Resolving Detonation NanoDiamond Size Evolution and Morphology

Article pubs.acs.org/JPCC

Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

Resolving Detonation Nanodiamond Size Evolution and Morphology at Sub-Microsecond Timescales during High-Explosive Detonations

Downloaded via BUFFALO STATE on July 30, 2019 at 15:58:41 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Joshua A. Hammons,*,† Michael H. Nielsen,† Michael Bagge-Hansen,† Sorin Bastea,† William L. Shaw,† Jonathan R. I. Lee,† Jan Ilavsky,§ Nicholas Sinclair,∥ Kamel Fezzaa,§ Lisa M. Lauderbach,† Ralph L. Hodgin,‡ Daniel A. Orlikowski,† Laurence E. Fried,† and Trevor M. Willey*,† †

Physical and Life Sciences and ‡Science Technology and Engineering, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States § X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass, Lemont, Illinois 60439, United States ∥ Dynamic Compression Sector, Washington State University, 9700 S. Cass, Lemont, Illinois 60439, United States S Supporting Information *

ABSTRACT: Characterization of the initial morphology of detonation nanodiamond (DND) has been the focus of many research studies that aim to develop a fundamental understanding of carbon condensation under extreme conditions. Identifying the pathways of DND formation has the potential for significant impact on many of the controlled synthesis of nanoscale carbon with a tailored functionality; currently, a wide range of possible (and conflicting) mechanisms of nucleation and growth have been proposed, and further research is essential. Building a comprehensive understanding of DND formation is challenging because it requires in situ characterization on the sub-microsecond (sub-μs) timescale during a high-explosive detonation. In this study, time-resolved small-angle X-ray scattering (TR-SAXS) is used to reveal the early-stage DND morphology from 1 μs) in situ and recovered DND exhibits consistent features in the I(q) curve. Such a close similarity allows a high-fidelity SAXS model derived from the ex situ SAXS and TEM measurements to be applied to the in situ data, which yields new insight into the early-stage ( 0.02 Å−1, the intensity decays in a power-law-like fashion until q ∼ 0.07 Å−1 where a broad Guinier knee is observed. Such decay is consistent with the observation of aggregated DND, and the location of the Guinier knee corresponds well with DND sizes observed by TEM imaging. Consistent with prior studies,23,43 TEM imaging shown in Figure 2b indicates that the surfaces of the diamond particles are not smooth and well defined, which will manifest as a deviation from Porod scattering52 at high q. Instead, typically hemispherical protrusions that extend ∼1 nm from the surface (Figure 2b) are observed. These protrusions are referred to here as surface texture since SAXS is only sensitive to the presence of surface heterogeneities and not specific shapes in this case. Electron diffraction (ED) analysis of recovered detonation products confirms a diamond crystal structure (Figure 2c). Only the 111 peak from diamond can be observed in the WAXS data of the recovered detonation products (Figure 2d). Though graphite also has two reflections (100 and 101) in the same region as the 111 of diamond, other reflections from graphite that should be higher in intensity (004 and 110) were not observed, indicating limited, if any, evidence of graphitic nanostructure formation via WAXS; in contrast, sharp peaks from the Pt wire that was used to mechanically maintain intimate contact between the HE and the detonator are also observed. Altogether, the SAXS, WAXS, TEM, and ED confirm the presence of aggregated DND, which have a core size of ∼4 nm and surface texture that is expected.36 Since scattering from the DND dominates the ex situ SAXS data at q > 0.02 Å−1 (Figure

■

RESULTS AND DISCUSSION Ex Situ USAXS/SAXS/WAXS and TEM. The recovered soot morphology observed by USAXS and TEM spans many length scales and is shown in Figure 2a. In general, the TEM data for the recovered detonation products is consistent with prior works where graphitic ribbons and nanodiamond are observed via high-resolution EELS measurements.37 Unlike other, lowerenergy, high explosives such as TNT and 1,3,5-trinitro-2-[2[2,4,6-trinitrophenyl]ethenyl]benzene (HNS),16 the DND is more abundant in composition B14,50 and, therefore, DND is expected to dominate the SAXS since it is denser than graphite51 and has a higher mass fraction.14,50 Because of the limited number of these agglomerates, it is uncertain from TEM characterization whether a typical aggregate size exists that corresponds to the mesoscale (∼1 μm) feature seen in the SAXS data or whether that feature represents Pt particles, which come from the Pt wire used in the detonation setup for the recovered detonation products. The latter explanation is more likely because a broad Guinier region at q ∼ 0.001 Å−1 is also observed in recovered products from the detonation of 3,4-bis[3nitrofurazan-4-yl]-furoxan and HNS, which are known to produce very different carbon morphologies (Section S3, Supporting Information). Aggregated DND particles between 5 and 7 nm (including surface texture) are observed by TEM and shown in Figure 2a. D

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C 2a), a q-range of 0.02−0.4 Å−1 was selected for the in situ TRSAXS measurements to enable the investigation of the dynamic evolution of the diamond observed by TEM. In Situ TR-SAXS vs ex Situ USAXS. The morphology of DND obtained from the recovered detonation can be directly compared with that obtained in situ by comparing the general features of the USAXS in Figure 2a with those obtained by TRSAXS (Figure 3). Both the USAXS and TR-SAXS contain a

