 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-2/section-b/20/ii/solution

C = a n^{2} + nm + m^{2}, D = \frac{C}{π} .

For

(12, 12)

D = \frac{0.246 432}{π} = 1.63 nm .

Approximating the closest wall-to-wall separation by the graphite interlayer spacing

d_{002} = c /2 = 0.3355 nm

gives the nearest-neighbour axis separation in a triangularly packed bundle:

s = D + d_{002} ≃ 1.96 nm .

This assumes undeformed circular tubes with a graphitic contact gap. Faceting, flattening, adsorbates or pressure can alter a real bundle's spacing.

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