Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH 4 ) 2 SO 4 from Single-Angle Reflectance

Abstract

In combination with other parameters, the real, n( $\tilde{ṽ}$ ), and imaginary, k( $\tilde{ṽ}$ ), components of the complex refractive index, $\hat{n}$ = 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( $\tilde{ṽ}$ ) and k( $\tilde{ṽ}$ ) 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.

Keywords

Optical constants index of refraction single-angle reflectance spectroscopy specular reflectance ellipsometry ammonium sulfate pellet formation Kramers–Kronig transform

Introduction

Both the real, n( $\tilde{ṽ}$ ), and imaginary, k( $\tilde{ṽ}$ ), components of the complex index of refraction, $\hat{n}$ = n + ik, are vital input parameters for modeling the reflectance, refraction, absorption, and emissivity of a material^1–6 and thus serve as valuable reference data. A common method of determining n and k of solid materials is to measure the change in amplitude of light reflected from a material as a function of frequency, R( $\tilde{ṽ}$ ), over a broad wavelength range, and then apply the Kramers–Kronig transform (KKT) to derive the optical constants.⁷ Obtaining optical constant values with this method is often challenging, however, due to the limited availability of materials in forms suitable for optical measurement.⁸ The best results for n and k using this type of measurement come from bulk, polished-facet homogeneous materials that have minimal defects, such as crystals, where the Fresnel equations are valid and there is no appreciable light scattering.

Due to its importance in atmospheric science and agriculture, there have been several attempts to assess the n/k values for ammonium sulfate. In 1976, Toon et al.⁹ grew single crystals of this important solid that were large enough for transmission and reflectance measurements, yielding n/k data. The authors used the reflectance/transmittance method to derive the values for (NH₄)₂SO₄, but also literature data to derive values for NaCl and Al₂O₃. The n/k optical constant measurements represented a significant achievement since (i) the high-quality (NH₄)₂SO₄ crystal took more than a year to grow, (ii) they provided estimates for their systematic measurement errors, and (iii) they made quantitative comparisons with previously published results. While the seminal (NH₄)₂SO₄ measurements were an achievement, the data were recorded at coarse spectral resolution (57 digital points between 250 and 5000 cm⁻¹) and discrepancies were observed when the optical constants were used to fit experimental extinction spectra.^10,11 Our previous work has similarly demonstrated^8,12 how simply increasing the spectral resolution can change the derived k values by as much as 28%. In 2006, Earle et al.¹⁰ reported better-resolved (2 cm⁻¹) optical constants for crystalline ammonium sulfate at 298 K, as well as at 213, 223, and 243 K. Using an aerosol flow tube, they derived optical constants from transmission measurements of dry (NH₄)₂SO₄ aerosols. While their optical constants are in only modest agreement with Toon et al.'s results,⁹ Earle et al.'s higher resolution measurements have been found to better reproduce transmission spectra, especially of atmospheric aerosols.

For most materials, however, it is impractical or impossible to obtain uniform crystals that are large enough (centimeter sized) for reflectance measurements^8,13; most solids can only be acquired as powders or amorphous materials, often presenting as solid mixtures (e.g., minerals). Growing crystals from such powders is difficult and time-consuming, and in most cases impossible.^12,13 Due to the lack of such crystals for most substances, alternative methods for extracting n/k from materials other than single crystals include in situ evaporation techniques¹⁴ as well as pressing the powder form into a uniform pellet or disk for reflectance measurements. The salt (NH₄)₂SO₄ was selected not only due to its importance in atmospheric chemistry, but because its n and k values have been previously reported, and the powder flows relatively easily to form pellets with measured densities close to its literature value. The broader goals of our studies are thus to determine (i) if pellets of pure material powders formed at high pressures can yield reliable optical constants n and k as determined using single-angle reflectance spectroscopy¹⁵ comparable to its crystalline analog^16–20 and (ii) how the methods can be optimized to produce optical-quality pellets. Specifically, using the values from Toon et al.⁹ and Earle et al.¹⁰ as literature benchmarks, the quality of pressed (NH₄)₂SO₄ pellets and their associated optical constants are assessed by comparing the literature n/k values to those derived using near-normal angle specular reflectance using a Fourier transform infrared (FT-IR) spectrometer followed by KKT.

The single-angle reflectance technique quantitatively measures the change in amplitude of light reflected from the material of interest on an absolute scale as a function of wavelength over a wide spectral range.^8,12 Using the broadest λ range possible (e.g., including the far- and near-infrared) allows for more accurate application of the Kramers–Kronig relationship,¹³ which is employed numerically to obtain the optical constants. Another method, infrared spectroscopic ellipsometry (IRSE), based on the measurement of the changes in amplitude, tan Ψ, and phase, Δ, of polarized light reflected from the sample can also be used,^21,22 and will be discussed in a companion paper.²³ The intercomparison of four data sets of optical constants for ammonium sulfate (vide infra) shows significant variability but very good agreement between single-angle reflectance spectroscopy and IRSE, indicating promise for measuring the optical constants of other materials by the pellet pressing method.

Experimental

Single-Angle Infrared Reflectance Spectroscopy: Kramers–Kronig transform

The single-angle reflectance method to determine n and k has been used for decades.^8,13,19,24 The method measures a sole experimental parameter to determine n( $\tilde{ṽ}$ ) and k( $\tilde{ṽ}$ ), namely the quantitative specular reflectance R( $\tilde{ν}$ ) (sometimes expressed in angular frequency R(ω)) of the material as a function of wavenumber relative to a nominal 100% reflector at a fixed angle of incidence, typically close to normal. The KKT is formulated such that the phase rotation angle ϕ( $\tilde{ṽ}$ ) is calculated from R as a function of wavenumber, $\tilde{ṽ}$

({\tilde{ṽ}}_{m}) = 2 \frac{{\tilde{ṽ}}_{m}}{π} \int_{0}^{\infty} ln (\sqrt{R (- 4 pt \tilde{}})) {\tilde{ṽ}}^{2} - {\tilde{ṽ}}_{m} d \tilde{ṽ}

(1)

Obviously, evaluating the integral from 0 to ∞ cm⁻¹ as per Eq. 1 is not possible and requires certain approximations, making the data analysis more challenging. The optical constants n/k are derived from the measured reflectance and phase angle via the following relations⁷

n (\tilde{ṽ}) = \frac{[1 - R (\tilde{ṽ})]}{[1 + R (\tilde{ṽ}) - 2 \sqrt{R (\tilde{ṽ})} cos φ (\tilde{ṽ})]}

(2)

and

k (\tilde{ṽ}) = \frac{- 2 \sqrt{R (\tilde{ṽ})} sin φ (\tilde{ṽ})}{[1 + R (\tilde{ṽ}) - 2 \sqrt{R (\tilde{ṽ})} cos φ (\tilde{ṽ})]}

(3)

