Single-angle reflectance spectroscopy to determine the optical constants n and k: considerations in the far-infrared domain

Optimal Spectral Resolution for Infrared Studies of Solids and Liquids

Due to a legacy originating in the limited capability of early computers, the spectroscopic resolution used in Fourier transform infrared spectroscopy and other systems has largely been implemented using only powers of two for more than 50 years. In this study, we investigate debunking the spectroscopic lore of, e.g., using only 2, 4, 8, or 16 cm-1 resolution and determine the optimal resolution in terms of both (i) a desired signal-to-noise ratio and (ii) efficient use of acquisition time. The study is facilitated by the availability of solids and liquids reference spectral data recorded at 2.0 cm-1 resolution and is based on an examination in the 4000-400 cm-1 range of 61 liquids and 70 solids spectra, with a total analysis of 4237 peaks, each of which was also examined for being singlet/multiplet in nature. Of the 1765 liquid bands examined, only 27 had widths <5 cm-1. Of the 2472 solid bands examined, only 39 peaks have widths <5 cm-1. For both the liquid and solid bands, a skewed distribution of peak widths was observed: For liquids, the mean peak width was 24.7 cm-1 but the median peak width was 13.7 cm-1, and, similarly, for solids, the mean peak width was 22.2 cm-1 but the median peak width was 11.2 cm-1. While recognizing other studies may differ in scope and limiting the analysis to only room temperature data, we have found that a resolution to resolve 95% of all bands is 5.7 cm-1 for liquids and 5.3 cm-1 for solids; such a resolution would capture the native linewidth (not accounting for instrumental broadening) for 95% of all the solids and liquid bands, respectively. After decades of measuring liquids and solids at 4, 8, or 16 cm-1 resolution, we suggest that, when accounting only for intrinsic linewidths, an optimized resolution of 6.0 cm-1 will capture 91% of all condensed-phase bands, i.e., broadening of only 9% of the narrowest of bands, but yielding a large gain in signal-to-noise with minimal loss of specificity.

Method to derive the infrared complex refractive indices n(λ) and k(λ) for organic solids from KBr pellet absorption measurements

Obtaining the complex refractive index vectors n(ν~) and k(ν~) allows calculation of the (infrared) reflectance spectrum that is obtained from a solid in any of its many morphological forms. We report an adaptation to the KBr pellet technique using two gravimetric dilutions to derive quantitative n(ν~)/k(ν~) for dozens of powders with greater repeatability. The optical constants of bisphenol A and sucrose are compared to those derived by other methods, particularly for powdered materials. The variability of the k values for bisphenol A was examined by 10 individual measurements, showing an average coefficient of variation for k peak heights of 5.6%. Though no established standards exist, the pellet-derived k peak values of bisphenol A differ by 11% and 31% from their single-angle- and ellipsometry-derived values, respectively. These values provide an initial estimate of the precision and accuracy of complex refractive indices that can be derived using this method. Limitations and advantages of the method are discussed, the salient advantage being a more rapid method to derive n/k for those species that do not readily form crystals or specular pellets.

Twice-Modulated Light in Fourier Transform Infrared (FT-IR) Spectrometers from Reflective Samples: Avoiding Distorted Intensity Values

We document an artifact associated with the back reflection from samples or sampling accessories in Fourier transform spectrometers. Samples oriented normal to the incoming modulated beam can reflect light back to the interferometer and this light (the percentage dependent on the sample's refractive index) is modulated by the interferometer a second time resulting in light erroneously appearing at twice its true frequency. The phenomenon occurs across the spectrum but is most apparent when positive-going narrow absorption peaks at 1f display as negative-going peaks at 2f. We have redressed the artifact by implementing a rotation stage directly beneath the sample holder: As the stage is rotated through small angles relative to beam normal, the back-reflected light does not enter the interferometer and the artifact disappears. The observation is relevant to several IR sampling methods: gas/liquid cells, alkali halide pellets, reflectance accessories, etc.

Calculation of Spectral Optical Constants Using Combined Ellipsometric and Reflectance Methods for Smooth and Rough Bulk Samples

Spectra of the optical constants n and k of a substance are often deduced from spectroscopic measurements, performed on a thick and homogeneous sample, and from a model used to simulate these measurements. Spectra obtained for n and k using the ellipsometric method generally produce polarized reflectance simulations in strong agreement with the experimental measurements, but they sometimes introduce significant discrepancies over limited spectral ranges, whereas spectra of n and k obtained with the single-angle reflectance method require a perfectly smooth sample surface to be viable. This paper presents an alternative method to calculate n and k. The method exploits both ellipsometric measurements and s-polarized specular reflectance measurements, and compensates for potential surface scattering effects with the introduction of a specularity factor. It is applicable to bulk samples having either a smooth or a rough surface. It provides spectral optical constants that are consistent with s-polarized reflectance measurements. Demonstrations are performed in the infrared region using a glass slide (smooth surface) and a pellet of compressed ammonium sulfate powder (rough surface).

Combining spectroscopic techniques to determine the optical constants of powdered lactose

A method for deriving the optical constants (n/k) of organic powdered materials using pressed pellets in the mid-infrared spectral range is introduced that combines variable angle spectroscopic ellipsometry and transmission spectroscopy. The approach is applied to anhydrous lactose, in which three different forms of pellets were pressed and measured: a pure lactose pellet and a mixed lactose/potassium bromide (KBr) pellet with a large analyte percentage were used for ellipsometric measurements, and a KBr transmission pellet with only a small analyte percentage was used for transmission measurements. The transmittance data provide an initial set of oscillators and improve the spectral fitting of weak absorption features (k<0.01). Ellipsometric data for the pure and mixed pellets are then fit simultaneously to derive the final n/k values for lactose from 6000-400cm^-1. An alternative method just using the ellipsometric data from the mixed pellet and the transmittance data is also presented and shows good agreement with the multi-sample analysis, providing a simpler method for powders that do not press easily into pure pellets. Finally, the derived optical constants were used to model the reflectance data, demonstrating a good match with the measured reflectance spectra if non-idealities are included.