terminates at q ∼ 0.1 Å−1 (dashed line in Figure 3), while the intensity decay that follows is steeper than a Porod decay up to q = 0.2 Å−1. Beyond 0.2 Å−1, the intensity decay is shallower than a Porod decay. These deviations that occur well beyond the Guinier knee indicate that the scattering population does not have a smooth and well-defined surface. This assignment is consistent with the ∼1 nm surface heterogeneities observed via TEM imaging (Figure 2a,b). Comparable deviations from Porod scattering, Ires(q), are observed in the ex situ SAXS and the in situ TR-SAXS, which indicates that the scattering from the smallscale heterogeneities in the recovered DND is equivalent. Further agreement between the in situ and ex situ data is observed in the Guinier region (0.05 Å−1 < q < 0.09 Å−1), which is associated with structures that have a radius of gyration of 2.5 nm; assuming spherical particles,52 a radius of gyration of 2.5 nm corresponds to particles of ∼6 nm diameter, which is in good agreement with the DND sizes observed by TEM in Figure 2a. The intensity decay at q < 0.05 Å−1 is steeper in the ex situ SAXS data, which can be attributed to the presence of Pt particles. Mesoscale Pt particles should not be present in the TR-SAXS data because no Pt is present in or around the high explosive. With the exception of the larger scattering phases, we conclude that the detonation recovery was successful in capturing the early-stage DND morphology. Furthermore, the TR-SAXS and ex situ USAXS have a similar shape, which means that the model derived for the ex situ data can be applied to the in situ data with good confidence. The time evolution of the TR-SAXS data shown in Figure 3 indicates some subtle changes in the DND morphology. Very little change in the deviation from Porod scattering can be observed, which suggests that the surface texture persists after the detonation front passes through the X-ray beam path. A slight shift in q (∼40%) of the Guinier region between 0.10 μs and 0.26 μs (arrow in Figure 3) indicates that there is an observable increase in the size distribution of the DND; beyond 0.3 μs, there are, at best, subtle changes in the size distribution of the DND. The scattering in the low-q region in Figure 3 is consistent with the presence of aggregated particles observed by TEM in Figure 2a. Although a mass-fractal dimension between 1.4 and 1.6 can be used to describe this region, at least a decade in q is needed to obtain reliable values for the mass-fractal dimensions,53 which is unavailable from the q-range measured in the TR-SAXS for this paper. However, a fractal dimension between 1.4 and 1.6 is consistent with a mass-fractal aggregate54 observed by TEM. Altogether, these observations provide the framework for quantifying the evolution in size with a SAXS model that is based on the morphological observations in the TEM images shown in Figure 2a,b. Thermochemical Simulations. The purpose of the thermochemical simulations is to provide insight into the possible carbon phases that are present early in the detonation since such information cannot be extracted from the TR-SAXS alone. The simulation results allow an estimation of the overall volume fraction of condensed/solid nanocarbon (6 nm) that is in the diamond phase, νdiamond, early in the detonation and, by extension, the X-ray path length as a function of time. It is important to note that these simulations cannot determine whether the nondiamond carbon is on the surface of the DND or separate phases. No liquid phase carbon is produced in the simulations and therefore the balance volume fraction (1 − νdiamond) is graphite. Figure 4a shows how the X-ray beam path is oriented relative to the detonation front. As the detonation progresses, the simulation calculates the total volume fraction of

Figure 3. Log−log plot that compares the TR-SAXS data collected at 0.1, 0.25, and 1 μs after the detonation front passes through the X-ray beam vs the desmeared SAXS data collected from the recovered soot on the USAXS beamline at 9-IDC. The shape of the I(q) curves is described by three distinct regions: low-q, Guinier, and high-q regions where the intensity curve can be analyzed to understand aggregation, particle size, and particle surface, respectively. The deviation from Porod scattering for all three curves is demonstrated by the residual, Ires(q), which is obtained from a fit of a Porod decay and background (dashed lines). The Ires(q) curves are displayed in the inset.

broad Guinier knee that is preceded by a power-law-like decay in intensity and is followed by a steep decay that deviates from Porod decay, similar to the behavior previously reported in the literature.23,25 While it is common in SAS analysis to simply fit a power-law decay to this region and draw conclusions about the surface from the exponent, a distinct approach is adopted in this paper: the deviation from Porod decay is addressed first, followed by a comprehensive model that accounts for both the particle size and surface. To demonstrate the deviation from Porod scattering, the high-q portion of the TR-SAXS data was fit to the equation I(q) = Bq−4 + b

(1)

where the prefactor, B, and flat background, b, are varied to fit the intensity in the q-range: 0.12 Å−1 < q < 0.4 Å−1.52 The flat background was included in the fit to account for both incoherent scattering and elastic gaseous scattering. The normalized residual intensity, Ires(q), obtained from these fits oscillates at about zero. At early times (tdet ∼ 0.01 μs), the oscillations in Ires(q) at q ∼ 0.15 Å−1 may be attributed to Guinier scattering from the smaller particle sizes. However, at later times, the Guinier knee from the mean-sized particles E

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

length density between graphite layers, ρg is the estimated scattering length density of the graphene-like layers, (17 × 1010 cm−2), ρbulk is the volume average scattering length density of the bulk, and R is the radius of the diamond core. The function, Fsphere(q,r), is the normalized scattering amplitude of a sphere,15 V(r) is the volume of a sphere of radius r, Sf(dm,R) is the structure factor of a mass-fractal aggregate55 with a fractal dimension of dm and termination radius equal to the median radius of the DND, and R̃ and Dln (R,R̃ ,σ) are a log−normal probability function with a standard deviation, σ, that accounts for the size distribution52 of DND using 100 particle sizes between 0.01R̃ and 100R̃ within the summation in eq 4. The values chosen for ρd and ρg provided sufficient contrast to capture the scattering contribution of the surface texture, which ultimately affects the size distribution. If this scattering contribution is ignored, ISS(q,R) would be replaced by the scattered intensity of a sphere15 of radius, ISS(q,R). The size distribution obtained from the two cases is compared later in the article to demonstrate the importance of the scattering contribution from the surface texture. Although the scattering length density of the electron-depleted space between graphenelike layers, ρd, can be fit to the TR-SAXS data collected only at very high q, it is relatively insensitive and therefore approximated as 0 (vacuum) for the ex situ DND and 10 × 1010 cm−2 for the in situ DND. The value of ρg was chosen to be slightly lower than graphite (∼19 × 1010 cm−2) since the layers have some angular heterogeneity and do not uniformly cover the entire surface. The factor, ⟨Δη⟩, is the volume average contrast of the entire mediansized particle and serves to remove nonlinearities in the fitting. Together, KDND and ⟨Δη⟩ can be used to calculate the volume fraction of DND, νDND, with the assumption that the real value of ρbulk is near that of static composition B or near water for the recovered products (see Section S4, Supporting Information). In addition to DND aggregates, larger phases discussed previously are also observed and are modeled as a two-level unified equation56 that consists of scattering from a very large phase (>5 μm), IH(q), and a phase on the order of hundreds of nanometers, IM(q). With the limitation that these phases scatter X-rays independently of the DND and one another, their scattering contributions are simply additive. In this way, the unified equation is used as an empirical model that describes the small-angle scattering from larger phases that are ambiguous since the sole purpose of modeling these phases is to account for the scattering that underlies the scattering from the DND. The total USAXS data from the recovered detonation products, Idp(q), is fit to the model equation

Figure 4. Results of the thermochemical simulations: (a) a schematic showing the X-ray beam path through the detonating explosive that simulated the actual TR-SAXS experiment; in the simulation, the detonation front moves vertically (perpendicular to the X-rays) and the colors in the detonating explosive correspond to temperatures indicated in the legend; and (b) a plot of the estimated volume fraction of the condensed carbon that is calculated to be diamond based on the phase diagram for 6 nm carbon particulates in the X-ray path, νdiamond, from the end of the reaction zone (0.08 μs) as a function of time after the detonation front, tdet.

