incidence reflection from the window-sample interface and a double-pass transmission through the sample. The sample diameter can be as large as 6 mm. We have a set of sample spacers that allows different sample thickness from 0.25 to 4 mm. The two holes on the backside of the spacer are the high pressure inlet and outlet. A gas or liquid pressure transmitting medium with pressure up to 34.4 MPa (the pressure rating of the diamond window) can be guided into the cell from the inlet and released by the outlet. The reflected radiation, carrying sample’s spectral information, is detected using electro-optic (EO) sampling with ZnTe.
Fig. 1 Diagrams of the experimental setup. (a) The overall layout of the setup. THz pulses are generated by the PCA, and then send into the pressure cell. The reflected wave is detected by EO sampling method. (b) A closer view of the pressure cell. A diamond window and a sample spacer forms a sample chamber that allows solid or liquid sample placed inside. The high pressure is introduced from the high pressure inlet and released from the high pressure outlet.
In order to control the temperature, the pressure cell is placed into a vacuum chamber with a liquid nitrogen cold finger and a resistance wire heater in contact. A piece of thin plastic film (not shown in the figure) serves as the THz window of the vacuum chamber, adequate for maintaining a rough vacuum. Due to the small thickness and low refractive index of the plastic film, the Fresnel reflections are tiny, and therefore Fabry-Perot multiple reflections inside the film are negligible. The temperature is monitored by two thermocouples and stabilized by a proportional–integral–derivative (PID) controller which controls the current going through the resistance wire heater. The temperature can be tuned from 100 K to 473 K, with estimated stability of ± 0.3 K.
3. Methods of data analysis
The detected THz time-domain waveform have multiple pulses, due to the Fabry-Perot effect in the diamond window and the sample chamber. A typical time-domain waveform of an empty 2 mm thick sample chamber is shown in Fig. 2(a). The waveform clearly shows distinct pulses. The 1st and 2nd pulses correspond to the reflection from the front and back surfaces of the diamond window; the 3rd, 4th, and 5th pulses correspond to the multiple reflections inside the sample chamber. An asymmetric Tukey window is used to numerically truncate the waveform to keep only the 3rd pulse, because it contains the spectral information of the reference (or sample, if the cell is not empty). Although the 4th and 5th pulses also contain spectral information, we do not analyze them because they are very likely to overlap with the tails of the preceding pulses, increasing the difficulty of data processing. For opaque or strongly absorbing samples, it is also possible to analyze the 2nd pulse, which would contain spectroscopic information due to the reflection from the window-sample interface. In this case, we would need to account for the weak temperature dependence of the refractive index of the diamond window, which can be found in [30].
Fig. 2 (a) A typical time-domain waveform (blue) of an empty 2 mm long sample chamber. The 1st and 2nd pulses correspond to the reflection from the front and back surfaces of the diamond window; the 3rd, 4th, and 5th pulses correspond to the multiple reflections inside the sample chamber. The waveform is truncated with an asymmetric Tukey window (red) to keep only the 3rd pulse. (b) the amplitude spectrum of the truncated time-domain waveform.
Figure 2(b) shows the spectrum of the truncated waveform using the window function shown in Fig. 2(a). When measured with an empty cell (as for the data shown here), this serves as the reference of the measurements. The analogous spectrum obtained with a sample placed in the cell is extracted using the same windowing procedure. With the spectra of the sample and the reference, the refractive index and absorption coefficient of the sample can be obtained using:
where n and α are the refractive index and absorption coefficient of the sample, nd = 2.384 is the refractive index of diamond (assumed to be dispersionless), n0 is the refractive index of the reference (equal to 1 if the reference is air), c is the vacuum speed of light, d is the thickness of the sample chamber and R is the complex ratio of the spectra of sample to reference.The spectral resolution depends on the thickness and refractive index of the sample. Since, for the time-domain waveform, we do not want to include pulses other than the 3rd one, the length of the Tukey window for truncating the waveform is about the distance between the 3rd and the 4th pulses, which is 2nd/c. As a result, the spectral resolution is about c/2nd. For instance, measuring a sample with a thickness of 2 mm and a refractive index of 1.5 in the pressure cell will give a spectral resolution of about 0.05 THz.
