Preferred Void Orientation in Uniaxially Pressed PBX 9502Joseph T. Mang* [a] and Rex P. Hjelm [a], [b]

______________________________________________________________________Abstract: Ultra- and small-angle neutron scattering techniques were used to study the morphology of voids in directions parallel and perpendicular to the compaction plane of a uniaxially pressed cylinder of PBX 9502. Two-dimensional scattering patterns from samples cut parallel to the compaction plane had circular equal-intensity contours, implying that along this view the voids are circular or randomly oriented. Identical measurements of samples cut perpendicular to the compaction plane produced elliptical equal-intensity contours, indicating preferred orientation of voids. Analysis of the two dimensional scattering patterns confirmed that the voids are non-spherical with an average aspect

ratio of 1.20, flattened so that the larger dimensions of the voids lie within the compaction plane. Model analysis of the combined ultra- and small-angle neutron scattering curves revealed that the PBX 9502 porosity is interconnected, in the form of aggregates comprised of non-spherical, primary voids. The volume dimension was found to be the same in both directions, indicating that the aggregate is randomly oriented throughout the sample, and that it is the primary voids that are preferentially oriented. Void interfaces with the surrounding matrix were found to be rough or polydisperse, with a common roughness dimension or polydispersity in all directions.

Keywords: PBX 9502, anisotropy, porosity, SANS ________________________________________________________________________________________________________

1 IntroductionConsolidation of a powder to high density imparts physical changes to the individual grains, including reorientation, deformation, and fracture [1, 2]. These changes can be found in materials as diverse as metals [3], rocks [4] and high explosives (HEs) [5], and can result in complex microstructures. For manufactured materials, the microstructure that evolves during consolidation is dependent upon details of the pressing process, such as temperature, applied pressure, and method (e.g. uniaxial or isostatic) [6]. Similar aspects are at work in rock formations, but in this case natural processes dictate the details associated with its geological formation [4]. Though they are very distinct materials, interesting similarities can be found between the microstructure of rock formations and consolidated high explosives. In each, complex pore and surface morphologies exist that define their properties. Experimental studies have provided evidence of fractal void networks and fractal void surface structures [4, 5, 7-13] within the microstructure of each material. While microstructural features such as void size and void

connectivity are important to characterize hydrological properties of geological samples [4], these same features in an HE are known to influence shock sensitivity and flame propagation, and are naturally of interest from both safety and performance perspectives [5,14].

Due to its application and intriguing anisotropic thermal properties, the insensitive high explosive composite, PBX 9502, and its constituents have been well studied [2, 5, 15-21]. PBX 9502 is a two component composite, consisting of 95 wt.-% of the crystalline high explosive, TATB (1,3,5-Triamino-2,4,6-trinitrobenzene), and 5 wt.-% Kel-F 800 (Kel-F) binder. PBX 9502 is produced as a molding powder, which can be heated and pressed either uniaxially or isostatically, depending upon the scale and intended application, to produce experimental parts. For many small-scale applications, PBX 9502 is uniaxially die pressed into the form of a right circular cylinder.

TATB molecules form sheets (much like graphite), and grow into non-spherical crystallites that have been compared to a stack of cards [18]. Due to the weak van der Waals interactions between sheets, TATB exhibits a small shear modulus parallel to the sheets that results in slippage of the crystal planes during compaction, facilitating the filling of void space and preferred orientation of the plane [19].

It has been observed that the TATB sheets prefer to align perpendicular to the pressing direction in uniaxially pressed samples [20], and Schwarz recently demonstrated that TATB crystals align parallel to the shear planes in isostatically pressed PBX 9502 parts [21].

While TATB crystals are known to preferably orient during compaction [20, 21], it is unknown how the void space within the compact is influenced by the alignment. Given the anisotropic morphology of the TATB crystals, it is possible for anisotropic voids to form, and their orientation to couple to the crystal orientation. Preferred orientation of void space, which can influence processes, such as natural gas migration [4, 22, 23], has been reported for geological samples. For high explosives, void orientation could have a profound impact on shock sensitivity. The formation of locally heated regions (known as hot spots) under shock conditions is well accepted as

the source of initiation in heterogeneous HEs such as PBX 9502. Hot spots can originate from processes such as void collapse and jetting, and a definite void orientation with respect to a shock front can influence these processes. Recent numerical studies of the high explosive HMX have demonstrated that the orientation of a void (or crack) relative to the shock front plays a role in determining its response [24].

Ultra- and Small-angle scattering techniques employing neutrons (USANS/SANS) or X-rays (USAXS/SAXS) have become valuable tools for probing the microstructure of high explosives over length scales between 0.001 – 10 m, fully covering the critical range for hot spot formation [5, 15, 17, 25, 26]. A significant advantage of the techniques over other characterization methods is that they can be applied to as-pressed HE parts. This enables a quantitative measure of microstructural properties that are known to influence shock sensitivity, providing new perspectives on porosity.

As discussed later, previous small-angle scattering studies have utilized distinct void morphologies to quantify the porosity of TATB-based HEs [5, 15, 17]. The two approaches provide equivalent information [28], and a definitive determination of void morphology has not been made, though complementary techniques have found evidence of fractal structure in TATB [10-13]. Based upon this information, the current data, and our previous USANS and SANS measurements of consolidated TATB, in this work, we present a ramified description of the porosity in PBX 9502. Within the model, voids are considered as correlated structures with geometry given by a mass or volume dimension (Df). Additional parameters obtained from the analysis, such as the mean void size (r) and the surface dimension (Ds), allow a more global understanding of porosity and may provide insight into TATB thermal expansion mechanisms and PBX 9502 detonation properties.

