**Predicting Macroscale Effects Through Nanoscale Features**

Victor J. Bellitto1 and Mikhail I. Melnik2 *1Naval Surface Warfare Center 2School of Engineering Technology, Southern Polytechnic State University, Marietta, GA USA* 

#### **1. Intoduction**

174 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

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Atomic force microscopy is extremely useful in the study of surface defects in crystals by providing topographical data at the nanometric scale. With the aide of advanced statistical analysis, nanoscale surface data acquired through atomic force microscopy can also be utilized to predict behavior at the macroscale. The behavioral model presented is the measure of shock sensitivity required to produce detonation of explosive crystal test samples. The surfaces studied were of 7 different varieties of (RDX) crystalline explosives from 5 manufacturers (Doherty & Watts, 2008). It has been speculated that particle size, crystal defects, density and crystal morphology may play a role in the shock sensitivity of RDX and there have been numerous attempts to quantify and/or link particular features of the explosive particles to the shock sensitivity behavior of their larger compositions (Doherty and Watts, 2008). The shock sensitivity data were obtained from model test compositions prepared as polymer-bonded explosives using hydroxy-terminated polybutadiene (HTPB) as the binder. The shock sensitivity, measured in a gap test, is the shock required to produce a detonation of the test composition 50% of the time. Varied card thicknesses of poly(methyl-methacrylate) (PMMA) are used to attenuate the initiating charge entering the sample tube. The shock pressure (GPa) impacting the sample is determined by the number of cards. A small number of cards translate to a larger shock and thus a less shock sensitive sample.

#### **2. Experimental**

The AFM analysis of the RDX crystal surfaces was performed using a Multimode V scanning probe microscope (Veeco Metrology Group). The instrument was operated in Tapping Mode, where topographical analysis is performed with minimal contact of the surface. The crystal topography is mapped by lightly tapping the surface with an oscillating probe tip. The sample surface topography modifies the cantilever's oscillation amplitude and the topography image is obtained by monitoring these changes while closing the z feedback loop to minimize them. A first order algorithm supplied by Veeco was used to "flatten" the images. The flatten command modifies the scanned image removing tilt and thus leveling the image.

Predicting Macroscale Effects Through Nanoscale Features 177

Fig. 2. AFM scan images obtained from the same particle of material II. A roughness measurement of 9.81 nm was obtained for image on the left while 24.4 nm was obtained for

Fig. 3. AFM scan images obtained from the same particle of material III. A roughness measurement of 9.31 nm was obtained for image on the left while 21.5 nm was obtained for

image on the right.

image on the right.

A variety of surface features were observed including edge and screw dislocations, voids, cracks, peaks, valleys, plateaus, etc. Examples of images acquired of the RDX particles surfaces are shown in Fig. 1-7. They are presented as amplitude images since they more easily display the shape of the sample surface. The amplitude image is equivalent to a map of the slope of the sample. The z-scale shows the tip deflection as it encountered sample topography. The amplitude image on harder samples better highlights the edges of features while on softer samples it can depict subsurface features better than the topography image.

The root mean square (*RMS*) calculation (R) of the surface imagery acquired in height mode was used to determine the roughness and to quantify the different surface topologies. The roughness was calculated by finding the median surface height for the scanned image and then evaluating the standard deviation. The equation for determining the surface roughness is

$$R\_1 = \left(\frac{1}{MN} \sum\_{k=0}^{M-1} \sum\_{l=0}^{N-1} \left[ z\left(\boldsymbol{x}\_{k'} \boldsymbol{y}\_l\right) - \boldsymbol{\mu} \right]^2\right)^{0.5}$$

where μ is the mean value of the height, *z*, across in-plane coordinates *(x,y)*:

$$\mu = \frac{1}{\text{MN}} \sum\_{k=0}^{M-1} \sum\_{l=0}^{N-1} z(x\_{k'} y\_l) \dots$$

The necessity to add objectivity to the consistency across the surface is demonstrated by Fig. 1-7. Although the side by side images obtained are from the same particle they demonstrate two very different surface morphologies and/or different roughness measurements.

Fig. 1. AFM scan images obtained from the same particle of material I. A roughness measurement of 18.9 nm was obtained for image on the left while 29.6 nm was obtained for image on the right.