Single-Angle Infrared Reflectance: Instrumental

Experimentally, the reflectance R( $\tilde{ṽ}$ ) is measured on an absolute scale relative to a 100% reflector. The angle θ_i (θ_r) is measured between the incident (reflected) light propagation vector and the sample's surface normal; near-normal reflectance is used where for this instrument (Bruker A510/Q-T) the angle is small with θ_i = θ_r = 11°. The percent reflectance was measured relative to a first-surface gold mirror (Thorlabs PF10-03-M03), subsequently calibrated for non-100% reflectance using data from Babar and Weaver.²⁵ The A510 accessory was housed in the evacuated sample compartment of a Bruker IFS 66v/S FT-IR which can be configured^26,27 with different optical components to provide continuous spectral coverage from the far-infrared (IR) (∼5 cm⁻¹) to the ultraviolet (50 000 cm⁻¹).^8,28 Sample mounts were carefully prepared so that reflectance was observed from the first surface of the sample and not from the back of the sample or the mounts. The sample holders (Pike Technologies, PN 162-5610) are constructed of aluminum with a low-force spring clamp on the back to hold the sample vertically in place, with a specially constructed low-reflectance mask that has a proprietary carbon nanotube black coating to reduce stray light.^13,29 The cylindrical pellet was rotated in the holder before collecting the spectrum to maximize signal; effects are discussed below. Reflection measurements were made over the 7500 to ∼30 cm⁻¹ optical range. Spectra were recorded at 2.0 cm⁻¹ resolution in the far-IR (600–30 cm⁻¹) and at 4.0 cm⁻¹ in the mid-IR (7500–400 cm⁻¹). In the mid-IR, a glow bar source, Ge–KBr beamsplitter, and a deuterium triglycine sulfate (DTGS) detector were used, and for the far-IR, a glow bar source, Ge–Mylar beamsplitter, and DTGS detector (polyethylene window) were employed. While nearly all mid-IR data reported here were recorded at 4.0 cm⁻¹ resolution, for the final optimized data set (available as Supplemental Material), a resolution of 2.0 cm⁻¹ was used. For each spectrum, 512 interferograms were averaged and transformed using Boxcar apodization and Mertz phase correction for the mid-IR data, but the power spectrum phase-correction method was employed for the far-IR data due to the broad interferograms. The far-IR and mid-IR spectra were concatenated using the “merge” function in Bruker OPUS 5.5 software.³⁰ The final step prior to the KKT is to extrapolate the R( $\tilde{ṽ}$ ) data to zero wavenumbers using a quartic relationship of the form

R (\tilde{ṽ}) = R (0) + a {\tilde{ṽ}}^{2} + b {\tilde{ṽ}}^{4}

(4)

where a and b are fitting parameters determined by least-squares regression of low-frequency experimental data. Previous work^12,13 has shown the extrapolation to zero (see Eq. 4) can have significant effects on the derived n/k values. Experimental spectra were thus recorded to as low a frequency as possible but detectors that can measure to even lower wavenumbers such as a helium-cooled bolometer were not used due to added expense and labor. For ammonium sulfate, the low-resolution data did not indicate any significant bands in the very far-IR, as was seen, for example,⁸ with CaF₂ and BaF₂. The lowest (NH₄)₂SO₄ band was found to occur at 210 cm⁻¹; this feature is not included in the following discussion, however, because previous works do not report it and we could therefore make no comparisons. The n(

\tilde{ṽ}

) and k(

\tilde{ṽ}

) values were then obtained from the reflectance measurements using the KKT algorithm in OPUS,³⁰ noting that the algorithm does not account for voids or defects in the material.

This earlier study also demonstrated that sample positioning, sample masks, and optical alignment are crucial in the single-angle experiment; the R( $\tilde{ṽ}$ ) data must be quantitative relative to a 100% reflector. That is, the data are not self-ratioing as in a transmission experiment, and any effects not associated with relative reflectance differences between sample and gold lead to artifacts throughout the spectrum. These interlinked parameters are especially important in the far-IR where diffraction and other effects become more significant^12,13 and artifacts associated with inappropriate aperture size are difficult to avoid. Preliminary calibration experiments were therefore conducted to determine optimal mask and aperture sizes using a crystal z-cut quartz window. Sample spot size and accessory alignment were both first visually inspected using an Hg lamp source and a quartz beamsplitter. The normal image magnification in the Bruker IFS 66v/S sample compartment without any accessory is 1.17, meaning a 5.0 mm aperture has a theoretical spot size of 5.85 mm. According to Spitzer, the z-cut crystal of natural quartz has a nominal reflectance of 92.6% for the band³¹ centered near 470 cm⁻¹. Figure 1a shows that as the spot size on the mirror with the 6 mm mask becomes too large, artifacts arise as manifested by the >100% reflectance observed for the 5 mm aperture data (green trace). The other traces show that for aperture sizes <3.5 mm a consistent reflectance value of 94.9% is obtained near 470 cm⁻¹. However, for the 8 mm mask, this artifact is observed for aperture sizes >6 mm with a value of 94% (Fig. 1b). The reflectance variation can be explained by fluctuations of mounting and positioning of the sample.³¹ Consequently, the 8 mm mask with the 5 mm aperture was selected for reflectance measurements because it allows for a greater light throughput. Due to a limited number of sample masks and the ∼10 mm clear aperture of pellet, 8 mm sample masks were used for all experiments, since the aperture setting for the reference (Au mirror) and sample (quartz) was the same for each spectrum (see Fig. 1).

Materials, Sample Sieving and Drying, Particle Size Distribution

Ammonium sulfate was purchased from Sigma-Aldrich (A5132, ReagentPlus, ≥99.0%). Prior to sieving, powder was taken directly from the bottle and ground using a mortar and pestle to obtain more of the smaller diameter particles: Without grinding, there were almost no particles smaller than 150 µm. Sieving was then performed using an Advantech Sonic Sifter to separate the ground samples into various size fractions using the following sieve diameters: 53, 90, 150, 212, 355, and 500 µm. In some cases, a single sieve was used to obtain all particle sizes below a specific diameter.

For the original powder, as well as the ground and sieved fractions, a digital microscope (Keyence VHX-1000) with 16-bit resolution was utilized to obtain photomicrographs (see Fig. 2) of different (NH₄)₂SO₄ sieve fractions and to measure the diameters of individual particles.¹⁷ Good separation was ensured by spreading the particles over a glass slide. The microscope software differentiates the brightness in the image and extracts the bright portions to produce a binary image by joining the contiguous bright portions. Using an assumption that all adjacent bright points are part of the same object, the software calculates the perimeter and area of each object.¹⁷ The equation d = $2 \sqrt{A / c}$ is used to calculate the mean particle diameter d by approximating that each particle is spherical (a significant approximation per Fig. 2). Table I gives the average diameter of each sieve fraction in which approximately 200 particles were measured to calculate the averages.

Table I.

Particle size fractions and mean particle sizes of the original powder and of ground and sieved ammonium sulfate as measured by optical microscopy.

Sieve size fractions (µm)	Mean particle diameter (µm)
Original powder	1104 ± 361
Mean fraction sizes after sieving
>500	786 ± 136
500–355	522 ± 69
355–212	318 ± 56
212–150	225 ± 51
150–90	125 ± 29
90–53	96 ± 19
<53	32 ± 14

Due to its hygroscopic behavior, (NH₄)₂SO₄ powders were also dried in a vacuum oven with a slow ramp rate up to 110 ℃ to remove any water adsorbed during the grinding and sieving processes. After drying, the oven temperature was cooled to room temperature under a nitrogen purge to bring the oven back to atmospheric pressure at zero humidity. The slow heating profile is used to avoid discoloration of the powder.

Pellet Preparation

Pellets of ammonium sulfate were pressed at two different diameters: 13 and 20 mm. Approximately 2.0 g of powder was used to press each 20 mm pellet, whereas 0.15 g to 0.8 g was used for the 13 mm pellets. As described above, prior to sieving, the powder was first ground using a mortar and pestle. For the 13 mm pellets, a second grinding was also performed using a Wig-L-Bug ball mill. This supplementary ball-mill grinding was not implemented for the 20 mm pellets (except for one 20 mm pellet in the grinding study, see Table S2) since the canister has a relatively small volume and cannot efficiently grind masses >0.15 g. The ball mill grinding was performed in two rounds of 25 s each, with intermittent mixing of the powder with a spatula.

Two different dies and two different presses were used to press ammonium sulfate powders: An evacuable pellet die set from Pike Technologies along with a two-post, 10 ton manual press (Carver 3851-0) was used for the 13 mm pellets, and a 20 mm die set (International Crystal Laboratories #0012-5223)¹⁵ along with a four-post, 20 ton manual hydraulic press (Carver #4128) were used for the 20 mm pellets. The stainless-steel dies were at room temperature (between 21 and 23 ℃) during the pressing and were actively pumped by a diaphragm pump to avoid entrapping any water vapor. The various time–pressure conditions used to press pellets are summarized in Table S1. Pellets were stored in a dry box when not in use.