This work describes USANS and SANS measurements that were performed on a uniaxially pressed sample of PBX 9502 in directions parallel and perpendicular to the pressing direction in order to characterize its porosity and to determine if microstructural voids become preferentially oriented as a result of the compaction process. A pressed cylinder of PBX 9502 was sectioned axially and radially to facilitate the measurements (Fig. 1). In this way, the current study represents a unique application of the scattering techniques to high explosive systems. Typically, samples are produced as thin cylinders, and radiation (neutrons

[a] J. T. MangLos Alamos National LaboratoryP. O. Box 1663Los Alamos, NM 87547 (USA)*E-mail:jtmang@lanl.gov

[b] R. P. HjelmLos Alamos National LaboratoryP. O. Box 1663Los Alamos, NM 87547 andNew Mexico Consortium Los Alamos, NM 87544 (USA)

or X-rays) is incident along the axis of the cylinder (in the pressing direction), permitting only the voids in the plane perpendicular to the pressing direction to be probed, in what we will call the compaction plane (Fig. 1). No preferred orientation of voids has been reported for TATB or PBX 9502 studies performed in this geometry [5, 15, 17]. Sectioning of the larger sample permitted voids perpendicular to the compaction plane to be assessed. Mean void size, volume and surface dimensions are reported at several depths in directions parallel and perpendicular to the compaction plane. Two-dimensional images of the void scattering patterns were obtained and evaluated for anisotropy. It was found that the voids in a uniaxially pressed piece of PBX 9502 are preferentially oriented in a plane perpendicular to the compaction plane.

2 Experimental Section Neutron scattering intensity, I(Q), is measured as a function of the scattering vector, Q, of magnitude Q = (4/)sin, where, is the wavelength of the incident neutrons and is half of the scattering angle [27]. Q is the scattering wave number having the dimension of inverse length, and smaller Q-values naturally correspond to larger length scales. Fluctuations in the neutron scattering length density, (r), within a sample give rise to coherent neutron scattering. In a pressed piece of PBX 9502, these fluctuations arise from the scattering length density contrast,among different components (TATB, Kel-F, voids) of the composite, that comprise the microstructure. The difference in the scattering length density between components in a material determines the ability to discern their interfaces. As the coherent neutron scattering intensity is proportional to the averaged squared fluctuations in the contrast Δ ρ2, and there is little difference between the scattering length density of TATB and Kel-F 800 (Table 1), giving a ratio of 29 in scaling of the intensity from TATB-void contrast, verses TATB-Kel-F 800 contrast. This is without taking into account the relatively small proportion of binder in PBX 9502. Thus, the measured scattering intensity from PBX 9502 arises primarily from the void phase ( = 0), contrasted with TATB and Kel-F. A simple two-phase approximation can then be used for analysis, with an average scattering length density ( = 4.83 x 1010 cm-2) for the TATB/Kel-F matrix. We verify in more detail the two phase approach below by comparison of scattering from PBX 9502, and a neat pressed

sample of TATB with the scattering from the internal structure of compression molded Kel-F.

Figure 1. PBX 9502 samples: (a) the original sample, highlighting the compaction plane (b) parallel and (c) perpendicular cut samples.

Table 1. Neutron scattering length densities.

Material Formula density (g/cc) (x 1010 cm-2)Kel-F 800 F11C8Cl3H2 1.998a 3.98

TATB C6H6N6O6 1.937b 4.89Void -- -- 0

a reference 29b references 6, 18, 30

The coherent scattering measured by USANS/SANS is proportional to the squared Fourier transform of (r), and thus possesses no phase information. Data analysis involves the development of a physical model and comparing its calculated scattering curve to the measured data. Due to the loss of phase information, the observed scattering sometimes is described by more than one physical model. This is true of the porosity in PBX 9502 and TATB systems, which have been accurately modeled as both randomly dispersed spherical and correlated, ramified morphologies [5, 15, 17, and 28]. Thus, distinct features in the measured scattering intensity can be indicative of either or both aspects of the void structure. Complementary techniques, that overlap the USANS size range, and are capable of providing real space images of the microstructure are also useful in this regard to understand to what

degree each aspect is important to the model. Recent micro (3 m resolution) [12] and nano x-ray computed tomography (30 nm resolution) studies, have found evidence of fractal pore networks [12, 13], and fractal surface properties of pores [13] in consolidated [12] and powder samples of TATB [13]. A fractal surface morphology of high explosives has been suggested, based upon SANS [8], SAXS [9], and atomic force microscopy measurements [10, 11]. The SAXS measurements performed on TATB indicated differences in surface properties depending upon material lot and manufacturer [9].

A fractal description of porosity in pressed high explosives considers the pores as a network of interconnected aggregates composed of a primary void structure. Within this description, the mean size of the primary void structure that forms a pore is quantifiable, along with a measure of its correlation (volume dimension) and surface properties (surface dimension). The scattered neutron intensity from a hierarchical system is recognizable by the appearance of one or more Guinier regions, indicated by a “knee” in the scattering curve, separated by a power-law decay of intensity with increasing Q. Guinier regions correspond to a hierarchy of characteristic, discrete length scales within the structure [31]. The power-law regions, where the scattered intensity decreases as Q-, describe the volume- or surface- geometry or void size polydispersity [32] of the scattering feature. In either case, can take on non-integer values. Here we borrow from the dimensional concepts of fractals, even though the structures are not necessarily fractal in the sense of being self-similar. For the case of volume dimension, the dimension, Df, and for surface roughness, the dimension is, Ds [33]. The parameters are readily derived from the measured USANS/SANS data and provide valuable insight into the network structure, void roughness and or polydispersity. The volume dimension (1 < Df < 3) is indicative of the void connectivity, with larger values of Df

indicating a more volume-filling or ramified network of voids. In comparison, the surface dimension (2 < Ds < 3) measures the degree of irregularity (or roughness) of the interface of voids with or adjacent to TATB crystals and or from polydispersity of the voids. A smooth interface from structure of uniform sizes would have = 4 and Ds = 2. We use the term surface dimension to indicate deviations from the Q-4 Porod scattering, due to surface roughness or polydispersity [32].

