Glassy carbon, NIST Standard Reference Material (SRM 3600): hydrogen content, neutron vibrational density of states and heat capacity

Commercial glassy carbon plates (NIST SRM 3600) being used as absolute intensity calibration standards in small-angle X-ray scattering applications are further characterized in terms of hydrogen content, vibrational density of states and specific heat capacity.


Introduction
A study (Zhang et al., 2010) at the Advanced Photon Source (APS) of Argonne National Laboratory characterized glassy carbon plates obtained from Alfa Aesar 1 for use in absolute intensity calibrations for small-angle X-ray scattering (SAXS) applications. Zhang et al. demonstrated that selected commercially available glassy carbon plates are sufficiently homogeneous and stable to serve as calibration standards and have made these plates available to several laboratories for this purpose. This material has been more formally developed as a new NIST Standard Reference Material (SRM 3600, 2017), as described in a recent article in this journal (Allen et al., 2017). To further characterize these same plates, we have determined their hydrogen content and also performed neutron inelastic scattering measurements to determine the lattice vibrational spectrum. This, in turn, is used to calculate the heat capacity for comparison with measurements presented here on a similar sample.

Properties and structure of NIST SRM 3600
The plates provided to us by APS for this study were obtained from Alfa Aesar (AA), Ward Hill, MA, USA, stock No. 30821. Batch details are given elsewhere (Allen et al., 2017;SRM 3600, 2017;Zhang et al., 2010). AA purchases its glassy carbon ISSN 1600-5767 plates from Hochtemperatur-Werkstoffe GmbH (HTW), Thierhaupten, Germany, which designates them as SIGRADUR G (called Type-2 by AA) and provides tables of their properties (HTW, 2017). Highly impermeable, hard Type-2 materials have zero open porosity, a service temperature of 3273 K and a density of 1.42 g cm À3 . Here we describe selected results from the literature appropriate to glassy carbon prepared similarly to AA Type-2. An early proposal based on X-ray diffraction measurements (Franklin, 1951) was that glassy carbon produced by pyrolysis at 3273 K be classified as non-graphitizing carbon. Subsequent neutron elastic scattering measurements (Mildner, 1974) out to a momentum transfer Q = 25 Å À1 were used to produce a radial distribution function to provide evidence that glassy carbon treated at 3273 K contains very few tetrahedral bonds. In a later analysis (Mildner & Carpenter, 1982), peaks were reported at 1.425, 2.35 and 2.83 Å , and a shoulder at 3.415 Å . The three peaks correspond to the C1-C2, C1-C3 and C1-C4 distances on a C 6 hexagon. The shoulder is interpreted as the interlayer C-C distance seen in graphite. More recently, a study (Jurkiewicz et al., 2017) was performed on a series of glassy carbons produced from a furfuryl alcohol precursor heat-treated to temperatures ranging from 1073 to 2773 K. The material produced at 2773 K, GC2500, may be expected to most closely resemble the higher-temperature AA Type-2 material and the materials studied by Mildner & Carpenter. X-ray and neutron diffraction measurements were used by Jurkiewicz et al. to provide structure factors and pair distribution functions, which they found to be in substantial agreement with each other. These were then compared with model calculations based on turbostratically amassed, curved graphene fragments containing specific defects and relaxed via molecular dynamics methods to produce a variety of structures, including parts resembling fullerenes. In brief, the models of Jurkiewicz et al. appear to provide a plausible explanation for the hardness of glassy carbons, their occluded porosity, their chemical inertness and the approach to graphite-like fragments with increasing heat-treatment temperature.