nanodiamond in the X-ray beam path as a function of time since the detonation front was aligned with the X-rays (tdet = 0). The results indicate that temperature−pressure conditions for nanoparticle condensates are conducive to the diamond phase, with nondiamond (graphitic in the phase diagram) fraction increasing to a few percents at 2 μs (Figure 4b); therefore, thermochemical predictions point to diamond as the dominant carbon phase during the entire TR-SAXS experimental time window. In Situ DND Morphology and Modeling. The morphology and size of the DND collected from the recovery detonation in ice were assessed by TEM imaging and used to formulate the scattering model for the in situ TR-SAXS experiments; other candidate models that are not supported by TEM are discussed in the following section. Surface heterogeneities, observed by earlier SAXS/WAXS studies of DND43 and predicted by density functional theory calculations,42 are observed by TEM imaging (Figure 2b). The simplest small-angle scattering model that can account for this DND morphology assumes spherical symmetry and is based upon a diamond core with a surface shell composed of two ∼3 Å thick graphene-like layers separated by a distance of 3 Å; this entire textured surface shell protrudes 9 Å from the diamond surface. The small-angle scattering from such a system is derived from the scattering of a spherically symmetric phase,15 ISS(q), and is given by the equations [A s(R , q , ρD , ρg ) + A s(R + 3 Å, q , ρg , ρd )

Idp(q , G , B , P , BH , R̃ , σ , KDND , b)

+ A s(R + 6 Å, q , ρd , ρg ) + A s(R + 9

= IDND(q , R̃ , σ , KDND) + IM(q , G , B , P) + IH(q , BH )

2

ISS(q , R ) =

Å, q , ρg , ρbulk )]

+b

ÅÄÅ ÅÄ qR g ÅÅ ÅÅ ÅÅ ÅÅerf ij −q2R g2 yz Å ÅÅ 6 Å zz + BÅÅ ÅÇ IM(q , G , B , P) = G expjjjj zz ÅÅ j 3 z ÅÅ q ÅÅ k { ÅÅ ÅÅÇ

V (R + 9 Å) (2)

A s(r , q , ρc , ρs ) = [ρc − ρs ]V (r )Fsphere(q , r )

( )

(3)

IDND(q , R̃ , σ , KDND) = Sf (dm , R̃ )

KDND ⟨Δη2⟩

100R̃

∑ 0.01R̃

ISS(q , R )D ln(R , R̃ , σ )ΔR

É ÑÉÑ3 ÑÑÑP ÑÑ ÑÑ ÑÑ ÑÑ ÑÑÖ ÑÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÖ

(5)

(6) (4)

where KDND is a scaling constant, ρD is the scattering length density of diamond (29.7 × 1010 cm−2), ρd is the scattering

IH(q , BH ) = F

BH q4

(7) DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

diamond size, R̃ , found by the SAXS modeling (Table 1) is also in good agreement with the value found by analyzing the Scherrer broadening of the diamond 111 observed in the WAXS (Figure 2d). If, on the other hand, the surface texture is not accounted for in the model fitting (i.e., smooth spheres), a very broad size distribution that includes a relatively high volume fraction of small (≤3 nm) DND particles is obtained from the modeling and also shown in Figure 5. Since particle size analysis of the TEM images reveals almost no particles less than 3 nm and few particles above 8 nm, the spherical particle model is inconsistent with the TEM imaging. It is noteworthy that despite their low number, the particles with dimensions of >8 nm are not insignificant in the volume distribution, i.e., the volume of a single 10 nm particle is much larger than that of a 4 nm particle (Section S4, Supporting Information). With these observations in mind, it is concluded that eq 4 accurately models the SAXS from DND and can be applied to the TR-SAXS data. DND Formation and Size Evolution. With the small-angle scattering model from DND established in the previous section, the TR-SAXS data could be fit to eq 4 to extract the evolution in DND size as a function of time/distance behind the detonation front. As polychromaticity can affect the size distribution,21,22 the model is wavelength-smeared to fit the TR-SAXS data using the equation

where b is the flat background, the medium-sized phases are described by a median radius of gyration, Rg, and power-law scaling, B, and exponent, P, and large phases are only described by the Porod approximation, which consists of a scaling factor, BH, and exponent of 4. Equation 5 is fit to the desmeared USAXS data to extract the size distribution of DND, which is used to calculate the volume fraction of each diameter particle, νDND(D), and shown in Figure 5 along with a representative TEM image of

Ism(⟨q⟩, R̃ , σ , KDND , b) Figure 5. Plot of the volume fraction, νDND, for each DND size of diameter, D, for the particle + surface texture (blue), the whole particle assuming that the DND were spheres (red) and the number distribution obtained from TEM imaging of 150 particles (black). A representative TEM image is included in the figure as an inset. The number distribution for the spherical particles obtained by TEM is arbitrarily scaled for comparison to the volume distributions obtained by the fitting of eq 4 and for spherical particles.

=

∫q

qmax

R̂(q , ⟨q⟩)IDND(q , R̃ , σ , KDND) dq + b

min

(8)

where R̂ (q,⟨q⟩) is the normalized smearing function that includes the first harmonic of the undulator profile, calculated to have an FWHM of ∼10%. Details of how the normalized smearing function was generated can be found in Section S1, Supporting Information. A total of four parameters, KDND, R̃ , σ, and b, were fit to the TR-SAXS data and shown for select data in Figure 6a; due to insufficient q-range at low-q, it was necessary to fix the fractal dimension, dm, for which a value of 1.4 was selected. Model fits to all of the data can be found in Section S2 (Supporting Information), and the time evolution of the U17.2 data is shown in Figure 6b,c. By including the surface texture, eq 4 is able to capture the deviation from Porod scattering at high q and is shown in the inset of Figure 6a, where the residual is now much lower than in Figure 3 and is more randomly distributed about zero. The time evolution of the four fit parameters is categorized by their effect on the scaling (KDND and b) and the shape (R̃ and σ) of the SAXS data (Figure 6b,c, respectively). As tdet increases after the detonation front passes, the scattering length density of the bulk, ρbulk, will decrease significantly as the gas expands and, as a result, increase the contrast of the DND and therefore the intensity scaling. During this time, the diamond is also expanding, which decreases the volume fraction and the intensity scaling. The net result of these two effects is an initial increase in KDND and b, followed by a decrease at late times (Figure 6c), which suggests that the gas is expanding faster than