The current USANS and SANS data were analyzed as a two-phase system using an

empirical model that is a special case of the modified Ornstein-Zernike (MOZ) model utilized by Hurd et al [34]. The MOZ function was chosen because it returns comparable microstructural information to that of the model applied previously to high explosives [5], and unlike the previous model, the MOZ function is not restricted to isotropically scattering systems [25]. For porous systems, in the limit of an infinite fractal aggregate, the model provides a measure of the volume and surface dimensions and the primary void size:

I (Q )i =Ioi Q-Df (1+Q2r i

2 )Ds+ Df -62 , (1)

i = c, y or z and,

I( Q )c = ⟨I (Q cosϕ, Qsinϕ,0 ) ⟩0<ϕ<2π

I( Q )Y= ⟨ I (0, Q sinϕ, Qcosϕ ) ⟩- π

12 <ϕ+π2 < π

12

I( Q )Z = ⟨I (0, Q sinϕ, Q cosϕ ) ⟩ -π/12<ϕ<π/12.

Here, the intensity components are the averages taken over the azimuthal angle, (Fig. 2), over the indicated domain. In Eq. 1, the voids are considered as correlated volumes without a distinct shape. However, the void radius of gyration (rg) can be determined from the model parameters [34],

r gi=[ 3 (6−D s−Df )2 ]

12

r i.

(2)

Ioi (Eq. 1) is a constant, and in the limit of an infinite aggregate, has the units of cm-1-Df. Ioi

contains details of the microstructure, including the void volume fraction and the scattering length density contrast between the average scattering length density of the object, here, a void, and that of the surrounding media. For finite, randomly oriented objects Ioi can be utilized to calculate the void volume fraction. However, in the current case, where the physical extent of the pore structure is unknown, and anisotropy exists, Ioi

cannot be used in this capacity. As discussed later, the model-independent Porod Invariant method [27] is applicable for porosity determination in this case.

For the current study, PBX 9502 molding powder (lot 891-004) was uniaxially die pressed, at a temperature of 110 o C, into a 2.54 cm x 2.54 cm cylinder having a density of 1.893 ± 0.004 g/cc

(97.5% TMD), as determined by the Archimedes method. The cylinder was then cut, using a diamond saw blade, in directions parallel and perpendicular to the pressing direction (Fig. 1) to produce individual samples. Samples cut parallel to the compaction plane (Fig. 1b) had the shape of a semi-circular disk (r = 1.27 cm, t = 0.15 cm) and those cut perpendicular (Fig. 1c) to the compaction plane were rectangular solids (l = 2.54 cm, w = 2.54 cm, t = 0.15 cm). Five parallel cut samples were studied, corresponding to positions ranging from 0.45 - 1.35 cm from the top of the original sample (Table 2). Perpendicular cut samples, centered at 0.075 and 0.225 cm from the original cylinder axis (Table 2), were each probed at two locations (top and middle). Neutron transmissions were ~ 0.9 for all of the samples studied, so no correction for multiple scattering was required during analysis [5].

Table 2. PBX 9502 samples and their locations relative to the original pressed cylinder.

Parallel Cut SamplesSample Locationa Area Probed

C-1 0.45 MiddleC-2 0.60 MiddleC-3 0.90 MiddleC-4 12.0 MiddleC-5 13.5 Middle

Perpendicular Cut SamplesSample Locationb Area Probed

E-1t 0.075 Top E-1m 0.075 MiddleE-2t 0.225 Top

E-2m 0.225 Middle a(distance from top, mm) b(distance from axis, mm)

USANS and SANS measurements were performed at the National Institute of Standards and Technology Center for Neutron Research (NCNR) using the BT-5 Perfect Crystal SANS instrument [35] with a monochromatic incident neutron beam with wavelength of 0.24 nm and the NGB 30-m SANS instrument [36] using a wavelength of 0.5 nm. The BT-5 instrument is a Bonse-Hart camera with a maximum effective Q-range of 0.0003 – 0.1 nm-1. Three different detector distances (1, 8, and 13 meters) were used on the NGB instrument to obtain a Q-range of 0.017 – 5.3 nm-1. The combination of the two instruments probed pores in the size range from 0.001 – 10 m. Data were reduced by conventional methods and corrected for empty cell and background scattering [37]. The USANS data obtained from BT-5 were corrected for slit smearing using the well-known Lake procedure [38, 39], allowing the scattering data from the two

instruments to be combined into a single curve. USANS data from samples exhibiting anisotropic scattering were rescaled according to the method derived by Gu and Mildner [4, 22, 23].

The SANS instrument (NGB) utilizes a two dimensional detector to record the scattered neutrons. Samples that were cut parallel (Fig. 1b) to the compaction plane (Qy-Qx plane) produced symmetric equal-intensity (azimuthally isotropic) scattering contours and were azimuthally averaged to obtain I(Q)c vs. Q scattering curves (Fig. 2a). Perpendicular (Fig. 1c) cut samples (Qy-Qz plane) produced asymmetric (anisotropic) elliptical, equal-intensity scattering contours and were reduced to an I(Q)i vs. Q format by taking sector ( = ±15o) averages in the horizontal (Qy, = 90o, 270o) and vertical (Qz, = 0o, 180o) directions of the detector plane (Fig. 2b). To quantify the degree of anisotropy, the scattering intensity as a function of the azimuthal angle () for an annular ring of a chosen Q-value (Qo) was obtained for the parallel and perpendicular cut samples. A hallmark of anisotropic scattering is the appearance of intensity peaks, corresponding to scatter from the short axis of the voids ( = 0), in a plot of I(,Qo) vs which can be expressed as [4, 22, 23],

I (ϕ ,Q o )= Qo-α (a−2[cos2ϕ+(ab )

2

sin2ϕ ])-α2

.

