A HIGH-RESOLUTION VACUUM ULTRAVIOLET LASER PHOTOIONIZATION AND PHOTOELECTRON STUDY OF THE CO ATOM

There has been considerable effort in calculating atomic data, such as atomic energy levels, transition probabilities, and photoionization cross sections, in order to interpret the opacities of stellar envelopes due to their relevance to the understanding of stellar structure and stellar pulsations (Seaton 1987, 1999; Seaton et al. 1994). Iron-group elements (Fe, Ni, and Co) have very low mass per nucleon and are the final products of the thermonuclear processes (Merer 1989). Thus, they have significant abundances in stars and interstellar media and contribute significantly to the opacities of stellar envelopes. The need for accurate photoionization cross sections and high-quality spectroscopic data for modeling stellar spectra has prompted collaborative efforts, such as the Opacity Project and the IRON Project, whose main goal is focused on computing the excitation cross sections of iron-group elements and their ions (Hummer et al. 1993; Berrington & Pelan 1995). Thus, vacuum ultraviolet (VUV) photoionization cross-section measurements of Fe, Ni, and Co are recognized to be of significant importance in astrophysics.

The contents of chemical elements in stars, gas clouds, and galaxies in the cosmos are usually determined from its absorption spectrum (Asplund 2008). The cobalt atom is an important element involved in the stellar evolution because of its role in the formation of stable iron isotopes through the supernova nucleosynthesis decay pathway of ⁵⁶Ni $\to$ ⁵⁶Co $\to$ ⁵⁶Fe. Due to the fact that autoionizing Rydberg series are major features in the absorption spectra of atoms and their ions as indicated in our previous photoionization studies of ⁵⁶Fe and ⁵⁸Ni (Reed et al. 2009; Shi et al. 2012), the present high-resolution photoionization study of Co is expected to contribute to modelings of stellar spectra and thus improve understanding of the formation of stars and supernovae (SNe). For the analysis of SNe Ia and core-collapse SNe, the photoionization transitions of iron-group elements are particularly important due to their high abundances in SNe (Woosley & Weaver 1995; Hillebrandt & Niemeyer 2000; Mazzali et al. 2007).

Although there have been many spectroscopic studies on Co⁺, most of the previous studies were focused on the determination of energy levels of Co⁺. For example, Pickering et al. recorded high-resolution spectra of ionized Co by Fourier transform spectroscopy in the energy range 3000–70,422 cm⁻¹ and identified 2373 levels of Co⁺ (Pickering et al. 1998). However, their experiment was unable to provide the information on the cross sections of excitation transitions to those Co⁺ levels. Dyke and coworkers tried to determine the relative photoionization cross sections of Co by measuring the He i photoelectron spectrum of gaseous Co atoms generated in a hot oven (Dyke et al. 1982). However, the inherent limitation in the spectral resolution of the latter He i photoelectron study rendered most of the photoelectron bands unresolvable. The lack of high-resolution experimental data for photoionization cross sections of the Co atom impedes the interpretation of stellar spectra because the overwhelming majority of current theoretical predictions of photoionization cross sections are not accurate enough to allow reliable modeling of stellar opacities.

The current need for accurate photoionization data for iron-group elements is the primary motivation for our VUV photoionization studies of the iron-group elements. In an effort to establish a high-quality photoionization database for transition metal atoms, we have initiated a project to perform a high-resolution VUV laser photoionization and photoelectron study of the iron-group elements. As pointed out above, we have successfully measured the high-resolution photoionization efficiency (PIE) spectra of ⁵⁶Fe and ⁵⁸Ni near their ionization thresholds. These data, along with the PIE data of the Co atom reported in the present study, are expected to be useful for the interpretation of the stellar spectra and for benchmarking first-principles theoretical calculations of photoionization cross sections for the iron-group elements.