Pellet Characterization

The surfaces of two 20 mm pellets were characterized using the same Keyence digital microscope (see the Materials, Sample Sieving and Drying, Particle Size Distribution section) but also a scanning electron microscope (SEM). For the SEM analysis, samples were mounted on carbon tape-covered aluminum SEM stubs (Ted Pella, Redding, CA), and sputter-coated with carbon. They were imaged with a high-resolution Helios 600 Nanolab Dual Beam SEM (FEI, Hillsboro, OR) at 5 keV. Figure 3a depicts photomicrographs of the surfaces; pellet 130 was chosen because it gave a high reflectance value, whereas the reflectance for pellet 66 was significantly lower (see Tables S2 and S3 for pressing conditions). As discussed below, the quality of the surface has a significant effect on the specular reflectance.

In addition to the optical measurements, other methods were considered to assess the quality of the pellet, namely its density. Using the measured mass and volume (assuming a cylinder of volume V = πr²t, where t is the pellet thickness), an experimental density ρ_pellet was calculated and compared to the literature value³² for ammonium sulfate, ρ_lit = 1.769 ± 0.003 g/cm³. From these values, the pellet void space was calculated as [1–(ρ_pellet/ρ_lit)] × 100. For each pellet, thickness t and diameter d were measured using a caliper to 0.01 mm and the mass was measured to ±0.0001 g on a four-position balance. Table S2 summarizes the parameters for 43 pellets and how they were investigated in a systematic fashion. Typical masses of (NH₄)₂SO₄ used to press 13 mm and 20 mm pellets were 0.15 g and 2.0 g, respectively. However, for the diameter study (13 versus 20 mm), 13 mm pellets were pressed using a mass of ∼0.8 g to match the thickness of the 20 mm pellet.

Results

Assessing the Results: Maximizing Reflectance

One goal of this study is to try to understand which parameters can be controlled so as to ultimately deliver the most reliable single-angle n/k values for (NH₄)₂SO₄. A second goal is to develop general experimental protocols for those substances which do not easily form single crystals and must be studied as a pellet to get the n/k vectors. In order to optimize parameters for the single-angle pellet pressing method, rather than using, e.g., median or mean %R values, only those methods were retained that resulted in maximizing the %R values, particularly for strongly reflecting bands such as the first-surface-scattering reststrahlen bands,¹⁷ e.g., the ν₃( ${SO}_{4}^{2 -}$ ) band^33–35 at 1106 cm⁻¹. The rationale for using only maximal R values is that unlike other optical methods to determine n/k, such as ellipsometry, the single-angle reflectance technique requires exactly that: perfect specular reflectance from a planar surface at a fixed angle of incidence and a fixed angle of reflection such that the Fresnel equations be operant. Any phenomenon or artifact that either adds or detracts to the quantity of specularly reflected light (e.g., light scattering or reflection off the sample mount) invalidates the Kramers–Kronig approximation and thus the n/k results. In the case of generating a pressed pellet, however, almost any phenomenon that leads to an imperfect reflecting surface leads to scattering, diffuse reflection or refraction, all of which result in lower %R values. Such effects include, e.g., roughened or porous surfaces with digs, voids, or non-planar inhomogeneities. Other phenomena leading to reduced R include cracks, chemical impurities, surface hydration, “fogging”, etc. The only common sample phenomenon that can lead to (artificially) increased light levels is reflection from the pellet's rear surface, but in most cases the effect is small and measures were taken to avoid this.⁸ As described below, a primary goal of all experiments was thus to tweak the parameter so as to maximize R using one or more of the reststrahlen bands. For each parameter, most data were evaluated primarily using the ν₃( ${SO}_{4}^{2 -}$ ) band^33–35 at 1106 cm⁻¹ as it has the strongest reflectance and thus displays the greatest %R change in reflectance. For the best pellets and best alignment, the largest reflectance values for this ν₃ band were on the order of 54 to 55% (relative to gold); the parameter studies are described in turn, in most cases displaying both maximized as well as non-optimal data.

Powder Particle Size and Grinding

The powder particle sizes that go into forming the pellets turned out to be a key parameter in yielding specimens suited for reflectance spectroscopy. To investigate this parameter, different combinations of particle fractions were studied to determine optimal conditions for obtaining the most reflective (NH₄)₂SO₄ pellet. The list is extensive and includes various particle sizes ranging from very small (<53 µm) to very large (>500 µm), along with mixtures of various fraction ratios, as shown in Table S3.

Two conditions were found to be particularly important in producing high reflectance values including: (i) the mixing of particle fractions and (ii) the use of small particles with diameters <90 µm. The first is supported by the theory that larger particles fill up a certain amount of space, while smaller particles fill the voids produced by the larger particles.³⁶ Moreover, ground particles become less spherical and can nest better, aiding in filling the voids.³⁶ The best reflectance was obtained by using greater fractions of smaller particles: In particular, by using two different sieving fractions, namely <53 µm and 53–90 µm in a 40/60 mass ratio, respectively, and then grinding this mixture further still with a Wig-L-Bug ball mill.

The grinding effects were studied for both 13 mm and 20 mm pellets. Two sets of 13 mm pellets were prepared: one set included three pellets composed of fresh powder taken directly from the bottle, and the other set of three pellets was composed of particles (after sieving) with diameters <250 µm. Each of the sets included a pellet prepared from (i) unground powder, (ii) powder ground with a mortar and pestle, and (iii) powder ground using a mortar and pestle followed by the ball mill.

Generally, the ball mill was not used for the 20 mm pellets because the canister is relatively small and consequently it can efficiently grind only small quantities (∼0.15 g). However, to reveal the influence of grinding with a Wig-L-Bug ball mill on the obtained reflectance values, two 20 mm pellets with a mixture of <53 µm and 53–90 µm in a ratio of 40/60 were also prepared: one with ground powder from the mortar and pestle prior to sieving (pellet #91) and one with an additional grinding using the ball mill prior to pressing (pellet #130). To prepare this 2 g sample, several 0.15 g fractions were ground and combined before pressing.

Table II reports the average particle size (as measured by optical microscopy) for each of these cases along with the reflectance values at the 1106 cm⁻¹ vibrational band. It is important to mention that the particle size distribution measurement for the ground powder was challenging since the smallest particles tend to agglomerate. Consequently, some of the bigger particles could be considered an “agglomeration” instead of a single particle and were inevitably discriminated. Moreover, the optical microscope has limitations in detecting small particles on the order of 5 µm or less due to diffraction. Particle sizes reported in Table II can thus be considered estimates; greater fractions of fine particles were obtained when the ball mill was used. For both 13 mm and 20 mm pellets, the reflectance is higher when the ammonium sulfate is first ground with a mortar and pestle followed by grinding with a ball mill to yield smaller particle sizes.

Table II.

Reflectance of 13 and 20 mm pellets with different particle formulations and different grinding procedures.

Pellet #	Average particle diameter (µm)	Pellet diameter (mm)	%R at 1106 cm⁻¹
Fresh from bottle, no sieving
138 (unground powder)	1104	13	49.6
144 (powder ground with mortar and pestle only)	11	13	50.5
140 (powder ground with mortar and pestle + ball mill)	5	13	54.2
<250 µm sieve
85 (unground powder)	166	13	49.7
86 (powder ground with mortar and pestle only)	97	13	51.2
87 (powder ground with mortar and pestle + ball mill)	20	13	52.5
40% < 53 µm and 60% 53–90 µm
91 (powder ground with mortar and pestle only)	–	20	50.4
130 (powder ground with mortar and pestle + ball mill)	16	20	53.2

Note: Additional grinding with the ball mill led to greater fractions of the smallest particles.