(3)

In Eq. 3, a/b is the void aspect ratio, and is the exponent determined from analysis of the sector average. For isotropic scattering (a/b = 1) the plot of I(,Qo) is a flat line, as anticipated from Eq. 3.

In contrast to NGB, which has pinhole collimation geometry and a 2-dimensional detector, the BT-5 instrument utilizes single slit collimation geometry and a single channel detector. This geometry accesses only one dimension along the line of the collimated incident beam. A single measurement on BT-5 was sufficient for the samples cut parallel to the compaction plane, but two separate measurements, one along Qy and one along Qz, were required to characterize the larger length scale anisotropy in the perpendicular cut samples.

3 Results and Discussion3.1 Scattering ResultsExamples of the two dimensional scattering patterns obtained at a detector distance of 13

meters from samples cut parallel (C-5) and perpendicular (E-1m) to the compaction plane, at the ~ center of the original pressed cylinder, are shown in Figure 2. Scattering from C-5 resulted in circular equal-intensity, isotropic (Fig 2a) contours and elliptical equal-intensity, anisotropic contours were generated by E-1m (Fig 2b).

Figure 2. Equal intensity contour plots from samples C-5 and E1m, indicating azimuthal (a) and sector averages (b). Qz in (a) and Qx in (b) are perpendicular to the plane of the image.

The isotropic scattering contours of sample C-5 imply that voids, as viewed along the compression axis, have approximately circular shape or random orientation within the compaction plane that confers azimuthal symmetry about the normal to the plane. In contrast, the anisotropic scattering contours arising from E-1m indicate a preferred orientation of non-spherical voids perpendicular to the compaction plane. The long axis of the anisotropic intensity contours lie along Qz (perpendicular to the compaction plane), indicating that the void dimension in this direction is smaller than that within the compaction plane. This implies that during pressing the voids become flattened within the compaction plane. An oriented,

oblate ellipsoidal void morphology or a tri-axial ellipsoid is consistent with these observations. Their projection into the compaction plane is circular or randomly oriented, which accounts for the circular contours measured for sample C-5 in light of the elliptical contours of E-1m.

Figure 3. SANS curves from averaging the circular contours of the parallel cut sample (Ic, C-5) and sector averaging the elliptical contours of the perpendicular cut sample (Iy and Iz, E1m).

The two-dimensional data of figure 2 were azimuthally or sector averaged as a function of Q to produce the scattering curves shown in Fig. 3. Ic(Q) corresponds to sample C-5 and was obtained by averaging over -values from 0 to 360o. Iy(Q) and Iz(Q) pertain to sample E-1m and, due to the observed anisotropy, were obtained by performing 30o sector averages centered along the Qy and Qz

axes, respectively. As seen in figure 3, Iy(Q) and Ic(Q) are coincident, indicating that they correspond to the same void dimension within the compaction plane. Iz(Q) has a larger intensity than either Iy(Q) or Ic(Q), supporting the notion that Iz(Q) derives from a distinct void dimension. All three curves arise from interfacial scattering and can be represented by a simple power law, I(Q) = IoQ-. An average value of = 3.79 ± 0.03 was determined for the three curves, corresponding to an average surface dimension of Ds = 2.21 ± 0.03.

Figure 4. Azimuthally averaged data for the parallel and perpendicular cut samples (C-5 & E1m). The solid lines are fits to Eq. 3 to determine the void aspect ratio.

Figure 4 shows the SANS scattering intensity as a function of the azimuthal angle () for the annular ring, Q = 0.1 nm-1, for samples C-5 and E-1m. The anisotropy of E-1m is evident in the resulting curve that displays peaks at angles corresponding to the ±Qz axis, whereas the C-5 curve is flat, confirming the SANS isotropy due to the circular symmetry of the void population within the compaction plane. The scattering curve from E-1m was fit to Eq. 3 to determine the void aspect ratio, a/b = 1.19 ± 0.01 (Table 3), with Q = 0.1 nm-1

and = 3.79. Analysis of annular rings centered at different Q-values gave identical aspect ratios. As anticipated from the uniform, circular contours, a similar fit of the data from sample C-5 yielded a/b = 1.00 ± 0.01.

Desmeared USANS data from the C-5 and E-1m samples are shown in Fig. 5 along with the corresponding SANS curve on a log-log scale. USANS data, Iz(Q) (Fig. 5a) and Iy(Q) (Fig. 5b), were obtained from measurements along the Qz

and Qy directions of sample E-1m, and Ic(Q) (Fig. 5c) corresponds to a single measurement in the center of sample C-5.

Distinct features are visible in the USANS scattering curves. Each curve displays a region of power-law scattering at the lowest Q-values, followed by a Guinier region that corresponds to a characteristic void size within the microstructure. Power-law fits of each USANS curve over the Q-range between 3.5 x 10-4 – 5.0 x 10-3 nm-1 yielded

an average exponent value of 1.58 ± 0.01. Good overlap of the USANS and SANS data sets was obtained, facilitating analysis of the combined curves with the MOZ model.

The features of the E-1m and C-5 scattering curves are consistent with a ramified network of voids within the PBX 9502 microstructure. The low-Q power-law observed in USANS suggests a volume structure (Df = 1.58 ± 0.01) for the pore network. The Guinier region arises from the primary void structure, and the interfacial scattering suggests rough interfaces between the primary phase (TATB/Kel-F) and the voids and/or a distribution of the rc-ry radii of the ellipsoids.