For many condensed matter systems, this is adequate resolution. However, in some cases, interesting spectral features such as the pressure and temperature dependence of narrow phonon resonance frequencies cannot be adequately resolved by such a resolution. In order to address this problem, a zero-padded Fourier transform (ZPFT) can be used to more accurately estimate the spectral location of a peak. With a carefully chosen time-domain window to avoid artifacts, the ZPFT can give a more accurate determination of the frequencies of resonance peaks, but the linewidth of the peak might be inaccurate due to the effect of the time-domain windowing.
4. Results and discussion
To illustrate the capabilities of the cell, we have performed pressure- and temperature-dependent THz-TDS measurements of gaseous and liquid nitrogen, as well as the homochiral molecule R-camphor, which we have previously characterized at ambient pressure [1].
4.1 Nitrogen
Compressed nitrogen gas (99.998% purity, 6 kpsi pressure) was guided into the 2 mm thick empty sample chamber with a regulator to control the pressure. The nitrogen served as the source of pressure and the sample itself. The sample was cooled down to temperatures from 100.8 to 140 K. At each temperature, various pressures up to 10 MPa were applied to the sample, and the pressure-dependent THz time-domain waveforms were recorded.
At ambient pressure, the gas-liquid phase transition temperature of nitrogen is 77 K, which cannot be reached by our device. However, the transition temperature rapidly increases as the pressure increases. As a result, we are able to liquefy nitrogen in the pressure cell at moderately high pressure. The absorptions of gaseous and liquid nitrogen at THz frequencies are very small [31], so it is challenging to characterize the phase transition by the absorption coefficient. However, the difference of the refractive indices for the two phases is relatively large. Consequently, we can track the phase transition of the sample by measuring its refractive index.
Figure 3 shows the recorded time-domain waveform under pressures of 0.02 MPa and 8.94 MPa at 100.8 K. At each pressure, the 1st pulse corresponds to the reflection from the back surface of the diamond window, and the 2nd pulse corresponds to the double-pass transmission through the sample. Since nitrogen is nearly dispersionless in THz spectral range, the refractive index of the sample can be evaluated from the distance between the 1st and 2nd pulse in the time domain. Figure 4 shows the measured refractive indices of the sample as a function of pressure at various temperatures. For temperatures smaller than the critical temperature of nitrogen Tc = 126 K, a discontinuity of the refractive index can be observed, meaning that there is a sharp gas-liquid phase transition, where liquid phase has higher refractive index. However, the discontinuity decreases as the temperature increases, and finally disappears for temperatures higher than Tc. Above Tc, the distinction between gaseous and liquid nitrogen is blurred, indicating the existence of supercritical state.
Fig. 3 THz time-domain waveforms of the nitrogen under pressures of 0.02 MPa (blue) and 8.94 MPa (red) measured at 100.8 K. At this temperature, nitrogen is in gas phase under 0.02 MPa pressure and in liquid phase under 300 MPa. At each pressure, the 1st pulse corresponds to the reflection from the back surface of the diamond window, and the 2nd pulse corresponds to the double-pass transmission through the sample. The shift of the 2nd pulse in time-domain comes from the different refractive index of gaseous and liquid nitrogen.
Fig. 4 THz refractive index (from measurements) (data points) and mass density (from literature [32]) (curves) of nitrogen as functions of pressure at 100.8 K (blue), 109.9 K (magenta), 113.8 K (green), 125 K (orange), 130.7 K (black) and 140 K (red). For temperatures below Tc = 126 K (the first four curves), discontinuities of the refractive indices and densities can be observed, meaning that there is a sharp gas-liquid phase transition. For temperatures above Tc (the last two curves), there is no discontinuity, meaning that the nitrogen is now a supercritical fluid, where the distinction between gas and liquid is blurred.