the recovered DND particles; a total of four parameters from the large phases and three parameters from eq 4 (DND) and b were fit to the USAXS data and are summarized in Table 1. The larger phases that scatter at low q have scaling constants (G and B), a radius of gyration, Rg, of 335 nm, and a power-law exponent, P, of 3.37 that are consistent with a phase with a roughened surface.58,59 In light of these results, the larger phases are attributed to Pt particulate for three reasons: (i) the powerlaw decay is much steeper than that associated with the DND and cannot be attributed to mass-fractal scattering,53 (ii) this steep power-law decay is absent from the TR-SAXS, where Pt was not used and therefore not present during the measurement, and (iii) the same scattering is consistently and exclusively observed in USAXS data recorded for other high explosives suspended in ice by Pt wire (see the Supporting Information). Therefore, eq 5 is able to model the small-angle scattering from the recovered detonation products from comp B. The overall particle sizes (diamond core + texture) obtained from the least-squares fitting of the ex situ SAXS data agree well with the typical sizes observed by TEM (Figure 5). The median

Table 1. Values of All of the Fit Parameters Obtained by Least-Squares Fitting of Eq 5 to the ex Situ USAXS Dataa large phase

background

KDND (cm−4)

DND R̃ (nm)

σ

G (cm−1) × 106

Rg (nm)

mesoscale phase B (cm−1 Å−P) × 10−5

P

BH (cm−1 Å−4) × 10−8

b (cm−1)

0.089 ± 0.003

1.9 ± 0.3

0.35 ± 0.02

2.5 ± 0.1

335 ± 7

2.2 ± 0.1

3.37 ± 0.01

3.14 ± 0.03

0.0020 ± 0.0002

a

Errors were obtained from the Jacobian matrix within the lmfit57 module for python. G

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 6. Log−log plot of select TR-SAXS data from 0.103 μs (red) to 0.87 μs (blue) with the model fits of eq 4 via eq 8 (black lines) (a) along with the fit parameters that affect the shape of I(q)R̃ (solid circles) and σ (open squares) (b) and scaling parameters KDND (solid circles) and b (open squares) (c). The residual intensities for the model fits in the high-q region are shown in the inset and vary randomly about zero, with lower magnitudes compared to those shown in Figure 3. The error bars associated with the fit parameters were obtained from the Jacobian matrix within the lmfit module.

the DND. On the other hand, both R̃ and σ increase rapidly up to ∼0.3 μs, followed by a slight increase in R̃ toward steady-state values (Figure 6b). Interestingly, both R̃ and σ increase by just over 10%, which could be associated with both particle growth and/or broadening of the size distribution. Unfortunately, these experiments were unable to determine the physical mechanism behind this evolution. Nevertheless, the model fitting is able to extract an apparent increase in DND size with time after the detonation front. As the SAXS is dominated by the volume mean DND size, the temporal evolution in the mean diameter, D̅ core, provides insight into when the change in size occurs. From the least-squares fitting of eq 4 to the TR-SAXS data obtained from several different detonations at three different instrument configurations, the time evolution of the mean diameter of the diamond core, D̅ core (Figure 7), is extracted from fit parameters by the relationship ̃

ln R + σ Dcore ̅ = 2e

2

/2

(9)

Figure 7. Plot of the time evolution of the mean diameter of the diamond core, D̅ core, calculated (eq 9) from fit parameters obtained from the TR-SAXS data modeling (eq 4 via eq 8). The diameter of the entire DND would be equal to D̅ core + 1.8 nm. The increased scatter in D̅ core from the U18 is due to the limited q-range evaluated, which was unable to capture the entire Guinier region of the DND scattering. The errors in D̅ core were taken from the Jacobian matrix using the lmfit module, and the errors in tdet are taken from the detonation front curvature, which results in a time-average observation of the DND size at any moment in time.32

Results from both configurations agree well and indicate only subtle changes in the size distribution of the DND beyond 0.3 μs after the detonation front. When ρD is fit to the high-q data, values higher than the steady-state average are obtained within the reaction zone tdet < 0.01 μs and briefly at tdet ∼ 0.5 μs, which suggest that the surface reconstructions may not be present during initial DND particle formation (Figure S5) and some slight evolution in contrast during cooling. However, the error of ρd is high and the values fluctuate about the value of 10 × 1010 cm−2, which was used as an estimate in the model fitting of data collected from the U17.2. With the assumption that the surrounding bulk is near the density of the undetonated pellet, a total volume fraction of 0.03 is estimated at 0.3 μs. Prior to 0.3 μs, the mean diamond core size is smaller, particularly in the U17.2 data, but within the full width at half-maximum, FWHM, of the distribution found at in the microsecond time regime of the TR-SAXS and in the recovered detonation products (SAXS). The real-time data obtained theoretically (Figure 4b) and experimentally (Figure 7) provide valuable insight into how DND is formed during a high-explosive detonation. At times earlier than 0.1 μs after the detonation front, DND is observed by TR-SAXS, albeit with a size distribution only slightly smaller

than in the steady state. It is unclear whether this modest increase in the mean size is due to growth, expansion, or simply the presence of larger particles formed from elsewhere in the comp B pellet. As no liquid carbon is expected from the thermochemical simulations, our data indicate that the molecular carbon is broken down and condensed directly into the diamond phase very near the end of the reaction zone (C−J plane). These results contradict the theory that DND condenses from liquid27,28 and grows for 2 μs after the C−J plane,17 as has been observed/predicated for comparable TNT/RDX high explosives. It bears mention, however, that condensation from the liquid phase is plausible for explosives capable of reaching appropriate carbon liquid temperatures and pressures for given H