Improved Infrared Optical Constants from Pressed Pellets: II. Ellipsometric n and k Values for Ammonium Sulfate with Variability Analysis

Infrared reflectance analysis is facilitated via the comparison of spectra recorded in situ to a databank of actual or synthetic infrared reflectance spectra. It has recently been shown that reference spectra corresponding to the many different morphological forms of the same chemical can be generated synthetically using the imaginary, k, and real, n, components of the complex refractive index, n∼ = n + ik. One method to obtain the n and k vectors is infrared ellipsometry, which measures the changes in amplitude, tan Ψ, and phase, Δ, of polarized light reflected from the sample both as a function of wavenumber and angle of incidence. The method requires specularly reflected light, so best results are usually obtained with polished planar samples of large surface area. Due to the difficulties of obtaining such samples, however, we investigate the possibility of pressing powders of neat materials and obtaining the corresponding optical constants from the pellets. In this paper, variability in the sample pellet and preparation method is investigated, as is variability in the fitting procedure for the derived optical constants. The n/k vectors are derived from the measured ellipsometric parameters, tan ψ and Δ, as they are fit by an oscillator model which yield n(ν∼) and k(ν∼) vectors as a function of wavenumber, ν∼. Construction of the oscillator model is not automatic and depends on significant input from the analyst as well as the sample's physical characteristics. For pellet pressing, the experimental variability was found to be minimized for size-selected powdered samples as gauged by the minimal variance in ψ and Δ for three different pellets; similarly, the analytical precision for multiple measurements of the same pellet was also quite good, suggesting that a pressed pellet is a viable sample preparation method. Experimental variabilities were comparatively small; the greatest variability came in the analytic fitting procedure with differences in the k-peak values up to 10% for only the sharpest bands arising from four different fits to the same data set. The final ellipsometric n/k data are compared to literature values obtained from crystalline ammonium sulfate ((NH₄)₂SO₄) samples as well as single-angle reflectance measurements that also used pressed pellets. Comparison with the previous literature values shows generally good agreement, although larger k-values are observed for the independent sets of data derived from pressed pellets. These data are suggested as an improved set of optical constants for (NH₄)₂SO₄.

Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH4)2SO4 from Single-Angle Reflectance

In combination with other parameters, the real, n(ṽ∼), and imaginary, k(ṽ∼), components of the complex refractive index, n^ = n + ik, can be used to simulate the optical properties of a material in different forms, e.g., its infrared spectra. Ultimately, such n/k values can be used to generate a database of synthetic reflectance spectra for the different morphologies to which experimental data can be compared. But obtaining reliable values of the optical constants n/k for solid materials is challenging due to the lack of optical quality specimens, usually crystals, large enough to measure. An alternative to crystals is to press the powder into a uniform disk. We have produced pellets from ammonium sulfate, (NH₄)₂SO₄, powder and derived the pellets' n and k values via single-angle reflectance using a specular reflectance device in combination with a Fourier transform infrared spectrometer. The single-angle technique measures amplitude of light reflected from the material as a function of wavelength over a wide spectral domain; the optical constants are determined from the reflectance data using the Kramers-Kronig relationship. We investigate several parameters associated with the pellets and pellet formation and their effects upon delivering the most reliable n/k values. Parameters studied include pellet diameter, mass, and density (void space), drying, grinding, sieving, and particle size in the pellet formation, as well as pressing pressure and duration. Of these parameters, using size-selected mixtures of dried, small (<50 µm) particles and pressing at ≥10 tons for at least 30 min were found key to forming highly reflective samples. Comparison of two sets of previous literature n(ṽ∼) and k(ṽ∼) values obtained from crystalline (NH₄)₂SO₄ both as crystal reflectance as well as extinction spectra of aerosols measured in a flow tube shows reasonable agreement, but suggests the present values, as confirmed from two independent techniques, represent a substantial improvement for n/k values for (NH₄)₂SO₄, also demonstrating promise to measure the optical constants of other materials.

Optical and Chemical Characterization of Uranium Dioxide (UO2) and Uraninite Mineral: Calculation of the Fundamental Optical Constants

Uranium dioxide (UO₂) is a material with historical and emerging applications in numerous areas such as photonics, nuclear energy, and aerospace electronics. While often grown synthetically as single-crystal UO₂, the mineralogical form of UO₂ called uraninite is of interest as a precursor to various chemical processes involving uranium-bearing chemicals. Here, we investigate the optical and chemical properties of a series of three UO₂ specimens: synthetic single-crystal UO₂, uraninite ore of relatively high purity, and massive uraninite mineral containing numerous impurities. An optical technique called single-angle reflectance spectroscopy was used to derive the optical constants n and k of these uranium specimens by measuring the specular reflectance spectra of a polished surface across the mid- and far-infrared spectral domains (ca. 7000-50 cm^-1). X-ray diffractometry, scanning electron microscopy, and energy-dispersive X-ray spectroscopy were further used to analyze the surface composition of the mineralogical forms of UO₂. Most notably, the massive uraninite mineral was observed to contain significant deposits of calcite and quartz in addition to UO₂ (as well as other metal oxides and radioactive decay products). Knowledge of the infrared optical constants for this series of uranium chemicals facilitates nondestructive, noncontact detection of UO₂ under a variety of conditions.