J. Phys. Chem. C 2007, 111, 2235-2241
2235
Surface Nonlinear Vibrational Spectroscopy of Energetic Materials: HMX Eric Surber, Aaron Lozano, Alexei Lagutchev, Hackjin Kim,† and Dana D. Dlott* School of Chemical Sciences, UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801 ReceiVed: October 16, 2006; In Final Form: NoVember 22, 2006
The surfaces of solution-grown β-HMX (β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) crystals were studied using vibrational sum-frequency generation spectroscopy (SFG). In earlier work (Kim, H.; Lagutchev, A.; Dlott, D. D. Propellants, ExplosiVes, Pyrotechnics 2005, 31, 116), such SFG spectra evidenced considerable variability as the ∼200-µm diameter laser beam was translated over crystal surfaces. We have now found this variability results from ubiquitous small deposits of δ-HMX on the surface of β-HMX single crystals. SFG is a selective probe of molecules in noncentrosymmetric environments. Since β-HMX is centrosymmetric, only the surface is SFG-active; however, δ-HMX is noncentrosymmetric, so a tiny δ-HMX deposit on a β-HMX surface could dominate the SFG spectrum. We have found that rapid evaporation from tiny droplets of HMX solution produces only δ-HMX, presumably because the polar boat conformation of δ-HMX is stabilized in solution. We believe the δ-HMX deposits are created by the rapid drying of droplets of mother liquor clinging to solution-grown crystal surfaces. In this paper, we present SFG spectra of δ-HMX nanocrystals and β-HMX surfaces in the CH-stretch and NO2-stretch regions. Through an analysis of the β-HMX/δ-HMX SFG intensity ratios and the surface variability, we deduce that the δ-HMX deposits we observe have dimensions of a few micrometers and a mean surface coverage that, depending on crystal growth conditions, ranges from 0.1 to 1 µg/cm2. The implications of these δ-HMX sites for energetic material performance are discussed briefly.
Introduction A great deal of the ignition and impact initiation phenomena associated with energetic materials (EM) involves surfaces and interfaces.1 For instance, combustion occurs at gas-solid (or gas-liquid) interfaces; impact initiation frequently involves hot spot formation2 at moving-edge dislocations,3 voids, or cracks;4 and the mechanical strength of plastic-bonded explosives (PBX) is determined largely by adhesion between the solid EM and the polymer binders and fillers. Recently, we reported5 the application of vibrational sum-frequency generation (SFG) spectroscopy to study EM surfaces and interfaces. SFG is a selective probe of molecules in noncentrosymmetric environments, so with centrosymmetric materials, surface or interface molecules dominate the SFG spectra. The materials studied were constituents of high-performance PBX, such as PBX 9501 and LX-14. These were the β-isomorph of solution-grown HMX crystals (β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) and the Estane 5703 polymer. We also obtained SFG spectra of the HMX-Estane interface. Note that HMX has the chemical formula (CH2-N-NO2)4. (The chemical structure of HMX and the crystal structure of β-HMX are shown in Figure 11, which appears later in this paper.) Both methylene and nitro surface stretching transitions were observed by SFG, and their frequency shifts relative to the bulk were discussed.5 On the surface of the (011) plane, there are two distinguishable types of methylene and nitro groups that lie approximately within the plane and perpendicular to the plane. One of the interesting results of the study was the variability of the SFG spectra of solution-grown β-HMX crystals.5 The * To whom correspondence should be addressed. E-mail: dlott@ scs.uiuc.edu. † Permanent address: Department of Chemistry, Chungnam National University, Taejon 305-764, Korea.
