A new technique for determining the refractive index of ices at cryogenic temperatures

Abstract

A reflection–absorption optical (RAO) spectrometer, operating across the ultra-violet/visible (UV/visible) wavelength region, has been developed that allows simultaneous measurements of optical properties and thickness of thin solid films at cryogenic temperatures in ultrahigh vacuum. The RAO spectrometer enables such measurements to be made after ice deposition, as opposed to most current approaches which make measurements during deposition. This allows changes in the optical properties and in the thickness of the film to be determined subsequent to thermal, photon or charged particle processing. This is not possible with current techniques. A data analysis method is presented that allows the wavelength dependent n and k values for ices to be extracted from the reflection–absorption spectra. The validity of this analysis method is shown using model data from the literature. New data are presented for the reflection UV/visible spectra of amorphous and crystalline single component ices of benzene, methyl formate and water adsorbed on a graphite surface. These data show that, for benzene and methyl formate, the crystalline ice has a larger refractive index than amorphous ice, reflecting changes in the electronic environment occurring in the ice during crystallisation. For water, the refractive index does not vary with ice phase.

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Introduction

In order to understand the nature of materials in remote, extreme or production environments, observations of radiation scattering have long been employed. Encoded within the scattered radiation are details of size, shape and spectroscopy (composition) of the scattering centres. These can be interpreted using appropriate theoretical descriptions for bulk materials, thin films or granular materials. Knowledge of the optical constants of materials is fundamental to interpreting this data across the electromagnetic spectrum. However, it is especially important in the infrared and optical regions when considering dust grains and thin films growing on them in our atmosphere, throughout the solar system and in the interstellar medium.^1–5 Likewise, measurements of optical constants play an important characterisation and quality assurance role in a range of fields from geology⁶ to the food industry⁷ and optical technologies.^8–10 Of particular relevance to this work is the examination of optical constants of astrochemical ice analogues.^11–13 Ices form on dust grains in space at low temperatures when atoms reactively accrete to form molecules and gas phase molecules accrete onto dust grains in a range of astrophysical environments.¹⁴

The optical constants define how light interacts with a material. For a non-absorbing medium, the key optical constant is the refractive index, n, which is given by the ratio of the velocity of light in a vacuum to the propagation velocity of light in the material. However, this description does not take into account the absorption of light by the material. To do this, we must define the complex refractive index, m, which is given in terms of refraction and absorption coefficients, n and k respectively (eqn (1)).

m = n + ik (1)

As both n and k are strongly dependent on wavelength, m itself must also be wavelength dependent. The value of m, through the Fresnel coefficients for reflection and transmission,^15,16 determines the ratio of reflected and transmitted intensities as light propagates across an interface between two different media.

Typically, the Kramers–Kronig (KK) relationship has been used to determine ice refractive indices from experimental spectra.^{11,13,17–25} The KK method is a powerful tool, but several issues have recently been identified that can result in the recovery of incorrect or incomplete refractive index data.²⁶ In particular, the KK method requires an accurate value of the ice thickness, d. This is often estimated using assumptions^21,27–30 or only measured during ice deposition.^{11,22,23,31–35} He–Ne laser interferometry is often used to make such measurements. Fig. 1 illustrates the production of interference fringes as light is reflected from a reflective substrate supporting a thin transmissive ice film. Measuring the thickness of an ice during deposition means that the effect of post-deposition processing or particle bombardment³⁶ on its thickness cannot be measured and therefore neither can the refractive index.²⁶ Finally, in order to perform the KK analysis the Fresnel coefficients for transmission are required. Therefore, only ices deposited on a transmitting substrate can be examined and experimental arrangements utilising the significant sensitivity advantage of reflection–absorption on a reflective substrate are not suitable.

Fig. 1 Schematic diagram illustrating the origin of interference fringes at the interface of a transmissive film (ice) and reflective substrate (highly oriented pyrolytic graphite, HOPG). I and R represent the incident and reflected beams respectively. θ₀, θ₁ and θ₂ are the angles of incidence, refraction due to the ice and refraction due to the HOPG substrate respectively. The ice thickness is d, and n₁ and k₁ are the ice optical parameters. n₀ is the refractive index of the vacuum, equal to 1, and n₂ and k₂ are the substrate optical properties.

In light of the above, we have designed and developed a RAO spectroscopy apparatus to simultaneously determine the UV/visible refractive index and thickness of ices deposited on a reflective surface under ultrahigh vacuum. This apparatus has previously been demonstrated in measurements of the real part of the refractive index of amorphous benzene (C₆H₆) ice as a proof of concept.²⁶ The apparatus allows n and d to be simultaneously determined ab initio and in a single experimental procedure. Additionally, as spectra are recorded after the ice has been deposited, the effect of processing can be measured.²⁶

The work described here presents a comparison of the refractive index of amorphous and crystalline C₆H₆, methyl formate (CH₃OCHO, MF) and water (H₂O) ices and provides an explanation for the differences observed. These systems are being investigated in this work due to their relevance to astrochemistry^37–41 and their contrasting optical spectroscopy. H₂O is the most abundant component of interstellar, cometary and planetary ices and is optically transparent in thin films above 220 nm. C₆H₆ is the prototype of the (poly)cyclic aromatic hydrocarbon compound family which represents a sink for around 20% of all galactic carbon and has a characteristic UV spectroscopy dominated by excitation of π electrons. MF is readily formed by energetic processing of simple models of interstellar ices and is observed in warm pre-stellar environments. While MF absorbs in the UV, the spectra are weak in comparison to those of C₆H₆.