Comparison of the scatter from C-5 with those from Kel-F 800 and neat compressed TATB in Fig. 5c validates the use of the two phase model in our analysis, The coherent neutron scattering from the internal structure of the Kel-F binder is more than three orders of magnitude lower than that from the PBX 9502 sample for Q-values less than 0.01 nm-1. For larger Q-values, near the signature of the Kel-F domain structure, the scattering from the binder remains more than an order of magnitude lower than the coherent signal from PBX 9502. The SANS scattering from a neat pressed sample of TATB (Fig. 5c) at a similar pressed density (1.891 g/cc) as the PBX 9502 sample (1.893 g/cc) shows the same void surface properties as PBX 9502, suggesting no influence of the scatter from the binder in this Q-range.

Table 3. Void Parameters for Perpendicular Cut Samples.

Sample ry (nm) rz (nm) ry/ rz a/b H

E-1t -- -- -- 1.20 ± 0.01 0.099

E-1m 95 ± 4 85 ± 3 1.13 ± 0.06

1.19 ± 0.01 0.091

E-2t -- -- -- 1.20 ± 0.01 0.102

E-2m 94 ± 4 83 ± 3 1.13 ± 0.06

1.19 ± 0.01 0.093

The solid lines in figure 5 are the results of fits of the MOZ model to the combined USANS/SANS

Figure 5. USANS and SANS data for the, a, E1m

and, b, C-5 samples. Power-law dimensional features are evident in the data. The solid lines are fits to the MOZ model. c: Comparison of scattering data from C-5 (center) with compressed neat TATB and Kel-F 800 USAXS and SANS. USAXS data from Kel-F 800 has been scaled by the ratio of the neutron to x-ray scattering length densities and overlaps the data from Kel-F 800. Neat TATB SANS has been rescaled for clarity. The data overlapped the PBX 9502 data before scaling.

scattering curves. During fitting, values for Df and Ds were fixed to their mean values. Primary void sizes obtained through analysis are summarized in Tables 2 & 3. The resulting primary void aspect ratio, ry/rz = 1.13 ± 0.06, is in good agreement with that found from analysis of the elliptical contours (Table 3). rc was found to be equivalent to ry as expected from the SANS analysis (Table 4).

Additional USANS and SANS measurements were made at the center of a second perpendicular cut sample, E-2m (Fig. 6), which was cut farther from the axis of the original PBX 9502 cylinder (Table 2). Anisotropy, resembling that of the sample E-1m was observed, and had an identical void aspect ratio of a/b = 1.19 ± 0.01, determined through analysis of the annular ring centered at Q = 0.1 nm-1 (Fig. 6). Average values for Df (1.57 ± 0.01) and Ds (2.20 ± 0.02) were determined by power law analysis. Utilizing these average values, the combined curves (Fig. 7) were analyzed using the MOZ model. The void aspect ratio, ry/rz = 1.13 ± 0.06, agrees with that determined by analysis of the azimuthal data. All of the pore parameters obtained for E-2m are similar to the values obtained for E-1m (Table 3), indicating little variation of the microstructure over this distance.

Figure 6. Azimuthally averaged data for C-5 & E2m. Inset: Elliptical contours measured for sample E2m.

SANS measurements were performed on each perpendicular cut sample at a second location, near the top of the sample to determine if the void aspect ratio changed along the sample axis. The scattering anisotropy of the

perpendicular cut samples (E-1t and E-2t) is readily contrasted with the uniform scattering of the sample cut parallel to the compaction plane (C-1) in the combined contour plots of figure 8. Analysis of the SANS data from samples E-1t and E-2t for the annular ring centered at Q = 0.1 nm-1, according to Eq. 3, revealed a void aspect ratio of 1.20 ± 0.01 for E-1t and E-2t, equivalent to that measured at the sample center (Table 3).

Figure 7. Combined USANS and SANS data for the E2m sample. Power-law dimensional features are evident in the data. The solid lines are fits to the MOZ model.

Table 4. Void Parameters for Parallel Cut Samples

Sample rc (nm)C-1 101 ± 2C-2 99 ± 2

C-3 99 ± 2C-4 98 ± 2C-5 100 ± 2

USANS and SANS measurements were also made on parallel cut samples at several positions along the axis of the original sample. All of these samples displayed circular equal-intensity contours, indicating no preferred orientation of the voids. Analysis of the combined USANS/SANS curves revealed no significant variation in pore structure (Df = 1.57 ± 0.01), surface dimension (Ds

= 2.21 ± 0.01), or primary pore size along the sample axis (Table 4).

Figure 8. Combined contour plots for the perpendicular cut samples (a) E-1t and (b) E-2t

with the corresponding parallel cut sample, C-1.

The scattering contours provide evidence of preferred void orientation, from which quantification of the degree of void orientation, through calculation of the Hermans orientation parameter, will be important in determining the

influence that void alignment has on the shock properties of PBX 9502. The Hermans orientation parameter, H, is given by [4, 22, 23, 40]:

H= 3⟨cos2ϕ ⟩ -1

2, where,

⟨ cos2 ϕ ⟩=∫

0

π2

I (ϕ ) cos2 (ϕ )sin (ϕ ) dϕ

∫0

π2

I ( ϕ) sin (ϕ ) dϕ

.

(4)

In equation 4, I() is the azimuthal scattering intensity centered at a given Q-value (Fig. 4), and the angle brackets represent an average over I. For randomly oriented voids H = 0, and H = 1 for uniform void orientation. For the samples discussed here, H ranged from 0.091 – 0.102 (Table 3), indicating weak orientational order.