Packing Density, Void Space

One parameter to consider is whether maximal particle packing theoretically leads to a denser pellet and thus greater reflectance. However, as also suggested by Volz,³⁷ it is the surface packing density with individual grains being better aligned at the surface that probably wreak a more significant influence on R than bulk pellet density itself. As seen in Table III, this is found to be true as no obvious correlation was observed between pellet density (or resulting void space) and reflectance, signifying that specular reflectance due to surface phenomena^16–18 as represented by the reststrahlen band at 1106 cm⁻¹ appears to play a greater role than bulk pellet properties. In Table III, the pellets are arranged in order of decreasing reflectance.

Table III.

Comparison of (NH₄)₂SO₄ pellet specular reflectance at 1106 cm^–1 and density (void space).

13 mm pellets
Pellet #	122	100	82	87	138	37	49	92	90	20
%R	55.0	53.9	53.7	52.5	49.6	49.4	49.2	49.2	49.1	41.7
Void space (%)	2.9	1.2	0.37	0.06	0.93	2.7	1.8	1.0	3.8	3.5
20 mm pellets
Pellet #	130	91	89	93	76	61	73	79	63	66
%R	53.2	50.4	49.4	49.2	49.2	49.0	48.7	48.4	46.7	44.2
Void space (%)	1.4	2.8	4.0	3.5	3.9	3.2	3.9	4.8	4.8	4.5

Note: The void space was calculated as [1–(ρ_pellet/ρ_lit)] × 100.

When there exist more defects at the surface, (diffuse) scattering effects become more apparent, and the overall specular reflectance is in turn reduced. That is, a rough or porous surface with irregularities leads to greater diffuse reflectance and less specular component. But the specular response is crucial as it is the sole signal for single-angle reflectance. During the pressing process, it is hypothesized that smaller particles or a microcrystalline continuum are incorporated to formulate the surface. This generates a “smooth” and more specular surface (independent of the bulk density), leading to higher band reflectance (and thus higher k) values.

The degree of diffuse scattering of light from a surface depends on several parameters, including (i) the wavelength and (ii) the angle of incidence of the light wave. The Rayleigh criterion³⁸ can provide an estimate of surface roughness by estimating the value at which a surface irregularity or particle of height h becomes too large for light to reflect in a specular manner, i.e., results in diffuse scattering. The dimension of the surface irregularity h is calculated via Eq. 5, where λ is the wavelength of the incident/reflected light and θ the angle of incidence

h < \frac{λ}{8 cos θ}

(5)

When this relation holds, the surface is considered smooth, and primarily specular reflectance is observed. Using parameters from the present experiment (θ = 11°), and assuming λ = 10 µm, h is found to be 1.27 µm, with h = 12.7 µm for λ = 100 µm, etc. As seen in Eq. 5, the value is wavelength specific, but suggests that for IR studies, the surface needs to be planar to the order of a few µm or better. Any surface defects must be (approximately) less than such values in order to obtain specular reflectance, with specular behavior more difficult to achieve at shorter λ. For the present experiment, Rayleigh height h was found to be 2.04 µm, 1.15 µm, and 0.89 µm at the wavelengths of key ammonium sulfate bands, namely λ = 16 µm (615 cm⁻¹), 9 µm (1106 cm⁻¹), and 7 µm (1415 cm⁻¹), respectively.

Figure 3a depicts photomicrographs obtained by optical microscopy for a smooth (#130, R = 53.2% at 1106 cm⁻¹) and a rough (#66, R = 44.2% at 1106 cm⁻¹) 20 mm pellet surface. Only qualitative estimates of the surface texture can be gleaned from these photos, since no quantitative data can be obtained of the surface in terms of defects and irregularities. However, SEM pictures of the same two surfaces are presented in Fig. 3b at three different magnifications (1000×, 5000×, and 12 000×). At 1000 × magnification, it is possible to observe larger surface defects for pellet 66 (in the form of voids) compared to pellet 130. At higher magnification (12 000×), defects can be measured and, for pellet 66, voids on the order of 5 to 8 µm (bottom right frame) were observed compared to ≤1 µm for pellet 130. Based on the calculated Rayleigh criterion, the lack of several micron-sized defects in pellet 130 most likely plays a role in its higher degree of specular reflectance, since h in this spectral region is 1 to 2 µm. Conversely, since many surface defects of pellet 66 are approximately ≥ 2 µm, the surface roughness is higher, yielding a higher scattering contribution and consequently reducing the specular reflectance. Even if all defects on the surface are not <2 µm, in general, the micromorphological conditions of the surface of pellet 130 favor specular reflectance obeying the Fresnel equations.

Pellet Formation: Application of Drying

The application of heat to the (NH₄)₂SO₄ sample to dry the powder was also found to be an important step to obtain optical quality pellets; the parameter is linked to the particle size (Powder Particle Size and Grinding section) as well, since sorption of water by the analyte leads to clumping of the particles and an increased median particle size. This parameter may also be sample-specific: drying is clearly more necessary for certain hygroscopic (inorganic) salts, but perhaps less so, or not at all, for hydrophobic powders. For most samples, the ammonium sulfate powder was therefore dried at 110 ℃ in a vacuum oven prior to pellet pressing to remove any adsorbed water, as described in the Materials, Sample Sieving and Drying, Particle Size Distribution section. As seen in Table IV, drying the salt sample prior to generating the pellet led to substantially higher reflectance for the strong bands for ground (NH₄)₂SO₄ in 20 mm pellets. For example, for pellet 7, whose powder was ground and sieved to diameters <355 µm prior to pressing, an increase of 9.4 %R in the 1106 cm⁻¹ band (a fractional increase of 19%) was observed compared to its non-dried counterpart, pellet 6. The effect is smaller in the 13 mm pellet case; pellet 23, whose powder was ground and sieved to diameters <250 µm, displays an increase of 1.7 %R (a 3.3% fractional increase) when compared to pellet 52, which was not dried. When comparing the effects of drying with the most effective pellet parameters (pellets 131 and 122), an increase of 4.5 %R was observed (a fractional increase of 8.2%). In light of this, all subsequent powders were dried to eliminate this effect since the humidity in the room and water adsorption of the powder over time were both found to affect the reflectance value.

Table IV.

Effects of drying on the measured infrared reflectance of ammonium sulfate at 1106 cm^–1 as measured by fixed-angle reflectance.

Pellet #	Diameter	Composition	Dried?	%R at 1106 cm⁻¹
6	20 mm	Ground powder and sieved <355 µm	No	40.3
7	20 mm	Ground powder and sieved <355 µm	Yes	49.7
52	13 mm	Ground powder and sieved <250 µm	No	49.1
23	13 mm	Ground powder and sieved <250 µm	Yes	50.8
131	13 mm	Powder ground with mortar and pestle + Wig-L-Bug, 40% < 53 µm, 60% 53–90 µm	No	50.5
122	13 mm		Yes	55.0

Pellet Diameter and Pellet Formation Pressure

As discussed above, pellets of 13 and 20 mm diameter were prepared using different dies and different presses. The applied pressure (force/surface area) was calculated for both pellet sizes/presses: For 9 100 kg (20 000 lb; 13 mm dies) and 18 200 kg (40 000 lb; 20 mm dies), these forces correspond to 9.7 × 10⁴ lb/in² and 8.2 × 10⁴ lb/in², respectively. Moreover, for this specific study, the mass of powder used to make some of the 13 mm pellets was adjusted to match the thickness of the resultant 20 mm pellets. Reflectance values for (blends of) three different sieve sizes (≤250 µm, 50:50 mix of ≤ 53 and 53–90 µm, and a 40:60 mix of ≤53 and 53–90 µm) yielded very similar results between the 13 and 20 mm pellets, demonstrating that the pellet size had minimal effect. However, for 13 mm pellets with lower masses, the use of a Wig-L-Bug ball mill to further powder the salt before pressing (a method often used for KBr transmission pellets)³⁹ was shown to significantly improve the reflectance.