C₆H₆ has well-characterised surface behaviour relevant to astrochemistry^42–44 and has well defined UV/visible absorption behaviour that can be used as a benchmark.^45–47 In previous work,⁴⁴ multilayers of C₆H₆ deposited on HOPG at 25 K have been shown to undergo a phase change after annealing to 90 K. This phase change was shown by changes in the reflection–absorption infrared (RAIR) spectrum of C₆H₆ upon annealing. Other authors have also observed this thermally induced phase change using vibrational spectroscopy methods. Jakob and Menzel⁴⁸ deposited multilayers of C₆H₆ on Ru(001) at 53 K in its amorphous form, and observed splitting of several RAIRS bands upon annealing the ice to 127 K. Raman spectra recorded by Ishii et al. show band splitting after annealing C₆H₆ ices deposited at 17 K on gold coated Cu to 58 K, indicative of crystallisation.⁴⁹ In the same study, X-ray diffraction measurements⁴⁹ confirmed the lack of order in the initially deposited films, and showed that the annealed films were fully crystalline. Swiderek et al. used electron energy loss spectroscopy (EELS) to show that films of C₆H₆ deposited on Pt at 32 K gave different spectra compared to films deposited at 100 K.⁴⁹ Specifically, vibronic bands assigned to the ³B_1u ← ¹A_1g transition were sharper and shifted to higher energy loss in crystalline benzene compared to amorphous ice.⁵⁰

In addition to examining the phase change itself, several authors have found that C₆H₆ deposited at elevated temperatures directly forms an ordered or crystalline phase. When C₆H₆ is deposited at 110 K on Cu(111), an initial chemisorbed layer forms, lying flat on the surface.⁵¹ Subsequently deposited C₆H₆ adsorbs as an almost parallel oriented physisorbed bilayer, which is followed by the growth of ordered multilayers.⁵¹ This behaviour was shown by a combination of temperature programmed desorption (TPD), high resolution EELS (HREELS) and near edge X-ray absorption fine structure (NEXAFS) measurements.⁵¹ Similar results were also observed for C₆H₆ deposited at 120 K on Ru(001), shown by TPD and HREELS.⁵² On graphite, neutron diffraction experiments suggest that an initial, flat-lying, physisorbed monolayer forms when C₆H₆ is deposited at 100 K, followed by the growth of crystalline multilayers.⁵³

The effect of the benzene phase change on the electronic spectrum of C₆H₆ ice was recently examined in detail by Dawes et al.⁴⁵ Transmission spectra were recorded in the wavelength range 115–340 nm for C₆H₆ deposited on a MgF₂ window at 25 K. C₆H₆ was crystallised by annealing the ice deposited at 25 K to 90 K for 2 minutes, and subsequently several band shifts and line profile changes were observed in the spectrum.

Whilst the C₆H₆ phase change has previously been described spectroscopically, the effect of the phase change on the refractive index of C₆H₆ ices has not been examined. Indeed only one study has determined the refractive index of crystalline C₆H₆ ice. Romanescu et al. split the output of a HeNe laser into two beams which were then reflected off a Au substrate at different reflection angles during deposition of C₆H₆ at 100 K.⁵⁴ The period of the resulting interference fringes, and the known reflection angles, were used to determine an n value of 1.54 ± 0.02 for the crystalline C₆H₆ ice.⁵⁴ This is higher than the value of n = 1.43 ± 0.07 previously determined by our group for amorphous C₆H₆ ice.²⁶

In addition to comparing the real parts of the refractive indices of amorphous and crystalline ices, we present a new analysis method which allows the determination of the complex refractive index m as a function of wavelength from experimental reflection–absorption spectra for an ice. No prior knowledge of the transmission Fresnel coefficients is required, in contrast to the KK analysis. Hence ices deposited on opaque surfaces can be successfully examined. The analysis method is based on the work of Kozlova et al.,⁵⁵ who determined m for lithium niobite (LiNbO₃) thin films and single crystals on an opaque Si substrate. This is the first time such a method has been applied to astronomically relevant molecular systems.

Experimental methodology

The data presented here were recorded using a new reflection absorption optical (RAO) spectrometer,²⁶ attached to an ultrahigh vacuum (UHV) chamber.⁵⁶ A highly oriented pyrolytic graphite (HOPG) surface is mounted in the vacuum chamber on the end of a copper cold finger, connected to a closed-cycle helium refrigerator (SHI-APD). This is used as a carbonaceous interstellar dust grain analogue surface.^12,57–62 The helium refrigerator allows a base temperature of 26 K to be achieved and the typical base pressure in the chamber is ≤2 × 10⁻¹⁰ mbar. The sample is cleaned by heating to 250 K for 3 minutes, and cleanness is confirmed by the lack of any desorption, as measured by a mass spectrometer, during a heating ramp.

The design and installation of the RAO apparatus has been described in detail elsewhere.²⁶ Briefly, a UHV compatible, stainless steel lens assembly was designed which allowed UV/visible light to be fed into the chamber, reflected from the HOPG substrate and subsequently collected via fibre optic cables and analysed by a compact dispersive spectrophotometer (Ocean Optics QE Pro). This assembly is connected to a linear drive (Vacgen Ltd) which allows the angle of incidence (and hence angle of reflection) to be varied from near normal to almost grazing incidence. The range of angles of incidence achieved is 31°–68° with respect to the surface normal. Light is provided by an Ocean Optics DH-2000-S-DUV-TTL source with a spectral range of 190–900 nm.