Hydrogen content of NIST SRM 3600
Since the cross section for scattering neutrons from hydrogen is more than an order of magnitude greater than that from carbon, hydrogen has a significant impact on SANS measurements; hence, knowledge of the hydrogen content is important in assessing the usefulness of these plates for intensity standards applications. Therefore, we measured the hydrogen content of one of the plates from the APS collection by thermal neutron prompt gamma activation analysis using the NGD spectrometer at the NIST Center for Neutron Research (NCNR) (Paul et al., 2015). The plate was found to have a hydrogen content of 40 AE 2 mg kg À1 , or (4.8 AE 0.2) Â 10 À4 (mol H)/(mol C), with a 95% confidence interval. This measurement is expected to be statistically representative of the plates supplied to us. For comparison, using a different technique, Albers et al. (2016) found 60 AE 20 mg kg À1 for a Type-2 glassy carbon (GC) plate purchased from AA. The low hydrogen content also gives us confidence that the vibrational spectrum to be discussed below exhibits no observable carbon-hydrogen vibrational features, and this is confirmed by comparison with measurements on graphite, also discussed below.
In addition, we have determined the hydrogen content of Type-1 beads purchased from AA (product No. 41497, lot Y198034, 630-1000 mm diameter). Type-1 material has a maximum service temperature of 1273 K. Using the same method, we found it to contain 3082 AE 150 mg kg À1 , or (3.68 AE 0.18) Â 10 À2 (mol H)/(mol C), of hydrogen, which is approximately 77 times the hydrogen content of AA Type-2 material. This relatively large value is evidence that not all of the hydrogen was removed from the starting material at the lower pyrolysis temperature. We confirmed that the neutron inelastic scattering vibrational spectrum (not shown here) of these AA Type-1 beads shows the same characteristic carbonhydrogen modes seen elsewhere (Parker et al., 2013) and not seen in the AA Type-2 material described in this work.

Methods and results of neutron scattering measurements
Two sets of neutron inelastic scattering measurements were made on different samples of low-hydrogen glassy carbon. The first (Kamitakahara et al., 1992;Kamitakahara, 1996) was made on a sample provided by Professor Jeffrey S. Lannin of Penn State University. It was manufactured from an unspecified high-temperature decomposition of an organic polymer by Sloan Inc. for use in an electron beam evaporation boat. This sample displayed an X-ray diffraction pattern resembling graphite, with very broad peaks consistent with crystalline order over $3 nm . Although neither the heat-treatment temperature of this material nor its hydrogen content is known by us, we expect that since it was part of an electron beam evaporation boat it was probably made of hightemperature material similar to AA Type-2 material, and, indeed, apart from a small band around 150 meV of low statistical significance, no other hydrogen vibrational features were reported by Kamitakahara. Neutron inelastic scattering measurements on this sample were made using the IN4 timeof-flight spectrometer at the Institut Laue-Langevin. The IN4 measurements, made at room temperature, were corrected for mulitphonon scattering. These measurements are expected to give a reasonable representation of the spectrum in the region below 50 meV because of adequate sampling over the momentum-transfer variable Q.
The second set of measurements, made at the NCNR and reported in this work, was taken on the AA Type-2 plates provided to us. The neutron vibrational density of states (VDOS) spectrum was measured using the Filter Analyzer Spectrometer (BT4-FANS) (Udovic et al., 2008). The plates were enclosed in a thin-walled aluminium can and cooled to 4.2 K using a top-loading displex refrigerator. A Cu(220) monochromator with a 60 0 pre-and 40 0 post-collimation was research papers used to provide an energy range from $30 to $250 meV with an energy resolution (full width at half-maximum) ranging smoothly from $2 meV at 30 meV to $16 meV at 200 meV.
In order to compare the FANS measurements with the earlier IN4 measurements on the Lannin sample, the FANS data were scaled to match the peaks visible in both sets of measurements in the region from 60 to 90 meV. Fig. 1 shows the result. The observed spectrum is in substantial agreement with recent measurements (Albers et al., 2016) that were made on an AA Type-2 glassy carbon plate.