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

equations can be fit to the data to extract a similar increase in DND size within the first 0.3 μs, as shown in Figure 7. Beyond 0.3 μs, both model fits indicate that the overall mean DND diameter is ∼6 nm, which is in agreement with the more specific DND model used here (Figure 5). Nonetheless, the unified equations can be ambiguous and misleading when used to extract information from the high-q region of the SAXS data. If the deviation from Porod scattering is accounted for by changing the power-law exponent (single level), one might conclude that the DND transitions from a surface gradient to a fractal-like surface.59 A separate unified level can also be used to account for the Porod deviations at high q by assuming the presence of small features that have a radius of gyration of ∼10 Å. In both cases, the deviation in Porod scattering is treated differently and therefore the unified equations cannot account for the DND morphology in a meaningful way. Rather, the unified equations treat the deviation from Porod scattering ambiguously but allow for the overall mean size of the DND to be extracted from the TR-SAXS data. More specific treatment of the high-q scattering can be achieved by employing different core−shell systems and raspberry particle models. Two different core−shell systems have been proposed for DND: (1) aggregated diamonds with a gradient shell observed by prior TEM imaging23 and (2) aggregated lamellae;24 in the latter study, only a portion of the I(q) data was fit.24 The core−shell gradient model was developed and applied to separate regions (Guinier and Porod).23 Here, the core−shell gradient model was fit to the entire scattering region using one single model, but the results were inconsistent with the TEM data, specifically diamond cores that are 2 nm and shell thicknesses that are slightly larger than observed by TEM imaging. Similarly, the aggregated lamellae model reported previously also results in the assignment of particle radii that are much smaller (1.3−3 nm)24 than are observed by TEM imaging. Yet another candidate model is the raspberry particle model, which was originally developed for Pickering emulsions where small particles exist at the interface of a liquid phase.63 Though no evidence of raspberry particles can be found in the TEM imaging, such a morphology could be realized in the reaction zone where nascent diamond phases briefly decorate the surface of larger diamond particles before coalescing into a single particle (Section S2.4, Supporting Information). The raspberry morphology can model the data and provide a slightly narrower and larger size distribution than a purely spherical morphology. In all three of these cases, an increase in mean size can be extracted from the TR-SAXS data. However, all three morphologies are physically very different from each other and suggest different formation mechanisms that produce the surface texture. The scattering from DND can therefore lead to broad speculation and ambiguity regarding how DND is formed. In this study, the ambiguity is significantly reduced with the TEM imaging of recovered products that have very similar small-angle scattering compared with that of latetime TR-SAXS (Figure 3). The overall effect of polychromaticity is model-dependent and also affects the size distribution that one obtains from the modeling.21 The size distributions obtained from the late-time (polychromatic) TR-SAXS (6 μs) should be comparable to those obtained by the ex situ (monochromatic) USAXS measurements and are shown in Figure 8. On the other hand, the size distribution obtained by assuming spherical particles is different between the TR-SAXS and USAXS data. If the DND were perfect spheres, a relatively higher volume fraction of small

particulate sizes.27 The apparent solid-phase condensation (Figure 4b), on the other hand, may affect the surface texture at high q, as the growth process occurs very rapidly at a solid (diamond) surface. A reduction of contrast in the surface texture is observed in the initial/early-stage TR-SAXS data (tdet ∼ 0.01 μs) where the scattering length density of the protrusions, ρD, is slightly higher than observed in the microsecond regime (Figure S5). However, the presence of surface texture at the C−J plane and beyond (>0.1 μs) suggests that these surfaces persist into the microsecond time domain, without any significant further graphitization (Figure 4b). Based on Figures 4b and 7 the DND formation occurs in the reaction zone (tdet < 0.1 μs) and does not significantly increase in size or graphitize into the microsecond time domain. One proposed mechanism for nanodiamond growth during detonation is the growth of diamond via nascent adamantane29,30 Although adamantane is too small to be observed by SAXS (Figure 7), recent synchrotron X-ray experiments suggest that its presence in the detonation, specifically within the reaction zone, facilitates nanodiamond formation.60 In this event, TR-SAXS with improved time and q resolution would enable experimental validation of this mechanism of DND growth in the 1 nm size to a 3 nm size regime during the first 0.1 μs after the detonation front. However, such an experiment would also require a detonation wave with little to no curvature so that TR-SAXS data contains only information from a specific point in the detonation wave, instead of a volume average from different points (Figure 4a). The results obtained from the highq TR-SAXS (Figures S4 and S5) suggest that the high-q region (q > 0.1 Å−1) would contain the most information. Another approach might also be to determine the carbon speciation in the reaction zone via time-resolved X-ray absorption61 to determine whether diamond grows from the attachment of carbon via CO oxidation,30 free carbon,29 or other carbon allotropes. As the DND surface chemistry varies with the synthesis route,62 our results suggest that the surface texture might be tunable early in the detonation and persist microseconds after the detonation wavefront has passed. Resolving Model Ambiguity. The scattering model chosen is key to correctly identifying how the DND morphology evolves in the first few hundreds of nanoseconds. Previously, a specific model (eq 4) was formulated from the TEM imaging and applied to the SAXS and TR-SAXS data. This approach accounts for the surface texture in a direct way by accounting for the interference scattering between the diamond, graphene-like layers, and the depleted region between them. However, it is important to note that the total surface area of the graphene layers can only be estimated since it is their scattering interference and not their size that is resolved with SAXS. Though the surface texture is not strictly spherically symmetric with the diamond core (Figure 2b), eq 4 is able to account for the high-q scattering that could otherwise be attributed to other heterogeneities. Based on the raw data shown in Figure 6, it is the presence of surface texture that results in a departure from Porod scattering. However, this departure could be attributed to a number of different morphologies that, though possible, either do not agree with the TEM imaging or are ambiguous. To demonstrate this point, the modeling results of other studies along with four different morphologies, core−shell gradient,23 raspberry particles,63 and two-level and one-level unified equations,56,58 are compared with the TEM imaging and eq 4. Details for all of these models and their results are provided in Section S3, Supporting Information. Both of the unified I

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

with DND sizes found through the ex situ TEM analysis, approximately 6 nm if one includes the surface texture. While some increase in the DND size distribution is observed at tdet > 0.1 μs, no monotonic increase in the DND surface texture is observed and therefore we conclude that the graphitization of DND is not significant after formation and is confirmed with thermochemical simulations. As with many systems in small-angle scattering, more than one model can be fit to the data. Other candidate models proposed in the literature were explored here to show that the choice of the scattering model is very important in understanding the earlystage morphology of DND. High-resolution TEM imaging of carefully recovered DND and ex situ USAXS/SAXS/WAXS greatly improve the confidence in the choice of scattering model. The scattering from polychromatic X-rays can also affect the size distribution if the surface texture is not accounted for in the modeling. Ultimately, accounting for the presence of the surface texture is essential for an accurate scattering model.

■

Figure 8. Plot of the volume fraction distribution, νDND, obtained from the ex situ USAXS data (closed circles) and the in situ TR-SAXS data (open circles) by assuming a size distribution of spheres (red) and eq 4 (black).