C₆H₆ (Sigma-Aldrich, ≥99.9%), MF (Sigma Aldrich, anhydrous 99%) and deionised H₂O were further purified prior to use by repeated freeze–pump–thaw cycles. Ices were grown on the HOPG surface by admitting vapour into the UHV chamber via a high precision leak valve. During deposition, the surface is positioned facing the leak valve outlet. Dosing in this manner (direct dosing) allows ices to be grown which are thick enough to produce interference fringes. The total exposure is reported in Langmuir, L_m, where 1L_m = 1 × 10⁻⁶ mbar s. UV/visible reflection–absorption spectra are produced by recording reflection spectra of the surface before (background spectrum, R₀) and after (sample spectrum, R) dosing. The surface is rotated to face the leak valve outlet for dosing and then is returned to its original position during this procedure. The UV/visible spectra are presented in the form ΔR/R as a function of wavelength, where ΔR/R = (R − R₀)/R₀. This corrects for the fact that the light source intensity is not equal across the entire spectral range.⁶³ All UV/visible spectra presented are the average of 128 scans with an integration time of 250 ms per scan. These parameters were chosen by trial and error to obtain the highest signal without saturating the CCD array detector. RAIR spectra for ices were also recorded using a Thermo-Nicolet FTIR spectrometer coupled to a liquid nitrogen cooled mercury cadmium telluride detector. RAIR spectra are the result of the co-addition of 256 scans at a resolution of 4 cm⁻¹ and are also presented in the form of ΔR/R.

Where ices have been annealed, the ices were deposited at base temperature and subsequently heated linearly to the annealing temperature. They were held at the annealing temperature for 3 minutes before returning to base temperature and recording a UV/visible or RAIR spectrum.

Data analysis

The UV/visible spectra were first analysed using a method developed by Harrick for use in the infrared,⁶⁴ and adapted to our system in previous work.²⁶ This allows the ice thickness, d, and the real part of the refractive index, n, to be determined by examining the spacing between the extrema of the interference fringes produced at different angles of incidence. Unlike previous methods, n and d are determined using a single experimental procedure, and any effect of processing the ice on these values can be examined as they are measured after the ice has been grown. Whilst this serves as a proof of concept for the apparatus and gives accurate values of n and d for the ices examined, this method does not give information about the imaginary part of the refractive index, k, nor the wavelength dependence of the complex refractive index. This is essential if the data are to be used in simulating the optical properties of ices in astronomical environments.

In order to determine m as a function of wavelength for an optically opaque surface, a method was developed based on the work of Kozlova et al.⁵⁵ The analysis works by taking a starting value of n, along with other parameters described below including an initial guess of k, and using these to simulate a reflectance spectrum, (ΔR/R)_sim. The simulated spectrum is then compared to the experimental one, (ΔR/R)_exp, and a match parameter is determined. The values of n and k are then varied until a good match between (ΔR/R)_exp and (ΔR/R)_sim is found. With reference to Fig. 1, the input parameters can be determined. The angle of incidence, θ₀, refractive index of the vacuum, n₀ (equal to 1), complex refractive index of the ice, m₁ (where m₁ = n₁ + ik₁), ice thickness, d, and the complex refractive index of the HOPG, m₂ (equal to n₂ + ik₂) all contribute to (ΔR/R)_exp. In the case of HOPG, there are two sets of optical parameters as HOPG is birefringent: one set for p-polarised light (n_2p and k_2p) and the second for s-polarised light (n_2s and k_2s) yielding complex refractive indices m_2p and m_2s. Both of these optical parameters must be taken into account in the analysis, as the incident light is unpolarised. In this work, the optical parameters used for HOPG are those determined by Djurišić and Li.⁶⁵

Using the parameters described, the Fresnel coefficients of reflection for s- and p-polarised light for the vacuum/ice, ice/substrate and vacuum/substrate interfaces, can be determined. These are r_1p and r_1s (vacuum/ice), r_2p and r_2s (ice/substrate) and r_0,2p and r_0,2s (vacuum/substrate) as given by eqn (2)–(7).^16,55

In eqn (2)–(7), θ₁, θ_2p and θ_2s are the complex angles of refraction at each interface given by eqn (8)–(10).⁵⁵Using the Fresnel coefficients, it is possible to calculate R_sim and R_0sim, which are comprised of the reflection coefficients for s- and p-polarised light, R_s and R_p respectively, for the ice, and R_0s and R_0p for the clean surface. The reflection coefficients are calculated using eqn (11)–(14).⁵⁵

R_0p = |r_0,2p|² (13)

R_0s = |r_0,2s|² (14)

In eqn (11) and (12), δ is the complex phase thickness and describes the phase change introduced in the reflected light. It is given by eqn (15)⁵⁵where λ is the wavelength of the light. R_0sim and R_sim are given by eqn (16) and (17).⁵⁵

R_sim = R_p + R_s (16)

R_0sim = R_0p + R_0s (17)

Using eqn (2)–(17), a simulated reflectance spectrum, (ΔR/R)_sim, for a given ice can be produced. This can be compared to the experimental spectrum, (ΔR/R)_exp, to give a match parameter, s, which is calculated according to eqn (18).The parameter s is minimised using a least squares function and, via an iterative process, the target parameters, n₁ and k₁, can be determined.

A Python code was written to perform the analysis described. The required inputs are the experimental reflection spectra at each reflection angle and the ice thickness examined, with the reflection angles and thicknesses determined using the Harrick method.^26,64 Additionally, the HOPG optical parameters are necessary. The outputs of the analysis code are the determined wavelength dependent values of n₁ and k₁, as well as the simulated spectra for each ice thickness and reflection angle. The code can be found in the ESI,‡ Appendix E1.