Determination of the total porosity () of a pressed HE part is critical to understanding shock sensitivity and detonation velocity [2, 20]. This is especially true when investigating the influence of mechanical and/or thermal insult on HE microstructure. For pristine samples, is typically measured by bulk volumetric or Archimedes methods, but can also be calculated from USANS and SANS data. This ability is particularly useful for quantifying the void volume fraction of materials after an insult when bulk or Archimedes methods are inapplicable. For a two-phase porous system, the Porod Invariant is commonly used to calculate porosity as it provides a model-independent determination of

QP3d =∫0

∞

I (Q )d3 Q =8 π3 Δρ2Φ (1-Φ ) .

For three-dimensionally isotropic scattering samples, the small-angle scattering intensity is independent of direction. The three dimensional integral that defines the scattering invariant can be reduced to one dimension, and it is straight forward to calculate [27],

QP =∫0

∞

Q2 Ip (Q )dQ =2 π2Δρ2 Φ (1-Φ ) . (5)

In Eq. 5, Ip(Q) is the powder averaged scattering intensity. For the current anisotropically scattering

samples, determination of is more complex. As the scattering intensity from a sample cut along the compression axis is dependent upon the azimuthal angle (Eq. 3), the Porod Invariant is two-dimensional. Straightforward application of Eq. 5 to either the parallel or perpendicular cut samples, can lead to an erroneous determination of the total porosity. Currently, the most accurate method for determining the porosity from USANS/SANS data of anisotropically scattering samples is through calculation of the modified Porod Invariant that accounts for anisotropy. For anisotropically scattering porous materials, Gu and Mildner [23] showed that the powder averaged scattering intensity can be expressed as, Ip = pQ-, and the invariant can again be written as a one dimensional integral in Q [23],

QP1d =QP3d

4π=∫

0

∞

pα Q2-α dQ=2 π2 Δρ2 Φ (1-Φ ),

(6) where,

pα = bα∫0

π2

( 1-k2 [cosϕ ]2 )- α

2 sinϕ dϕ; k2=1 -(ba )

2.

(7)

Eq. 7 can be solved analytically, and relationships among Ip (Q), Iz (Q), and Iy (Q) obtained [23],

Ip (Q ) = (ab )-2α3 I

z(Q ) = (ab )

α3 I

y(Q ).

(8)

Eq. 8, utilizing the relationship with Iz(Q) or Iy(Q), can be substituted into Eq. 5 in order to determine . The fitted model functions were used to calculate the Invariant in order to extrapolate to the limits of the integral in Eq. 5. The average total porosity determined for samples E-1m and E-2m, using both forms of Ip(Q), are listed in Table 5, and are in good agreement with the value determined for the original pressed cylinder of PBX 9502. Values of the volume fraction, calculated with Eq. 5, and utilizing the Z, Y and c scattering components without the anisotropy correction, are listed in Table 5 for comparison.

Table 5. Total Sample Porosity

Sample Z Y c

Cylinder 0.025 ± 0.002a -- -- --

E-1m 0.027 ± 0.003b 0.039c 0.023c 0.024c

E-2m 0.027 ± 0.003b 0.039c 0.023c 0.024c

a(Archimedes method) b(average using IZ or IY in Eq. 5) c(not corrected for anisotropy)

3.2 DiscussionProcessing parameters are known to influence

the microstructure of a consolidated piece of a high explosive. In turn, HE shock properties and performance are linked to its microstructure. The current study has revealed that pores within a uniaxially-pressed sample of PBX 9502 possess a ramified volume dimensional structure. Df was found to be equal in directions parallel and perpendicular to the compaction plane, suggesting that the geometry of the void correlations is similar, regardless of the direction of the view. However, the primary voids that comprise the aggregate are non-spherical and have a preferred orientation with the larger axis in the compaction plane.

Preferred void orientation can affect the shock propagation within a HE. This effect may be significant for insensitive high explosives, such as PBX 9502, whose ignition and performance depend upon exacting criteria. Measurement of the two dimensional scattering pattern via SANS provides several new pieces of microstructural information, including the void alignment angle, void aspect ratio, and the degree of void orientation. The Hermans orientational parameter is useful as it can be readily quantified as a function of pressing conditions, for example, permitting a thorough understanding of void orientation that may assist the further development of microstructural-aware performance models [41]. Void alignment is readily determined from the orientation of the equal-intensity contours (Fig. 2b). For the current samples, voids were best described as ellipsoids with the larger, rc-ry

preferentially oriented within the compaction plane.

Historically, PBX 9502 performance as measured by corner turning ability varies among material lots [42]. It has been surmised that subtle differences in the microstructure are at the root of these variations. Indeed such microstructural variation can be anticipated as the size and shape of TATB crystallites and molding powder prills differ among lots. Control of the final microstructure then, may alleviate the known performance variations. The current measurements provide a means to extract new and potentially valuable microstructural information that can help unravel the performance

puzzle of PBX 9502. Using the scattering tools described here, quantification of subtle microstructural variations, including void size, shape and degree of orientation is possible. This level of detail may permit fine-tuning of processing and pressing conditions for the purpose of producing a uniform microstructure, and hence performance among PBX 9502 lots; thus, overcoming their inherent differences.

4 ConclusionUSANS and SANS techniques were applied to measure the porosity, in directions parallel and perpendicular to the compaction plane, of a uniaxially pressed cylinder of PBX 9502. These measurements represent a unique application of small angle scattering techniques to high explosives. Two-dimensional scattering patterns of samples cut parallel to the compaction plane gave rise to circular equal intensity contours that are indicative of randomly oriented and or azimuthally symmetrical void structures as viewed down the compression axis. In contrast, equal intensity scattering contours from samples cut perpendicular to the compaction plane were found to be elliptical, indicating that the voids are non-spherical and preferentially oriented in the compression plane.