Most recently, important interactions involving VUV photoionization of Co⁺ have been calculated using the sophisticated relativistic Dirac Atomic R-matrix Codes (Tynall et al. 2016). Transition probabilities and oscillator strengths for Co⁺ levels of astrophysical interest have also been computed at VUV photon energies up to 114 nm based on a relativistic Hartree–Fock model (Quinet et al. 2016). The photoionization transition line widths and state-resolved photoionization cross sections for the formation of Co⁺ obtained here, along with the theoretical calculations, are expected to provide a more completed excitation and de-excitaion network for Co and its ions in low ionization stages. Furthermore, we believe that the photoionization cross sections obtained in this experiment  would stimulate state-of-the-art theoretical photoionization calculations of the Co atom.

The experimental arrangement and procedures employed here are similar to those used in the previous VUV photoionization and photoelectron studies of Fe and Ni atoms and have been described in previous publications (Reed et al. 2009; Shi et al. 2012). Thus, only a brief description is given below. The apparatus consists of a tunable VUV laser photoionization source (tunable range = 7–19 eV, optical bandwidth = 0.4 cm⁻¹ [FWHM]) operated at a repetition rate of 30 Hz, a laser ablation metal beam source for the generation of the supersonically cooled Co atom sample in the form of an atomic beam, an ion time-of-flight (TOF) mass spectrometer for photoion detection, and an electron TOF spectrometer for the detection of pulsed field ionization photoelectrons (PFI-PEs).

The VUV laser comprises two independently tunable dye lasers (Lambda Physik, Model FL-3002 and Model FL-2002) pumped by an identical YAG laser (Spectra Physics, Model PRO-230; repetition rate = 30 Hz) using the second (532 nm) and/or third (355 nm) harmonic outputs. The VUV laser radiation was obtained by four-wave difference-frequency (2ω₁–ω₂) mixing schemes using Xe gas in the form of a pulsed jet as the nonlinear medium. Here ω₁ and ω₂ are the respective ultraviolet (UV) and visible (VIS) outputs of the two dye lasers. The UV ω₁ output was set to match the 2ω₁ resonance transitions of Xe (5p $\to$ 6p or 5p $\to$ 6p') at 80,118.962 or 89,860.538 cm⁻¹, respectively. The VIS ω₂ was tuned to produce the tunable VUV difference-frequency (2ω₁–ω₂) range required by the experiment. The VIS ω₂ frequency was calibrated by a Coherent wavemeter. An off-axis focusing lens was used to select the VUV (2ω₁–ω₂) frequencies of interest by rejecting the unwanted fundamental frequencies ω₁ and ω₂ and the VUV sum-frequency (2ω₁ + ω₂) before entering the photoionization region. The VUV (2ω₁–ω₂) intensity was measured by a copper photoelectric detector.

Gaseous Co atoms were generated by laser ablation on a rotating and translating Co rod (American Element, 99% purity) by using the second harmonic (532 nm) output of an Nd:YAG laser (Continuum, Surelite-1–30; repetition rate = 30 Hz) with a pulse energy of $\approx 2$ mJ. The gaseous Co sample thus formed was further cooled by supersonic expansion and skimmed by a circular skimmer (diameter = 1 mm) in the beam source chamber prior to entering the photoionization region of the photoionization chamber. A pair of electrostatic deflection plates was installed between the skimmer and the photoionization region and was biased at a dc field of $\approx 100\,{\rm{V}}\,{\mathrm{cm}}^{-1}$ in order to minimize the charged and metastable Rydberg species produced in the laser ablation process entering into the photoionization region.

For VUV–PIE detections, a dc electric field of 50 V cm⁻¹ was used to extract photoions from the photoionization region toward the ion TOF mass spectrometer. In VUV laser PFI-PE measurements, a dc field of 0.15 V cm⁻¹ was employed to disperse prompt photoelectrons. The PFI of excited high-n Rydberg species was achieved by using a PFI field of 1.0 V cm⁻¹ at a delay of 800 ns with respect to the application of the VUV laser pulse at the photoionization region. The ion (or electron) signal was detected by a dual set of microchannel plate detectors.