In order to test the theory and the code, test data with known values of n₁ and k₁ were used as a benchmark. The values of n₁ were those of Kofman et al.⁶⁶ determined for amorphous solid water (ASW). Fig. 2 plots n as a function of wavelength determined by Kofman et al.⁶⁶ The data are fitted with a polynomial function in order to determine n across the full wavelength range used in this work. It should be noted that the wavelength range has an upper limit of 591 nm due to the availability of the HOPG optical parameters.

Fig. 2 Real part of the refractive index, n, of amorphous water ice as a function of wavelength. The red squares represent the values reported by Kofman et al.⁶⁶ The blue line is a fit to the data to give n across the wavelength range used to test the analysis method.

Kofman et al.⁶⁶ did not determine wavelength dependent values of k for ASW, therefore a constant value of 0.01 was assumed. This value was chosen, as previously reported values in the relevant wavelength region tend to be small (≪0.5) and positive for water.^25,67 In any case, the specific value used is less important than the fact that it is known. The values of n and k for ASW were used to produce simulated reflection spectra using a separate Python code, shown in the ESI,‡ Appendix E2. The code takes the known values of θ, d, λ, n_2s, k_2s, n_2p, k_2p, n₁ and k₁ and uses eqn (2)–(17) to give simulated ΔR/R spectra. Spectra were simulated with ice thicknesses between 100 and 500 nm. An example of a simulated water spectrum is shown in Fig. 3A (blue trace) for an ASW ice thickness of 400 nm and a reflection angle of 53°.

Fig. 3 Comparison of the results of the analysis with the input values: (A) comparison of a spectrum used as an input for the analysis code (blue line) and the output spectrum (red triangles); (B) and (C) are the real and complex parts of the refractive index of water ice respectively as a function of wavelength. The blue lines are the values used to produce the input spectrum and the red empty circles are the results produced by the analysis.

The simulated ASW spectra were then used as input (ΔR/R)_exp data for the analysis code. Fig. 3 shows the results of the analysis. Fig. 3B and C show the calculated, wavelength dependent, values of n and k (red open circles) respectively. The input values are also shown as blue lines. Fig. 3B shows that the calculated n values from the simulated ASW spectra agree very well with those determined by Kofman et al.⁶⁶ Similarly, Fig. 3C shows that the determined k values are in excellent agreement with the assumed value of 0.01, with only very small variations observed around 350 and 560 nm. In fact, the determined values of k differ from the assumed value by less than 0.05%. Fig. 3A shows that this small variation is insignificant, as the simulated spectrum matches the input spectrum very well. Clearly the data analysis method presented here works well for the analysis of UV/visible reflection–absorption spectra of ices on opaque or reflective surfaces.

Experimental results

Initially, RAIRS was used to characterise the ices grown on HOPG. Infrared spectra of C₆H₆,^{42,44,45,48,52,68,69} MF^70–75 and H₂O^{42,43,56,76–78} ices have all been recorded previously and are used as a benchmark for the spectra presented here. Fig. 4 shows several RAIR spectra of C₆H₆ ices. Fig. 4A shows the wavenumber region 3150–2950 cm⁻¹ and Fig. 4B shows the region 1600–950 cm⁻¹. The red spectrum shown in Fig. 4 is that of 500L_m of C₆H₆ deposited on HOPG at 27 K. At this deposition temperature, benzene is in its amorphous form.^44,45 The bands in the amorphous C₆H₆ spectrum at 3090 cm⁻¹ and 3032 cm⁻¹ (Fig. 4A) and those at 1479 cm⁻¹ and 1036 cm⁻¹ (Fig. 4B) have been observed previously.⁴² They are assigned to the C–H stretch (ν(CH)_aromatic), ν(CH) combination mode, aromatic C–C stretch (ν(CC)_aromatic) and C–H in plane deformation (δ(CH)_in-plane) mode of C₆H₆ respectively.^68,69,79 In addition to these bands, several other features are observed in the spectra, which can be assigned by comparison with the literature.^{48,52,68,69,79} The band at 3068 cm⁻¹ is assigned to the ν(CH)_aromatic mode of C₆H₆. The bands at 1176 cm⁻¹ and 1148 cm⁻¹ are assigned to δ(CH)_in-plane modes and the band at 973 cm⁻¹ is the δ(CH)_{out of plane} mode. Tentative assignments of the bands at 1402 cm⁻¹ and 1012 cm⁻¹ are given based on their frequencies. These are assigned to ν(CC)_aromatic and δ(CH) modes respectively. The appearance of additional bands compared to previous work is explained by the fact that the ices examined by Salter et al.⁴⁴ are estimated to be approximately 10 nm thick, whereas those in this work are of the order of hundreds of nm thick.²⁶

Fig. 4 RAIR spectra of 500L_m of C₆H₆ ice deposited on HOPG. The red spectrum represents C₆H₆ deposited at 27 K. The blue trace represents the ice in the red trace annealed to 90 K. The green trace is that for ice deposited at 70 K.