Pellet Formation–Duration of Press

Another parameter known to affect the optical quality of the pellet is the duration and magnitude of the press, i.e., at what pressures for what time intervals? Many of these procedures have, e.g., been optimized for KBr pellets^39,40 as used in IR transmission spectroscopy, but KBr is softer than salts such as ammonium sulfate. It is known that incrementally increasing the weight (pressure) generally leads to better pellets. To test this hypothesis, Method 1 directly ramped the weight to 18 143.695 kg (40 000 lb) for the 20 mm pellets, while several other methods (e.g., Method 3a, Table SI) ramped up the weight over the course of the first 15 min and then held it at a constant weight of 18 200 kg (40 000 lb) for differing durations ranging from 2 min to 12 h, as seen in Fig. 4a. In this analysis, the pellet mixing conditions were constant (6%, 90–150 µm; 48%, 150–212 µm, 46% > 500 µm) and only the pressing time was varied. It is seen that for pellets with pressing times between 2 and 60 min, their reflectance values are lower, but, at least for the 20 mm die, after approximately 90 min, there appears to be a threshold time beyond which the reflectance no longer increases. A similar trend was observed for the 13 mm pellet die (Fig. 4b), although the overall reflectance values were more consistent, even for relatively short pressing times (30 min). The reflectance of the 20 mm pellets does not surpass ∼50% despite the long pressing times, whereas all the 13 mm pellets demonstrate reflectance values above 52%. As discussed in Section 3.2, this is likely due to pellet composition: The 13 mm pellets consisted of a mixture of 40% < 53 µm and 60% 53–90 µm diameter particles that were ball-milled prior to pressing, whereas the 20 mm pellets were prepared only with powder ground with a mortar and pestle. The 13 mm pellets thus have generally higher reflectance values due to the greater fractions of small particles. Typically, values of reflectance in the 1106 cm⁻¹ band are approximately R = 0.54 for 13 mm and R = 0.49 for 20 mm, respectively.

Homogeneity and Spectral Quality of the Reflecting Surface

To confirm that a smooth surface is a key parameter for high reflectance values, the effects of surface homogeneity on the reflectivity of (NH₄)₂SO₄ pellets were also studied. By rotating the pellet in the sample holder ∼72° each turn, the specular R were measured at five independent spots on the surface of both a nominally smooth (planar) pellet (#100) and a less-smooth pellet (#37) – these pellets were chosen because small (#100) and large (#37) changes in %R were initially observed when attempting to maximize the signal. In theory, because the focal spot of illumination is constant, this rotation should measure the same spot on the pellet surface, yielding identical reflectance values. However, due to simple apparati (no goniometer, only manual sample rotation), slight translations and tilts emerge with rotation, resulting in measurement of different spots, albeit with some overlap of the original illumination spots. Myriad factors can cause such variations including small cavities or voids, impurities on the surface, and powder inhomogeneity, to name but a few. Some examples of cavities and voids can be observed in Fig. 3. Another point to consider is the crystal structure of ammonium sulfate, which is orthorhombic at room temperature and thus has an (s- versus p-) polarization effect to which the reflectance value is linked.³⁷

A pressed pellet of powder (compared to a single crystal) is, at best, an average of microcrystals with various polarization directions, some spots preferentially polarizing/reflecting more light than others.^37,41 Although polarization effects are not expected at small incidence angles, we have considered the possibility of slight polarization effects from microcrystalline domains in the pressed powders. As seen in Fig. 5, the calculated ss- and pp-reflectance (using the optical constants from Myers et al.²³) for this angle of incidence (11°) are compared with single-angle reflectance results. The calculated spectra vary by only 1.5%R at the ν₃( ${SO}_{4}^{2 -}$ ) band, indicating that polarization effects are minimal for near-normal single-angle reflectance spectrum of a pressed ammonium sulfate pellet. Although the effect is small at 11°, the polarization effects are much greater for larger off-axis angles as is well known and is seen in the companion paper.²³

Figure 6a displays the result for three different IR reflectance bands, namely at 1415, 1106, and 615 cm⁻¹ for ν₄( ${NH}_{4}^{+}$ ), ν₃( ${SO}_{4}^{2 -}$ ), and ν₄( ${SO}_{4}^{2 -}$ ), respectively, for pellet 37. For the rough pellet, relative differences in reflectance on the order of 5% (reflectance values from 47.0% to 49.4%) were observed, revealing that slight variations on the surface and/or polarization effects can lead to significantly different specular responses. Figure 6 demonstrates that the specular reflectance of the surface can be affected by simply measuring a different spot on the surface, and optical constant calculations (k values) can be underestimated if a non-ideal spot on the surface is chosen. Figure 6b shows the same analysis on the more planar, homogenous surface (R_peak 52.5 to 53.9%) of pellet 100, revealing that not only are greater R_peak values obtained from the smoother surface, but the variability in reflectance can be reduced with careful disk preparation.

Reproducibility Using Optimal Parameters

Finally, using only the optimal parameters and preparation methods as outlined above, a series of 10 pellets were prepared and measured separately to estimate the variability (analytical precision) in the measurements. The results are seen in Fig. 7a. The inset of the spectral region that manifests the largest %R variation is shown, and the pellets are listed in order of highest to lowest reflectance (the single-angle reflectance spectra of the 10 optimized pellets from 1500 to 450 cm⁻¹ is presented in Figure S1, Supplemental Material). The reflectance at 1106 cm⁻¹ varies from 55.0% to 52.8% over the 10 pellets yielding a relatively small fractional variation of 4.0%.

The small sinusoidal waves visible across the peak maxima in the inset of Fig. 7a are ascribed to spectral fringing, i.e., an étalon formed between the pellet's front and back surfaces. This effect is commonly observed in thin films or pellets composed of IR transmitting materials.⁴² However, spectral fringing was observed here especially for those pellets pressed with optimal parameters because (i) these pellets are extremely thin (∼0.6 mm) and (ii) the pellet surfaces are smooth and parallel with fewer voids, causing the pellets to become more transparent.

Using the R( $\tilde{ṽ}$ ) data from the series of 10 optimized pellets, these same 10 spectra were truncated from 5000 to 50 cm⁻¹, extrapolated to zero cm⁻¹ and the KKT was performed to obtain the optical constants n and k for each spectrum. Only wavenumbers <5000 cm⁻¹ were included in this calculation because small features were present at higher frequencies resulting, in some cases, in very slightly negative k values: a phenomenon that is not physically possible. Figure 7a displays the calculated n and k for the series of 10 pellets on the right and left axes, respectively. As observed for the reflectance values, the differences in n( $\tilde{ṽ}$ ) and k( $\tilde{ṽ}$ ) for the 10 spectra are minimal and in order to emphasize the differences log₁₀k is plotted in Fig. 7b.

One way in which the variability of pressing 10 pellets with the optimized protocol was assessed was by calculating the relative standard deviation for R(

\tilde{ṽ}

), n(

\tilde{ṽ}

), and k(

\tilde{ṽ}

), all across a broad spectral range (500–3500 cm⁻¹) and also at the peak of one band of interest near 1106 cm⁻¹ (the value is of course slightly shifted for the n and k vectors). Table V summarizes the relative standard deviation, defined as the standard deviation, σ, divided by the mean value, R_av, n_av, or k_av, along with the relative spread ((x_max–x_min)/x_av, x = R, n, k). At the peak of the ν₃(

{SO}_{4}^{2 -}

) band, all three analyses are comparable (resulting in low relative standard deviations) for R(

\tilde{ṽ}

), n(

\tilde{ṽ}

), and k(

\tilde{ṽ}

). Although both the relative spread and the relative standard deviation are consistently small between R(

\tilde{ṽ}

) and n(

\tilde{ṽ}

) when comparing across the large spectral region, that of k(

\tilde{ṽ}

) is rather large. This arises because large relative deviations occur when the reflectance (and k(

\tilde{ṽ}

) values) are very small (near zero); the small differences result in larger percentage changes. These small differences near the baseline are highlighted in the logarithmic plot of Fig. 7b.