Neutron scattering measurements on glassy carbon samples: discussion
The glassy carbon neutron VDOS of these plates of Type-2 material from AA is in substantial agreement with earlier measurements on the Lannin sample reported by Kamitakahara, differing in some details, mainly in the weighting of the three main peaks below 125 meV. On the other hand, the plates display a strong resemblance to powdered graphite. A comparison is made with the measurements of Rols et al. (2000) in Fig. 1. (The region below 50 meV in the graphite data is not expected to represent the neutron VDOS very well because of the limited region of the Q variable sampled in the filter-analyzer method used at BT4.) As seen in Fig. 1, the major features of GC, neglecting the weighting, line up remarkably well with graphite. It is by now well known that forms of carbon based on the fullerenes share many graphite-like features, consistent with graphitic structural motifs in these materials, and the same can be said of GC, as noted by Jurkiewicz et al.
We can gain some insight into the measured spectrum by comparison with the theory for graphite, which is well devel-oped (e.g. Wirtz & Rubio, 2004;Mounet & Marzari, 2005;Khalil, 2016). As shown in Fig. 2, beginning with lower energies, in the region below 125 meV four major spectral bands in GC around 20, 60, 80 and 100 meV match those in graphite. This gives us some assurance that the specific vibrations involved in these bands resemble those at the indicated labeled points of the graphite Brillouin zone, and the reader is referred to Wirtz & Rubio (2004) for details. The computed graphite VDOS of Kahlil below 60 meV shown in Fig. 2 appears to be in close agreement with our GC spectrum, again showing the usefulness of computational results in helping to identify vibrational features in GC. In the region above 125 meV where the resolution of the neutron spectrum is much lower (see Fig. 1), the agreement with theory for graphite is less impressive, but we may identify the broad peak around 175 meV in GC with optical modes in graphite, labeled TO(M) in Fig. 2.   Comparison of the adjusted VDOS of low-hydrogen-content glassy carbon in this work with an ab initio LDA/GGA (local-density approximation/generalized gradient approximation) model for graphite (Wirtz & Rubio, 2004), an ab initio dispersion-corrected density functional theory (DFT-D) calculation model for graphite (Khalil, 2016) and a 72-atom ab initio model of GC (Bhattarai & Drabold, 2017). The mode symbol labels for graphite are adapted from Wirtz & Rubio. Their unlabeled peak near 200 meV occurs at the top of the LO band.
In contrast to Raman and infrared spectroscopies, neutron scattering has the feature that, apart from conservation of energy and momentum, there are no other selection rules for monatomic materials. All modes, whether graphite like or arising from 'disorder' in the graphite or graphene lattices, will be included in the spectrum. Hence, to gain further insight into departures from graphite, probably due to disorder, we may consider Raman results. Extensive discussions of Raman spectroscopy as it relates to graphene, graphite and carbon nanotubes, including the D band, are given by several authors (e.g. Dresselhaus et al., 2010;Ferrari & Robertson, 2000). For GC we turn here instead to other work (Baranov et al., 1987;Wang et al., 1990). In particular, Wang et al. studied several forms of carbon, including glassy carbon samples from Tokai Electrode Mfg Co., Nagoya, Japan (GC10, GC20 and GC30 heat-treated at 1273, 2273 and 3273 K, respectively). We may consider their Tokai GC30 sample to be close in properties to AA Type-2 material. Beginning from their lowest-energy features, using a 458 nm exciting light, they identified a D band (in graphite powder at 1360 cm À1 ' 168.6 meV, in GC30 at 1363 cm À1 ' 169.0 meV). There are competing interpretations of this band (see e.g. Baranov et al., 1987;Ferrari & Robinson, 2000). Here we simply note that Wang et al. interpret the D band in terms of symmetry breaking at the edges of graphene planes in disordered materials. This band then probably adds to the TO(M)-like modes in the large band seen in Fig. 1  around 175 meV. In addition, Wang et al. identify an E 2g feature (in graphite powder at 1588 cm À1 ' 196.9 meV, and related modes in GC30 at 1586 cm À1 ' 196.6 meV) in the spectral region dominated by longitudinal optical modes in graphite which would contribute to the weak shoulder seen near 200 meV in GC and the stronger one in the Rols et al. graphite spectrum, both shown in Fig. 1.
A recent ab initio computational study (Bhattarai & Drabold, 2017) was made on atomic models of amorphous carbons having a variety of densities. In addition to a study of structural features, these authors have calculated the VDOS spectrum of these models. Here we choose to compare the calculated spectrum of a 72-atom model of amorphous carbon, designated c72_20ps, because it has nearly the same density as our Type-2 plate samples, namely 1.4 g cm À3 . This is the only ab initio study we know of on carbon specifically having the density of GC. The result is shown in Fig. 2. In spite of the small size of this fragment and apart from a general shift to lower energies, many of the features observed in our GC measurements are reproduced in their model, and hence this approach has the potential to relate specific atomic motions in GC to spectral features. In particular, their Fig. 5 shows that the modes measured in the present study are in a region of non-localized vibrations, as indicated by small inverse-participation ratios. Their Fig. 6 shows that the contributions of sp 3 and sp bonding to the VDOS are much smaller than those from sp 2 -bonded atoms, as is to be expected for graphitic materials. The supplemental material published with their work (available online) includes videos of atomic vibrations at several representative frequencies of the GC spectrum. Each video demonstrates a complexity arising from disorder that suggests that, while descriptions in terms of atomic motions in crystalline graphite provide useful insights, one must be cautious in applying them too literally to this glassy material.
4. Heat capacity measurements on a low-hydrogencontent glassy carbon sample 4.1. Method and results of heat capacity measurements Fig. 3 shows heat capacity measurements made on the Lannin sample using the continuous-cooling method. Details of the method are given in the PhD dissertation of Hui Li (1993). There appears to be a smooth sigmoidal systematic discrepancy depressing the data from approximately 150 to 225 K and augmenting it from 225 to 295 K with an amplitude of about 2% at 260 K. Smaller discrepancies of this same kind were seen in measurements on other materials in this region using this technique and apparatus. The source of this discrepancy has not been definitively determined, but may be related to departure from the assumption of thermal equilibrium between the sample and addendum during the temperature ramping. Apart from this sigmoidal discrepancy, typical accumulated errors arising from thermometry, spline fitting of the tables and other causes such as thermal lag during ramping in this procedure amounted to approximately AE2% at each temperature, with a 90% confidence interval. For the Lannin sample, unreliably noisy results in the regions between 50 and 75 K and between 140 and 155 K, probably due to poor thermal contact, were discarded.