surface variability was taken as an indicator that common methods for producing EM do not create reproducible surfaces, which might in part account for the variations in sensitivity behavior widely observed in EM. We have further investigated this variability and have now determined its cause. In experiments in which HMX was deposited on a surface by rapid evaporation from tiny droplets of HMX solutions, we found that the nanocrystals so created were predominantly the δ-isomorph of HMX.6 This led us to theorize that the surfaces of solution-grown β-HMX crystals might be contaminated by small deposits of δ-HMX. β-HMX crystals are centrosymmetric with Z ) 2 in the monoclinic P21/c space group.7 However, δ-HMX is noncentrosymmetric with Z ) 6 in the P61 space group,8 so the entire bulk is SFG-active. A tiny δ-HMX deposit on a β-HMX surface could dominate the SFG spectrum. We have found these ubiquitous δ-HMX deposits on HMX crystals grown in our laboratory at the University of Illinois (UIUC) by evaporation from acetone or acetonitrile and on crystals grown at Los Alamos National Laboratory (LANL) by slow cooling from DMSO. To our knowledge, the ubiquitous presence of δ-HMX on solution-grown β-HMX surfaces was not recognized until now. HMX exists in four isomorphic forms, denoted R, β, γ, and δ.6 Under ambient conditions, β-HMX is the thermodynamically stable isomorph.6 When heated to 167-183 °C, a β-to-δ transition occurs.6,9-12 This transition has frequently been discussed in the context of HMX safety and performance. Heating associated with storage, cookoff, or combustion9 can trigger the phase transition. The 6.7% volume increase can dramatically affect the defect, fracture, and void behavior of an EM.10 Furthermore δ-HMX is known to be more impactsensitive. The process of β-to-δ conversion has been investigated
10.1021/jp066801r CCC: $37.00 © 2007 American Chemical Society Published on Web 01/13/2007
2236 J. Phys. Chem. C, Vol. 111, No. 5, 2007
Surber et al.
using IR spectroscopy,9 X-ray crystallography,13,14 atomic force microscopy,10 and second-harmonic generation (SHG).11,12,14 SHG imaging of the β-to-δ conversion in PBX 950112 indicated that δ-to-β reconversion upon cooling, which is ordinarily very slow in crystalline HMX, is greatly facilitated by the presence of the binder/plasticizer mixture.15 In this paper, we show that fast evaporation from solution creates pure δ-HMX, and we obtain the first SFG spectra of this material. We also investigate the SFG spectrum of solutiongrown β-HMX crystals from UIUC and LANL using a type of SFG microscopy in which a 200-µm-diameter laser beam is scanned over crystal surfaces. This technique is used to investigate the surface distribution of δ-HMX deposits. By locating regions mostly free of δ-HMX, we identify the SFG spectrum of uncontaminated β-HMX surfaces. Experimental Materials. HMX synthesized using the method of Siele16 was provided by Dr. Randall Simpson and Dr. George Overturf of the Energetic Materials Center, Lawrence Livermore National Laboratory. Large single crystals of β-HMX were grown at UIUC in acetone or acetonitrile by slow evaporation. The largest, most optically homogeneous crystals were approximately 3 × 2 × 1 mm3 in size. X-ray diffraction was used to verify the crystal structure and crystal orientation.5 β-HMX crystals were also provided by Dr. Dan Hooks of Los Alamos National Laboratory. These LANL crystals were grown from DMSO by slow cooling. Additional HMX samples were made by spraying a 2 × 10-3 M solution of HMX in acetone with a Badger airbrush onto a substrate17 onto a glass slide with an ∼100-nm thin film of vapor-deposited Al, which is used as an adhesion promoter and to reflect more of the SFG signal into the detector. With the spray method, tiny droplets of HMX solution on the substrate evaporate rapidly, leaving behind an agglomerated mass of fine nanocrystalline powder. These nanocrystalline HMX films were characterized by profilometry. They have an average thickness of a few hundred nanometers and a rugged topography that includes some regions higher than 1 µm and some bare or almost bare patches. For IR measurements, we used either a KBr pellet containing pulverized solution-grown HMX crystals or a CaF2 window with a thin film of nanocrystalline HMX created by the spray method. The IR spectra were obtained using a Nicolet 750 FTIR spectrometer. SFG Spectroscopy. Vibrational SFG is a second-order nonlinear optical spectroscopic technique in which one incident pulse is an IR pulse that is resonant with molecular vibrational transitions and the other incident pulse is a nonresonant visible (here, 804-nm) pulse. A related method, SHG, has also been used to study δ-HMX. SHG is sensitive to the presence of δ-HMX but does not have the vibrational specificity of SFG, since in SHG, both incident pulses are nonresonant. SFG has been the subject of extensive reviews,18-21 and our SFG apparatus has been described previously.5,22 The SFG intensity, ISFG, is proportional to the square modulus of the nonlinear polarization, B PSFG, which itself depends on the second-order nonlinear susceptibility χ(2),