Table V.

Relative standard deviation and relative spread of the reflectance values, n( $\tilde{ṽ}$ ), and k( $\tilde{ṽ}$ ) for the 10 optimized pellets, both across a large frequency area and at the 1106 cm^–1 reststrahlen band.

	R( $\tilde{ṽ}$ )	n( $\tilde{ṽ}$ )	k( $\tilde{ṽ}$ )
Relative standard deviation (500–3500 cm⁻¹)	3.6%	2.3%	36.8%
Relative standard deviation	1.2% at 1106 cm⁻¹	1.4% at 1070 cm⁻¹	1.4% at 1089 cm⁻¹
Relative spread (500–2000 cm⁻¹)	12.3%	8.2%	98.9%
Relative spread	4.1% at 1106 cm⁻¹	4.2% at 1070 cm⁻¹	4.4% at 1089 cm⁻¹

Discussion

This study has shown, at least for moderately soft materials, that powdered forms of neat chemicals can be pressed at an appropriate pressure into pellets of sufficient planarity and homogeneity to yield specular behavior. We note that the specularity is essentially the complement of the diffuseness spectrum, D, which is defined as D = ρ_d/ρ, where ρ_d is the diffuse reflectance and ρ is the total reflectance.¹⁵ The diffuseness, D, is a reflectance analogue to the “haze factor”, b, used for visible transmission measurements; that is, for a window, b gauges the fraction of light transmitted diffusely.^15,43,44 Key elements to forming specularly reflecting pellets include use of sufficiently small and dried particles in the right sieve fractions, pressing for sufficient duration (ramped, for approximately 30 min total) at pressures of approximately 9 × 10⁴ lb/in² (final pressure). Such methods result in pellets that yield reliable optical constants. Future studies will investigate if such methods can be applied to harder materials.

In similar work, Volz³⁷ studied the near-normal reflectance of inorganics, though no attempt was made to derive the optical constants. He noted that crystalline substances may exhibit certain vibrational bands whose reflected intensity depends on beam polarization. He compared near-normal reflectance from reststrahlen bands of several inorganic species, both neat and mixed, as crystals but also as pressed pellets, including for ammonium sulfate. The near-normal reflectance of the pellets was recorded and Volz also found that, similar to the present work, only relatively small variations in R were observed once the particle sizes were small enough, mostly crystals and microcrystals ground with mortar and pestle to sizes of ∼10 µm and smaller, and most samples prepared with very fine particles. To press the pellets, Volz used higher pressures than in the present studies, namely 30 s at 160 000 lb/in² vis-a-vis the ∼97 000 lb/in² values used in this work. He noted that such high pressures only brought marginal gain; using only 40 000 lb/in² for 30 s, the calcite reflectance dropped only 10% from its maximal value. Using a beam condenser, his IR spot size was also much smaller with an effective sample area <1 mm², and with the incidence angle ranging from 2 to 15° and polarized 0–10° perpendicular to that plane. As expected, no polarization effects were observed for the pressed powders; presumably due to random microcrystal orientation and also the near-normal angles of incidence (similar to the only small changes observed in the present work, Fig. 5). For the pellets, including mixtures, Volz was also able to obtain specular reflectance comparable to those of pure crystals for softer substances such as KBr or (NH₄)₂SO₄ (Mohs hardness 1.5 and 2.3, respectively), but rightly pointed out the potential lack of applicability of the method to harder specimens such as quartz (Mohs hardness = 7) which do not readily flow nor compress. For the 20 or so species measured, the reflectance of the pressed powders ranged from approximately 40 to 100% of the values obtained from the corresponding crystals, the pellets of the harder materials (limestone, basalt, quartz) having the lower R values relative to crystalline species.

For the present work, (NH₄)₂SO₄ was chosen because it is compressible and also because its optical constants have been reported. Ammonium sulfate is in fact biaxial, but it was assumed that the three sets of optical constants are identical. Toon et al.⁹ found from their optical constant measurements of a macroscopic crystal of the material that indeed the three sets of optical constants were very close in value over much of the IR wavelength range. In that 1976 paper, Toon et al. first reported⁹ the optical constants of (NH₄)₂SO₄ obtained from a single crystal using reflectance–transmittance measurements on a dispersive IR system. Thirty years on, Earle et al.¹⁰ reported better-resolved optical constants for crystalline ammonium sulfate at 298 K, along with the n and k values at 213, 223, and 243 K. They derived n/k from extinction measurements of dry (NH₄)₂SO₄ aerosols using an aerosol flow tube coupled to a Fourier transform spectrometer. Besides these two literature data sets, in a separate effort, Pacific Northwest National Laboratory (PNNL) and Defence Research and Development Canada have generated values of n/k (NH₄)₂SO₄ using IRSE.²³ While derived differently, all three methods provide n/k data which can be used (either n/k directly or generating reflectance spectra via Fresnel equations) as benchmarks to which the present single-angle data can be compared.

A comparison for the four sets of k vector data is seen in Fig. 8 which displays the n( $\tilde{ṽ}$ ) and k( $\tilde{ṽ}$ ) results of (NH₄)₂SO₄ measured in the current studies via single-angle method and via ellipsometry in the companion paper.²³ The k values reported in Fig. 8 were derived from spectra with the highest obtained reflectance for both PNNL data sets. The plot also shows the Toon et al.⁹ data (c-axis single crystal) as well as from Earle et al.¹⁰ ((NH₄)₂SO₄ aerosols). What is to be gleaned from Fig. 8 is that the Toon et al. data are at a much lower spectroscopic resolution/digitally undersampled; we believe this results in peak values of k (and R) that are in some cases too low due to the lack of data points, as evidenced by, e.g., the k peak at 1089 cm⁻¹. While the extinction values (k) of Earle et al. are spectroscopically better resolved (digitally better sampled), they are also of significantly lower amplitude than either the Toon et al. data (shown as well in Fig. 4 in the Earle et al. paper¹⁰) or the PNNL single-angle or ellipsometric values; this is especially true for the strong bands. As seen in Fig. 8, the results indicate moderately good agreement between pelletized samples, aerosols, and single crystal specimens, although increased scattering from the pellet's surface may be more problematic at higher wavenumber as indicated by the slightly higher values of k for the pellet measurements (not seen in plot).

To better facilitate comparison of the k(

\tilde{ṽ}

) values between the data sets, the relative peak height differences (k_maxA-k_maxB)/k_maxA as well as band integrated differences (∫k_A – ∫k_B)/∫k_A – where A and B represent different data sets - were calculated as percentages for the peak heights and band integrals for each of the three strong bands ν₄(

{SO}_{4}^{2 -}

), ν₃(

{SO}_{4}^{2 -}

), and ν₄(

{NH}_{4}^{+}

), as well as two weaker

{NH}_{4}^{+}

bands at 3052 and 3220 cm⁻¹. These percent differences are reported in Table VI. There is excellent agreement for the k(

\tilde{ṽ}

) values between the single-angle reflectance measurements and the ellipsometry data for the pellet samples; differences in peak heights for the three strong isolated bands range from 2.6% to 4.4%, with a mean difference averaged over three peaks of 3.6%. If peak integrals are used rather than peak heights, the average difference between PNNL single-angle and PNNL ellipsometry is just 1.6%. The agreement between single-angle and ellipsometry does present one area of discrepancy, however: The single-angle spectrum displays a small feature (1–2%R) at 4160 cm⁻¹ attributed to volume scattering¹⁷ whose amplitude varies depending on the pellet. The feature leads to slightly negative k values around 3700–4200 cm⁻¹ and is not observed in the correspondingly featureless ellipsometric spectrum–IRSE measures the change in polarization of the radiation from the pellet surface. Since this phenomenon is an artifact associated with the effects of the KKT and the volume scattering band, the negative k values were arbitrarily set to +1.0 × 10⁻¹⁰. Further investigation to understand the phenomenon/artifact is underway. That peak notwithstanding, the fact that the two independent methods, i.e., single-angle reflectance and spectroscopic ellipsometry, give nearly identical results is compelling evidence that accurate values of k(

\tilde{ṽ}

)/n(

\tilde{ṽ}

) have been obtained. Indeed, we suggest the values reported here (and available as Supplemental Material) can supplant existing literature data for atmospheric and other retrievals.