C₆H₆ ice is known to undergo a thermally induced phase change.^{44,45,47,50,51,80} This phase change has previously been observed upon annealing to 90 K,⁴⁴ with total crystallisation being complete following annealing to 120 K. The blue trace in Fig. 4 shows the effect of annealing the amorphous C₆H₆ ice to 90 K. In Fig. 4A, the ν(CH)_aromatic mode at 3090 cm⁻¹ splits into two bands at 3091 cm⁻¹ and 3085 cm⁻¹, the second ν(CH)_aromatic mode red-shifts to 3066 cm⁻¹ and the ν(CH) combination band splits into two bands at 3037 cm⁻¹ and 3030 cm⁻¹. In Fig. 4B, the ν(CC)_aromatic band at 1479 cm⁻¹ increases in intensity and the second ν(CC)_aromatic band at 1402 cm⁻¹ shifts and splits into peaks at 1416 cm⁻¹ and 1404 cm⁻¹. The first δ(CH)_in-plane mode at 1176 cm⁻¹ disappears, whereas the peak at 1148 cm⁻¹ splits into bands at 1148 cm⁻¹ and 1142 cm⁻¹ and the mode at 1036 cm⁻¹ splits into two bands at 1040 cm⁻¹ and 1034 cm⁻¹. Finally the δ(CH) mode at 1012 cm⁻¹ shifts slightly to 1011 cm⁻¹ and the δ(CH)_{out of plane} mode at 973 cm⁻¹ splits to give bands at 987 cm⁻¹ and 974 cm⁻¹. These changes in the RAIR spectrum of C₆H₆ are in agreement with those previously assigned to crystallisation of the ice.^44,45,48

Further experiments were undertaken to examine whether crystalline C₆H₆ ice could be grown directly. A deposition temperature of 70 K was chosen as it was sufficiently high to crystallise C₆H₆, but far enough away from the desorption temperature of around 150 K, as shown in Fig. E1, ESI.‡ The green trace in Fig. 4A and B shows the RAIR spectrum of 500L_m of benzene deposited at 70 K. It is clearly identical to the annealed spectrum, and upon further annealing no changes were observed in any of the bands, indicating that the ice was fully crystalline. In light of these results, crystalline C₆H₆ ices were grown at a deposition temperature of 70 K, and amorphous C₆H₆ ices were deposited at base temperature.

Similar characterisation experiments were performed for MF and H₂O ices, both of which also undergo thermally induced phase changes. RAIR spectra of MF are shown in Fig. E2 in the ESI.‡ Additionally, band assignments are given in Table E1 in the ESI,‡ with reference to the literature.^{70,71,73–75,81,82} When MF is deposited at 27 K, it is in its amorphous form and subsequent annealing to 100 K causes the spectrum to change, indicative of an amorphous to crystalline phase transition.⁸³ However, when MF is deposited on the HOPG surface at 105 K, in an attempt to grow crystalline ice directly, the RAIR spectrum of the ice differs to that of the annealed ice (Fig. E2, ESI‡) and agrees with the spectra recorded by Modica and Palumbo.⁷⁰ Previous studies have shown that MF can exist in two crystalline forms,⁸² in line with our observations. In this work, only the form deposited at 105 K is examined, and this is referred to as crystalline MF. Fig. E3 of the ESI‡ shows RAIR spectra of H₂O ices grown at 27 K and at 135 K. At 27 K, the broad bands are typical of ASW, whereas the spectrum resulting from the ice grown at 135 K is typical of that observed for crystalline water ice (CI).^14,84

Fig. 5 shows UV/visible spectra of amorphous (Fig. 5A) and crystalline (Fig. 5B) C₆H₆ ices for a single C₆H₆ exposure and at two reflection angles. Several common features are immediately apparent. Firstly, the feature in all the spectra at 656 nm arises as an artefact from the light source and can be disregarded.^26,63 Interference fringes are also observed. These are used to determine the ice thickness and real part of the refractive index using the method of Harrick.^26,64 The extrema of the interference fringes shift in wavelength at different reflection angles and previous work has shown that increasing the exposure increases the number of interference fringes seen in the spectrum, as expected due to the increased ice thickness.²⁶

Fig. 5 UV/visible reflection–absorption spectra taken at two different reflection angles for 400L_m of amorphous (A) and crystalline (B) C₆H₆ ices deposited on HOPG.

In each spectrum in Fig. 5, absorption bands, which do not shift with C₆H₆ exposure, are also observed. The amorphous C₆H₆ spectra (Fig. 5A) show two absorption features. One is located at 214.8 nm and the other is observed as several peaks centred on approximately 255 nm. These absorption bands have been observed previously^{45–47,50,85–87} and are assigned to the ¹B_1u ← ¹A_1g and ¹B_2u ← ¹A_1g transitions of C₆H₆, respectively. The ¹B_1u ← ¹A_1g band in the amorphous C₆H₆ spectra in Fig. 5A appears as a broad peak with a maximum intensity at 214.8 nm. In the crystalline spectra (Fig. 5B), the intensity of this feature is lost. The reason for the disappearance of the ¹B_1u ← ¹A_1g band upon crystallisation is unclear. However, it should be noted that the intensity of the reflected light below approximately 220 nm is very low in our experiment, which may affect the clarity of the spectra below this wavelength.