The density curves of the nitrogen from literature [32] are also shown in Fig. 4. We find a strong correlation between the refractive index and density of fluid-state (gaseous, liquid and supercritical) nitrogen, which can be formulated as:
where n is the refractive index of nitrogen at THz frequencies, ρ is the mass density of nitrogen in g/cm3 and μ = 0.24 is the measured Gladstone-Dale coefficient for nitrogen. The literature value of Gladstone-Dale coefficient for nitrogen is also 0.24 [33], showing a good agreement.4.2 R-camphor
R-camphor crystals (98% purity, purchased from Sigma-Aldrich) were pressed into a tablet with a thickness of 400 µm and a diameter of 6 mm. The camphor tablet was attached to a piece of polyethylene (PE) tablet with a thickness of 2 mm to increase the spectral resolution by increasing the THz path length. Since R-camphor and PE has similar refractive indices [1,34], the reflection from the camphor-PE interface is negligible. The coupled tablet sample was placed into the pressure cell and subjected to pressures from 0.1 to 34.4 MPa using compressed nitrogen to pressurize the cell, with a step-size of 6.9 MPa. At each pressure, the tablet was cooled down from 257 to 237 K and then heated up to 257 K with a very gradual temperature changing rate of 0.1 K/min. THz time-domain waveforms were recorded at 1 K temperature intervals. Finally, the THz time domain waveform of a piece of PE tablet with a thickness of 2.4 mm and a diameter of 6 mm was measured in the pressure cell, as a reference. As discussed in section 3, the time-domain waveforms were truncated by a 20 ps window, corresponding to a 0.05 THz frequency resolution.
R-camphor has a solid-solid phase transition at ~242.7 K at ambient pressure [35], where the high temperature (HT) phase is a orientationally disordered phase and the low temperature (LT) phase is a orientationally ordered phase [36]. As shown in Fig. 5(b), the THz spectral differences of the two phases can be clearly observed: the HT phase has a flat absorption spectrum, corresponding to a broadband spectrum of vibrations characteristic of a glassy solid [1]. In contrast, the LT phase has distinct narrow peaks on its spectrum, corresponding to several well-resolved phonon modes, which can be assigned to specific inter- and intra-molecular motions [1].
Fig. 5 (a) Time domain waveform and (b) absorption spectrum of the HT phase (red) and LT phase (blue) of R-camphor.
By observing the sudden change of the spectrum between these two distinctly different states, we can extract the pressure-dependent phase transition temperature. In this case, the change is also clearly evident in the amplitude of the time-domain waveform. As shown in Fig. 6, the width of the phase transition is always less than 1 degree, within our temperature resolution. We plot the phase transition temperature as a function of applied pressure, and observe a nearly linear dependence. We also observe a hysteresis in the phase transition with a width of ~5 K; i.e. the phase transition temperatures are different as the sample is cooled and heated (Fig. 6 inset), indicative of a first-order phase transition [37]. The slopes of the temperature-pressure relationship are nearly identical for heating and cooling: 0.222 K/MPa for heating the sample and 0.225 K/MPa for cooling the sample. This is consistent with the results reported in earlier pressure dependent studies on camphor [35,38]. However, there are small shifts of the transition temperatures between our results and the previous results. We suspect the reasons for the shift are that the samples are from different vendors and with different purities and that the temperature scanning rates are different (we are varying the temperature much more slowly than in [35]).
Fig. 6 Phase transition temperature of R-camphor as a function of pressure. The phase transition temperatures and pressures are linearly related, with slopes 0.222 and 0.225 K/MPa for heating (red) and cooling (blue), respectively. The result consists with the literature [35] (green) very well. Inset: time-domain peak to peak amplitudes of the THz radiation as the sample was cooled down from 257 to 242 K and then heated up to 257 K with the temperature changing rate 0.1 K/min at 27.6 MPa fixed pressure. Hysteresis in the phase transition was observed.
In addition to this hysteretic behavior, we also observe a pressure-dependent frequency shift of the phonon resonances in the LT phase of camphor. The first three phonon resonances at 223 K (well below the order-disorder phase transition temperature) are indicated with arrows in Fig. 7(a), and their peak frequencies are estimated by the ZPFT technique, as noted above. Here, we do not analyze the phonon peak centered at ~2 THz, because its large absorption strength limits the signal-to-noise ratio of our measurements at these frequencies. Of course, one could improve this S/N ratio for this peak by using a thinner sample to reduce the attenuation of the signal. Figure 7(b) shows the pressure-dependence of the three lower resonance frequencies. The peak frequencies of the phonon resonances are 0.978, 1.212 and 1.498 THz at ambient pressure; these peaks blue-shift as the pressure increases, with slopes of 0.57, 0.65 and 0.85 THz/GPa for the 1st, 2nd and 3rd phonon peaks, respectively.
Fig. 7 Pressure-dependent spectra of the LT phase R-camphor measured at 223 K. (a) The absorption coefficient as a function of frequency at 0.1 (yellow) and 35 (magenta) MPa. The first three phonon peaks are labeled as the 1st, 2nd and 3rd peak. (b) Pressure-dependence of the peak frequencies of the 1st (red), 2nd (blue) and 3rd (green) phonon resonances.