Analysis of the azimuthally averaged data revealed that the microstructural voids are oblate ellipsoids with an average aspect ratio of 1.20, with the larger, rc-ry axis of the voids lying within the compaction plane. Combined USANS and SANS analysis using the MOZ model confirmed the void aspect ratio obtained from the azimuthal analysis, and suggested that the pores have a special correlation with geometry best described as a ramified structure. It is interesting that this association is the same for the compaction plane as for the plane perpendicular to it. Thus, the void correlation geometry from the pore volume fractal dimension was found to be the same in all directions. Void interfaces with the surrounding TATB/Kel-F were found to deviate from Q-4 Porod scatter, with a common surface dimension in all directions, from roughness and/or polydispersity.

Additional analysis of the SANS data revealed more detailed information on the degree of void orientation and the total porosity of the PBX 9502 samples. Along with the structural information, these results add another layer of microstructural detail that can be exploited during high explosive pressing activities to produce uniform microstructures across material lots, and inform

newly developed microstructural-aware models of high explosive performance.

Symbols and Abbreviations Void volume fraction Azimuthal detector angle Neutron wavelength Scattering length density Scattering length density contrastDf Volume dimensionDs Surface dimensionH Hermans parameterHE High explosiveI(Q) Differential cross section per unit volumeIp Powder averaged scattering intensityKel-F Poly(chlorotrifluoroethylene-co-vinylidene fluoride)MOZ Modified Orstein-ZernikeQ Scattering VectorQ Magnitude of the scattering vectorQP Porod invariantR Spherically equivalent radiusr radius of voidry r in the Qy directionrz r in the Qz directionrc r parallel to the compaction planeSANS Small-angle neutron scatteringTATB 1,3,5-Triamino-2,4,6-trinitrobenzeneTMD Theoretical maximum densityUSANS Ultra-Small-angle neutron scattering

AcknowledgementsWe acknowledge the support of the National

Institute of Standards and Technology, U.S. Department of Commerce, in providing neutron research facilities used in this work. Access to BT-5 was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under Agreement No. DMR-1508249.

References[1] P. Lamy, L. Brunet and G. Thomas, Modeling

the Porosity Evolution of a Powder under Uniaxial Compression, Propellants, Explos., Pyrotech. 2005, 30, 397.

[2] L. G. Hill, D. G. Thompson and H. H. Cady, On the Ratchet Growth of TATB-Based Explosives, Technical Report LA-UR-1102208, Los Alamos National Laboratory 2011.

[3] R. Lapovok, D. Tomus, J. Mang, Y. Estrin and T. C. Lowe, Evolution of Nanoscale Porosity

during Equal-Channel Angular Pressing of Titanium, Acta Mater. 2009, 57, 2909.

[4] X. Gin, D. R. Cole, G. Rother, D. F. R. Mildner and S. L. Brantley, Pores in Marcellus Shale: A Neutron Scattering and FIB-SEM Study, Energy Fuels 2015, 29, 1295.

[5] J. T. Mang and R. P. Hjelm, Fractal Networks of Inter-Granular Voids in Pressed TATB, Propellants, Explos., Pyrotech. 2013, 38, 831.

[6] B. Olinger, Compacting Plastic-Bonded Explosive Molding Powders to Dense Solids, Technical Report LA-14173, Los Alamos National Laboratory 2005.

[7] L. M. Anovitz, G. W. Lynn, D. R. Cole, G. Rother, L. F. Allard, W. A. Hamilton, L. Porcar, M. H. Kim, A New Approach to Quantification of Metamorphism Using Ultra-Small and Small Angle Neutron Scattering, Geochim. Cosmochim. Acta 2009, 73, 7303.

[8] C. A. Stoltz, B. P. Mason, J. Hooper, Neutron Scattering Study of Internal Void Structure in RDX, J. Appl. Phys. 2010, 107, 103527.

[9] D. M. Hoffman, T. M. Willey, A. R. Mitchell, S. C. Depiero, Comparison of New and Legacy TATBs, J. Energ. Mater. 2008, 26, 139.

[10] K. M. Cheng, X. Y. Liu, D. B. Guan, T. Xu, Z. Wei, Fractal Analysis of TATB-Based Explosive AFM Morphology at Different Conditions, Propellants, Explos. Pyrotech. 2007, 32, 301.

[11] Y. Wang, X. Song, D. Song, W. Jiang, H. Liu, F. Li, Dependence of the Mechanical Sensitivity on the Fractal Characteristics of Octahydro- 1,3,5,7-tetranitro-1,3,5,7-tetrazocine Particles, Propellants, Explos. Pyrotech. 2011, 36, 505.

[12] C. S. Woznick, D. G. Thompson, R. DeLuca, B. Patterson, T. A. Shear, Thermal Cycling and Ratchet Growth of As-Pressed TATB Pellets, in Shock Compression of Condensed Matter – 2018 AIP Conference Proceedings (American Institute of Physics, Melville, NY, 2018).

[13] Liang Chen, LiHui Wu, Yu Liu, and Wei Chen, In Situ Observation of Void Evolution in 1, 3, 5-triamino-2,4,6-trinitrobenzene under compression by Synchrotron Radiation X-ray nano-Computed Tomography, J. Synchrotron Rad. 2020, 27 127.

[14] H. L. Berghout, S. F. Son, C. B. Skidmore, D. J. Idar and B. W. Asay, Combustion of Damaged PBX 9501 Explosive, Thermochim. Acta 2002, 384, 261.

[15] D. G. Thompson, G. W. Brown, B. Olinger, J. T. Mang, B. Patterson, R. De Luca and S. Hagelberg, The Effects of TATB Ratchet Growth on PBX 9502, Propellants, Explos., Pyrotech. 2010, 35, 507.

[16] D. G. Thompson, C. Woznick and R. Deluca, Thermal Cycling and Ratchet Growth of TATB and PBX 9502, Propellants, Explos., Pyrotech. 2019, 44, 850.