Fig. 6 shows UV/visible spectra of amorphous and crystalline C₆H₆ in the region 230–280 nm, to highlight the ¹B_2u ← ¹A_1g transition. It is clear from Fig. 6 that the absorption due to the ¹B_2u ← ¹A_1g transition changes upon crystallisation of C₆H₆. The peaks in the crystalline C₆H₆ spectrum (blue trace) are blue shifted compared to the amorphous spectrum (red trace) by 0.7 nm. Additionally, the bands are sharpened in the crystalline spectrum. The full width at half maximum of the central band at approximately 255 nm is 2.63 nm in the amorphous spectrum, compared to 1.94 nm in the crystalline spectrum. The sharpening and blue shift of the ¹B_2u ← ¹A_1g bands in crystalline C₆H₆ is in excellent agreement with work by Dawes et al.⁴³ The positions of the peaks in amorphous and crystalline C₆H₆ ice are shown in Table 1, alongside the observations of Dawes et al.⁴⁵ The spectrum of crystalline C₆H₆ ice in Fig. 6 also contains minor peaks in between the bands listed in Table 1. These are possibly evidence of Davydov splitting,⁸⁸ where the presence of more than one equivalent molecular entity in the unit cell interacts to cause the splitting of electronic or vibrational bands. This effect has also been observed in UV/visible spectra of crystalline C₆H₆ ice recorded by Dawes et al.⁴⁵

Fig. 6 UV/visible reflection–absorption spectra of amorphous (red trace) and crystalline (blue trace) C₆H₆ on HOPG in the wavelength range 230–280 nm. In each case the C₆H₆ exposure is 400L_m and the reflection angle is 46°.

Table 1 Band positions of the ¹B_2u ← ¹A_1g transition in amorphous and crystalline C₆H₆ ice in this work and observed by Dawes et al.⁴⁵

Band position in this work/nm		Band position observed by Dawes et al.^45/nm
Amorphous C6H6	Crystalline C6H6	Amorphous C6H6	Crystalline C6H6 i
244.0	243.3	244.15	243.25
249.4	248.7	249.80	248.85
255.5	254.7	255.65	254.65
261.5	260.9	261.60	260.80
265.5	264.3	265.65	264.45

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UV/visible spectra of amorphous and crystalline MF and H₂O are shown in the ESI‡ as Fig. E4 and E5 respectively. In both cases, the characteristic interference fringes are shown. However, unlike the spectra of C₆H₆ in Fig. 5, no sharp absorption features are seen. For H₂O, this is in line with previous work which shows that no absorption is expected at wavelengths above 180 nm.^77,89–91 However, MF is known to show an absorption feature at 223 nm in the liquid phase.⁹² The reason that this feature is not observed in this work is unclear, particularly given that the absorption cross-sections of C₆H₆ and MF are of similar magnitudes.^45,92 One explanation may be that the dipole symmetry forbidden ¹B_1u and ¹B_2u states of C₆H₆ are only observed due to Herzberg–Teller vibronic coupling, which allows them to intensity steal from an allowed transition.⁴⁵ This may lead to an increase in absorption intensity of the C₆H₆ band which is not observed for MF.

The Harrick analysis^26,64 was applied to the UV/visible spectra of C₆H₆, MF and H₂O ices in order to determine the real part of the refractive index and the thicknesses of the ices. The determined values of n are shown in Table 2.

Table 2 Real part of the refractive indices for the ices examined in this work

Ice	Refractive index, n
Amorphous C6H6	1.43 ± 0.07^26
Crystalline C6H6	1.63 ± 0.08
Amorphous MF	1.23 ± 0.05
Crystalline MF	1.40 ± 0.08
ASW	1.38 ± 0.08
CI	1.40 ± 0.12

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The refractive index of amorphous C₆H₆ ice has previously been determined for the data presented here and has a value of n = 1.43 ± 0.07.²⁶ The data shown in Fig. 5 give a refractive index of 1.63 ± 0.08 for crystalline C₆H₆ ice. This is in agreement, within error, with the value of n = 1.54 ± 0.02 determined by Romanescu et al.⁵⁴ for C₆H₆ deposited at 100 K on a gold surface. It is also in agreement with previous work by Yamada and Person, which gives a value of n of 1.57 ± 0.05. The upper limit of the n value for amorphous MF ice is close to the value of 1.30 determined by Modica and Palumbo,⁷⁰ with the slight variation most likely due to a difference in deposition method. Whilst no literature values of n for crystalline MF ice are available, the agreement between the values determined for amorphous and crystalline C₆H₆ and amorphous MF with the literature suggest that the value for crystalline MF is reasonable. The determined values of n for ASW and CI are almost identical to each other within the error ranges. Similar behaviour has been observed in the literature, where the refractive index of water ice does not vary as a function of deposition temperature.^35,93

The determined real parts of the refractive indices in Table 2 were then used to calculate the thicknesses of the ices. Fig. 7 shows that for all amorphous and crystalline ices, there is a linear relationship between thickness and exposure. Errors in d are determined from the upper and lower limits of n.

Fig. 7 The thickness of C₆H₆, MF and H₂O ices as a function of exposure. The black squares are amorphous ices and the red circles are crystalline ices. Dotted lines show the fits, which are fixed with an intercept of 0.

In all cases, it is clear that crystalline ices are thinner than the amorphous ones. Tests were performed to ensure that the observed thickness difference was due to the phase change, rather than to a reduced sticking probability during deposition at elevated temperatures. Temperature programmed desorption, where the surface is linearly heated whilst desorption is monitored by a quadrupole mass spectrometer (QMS) was used to confirm this. The area under a plot of QMS intensity as a function of surface temperature, for a given mass fragment, is directly proportional to the amount of adsorbate on the surface.¹⁴ For C₆H₆, no decrease in sticking probability (TPD curve area) was observed between 27 K and 70 K. For MF and H₂O, a small decrease was found, which was corrected for by increasing the dose time at the higher deposition temperature. Hence, the change in thickness is solely a product of the ice phase.

The thickness difference between amorphous and crystalline ices can be expressed as a compaction factor, calculated from the ratio of weighted least squares linear fits to each set of data in Fig. 7. In each fit, the intercept is fixed at 0, as an exposure of 0L_m must have no thickness. The ratio of the gradients for the crystalline to amorphous C₆H₆ data gives a compaction factor of 0.74. This means that crystalline C₆H₆ ice is 0.74 times as thick as the amorphous ice for the same total amount of C₆H₆. The compaction factors for MF and H₂O are 0.74 and 0.82 respectively.