The pressure-dependence of phonon modes is often described in terms of Grüneisen parameter γi defined by [5,39]:
where ω is the phonon frequency, V is the volume, P is the pressure, and β is the isothermal compressibility. The γ−ω relationship strongly depends on the nature of the modes: in a given material, the Grüneisen parameters are roughly a constant for intermolecular modes, but roughly proportional to ω−2 for intramolecular modes [40]. Due to the lack of experimental data for β for camphor, we cannot extract values for γi. However, since β is roughly a constant, we can move β to the left hand side of Eq. (4), i.e.Then we can treat the product βγi as a new parameter, given by the slopes of the lines in Fig. 7(b), normalized to the zero-pressure mode frequencies.Figure 8 shows the correlation of the Grüneisen parameters and phonon frequencies for the three modes shown in Fig. 7. The product of the isothermal compressibility and Grüneisen parameters βγi of the three modes are roughly constant with an average 0.56 GPa−1, despite a significant spread in the mode frequencies. The nearly constant value of γi indicates that these three modes are primarily intermolecular in character. This conclusion is consistent with our earlier characterization of camphor using DFT calculation [1], in which the three dominant lowest-frequency modes (calculated to lie at 0.95, 1.36, and 1.54 THz) were associated with hindered rotational motion about either the a or c crystal axis. These are external modes because the molecular units are rotating with respect to one another, and are therefore sampling the intermolecular potential surface.
Fig. 8 Correlation between βγ and phonon frequency. The three data points correspond to the 1st, 2nd and 3rd phonon resonances, respectively. The compressibility-normalized Grüneisen parameter is independent of frequency, indicating that the three resonances are all intermolecular modes. The red line indicates the average value of βγ, which is about 0.56 per GPa. The error bars represent the uncertainties from the slopes of the peak-frequency-vs-pressure data.
We can further calculate the specific heat at constant volume CV of the LT phase of R-camphor. For intermolecular modes, the Grüneisen parameters can be related to the thermal expansion coefficient αV and specific heat at constant volume CV by [5]:
where ρ is the mass density. From literature we find approximate values for αV = 5.3 × 10−4 K−1 and ρ = 1.1 g cm−3 (ambient pressure) [35]. As a result, we extract a value for the calculated specific heat at constant volume: CV = 0.85 J K−1 g−1. The value of CV for the LT phase of camphor cannot be found from existing literature. However, since solids are highly incompressible, the specific heat at constant pressure CP could be a good point of comparison for CV. This value, CP = 1.15 J K−1 g−1 (at 222 K), can be found in the literature [41], and is of the same order as our determined value for CV. This is reasonable agreement given the many approximations, including large uncertainty in the value for αV.5. Conclusions
In conclusion, we introduce a high pressure cell that can be used for pressure- and temperature- dependent THz-TDS studies. The pressure tuning range is up to 34.4 MPa, and the temperature tuning range is from 100 to 473 K. The aperture size is as large as 8 mm, allowing the measurable frequencies down to 0.1 THz. We demonstrate the capability of the device by exploring the pressure-dependent THz spectra of nitrogen and R-camphor. For nitrogen, we observe the pressure-dependent refractive index. At temperatures lower than Tc, we observe discontinuities of the refractive index curve, indicating a sharp gas-liquid phase transition. At temperatures higher than Tc, the discontinuity disappears, indicating the existence of supercritical state. We also extract the Gladstone-Dale coefficient of fluid-state nitrogen, and find good agreement with the literature value. For R-camphor, we observe the pressure dependent phase transition temperature, and the slopes of the temperature-pressure relationship and the hysteresis of the phase transition consistent with the results in earlier studies. We also observe a pressure-dependent frequency-shift of the phonon resonances in the LT phase of camphor, not previously reported. The first three phonon peaks blue-shift as the pressure increases. Grüneisen parameters of the resonances indicate that they are primarily intermolecular in character. From these data, we estimate the specific heat of the LT phase camphor at 223 K and find reasonable agreement with the literature value. The capability to study the THz spectra of soft condensed matter under hydrostatic pressure opens up new and exciting possibilities for exploring the complex potential landscapes that are relevant for vibrations in this spectral range.
Funding
Robert A. Welch Foundation.
Acknowledgments
We gratefully acknowledge valuable conversations with Dr. Michael Ruggiero.
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