Figure 1 depicts the PIE spectrum of the Co atom recorded in the VUV energy range of 63,500–67,000 cm⁻¹ (7.87–8.31 eV) by measuring the Co⁺ intensity while scanning the energy of the VUV photoionization laser. The PIE spectrum of Co represents the plot of the I(Co⁺)/I(VUV) ratio versus the VUV photoionization energy, where I(Co⁺) and I(VUV) are the Co⁺ and the VUV intensities, respectively. Thus, the PIE spectrum provides information about the relative photoionization cross sections of the Co atom in the VUV photon energy range of interest. Due to the high-resolution nature of the VUV laser used in this experiment, many autoionizing resonances are well resolved in the VUV–PIE spectrum.

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We have also conducted VUV laser PFI-PE measurements in the same energy range of 63,500–67,000 cm⁻¹ and successfully observed four PFI-PE bands with their peak energies located at 63,564.0 ± 1.5, 63,698.7 ± 1.0, 64,514.2 ± 1.2, and 66,916.3 ± 2.0 cm⁻¹. The observation of these PFI-PE bands indicates the existence of electronic states of the Co⁺ ion at these peak energies. As described below, these PFI-PE peaks can be assigned to known photoionization transitions. These PFI-PE peak positions (listed in Table 1) have been corrected for the Stark shift of 2.0 cm⁻¹. As in previous studies, the Stark shift correction is taken to be half of the value predicted by the formula of $4.1\sqrt{F}$ in cm⁻¹, where F ≈ 1.1 V cm⁻¹ (Shi et al. 2012). The FWHM values observed for these PFI-PE peaks are assigned as the uncertainties of the PFI-PE peak energies. We find that the PFI-PE energy resolution achieved in the present PFI-PE measurement is within the FWHM range of 1.5–2.0 cm⁻¹ for the PFI-PE bands, indicating that these PFI-PE bands have minor perturbations by near resonance autoionizing Rydberg states.

Table 1.  Comparison of Ionization Energies (IEs) in cm⁻¹ Obtained from the Present VUV–PFI–PE and VUV–PIE Rydberg Series Measurements and Those Calculated Using Known Spectroscopic and IE Data

Photoionization Transitions	IE (cm−1)
Co(3d74s2 4F9/2) $\to$ Co+ (3d8 3F4)	63,564.0 ± 1.5a 63,564.5b
Co(3d74s2 4F7/2) $\to$ Co+ (3d8 3F3)	63,698.7 ± 1.0a 63,696.3c
Co(3d74s2 4F9/2) $\to$ Co+ (3d8 3F3)	64,514.2 ± 1.2a 64515.0c
Co(3d74s2 4F9/2) $\to$ Co+(3d74s1 5F5)	66,916.3 ± 2.0a 66,915.1c 66,914.97 ± 0.33d

Notes.

^aObtained from the present PFI-PE measurement. ^bObtained from Page & Gudeman (1990). ^cCalculated using known spectroscopic data and the IE value from the literature (see the text). ^dObtained based on the present PIE Rydberg series measurement.

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The observed PFI-PE bands are also depicted in Figure 1 as the lower stick spectra. However, since the relative intensities of these PFI-PE peaks have not been measured carefully, we have arbitrarily set all four PFI-PE bands of the Co atom to have the same intensity. The ionization energy (IE) of the Co atom was previously determined to be 7.8810 eV (63,564.5 cm⁻¹) by Page & Gudeman (1990) by employing the double-resonance fluorescence-dip technique. The latter IE value is found to be in excellent agreement with the lowest PFI-PE peak at 63,564.0 ± 1.5 cm⁻¹ observed in the present study.