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b02692. Details of the data reduction, instrument corrections, and SAXS modeling; all of the background-subtracted data and model fits from the U18 experiments (PDF)

particles would be present in the size distribution obtained from the TR-SAXS data compared with that from the USAXS data. Features in the TR-SAXS data that incorrectly suggest the presence of smaller particles can be attributed to the asymmetry in the undulator profile (Figure S1), where scattering from longer wavelengths has a higher intensity than shorter wavelengths at higher scattering angles. Therefore, smaller particles that would otherwise scatter at much higher q-values are artificially present in the size distribution; larger particles in the agglomerate do not contribute as much as the fractal-like scattering. This conclusion might lead one to speculate that smaller particles must grow or coalesce into larger particles. On the other hand, the size distribution obtained via eq 4 from the TR-SAXS data is similar to that obtained from the USAXS data. Therefore, the wavelength smearing does not significantly change the modeling results when the surface texture is included in the modeling but slightly affects the size distribution when the surface texture is not included by yielding a broader size distribution.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (J.A.H.). *E-mail: [email protected] (T.M.W.). ORCID

Joshua A. Hammons: 0000-0003-0107-1954 Laurence E. Fried: 0000-0002-9437-7700 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

■

■

ACKNOWLEDGMENTS This work was funded in its initial stages by LLNL LDRD 14ERD-018 and in its latter stages by NNSA’s Office of Defence and Nuclear Nonproliferation and Science Campaign 2 and performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. This publication is based upon the work performed at the Dynamic Compression Sector, which is operated by Washington State University under the U.S. Department of Energy (DOE)/National Nuclear Security Administration award no. DE-NA0002442. This research also used resources of the Advanced Photon Source (APS Sector 9ID-C, 32-ID-B, 35-ID-B), a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The authors thank Virginia Altoe and Shaul Aloni for the use of and assistance with the JEOL 2100F. TEM work utilized the Molecular Foundry, a DOE User Facility operated for the DOE Office of Science by Lawrence Berkeley National Laboratory under Contract No. DE-AC02-

CONCLUSIONS With this study, we are able to resolve the morphology of earlystage DND by comparing the time-resolved in situ SAXS to the SAXS from particulates recovered from similar detonations. Particulate recovery allows for extensive characterization with TEM on the recovered soot that is used to formulate a highfidelity scattering model, which can be applied to the in situ TRSAXS data. This model is compared with a simple spherical model to show how the high-q deviation in Porod decay could be misinterpreted as evidence of DND less than 3 nm in diameter. With a suitable scattering model, DND is observed within 0.1 μs, which indicates that formation occurs much earlier in the detonation than has been reported/predicted previously. Combined with thermochemical simulations, the in situ TRSAXS modeling indicates that carbon is condensed into a size distribution of diamond phases that have a mean size of ∼3 nm within the reaction zone. The mean diamond size of the distribution increases toward 4 nm up to 0.3 μs. Beyond 0.3 μs, the mean size does not significantly change and is consistent J

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

(17) Titov, V. M.; Tolochko, B. P.; Ten, K. A.; Lukyanchikov, L. A.; Pruuel, E. R. Where and When Are Nanodiamonds Formed under Explosion? Diamond Relat. Mater. 2007, 16, 2009−2013. (18) Watkins, E. B.; Velizhanin, K. A.; Dattelbaum, D. M.; Gustavsen, R. L.; Aslam, T. D.; Podlesak, D. W.; Huber, R. C.; Firestone, M. A.; Ringstrand, B. S.; Willey, T. M.; et al. Evolution of Carbon Clusters in the Detonation Products of the Triaminotrinitrobenzene (Tatb)-Based Explosive Pbx 9502. J. Phys. Chem. C 2017, 121, 23129−23140. (19) Huber, R. C.; Ringstrand, B. S.; Dattelbaum, D. M.; Gustavsen, R. L.; Seifert, S.; Firestone, M. A.; Podlesak, D. W. Extreme Condition Nanocarbon Formation under Air and Argon Atmospheres During Detonation of Composition B-3. Carbon 2018, 126, 289−298. (20) Gupta, Y. M.; Turneaure, S. J.; Perkins, K.; Zimmerman, K.; Arganbright, N.; Shen, G.; Chow, P. Real-Time, High-Resolution XRay Diffraction Measurements on Shocked Crystals at a Synchrotron Facility. Rev. Sci. Instrum. 2012, 83, No. 123905. (21) Chen, S.; Luo, S. N. Small-Angle Scattering of Polychromatic Xrays: Effects of Bandwidth, Spectral Shape and High Harmonics. J. Synchrotron Radiat. 2018, 25, 496−504. (22) Rubtsov, I. A.; Ten, K. A.; Pruuel, E. R.; Kashkarov, A. O.; Kremenko, S. I.; Voronin, M. S.; Shekhtman, L. I.; Zhulanov, V. V.; Tolochko, B. P. Methods to Restore the Dynamics of Carbon Condensation During the Detonation of High Explosives. J. Phys.: Conf. Ser. 2019, 1147, No. 012038. (23) Mykhaylyk, O. O.; Solonin, Y. M.; Batchelder, D. N.; Brydson, R. Transformation of Nanodiamond into Carbon Onions: A Comparative Study by High-Resolution Transmission Electron Microscopy, Electron Energy-Loss Spectroscopy, X-Ray Diffraction, Small-Angle X-Ray Scattering, and Ultraviolet Raman Spectroscopy. J. Appl. Phys. 2005, 97, No. 074302. (24) Firestone, M. A.; Dattelbaum, D. M.; Podlesak, D. W.; Gustavsen, R. L.; Huber, R. C.; Ringstrand, B. S.; Watkins, E. B.; Jensen, B.; Willey, T.; Lauderbauch, L. et al. Structural Evolution of Detonation Carbon in Composition B by X-ray Scattering, Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter2015; Chau, R., Germann, T., Oleynik, I., Peiris, S., Ravelo, R., Sewell, T., Eds.; American Physical Society, 2017. (25) Lebedev, V.; Kulvelis, Y.; Kuklin, A.; Vul, A. Neutron Study of Multilevel Structures of Diamond Gels. Condens. Matter 2016, 1, No. 10. (26) Mochalin, V. N.; Shenderova, O.; Ho, D.; Gogotsi, Y. The Properties and Applications of Nanodiamonds. Nat. Nanotechnol. 2012, 7, 11−23. (27) Malkov, I. Y.; Filatov, L. I.; Titov, V. M.; Litvinov, B. V.; Chuvilin, A. L.; Teslenko, T. S. Formation of Diamond from the Liquid-Phase of Carbon. Combust., Explos. Shock Waves 1993, 29, 542−544. (28) Danilenko, V. V. Specific Features of Synthesis of Detonation Nanodiamonds. Combust., Explos. Shock Waves 2005, 41, 577−588. (29) Dolmatov, V. Y.; Myllymaki, V.; Vehanen, A. A Possible Mechanism of Nanodiamond Formation During Detonation Synthesis. J. Superhard Mater. 2013, 35, 143−150. (30) Anisichkin, V. F. On the Mechanism of the Detonation of Organic High Explosives. Russ. J. Phys. Chem. B 2016, 10, 451−455. (31) Ershov, A. P.; Satonkina, N. P. Investigation of the Reaction Zone in Heterogeneous Explosives Substances Using an Electrical Conductivity Method. Combust., Explos. Shock Waves 2009, 45, 205−210. (32) Gustavsen, R. L.; Dattelbaum, D. M.; Watkins, E. B.; Firestone, M. A.; Podlesak, D. W.; Jensen, B. J.; Ringstrand, B. S.; Huber, R. C.; Mang, J. T.; Johnson, C. E.; et al. Time Resolved Small Angle X-Ray Scattering Experiments Performed on Detonating Explosives at the Advanced Photon Source: Calculation of the Time and Distance between the Detonation Front and the X-Ray Beam. J. Appl. Phys. 2017, 121, No. 105902. (33) Staver, A. M.; Ershov, A. P.; Lyamkin, A. I. Study of Detonations in Condensed Explosives by Conduction Methods. Combust., Explos. Shock Waves 1984, 20, 320−323. (34) Rubtsov, I. A.; Ten, K. A.; Pruuel, E. R.; Kashkarov, A. O.; Tolochko, B. P.; Zhulanov, V. V.; Shekhtman, L. I.; Piminov, P. A. The