Table VI.

Percent differences ((k_A–k_B)/k_A) × 100 and ((∫k_A–∫k_B)/∫k_A) × 100 for each of the five bands ν₄( ${SO}_{4}^{2 -}$ ) (614 cm⁻¹), ν₃( ${SO}_{4}^{2 -}$ ) (1089 cm⁻¹), ν₄( ${NH}_{4}^{+}$ ) (1417 cm⁻¹), ν₃( ${NH}_{4}^{+}$ )–1 (3052 cm⁻¹), and ν₃( ${NH}_{4}^{+}$ )–2 (3220 cm⁻¹), between four different data sets. Here k_A and k_B represent the simple maximum peak heights of the k vector of the given band for data sets A and B, respectively, whereas ∫k_A and ∫k_B represent the corresponding band integrals of the k vectors for the two data sets A and B. These are compared (A versus B, row versus column) between four independent sets of data : PNNL single-angle reflectance, PNNL ellipsometry,²³ Toon et al.,⁹ and Earle et al.¹⁰ Integrated area comparisons were not made for the ν₃( ${NH}_{4}^{+}$ ) bands because the two features overlap.

	Ellipsometry²³		Toon et al.⁹		Earle et al.¹⁰
	%diff. k_max	% diff. ∫k( $\tilde{ṽ}$ )	% diff. k_max	% diff. ∫k( $\tilde{ṽ}$ )	% diff. k_max	% diff. ∫k( $\tilde{ṽ}$ )
Single angle (PNNL)
ν₄ ( ${SO}_{4}^{2 -}$ )	4.4	1.0	20.0	24.1	23.2	11.4
ν₃ ( ${SO}_{4}^{2 -}$ )	2.6	1.8	16.2	3.1	28.1	20.7
ν₄ ( ${NH}_{4}^{+}$ )	3.9	2.0	4.8	14.7	20.8	11.9
ν₃ ( ${NH}_{4}^{+}$ ) –1	3.0		0.6		16.1
ν₃ ( ${NH}_{4}^{+}$ ) –2	0.3		2.5		21.2
Ellipsometry (PNNL)
ν₄ ( ${SO}_{4}^{2 -}$ )	—	—	23.5	23.3	19.6	12.3
ν₃ ( ${SO}_{4}^{2 -}$ )	—	—	18.4	4.9	29.9	19.3
ν₄ ( ${NH}_{4}^{+}$ )	—	—	0.9	16.4	23.8	10.0
ν₃ ( ${NH}_{4}^{+}$ ) –1	—	—	3.6		18.7
ν₃ ( ${NH}_{4}^{+}$ ) –2	—	—	2.2		20.9
Toon et al.
ν₄ ( ${SO}_{4}^{2 -}$ )			—	—	38.6	32.7
ν₃ ( ${SO}_{4}^{2 -}$ )			—	—	14.1	23.2
ν₄ ( ${NH}_{4}^{+}$ )			—	—	24.5	24.8
ν₃ ( ${NH}_{4}^{+}$ ) –1			—	—	15.6
ν₃ ( ${NH}_{4}^{+}$ ) –2			—	—	19.1

The differences between PNNL results (both using single angle and ellipsometry) and the Toon et al.⁹ (crystal) and Earle et al.¹⁰ (aerosol) results, however, are significantly larger, in some cases with PNNL peak height for k 28–30% stronger than the Earle et al. data for the one peak of ν₃( ${SO}_{4}^{2 -}$ ) peak at 1089 cm⁻¹, and typically 22% as averaged across the several stronger bands.

As seen in Fig. 8, the agreement of Toon et al. with the present single-angle and ellipsometry data is limited in part by spectroscopic resolution of the Toon et al.⁹ instrument; the lower spectral resolution of 1970s instrumentation likely plays a large role in the lack of agreement. The limited number of data points (just 57 between 250 and 5000 cm⁻¹) has a strong effect not only on resolution and digital spacing of the abscissa as seen in Fig. 8 but also affects the n/k amplitudes. If higher resolution instrumentation had been available at the time, the Toon et al. crystal data would likely agree well with the present results. Moreover, the low-spectral resolution of the Toon et al.⁹ data likely explains the significant differences between values obtained from the peak maxima and the integrated areas (see Table VI). In fact, as shown in Fig. 8, peak maxima of the Toon et al.⁹ spectrum are not as high at PNNL values; this is expected due to the lack of data points, but the integrated peak areas are similar to those of the PNNL spectral bands.

Earle et al.¹⁰ derived their n/k vectors by making FT-IR extinction measurements of dried ammonium sulfate powder in an aerosol flow tube. The data are at higher spectroscopic resolution and match the peak profiles of the two PNNL data sets well, but while the digital spacing is more consistent, there appears to be slight shifts in frequency calibration (peak position) and especially amplitude. Specifically, the Earle et al. data appear to have significantly lower k values, approximately 19 to 30% lower than either PNNL data set as compared across the three bands at 1417, 1089, and 614 cm⁻¹ (using k_max). The Earle et al. k values were also noted in Fig. 4 of their own paper¹⁰ as being significantly lower than the Toon et al.⁹ data. The methods in which the data are derived are very different, and the reasons for the disagreement are not immediately clear but one possibility is the analysis method to obtain n/k may not be fully applicable to such fine, non-spherical particles: Their SEM data indicated that not all the particles were perfectly spherical, and some may have agglomerated. As pointed out by both Weis and Ewing³⁵ and Clapp and Miller,⁴⁵ a limitation of Mie scattering theory is that it is not fully applicable to non-spherical particles.

For the ν₃( ${SO}_{4}^{2 -}$ ) band, in the Earle et al.¹⁰ data, an 11 cm⁻¹ peak shift to the blue is observed relative to the PNNL single-angle and ellipsometric data. The Earle et al. data were recorded from fine particles: When investigating the spectral profile effects of fine aerosols of NH₃ at cryogenic temperatures, Clapp and Miller⁴⁵ noted a similar approximately 10 cm⁻¹ blue shift in the aerosol spectrum of fine particles for those bands that satisfy the Fröhlich criteria⁴⁶ of n ∼ 0 and k ∼ √2. Although the k value of the ν₃( ${SO}_{4}^{2 -}$ ) band is larger than √2, the criteria are partially satisfied, and this may have had a (partial) effect on only this band for the Earle et al. particle extinction measurements, resulting in the blue shift. Moreover, the analysis methods of Clapp et al.⁴⁷ do not adequately account for all light scattering mechanisms for the particle sizes in the flow tube. Segal-Rosenheimer et al.⁴⁸ used a similar approach to Earle et al. but used very fine particles measuring extinction and particle size simultaneously. Due to the fine particles size, the extinction spectrum shows minimal scattering meaning the extinction cross-section is approximately equal to the absorption cross-section. Their derived k (and n) values appear closer to the present values when calculated directly from the extinction spectrum but the digital data are not available for quantitative comparison.