Discussion of heat capacity results
In the measured temperature range, the heat capacity of glassy carbon is expected to be mainly determined by the contribution arising from vibrations of atoms within the glassy matrix with a negligible electronic contribution. Knowing the spectrum of harmonic vibrations g(), the vibrational contribution to the heat capacity is given according to standard theory by Measured specific heat capacity of the low-hydrogen-content Lannin glassy carbon sample and comparisons with theory, graphite and previous work (Takahashi & Westrum, 1970).
where k B is the Boltzmann constant, h is Planck's constant and T is temperature. The central problem in using this result is the determination of the harmonic VDOS, g(). In this work we use instead the neutron vibrational density of states which is closely related to g() for this monatomic material. In order to use our VDOS measurements, the contributions to the spectrum that arise from multiple and multi-phonon scattering, expected to be slowly and smoothly increasing with energy, were estimated by subtracting an arbitrary background varying linearly with phonon energy E. The adjusted neutron VDOS shown in Fig. 2 was used to calculate the heat capacity from equation (1). While a reasonable improvement over no correction, this procedure can be expected to lead to some uncertainty in the weighting of the spectrum. The result of the heat capacity calculation using the adjusted VDOS is shown as the solid line in Fig. 3. While agreement between this prediction and the measurement is satisfactory, the arbitrary weighting in the neutron scattering spectrum introduced to correct for multiphonon scattering precludes a more precise comparison. It is more instructive to compare the heat capacity of the Lannin sample with that of graphite (spectroscopic grade, SP-1, powder from Union Carbide Corporation), which we also measured in this work by the continuous-cooling method. Given the close similarity of the measured vibrational spectra shown in Fig. 1, the heat capacities should not differ very much, and that is found to be the case. The graphite data exhibit a T 1.99 AE 0.04 dependence in the temperature range from 20 to 60 K, as is expected by theory for quasi-two-dimensional graphite. An analysis of our glassy carbon data between 20 and 50 K gives T 1.8 AE 1 , but this result is not expected to be very accurate, given the paucity of data points in this region. Our heat capacity measurement is also compared with measurements made on a GC30 rod sample from Tokai, showing substantial agreement, considering the sample and methodological differences (Takahashi & Westrum, 1970). Those workers report T 2.04 for the Tokai glassy carbon sample in the more useful low-temperature range between 5 and 30 K, in substantial agreement with the result for graphite.

Summary
Commercial Alfa Aesar Type-2 glassy carbon plates have been developed as absolute intensity calibration standards in SAXS measurements and designated as new NIST Standard Reference Material SRM 3600. We have further characterized this material by sampling a plate provided to us from APS and found that it has a hydrogen content of (4.8 AE 0.2) Â 10 À4 (mol H)/(mol C). We have measured the vibrational spectrum of a collection of these plates by neutron inelastic scattering. The measured spectrum strongly resembles that of graphite, allowing us to identify the likely atomic motions of major spectral features in this glassy material. We have measured the heat capacity of a low-hydrogen-content glassy carbon sample from 20 to 295 K and of graphite powder in the same range for comparison, finding substantial agreement. This agreement is to be expected from the vibrational spectral similarity of these two materials. Our measured vibrational spectrum of this lowhydrogen-content glassy carbon is used to calculate its heat capacity, and a favourable comparison is made between theory and experiment.