ISFG ∝ |P BSFG|2 ) |χ(2)(ωIR,ωvis)E BIRB Evis|2
(1)
where B E denotes an electric field. The symmetry properties of χ(2) lead to the well-known result that (in the dipole approximation) no SFG signal can be generated in centrosymmetric media.23 Thus, with HMX, one expects the SFG signal from
β-HMX to originate solely from the surface (in the absence of voids, cracks, or inclusions, an optical wavelength or more in dimension). On the other hand, SFG signals from δ-HMX are expected to originate from both surface and bulk; with macroscopic crystals, the bulk contribution is dominant. Our measurements use the broadband multiplex SFG technique.24,25 The IR pulse is a tunable broadband femtosecond pulse with a spectral width of ∼250 cm-1. This IR pulse spectrum determines the spectral region being probed. The visible pulse is a picosecond narrowband pulse at 804 nm, and its 5 cm-1 fwhm determines the spectral resolution. These pulses are incident on the sample at a 60° angle, and the coherent sumfrequency signal is detected with a multichannel spectrograph. All spectra used the ppp polarization condition. The β-HMX spectra were obtained with the beams incident on well-developed crystal faces. The SFG signals for CH-stretching (νCH) transitions near 3000 cm-1 were centered near 650 nm, and SFG signals for symmetric and antisymmetric nitro-stretching (νsNO2 and νaNO2) transitions in the 1400-1600 cm-1 range were centered near 720 nm. For reference, we compare our SFG spectra with IR spectra. Two points should be noted in such comparisons. The FTIR spectrometer is a dual-beam system that provides accurate intensity normalization across the entire spectrum. The broadband SFG spectrometer is a single-beam system, and SFG intensities are weighted by the spectrum of the broadband IR pulses. We did not try to normalize our spectra, although the normalized amplitudes or intensities of transitions studied with broadband SFG could be obtained by fitting to a sum of Lorentz line shape functions weighted by the approximately Gaussian IR pulse spectrum,26
[
ISFG(ω) ∝ exp -4 ln(2)
|
]
(ω - Ω)2 δ2
×
ANR exp(-iφ) +
NAν
∑ν ω - ω
ν
+ iΓν
|
2
(2)
where Ω and δ are the central frequency and width of the broadband IR pulse; ANR and φ are the amplitude and phase of the nonresonant signal; and for each transition, ν, NAν is the product of the molecular number density; the vibrational amplitude, ωV, is the central frequency; and ΓV is the inverse line width. According to eq 2, spectral intensities will drop off dramatically approximately (150 cm-1 from the IR pulse spectral peak. The IR spectrum depends on (is proportional to the Fourier transform of) the dipole correlation function, ; the Raman spectrum depends on the polarizability correlation function, ; but the SFG spectrum depends on the correlation function,27 . Both the β-HMX surface and the δ-HMX bulk are noncentrosymmetric, so all transitions seen in the IR are expected to be present in SFG; however, SFG relative intensities may differ radically from the IR intensities. In our apparatus, the IR laser beam diameter is somewhat greater than the visible beam,22,28 so the spatial resolution of SFG measurements is determined by the visible laser beam diameter of ∼200 µm. To investigate the variability of SFG spectra, the samples were placed on an x-y translator, and spectra were obtained with each sample, over an area of several square millimeters, on multiple spatially nonoverlapping regions. In other words, the measurement is a kind of SFG microscopy with spatial resolution of ∼200 µm. Typical signal acquisition
Vibrational Spectroscopy of Energetic Materials
Figure 1. SFG spectra (center five rows) obtained in the νCH region of a thin film of polycrystalline HMX produced by rapid evaporation from small droplets of acetone solution, as compared to IR spectra of β-HMX and δ-HMX. The SFG spectra show little variation as the SFG laser beams are scanned over the sample surface. Rapid evaporation produces nanocrystals that are predominantly δ-HMX.
Figure 2. SFG spectrum in the νNO2 region of a thin film of nanocrystalline δ-HMX, as compared to IR spectra of β-HMX and δ-HMX. SFG transitions below 1300 cm-1 were not observed because the broadband IR pulses had little intensity in this region.
J. Phys. Chem. C, Vol. 111, No. 5, 2007 2237
Figure 3. SFG spectra (center five rows) of the (011) face of a β-HMX crystal grown in acetone, in the νCH region. All SFG spectra contain both β-HMX and δ-HMX features.