In another approach, Pecharromán and Iglesias reported⁴⁹ an alternate method to determine the optical constants for isotropic materials such as ammonium sulfate using a variant effective-medium theory that is calculated based on measurement of an isotropic material's reflectance from a powdered sample. It employs an expression for the average dielectric constant of a heterogeneous system which shows percolation features. Finally, we note still another method to approximate the n/k values for ammonium sulfate was developed by Downing et al.⁵⁰ using molar fractional amounts of aqueous ammonium sulfate solutions at progressively higher concentrations (1.6, 2.4, and 3.2 M) and then extrapolating the derived k( $\tilde{ṽ}$ ) values to the solid crystalline form. The band integral $S = \int k (\tilde{ṽ}) d \tilde{ṽ}$ was extrapolated to correspond to the number density N of absorbers in the solid, assuming the signal-to-noise ratio remains constant. The extrapolated results compared reasonably well with results of Toon et al. but are not digitally available. However, the aqueous solution n/k data are in and of themselves valuable for modeling stratospheric (NH₄)₂SO₄ particles, since many solid species form aerosols (e.g., NaCl, (NH₄)₂SO₄) via water condensation. As noted, the optical constants of solids and solution forms can sometimes differ significantly, and the optical properties of both are valuable.^9,51

Conclusion

Laboratory, industrial, and standoff IR spectroscopies continue their exponential growth.^52,53 It has already been demonstrated⁵⁴ that laboratory reference data can readily be used for field detection of both solids and liquids, as well as gases⁵⁵ but increasingly the n/k vectors are used for modeling^5,56 the target signal both for liquids⁴ and solids.⁵⁴ Obtaining n/k for solids is more challenging, and one goal of this study was thus to (determine how to) prepare pellets with high surface smoothness, since the single-angle method measures only specular reflectance. We have recorded single-angle reflectance data of pelletized ammonium sulfate powder. (NH₄)₂SO₄ is an easy material with which to work; it flows well producing homogeneous pellets with void space typically on the order of 5% or less. To simplify the study, we did not consider using binders such as polyethylene glycol which are often used to bind particles and act as a lubricant during the pressing process.⁵⁷

The spectrum of each pellet was recorded in two spectral segments, including the mid- and far-IR. The two spectral segments for each pellet were trimmed (50 to 600 cm⁻¹ for the far-IR and 400–5000 cm⁻¹ for the mid-IR), concatenated into a single R( $\tilde{ṽ}$ ) spectrum, the R( $\tilde{ṽ}$ ) data extrapolated to $\tilde{ṽ}$ = 0 and the KKT performed to obtain the optical constants for each pellet. Key results indicate that the optimal reflectance is obtained only after certain procedures are followed in preparing the pellet. Any phenomenon or artifact that (diffusely) scatters or absorbs the IR rather than reflecting it in a specular fashion leads to (artificially) low and inaccurate k values. Key to optimal (maximized) reflectance is preparation of the powder; better results are obtained using (i) mostly smaller particles, e.g., <50 µm, and (ii) mixtures of different particle sizes, allowing for smaller particles to fill the voids created by packing of the larger particles. Drying the sample was found advantageous, presumably due to its hygroscopic nature, which otherwise leads to clumping and larger particles (this is likely limited to hygroscopic species such as (NH₄)₂SO₄). The additional grinding provided by the Wig-L-Bug ball mill proved to be an efficient method to obtain increased fractions of smaller particles and thus more specular surfaces. Finally, a last parameter found to be important included a gradual or ramped weight (5, 10, 15, 20 tons) with a final pressure of at least 8 to 10 × 10⁴ lb/in² for durations of 30 min or longer. The nature of the pellet surface was verified not only by reflectance but also by both optical and SEM microscopies.

Because most methods to determine the optical constants require (near-) crystalline materials, the pressed pellet/single-angle method offers a viable alternative to determine n/k. So long as optical quality pellets (highly specular faces) can be obtained, the method is reliable, faster, and significantly more economical than, e.g., spectroscopic ellipsometry. The results suggest that for some materials it may be possible to press a pellet of the powder form of the material and make optical constant measurements on the pellet rather than a single bulk crystal. It does suffer the drawback that, as demonstrated here, it can be challenging to prepare specular surfaces from powders.

In a companion paper,²³ we have also investigated the use of pressed pellets of (NH₄)₂SO₄ with the spectroscopic ellipsometry method to obtain the n( $\tilde{ṽ}$ ) and k( $\tilde{ṽ}$ ) vectors for ammonium sulfate across the far-IR spectrum and mid-IR spectrum. Spectroscopic ellipsometry has been demonstrated using a pellet, but while they need to be flat, the surfaces do not need to be of polished quality since only changes in polarization are recorded. Using these two distinct methods, we have found agreement of 2.6 to 4.4% levels for the peak height values of k for the stronger bands. The pellet single-angle and IRSE results have been compared to two sets of previous literature n( $\tilde{ṽ}$ ) and k( $\tilde{ṽ}$ ) values obtained from crystalline (NH₄)₂SO₄ as crystal reflectance, as well as extinction spectra of aerosols measured in a flow tube, both of which demonstrated modest agreement, but were not fully consistent with the present results. The excellent agreement using the two methods suggests using either the single-angle or ellipsometry data as new reference data as an improvement in n/k for atmospheric retrievals, for example. Both data sets are available to the reader as Supplemental Material.

Supplemental Material

sj-pdf-1-asp-10.1177_0003702820930009 - Supplemental material for Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH₄)₂SO₄ from Single-Angle Reflectance

Supplemental material, sj-pdf-1-asp-10.1177_0003702820930009 for Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH₄)₂SO₄ from Single-Angle Reflectance by Timothy J. Johnson, Emmanuela Diaz, Kendall D. Hughey, Tanya L. Myers, Thomas A. Blake, Alice C. Dohnalkova and Sarah D. Burton in Applied Spectroscopy

Footnotes

Acknowledgments

We thank Carolyn S. Brauer, Brent M. DeVetter, and Molly Kelly-Gorham for assistance in the earlier phases of this project.

Declaration of Conflicting Interests

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

Funding

The research is based upon work supported in part by the Office of the Director on National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via DOE contract DE-AC05-76RL01830. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. We thank our sponsor Dr. Kristin Dewitt for program support. PNNL is operated by Battelle for the U.S. Department of Energy under contract DE-AC05-76RLO1830.

ORCID iDs

Timothy J. Johnson

Tanya L. Myers

Alice C. Dohnalkova

Supplemental material

The supplemental material mentioned in the text, which includes Tables S1–S3, Figure S1, the data set for reflectance obtained with single-angle reflectance spectroscopy, and the associated n and k for our best pellet from 5000 to 0 cm⁻¹, is available in the online version of the journal.

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Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

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Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH 4 ) 2 SO 4 from Single-Angle Reflectance

Abstract

Keywords

Introduction

Experimental

Single-Angle Infrared Reflectance Spectroscopy: Kramers–Kronig transform

Single-Angle Infrared Reflectance: Instrumental

Materials, Sample Sieving and Drying, Particle Size Distribution

Pellet Preparation

Pellet Characterization

Results

Assessing the Results: Maximizing Reflectance

Powder Particle Size and Grinding

Packing Density, Void Space

Pellet Formation: Application of Drying

Pellet Diameter and Pellet Formation Pressure

Pellet Formation–Duration of Press

Homogeneity and Spectral Quality of the Reflecting Surface

Reproducibility Using Optimal Parameters

Discussion

Conclusion

Supplemental Material

sj-pdf-1-asp-10.1177_0003702820930009 - Supplemental material for Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH4)2SO4 from Single-Angle Reflectance

Footnotes

Acknowledgments

Declaration of Conflicting Interests

Funding

ORCID iDs

Supplemental material

References

Supplementary Material

sj-pdf-1-asp-10.1177_0003702820930009 - Supplemental material for Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH₄)₂SO₄ from Single-Angle Reflectance