Parameterizing Nanovolcanoes

ByGreg Madejski

Having generated some tomograms of various Au, NPN, and MgF2 nanostructures in the past months, I should be able to parameterize these structures. I have many questions about how the nanostructures actually effect SERS performance. In general, we can use these methods to more accurately and precisely describe our nanomembranes.

Hypothetical Factors

  • Surface Roughness ~= Material
    • Is MgF2 special? Evidence exists that NPN doesn’t have as nice SERS properties when coated with Au, but could we make it rougher with a different material/etching process?
    • Modeled as some deviation from a fitted curve
  • Conicity
    • Modeled as fitting to some hyperbolas, with some degree of fit.
      • Pinched ovals versus circles, which is better?
  • Pore Size
    • SERS properties should increase exponentially the closer the gold gets to itself. Yet 1085 has larger pores than the 1147 material.
      • How does this relate to the conicity?
      • How does the gold infiltrate these structures? I suspect a shallower cone allows the gold to get closer together.

 

To address these questions, we can begin with reslicing our tomograms. The tomograms I have generated have been made of slices through the Z-axis. Orthogonal views are illuminating (equivalent to crossectioning the membrane).

If we reslice the tomogram at 90 degrees, we can see the membrane with other detail (sizes of grains etc). The equivalent of a crossection in SEM. The XZ plane doesn’t have as much detail, because we didn’t tilt along that axis.

 

YZ planes of 1147 MgF2. Highlighted (my choice) boundaries are seen for the crossection of the nanomembrane. All voxels should be at the same scale of the normal tomogram.

 

From the YZ plane, we can quantify a number of properties. In this case, the cone angle was 18.86 degrees, and the pore radius was 34 pixels (0.5 nm/pixel = 17 nm). I adjusted the LUT to ‘Fire’ in Image J to better highlight the membrane area.

 

Reorienting around the tangent axis, we can see two hyperbolas

 

Two parts of the volcano have different curves, with different parameterizations. Establishing the parameters can be done by the asymptotic lines (angle and b) and vertex (a) for each parabola.

 

Hyperbolic Equations

 

Hyperbolas overlaid to better show differences. The red curve is shallower (entrance to nanovolcano) and would have surface roughness overlaid to best represent the surface. Take quadrant II red curve and quadrant III blue curve to make one surface.

Work to do

  • Automate process of curve extraction and equation generation.
    • Everything done by hand here should be automatically extracted
    • This work is one section; how do we tackle multiple curves in different projection planes?
  • Add in measurements of Surface roughness (deviations from goodness of fit?)
  • Goodness-of-fit curves

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