Figure 4. SFG spectra (center five rows) of the (110) face of a β-HMX crystal grown in acetone, in the νCH region, and its comparison to IR spectra of β-HMX and δ-HMX. All SFG spectra contain both β-HMX and δ-HMX features.
times were 5 min for the crystal samples and 1 min for thin film samples. Results Fast Evaporation Produces δ-HMX. IR spectra of HMX solution-grown β-HMX crystals ground into KBr pellets and HMX films produced by the spray method are shown in Figure 1 in the νCH region and in Figure 2 in the νNO2 region. Comparison with literature spectra29 shows that the KBr spectrum originates from predominantly β-HMX, whereas the thin films are predominantly δ-HMX. This remained true whether the solvent used for spray coating was acetone or acetonitrile. SFG spectra of the sprayed δ-HMX samples are also shown in Figures 1 and 2, where they are compared to IR spectra of both β- and δ-HMX polymorphs. In contrast to solution-grown β-HMX crystals, these spectra were more intense and were quite reproducible as the laser beams were scanned over the thin film surface. What variations were observed were attributed to variations in the thickness of the nanocrystalline film. Surfaces of β-HMX Crystals in the νCH Region. Many tens of SFG spectra were obtained from several solution-grown β-HMX crystals. These spectra always evidenced variability as the SFG laser beam was scanned over crystal surfaces. Some representative results from UIUC acetone-grown crystals are shown in Figures 3 and 4. In Figure 3, spectra were obtained from the (011) face; in Figure 4, the (110) face of a different
Figure 5. Comparison of relative SFG intensities in the νCH region from a LANL crystal and a UIUC crystal.
crystal was studied. Notice how the SFG spectra varies depending upon the position of the laser spot on the crystal. All spectra evidence a mixture of β-HMX and δ-HMX features. The spectra were arranged so the topmost spectra are dominated by β-HMX; the bottommost, by δ-HMX. SFG signals from LANL crystals in the νCH region were generally much more intense (typically 20×) than from UIUC crystals, as illustrated in Figure 5. The LANL crystal spectra also evidenced variability (see Figure 6), but were always dominated by the δ-HMX component. Surfaces of β-HMX Crystals in the νNO2 Region. Figure 7 shows SFG spectra in the νNO2 region, from the same UIUC crystal used to generate the νCH data in Figure 4. The spectra are quite different from the reference SFG spectra of δ-HMX,
2238 J. Phys. Chem. C, Vol. 111, No. 5, 2007
Surber et al. were localized on β-HMX surfaces or, instead, were located within inclusions throughout the crystal. It is the IR pulses in the νCH region that would be most likely to cause β-to-δ conversion, because unlike the visible pulses, these pulses are resonant with HMX transitions, and the IR pulses have higher energies. To estimate the steady-state temperature rise at the crystal surface, we use a method described previously,26 in which we first compute the singleshot temperature rise, ∆T, and then the steady-state rise, ∆Tss, in which the time interval between pulses, τrep, is 1 ms. The single-shot rise at the crystal surface is given by26
∆T ) Figure 6. SFG spectra (center five rows) from a β-HMX crystal grown in DMSO at LANL, in the νCH region, as compared to IR spectra of β-HMX and δ-HMX. The SFG spectra are dominated by δ-HMX surface deposits.
Figure 7. SFG spectra (center four rows) from a UIUC solution-grown β-HMX crystal in the νNO2 spectral region, as compared to IR spectra of β-HMX and δ-HMX. Comparison with SFG data for pure δ-HMX (Figure 2) indicates the transitions observed in SFG are predominantly due to β-HMX.
Figure 8. SFG spectra (center five rows) from a LANL solution-grown β-HMX crystal in the νNO2 spectral region, as compared to IR spectra of β-HMX and δ-HMX. The SFG spectra are dominated by δ-HMX deposits.