According to the NIST atomic database (Kramida et al. 2016), the four lowest spin–orbit levels of neutral Co are ⁴F_9/2, ⁴F_7/2, ⁴F_5/2, and ⁴F_3/2 (in ascending order), and the four lowest spin–orbit levels of the Co⁺ ion are ³F₄ , ³F₃, ³F₂, and ⁵F₅ (in ascending order). The energies of the ⁴F_7/2, ⁴F_5/2, and ⁴F_3/2 excited levels of neutral Co measured with respect to the ground ⁴F_9/2 state of Co have been reported to be 816.00, 1406.84, and 1809.33 cm⁻¹, respectively. The energies of the ³F₃, ³F₂, and ⁵F₅ excited spin–orbit levels of Co⁺ measured with respect to the ground ³F₄ state of Co⁺ have also been determined to be 950.51, 1597.32, and 3350.58 cm⁻¹, respectively. Thus, the IE of Co observed at 63,564.5 cm⁻¹ can be assigned as the photoionization transition Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₄). This IE[Co(⁴F_9/2) $\to$ Co⁺(³F₄)] value, along with the known spacings of the spin–orbit states for Co and Co⁺, allows the calculation of the photoionization transition energies from the ⁴F_9/2, ⁴F_7/2, ⁴F_5/2, and ⁴F_3/2 states of the Co atom to excited spin–orbit levels ³F₃, ³F₂, and ⁵F₅ of the Co⁺ ion.

We found that such IE calculations predict IE[Co(⁴F_9/2) $\to$ Co⁺(³F₃)] = 64,515 cm⁻¹ for Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₃), IE[Co(⁴F_9/2) $\to$ Co⁺(⁵F₅)] = 66,915.1 cm⁻¹ for Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d⁷4s^{1 5}F₅), and IE[Co(⁴F_7/2) $\to$ Co⁺(³F₃)] =63,699.0 cm⁻¹ for Co(3d⁷4s^{2 4}F_7/2) $\to$ Co⁺(3d^{8 3}F₃). These calculated IE values for the photoionization transitions are included in Table 1 to compare with the corresponding IE values observed by the PFI-PE measurements. The fact that these calculated photoionization transition energies are in excellent agreement with the corresponding PFI-PE peak energies indicates that the PFI-PE bands observed at 63,564.0 ± 1.5, 63,698.7 ± 1.0, 64,514.2 ± 1.2, and 66,916.3 ± 2.0 cm⁻¹ should be assigned to the photoionization transitions Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₄), Co(3d⁷4s^{2 4}F_7/2) $\to$ Co⁺(3d^{8 3}F₃), Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₃), and Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d⁷4s^{1 5}F₅), respectively, as shown in Table 1 and marked in Figure 1. To our best knowledge, with the exception of IE[Co(⁴F_9/2) $\to$ Co⁺(³F₄)], all other IE values have not been directly measured in previous studies.

The fact that no step-like structures correlating to these PFI-PE peaks can be observed in the PIE spectrum indicates that the contributions to the cross sections for the formations of Co⁺(3d^{8 3}F_4,3,2) and Co⁺ (3d⁷4s^{1 5}F₅) from Co(3d⁷4s^{2 4}F_9/2,7/2) by direct photoionization are very small compared to those by autoionization. The identification of the photoionization transition Co(3d⁷4s^{2 4}F_7/2) $\to$ Co⁺(3d^{8 3}F₃) shows that excited Co atoms in the excited Co(⁴F_7/2) state lying 816 cm⁻¹ above its ground Co(⁴F_9/2) state are produced by the Co ablation beam source and thus may give rise to other autoionizing structures from photoexcitation of the Co(⁴F_7/2) state.

The photoionization transition energy for Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₂), i.e., IE[Co(⁴F_9/2) $\to$ Co⁺(³F₂)], is predicted to be at 65,161.8 cm⁻¹. However, we were not successful in observing a PFI-PE band at this energy; instead, a PFI-PE band at 65,180 ± 4.0 cm⁻¹ was observed, which is about 20 cm⁻¹ higher than the calculated photoionization transition energy of 65,161.8 cm⁻¹. Judging from the large FWHM of 4.0 cm⁻¹ and the structure of this PFI-PE band, we conclude that it is strongly perturbed by near resonance autoionizing Rydberg states. This PFI-PE band might have its origin from photoexcitation of excited Co atoms produced by the laser ablation source.