05CH11231. M.H.N. acknowledges support from the Lawrence Fellowship.

■

ABBREVIATIONS SAXS, small-angle X-ray scattering; USAXS, ultrasmall-angle Xray scattering; SAS, small-angle scattering; TEM, transmission electron microscopy; ED, electron diffraction; EELS, electron energy loss spectrometry; DND, detonation nanodiamond; TNT, trinitrotoluene (2-methyl-1,3,5-trinitrobenzene); RDX, research department explosive (cyclotrimethylenetrinitramine); comp B, composition B

■

REFERENCES

(1) Danilenko, V. V. On the History of the Discovery of Nanodiamond Synthesis. Phys. Solid State 2004, 46, 595−599. (2) Greiner, N. R.; Phillips, D. S.; Johnson, J. D.; Volk, F. Diamonds in Detonation Soot. Nature 1988, 333, 440−442. (3) Perraki, M.; Proyer, A.; Mposkos, E.; Kaindl, R.; Hoinkes, G. Raman Micro-Spectroscopy on Diamond, Graphite and Other Carbon Polymorphs from the Ultrahigh-Pressure Metamorphic Kimi Complex of the Rhodope Metamorphic Province, Ne Greece. Earth Planet. Sci. Lett. 2006, 241, 672−685. (4) Huss, G. R. Meteoritic Nanodiamonds: Messengers from the Stars. Elements 2005, 1, 97−100. (5) Tong, Y.; Liu, R.; Zhang, T. L. The Effect of a Detonation Nanodiamond Coating on the Thermal Decomposition Properties of Rdx Explosives. Phys. Chem. Chem. Phys. 2014, 16, 17648−17657. (6) Gilmour, J. D.; Holland, G.; Verchovsky, A. B.; Fisenko, A. V.; Crowther, S. A.; Turner, G. Xenon and Iodine Reveal Multiple Distinct Exotic Xenon Components in Efremovka “Nanodiamonds”. Geochim. Cosmochim. Acta 2016, 177, 78−93. (7) Lewis, J. B.; Floss, C.; Gyngard, F. Origin of Nanodiamonds from Allende Constrained by Statistical Analysis of C Isotopes from Small Clusters of Acid Residue by Nanosims. Geochim. Cosmochim. Acta 2018, 221, 237−254. (8) Ott, U.; Besmehn, A.; Farouqi, K.; Hallmann, O.; Hoppe, P.; Kratz, K. L.; Melber, K.; Wallner, A. New Attempts to Understand Nanodiamond Stardust. Publ. Astron. Soc. Aust. 2012, 29, 90−97. (9) Moore, L.; Yang, J. Y.; Lang, T. T. H.; Osawa, E.; Lee, D. K.; Johnson, W. D.; Xi, J. Z.; Chow, E. K. H.; Ho, D. Biocompatibility Assessment of Detonation Nanodiamond in Non-Human Primates and Rats Using Histological, Hematologic, and Urine Analysis. ACS Nano 2016, 10, 7385−7400. (10) Zang, J.; Wang, Y.; Bian, L.; Zhang, J.; Meng, F.; Zhao, Y.; Qu, X.; Ren, S. Bucky Diamond Produced by Annealing Nanodiamond as a Support of Pt Electrocatalyst for Methanol Electrooxidation. Int. J. Hydrogen Energy 2012, 37, 6349−6355. (11) Zhang, T.; Liu, G.-Q.; Leong, W.-H.; Liu, C.-F.; Kwok, M.-H.; Ngai, T.; Liu, R.-B.; Li, Q. Hybrid Nanodiamond Quantum Sensors Enabled by Volume Phase Transitions of Hydrogels. Nat. Commun. 2018, 9, No. 3188. (12) Danilenko, V. V. Shock-Wave Sintering of Nanodiamonds. Phys. Solid State 2004, 46, 711−715. (13) Danilenko, V. V. Assessment of the Influence of Particle Size and Degree of Cohesion of Detonation Nanodiamonds on Their Thermal Stability. J. Superhard Mater. 2009, 31, 218−225. (14) Kozyrev, N. V.; Golubeva, E. S. Investigation of the Synthesis of Ultradispersed Diamonds in Mixtures of Tnt with Rdx, Hmx, and Petn. Combust., Explos. Shock Waves 1992, 28, 560−564. (15) Guinier, A.; Fournet, G. Small-Angle Scattering of X-rays; Wiley: New York, 1955. (16) Bagge-Hansen, M.; Lauderbach, L.; Hodgin, R.; Bastea, S.; Fried, L.; Jones, A.; van Buuren, T.; Hansen, D.; Benterou, J.; May, C.; et al. Measurement of Carbon Condensates Using Small-Angle X-Ray Scattering During Detonation of the High Explosive Hexanitrostilbene. J. Appl. Phys. 2015, 117, No. 245902. K