so we assign these transitions to β-HMX surface νNO2 transitions. Using the LANL crystal that generated the νCH data in Figures 5 and 6, in the νNO2 region shown in Figure 8, we see δ-HMX transitions only. Control Experiments. We performed two kinds of control experiments. The first were designed to check whether the δ-HMX transitions observed during measurements on β-HMX crystals might not be intrinsic to the crystal growth process but, instead, might have been created in situ by laser beam heating. The second were designed to see whether the δ-HMX deposits
JR FC
(3)
where J is the maximum pulse fluence at the beam center, R is the IR absorption coefficient, and FC is the volumetric heat capacity. Here, J ≈ 30 mJ/cm2; FC ≈ 4 J K-1 cm-3; and for νCH transitions, R ≈ 400 cm-1. Combining these parameters yields ∆T ) 3K. This heat is deposited within a surface layer 1/R ) 25 µm thick. The heated region corresponds roughly to a disc 200 µm in diameter that is ∼25 µm thick. Thermal conduction in the 25-µm direction is the most efficient cooling mechanism,30 so we assume one-dimensional thermal conduction, in which heat deposited at the surface is conducted into the bulk crystal with thermal diffusivity D. In a 1D geometry with surface heating,30 the thermal diffusion length in time τ, Λth, is (1/2)(2Dτ)1/2. The thermal conduction time constant τth is the time needed for heat to diffuse a distance equal to one absorption length, τth ) 2/(DR2). Under steady-state conditions (τth g τrep),26
∆Tss ≈ ∆T
τth τrep
(4)
For HMX, D ) 1.3 × 10-3 cm2/s,31 so τth ) 10 ms, and ∆Tss ) 30K, which is not nearly enough to induce β-to-δ transitions. To check these numerical estimates, we noted that there was no increase in the relative intensity of δ-HMX, even for longduration (hour-long) irradiation at the highest intensities. Starting with HMX surfaces that had not been previously irradiated, spectra were obtained using weakened pulses in which the IR intensities were attenuated by up to a factor of 4. When the IR pulse intensity was subsequently increased to its maximum value, no change in the δ-HMX spectrum was observed. We took a UIUC crystal whose surfaces gave spectra with variable contributions from δ-HMX, similar to what is seen in Figures 3 and 4, and cleaved the crystal parallel32 to the (011) plane. The SFG signal of the freshly cleaved surface was weak, so these spectra were obtained with extensive signal-averaging and somewhat lower spectral resolution. These SFG spectra evidenced little variability, and as shown in Figure 9, they appear to be dominated by β-HMX. This demonstrates that the δ-HMX we observe in the SFG of UIUC crystals is associated with crystal surfaces. Discussion Scanning an ∼200-µm-diameter SFG beam across the surface of solution-grown β-HMX crystals reveals a variable contribution from δ-HMX, which ranges from a minimal signal much smaller than the β-HMX contribution to an overwhelmingly dominant δ-HMX signal. Experiments on freshly cleaved surfaces of β-HMX indicate the δ-HMX is associated with the surface rather than the bulk. Intensity-dependent measurements
Vibrational Spectroscopy of Energetic Materials
Figure 9. SFG spectra from a solution-grown UIUC crystal show δ-HMX features. Spectra (at two locations) from the (011) plane of a freshly cleaved UIUC crystal shows no detectable δ-HMX, indicating that the δ-HMX exists primarily as deposits on crystal surfaces.
show the δ-HMX was produced during crystal growth, as opposed to being created by heating from the SFG laser. There is much more δ-HMX on the surfaces of crystals grown at LANL by slow cooling from DMSO than from crystals grown at UIUC by evaporation from acetone and acetonitrile. Since β-HMX is the most thermodynamically stable isomorph, the δ-HMX deposits must result from kinetics. In β-HMX, the molecules have a chair conformation;7 in δ-HMX, it is a boat conformation.8 The chair conformation is nonpolar, and the boat conformation is polar, so boat conformations may be stabilized by polar solvents. Rapid evaporation from polar solvents, thus, could have a tendency to favor δ-HMX. As our spray deposition experiments demonstrate, δ-HMX formation is greatly favored by fast evaporation. Thus, we believe the δ-HMX deposits on UIUC crystals grown in acetone or acetonitrile were formed during solution crystallization when the mother liquor evaporated to dryness or when a crystal was removed from the mother liquor and tiny droplets of the liquor clinging to the crystal face evaporated quickly. The situation with DMSO-grown crystals, such as those obtained from LANL, is much more complicated due to the unusual phase diagram for HMX/DMSO solutions, in which a solvated crystal containing HMX cocrystallized with two DMSO molecules has been observed.33 Curiously, when a solution with these solvated crystals was allowed to evaporate slowly, the residue contained β-HMX, R-HMX, and γ-HMX, but no δ-HMX. This observation suggests that it is rapid solvent evaporation that is needed for the formation of δ-HMX surface deposits. In our earlier paper,5 our β-HMX spectra were contaminated by δ-HMX contributions. In that paper, we analyzed SFG spectra that we judged representative of the crystal surface. Now knowing the SFG spectrum of δ-HMX, we can identify spatial regions with minimal δ-HMX to obtain the (presumably pure) spectrum of β-HMX. Such β-HMX spectra are shown in Figure 10. In the present work, we did not perform the polarization and crystal orientation dependent measurements reported earlier,5 but in retrospect, it seems clear that in the earlier paper, many spectra of νCH and νsNO2 actually resulted from surface deposits of δ-HMX. Our published spectra5 of νasNO2 do, however, appear to represent only β-HMX. We can estimate the surface coverage of δ-HMX, and to some degree, we can determine the spatial distribution and mean size of the δ-HMX deposits using SFG intensity ratios. We will use the νCH data for the (011) plane, since this is the most extensive and has the best signal-to-noise ratio. According to eq 2, the SFG intensity is proportional to the square of the number
J. Phys. Chem. C, Vol. 111, No. 5, 2007 2239
Figure 10. SFG and IR spectra in the νCH and νNO2 region. The SFG spectra refer to β-HMX crystal surfaces that evidence minimal contributions from δ-HMX. The vertical lines denote the peaks of β-HMX IR transitions from bulk crystals.