[17] T. Willey, T. van Buuren, J. Lee, G. Overturf, J. Kinney, J. Handly, B. Weeks and J. Ilavsky, Changes in Pore Size Distribution Upon Thermal Cycling of TATB-based Explosives Measured by Ultra-Small Angle X-ray Scattering, Propellants, Explos., Pyrotech. 2006, 31, 466.

[18] C. B. Skidmore, T. A. Butler and C. W. Sandoval, The Elusive Coefficients of Thermal Expansion in PBX 9502, Technical Report LA-14003, Los Alamos National Laboratory 2003.

[19] D. J. Luscher, M. A. Buehler, N. A. Miller, Self-consistent modeling of the influence of texture on the thermal expansion in polycrystalline TATB, Modeling Simul. Mater. Sci Eng. 2014, 22, 075008.

[20] R. N. Mulford and J. A. Romero, Sensitivity of the TATB-Based Explosive PBX-9502 after Thermal Expansion, AIP Conference Proceedings 1998, 429, 723.

[21] R. B. Schwarz, G. W. Brown, D. G. Thompson, B. Olinger, J. Furmanski and H. H. Cady, The Effect of Shear Strain on Texture in Pressed Plastic Bonded Explosives, Propellants, Explos., Pyrotech. 2013, 38, 685–694.

[22] X. Gu and D. F. R. Mildner, Ultra-Small-Angle Neutron Scattering with Azimuthal Asymmetry, J. Appl. Crystallogr. 2016, 49, 934.

[23] X. Gu and D. F. R. Mildner, Determination of Porosity in Anisotropic Fractal Systems by Neutron Scattering, J. Appl. Crystallogr. 2018, 51, 175.

[24] N. K. Rai, M. J. Schmidt and H. S. Udaykumar, Collapse of Elongated Voids in Porous Energetic Materials: Effects of Void Orientation and Aspect Ratio on Initiation, Phys. Rev. Fluids 2017, 2, 043201.

[25] J. T. Mang, R. P. Hjelm and E. G. Francois, Measurement of Porosity in a Composite High Explosive as a Function of Pressing Conditions by Ultra-Small-Angle Neutron Scattering with Contrast Variation, Propellants, Explos., Pyrotech. 2010, 35, 7.

[26] J. T. Mang and R. P. Hjelm, Small-Angle Neutron Scattering and Contrast Variation Measurement of the Interfacial Surface Area in PBX 9501 as a Function of Pressing Conditions, Propellants, Explos., Pyrotech. 2011, 36, 439.

[27] Small Angle X-ray Scattering (Eds: O. Glatter and O. Kratky), Academic Press, London, 1982.

[28] C. L. Armstrong and J. T. Mang, In-situ Small- and Ultra-Small Angle Neutron Scattering of Heated PBX 9502, 16th Symposium (International) on Detonation, Cambridge, MD, July 15 – 20, 2018.

[29] Ari S. Benjamin, Muhtar Ahart, Stephen A. Gramsch, Lewis L. Stevens, E. Bruce Orler, Dana M. Dattelbaum, and Russell J. Hemley, Acoustic Properties of Kel- F-800 Copolymer up to 85 GPa, J. Chem. Phys. 2012, 137, 014514.

[30] LASL Explosive Property Data (Eds: T. R. Gibbs and A. Popolato), University of California Press, Berkeley and Los Angeles, 1980.

[31] J. H. Lee, G. Beaucage, S. E. Praatsinis and S. Vemury, Fractal Analysis of Flame-Synthesized Nanostructured Silica and Titania Powders using Small-Angle X-ray Scattering, Langmuir 1998, 14, 5751.

[32] P. Pfeifer, Chemistry in Noninteger Dimensions Between Two and Three. I. Fractal Theory of Heterogeneous Surfaces, J. Chem. Phys. Rev. 1983, 79, 3558.

[33] J. Teixeira, Small-Angle Scattering by Fractal Systems, J. Appl. Crystallogr. 1998, 14, 5751.

[34] A. J. Hurd, D. W. Schaefer, and J. E. Martin, Surface and Mass Fractals in Vapor-Phase Aggregates, Phys. Rev. A 1987, 35, 2361.

[35] J. G. Barker, C. J. Glinka, J. J. Moyer, M. H. Kim, A. R. Drews and M. Agamalian, Design and Performance of a Thermal-neutron Double-Crystal Diffractometer for USANS at NIST, J. Appl. Cryst. 2005, 38, 1004.

[36] C. J. Glinka, et al., The 30 m Small-Angle Neutron Scattering Instruments at the National Institute of Standards and Technology, J. Appl. Crystallogr. 1998, 31, 430.

[37] S. R. Kline, Reduction and Analysis of SANS and USANS Data Using IGOR Pro, J. Appl. Crystallogr. 2006, 39, 895.

[38] J. A. Lake, An Iterative Method of Slit-Correcting Small Angle X-ray Data, Acta Crystallogr. 1967, 23, 191.

[39] J. Ilavsky and P. R. Jemian, Irena: tool suite for modeling and analysis of small-angle scattering, J. Appl. Crystallogr. 2009, 42, 347.

[40] M. M. Malwitz, S. Lin-Gibson, E. K. Hobbie, P. D. Butler and G. Schmidt, Orientation of Platelets in Multilayered Nanocomposite Polymer Films, J. Polym. Sci. Part B: Polym. Phys. 2003, 41, 3237.

[41] W. L. Perry, B. Clements, X. Ma and J. T. Mang, Relating Microstructure Temperature

and Chemistry to Explosive Ignition and Shock Sensitivity, Combust. Flame 2018, 190, 171.

[42] L. G. Hill and T. R. Salyer, The Los Alamos Enhanced Corner Turning (ECOT) Test, 16th

Symposium (International) on Detonation, Cambridge, MD, July 15 – 20, 2018.