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

(58) Hammouda, B. A New Guinier-Porod Model. J. Appl. Crystallogr. 2010, 43, 716−719. (59) Bale, H. D.; Schmidt, P. W. Small-Angle X-ray-Scattering Investigation of Submicroscopic Porosity with Fractal Properties. Phys. Rev. Lett. 1984, 53, 596−599. (60) Tolochko, B. P.; Chernyshev, A. P.; Bokhonov, B. B.; Ten, K. A.; Pruuel, E. R.; Lyakhov, N. Z. Investigation of Adamantane-Diamond Transformation. The Radical Mechanism of the Formation of Diamond Nanoparticles under Shock-Wave Action on Adamantane. J. Struct. Chem. 2016, 57, 1469−1476. (61) Bowron, D. T.; Díaz-Moreno, S. Analysis of Time-Resolved Energy-Dispersive X-ray Absorption Spectroscopy Data for the Study of Chemical Reaction Intermediate States. Anal. Chem. 2005, 77, 6445−6452. (62) Panich, A. M.; Shames, A. I. Comment on “Quantification of C C and CO Surface Carbons in Detonation Nanodiamond by Nmr”. J. Phys. Chem. C 2015, 119, 21286−21287. (63) Larson-Smith, K.; Jackson, A.; Pozzo, D. C. Small Angle Scattering Model for Pickering Emulsions and Raspberry Particles. J. Colloid Interface Sci. 2010, 343, 36−41.

Growth of Carbon Nanoparticles During the Detonation of Trinitrotoluene. J. Phys.: Conf. Ser. 2016, 754, No. 052004. (35) Chevrot, G.; Sollier, A.; Pineau, N. Molecular Dynamics and Kinetic Study of Carbon Coagulation in the Release Wave of Detonation Products. J. Chem. Phys. 2012, 136, No. 084506. (36) Galli, G. Computer-Based Modeling of Novel Carbon Systems and Their Properties, 1st ed.; Springer: Netherlands, 2010. (37) Chen, P. W.; Huang, F. L.; Yun, S. R. Characterization of the Condensed Carbon in Detonation Soot. Carbon 2003, 41, 2093−2099. (38) Pichot, V.; Risse, B.; Schnell, F.; Mory, J.; Spitzer, D. Understanding Ultrafine Nanodiamond Formation Using Nanostructured Explosives. Sci. Rep. 2013, 3, No. 2159. (39) Pichot, V.; Comet, M.; Risse, B.; Spitzer, D. Detonation of Nanosized Explosive: New Mechanistic Model for Nanodiamond Formation. Diamond Relat. Mater. 2015, 54, 59−63. (40) Mitev, D. P.; Townsend, A. T.; Paull, B.; Nesterenko, P. N. Microwave-Assisted Purification of Detonation Nanodiamond. Diamond Relat. Mater. 2014, 48, 37−46. (41) Dementjev, A. P.; Maslakov, K. I. Chemical State of Carbon Atoms on a Nanodiamond Surface: Growth Mechanism of Detonation Nanodiamond. Fullerenes, Nanotubes, Carbon Nanostruct. 2012, 20, 594−599. (42) Raty, J.-Y.; Galli, G.; Bostedt, C.; van Buuren, T. W.; Terminello, L. J. Quantum Confinement and Fullerenelike Surface Reconstructions in Nanodiamonds. Phys. Rev. Lett. 2003, 90, No. 037401. (43) Aleksenskii, A. E.; Baidakova, M. V.; Vul’, A. Y.; Siklitskii, V. I. The Structure of Diamond Nanoclusters. Phys. Solid State 1999, 41, 668−671. (44) Donnet, J. B.; Lemoigne, C.; Wang, T. K.; Peng, C. M.; Samirant, M.; Eckhardt, A. Detonation and Shock Synthesis of Nanodiamonds. Bull. Soc. Chim. Fr. 1997, 134, 875−890. (45) Avdeev, M. V.; Tomchuk, O. V.; Ivankov, O. I.; Alexenskii, A. E.; Dideikin, A. T.; Vul, A. Y. On the Structure of Concentrated Detonation Nanodiamond Hydrosols with a Positive Zeta Potential: Analysis of Small-Angle Neutron Scattering. Chem. Phys. Lett. 2016, 658, 58−62. (46) Ilavsky, J. Nika: Software for Two-Dimensional Data Reduction. J. Appl. Crystallogr. 2012, 45, 324−328. (47) Fan, L.; Degen, M.; Bendle, S.; Grupido, N.; Ilavsky, J. The Absolute Calibration of a Small-Angle Scattering Instrument with a Laboratory X-Ray Source. Journal of Physics. J. Phys.: Conf. Ser. 2010, 247, No. 012005. (48) Zhang, F.; Ilavsky, J.; Long, G. G.; Quintana, J. P. G.; Allen, A. J.; Jemian, P. R. Glassy Carbon as an Absolute Intensity Calibration Standard for Small-Angle Scattering. Metall. Mater. Trans. A 2010, 41, 1151−1158. (49) Souers, P. C.; Forbes, J. W.; Fried, L. E.; Howard, W. M.; Anderson, S.; Dawson, S.; Vitello, P.; Garza, R. Detonation Energies from the Cylinder Test and Cheetah V3.0. Propellants, Explos., Pyrotech. 2001, 26, 180−190. (50) Viecelli, J. A.; Ree, F. H. Carbon Particle Phase Transformation Kinetics in Detonation Waves. J. Appl. Phys. 2000, 88, 683−690. (51) Haynes, W. M., Ed.; Handbook of Chemistry and Physics, 97th ed.; CRC Press, Taylor and Francis Group, 2016. (52) Glatter, O.; Kratky, O. Small Angle X-ray Scattering; Academic Press: New York, 1982. (53) Martin, J. E.; Hurd, A. J. Scattering from Fractals. J. Appl. Crystallogr. 1987, 20, 61−78. (54) Schaefer, D. W.; Martin, J. E.; Wiltzius, P.; Cannell, D. S. Fractal Geometry of Colloidal Aggregates. Phys. Rev. Lett. 1984, 52, 2371− 2374. (55) Teixeira, J. Small-Angle Scattering by Fractal Systems. J. Appl. Crystallogr. 1988, 21, 781−785. (56) Beaucage, G. Approximations Leading to a Unified Exponential Power-Law Approach to Small-Angle Scattering. J. Appl. Crystallogr. 1995, 28, 717−728. (57) Newville, M.; Stensitzki, T.; Allen, D. B.; Ingargiola, A. Lmfit: Non-Linear Least-Square Minimization and Curve-Fitting for Python; Astrophysics Source Code Library, 2014. L

DOI: 10.1021/acs.jpcc.9b02692 J. Phys. Chem. C XXXX, XXX, XXX−XXX