density, N, or equivalently, the square of the surface mass coverage, M,
ISFG(δ-HMX) ISFG(β-HMX)
)
{
} {
[χ(2)N]δ-HMX
[χ(2)N]β-HMX
2
)
}
[χ(2)M]δ-HMX
[χ(2)M]β-HMX
2
(5)
In eq 5, the ratio of susceptibilities, χ(2)δ-HMX/χ(2)β-HMX, for a particular polarization condition depends on how the molecular susceptibilities and molecular orientations differ in the two crystal forms. At the present time, we do not have an experimental measurement of this ratio, but it seems reasonable to assume them to be approximately equal. In this approximation, eq 5 reduces to the squared ratio of the number density or mass density alone. Figure 11 is a schematic of the (011) plane of β-HMX with a δ-HMX surface deposit. The β-HMX νCH spectra originate from the surface methylene groups. As indicated in Figure 11, the surface methylene groups are located on the upper one-half of the molecules comprising the surface HMX layer. The lower one-half of these molecules are part of the bulk centrosymmetric crystal. The lattice constants for β-HMX are7 a ) 6.5 Å, b ) 11.0 Å, and c ) 7.4 Å. On the (011) plane, the area of a unit cell is ab ) 8 × 10-15 cm2, and it contains two half molecules. Thus, the effective surface coverage seen by SFG, Nβ-HMX, is 1.2 × 1014 cm-2. Since the molecular weight of HMX is 296, the effective surface mass coverage seen by SFG is Mβ-HMX ) 60 ng/cm2. In passing, it is interesting to note that the area probed by SFG is about 3 × 10-4 cm2, so our SFG spectra originate from a mass of HMX of ∼20 pg. This calculation tells us that in the case in which the β-HMX and δ-HMX SFG signals are about equal in intensity, the δ-HMX surface mass coverage is Mδ-HMX ) 60 ng/cm2. To learn something about the size of the δ-HMX surface deposits, we imagine the δ-HMX deposits to be cubic with sides having a mean length λavg on a square grid with mean spacing davg. In this admittedly oversimplified case,
lavg )
(
) (
Mδ-HMXdavg2 Fδ-HMX
1/3
)
1/2
)
ISFG (δ-HMX)Mβ-HMXdavg2 1/2
ISFG (β-HMX)Fδ-HMX
1/3
(6)
where Fδ-HMX ) 1.78 g/cm3,8 and Mβ-HMX ) 60 ng/cm2. Figure 12 shows some model calculations using eq 6. The SFG intensity ratio, ISFG(δ-HMX)/ISFG(β-HMX), defined in eq
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Surber et al.
Figure 11. The structure of the (011) surface of β-HMX. SFG probes a surface layer of β-HMX molecules approximately one-half molecule thick, plus the bulk of any δ-HMX surface deposits.
Figure 13. Optical micrographs of the surfaces of UIUC and LANL β-HMX crystals. The circle denotes the area of a region that generates an SFG spectrum.
Figure 12. The average spacing lavg between δ-HMX surface deposits as a function of the average size, davg, for the indicated values of the SFG intensity ratio δ-HMX/β-HMX. The observed SFG intensity ratio ranges from minimal to ∼30. The shaded areas are regions where the deposits are too close together or too far apart to be consistent with our measurements. This plot shows the average dimensions of a δ-HMX deposit are on the order of 1 µm for UIUC crystals and 10 µm for LANL crystals.
5 was observed to range from negligible (