A careful examination of the PIE spectrum shows an autoionizing Rydberg series converging to a Co⁺ ion state at around 66,915 cm⁻¹ that can be assigned to the photoionization transition Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺ (3d⁷4s^{1 5}F₅), as shown in Figure 1 and magnified in Figure 2. Least-squares fits of the observed E(n) values have been performed according to the standard Rydberg equation,

$$\begin{eqnarray}&&E(n)=\mathrm{IE}-{R}_{S}/{(n-\mu )}^{2}.\end{eqnarray} \tag{ 1 }$$

Here n, μ, and R_S represent the principal quantum number, the effective quantum defect, and the Rydberg constant for the Co atom, respectively. The R_S value of 109,736.2942 cm⁻¹ is obtained by using the formula R_S = R_∞/(1 + m_e/M), where R_∞ = 109,737.3157 cm⁻¹, M is the mass of the Co atom, and m_e is the rest mass of electrons. The least-squares fits give IE = 66,914.97 ± 0.33 cm⁻¹ for the formation of Co⁺(3d⁷4s^{1 5}F₅) from the Co(3d⁷4s^{2 4}F_9/2) ground state, which is consistent with the value IE[Co(⁴F_9/2) $\to$ Co⁺(⁵F₅)] = 66,916.3 ± 2.0 cm⁻¹ obtained in the PFI-PE measurement. The IE values determined in the PFI-PE experiments and derived from the analysis of the Rydberg series are compared in Table 1.

The electronic configuration of the ground electronic state of Co is [Ar]3d⁷4s². Thus, the formation of Co⁺(3d⁷4s^{1 5}F₅) from the Co(3d⁷4s^{2 4}F_9/2) ground state involves a one-electron process, i.e., the removal of an electron from the 4s orbital. The Rydberg series is expected to be a 3d⁷4s¹ (⁵F₅) np series. Based on the energies of the 3d⁷4s¹(⁵F₅)5p levels determined by Pickering et al., the quantum defect μ is calculated to be 2.17 (Pickering & Thorne 1996). Thus, the Rydberg series can be assigned to be 3d⁷4s¹ (⁵F₅) np (n = 19–38), and the average quantum defect derived from the least-squares fits is 1.9645. The energies and the assignments of the Rydberg levels are listed in Table 2. The strong autoionizing peaks present in the PIE spectrum that do not belong to the identified Rydberg series are listed in Table 3. They are also expected to contribute to the absorption spectrum of the Co atom.

Table 2.  Rydberg Series Converging to the Ionic Co⁺ (3d⁷4s^{1 5}F₅) Excited State from the Neutral Co(3d⁷4s^{2 4}F_9/2) Ground State

na	E(n)(expt)/cm−1 b	E(n)(fit)/cm−1 c	${\boldsymbol{\Gamma }}$/cm−1 d	${\boldsymbol{\mu }}$ e	IR f
19	66,537.04	66,533.82	2.4	1.9600	2.28
20	66,577.30	66,575.07	2.1	1.9726	1.81
21	66,611.83	66,609.96	2.3	1.9735	0.14
22	66,640.34	66,639.74	2.3	2.0105	0.77
23	66,668.86	66,665.37	1.9	1.884	1.54
24	66,688.51	66,687.58	2.4	1.9866	1.06
25	66,708.08	66,706.95	2.4	1.9691	1.24
26	66,724.74	66,723.94	2.4	1.982	0.79
27	66,739.61	66,738.94	2.4	1.9846	0.84
28	66,752.99	66,752.23	2.4	1.9720	0.52
29	66,764.89	66,764.08	2.4	1.9596	0.56
30	66,775.15	66,774.67	2.4	1.9854	0.51
31	66,784.67	66,784.19	2.3	1.9798	0.20
32	66,793.11	66,792.78	2.3	1.9909	0.26
33	66,800.54	66,800.54	2.2	2.0327	0.25
34	⋯	66,807.59	⋯	⋯	⋯
35	66,814.87	66,814.00	2.4	1.8905	0.62
36	66,820.34	66,819.86	2.4	1.9463	0.29
37	66,825.71	66,825.22532	2.3	1.9379	0.13
38	66,830.72	66,830.1462	2.4	1.9088	0.21
$\infty$	66914.97 ± 0.33g	⋯	⋯	1.9645 ± 0.0378	⋯

Notes.