Following the initial analysis, UV/visible spectra of amorphous and crystalline C₆H₆ ices were then used as input spectra for the analysis code, in order to determine the wavelength dependent values of n and k for the ices. Fig. 8 shows the output spectrum (blue trace) for an exposure of 400L_m C₆H₆ at a fixed reflection angle of 53° in the wavelength region 200–300 nm. The ¹B_1u ← ¹A_1g and ¹B_2u ← ¹A_1g transitions at 214 nm and 255 nm respectively are very well reproduced in the simulated spectrum. The values of n and k over the same wavelength range for C₆H₆ are shown in Fig. 9. The good agreement between the spectra in Fig. 8, as well as the data already shown in Fig. 3, indicates that the theory presented here is suitable to describe the physical processes which give rise to the observed reflection spectra.

Fig. 8 Comparison of reflection–absorption spectra, in the wavelength range 200 nm to 300 nm, of 400L_m amorphous C₆H₆ on HOPG. The red trace is the experimental spectrum. The blue trace is the simulated spectrum. The reflection angle is 53°.

Fig. 9 Calculated values of n (red trace) and k (blue trace) for amorphous C₆H₆ ice, used to produce the spectrum in Fig. 8.

Fig. 10 shows the same spectra as Fig. 8, but now across the entire wavelength range. Whilst the data shown in Fig. 8 show that the absorption features of benzene can be well reproduced by the code, Fig. 10 shows that the interference fringes at longer wavelengths are not well reproduced by the code.

Fig. 10 Comparison of the experimental and simulated reflection–absorption spectra, in the wavelength range 200–590 nm, of 400L_m amorphous C₆H₆ on HOPG. The red trace is the experimental spectrum and the blue trace is the simulated spectrum produced by the analysis code. The reflection angle is 53°.

Discussion

For both C₆H₆ and MF, Table 2 shows that the crystalline ices have a higher refractive index. This suggests that light impinging on the solid from a vacuum is slowed more upon entering the crystalline ice medium than the amorphous one. Similar behaviour has been reported for thin films of germanium selenide.⁹⁴ This change can be rationalised by considering the concept of the optical impedance, Z, of a medium. As proposed by Kronig,⁹⁵ optical impedance is defined as the ratio of the amplitudes of the perpendicular wave vectors in a propagating light wave, i.e. the ratio of the electronic wave vector, E, to the magnetic wave vector, H, and is shown in eqn (19).^95,96Also shown in eqn (19) is the relationship between impedance and the permeability, μ, and dielectric constant, ε, of a medium.⁹⁶ In the case of non-magnetic media, such as C₆H₆ or MF, μ = 1 and hence Z = ε^−1/2.⁹⁶

In an amorphous form, the molecules are randomly aligned, and hence the electronic environment is disordered, i.e. the electron cloud of each molecule is randomly aligned relative to its neighbours. Crystalline C₆H₆ ice consists of C₆H₆ molecules arranged in a herringbone structure.^{48,52,97–100} Therefore, there is a difference in the electronic environment in the two ice phases for each molecule. This will cause the dielectric constant, and hence impedance, of the ice to change. In order to explain the difference in refractive index between amorphous and crystalline ice, it is necessary to look at the relationship between the refractive index n and the optical impedance Z. The literature shows that n varies with ε^1/2.^16,95 Therefore n ∝ 1/Z, and hence a change in impedance must be accompanied by a change in refractive index.

For C₆H₆ and MF, the refractive index of crystalline ice is higher than that of amorphous ice; 1.63 ± 0.08 compared to 1.43 ± 0.07, and 1.23 ± 0.07 compared to 1.40 ± 0.08 respectively. This implies that Z is lower for crystalline C₆H₆ and MF ices than for the amorphous phase, and subsequently that the dielectric constant, ε, of the crystalline ice is higher than for amorphous ice, as shown in eqn (19). In agreement with this, crystalline materials have previously been shown to have higher values of ε than their amorphous counterparts.^{82,94,101,102} Recent theoretical work by Pilling and Bonfim also showed that an increase of ε would lead to an increase in the intensity of infrared bands, in agreement with the spectra shown in Fig. 4 and Fig. E2 (ESI‡).¹⁰³ The dielectric constant of a medium is also related to its polarizability,¹⁰³ and therefore our data suggest that crystalline C₆H₆ and MF ices are more polarisable than their amorphous counterparts. Unlike C₆H₆ and MF, the refractive indices of ASW and CI do not vary, and agree within the error limits. This is in agreement with previous work which has shown that the refractive index of H₂O ice does not vary with temperature.^35,93 It is not clear why the behaviour of H₂O differs from the other molecules in this work, but further investigations of this type on other molecules will help to clarify this.