A variety of surface features were observed including edge and screw dislocations, voids, cracks, peaks, valleys, plateaus, etc. Examples of images acquired of the RDX particles surfaces are shown in Fig. 1-7. They are presented as amplitude images since they more easily display the shape of the sample surface. The amplitude image is equivalent to a map of the slope of the sample. The z-scale shows the tip deflection as it encountered sample topography. The amplitude image on harder samples better highlights the edges of features while on softer samples it can depict subsurface features better than the topography image. The root mean square (*RMS*) calculation (R) of the surface imagery acquired in height mode was used to determine the roughness and to quantify the different surface topologies. The roughness was calculated by finding the median surface height for the scanned image and then evaluating the standard deviation. The equation for determining

> 0.5 <sup>2</sup> 1 1

*k l*

,

*k l*

0 0 <sup>1</sup> , *M N*

 

1 1

0 0 <sup>1</sup> , *M N*

 .

The necessity to add objectivity to the consistency across the surface is demonstrated by Fig. 1-7. Although the side by side images obtained are from the same particle they demonstrate

*k l zx y MN*

two very different surface morphologies and/or different roughness measurements.

Fig. 1. AFM scan images obtained from the same particle of material I. A roughness

measurement of 18.9 nm was obtained for image on the left while 29.6 nm was obtained for

*k l R z <sup>x</sup> <sup>y</sup> MN*

where μ is the mean value of the height, *z*, across in-plane coordinates *(x,y)*:

the surface roughness is

image on the right.

Fig. 2. AFM scan images obtained from the same particle of material II. A roughness measurement of 9.81 nm was obtained for image on the left while 24.4 nm was obtained for image on the right.

Fig. 3. AFM scan images obtained from the same particle of material III. A roughness measurement of 9.31 nm was obtained for image on the left while 21.5 nm was obtained for image on the right.

Predicting Macroscale Effects Through Nanoscale Features 179

Fig. 6. AFM scan images obtained from the same particle of material VI. A roughness measurement of 1.07 nm was obtained for image on the left while 3.7 nm was obtained for

Fig. 7. AFM scan images obtained from the same particle of material VII. A roughness measurement of 2.9 nm was obtained for image on the left while 4.69 nm was obtained for

image on the right.

image on the right.

Fig. 4. AFM scan images obtained from the same particle of material IV. A roughness measurement of 5.05 nm was obtained for image on the left while 20.9 nm was obtained for image on the right.

Fig. 5. AFM scan images obtained from the same particle of material V. A roughness measurement of 1.07 nm was obtained for image on the left while 3.7 nm was obtained for image on the right.

Fig. 4. AFM scan images obtained from the same particle of material IV. A roughness measurement of 5.05 nm was obtained for image on the left while 20.9 nm was obtained for

Fig. 5. AFM scan images obtained from the same particle of material V. A roughness measurement of 1.07 nm was obtained for image on the left while 3.7 nm was obtained for

image on the right.

image on the right.

Fig. 6. AFM scan images obtained from the same particle of material VI. A roughness measurement of 1.07 nm was obtained for image on the left while 3.7 nm was obtained for image on the right.

Fig. 7. AFM scan images obtained from the same particle of material VII. A roughness measurement of 2.9 nm was obtained for image on the left while 4.69 nm was obtained for image on the right.

Predicting Macroscale Effects Through Nanoscale Features 181

 Particle Level Data Material Level Data Material Particle Rpm Spm Rm Sm Sm I 1 19.100 6.531 18.270 4.131 5.929

II 1 10.518 7.730 8.425 4.853 6.120

III 1 13.794 8.236 16.040 11.033 7.457

IV 1 11.255 12.770 10.565 9.807 4.310

V 1 2.000 1.619 5.322 3.622 3.165

VI 1 15.740 4.633 10.067 3.612 4.784

VII 1 10.335 3.462 6.150 2.877 5.278

 2 14.617 1.994 3 10.128 3.229 4 23.467 3.704 5 24.040 5.198

 2 18.268 7.614 3 5.062 4.247 4 3.653 2.417 5 4.624 2.255

 2 7.014 3.723 3 25.006 16.742 4 22.335 17.346 5 12.052 9.121

 2 4.872 3.160 3 10.220 11.350 4 16.912 17.749 5 9.564 4.007

 2 6.207 1.698 3 10.244 7.900 4 3.396 4.034 5 4.762 2.856

 2 13.982 3.868 3 7.934 2.370 4 8.753 5.830 5 3.923 1.358

 2 5.120 2.169 3 12.820 7.432 4 1.482 1.041 5 0.994 0.281 Table 1. Construction of Measures of Surface Roughness