^aPrincipal quantum number. ^bExperimental energies of autoionizing peaks. ^cEnergies obtained based on the least-squares fit to the Rydberg equation. ^dFWHM of the auotionizing peak. ^eQuantum defects. ^fRelative intensities. ^gConvergence limit.

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Table 3.  The Peak Energies (E), FWHMs (Γ), and Relative Intensities (I_R) of Autoionizing Resonances Observed in the PIE Spectrum of Co in the Region of 63,500–67,000 cm⁻¹

E/cm−1	${\boldsymbol{\Gamma }}$/cm−1	IR
63,760.87	10.0	2.71
63,791.25	12.5	0.85
63,801.55	12.6	2.18
63,809.89	8.7	0.97
63,822.95	11.0	4.25
63,837.04	12.0	1.04
63,866.13	8.4	1.37
63,906.39	7.1	0.87
64,609.37	6.4	0.48
64,710.03	25.9	0.76
65,179.91	9.9	0.80
65,265.14	10.1	1.16
65,281.56	12.1	0.89
65,537.29	13.6	0.51
65,911.29	8.5	0.84
65,955.06	8.1	9.47
65,971.18	13.2	0.68
65,990.86	5.0	0.93
66,021.94	11.6	9.20
66,045.22	11.4	3.33
66,060.83	10.7	1.82
66,109.81	9.2	1.40
66,117.08	4.9	10.00
66,123.15	5.8	0.92
66,152.20	14.2	1.54
66,170.25	7.5	3.17
66,171.84	13.0	1.79
66,193.64	8.1	1.44
66,212.94	13.1	5.62
66,231.11	6.8	0.53
66,264.21	10.5	1.50
66,281.61	10.0	6.84
66,295.33	10.1	1.13
66,348.16	8.0	0.55
66,360.91	8.6	3.47
66,428.04	7.6	1.65
66,490.09	9.3	1.12
66,536.60	7.1	1.51

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The Co⁺ ion states formed in the photoionization transitions of Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₄), Co(3d⁷4s^{2 4}F_7/2) $\to$ Co⁺(3d^{8 3}F₃), and Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₃) necessarily involve a two-electron process. That is, while one of the 4s² electrons is ejected, the other 4s electron is simultaneously transferred to the 3d orbital to arrive at the 3d⁸ configuration for Co⁺. The involvement of a two-electron photoionization process may account for the significantly weaker autoionizing Rydberg structures converging to these Co⁺ ion states compared to the Co⁺(3d⁷4s^{1 5}F₅) ion state, as shown in the PIE spectrum of Figure 1.

We have conducted a high-resolution VUV–PIE and VUV–PFI–PE study of the Co atom in the energy range of 63,500–67,000 cm⁻¹, which covers the energy regions for photoionization transitions Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₄), Co(3d⁷4s^{2 4}F_7/2) $\to$ Co⁺(3d^{8 3}F₃), Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d^{8 3}F₃), and Co(3d⁷4s^{2 4}F_9/2) $\to$ Co⁺(3d⁷4s^{1 5}F₅). The PIE spectrum reveals highly resolved autoionizing resonances due to the high spectral resolution of our VUV laser system. A 3d⁷4s¹(⁵F₅)np (n = 19–38) Rydberg series has been identified. IE values for the formations of Co⁺(3d^{8 3}F_4,3) and Co⁺(3d^{8 5}F₅) from Co(3d⁷4s^{2 4}F_9/2) and Co(3d⁷4s^{2 4}F_7/2) have also been determined from the PFI-PE measurements. The IE values, the autoionizing Rydberg series, and the photoionization cross sections obtained in this experiment are valuable for understanding VUV stellar opacities (Kurucz 1992). We expect that the available high-resolution VUV laser photoionization data for Co/Co⁺, as well as Fe/Fe⁺ and Ni/Ni⁺, would further motivate state-of-the-art theoretical calculations for comparison with experimental results, thus benchmarking the theoretical calculations obtained in the Opacity Project and the IRON Project (Quinet et al. 2016; Tynall et al. 2016).

This material is based on work supported by the National Science Foundation under CHE-0910488, CHE-1462172, and CHE-1642501.