It was shown that the amount of adsorbate on the HOPG surface was consistent for all molecules at the various deposition temperatures. Therefore, the observed compaction shown in Fig. 7 is solely a consequence of the ice phase transition. This implies that crystalline ices are denser than their amorphous counterparts. However, care must be taken to not over-extrapolate from this data. The exact structures of amorphous C₆H₆ and MF ices are unknown. For example, if the ices are porous, the compaction may be due to a combination of pore collapse and decrease in intermolecular distances. For H₂O ice, the structure is well studied^{35,84,93,104,105} and ASW is known to be porous. In this work, the ASW is likely to be in its compact form, where the porosity is less than other forms of ASW but still significant.^104,105 Despite the fact that the refractive index of ASW and CI does not vary (Table 2), there is a clear compaction shown in Fig. 7. This is certainly in part due to loss of porosity. Westley et al.³⁵ found that in the temperature range 20–140 K, the density of H₂O ice remains constant. In this case, loss of porosity going from ASW to CI would be the sole reason for the observed compaction. Based on the compaction factor of 0.82, this suggests that porosity represents 18% of the ASW thickness, higher than typical estimates of 10%. Therefore, for H₂O ice, we conclude that a loss of porosity and a decrease in intermolecular distance upon the phase change is responsible for the observed compaction. Indeed, an increase in density of H₂O ice as a function of surface temperature has been previously observed.^93,106

The analysis used to determine the complex refractive index of an ice was shown to be valid using test data from the literature, as shown in Fig. 3. However, when the code is used to analyse the experimental C₆H₆ spectra, there is clearly a discrepancy between the input data and results (Fig. 10). This suggests that there is a systematic error in the experimental data which is not accounted for in the detailed analysis. The analysis reproduces the C₆H₆ absorption features (Fig. 8), but the interference fringes at wavelengths greater than approximately 270 nm are not well reproduced (Fig. 10). It is noted that the absorption features do not shift as the reflection angle is varied, whereas the relative positions of the interference fringes do shift, as shown in Fig. 5. It is therefore possible that an experimental uncertainty on the true value of θ leads to the observed discrepancy in Fig. 10. This uncertainty is likely due to the limits of precision of the differentially pumped rotary feedthrough which enables sample rotation, and the need to rotate the sample between recording a background spectrum and a sample spectrum. An alternative reason for the disagreement shown in Fig. 10 is that the structure of amorphous C₆H₆ ice is unknown. The presence of pores or small nuclei would cause a large amount of scatter and diffuse reflections of the light which would impact on the spectra, converting them from reflection–absorption spectra to diffuse-reflectance spectra. However, a similar discrepancy between the experimental and simulated spectra also exists for crystalline C₆H₆ ice. Therefore, we suggest that an error in reflection angle is a more likely explanation for this situation.

In order to test the effect of a mismatch between the experimental reflection angle and that used in the analysis code, the benchmarking procedure already described was repeated, but with an error of ±2° built into the value of θ. It was shown that this relatively small error on the experimental reflection angle, compared to the value of θ used in the analysis, has a dramatic effect on the results of the analysis, leading to inaccurate values of n and k for the ice (see Fig. E6, in the ESI‡). Furthermore, it results in a poor match between the interference fringes of the experimental and simulated spectra, similar to that shown in Fig. 10 for the experimental data (Fig. E7 in the ESI‡). Therefore we conclude that an uncertainty on reflection angle is the most likely cause of the discrepancy between the data sets shown in Fig. 10. This uncertainty was not found to impact the Harrick analysis,^26,64 as this method is dependent on the fringe spacing rather than the exact fringe positions. Experimental modifications are currently underway to remove this systematic error from the experiments. Nonetheless, the data presented here clearly demonstrate the usefulness of this new technique for simultaneously determining ice thickness and refractive index, as well as the applicability of the analysis method to the recorded data.

Conclusions

We have presented a new technique to simultaneously measure the refractive index and thickness of ices adsorbed on opaque substrates at cryogenic temperatures and UHV pressures. New data are reported for amorphous and crystalline C₆H₆, MF and H₂O ices adsorbed on an HOPG substrate. RAIRS shows that these phases can be identified from their infrared absorption spectra, as reported previously. UV/visible reflection–absorption spectra have allowed the determination of the refractive indices of the distinct ice phases.

Crystalline C₆H₆ is found to have a refractive index of 1.63 ± 0.08, whilst amorphous C₆H₆ ice has a lower refractive index of 1.43 ± 0.07.²⁶ Similarly, crystalline MF ice has a refractive index of 1.40 ± 0.08 compared to 1.23 ± 0.05 for amorphous MF. This difference is assigned to a change in the dielectric constant of the ice that occurs as a result of the phase change. H₂O shows different behaviour, with the two phases having almost identical refractive indices, in line with previous work. Further work is required to fully understand this behaviour.

We describe a novel analysis method to determine the wavelength dependent, complex refractive index of these ices. This method was tested using data from Kofman et al.⁶⁶ and was shown to correctly determine the complex refractive index of an ice from a UV/visible reflection–absorption spectrum. Applying the method to our experimental data has shown that the absorption features of amorphous benzene ice are excellently reproduced by the analysis method. This work has implications for the astrochemistry community, where the complex refractive index is used to simulate the optical properties of icy grains to account for scattering effects in spectroscopic measurements.

The method we have described is widely applicable to the measurement of refractive indices and thicknesses of ices in situ, thus allowing measurements to be made of ices that have been processed by heating, photon or charge particle irradiation. This provides a distinct advantage over previous techniques,^{11,22,23,31–35} where thickness and refractive index could only be measured during ice deposition.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

JWS thanks the University of Sussex for a PhD studentship. This work was funded by the STFC under grant numbers ST/M000869/1 and ST/M001075/1 at Sussex and Heriot-Watt respectively. The authors would like to thank Dr Adam Baskerville, Research Fellow at the University of Sussex, for his helpful discussions and guidance in writing the analysis code.

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Footnotes

† All data referred to in this manuscript are presented in either the manuscript or the electronic supplementary information (ESI).

‡ Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp02373f

§ Present address: Surrey Space Centre, University of Surrey, Guildford, Surrey, GU2 7XH, UK.

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